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b(.)45 b(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)
g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)85 b(10)345
3280 y(1.5.3)106 b(Matrix)31 b(Op)s(erations)58 b(.)46
b(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g
(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)85
b(10)136 3393 y(1.6)94 b(Numerical)30 b(Accuracy)h(and)f(En)m(vironmen)
m(tal)f(Enquiry)60 b(.)46 b(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g
(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)85 b(12)136 3506 y(1.7)94
b(Language)32 b(Bindings)48 b(.)e(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h
(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)
g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)85 b(13)136 3619
y(1.8)94 b(Error)30 b(Handling)60 b(.)45 b(.)h(.)g(.)f(.)h(.)g(.)g(.)f
(.)h(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)
h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)85
b(14)345 3731 y(1.8.1)106 b(Return)30 b(Co)s(des)38 b(.)45
b(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f
(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)
85 b(14)345 3844 y(1.8.2)106 b(Error)30 b(Handlers)61
b(.)46 b(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)
f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f
(.)85 b(14)0 4048 y FG(2)f(Dense)36 b(and)e(Banded)i(BLAS)2490
b(18)136 4161 y FK(2.1)94 b(Ov)m(erview)30 b(and)g(F)-8
b(unctionalit)m(y)57 b(.)45 b(.)h(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f
(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)
h(.)g(.)f(.)85 b(18)345 4274 y(2.1.1)106 b(Scalar)30
b(and)g(V)-8 b(ector)32 b(Op)s(erations)48 b(.)e(.)f(.)h(.)g(.)g(.)f(.)
h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h
(.)g(.)f(.)85 b(18)345 4387 y(2.1.2)106 b(Matrix-V)-8
b(ector)33 b(Op)s(erations)53 b(.)45 b(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h
(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)
g(.)f(.)85 b(18)345 4500 y(2.1.3)106 b(Matrix)31 b(Op)s(erations)58
b(.)46 b(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)
g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)85
b(19)136 4613 y(2.2)94 b(Matrix)31 b(Storage)g(Sc)m(hemes)58
b(.)46 b(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)
h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)85
b(22)345 4726 y(2.2.1)106 b(Con)m(v)m(en)m(tional)31
b(Storage)94 b(.)46 b(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f
(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)
85 b(22)345 4839 y(2.2.2)106 b(P)m(ac)m(k)m(ed)33 b(Storage)52
b(.)46 b(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)
f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f
(.)85 b(23)345 4951 y(2.2.3)106 b(Band)31 b(Storage)50
b(.)45 b(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)
g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g
(.)f(.)85 b(24)345 5064 y(2.2.4)106 b(Unit)30 b(T)-8
b(riangular)28 b(Matrices)86 b(.)45 b(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h
(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)
g(.)f(.)85 b(25)345 5177 y(2.2.5)106 b(Represen)m(tation)31
b(of)g(a)f(Householder)g(Matrix)52 b(.)46 b(.)g(.)f(.)h(.)g(.)g(.)f(.)h
(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)85
b(25)345 5290 y(2.2.6)106 b(Represen)m(tation)31 b(of)g(a)f(P)m(erm)m
(utation)h(Matrix)44 b(.)i(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g
(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)85 b(26)-214 64 y
FI(1)-214 177 y(2)-214 290 y(3)-214 403 y(4)-214 516
y(5)-214 628 y(6)-214 741 y(7)-214 854 y(8)-214 967 y(9)-230
1080 y(10)-230 1193 y(11)-230 1306 y(12)-230 1419 y(13)-230
1532 y(14)-230 1645 y(15)-230 1758 y(16)-230 1870 y(17)-230
1983 y(18)-230 2096 y(19)-230 2209 y(20)-230 2322 y(21)-230
2435 y(22)-230 2548 y(23)-230 2661 y(24)-230 2774 y(25)-230
2887 y(26)-230 3000 y(27)-230 3112 y(28)-230 3225 y(29)-230
3338 y(30)-230 3451 y(31)-230 3564 y(32)-230 3677 y(33)-230
3790 y(34)-230 3903 y(35)-230 4016 y(36)-230 4129 y(37)-230
4242 y(38)-230 4354 y(39)-230 4467 y(40)-230 4580 y(41)-230
4693 y(42)-230 4806 y(43)-230 4919 y(44)-230 5032 y(45)-230
5145 y(46)-230 5258 y(47)-230 5371 y(48)p eop
%%Page: 4 4
4 3 bop 136 91 a FK(2.3)94 b(In)m(terface)32 b(Issues)59
b(.)45 b(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)
g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g
(.)f(.)h(.)g(.)f(.)85 b(26)345 204 y(2.3.1)106 b(Naming)30
b(Con)m(v)m(en)m(tions)46 b(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f
(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)
h(.)g(.)f(.)85 b(26)345 317 y(2.3.2)106 b(Argumen)m(t)31
b(Aliasing)48 b(.)e(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g
(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)
f(.)85 b(26)136 430 y(2.4)94 b(In)m(terface)32 b(Issues)e(for)g(F)-8
b(ortran)31 b(95)k(.)46 b(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g
(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)
f(.)85 b(26)345 543 y(2.4.1)106 b(F)-8 b(ortran)31 b(95)h(Mo)s(dules)85
b(.)45 b(.)h(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)
g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)85
b(26)345 656 y(2.4.2)106 b(Indexing)32 b(.)45 b(.)h(.)g(.)f(.)h(.)g(.)g
(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)
f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)85
b(26)345 769 y(2.4.3)106 b(Design)31 b(of)f(the)h(F)-8
b(ortran)31 b(95)g(In)m(terfaces)47 b(.)f(.)g(.)f(.)h(.)g(.)f(.)h(.)g
(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)85
b(27)345 882 y(2.4.4)106 b(Matrix)31 b(Storage)g(Sc)m(hemes)50
b(.)c(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h
(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)85
b(28)345 995 y(2.4.5)106 b(F)-8 b(ormat)32 b(of)f(the)f(F)-8
b(ortran)31 b(95)g(bindings)69 b(.)46 b(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g
(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)85
b(28)345 1108 y(2.4.6)106 b(Error)30 b(Handling)51 b(.)46
b(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h
(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)85
b(29)136 1220 y(2.5)94 b(In)m(terface)32 b(Issues)e(for)g(F)-8
b(ortran)31 b(77)k(.)46 b(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g
(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)
f(.)85 b(30)345 1333 y(2.5.1)106 b(F)-8 b(ortran)31 b(77)h(Include)c
(File)90 b(.)46 b(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g
(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)85
b(30)345 1446 y(2.5.2)106 b(Indexing)32 b(.)45 b(.)h(.)g(.)f(.)h(.)g(.)
g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g
(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)85
b(30)345 1559 y(2.5.3)106 b(Arra)m(y)31 b(Argumen)m(ts)j(.)46
b(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g
(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)85
b(30)345 1672 y(2.5.4)106 b(Matrix)31 b(Storage)g(Sc)m(hemes)50
b(.)c(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h
(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)85
b(31)345 1785 y(2.5.5)106 b(F)-8 b(ormat)32 b(of)f(the)f(F)-8
b(ortran)31 b(77)g(bindings)69 b(.)46 b(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g
(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)85
b(31)345 1898 y(2.5.6)106 b(Error)30 b(Handling)51 b(.)46
b(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h
(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)85
b(31)136 2011 y(2.6)94 b(In)m(terface)32 b(Issues)e(for)g(C)36
b(.)45 b(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)
g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g
(.)f(.)85 b(32)345 2124 y(2.6.1)106 b(C)30 b(Include)f(File)91
b(.)46 b(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)
f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f
(.)85 b(32)345 2237 y(2.6.2)106 b(Indexing)32 b(.)45
b(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f
(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)
h(.)g(.)f(.)85 b(32)345 2350 y(2.6.3)106 b(Handling)29
b(of)h(complex)g(data)h(t)m(yp)s(es)d(.)45 b(.)h(.)g(.)g(.)f(.)h(.)g(.)
f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f
(.)85 b(32)345 2462 y(2.6.4)106 b(Return)30 b(v)-5 b(alues)30
b(of)g(complex)g(functions)k(.)46 b(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f
(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)85
b(32)345 2575 y(2.6.5)106 b(Aliasing)29 b(of)h(argumen)m(ts)75
b(.)46 b(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)
f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)85
b(33)345 2688 y(2.6.6)106 b(Arra)m(y)31 b(argumen)m(ts)57
b(.)46 b(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)
h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)85
b(33)345 2801 y(2.6.7)106 b(Matrix)31 b(Storage)g(Sc)m(hemes)50
b(.)c(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h
(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)85
b(33)345 2914 y(2.6.8)106 b(F)-8 b(ormat)32 b(of)f(the)f(C)g(bindings)
71 b(.)45 b(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h
(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)85
b(33)345 3027 y(2.6.9)106 b(Error)30 b(Handling)51 b(.)46
b(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h
(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)85
b(33)136 3140 y(2.7)94 b(Numerical)30 b(Accuracy)h(and)f(En)m(vironmen)
m(tal)f(Enquiry)60 b(.)46 b(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g
(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)85 b(34)136 3253 y(2.8)94
b(Language)32 b(Bindings)48 b(.)e(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h
(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)
g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)85 b(35)345 3366
y(2.8.1)106 b(Ov)m(erview)75 b(.)46 b(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g
(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)
f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)85 b(36)345
3479 y(2.8.2)106 b(Reduction)30 b(Op)s(erations)67 b(.)46
b(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h
(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)85
b(38)345 3592 y(2.8.3)106 b(Generate)32 b(T)-8 b(ransformations)45
b(.)g(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g
(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)85 b(43)345
3704 y(2.8.4)106 b(V)-8 b(ector)32 b(Op)s(erations)74
b(.)46 b(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)
g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)85
b(47)345 3817 y(2.8.5)106 b(Data)32 b(Mo)m(v)m(emen)m(t)h(with)c(V)-8
b(ectors)58 b(.)46 b(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)
h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)85
b(50)345 3930 y(2.8.6)106 b(Matrix-V)-8 b(ector)33 b(Op)s(erations)53
b(.)45 b(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)
g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)85 b(53)345
4043 y(2.8.7)106 b(Matrix)31 b(Op)s(erations)58 b(.)46
b(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g
(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)85
b(69)345 4156 y(2.8.8)106 b(Matrix-Matrix)31 b(Op)s(erations)38
b(.)45 b(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)
g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)85 b(83)345
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(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)
g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)40
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b(.)45 b(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)
g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g
(.)f(.)40 b(174)136 543 y(A.4)71 b(F)-8 b(ortran)32 b(95)f(Mo)s(dules)
22 b(.)46 b(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f
(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)
h(.)g(.)f(.)40 b(176)136 656 y(A.5)71 b(F)-8 b(ortran)32
b(77)f(Include)d(File)f(.)46 b(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)h
(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)
h(.)g(.)f(.)h(.)g(.)f(.)40 b(178)136 769 y(A.6)71 b(C)30
b(Include)f(Files)64 b(.)45 b(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f
(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)
h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)40 b(178)0 973
y FG(B)62 b(Legacy)36 b(BLAS)2982 b(180)136 1086 y FK(B.1)75
b(In)m(tro)s(duction)27 b(.)46 b(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)
h(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h
(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)40
b(180)136 1198 y(B.2)75 b(C)30 b(in)m(terface)h(to)g(the)g(Legacy)h
(BLAS)24 b(.)46 b(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g
(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)40
b(180)345 1311 y(B.2.1)87 b(Naming)30 b(sc)m(heme)38
b(.)46 b(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)
f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f
(.)40 b(180)345 1424 y(B.2.2)87 b(Indices)29 b(and)h(I)p
1157 1424 28 4 v 33 w(AMAX)36 b(.)45 b(.)h(.)g(.)f(.)h(.)g(.)f(.)h(.)g
(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)
g(.)f(.)h(.)g(.)f(.)40 b(181)345 1537 y(B.2.3)87 b(Character)31
b(argumen)m(ts)k(.)45 b(.)h(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g
(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)
f(.)40 b(181)345 1650 y(B.2.4)87 b(Handling)29 b(of)h(complex)g(data)h
(t)m(yp)s(es)d(.)45 b(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h
(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)40
b(181)345 1763 y(B.2.5)87 b(Return)30 b(v)-5 b(alues)30
b(of)g(complex)g(functions)k(.)46 b(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f
(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)40
b(182)345 1876 y(B.2.6)87 b(Arra)m(y)31 b(argumen)m(ts)57
b(.)46 b(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)
h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)40
b(183)345 1989 y(B.2.7)87 b(Aliasing)29 b(of)h(argumen)m(ts)75
b(.)46 b(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)
f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)40
b(185)345 2102 y(B.2.8)87 b(C)30 b(in)m(terface)h(include)d(\014le)47
b(.)f(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f
(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)40
b(186)345 2215 y(B.2.9)87 b(Error)30 b(c)m(hec)m(king)79
b(.)46 b(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)
f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f
(.)40 b(186)345 2328 y(B.2.10)i(Rules)30 b(for)g(obtaining)f(the)h(C)g
(in)m(terface)h(from)f(the)h(F)-8 b(ortran)31 b(77)80
b(.)45 b(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)40
b(186)345 2440 y(B.2.11)i(cblas.h)30 b(include)e(\014le)67
b(.)46 b(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)
g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)40
b(186)345 2553 y(B.2.12)i(Using)30 b(F)-8 b(ortran)31
b(77)g(BLAS)f(to)h(supp)s(ort)e(ro)m(w-ma)5 b(jor)31
b(BLAS)f(op)s(erations)91 b(.)46 b(.)g(.)f(.)h(.)g(.)f(.)40
b(187)0 2757 y FG(C)60 b(Journal)36 b(of)f(Dev)m(elopmen)m(t)2508
b(196)136 2870 y FK(C.1)104 b(En)m(vironmen)m(tal)29
b(Routine)h(for)g(E\013ectiv)m(e)h(use)f(of)h(Cac)m(he,)g(Pip)s
(elining)26 b(and)k(Registers)43 b(.)i(.)h(.)g(.)f(.)40
b(197)345 2983 y(C.1.1)85 b(In)m(tro)s(duction)90 b(.)45
b(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f
(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)
40 b(197)345 3096 y(C.1.2)85 b(Language)32 b(Extensions)d(for)h(the)h
(Cac)m(he)h(.)46 b(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h
(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)40 b(197)345 3209
y(C.1.3)85 b(F)-8 b(or)31 b(E\016cien)m(t)g(LA)f(Soft)m(w)m(are)68
b(.)45 b(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)
g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)40 b(198)345
3322 y(C.1.4)85 b(Adv)-5 b(an)m(tages)32 b(of)f(this)e(approac)m(h)24
b(.)46 b(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)
f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)40 b(198)345
3435 y(C.1.5)85 b(Disadv)-5 b(an)m(tages)32 b(of)f(this)e(approac)m(h)
58 b(.)45 b(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h
(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)40 b(198)136 3548
y(C.2)73 b(Distributed-memory)29 b(Dense)i(BLAS)h(.)45
b(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f
(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)40 b(200)136
3660 y(C.3)73 b(F)-8 b(ortran)32 b(95)f(Thin)d(BLAS)36
b(.)46 b(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)
f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f
(.)40 b(206)345 3773 y(C.3.1)85 b(In)m(tro)s(duction)90
b(.)45 b(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)
g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g
(.)f(.)40 b(206)345 3886 y(C.3.2)85 b(Design)31 b(of)f(F)-8
b(ortran)31 b(95)g(In)m(terfaces)63 b(.)45 b(.)h(.)g(.)g(.)f(.)h(.)g(.)
f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f
(.)40 b(206)345 3999 y(C.3.3)85 b(In)m(terfaces)32 b(for)e(Real)g(Data)
59 b(.)46 b(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f
(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)40
b(207)345 4112 y(C.3.4)85 b(In)m(terfaces)32 b(for)e(Complex)f(Data)e
(.)46 b(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f
(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)40 b(211)345
4225 y(C.3.5)85 b(Error)30 b(c)m(hec)m(king)79 b(.)46
b(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h
(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)40
b(211)345 4338 y(C.3.6)85 b(Comparison)29 b(with)g(the)i(F)-8
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(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)40 b(211)345
4451 y(C.3.7)85 b(Conclusion)c(.)46 b(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f
(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)
h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)40 b(213)345
4564 y(C.3.8)85 b(F)-8 b(urther)30 b(Details:)41 b(Sp)s(eci\014c)29
b(pro)s(cedures)g(for)h(gemm)23 b(.)46 b(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)
g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)40 b(214)136 4677
y(C.4)73 b(In)m(terv)-5 b(al)31 b(BLAS)91 b(.)45 b(.)h(.)g(.)f(.)h(.)g
(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)g(.)f(.)h(.)g(.)f(.)h(.)g(.)
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b(219)345 4790 y(C.4.1)85 b(In)m(tro)s(duction)90 b(.)45
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40 b(219)345 4902 y(C.4.2)85 b(F)-8 b(unctionalit)m(y)62
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(.)f(.)40 b(220)345 5015 y(C.4.3)85 b(In)m(terface)32
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b(227)4084 64 y FI(1)4084 177 y(2)4084 290 y(3)4084 403
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m(terest.)0 4796 y FG(Chapters)26 b(2{4)d FK(con)m(tain)g(a)h
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b FK(presen)m(ts)0 5022 y(areas)24 b(of)g(researc)m(h)g(that)g(are)g
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b(at)j(the)f(meetings)g(of)g(the)g(forum.)42 b(A)31 b
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(an)g FG(Index)g FK(of)0 5248 y(routine)e(names.)-214
64 y FI(1)-214 177 y(2)-214 290 y(3)-214 403 y(4)-214
516 y(5)-214 628 y(6)-214 741 y(7)-214 854 y(8)-214 967
y(9)-230 1080 y(10)-230 1193 y(11)-230 1306 y(12)-230
1419 y(13)-230 1532 y(14)-230 1645 y(15)-230 1758 y(16)-230
1870 y(17)-230 1983 y(18)-230 2096 y(19)-230 2209 y(20)-230
2322 y(21)-230 2435 y(22)-230 2548 y(23)-230 2661 y(24)-230
2774 y(25)-230 2887 y(26)-230 3000 y(27)-230 3112 y(28)-230
3225 y(29)-230 3338 y(30)-230 3451 y(31)-230 3564 y(32)-230
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4129 y(37)-230 4242 y(38)-230 4354 y(39)-230 4467 y(40)-230
4580 y(41)-230 4693 y(42)-230 4806 y(43)-230 4919 y(44)-230
5032 y(45)-230 5145 y(46)-230 5258 y(47)-230 5371 y(48)p
eop
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4 13 bop 0 -165 a FK(4)2483 b FA(CHAPTER)29 b(1.)72 b(INTR)m(ODUCTION)
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643 y(con)m(v)m(en)m(tions)g(in)d(notation,)i(and)e(o)m(v)m(erall)i
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830 y FJ(\017)46 b FG(Chapter)g(2:)71 b(Dense)47 b(and)f(Banded)h(BLAS)
41 b FK(presen)m(ts)g(the)g(functionalit)m(y)e(and)h(language)h(bind-)
227 943 y(ings)h(for)g(prop)s(osed)f(\\new")h(dense)g(and)g(banded)f
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1056 y(computing.)136 1244 y FJ(\017)k FG(Chapter)38
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1357 y(\\new")e(sparse)f(BLAS)g(routines)f(for)i(serial)e(and)h(shared)
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b(4:)49 b(Extended)36 b(and)g(Mixed)g(Precision)i(BLAS)31
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1657 y(guage)c(bindings)21 b(for)k(prop)s(osed)e(extended-)i(precision)
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1770 y(and)30 b(shared)g(memory)g(computing.)136 1958
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(hapters.)136 2145 y FJ(\017)46 b FG(Legacy)32 b(BLAS)c
FK(con)m(tains)g(alternativ)m(e)f(language)h(bindings)c(for)k(the)f
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y(for)i(dense)g(and)g(band)f(matrix)h(computations.)136
2446 y FJ(\017)46 b FG(Journal)38 b(of)g(Dev)m(elopmen)m(t)32
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g(enquiry)f(routines,)227 2559 y(Distributed-memory)e(dense)h(BLAS,)g
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b(al)30 b(BLAS.)0 2845 y FE(1.4)116 b(Nomenclature)37
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3404 y Fx(1.4.1)97 b(Notation)0 3576 y FK(The)30 b(follo)m(wing)f
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b Fy(C)37 b FK({)31 b(matrices)136 3976 y FJ(\017)46
b Fy(D)s FK(,)31 b Fy(D)436 3990 y Fw(L)488 3976 y FK(,)g
Fy(D)619 3990 y Fw(R)707 3976 y FK({)g(diagonal)e(matrices)136
4164 y FJ(\017)46 b Fy(H)38 b FK({)30 b(Householder)g(matrix)136
4352 y FJ(\017)46 b Fy(J)40 b FK({)30 b(symmetric)g(tridiagonal)f
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g(matrix)136 4727 y FJ(\017)46 b Fy(T)d FK({)31 b(triangular)e(matrix)
136 4914 y FJ(\017)46 b Fy(op)p FK(\()p Fy(A)p FK(\))31
b({)g(denotes)g Fy(A)p FK(,)g(or)f Fy(A)1194 4881 y Fw(T)1279
4914 y FK(or)h Fy(A)1459 4881 y Fw(H)1557 4914 y FK(where)e
Fy(A)i FK(is)e(a)i(matrix.)136 5102 y FJ(\017)46 b FK(transp)s(ose)30
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s(ose)32 b({)e(denotes)h Fy(A)1519 5257 y Fw(H)1617 5290
y FK(where)f Fy(A)g FK(is)g(a)h(complex)f(Hermitian)f(matrix.)4084
64 y FI(1)4084 177 y(2)4084 290 y(3)4084 403 y(4)4084
516 y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084 967
y(9)4069 1080 y(10)4069 1193 y(11)4069 1306 y(12)4069
1419 y(13)4069 1532 y(14)4069 1645 y(15)4069 1758 y(16)4069
1870 y(17)4069 1983 y(18)4069 2096 y(19)4069 2209 y(20)4069
2322 y(21)4069 2435 y(22)4069 2548 y(23)4069 2661 y(24)4069
2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
3677 y(33)4069 3790 y(34)4069 3903 y(35)4069 4016 y(36)4069
4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
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5 14 bop 0 -165 a FA(1.4.)72 b(NOMENCLA)-8 b(TURE)30
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842 y FJ(\017)46 b Fy(x)279 856 y Fw(i)338 842 y FK(-)30
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eop
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6 15 bop 0 -165 a FK(6)2483 b FA(CHAPTER)29 b(1.)72 b(INTR)m(ODUCTION)
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%%Page: 9 19
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eop
%%Page: 10 20
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%%Page: 15 25
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eop
%%Page: 16 26
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%%Page: 17 27
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%%Page: 18 28
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%%Page: 19 29
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1419 y(13)-230 1532 y(14)-230 1645 y(15)-230 1758 y(16)-230
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2322 y(21)-230 2435 y(22)-230 2548 y(23)-230 2661 y(24)-230
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4580 y(41)-230 4693 y(42)-230 4806 y(43)-230 4919 y(44)-230
5032 y(45)-230 5145 y(46)-230 5258 y(47)-230 5371 y(48)p
eop
%%Page: 20 30
20 29 bop 0 -165 a FK(20)1930 b FA(CHAPTER)30 b(2.)71
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1494 y Fu(\000)p FC(1)2116 1527 y Fy(x;)40 b(x)25 b FJ( )h
Fy(\013T)2551 1494 y Fu(\000)p Fw(T)2661 1527 y Fy(x)p
2876 1560 V 215 w FK(TR,TB,TP)p 3594 1560 V 277 w(SV)p
4080 1560 V 0 1564 4083 4 v -2 1677 4 113 v 50 1643 a(Rank)k(one)h(up)s
(dates)p 1652 1677 V 934 w Fy(A)25 b FJ( )g Fy(\013xy)2071
1610 y Fw(T)2147 1643 y FK(+)20 b Fy(\014)5 b(A)p 2876
1677 V 566 w FK(GE)p 3594 1677 V 585 w(R)p 4080 1677
V -2 1790 V 110 1756 a(and)30 b(symmetric)g(\()p Fy(A)c
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b(,HP)p 3594 1790 V 159 w(R)p 4080 1790 V -2 1903 V 110
1869 a(rank)30 b(one)h(&)f(t)m(w)m(o)i(up)s(dates)p 1652
1903 V 632 w Fy(A)25 b FJ( )g FK(\()p Fy(\013x)p FK(\))p
Fy(y)2141 1836 y Fw(T)2218 1869 y FK(+)19 b Fy(y)s FK(\()p
Fy(\013x)p FK(\))2536 1836 y Fw(T)2613 1869 y FK(+)h
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3594 1903 V 159 w(R2)p 4080 1903 V 0 1906 4083 4 v 1220
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b FK(represen)m(ts)26 b(an)f(upp)s(er)e(or)j(lo)m(w)m(er)g(triangular)0
2661 y(matrix,)h(whic)m(h)e(can)i(b)s(e)f(unit)f(or)h(non-unit)f
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Fy(J)38 b FK(is)28 b(a)i(symmetric)e(tridiagonal)f(matrix.)40
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3241 4 113 v 50 3207 a(Matrix)g(norms)p 942 3241 V 397
w Fy(r)d FJ( )f(jj)p Fy(A)p FJ(jj)1347 3221 y FC(1)1387
3207 y Fy(;)15 b(r)28 b FJ( )e(jj)p Fy(A)p FJ(jj)1781
3221 y FC(1)p Fw(R)1875 3207 y Fy(;)15 b(r)28 b FJ( )d(jj)p
Fy(A)p FJ(jj)2268 3221 y Fw(F)2328 3207 y Fy(;)p 2401
3241 V 100 w FK(GE,GB,SY,HE,SB,HB,)p 3418 3241 V 3475
3207 28 4 v 135 w(NORM)p 4355 3241 4 113 v -2 3354 V
942 3354 V 994 3320 a Fy(r)i FJ( )f(jj)p Fy(A)p FJ(jj)1347
3334 y Fu(1)1422 3320 y Fy(;)15 b(r)29 b FJ( )c(jj)p
Fy(A)p FJ(jj)1816 3334 y Fu(1)p Fw(R)1945 3320 y Fy(;)p
2401 3354 V 483 w FK(SP)-8 b(,HP)g(,TR,TB,TP)p 3418 3354
V 4355 3354 V -2 3467 V 942 3467 V 994 3433 a Fy(r)27
b FJ( )f(jj)p Fy(A)p FJ(jj)1347 3447 y Fw(max)1492 3433
y Fy(;)15 b(r)28 b FJ( )d(jj)p Fy(A)p FJ(jj)1885 3447
y Fw(maxR)p 2401 3467 V 3418 3467 V 4355 3467 V -2 3580
V 50 3546 a FK(Diagonal)30 b(scaling)p 942 3580 V 293
w Fy(A)25 b FJ( )g Fy(D)s(A;)41 b(A)25 b FJ( )g Fy(AD)p
2401 3580 V 686 w FK(GE,GB)p 3418 3580 V 3475 3546 28
4 v 756 w(DIA)m(G)p 3745 3546 V 34 w(SCALE)p 4355 3580
4 113 v -2 3693 V 942 3693 V 994 3659 a Fy(A)g FJ( )g
Fy(D)1278 3673 y Fw(L)1331 3659 y Fy(AD)1474 3673 y Fw(R)p
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28 4 v 756 w(LRSCALE)p 4355 3693 4 113 v -2 3806 V 942
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V 1029 w FK(SY,HE,SB,HB,SP)-8 b(,HP)p 3418 3806 V 3475
3772 28 4 v 193 w(LRSCALE)p 4355 3806 4 113 v -2 3919
V 942 3919 V 994 3885 a Fy(A)25 b FJ( )g Fy(A)c FK(+)f
Fy(B)5 b(D)p 2401 3919 V 921 w FK(GE,GB)p 3418 3919 V
3475 3885 28 4 v 756 w(DIA)m(G)p 3745 3885 V 34 w(SCALE)p
4083 3885 V 32 w(A)m(CC)p 4355 3919 4 113 v -2 4032 V
50 3998 a(Matrix)30 b(acc)i(and)d(scale)p 942 4032 V
121 w Fy(B)g FJ( )d Fy(\013A)20 b FK(+)g Fy(\014)5 b(B)g(;)41
b(B)30 b FJ( )25 b Fy(\013A)1983 3965 y Fw(T)2059 3998
y FK(+)19 b Fy(\014)5 b(B)p 2401 4032 V 179 w FK(GE,GB,SY,SB,)p
3418 4032 V 3475 3998 28 4 v 447 w(A)m(CC)p 4355 4032
4 113 v -2 4145 V 942 4145 V 2401 4145 V 2453 4111 a(SP)-8
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v 447 w(ADD)p 4355 4258 4 113 v -2 4370 V 942 4370 V
2401 4370 V 2453 4337 a(SP)-8 b(,TR,TB,TP)p 3418 4370
V 4355 4370 V 0 4374 4357 4 v 688 4541 a(T)g(able)30
b(2.6:)42 b(Matrix)30 b(Op)s(erations)f({)i Fy(O)s FK(\()p
Fy(n)2129 4508 y FC(2)2168 4541 y FK(\))g(\015oating)f(p)s(oin)m(t)f
(op)s(erations)4084 64 y FI(1)4084 177 y(2)4084 290 y(3)4084
403 y(4)4084 516 y(5)4084 628 y(6)4084 741 y(7)4084 854
y(8)4084 967 y(9)4069 1080 y(10)4069 1193 y(11)4069 1306
y(12)4069 1419 y(13)4069 1532 y(14)4069 1645 y(15)4069
1758 y(16)4069 1870 y(17)4069 1983 y(18)4069 2096 y(19)4069
2209 y(20)4069 2322 y(21)4069 2435 y(22)4069 2548 y(23)4069
2661 y(24)4069 2774 y(25)4069 2887 y(26)4069 3000 y(27)4069
3112 y(28)4069 3225 y(29)4069 3338 y(30)4069 3451 y(31)4069
3564 y(32)4069 3677 y(33)4069 3790 y(34)4069 3903 y(35)4069
4016 y(36)4069 4129 y(37)4069 4242 y(38)4069 4354 y(39)4069
4467 y(40)4069 4580 y(41)4069 4693 y(42)4069 4806 y(43)4069
4919 y(44)4069 5032 y(45)4069 5145 y(46)4069 5258 y(47)4069
5371 y(48)p eop
%%Page: 21 31
21 30 bop 0 -165 a FA(2.1.)72 b(O)m(VER)-10 b(VIEW)31
b(AND)g(FUNCTIONALITY)2028 b FK(21)p 24 715 3853 4 v
22 828 4 113 v 74 794 a(Matrix)30 b(matrix)g(pro)s(duct)p
1066 828 V 133 w Fy(C)h FJ( )26 b Fy(\013AB)f FK(+)20
b Fy(\014)5 b(C)q(;)41 b(C)32 b FJ( )25 b Fy(\013A)2169
761 y Fw(T)2225 794 y Fy(B)g FK(+)19 b Fy(\014)5 b(C)p
2748 828 V 269 w FK(GE)p 3122 828 V 241 w(MM)p 3874 828
V 22 941 V 1066 941 V 1118 907 a Fy(C)31 b FJ( )26 b
Fy(\013AB)1531 874 y Fw(T)1606 907 y FK(+)20 b Fy(\014)5
b(C)q(;)41 b(C)32 b FJ( )25 b Fy(\013A)2224 874 y Fw(T)2280
907 y Fy(B)2354 874 y Fw(T)2429 907 y FK(+)19 b Fy(\014)5
b(C)p 2748 941 V 3122 941 V 3874 941 V 1068 944 2809
4 v 22 1053 4 113 v 1066 1053 V 1118 1020 a(C)31 b FJ( )26
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FJ( )25 b Fy(\013B)5 b(A)20 b FK(+)g Fy(\014)5 b(C)p
2748 1053 V 324 w FK(SY,HE)p 3122 1053 V 100 w(MM)p 3874
1053 V 24 1057 3853 4 v 22 1170 4 113 v 74 1136 a(T)-8
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FJ( )d Fy(\013T)13 b(B)5 b(;)40 b(B)30 b FJ( )25 b Fy(\013B)5
b(T)p 2748 1170 V 803 w FK(TR)p 3122 1170 V 241 w(MM)p
3874 1170 V 22 1283 V 1066 1283 V 1118 1249 a Fy(B)29
b FJ( )d Fy(\013T)1457 1216 y Fw(T)1512 1249 y Fy(B)5
b(;)40 b(B)30 b FJ( )25 b Fy(\013B)5 b(T)2064 1216 y
Fw(T)p 2748 1283 V 3122 1283 V 3874 1283 V 24 1286 3853
4 v 22 1396 4 113 v 74 1362 a FK(T)-8 b(riangular)28
b(solv)m(e)p 1066 1396 V 405 w Fy(B)h FJ( )d Fy(\013T)1457
1329 y Fu(\000)p FC(1)1551 1362 y Fy(B)5 b(;)40 b(B)30
b FJ( )25 b Fy(\013B)5 b(T)2103 1329 y Fu(\000)p FC(1)p
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3874 1396 V 22 1508 V 1066 1508 V 1118 1475 a Fy(B)29
b FJ( )d Fy(\013T)1457 1442 y Fu(\000)p Fw(T)1567 1475
y Fy(B)5 b(;)40 b(B)30 b FJ( )25 b Fy(\013B)5 b(T)2119
1442 y Fu(\000)p Fw(T)p 2748 1508 V 3122 1508 V 3874
1508 V 24 1512 3853 4 v 22 1621 4 113 v 74 1587 a FK(Symmetric)29
b(rank)h Fy(k)j FK(&)d(2)p Fy(k)p 1066 1621 V 104 w(C)h
FJ( )26 b Fy(\013AA)1525 1554 y Fw(T)1601 1587 y FK(+)20
b Fy(\014)5 b(C)q(;)41 b(C)32 b FJ( )25 b Fy(\013A)2219
1554 y Fw(T)2274 1587 y Fy(A)c FK(+)f Fy(\014)5 b(C)p
2748 1621 V 224 w FK(SY,HE)p 3122 1621 V 100 w(RK)p 3874
1621 V 1068 1625 2809 4 v 22 1734 4 113 v 104 1700 a(up)s(dates)29
b(\()p Fy(C)k FK(=)25 b Fy(C)746 1667 y Fw(T)800 1700
y FK(\))p 1066 1734 V 283 w Fy(C)31 b FJ( )26 b Fy(\013AJ)9
b(A)1584 1667 y Fw(T)1660 1700 y FK(+)20 b Fy(\014)5
b(C)q(;)41 b(C)32 b FJ( )25 b Fy(\013A)2278 1667 y Fw(T)2334
1700 y Fy(J)9 b(A)20 b FK(+)g Fy(\014)5 b(C)p 2748 1734
V 106 w FK(SY,HE)p 3122 1734 V 3178 1700 28 4 v 133 w(TRIDIA)m(G)p
3615 1700 V 33 w(RK)p 3874 1734 4 113 v 1068 1738 2809
4 v 22 1847 4 113 v 1066 1847 V 1118 1813 a Fy(C)31 b
FJ( )26 b FK(\()p Fy(\013A)p FK(\))p Fy(B)1601 1780 y
Fw(T)1677 1813 y FK(+)20 b Fy(B)5 b FK(\()p Fy(\013A)p
FK(\))2038 1780 y Fw(T)2114 1813 y FK(+)20 b Fy(\014)5
b(C)i FK(,)p 2748 1847 V 441 w(SY,HE)p 3122 1847 V 100
w(R2K)p 3874 1847 V 22 1960 V 1066 1960 V 1118 1926 a
Fy(C)31 b FJ( )26 b FK(\()p Fy(\013A)p FK(\))1527 1893
y Fw(T)1583 1926 y Fy(B)f FK(+)20 b Fy(B)1842 1893 y
Fw(T)1896 1926 y FK(\()p Fy(\013A)p FK(\))i(+)e Fy(\014)5
b(C)p 2748 1960 V 3122 1960 V 3874 1960 V 1068 1963 2809
4 v 22 2073 4 113 v 1066 2073 V 1118 2039 a(C)31 b FJ( )26
b FK(\()p Fy(\013AJ)9 b FK(\))p Fy(B)1660 2006 y Fw(T)1736
2039 y FK(+)20 b Fy(B)5 b FK(\()p Fy(\013AJ)k FK(\))2156
2006 y Fw(T)2232 2039 y FK(+)20 b Fy(\014)5 b(C)i FK(,)p
2748 2073 V 323 w(SY,HE)p 3122 2073 V 3178 2039 28 4
v 133 w(TRIDIA)m(G)p 3615 2039 V 33 w(R2K)p 3874 2073
4 113 v 22 2186 V 1066 2186 V 1118 2152 a Fy(C)31 b FJ( )26
b FK(\()p Fy(\013AJ)9 b FK(\))1586 2119 y Fw(T)1642 2152
y Fy(B)25 b FK(+)20 b Fy(B)1901 2119 y Fw(T)1955 2152
y FK(\()p Fy(\013AJ)9 b FK(\))22 b(+)e Fy(\014)5 b(C)p
2748 2186 V 3122 2186 V 3874 2186 V 1068 2189 2809 4
v 24 2189 3853 4 v 537 2356 a FK(T)-8 b(able)30 b(2.7:)41
b(Matrix-Matrix)31 b(Op)s(erations)e({)i Fy(O)s FK(\()p
Fy(n)2281 2323 y FC(3)2320 2356 y FK(\))f(\015oating)h(p)s(oin)m(t)e
(op)s(erations)p 0 3980 3970 4 v -2 4092 4 113 v 50 4059
a(Matrix)h(cop)m(y)p 779 4092 V 296 w Fy(B)g FJ( )25
b Fy(A)p 1631 4092 V 570 w FK(GE,GB,SY,HE,SB,HB,SP)-8
b(,HP)g(,TR,TB,TP)p 3366 4092 V 3423 4059 28 4 v 135
w(COPY)p 3968 4092 4 113 v -2 4205 V 779 4205 V 830 4171
a Fy(B)30 b FJ( )25 b Fy(A)1113 4139 y Fw(T)p 1631 4205
V 1683 4171 a FK(GE,GB)p 3366 4205 V 3423 4171 28 4 v
1474 w(COPY)p 3968 4205 4 113 v -2 4318 V 50 4284 a(Matrix)30
b(transp)s(ose)p 779 4318 V 99 w Fy(A)c FJ( )f Fy(A)1108
4251 y Fw(T)p 1631 4318 V 1683 4284 a FK(GE)p 3366 4318
V 3423 4284 28 4 v 1634 w(TRANS)p 3968 4318 4 113 v -2
4431 V 50 4397 a(P)m(erm)m(ute)31 b(Matrix)p 779 4431
V 142 w Fy(A)26 b FJ( )f Fy(P)13 b(A)p FK(,)31 b Fy(A)25
b FJ( )g Fy(AP)p 1631 4431 V 113 w FK(GE)p 3366 4431
V 3423 4397 28 4 v 1634 w(PERMUTE)p 3968 4431 4 113 v
0 4435 3970 4 v 1126 4589 a(T)-8 b(able)30 b(2.8:)42
b(Data)32 b(Mo)m(v)m(emen)m(t)h(with)c(Matrices)-214
64 y FI(1)-214 177 y(2)-214 290 y(3)-214 403 y(4)-214
516 y(5)-214 628 y(6)-214 741 y(7)-214 854 y(8)-214 967
y(9)-230 1080 y(10)-230 1193 y(11)-230 1306 y(12)-230
1419 y(13)-230 1532 y(14)-230 1645 y(15)-230 1758 y(16)-230
1870 y(17)-230 1983 y(18)-230 2096 y(19)-230 2209 y(20)-230
2322 y(21)-230 2435 y(22)-230 2548 y(23)-230 2661 y(24)-230
2774 y(25)-230 2887 y(26)-230 3000 y(27)-230 3112 y(28)-230
3225 y(29)-230 3338 y(30)-230 3451 y(31)-230 3564 y(32)-230
3677 y(33)-230 3790 y(34)-230 3903 y(35)-230 4016 y(36)-230
4129 y(37)-230 4242 y(38)-230 4354 y(39)-230 4467 y(40)-230
4580 y(41)-230 4693 y(42)-230 4806 y(43)-230 4919 y(44)-230
5032 y(45)-230 5145 y(46)-230 5258 y(47)-230 5371 y(48)p
eop
%%Page: 22 32
22 31 bop 0 -165 a FK(22)1930 b FA(CHAPTER)30 b(2.)71
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141 1045 y(In)g(the)h(examples)g(b)s(elo)m(w,)f FJ(\003)h
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2137 y(elemen)m(t)31 b Fy(a)384 2151 y Fw(ij)475 2137
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b(j)5 b FK(\),)33 b(assuming)c(one-based)h(indexing.)141
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2702 y(If)24 b(a)g(matrix)g(is)f FG(triangular)h FK(\(upp)s(er)e(or)j
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(b)s(e)g(set.)52 b(Suc)m(h)0 2928 y(elemen)m(ts)26 b(are)g(indicated)e
(b)m(y)h FJ(\003)h FK(in)e(the)i(examples)f(b)s(elo)m(w.)38
b(F)-8 b(or)26 b(example,)h(assuming)d(zero-based)i(indexing)e(and)0
3041 y Fy(n)h FK(=)g(3:)p 273 3152 3355 4 v 271 3265
4 113 v 488 3231 a FD(order)p 940 3265 V 378 w(uplo)p
1459 3265 V 213 w FK(T)-8 b(riangular)28 b(matrix)i Fy(A)p
2370 3265 V 307 w FK(Storage)i(in)d(arra)m(y)i(A)p 3626
3265 V 273 3268 3355 4 v 271 3617 4 349 v 339 3465 a(blas)p
502 3465 28 4 v 32 w(colma)5 b(jor)p 940 3617 4 349 v
116 w(blas)p 1154 3465 28 4 v 32 w(upp)s(er)p 1459 3617
4 349 v 1535 3271 a Ft(0)1535 3418 y(B)1535 3471 y(@)1649
3352 y Fy(a)1697 3366 y FC(00)1855 3352 y Fy(a)1903 3366
y FC(01)2061 3352 y Fy(a)2109 3366 y FC(02)1855 3465
y Fy(a)1903 3479 y FC(11)2061 3465 y Fy(a)2109 3479 y
FC(12)2061 3578 y Fy(a)2109 3592 y FC(22)2225 3271 y
Ft(1)2225 3418 y(C)2225 3471 y(A)p 2370 3617 V 2422 3465
a Fy(a)2470 3479 y FC(00)2590 3465 y FJ(\003)46 b(\003)26
b Fy(a)2800 3479 y FC(01)2900 3465 y Fy(a)2948 3479 y
FC(11)3068 3465 y FJ(\003)46 b Fy(a)3207 3479 y FC(02)3307
3465 y Fy(a)3355 3479 y FC(12)3455 3465 y Fy(a)3503 3479
y FC(22)p 3626 3617 V 273 3620 3355 4 v 271 3969 4 349
v 322 3817 a FK(blas)p 485 3817 28 4 v 32 w(ro)m(wma)5
b(jor)p 940 3969 4 349 v 100 w(blas)p 1154 3817 28 4
v 32 w(upp)s(er)p 1459 3969 4 349 v 1535 3623 a Ft(0)1535
3770 y(B)1535 3823 y(@)1649 3704 y Fy(a)1697 3718 y FC(00)1855
3704 y Fy(a)1903 3718 y FC(01)2061 3704 y Fy(a)2109 3718
y FC(02)1855 3817 y Fy(a)1903 3831 y FC(11)2061 3817
y Fy(a)2109 3831 y FC(12)2061 3930 y Fy(a)2109 3944 y
FC(22)2225 3623 y Ft(1)2225 3770 y(C)2225 3823 y(A)p
2370 3969 V 2422 3817 a Fy(a)2470 3831 y FC(00)2570 3817
y Fy(a)2618 3831 y FC(01)2718 3817 y Fy(a)2766 3831 y
FC(02)2886 3817 y FJ(\003)46 b Fy(a)3025 3831 y FC(11)3125
3817 y Fy(a)3173 3831 y FC(12)3293 3817 y FJ(\003)g(\003)26
b Fy(a)3503 3831 y FC(22)p 3626 3969 V 273 3972 3355
4 v 271 4321 4 349 v 339 4169 a FK(blas)p 502 4169 28
4 v 32 w(colma)5 b(jor)p 940 4321 4 349 v 128 w(blas)p
1166 4169 28 4 v 31 w(lo)m(w)m(er)p 1459 4321 4 349 v
1535 3975 a Ft(0)1535 4122 y(B)1535 4175 y(@)1649 4056
y Fy(a)1697 4070 y FC(00)1649 4169 y Fy(a)1697 4183 y
FC(10)1855 4169 y Fy(a)1903 4183 y FC(11)1649 4282 y
Fy(a)1697 4296 y FC(20)1855 4282 y Fy(a)1903 4296 y FC(21)2061
4282 y Fy(a)2109 4296 y FC(22)2225 3975 y Ft(1)2225 4122
y(C)2225 4175 y(A)p 2370 4321 V 2422 4169 a Fy(a)2470
4183 y FC(00)2570 4169 y Fy(a)2618 4183 y FC(10)2718
4169 y Fy(a)2766 4183 y FC(20)2886 4169 y FJ(\003)46
b Fy(a)3025 4183 y FC(11)3125 4169 y Fy(a)3173 4183 y
FC(21)3293 4169 y FJ(\003)g(\003)26 b Fy(a)3503 4183
y FC(22)p 3626 4321 V 273 4324 3355 4 v 271 4673 4 349
v 322 4521 a FK(blas)p 485 4521 28 4 v 32 w(ro)m(wma)5
b(jor)p 940 4673 4 349 v 112 w(blas)p 1166 4521 28 4
v 31 w(lo)m(w)m(er)p 1459 4673 4 349 v 1535 4327 a Ft(0)1535
4474 y(B)1535 4527 y(@)1649 4408 y Fy(a)1697 4422 y FC(00)1649
4521 y Fy(a)1697 4535 y FC(10)1855 4521 y Fy(a)1903 4535
y FC(11)1649 4634 y Fy(a)1697 4648 y FC(20)1855 4634
y Fy(a)1903 4648 y FC(21)2061 4634 y Fy(a)2109 4648 y
FC(22)2225 4327 y Ft(1)2225 4474 y(C)2225 4527 y(A)p
2370 4673 V 2422 4521 a Fy(a)2470 4535 y FC(00)2590 4521
y FJ(\003)46 b(\003)26 b Fy(a)2800 4535 y FC(10)2900
4521 y Fy(a)2948 4535 y FC(11)3068 4521 y FJ(\003)46
b Fy(a)3207 4535 y FC(20)3307 4521 y Fy(a)3355 4535 y
FC(21)3455 4521 y Fy(a)3503 4535 y FC(22)p 3626 4673
V 273 4676 3355 4 v 141 4847 a FK(Routines)33 b(that)h(handle)e
FG(symmetric)g FK(or)h FG(Hermitian)f FK(matrices)h(allo)m(w)g(for)g
(either)g(the)h(upp)s(er)d(or)j(lo)m(w)m(er)0 4960 y(triangle)23
b(of)i(the)f(matrix)f(\(as)i(sp)s(eci\014ed)e(b)m(y)h
FD(uplo)p FK(\))f(to)i(b)s(e)e(stored)i(in)e(the)h(corresp)s(onding)e
(elemen)m(ts)j(of)f(the)g(arra)m(y;)0 5073 y(the)31 b(remaining)d
(elemen)m(ts)j(of)f(the)h(arra)m(y)g(need)f(not)g(b)s(e)g(set.)42
b(F)-8 b(or)31 b(example,)f(when)f Fy(n)c FK(=)g(3:)4084
64 y FI(1)4084 177 y(2)4084 290 y(3)4084 403 y(4)4084
516 y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084 967
y(9)4069 1080 y(10)4069 1193 y(11)4069 1306 y(12)4069
1419 y(13)4069 1532 y(14)4069 1645 y(15)4069 1758 y(16)4069
1870 y(17)4069 1983 y(18)4069 2096 y(19)4069 2209 y(20)4069
2322 y(21)4069 2435 y(22)4069 2548 y(23)4069 2661 y(24)4069
2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
3677 y(33)4069 3790 y(34)4069 3903 y(35)4069 4016 y(36)4069
4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 23 33
23 32 bop 0 -165 a FA(2.2.)72 b(MA)-8 b(TRIX)31 b(STORA)m(GE)f(SCHEMES)
2263 b FK(23)p 280 3 3340 4 v 278 116 4 113 v 495 82
a FD(order)p 947 116 V 378 w(uplo)p 1467 116 V 213 w
FK(Hermitian)29 b(matrix)h Fy(A)p 2362 116 V 308 w FK(Storage)h(in)e
(arra)m(y)i(A)p 3618 116 V 280 120 3340 4 v 278 468 4
349 v 347 317 a(blas)p 510 317 28 4 v 32 w(colma)5 b(jor)p
947 468 4 349 v 116 w(blas)p 1162 317 28 4 v 32 w(upp)s(er)p
1467 468 4 349 v 1535 123 a Ft(0)1535 269 y(B)1535 322
y(@)1649 204 y Fy(a)1697 218 y FC(00)1855 204 y Fy(a)1903
218 y FC(01)2061 204 y Fy(a)2109 218 y FC(02)1650 316
y FK(\026)-46 b Fy(a)1697 330 y FC(01)1855 316 y Fy(a)1903
330 y FC(11)2061 316 y Fy(a)2109 330 y FC(12)1650 429
y FK(\026)g Fy(a)1697 443 y FC(02)1856 429 y FK(\026)g
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317 y FJ(\003)46 b Fy(a)3199 331 y FC(02)3299 317 y Fy(a)3347
331 y FC(12)3447 317 y Fy(a)3495 331 y FC(22)p 3618 468
V 280 472 3340 4 v 278 820 4 349 v 330 669 a FK(blas)p
493 669 28 4 v 32 w(ro)m(wma)5 b(jor)p 947 820 4 349
v 100 w(blas)p 1162 669 28 4 v 32 w(upp)s(er)p 1467 820
4 349 v 1535 475 a Ft(0)1535 621 y(B)1535 674 y(@)1649
556 y Fy(a)1697 570 y FC(00)1855 556 y Fy(a)1903 570
y FC(01)2061 556 y Fy(a)2109 570 y FC(02)1650 668 y FK(\026)-46
b Fy(a)1697 682 y FC(01)1855 668 y Fy(a)1903 682 y FC(11)2061
668 y Fy(a)2109 682 y FC(12)1650 781 y FK(\026)g Fy(a)1697
795 y FC(02)1856 781 y FK(\026)g Fy(a)1903 795 y FC(12)2061
781 y Fy(a)2109 795 y FC(22)2225 475 y Ft(1)2225 621
y(C)2225 674 y(A)p 2362 820 V 2414 669 a Fy(a)2462 683
y FC(00)2562 669 y Fy(a)2610 683 y FC(01)2710 669 y Fy(a)2758
683 y FC(02)2878 669 y FJ(\003)46 b Fy(a)3017 683 y FC(11)3117
669 y Fy(a)3165 683 y FC(12)3285 669 y FJ(\003)g(\003)26
b Fy(a)3495 683 y FC(22)p 3618 820 V 280 824 3340 4 v
278 1172 4 349 v 347 1021 a FK(blas)p 510 1021 28 4 v
32 w(colma)5 b(jor)p 947 1172 4 349 v 127 w(blas)p 1173
1021 28 4 v 32 w(lo)m(w)m(er)p 1467 1172 4 349 v 1535
827 a Ft(0)1535 973 y(B)1535 1026 y(@)1649 908 y Fy(a)1697
922 y FC(00)1856 908 y FK(\026)-46 b Fy(a)1903 922 y
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Ft(1)2225 973 y(C)2225 1026 y(A)p 2362 1172 V 2414 1021
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1035 y FC(22)p 3618 1172 V 280 1176 3340 4 v 278 1524
4 349 v 330 1373 a FK(blas)p 493 1373 28 4 v 32 w(ro)m(wma)5
b(jor)p 947 1524 4 349 v 111 w(blas)p 1173 1373 28 4
v 32 w(lo)m(w)m(er)p 1467 1524 4 349 v 1535 1179 a Ft(0)1535
1325 y(B)1535 1378 y(@)1649 1260 y Fy(a)1697 1274 y FC(00)1856
1260 y FK(\026)-46 b Fy(a)1903 1274 y FC(10)2062 1260
y FK(\026)g Fy(a)2109 1274 y FC(20)1649 1373 y Fy(a)1697
1387 y FC(10)1855 1373 y Fy(a)1903 1387 y FC(11)2062
1373 y FK(\026)g Fy(a)2109 1387 y FC(21)1649 1485 y Fy(a)1697
1499 y FC(20)1855 1485 y Fy(a)1903 1499 y FC(21)2061
1485 y Fy(a)2109 1499 y FC(22)2225 1179 y Ft(1)2225 1325
y(C)2225 1378 y(A)p 2362 1524 V 2414 1373 a Fy(a)2462
1387 y FC(00)2582 1373 y FJ(\003)46 b(\003)26 b Fy(a)2792
1387 y FC(10)2892 1373 y Fy(a)2940 1387 y FC(11)3060
1373 y FJ(\003)46 b Fy(a)3199 1387 y FC(20)3299 1373
y Fy(a)3347 1387 y FC(21)3447 1373 y Fy(a)3495 1387 y
FC(22)p 3618 1524 V 280 1528 3340 4 v 0 1732 a Fx(2.2.2)97
b(P)m(ack)m(ed)34 b(Sto)m(rage)0 1904 y FK(Symmetric,)25
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(more)g(compactly)-8 b(,)27 b(if)c(the)h(relev)-5 b(an)m(t)25
b(triangle)0 2017 y(\(again)36 b(as)f(sp)s(eci\014ed)f(b)m(y)h
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(ws)35 b FK(in)f(a)i(one-dimensional)d(arra)m(y)-8 b(.)57
b(In)35 b(the)0 2130 y(BLAS,)g(arra)m(ys)h(that)g(hold)e(matrices)h(in)
g(pac)m(k)m(ed)h(storage,)i(ha)m(v)m(e)f(names)e(ending)f(in)g(`P'.)i
(So,)h(in)d(the)h(case)i(of)0 2243 y(zero-based)k(addressing)e(as)h(in)
f(C,)h(w)m(e)h(ha)m(v)m(e)g(the)g(follo)m(wing)d(form)m(ulas)i(\(F)-8
b(or)41 b(one-based)f(addressing,)i(as)e(in)0 2356 y(F)-8
b(ortran,)31 b(replace)g Fy(i)f FK(b)m(y)h Fy(i)20 b
FJ(\000)g FK(1)31 b(and)e Fy(j)36 b FK(b)m(y)31 b Fy(j)26
b FJ(\000)19 b FK(1)31 b(in)e(these)i(form)m(ulas\).)136
2568 y FJ(\017)46 b FK(if)30 b FD(uplo)46 b(=)i(blas)p
843 2568 29 4 v 33 w(upper)29 b FK(then)330 2756 y FG({)45
b FK(if)30 b FD(order)46 b(=)h(blas)p 1090 2756 V 34
w(colmajor)p FK(,)28 b Fy(a)1603 2770 y Fw(ij)1694 2756
y FK(is)h(stored)i(in)e(AP\()p Fy(i)21 b FK(+)f Fy(j)5
b FK(\()p Fy(j)27 b FK(+)20 b(1\))p Fy(=)p FK(2\))32
b(for)e Fy(i)c FJ(\024)f Fy(j)5 b FK(;)330 2902 y FG({)45
b FK(if)30 b FD(order)46 b(=)h(blas)p 1090 2902 V 34
w(rowmajor)p FK(,)28 b Fy(a)1603 2916 y Fw(ij)1694 2902
y FK(is)h(stored)i(in)e(AP\()p Fy(j)d FK(+)20 b Fy(i)p
FK(\(2)p Fy(n)h FJ(\000)f Fy(i)g FJ(\000)g FK(1\))p Fy(=)p
FK(2\))33 b(for)d Fy(i)25 b FJ(\024)g Fy(j)5 b FK(;)136
3089 y FJ(\017)46 b FK(if)30 b FD(uplo)46 b(=)i(blas)p
843 3089 V 33 w(lower)29 b FK(then)330 3277 y FG({)45
b FK(if)30 b FD(order)46 b(=)h(blas)p 1090 3277 V 34
w(colmajor)p FK(,)28 b Fy(a)1603 3291 y Fw(ij)1694 3277
y FK(is)h(stored)i(in)e(AP\()p Fy(i)21 b FK(+)f Fy(j)5
b FK(\(2)p Fy(n)21 b FJ(\000)f Fy(j)26 b FJ(\000)20 b
FK(1\))p Fy(=)p FK(2\))32 b(for)e Fy(j)h FJ(\024)25 b
Fy(i)p FK(.)330 3423 y FG({)45 b FK(if)30 b FD(order)46
b(=)h(blas)p 1090 3423 V 34 w(rowmajor)p FK(,)28 b Fy(a)1603
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Fy(j)d FK(+)20 b Fy(i)p FK(\()p Fy(i)h FK(+)f(1\))p Fy(=)p
FK(2\))33 b(for)d Fy(j)h FJ(\024)25 b Fy(i)p FK(.)141
3636 y(F)-8 b(or)31 b(example,)g(assuming)e(zero-based)i(indexing:)p
319 3765 3262 4 v 317 3878 4 113 v 534 3844 a FD(order)p
986 3878 V 378 w(uplo)p 1506 3878 V 213 w FK(T)-8 b(riangular)29
b(matrix)g Fy(A)p 2417 3878 V 100 w FK(P)m(ac)m(k)m(ed)j(storage)g(in)d
(arra)m(y)i(ap)p 3579 3878 V 319 3881 3262 4 v 317 4230
4 349 v 385 4078 a(blas)p 548 4078 28 4 v 32 w(colma)5
b(jor)p 986 4230 4 349 v 117 w(blas)p 1201 4078 28 4
v 31 w(upp)s(er)p 1506 4230 4 349 v 1581 3884 a Ft(0)1581
4030 y(B)1581 4084 y(@)1696 3965 y Fy(a)1744 3979 y FC(00)1901
3965 y Fy(a)1949 3979 y FC(01)2107 3965 y Fy(a)2155 3979
y FC(02)1901 4078 y Fy(a)1949 4092 y FC(11)2107 4078
y Fy(a)2155 4092 y FC(12)2107 4191 y Fy(a)2155 4205 y
FC(22)2271 3884 y Ft(1)2271 4030 y(C)2271 4084 y(A)p
2417 4230 V 2561 4078 a Fy(a)2609 4092 y FC(00)2724 4078
y Fy(a)2772 4092 y FC(01)2867 4078 y Fy(a)2915 4092 y
FC(11)2724 4127 y Ft(|)p 2761 4127 59 10 v 59 w({z)p
2894 4127 V 59 w(})3030 4078 y Fy(a)3078 4092 y FC(02)3173
4078 y Fy(a)3221 4092 y FC(12)3316 4078 y Fy(a)3364 4092
y FC(22)3030 4127 y Ft(|)p 3067 4127 130 10 v 130 w({z)p
3271 4127 V 130 w(})p 3579 4230 4 349 v 319 4233 3262
4 v 317 4582 4 349 v 369 4430 a FK(blas)p 532 4430 28
4 v 32 w(ro)m(wma)g(jor)p 986 4582 4 349 v 100 w(blas)p
1201 4430 28 4 v 31 w(upp)s(er)p 1506 4582 4 349 v 1581
4236 a Ft(0)1581 4382 y(B)1581 4436 y(@)1696 4317 y Fy(a)1744
4331 y FC(00)1901 4317 y Fy(a)1949 4331 y FC(01)2107
4317 y Fy(a)2155 4331 y FC(02)1901 4430 y Fy(a)1949 4444
y FC(11)2107 4430 y Fy(a)2155 4444 y FC(12)2107 4543
y Fy(a)2155 4557 y FC(22)2271 4236 y Ft(1)2271 4382 y(C)2271
4436 y(A)p 2417 4582 V 2561 4430 a Fy(a)2609 4444 y FC(00)2704
4430 y Fy(a)2752 4444 y FC(01)2847 4430 y Fy(a)2895 4444
y FC(02)2561 4479 y Ft(|)p 2598 4479 130 10 v 130 w({z)p
2802 4479 V 130 w(})3010 4430 y Fy(a)3058 4444 y FC(11)3153
4430 y Fy(a)3201 4444 y FC(12)3010 4479 y Ft(|)p 3047
4479 59 10 v 59 w({z)p 3180 4479 V 59 w(})3316 4430 y
Fy(a)3364 4444 y FC(22)p 3579 4582 4 349 v 319 4585 3262
4 v 317 4934 4 349 v 385 4782 a FK(blas)p 548 4782 28
4 v 32 w(colma)g(jor)p 986 4934 4 349 v 128 w(blas)p
1212 4782 28 4 v 32 w(lo)m(w)m(er)p 1506 4934 4 349 v
1581 4588 a Ft(0)1581 4734 y(B)1581 4788 y(@)1696 4669
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FC(10)1901 4782 y Fy(a)1949 4796 y FC(11)1696 4895 y
Fy(a)1744 4909 y FC(20)1901 4895 y Fy(a)1949 4909 y FC(21)2107
4895 y Fy(a)2155 4909 y FC(22)2271 4588 y Ft(1)2271 4734
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4796 y FC(00)2704 4782 y Fy(a)2752 4796 y FC(10)2847
4782 y Fy(a)2895 4796 y FC(20)2561 4831 y Ft(|)p 2598
4831 130 10 v 130 w({z)p 2802 4831 V 130 w(})3010 4782
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FC(21)3010 4831 y Ft(|)p 3047 4831 59 10 v 59 w({z)p
3180 4831 V 59 w(})3316 4782 y Fy(a)3364 4796 y FC(22)p
3579 4934 4 349 v 319 4937 3262 4 v 317 5286 4 349 v
369 5134 a FK(blas)p 532 5134 28 4 v 32 w(ro)m(wma)g(jor)p
986 5286 4 349 v 111 w(blas)p 1212 5134 28 4 v 32 w(lo)m(w)m(er)p
1506 5286 4 349 v 1581 4940 a Ft(0)1581 5086 y(B)1581
5140 y(@)1696 5021 y Fy(a)1744 5035 y FC(00)1696 5134
y Fy(a)1744 5148 y FC(10)1901 5134 y Fy(a)1949 5148 y
FC(11)1696 5247 y Fy(a)1744 5261 y FC(20)1901 5247 y
Fy(a)1949 5261 y FC(21)2107 5247 y Fy(a)2155 5261 y FC(22)2271
4940 y Ft(1)2271 5086 y(C)2271 5140 y(A)p 2417 5286 V
2561 5134 a Fy(a)2609 5148 y FC(00)2724 5134 y Fy(a)2772
5148 y FC(10)2867 5134 y Fy(a)2915 5148 y FC(11)2724
5183 y Ft(|)p 2761 5183 59 10 v 59 w({z)p 2894 5183 V
59 w(})3030 5134 y Fy(a)3078 5148 y FC(20)3173 5134 y
Fy(a)3221 5148 y FC(21)3316 5134 y Fy(a)3364 5148 y FC(22)3030
5183 y Ft(|)p 3067 5183 130 10 v 130 w({z)p 3271 5183
V 130 w(})p 3579 5286 4 349 v 319 5289 3262 4 v -214
64 a FI(1)-214 177 y(2)-214 290 y(3)-214 403 y(4)-214
516 y(5)-214 628 y(6)-214 741 y(7)-214 854 y(8)-214 967
y(9)-230 1080 y(10)-230 1193 y(11)-230 1306 y(12)-230
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1870 y(17)-230 1983 y(18)-230 2096 y(19)-230 2209 y(20)-230
2322 y(21)-230 2435 y(22)-230 2548 y(23)-230 2661 y(24)-230
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4129 y(37)-230 4242 y(38)-230 4354 y(39)-230 4467 y(40)-230
4580 y(41)-230 4693 y(42)-230 4806 y(43)-230 4919 y(44)-230
5032 y(45)-230 5145 y(46)-230 5258 y(47)-230 5371 y(48)p
eop
%%Page: 24 34
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5371 y(48)p eop
%%Page: 25 35
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eop
%%Page: 26 36
26 35 bop 0 -165 a FK(26)1930 b FA(CHAPTER)30 b(2.)71
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eop
%%Page: 27 37
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3433 4400 V 691 4512 V 743 4479 a(a\(i,:\))p 1559 4512
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eop
%%Page: 28 38
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%%Page: 29 39
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eop
%%Page: 30 40
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eop
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eop
%%Page: 33 43
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%%Page: 34 44
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5145 y(46)4069 5258 y(47)4069 5371 y(48)p eop
%%Page: 35 45
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eop
%%Page: 36 46
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eop
%%Page: 37 47
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(up)s(date\))330 4883 y FG({)45 b FK(SY)p 551 4883 V
33 w(TRIDIA)m(G)p 988 4883 V 33 w(R2K)30 b(\(Symmetric)g(rank-2k)h(up)s
(date)e(with)g(tridiagonal)g(matrix\))330 5028 y FG({)45
b FK(HE)p 562 5028 V 33 w(TRIDIA)m(G)p 999 5028 V 33
w(R2K)31 b(\(Hermitian)e(rank-2k)i(up)s(date)e(with)g(tridiagonal)g
(matrix\))136 5214 y FJ(\017)46 b FK(Data)32 b(Mo)m(v)m(emen)m(t)h
(with)c(Matrices)i(\(section)g(2.8.9\))330 5400 y FG({)45
b FJ(f)p FK(GE,GB,SY,SB,SP)-8 b(,TR,TB,TP)p FJ(g)p 1695
5400 V 35 w FK(COPY)30 b(\(Matrix)h(cop)m(y\))-214 64
y FI(1)-214 177 y(2)-214 290 y(3)-214 403 y(4)-214 516
y(5)-214 628 y(6)-214 741 y(7)-214 854 y(8)-214 967 y(9)-230
1080 y(10)-230 1193 y(11)-230 1306 y(12)-230 1419 y(13)-230
1532 y(14)-230 1645 y(15)-230 1758 y(16)-230 1870 y(17)-230
1983 y(18)-230 2096 y(19)-230 2209 y(20)-230 2322 y(21)-230
2435 y(22)-230 2548 y(23)-230 2661 y(24)-230 2774 y(25)-230
2887 y(26)-230 3000 y(27)-230 3112 y(28)-230 3225 y(29)-230
3338 y(30)-230 3451 y(31)-230 3564 y(32)-230 3677 y(33)-230
3790 y(34)-230 3903 y(35)-230 4016 y(36)-230 4129 y(37)-230
4242 y(38)-230 4354 y(39)-230 4467 y(40)-230 4580 y(41)-230
4693 y(42)-230 4806 y(43)-230 4919 y(44)-230 5032 y(45)-230
5145 y(46)-230 5258 y(47)-230 5371 y(48)p eop
%%Page: 38 48
38 47 bop 0 -165 a FK(38)1930 b FA(CHAPTER)30 b(2.)71
b(DENSE)30 b(AND)h(BANDED)h(BLAS)330 91 y FG({)45 b FJ(f)p
FK(HE,HB,HP)p FJ(g)p 964 91 28 4 v 35 w FK(COPY)30 b(\(Matrix)g(cop)m
(y\))330 237 y FG({)45 b FJ(f)p FK(GE)p FJ(g)p 655 237
V 34 w FK(TRANS)30 b(\(Matrix)h(transp)s(osition\))330
384 y FG({)45 b FJ(f)p FK(GE)p FJ(g)p 655 384 V 34 w
FK(PERMUTE)30 b(\(P)m(erm)m(ute)i(matrix\))136 571 y
FJ(\017)46 b FK(En)m(vironmen)m(tal)29 b(Enquiry)f(\(section)j
(2.8.10\))330 759 y FG({)45 b FK(FPINF)m(O)31 b(\(En)m(vironmen)m(tal)f
(enquiry\))0 1002 y Fx(2.8.2)97 b(Reduction)33 b(Op)s(erations)0
1246 y FK(DOT)d(\(Dot)i(Pro)s(duct\))1351 b Fy(x;)15
b(y)28 b FJ(2)d Fz(I)-17 b(R)2497 1210 y Fw(n)2544 1246
y Fy(;)15 b(r)28 b FJ( )d Fy(\014)5 b(r)23 b FK(+)d Fy(\013x)3090
1213 y Fw(T)3145 1246 y Fy(y)29 b FK(=)24 b Fy(\014)5
b(r)23 b FK(+)d Fy(\013)3599 1140 y Fw(n)p Fu(\000)p
FC(1)3606 1165 y Ft(X)3608 1347 y Fw(i)p FC(=0)3747 1246
y Fy(x)3799 1260 y Fw(i)3827 1246 y Fy(y)3872 1260 y
Fw(i)720 1595 y Fy(x;)15 b(y)28 b FJ(2)d Fz(l)-46 b(C)1027
1558 y Fw(n)1074 1595 y Fy(;)15 b(r)28 b FJ( )d Fy(\014)5
b(r)23 b FK(+)d Fy(\013x)1620 1562 y Fw(T)1676 1595 y
Fy(y)28 b FK(=)d Fy(\014)5 b(r)23 b FK(+)d Fy(\013)2129
1489 y Fw(n)p Fu(\000)p FC(1)2136 1514 y Ft(X)2139 1697
y Fw(i)p FC(=0)2277 1595 y Fy(x)2329 1609 y Fw(i)2357
1595 y Fy(y)2402 1609 y Fw(i)2461 1595 y FK(or)30 b Fy(r)e
FJ( )d Fy(\014)5 b(r)23 b FK(+)d Fy(\013x)3078 1562 y
Fw(H)3145 1595 y Fy(y)29 b FK(=)24 b Fy(\014)5 b(r)23
b FK(+)d Fy(\013)3599 1489 y Fw(n)p Fu(\000)p FC(1)3606
1514 y Ft(X)3608 1697 y Fw(i)p FC(=0)3764 1595 y FK(\026)-62
b Fy(x)3799 1609 y Fw(i)3827 1595 y Fy(y)3872 1609 y
Fw(i)141 1851 y FK(The)26 b(routine)f Fv(DOT)g FK(adds)g(the)i(scaled)e
(dot)i(pro)s(duct)d(of)j(t)m(w)m(o)g(v)m(ectors)g Fy(x)f
FK(and)g Fy(y)j FK(in)m(to)c(a)i(scaled)f(scalar)g Fy(r)s
FK(.)38 b(The)0 1964 y(routine)32 b(returns)g(immediately)f(if)h
Fv(n)h FK(is)f(less)g(than)h(zero,)i(or,)e(if)f Fv(b)s(eta)h
FK(is)f(equal)g(to)i(one)f(and)g(either)f Fv(alpha)g
FK(or)h Fv(n)0 2077 y FK(is)f(equal)h(to)i(zero.)50 b(If)33
b Fv(alpha)f FK(is)h(equal)g(to)h(zero)g(then)f Fy(x)h
FK(and)e Fy(y)k FK(are)e(not)g(read.)50 b(Similarly)-8
b(,)31 b(if)h Fv(b)s(eta)h FK(is)f(equal)h(to)0 2190
y(zero,)e Fy(r)h FK(is)c(not)i(read.)40 b(As)30 b(describ)s(ed)d(in)h
(section)i(2.5.3,)h(the)f(v)-5 b(alue)29 b Fv(incx)g
FK(or)h Fv(incy)f FK(less)g(than)g(zero)i(is)d(p)s(ermitted.)0
2303 y(Ho)m(w)m(ev)m(er,)33 b(if)c Fv(incx)h FK(or)h
Fv(incy)f FK(is)f(equal)h(to)h(zero,)h(an)e(error)g(\015ag)h(is)e(set)i
(and)f(passed)g(to)h(the)f(error)g(handler.)141 2416
y(When)g Fy(x)g FK(and)f Fy(y)k FK(are)e(complex)e(v)m(ectors,)j(the)e
(v)m(ector)i(comp)s(onen)m(ts)e Fy(x)2564 2430 y Fw(i)2622
2416 y FK(are)h(used)e(unconjugated)h(or)g(conju-)0 2528
y(gated)c(as)e(sp)s(eci\014ed)f(b)m(y)h(the)h(op)s(erator)g(argumen)m
(t)g Fv(conj)p FK(.)39 b(If)24 b Fy(x)h FK(and)f Fy(y)j
FK(are)e(real)f(v)m(ectors,)j(the)e(op)s(erator)f(argumen)m(t)0
2641 y Fv(conj)31 b FK(has)f(no)h(e\013ect.)136 2854
y FJ(\017)46 b FK(F)-8 b(ortran)31 b(95)h(binding:)514
3104 y FD(SUBROUTINE)45 b(dot\()h(x,)h(y,)h(r)f([,)g(conj])g([,)g
(alpha])f([,)h(beta])f(\))609 3217 y(<type>\(<wp>\),)e(INTENT)i(\(IN\))
h(::)g(x\(:\),)g(y\(:\))609 3330 y(<type>\(<wp>\),)d(INTENT)i
(\(INOUT\))g(::)h(r)609 3443 y(TYPE)g(\(blas_conj_type\),)c
(INTENT\(IN\),)i(OPTIONAL)g(::)i(conj)609 3555 y(<type>\(<wp>\),)d
(INTENT)i(\(IN\),)h(OPTIONAL)e(::)i(alpha,)g(beta)514
3668 y(where)609 3781 y(x)h(and)e(y)i(have)f(shape)f(\(n\))136
4031 y FJ(\017)g FK(F)-8 b(ortran)31 b(77)h(binding:)514
4256 y FD(SUBROUTINE)45 b(BLAS_xDOT\()g(CONJ,)h(N,)h(ALPHA,)f(X,)h
(INCX,)g(BETA,)f(Y,)h(INCY,)g(R)g(\))514 4369 y(INTEGER)523
b(CONJ,)46 b(INCX,)g(INCY,)h(N)514 4482 y(<type>)571
b(ALPHA,)46 b(BETA,)g(R)514 4595 y(<type>)571 b(X\()47
b(*)g(\),)h(Y\()f(*)g(\))136 4820 y FJ(\017)f FK(C)30
b(binding:)227 5045 y FD(void)47 b(BLAS_xdot\()e(enum)i(blas_conj_type)
c(conj,)k(int)g(n,)g(SCALAR_IN)e(alpha,)991 5158 y(const)h(ARRAY)h(x,)g
(int)g(incx,)f(SCALAR_IN)f(beta,)i(const)f(ARRAY)g(y,)991
5271 y(int)h(incy,)f(SCALAR_INOUT)f(r)i(\);)4084 64 y
FI(1)4084 177 y(2)4084 290 y(3)4084 403 y(4)4084 516
y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084 967 y(9)4069
1080 y(10)4069 1193 y(11)4069 1306 y(12)4069 1419 y(13)4069
1532 y(14)4069 1645 y(15)4069 1758 y(16)4069 1870 y(17)4069
1983 y(18)4069 2096 y(19)4069 2209 y(20)4069 2322 y(21)4069
2435 y(22)4069 2548 y(23)4069 2661 y(24)4069 2774 y(25)4069
2887 y(26)4069 3000 y(27)4069 3112 y(28)4069 3225 y(29)4069
3338 y(30)4069 3451 y(31)4069 3564 y(32)4069 3677 y(33)4069
3790 y(34)4069 3903 y(35)4069 4016 y(36)4069 4129 y(37)4069
4242 y(38)4069 4354 y(39)4069 4467 y(40)4069 4580 y(41)4069
4693 y(42)4069 4806 y(43)4069 4919 y(44)4069 5032 y(45)4069
5145 y(46)4069 5258 y(47)4069 5371 y(48)p eop
%%Page: 39 49
39 48 bop 0 -165 a FA(2.8.)72 b(LANGUA)m(GE)32 b(BINDINGS)2578
b FK(39)p 0 91 3900 6 v 0 204 a(NORM)30 b(\(V)-8 b(ector)33
b(norms\))1313 b Fy(r)28 b FJ( )d(jj)p Fy(x)p FJ(jj)2572
218 y FC(1)2613 204 y Fy(;)30 b FJ(jj)p Fy(x)p FJ(jj)2820
218 y FC(1)p Fw(R)2914 204 y Fy(;)h FJ(jj)p Fy(x)p FJ(jj)3122
218 y FC(2)3162 204 y Fy(;)15 b FJ(jj)p Fy(x)p FJ(jj)3354
218 y Fu(1)3430 204 y Fy(;)46 b(or)33 b FJ(jj)p Fy(x)p
FJ(jj)3771 218 y Fu(1)p Fw(R)141 430 y FK(The)27 b(routine)f
Fv(NORM)g FK(computes)h(the)g FJ(jj)13 b(\001)g(jj)1636
444 y FC(1)1678 430 y FK(,)28 b FJ(jj)13 b(\001)g(jj)1882
444 y FC(1)p Fw(R)1977 430 y FK(,)28 b FJ(jj)13 b(\001)g(jj)2181
444 y FC(2)2223 430 y FK(,)27 b FJ(jj)13 b(\001)g(jj)2426
444 y Fu(1)2503 430 y FK(,)28 b(or)f FJ(jj)13 b(\001)g(jj)2815
444 y Fu(1)p Fw(R)2972 430 y FK(of)28 b(a)f(v)m(ector)i
Fy(x)d FK(dep)s(ending)0 543 y(on)k(the)h(v)-5 b(alue)30
b(passed)g(as)g(the)h Fv(no)m(rm)g FK(op)s(erator)g(argumen)m(t.)141
656 y(If)j FD(norm)46 b(=)i(blas)p 768 656 29 4 v 33
w(frobenius)p 1233 656 V 32 w(norm)p FK(,)34 b(an)g(error)g(\015ag)h
(is)e(not)h(raised,)h(and)e(the)i(t)m(w)m(o-norm)g(is)e(returned)g(to)0
769 y(the)d(user.)39 b(If)29 b Fv(n)h FK(is)e(less)h(than)g(or)h(equal)
f(to)h(zero,)g(this)f(routine)f(returns)g(immediately)g(with)g(the)i
(output)f(scalar)0 882 y Fv(r)34 b FK(set)h(to)h(zero.)53
b(The)34 b(resulting)f(scalar)h Fv(r)g FK(is)g(alw)m(a)m(ys)h(real)f
(and)g(its)f(v)-5 b(alue)34 b(is)g(as)g(de\014ned)g(in)f(section)h
(2.1.1.)55 b(As)0 995 y(describ)s(ed)33 b(in)g(section)i(2.5.3,)j(the)c
(v)-5 b(alue)35 b Fv(incx)f FK(less)g(than)h(zero)g(is)f(p)s(ermitted.)
52 b(Ho)m(w)m(ev)m(er,)38 b(if)c Fv(incx)g FK(is)g(equal)g(to)0
1108 y(zero,)d(an)g(error)f(\015ag)g(is)g(set)h(and)e(passed)h(to)h
(the)g(error)f(handler.)136 1317 y FJ(\017)46 b FK(F)-8
b(ortran)31 b(95)h(binding:)514 1564 y FD(REAL\(<wp>\))45
b(FUNCTION)g(norm\()i(x)g([,)g(norm])g(\))609 1677 y(<type>\(<wp>\),)d
(INTENT)i(\(IN\))h(::)g(x\(:\))609 1790 y(TYPE)g(\(blas_norm_type\),)c
(INTENT)j(\(IN\),)g(OPTIONAL)g(::)h(norm)514 1903 y(where)609
2016 y(x)h(has)e(shape)h(\(n\))136 2262 y FJ(\017)f FK(F)-8
b(ortran)31 b(77)h(binding:)514 2485 y FD(<rtype>)45
b(FUNCTION)h(BLAS_xNORM\()f(NORM,)h(N,)h(X,)g(INCX)g(\))514
2598 y(INTEGER)570 b(INCX,)47 b(N,)g(NORM)514 2711 y(<type>)618
b(X\()48 b(*)f(\))136 2933 y FJ(\017)f FK(C)30 b(binding:)227
3155 y FD(void)47 b(BLAS_xnorm\()e(enum)h(blas_norm_type)e(norm,)j(int)
f(n,)i(const)e(ARRAY)g(x,)1039 3268 y(int)h(incx,)f(RSCALAR_INOUT)e(r)k
(\);)p 0 3490 3900 6 v 0 3656 a FK(SUM)30 b(\(Sum\))3007
b Fy(r)28 b FJ( )3672 3550 y Fw(n)p Fu(\000)p FC(1)3678
3575 y Ft(X)3681 3757 y Fw(i)p FC(=0)3820 3656 y Fy(x)3872
3670 y Fw(i)141 3881 y FK(The)34 b(routine)g Fv(SUM)e
FK(computes)j(the)g(sum)e(of)i(the)f(en)m(tries)h(of)f(a)h(v)m(ector)h
Fy(x)p FK(.)53 b(If)34 b Fv(n)g FK(is)g(less)g(than)g(or)g(equal)g(to)0
3994 y(zero,)c(this)f(routine)f(returns)g(immediately)f(with)h(the)i
(output)e(scalar)i Fv(r)f FK(set)h(to)f(zero.)42 b(As)29
b(describ)s(ed)e(in)h(section)0 4107 y(2.5.3,)36 b(the)e(v)-5
b(alue)33 b Fv(incx)g FK(less)g(than)g(zero)h(is)f(p)s(ermitted.)48
b(Ho)m(w)m(ev)m(er,)36 b(if)d Fv(incx)g FK(is)g(equal)f(to)j(zero,)g
(an)e(error)g(\015ag)h(is)0 4220 y(set)d(and)f(passed)g(to)h(the)f
(error)g(handler.)136 4430 y FJ(\017)46 b FK(F)-8 b(ortran)31
b(95)h(binding:)514 4652 y FD(<type>\(<wp>\))44 b(FUNCTION)i(sum\()g(x)
i(\))609 4765 y(<type>\(<wp>\),)c(INTENT)i(\(IN\))h(::)g(x\(:\))514
4878 y(where)609 4991 y(x)h(has)e(shape)h(\(n\))227 5213
y FK(This)29 b(is)g(the)i(same)g(as)f(the)h(F)-8 b(ortran)31
b(95)g(in)m(trinsic)d(function)h Fv(SUM)p FK(.)136 5400
y FJ(\017)46 b FK(F)-8 b(ortran)31 b(77)h(binding:)-214
64 y FI(1)-214 177 y(2)-214 290 y(3)-214 403 y(4)-214
516 y(5)-214 628 y(6)-214 741 y(7)-214 854 y(8)-214 967
y(9)-230 1080 y(10)-230 1193 y(11)-230 1306 y(12)-230
1419 y(13)-230 1532 y(14)-230 1645 y(15)-230 1758 y(16)-230
1870 y(17)-230 1983 y(18)-230 2096 y(19)-230 2209 y(20)-230
2322 y(21)-230 2435 y(22)-230 2548 y(23)-230 2661 y(24)-230
2774 y(25)-230 2887 y(26)-230 3000 y(27)-230 3112 y(28)-230
3225 y(29)-230 3338 y(30)-230 3451 y(31)-230 3564 y(32)-230
3677 y(33)-230 3790 y(34)-230 3903 y(35)-230 4016 y(36)-230
4129 y(37)-230 4242 y(38)-230 4354 y(39)-230 4467 y(40)-230
4580 y(41)-230 4693 y(42)-230 4806 y(43)-230 4919 y(44)-230
5032 y(45)-230 5145 y(46)-230 5258 y(47)-230 5371 y(48)p
eop
%%Page: 40 50
40 49 bop 0 -165 a FK(40)1930 b FA(CHAPTER)30 b(2.)71
b(DENSE)30 b(AND)h(BANDED)h(BLAS)514 91 y FD(<type>)46
b(FUNCTION)f(BLAS_xSUM\()g(N,)i(X,)h(INCX)e(\))514 204
y(INTEGER)570 b(INCX,)47 b(N)514 317 y(<type>)618 b(X\()48
b(*)f(\))136 508 y FJ(\017)f FK(C)30 b(binding:)227 698
y FD(void)47 b(BLAS_xsum\()e(int)i(n,)g(const)f(ARRAY)h(x,)g(int)g
(incx,)f(SCALAR_INOUT)f(sum)i(\);)p 0 888 3900 6 v 0
1001 a FK(MIN)p 189 1001 28 4 v 33 w(V)-10 b(AL)30 b(\(Min)g(v)-5
b(alue)30 b(&)g(lo)s(cation\))1290 b Fy(k)s(;)15 b(x)2774
1016 y Fw(k)2878 1001 y FK(suc)m(h)30 b(that)h Fy(k)d
FK(=)d(arg)46 b(min)3593 1060 y FC(0)p Fu(\024)p Fw(i<n)3820
1001 y Fy(x)3872 1015 y Fw(i)141 1227 y FK(The)e(routine)g
Fv(MIN)p 844 1227 V 33 w(V)-8 b(AL)44 b FK(\014nds)f(the)i(smallest)f
(comp)s(onen)m(t)h(of)g(a)g(real)f(v)m(ector)i Fy(x)f
FK(and)f(determines)g(the)0 1340 y(smallest)35 b(o\013set)i(or)f(index)
e Fy(k)39 b FK(suc)m(h)d(that)h Fy(x)1520 1355 y Fw(k)1597
1340 y FK(=)61 b(min)1702 1398 y FC(0)p Fu(\024)p Fw(i<)p
Fo(n)1923 1340 y Fy(x)1975 1354 y Fw(i)2003 1340 y FK(.)c(This)34
b(v)-5 b(alue)36 b Fy(x)2591 1355 y Fw(k)2669 1340 y
FK(is)f(returned)g(b)m(y)g(the)i(routine)e(and)0 1489
y(denoted)30 b(b)m(y)f(arg)43 b(min)610 1547 y FC(0)p
Fu(\024)p Fw(i<)p Fo(n)830 1489 y Fy(x)882 1503 y Fw(i)940
1489 y FK(b)s(elo)m(w.)d(When)29 b(the)h(v)-5 b(alue)29
b(of)h(the)g Fv(n)f FK(argumen)m(t)h(is)f(less)g(than)g(or)g(equal)h
(to)g(zero,)h(the)0 1643 y(routine)i(should)f(initialize)g(the)i
(output)g(scalars)g Fv(k)g FK(to)h(the)g(largest)f(in)m(v)-5
b(alid)32 b(index)g(or)j(o\013set)g(v)-5 b(alue)33 b(\(negativ)m(e)0
1756 y(one)c(or)g(zero\))i(and)d Fv(r)h FK(to)h(zero.)41
b(As)29 b(describ)s(ed)e(in)h(section)h(2.5.3,)i(the)e(v)-5
b(alue)29 b Fv(incx)g FK(less)f(than)h(zero)h(is)e(p)s(ermitted.)0
1869 y(Ho)m(w)m(ev)m(er,)33 b(if)c Fv(incx)h FK(is)g(equal)g(to)h
(zero,)g(an)f(error)g(\015ag)h(is)f(set)g(and)g(passed)g(to)h(the)g
(error)f(handler.)227 2047 y Fz(A)-5 b(dvic)g(e)33 b(to)g(users.)81
b FK(The)30 b(routine)g Fv(MIN)p 1614 2047 V 33 w(V)-8
b(AL)30 b FK(strictly)f(op)s(erates)i(on)g(real)f(v)m(ectors.)42
b(This)29 b(routine)g(is)h(not)227 2160 y(de\014ned)f(for)i(complex)f
(v)m(ectors.)42 b(\()p Fz(End)33 b(of)g(advic)-5 b(e)33
b(to)g(users.)p FK(\))136 2338 y FJ(\017)46 b FK(F)-8
b(ortran)31 b(95)h(binding:)514 2528 y FD(SUBROUTINE)45
b(min_val\()g(x,)i(k,)h(r)f(\))609 2641 y(REAL\(<wp>\),)e(INTENT)h
(\(IN\))h(::)g(x\(:\))609 2754 y(INTEGER,)f(INTENT)g(\(OUT\))g(::)h(k)
609 2867 y(REAL\(<wp>\),)e(INTENT)h(\(OUT\))g(::)h(r)514
2980 y(where)609 3093 y(x)h(has)e(shape)h(\(n\))136 3283
y FJ(\017)f FK(F)-8 b(ortran)31 b(77)h(binding:)514 3474
y FD(SUBROUTINE)45 b(BLAS_xMIN_VAL\()f(N,)j(X,)g(INCX,)f(K,)h(R)h(\))
514 3587 y(INTEGER)570 b(INCX,)47 b(K,)g(N)514 3700 y(<rtype>)570
b(R)514 3813 y(<rtype>)g(X\()48 b(*)f(\))136 4003 y FJ(\017)f
FK(C)30 b(binding:)227 4193 y FD(void)47 b(BLAS_xmin_val\()d(int)j(n,)g
(const)f(RARRAY)g(x,)i(int)e(incx,)h(int)g(k,)1182 4306
y(RSCALAR_INOUT)d(r)j(\);)p 0 4497 3900 6 v 0 4610 a
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5371 y(48)p eop
%%Page: 41 51
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eop
%%Page: 42 52
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(const)f(RARRAY)g(x,)i(int)e(incx,)h(int)g(k,)1182 993
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FJ(j)p FK(\))141 1557 y(The)25 b(routine)g Fv(AMAX)p
900 1557 V 31 w(V)-8 b(AL)25 b FK(\014nds)f(the)i(o\013set)h(or)e
(index)f(of)i(the)g(largest)g(comp)s(onen)m(t)g(of)f(a)h(v)m(ector)i
Fy(x)d FK(and)g(also)0 1670 y(returns)30 b(the)h(largest)h(comp)s(onen)
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(absolute)f(v)-5 b(alue.)42 b(When)31 b(the)g(v)-5 b(alue)0
1782 y(of)29 b(the)g Fv(n)g FK(argumen)m(t)h(is)e(less)g(than)h(or)f
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eop
%%Page: 43 53
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2759 y(where)609 2872 y(x)h(has)e(shape)h(\(n\))136 3095
y FJ(\017)f FK(F)-8 b(ortran)31 b(77)h(binding:)514 3318
y FD(SUBROUTINE)45 b(BLAS_xSUMSQ\()f(N,)j(X,)g(INCX,)g(SSQ,)f(SCL)h(\))
514 3431 y(INTEGER)570 b(INCX,)47 b(N)514 3544 y(<rtype>)570
b(SCL,)47 b(SSQ)514 3657 y(<type>)618 b(X\()48 b(*)f(\))136
3881 y FJ(\017)f FK(C)30 b(binding:)227 4104 y FD(void)47
b(BLAS_xsumsq\()d(int)j(n,)g(const)g(ARRAY)f(x,)h(int)g(incx,)g
(RSCALAR_INOUT)d(ssq,)1086 4217 y(RSCALAR_INOUT)h(scl)h(\);)p
0 4440 3900 6 v 0 4683 a Fx(2.8.3)97 b(Generate)34 b(T)-8
b(ransfo)m(rmations)0 4855 y FK(GEN)p 206 4855 28 4 v
33 w(GR)m(OT)31 b(\(Generate)h(Giv)m(ens)e(rotation\))1553
b(\()p Fy(c;)15 b(s;)g(r)s FK(\))26 b FJ( )f FK(rot)q(\()p
Fy(a;)15 b(b)p FK(\))141 5081 y(The)30 b(routine)f Fv(GEN)p
825 5081 V 33 w(GROT)h FK(constructs)g(a)h(Giv)m(ens)f(plane)g
(rotation)g(so)h(that)1348 5200 y Ft( )1493 5287 y Fy(c)120
b(s)1456 5400 y FJ(\000)t FK(\026)-49 b Fy(s)84 b(c)1736
5200 y Ft(!)1822 5344 y FJ(\001)1868 5200 y Ft( )1975
5287 y Fy(a)1979 5400 y(b)2064 5200 y Ft(!)2155 5344
y FK(=)2251 5200 y Ft( )2359 5287 y Fy(r)2358 5400 y
FK(0)2445 5200 y Ft(!)2526 5344 y Fy(;)-214 64 y FI(1)-214
177 y(2)-214 290 y(3)-214 403 y(4)-214 516 y(5)-214 628
y(6)-214 741 y(7)-214 854 y(8)-214 967 y(9)-230 1080
y(10)-230 1193 y(11)-230 1306 y(12)-230 1419 y(13)-230
1532 y(14)-230 1645 y(15)-230 1758 y(16)-230 1870 y(17)-230
1983 y(18)-230 2096 y(19)-230 2209 y(20)-230 2322 y(21)-230
2435 y(22)-230 2548 y(23)-230 2661 y(24)-230 2774 y(25)-230
2887 y(26)-230 3000 y(27)-230 3112 y(28)-230 3225 y(29)-230
3338 y(30)-230 3451 y(31)-230 3564 y(32)-230 3677 y(33)-230
3790 y(34)-230 3903 y(35)-230 4016 y(36)-230 4129 y(37)-230
4242 y(38)-230 4354 y(39)-230 4467 y(40)-230 4580 y(41)-230
4693 y(42)-230 4806 y(43)-230 4919 y(44)-230 5032 y(45)-230
5145 y(46)-230 5258 y(47)-230 5371 y(48)p eop
%%Page: 44 54
44 53 bop 0 -165 a FK(44)1930 b FA(CHAPTER)30 b(2.)71
b(DENSE)30 b(AND)h(BANDED)h(BLAS)0 91 y FK(where)e Fy(c)g
FK(is)f(alw)m(a)m(ys)i(a)f(real)g(scalar)g(and)g Fy(c)1440
58 y FC(2)1499 91 y FK(+)20 b FJ(j)p Fy(s)p FJ(j)1683
58 y FC(2)1753 91 y FK(is)29 b(equal)g(to)i(one.)41 b(The)30
b(scalars)g Fy(a)g FK(and)g Fy(b)g FK(are)g(unc)m(hanged)g(on)0
204 y(exit.)41 b Fy(c)p FK(,)31 b Fy(s)e FK(and)h Fy(r)j
FK(are)e(de\014ned)e(precisely)g(as)i(follo)m(ws,)e(where)h(w)m(e)h
(use)f(the)h(function)1376 469 y(sign)o(\()p Fy(x)p FK(\))26
b FJ(\021)1777 325 y Ft(\()1885 412 y Fy(x=)p FJ(j)p
Fy(x)p FJ(j)84 b FK(if)32 b Fy(x)25 b FJ(6)p FK(=)g(0)1885
525 y(1)238 b(if)32 b Fy(x)25 b FK(=)g(0)0 749 y(De\014ning)k(Giv)m
(ens)h(rotations:)157 862 y(if)f Fy(b)c FK(=)g(0)31 b(\(includes)d(the)
j(case)g Fy(a)26 b FK(=)e Fy(b)i FK(=)f(0\))313 975 y
Fy(c)h FK(=)f(1)313 1088 y Fy(s)g FK(=)g(0)313 1201 y
Fy(r)j FK(=)d Fy(a)157 1314 y FK(elseif)k Fy(a)c FK(=)g(0)31
b(\()p Fy(b)g FK(m)m(ust)f(b)s(e)g(nonzero\))313 1427
y Fy(c)c FK(=)f(0)313 1540 y Fy(s)g FK(=)g(sign)o(\()666
1516 y(\026)669 1540 y Fy(b)p FK(\))313 1653 y Fy(r)j
FK(=)d FJ(j)p Fy(b)p FJ(j)157 1765 y FK(else)30 b(\()p
Fy(a)g FK(and)g Fy(b)h FK(b)s(oth)e(nonzero\))313 1879
y Fy(c)d FK(=)f FJ(j)p Fy(a)p FJ(j)p Fy(=)617 1806 y
Ft(p)p 701 1806 379 4 v 701 1879 a FJ(j)p Fy(a)p FJ(j)799
1853 y FC(2)859 1879 y FK(+)20 b FJ(j)p Fy(b)p FJ(j)1039
1853 y FC(2)313 1993 y Fy(s)25 b FK(=)g(sign)o(\()p Fy(a)p
FK(\))749 1969 y(\026)752 1993 y Fy(b)q(=)837 1920 y
Ft(p)p 920 1920 V 73 x FJ(j)p Fy(a)p FJ(j)1018 1967 y
FC(2)1078 1993 y FK(+)20 b FJ(j)p Fy(b)p FJ(j)1258 1967
y FC(2)313 2107 y Fy(r)28 b FK(=)d(sign)o(\()p Fy(a)p
FK(\))753 2034 y Ft(p)p 837 2034 V 837 2107 a FJ(j)p
Fy(a)p FJ(j)935 2081 y FC(2)995 2107 y FK(+)20 b FJ(j)p
Fy(b)p FJ(j)1175 2081 y FC(2)157 2220 y FK(endif)0 2433
y(When)30 b Fy(a)h FK(and)e Fy(b)i FK(are)f(real,)940
2409 y(\026)944 2433 y Fy(b)g FK(ma)m(y)h(b)s(e)f(replaced)f(b)m(y)i
Fy(b)p FK(.)227 2645 y Fz(A)-5 b(dvic)g(e)38 b(to)g(implementors.)117
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y(b)s(e)42 b(accurate.)78 b(W)-8 b(e)43 b(recommend)f(one)g(of)h(the)f
(implemen)m(tations)f(describ)s(ed)f(in)h([9)q(].)76
b(W)-8 b(e)43 b(note)g(that)227 2871 y(the)36 b(ab)s(o)m(v)m(e)g
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(in)e(the)h(subroutine)f Fv(CLARTG)g FK(of)i(the)227
2984 y(LAP)-8 b(A)m(CK)32 b([6])g(soft)m(w)m(are)g(library)-8
b(,)30 b(but)g(di\013ers)g(sligh)m(tly)f(from)i(the)g(de\014nitions)e
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(di\013eren)m(t)h(Giv)m(ens)227 3210 y(rotations)31 b(con)m(tin)m(ue)g
(to)g(function)e(correctly)h([9)q(].)41 b(\()p Fz(End)33
b(of)g(advic)-5 b(e)33 b(to)g(implementors.)p FK(\))136
3422 y FJ(\017)46 b FK(F)-8 b(ortran)31 b(95)h(binding:)514
3647 y FD(SUBROUTINE)45 b(gen_grot\()g(a,)i(b,)g(c,)g(s,)h(r)f(\))609
3760 y(<type>\(<wp>\),)d(INTENT)i(\(IN\))h(::)g(a,)g(b)609
3873 y(REAL\(<wp>\),)e(INTENT)h(\(OUT\))g(::)h(c)609
3986 y(<type>\(<wp>\),)d(INTENT)i(\(OUT\))h(::)g(s,)g(r)136
4211 y FJ(\017)f FK(F)-8 b(ortran)31 b(77)h(binding:)514
4436 y FD(SUBROUTINE)45 b(BLAS_xGEN_GROT\()e(A,)k(B,)h(C,)f(S,)g(R)g
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(\);)4084 64 y FI(1)4084 177 y(2)4084 290 y(3)4084 403
y(4)4084 516 y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084
967 y(9)4069 1080 y(10)4069 1193 y(11)4069 1306 y(12)4069
1419 y(13)4069 1532 y(14)4069 1645 y(15)4069 1758 y(16)4069
1870 y(17)4069 1983 y(18)4069 2096 y(19)4069 2209 y(20)4069
2322 y(21)4069 2435 y(22)4069 2548 y(23)4069 2661 y(24)4069
2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
3677 y(33)4069 3790 y(34)4069 3903 y(35)4069 4016 y(36)4069
4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 45 55
45 54 bop 0 -165 a FA(2.8.)72 b(LANGUA)m(GE)32 b(BINDINGS)2578
b FK(45)p 0 91 3900 6 v 0 204 a(GEN)p 206 204 28 4 v
33 w(JR)m(OT)30 b(\(Generate)i(Jacobi)e(rotation\))1382
b(\()p Fy(a;)15 b(b;)g(c;)g(s)p FK(\))27 b FJ( )e FK(jrot\()p
Fy(x;)15 b(y)s(;)g(z)t FK(\))141 430 y(The)30 b(routine)f
Fv(GEN)p 825 430 V 33 w(JROT)h FK(constructs)h(a)g(Jacobi)f(rotation)g
(so)h(that)956 529 y Ft( )1063 617 y Fy(a)83 b FK(0)1064
729 y(0)88 b Fy(b)1281 529 y Ft(!)1372 673 y FK(=)1468
529 y Ft( )1612 617 y Fy(c)124 b FK(\026)-48 b Fy(s)1575
729 y FJ(\000)p Fy(s)84 b(c)1856 529 y Ft(!)1942 673
y FJ(\001)1987 529 y Ft( )2094 617 y Fy(x)f(y)2103 729
y FK(\026)-51 b Fy(y)88 b(z)2319 529 y Ft(!)2405 673
y FJ(\001)2450 529 y Ft( )2559 617 y Fy(c)d FJ(\000)t
FK(\026)-49 b Fy(s)2557 729 y(s)120 b(c)2838 529 y Ft(!)2919
673 y Fy(;)0 949 y FK(If)30 b(JR)m(OT)g(=)g(blas)p 633
949 V 31 w(inner)p 868 949 V 31 w(rotation,)h(then)g(the)f(rotation)h
(is)e(c)m(hosen)i(so)g(that)g Fy(c)25 b FJ(\025)2872
914 y FC(1)p 2842 929 95 4 v 2842 938 a Fu(p)p 2901 938
36 3 v 55 x FC(2)2946 949 y FK(.)0 1088 y(If)30 b(JR)m(OT)g(=)g(blas)p
633 1088 28 4 v 31 w(outer)p 871 1088 V 34 w(rotation,)h(then)f(the)g
(rotation)h(is)e(c)m(hosen)i(so)g(that)g(0)26 b FJ(\024)e
Fy(c)i FJ(\024)3043 1052 y FC(1)p 3014 1067 95 4 v 3014
1076 a Fu(p)p 3073 1076 36 3 v 55 x FC(2)3118 1088 y
FK(.)0 1216 y(If)k(JR)m(OT)g(=)g(blas)p 633 1216 28 4
v 31 w(sorted)p 907 1216 V 33 w(rotation,)h(then)f(the)h(rotation)g(is)
e(c)m(hosen)i(so)g(that)g Fy(abs)p FK(\()p Fy(a)p FK(\))25
b FJ(\025)g Fy(abs)p FK(\()p Fy(b)p FK(\).)141 1329 y(On)32
b(en)m(try)-8 b(,)34 b(the)f(argumen)m(t)h Fv(x)e FK(con)m(tains)h(the)
g(v)-5 b(alue)32 b Fy(x)p FK(,)i(and)e(on)h(exit)g(it)f(con)m(tains)h
(the)g(v)-5 b(alue)32 b Fy(a)p FK(.)48 b(On)32 b(en)m(try)-8
b(,)0 1442 y(the)34 b(argumen)m(t)f Fv(y)h FK(con)m(tains)f(the)h(v)-5
b(alue)32 b Fy(y)s FK(.)50 b(On)32 b(en)m(try)-8 b(,)35
b(the)f(argumen)m(t)g Fv(z)f FK(con)m(tains)g(the)h(v)-5
b(alue)32 b Fy(z)t FK(,)j(and)e(on)g(exit)0 1555 y(it)i(con)m(tains)g
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Fv(x)f FK(and)f Fv(z)h FK(are)g(real)g(scalars,)h(and)f(argumen)m(t)h
Fv(c)f FK(is)f(alw)m(a)m(ys)i(a)f(real)0 1668 y(scalar)30
b(and)g Fy(c)474 1635 y FC(2)534 1668 y FK(+)20 b FJ(j)p
Fy(s)p FJ(j)718 1635 y FC(2)788 1668 y FK(is)29 b(equal)h(to)h(one.)227
1877 y Fz(A)-5 b(dvic)g(e)39 b(to)h(implementors.)124
b FK(High-qualit)m(y)36 b(implemen)m(tations)g(of)i(this)e(routine)g
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b(the)h(accuracy)g(of)g(the)f(algorithms)g(used)f(in)g(those)i
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2102 y(bilit)m(y)21 b(problems)g(this)h(represen)m(ts.)39
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2871 y(REAL\(<wp>\),)e(INTENT)h(\(OUT\))g(::)h(c)609
2984 y(<type>\(<wp>\),)d(INTENT)i(\(OUT\))h(::)g(s)609
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FJ(\017)e FK(C)30 b(binding:)227 4321 y FD(void)47 b(BLAS_xgen_jrot\()d
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4433 y(SCALAR_IN)g(y,)i(RSCALAR_INOUT)d(z,)j(RSCALAR_INOUT)e(c,)1230
4546 y(SCALAR_INOUT)f(s)j(\);)p 0 4768 3900 6 v 0 4880
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Fy(;)141 5106 y FK(The)30 b(routine)f Fv(GEN)p 825 5106
V 33 w(HOUSE)h FK(generates)i(an)e(elemen)m(tary)h(re\015ector)g
Fy(H)38 b FK(of)30 b(order)g Fy(n)p FK(,)g(suc)m(h)g(that)1320
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5355 y FK(\))25 b(=)g(\()1813 5299 y Fy(\014)1819 5412
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5355 y Fy(H)j FK(=)25 b Fy(I)7 b(;)-214 64 y FI(1)-214
177 y(2)-214 290 y(3)-214 403 y(4)-214 516 y(5)-214 628
y(6)-214 741 y(7)-214 854 y(8)-214 967 y(9)-230 1080
y(10)-230 1193 y(11)-230 1306 y(12)-230 1419 y(13)-230
1532 y(14)-230 1645 y(15)-230 1758 y(16)-230 1870 y(17)-230
1983 y(18)-230 2096 y(19)-230 2209 y(20)-230 2322 y(21)-230
2435 y(22)-230 2548 y(23)-230 2661 y(24)-230 2774 y(25)-230
2887 y(26)-230 3000 y(27)-230 3112 y(28)-230 3225 y(29)-230
3338 y(30)-230 3451 y(31)-230 3564 y(32)-230 3677 y(33)-230
3790 y(34)-230 3903 y(35)-230 4016 y(36)-230 4129 y(37)-230
4242 y(38)-230 4354 y(39)-230 4467 y(40)-230 4580 y(41)-230
4693 y(42)-230 4806 y(43)-230 4919 y(44)-230 5032 y(45)-230
5145 y(46)-230 5258 y(47)-230 5371 y(48)p eop
%%Page: 46 56
46 55 bop 0 -165 a FK(46)1930 b FA(CHAPTER)30 b(2.)71
b(DENSE)30 b(AND)h(BANDED)h(BLAS)0 91 y FK(where)38 b
Fy(\013)g FK(and)g Fy(\014)43 b FK(are)c(scalars,)h(and)d
Fy(x)h FK(is)g(an)g(\()p Fy(n)25 b FJ(\000)g FK(1\)-elemen)m(t)40
b(v)m(ector.)65 b Fy(\014)44 b FK(is)37 b(alw)m(a)m(ys)i(a)f(real)g
(scalar.)64 b Fy(H)45 b FK(is)0 204 y(represen)m(ted)30
b(in)f(the)i(form)1438 366 y Fy(H)i FK(=)25 b Fy(I)i
FJ(\000)20 b Fy(\034)10 b FK(\()1929 309 y(1)1928 422
y Fy(v)2016 366 y FK(\)\()43 b(1)83 b Fy(v)2304 333 y
Fw(T)2401 366 y FK(\))p Fy(;)0 666 y FK(where)28 b Fy(\034)38
b FK(is)27 b(a)h(scalar)h(and)e Fy(v)k FK(is)d(a)g(\()p
Fy(n)16 b FJ(\000)f FK(1\)-elemen)m(t)30 b(v)m(ector.)41
b Fy(\034)e FK(is)27 b(called)g(the)h(Householder)g(scalar)g(and)3638
522 y Ft( )3746 609 y FK(1)3745 722 y Fy(v)3834 522 y
Ft(!)0 839 y FK(the)e(Householder)g(v)m(ector.)41 b(Note)27
b(that)g(when)e Fy(x)i FK(is)e(a)h(complex)g(v)m(ector,)j
Fy(H)34 b FK(is)25 b(not)h(Hermitian.)38 b(If)26 b(the)h(elemen)m(ts)0
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Fy(H)33 b FK(is)25 b(tak)m(en)h(to)h(b)s(e)e(the)g(unit)g(matrix.)38
b(Otherwise,)0 1065 y(the)g(real)g(part)f(of)h Fy(\034)48
b FK(is)37 b(greater)i(than)f(or)g(equal)f(to)i(one)f(and)f(less)g
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b(the)0 1178 y(absolute)30 b(v)-5 b(alue)30 b(of)g(the)h(quan)m(tit)m
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b(,)28 b(the)0 1403 y(v)m(ector)k(argumen)m(t)f Fv(x)f
FK(is)g(o)m(v)m(erwritten)h(with)e(the)i(v)m(ector)h
Fy(v)s FK(.)41 b(If)30 b Fv(n)g FK(is)g(less)f(than)i(or)f(equal)g(to)h
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1629 y Fv(incx)29 b FK(less)g(than)g(zero)h(is)f(p)s(ermitted.)39
b(Ho)m(w)m(ev)m(er,)32 b(if)c Fv(incx)h FK(is)g(equal)g(to)h(zero,)g
(an)g(error)e(\015ag)i(is)f(set)h(and)e(passed)h(to)0
1742 y(the)i(error)f(handler.)227 1955 y Fz(A)-5 b(dvic)g(e)35
b(to)g(implementors.)95 b FK(High-qualit)m(y)31 b(implemen)m(tations)g
(of)h(this)g(routine)f Fv(GEN)p 3283 1955 28 4 v 33 w(HOUSE)h
FK(should)227 2068 y(b)s(e)e(accurate.)43 b(The)30 b(subroutines)e
Fv(SLARF)m(G)h FK(and)h Fv(CLARF)m(G)g FK(of)h(the)f(LAP)-8
b(A)m(CK)31 b([6)q(])g(soft)m(w)m(are)g(library)e(are)227
2180 y(examples)37 b(of)h(suc)m(h)f(an)h(accurate)h(implemen)m(tation.)
61 b(High-qualit)m(y)37 b(implemen)m(tations)f(should)f(do)s(cu-)227
2293 y(men)m(t)30 b(the)f(accuracy)i(of)e(the)g(algorithms)f(used)h(in)
f(those)h(functions)f(so)h(as)h(to)g(alleviate)f(the)g(p)s(ortabilit)m
(y)227 2406 y(problems)g(this)g(represen)m(ts.)41 b(\()p
Fz(End)33 b(of)g(advic)-5 b(e)33 b(to)g(implementors.)p
FK(\))227 2619 y Fz(A)-5 b(dvic)g(e)30 b(to)h(users.)79
b FK(Routines)26 b(to)j(apply)d(Householder)g(transformations)h(are)h
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Fv(xORMyy)f FK(of)i(the)g(LAP)-8 b(A)m(CK)29 b([6)q(])f(soft)m(w)m(are)
j(library)26 b(are)j(examples)f(of)h(suc)m(h)f(implemen)m(tations.)227
2845 y(\()p Fz(End)33 b(of)g(advic)-5 b(e)33 b(to)h(users.)p
FK(\))136 3057 y FJ(\017)46 b FK(F)-8 b(ortran)31 b(95)h(binding:)514
3282 y FD(SUBROUTINE)45 b(gen_house\()g(alpha,)h(x,)h(tau)g(\))609
3395 y(<type>\(<wp>\),)d(INTENT)i(\(INOUT\))g(::)h(alpha)609
3508 y(<type>\(<wp>\),)d(INTENT)i(\(INOUT\))g(::)h(x\(:\))609
3621 y(<type>\(<wp>\),)d(INTENT)i(\(OUT\))h(::)g(tau)514
3734 y(where)609 3847 y(x)h(has)e(shape)h(\(n\))136 4072
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y FD(SUBROUTINE)45 b(BLAS_xGEN_HOUSE\()e(N,)k(ALPHA,)f(X,)h(INCX,)g
(TAU)g(\))514 4410 y(INTEGER)570 b(INCX,)47 b(N)514 4522
y(<type>)618 b(ALPHA,)47 b(TAU)514 4635 y(<type>)618
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5085 y FD(void)47 b(BLAS_xgen_house\()c(int)k(n,)g(SCALAR_INOUT)e
(alpha,)h(ARRAY)g(x,)h(int)g(incx,)1277 5198 y(SCALAR_INOUT)e(tau)i
(\);)4084 64 y FI(1)4084 177 y(2)4084 290 y(3)4084 403
y(4)4084 516 y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084
967 y(9)4069 1080 y(10)4069 1193 y(11)4069 1306 y(12)4069
1419 y(13)4069 1532 y(14)4069 1645 y(15)4069 1758 y(16)4069
1870 y(17)4069 1983 y(18)4069 2096 y(19)4069 2209 y(20)4069
2322 y(21)4069 2435 y(22)4069 2548 y(23)4069 2661 y(24)4069
2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
3677 y(33)4069 3790 y(34)4069 3903 y(35)4069 4016 y(36)4069
4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 47 57
47 56 bop 0 -165 a FA(2.8.)72 b(LANGUA)m(GE)32 b(BINDINGS)2578
b FK(47)0 91 y Fx(2.8.4)97 b(V)m(ecto)m(r)34 b(Op)s(erations)0
263 y FK(RSCALE)29 b(\(Recipro)s(cal)h(Scale\))2430 b
Fy(x)25 b FJ( )g Fy(x=\013)141 489 y FK(The)37 b(routine)f
Fv(RSCALE)g FK(scales)h(the)g(en)m(tries)g(of)g(a)h(v)m(ector)g
Fy(x)f FK(b)m(y)g(the)g(real)g(scalar)g(1)p Fy(=\013)p
FK(.)62 b(The)36 b(scalar)h Fy(\013)h FK(is)0 602 y(alw)m(a)m(ys)g
(real)f(and)f(supp)s(osed)f(to)j(b)s(e)f(nonzero.)61
b(This)35 b(should)h(b)s(e)g(done)h(without)f(o)m(v)m(er\015o)m(w)j(or)
e(under\015o)m(w)f(as)0 715 y(long)k(as)i(the)f(\014nal)e(result)h
Fy(x=\013)i FK(do)s(es)e(not)h(o)m(v)m(er\015o)m(w)i(or)d(under\015o)m
(w.)71 b(If)41 b Fv(n)f FK(is)g(less)g(than)h(or)g(equal)f(to)i(zero,)0
827 y(this)c(routine)h(returns)f(immediately)-8 b(.)66
b(As)40 b(describ)s(ed)d(in)h(section)h(2.5.3,)44 b(the)c(v)-5
b(alue)39 b Fv(incx)g FK(less)g(than)g(zero)h(is)0 940
y(p)s(ermitted.)61 b(Ho)m(w)m(ev)m(er,)42 b(if)36 b Fv(incx)i
FK(is)f(equal)g(to)h(zero)h(or)e(if)g Fv(alpha)f FK(is)h(equal)g(to)i
(zero,)h(an)e(error)f(\015ag)h(is)e(set)j(and)0 1053
y(passed)30 b(to)h(the)g(error)f(handler.)227 1262 y
Fz(A)-5 b(dvic)g(e)38 b(to)g(implementors.)117 b FK(High-qualit)m(y)35
b(implemen)m(tations)f(of)i(this)f(routine)g Fv(RSCALE)h
FK(should)e(b)s(e)227 1375 y(accurate.)41 b(The)24 b(subroutine)e
Fv(xRSCL)i FK(of)h(the)g(LAP)-8 b(A)m(CK)25 b([6)q(])g(soft)m(w)m(are)h
(library)c(is)i(an)g(example)h(of)g(suc)m(h)f(an)227
1488 y(accurate)h(implemen)m(tation.)38 b(High-qualit)m(y)22
b(implemen)m(tations)g(should)g(do)s(cumen)m(t)h(the)h(accuracy)h(of)f
(the)227 1601 y(algorithms)k(used)h(in)f(those)h(functions)f(so)h(as)h
(to)g(alleviate)f(the)g(p)s(ortabilit)m(y)e(problems)h(this)g(represen)
m(ts.)227 1714 y(\()p Fz(End)33 b(of)g(advic)-5 b(e)33
b(to)h(implementors.)p FK(\))136 1923 y FJ(\017)46 b
FK(F)-8 b(ortran)31 b(95)h(binding:)514 2144 y FD(SUBROUTINE)45
b(rscale\()g(alpha,)i(x)g(\))609 2257 y(REAL\(<wp>\),)e(INTENT)h
(\(IN\))h(::)g(alpha)609 2370 y(<type>\(<wp>\),)d(INTENT)i(\(INOUT\))g
(::)h(x\(:\))514 2483 y(where)609 2596 y(x)h(has)e(shape)h(\(n\))136
2817 y FJ(\017)f FK(F)-8 b(ortran)31 b(77)h(binding:)514
3039 y FD(SUBROUTINE)45 b(BLAS_xRSCALE\()f(N,)j(ALPHA,)f(X,)h(INCX)g
(\))514 3152 y(INTEGER)570 b(INCX,)47 b(N)514 3265 y(<rtype>)570
b(ALPHA)514 3378 y(<type>)618 b(X\()48 b(*)f(\))136 3599
y FJ(\017)f FK(C)30 b(binding:)227 3821 y FD(void)47
b(BLAS_xrscale\()d(int)j(n,)g(RSCALAR_IN)e(alpha,)h(ARRAY)h(x,)g(int)g
(incx)f(\);)p 0 4042 3900 6 v 0 4155 a FK(AXPBY)31 b(\(Scaled)f(v)m
(ector)i(accum)m(ulation\))1870 b Fy(y)28 b FJ( )d Fy(\013x)c
FK(+)f Fy(\014)5 b(y)141 4381 y FK(The)31 b(routine)f
Fv(AXPBY)g FK(scales)h(the)h(v)m(ector)h Fy(x)e FK(b)m(y)g
Fy(\013)h FK(and)f(the)g(v)m(ector)i Fy(y)h FK(b)m(y)d
Fy(\014)5 b FK(,)32 b(adds)f(these)h(t)m(w)m(o)g(v)m(ectors)h(to)0
4494 y(one)e(another)f(and)g(stores)h(the)g(result)e(in)g(the)i(v)m
(ector)h Fy(y)s FK(.)41 b(If)29 b Fv(n)i FK(is)e(less)h(than)g(or)h
(equal)f(to)h(zero,)g(or)g(if)e Fy(\013)i FK(is)e(equal)0
4607 y(to)k(zero)g(and)e Fy(\014)38 b FK(is)31 b(equal)g(to)i(one,)g
(this)e(routine)g(returns)g(immediately)-8 b(.)45 b(As)32
b(describ)s(ed)e(in)h(section)h(2.5.3,)j(the)0 4719 y(v)-5
b(alue)35 b Fv(incx)g FK(or)h Fv(incy)f FK(less)g(than)g(zero)h(is)e(p)
s(ermitted.)55 b(Ho)m(w)m(ev)m(er,)39 b(if)34 b(either)h
Fv(incx)g FK(or)h Fv(incy)f FK(is)f(equal)h(to)h(zero,)i(an)0
4832 y(error)30 b(\015ag)h(is)e(set)i(and)f(passed)g(to)h(the)f(error)g
(handler.)136 5041 y FJ(\017)46 b FK(F)-8 b(ortran)31
b(95)h(binding:)514 5287 y FD(SUBROUTINE)45 b(axpby\()h(x,)h(y)g([,)h
(alpha])e([,)h(beta])f(\))609 5400 y(<type>\(<wp>\),)e(INTENT)i(\(IN\))
h(::)g(x\(:\))-214 64 y FI(1)-214 177 y(2)-214 290 y(3)-214
403 y(4)-214 516 y(5)-214 628 y(6)-214 741 y(7)-214 854
y(8)-214 967 y(9)-230 1080 y(10)-230 1193 y(11)-230 1306
y(12)-230 1419 y(13)-230 1532 y(14)-230 1645 y(15)-230
1758 y(16)-230 1870 y(17)-230 1983 y(18)-230 2096 y(19)-230
2209 y(20)-230 2322 y(21)-230 2435 y(22)-230 2548 y(23)-230
2661 y(24)-230 2774 y(25)-230 2887 y(26)-230 3000 y(27)-230
3112 y(28)-230 3225 y(29)-230 3338 y(30)-230 3451 y(31)-230
3564 y(32)-230 3677 y(33)-230 3790 y(34)-230 3903 y(35)-230
4016 y(36)-230 4129 y(37)-230 4242 y(38)-230 4354 y(39)-230
4467 y(40)-230 4580 y(41)-230 4693 y(42)-230 4806 y(43)-230
4919 y(44)-230 5032 y(45)-230 5145 y(46)-230 5258 y(47)-230
5371 y(48)p eop
%%Page: 48 58
48 57 bop 0 -165 a FK(48)1930 b FA(CHAPTER)30 b(2.)71
b(DENSE)30 b(AND)h(BANDED)h(BLAS)609 91 y FD(<type>\(<wp>\),)44
b(INTENT)i(\(INOUT\))g(::)h(y\(:\))609 204 y(<type>\(<wp>\),)d(INTENT)i
(\(IN\),)h(OPTIONAL)e(::)i(alpha,)g(beta)514 317 y(where)609
430 y(x)h(and)e(y)i(have)f(shape)f(\(n\))227 680 y FK(The)30
b(default)g(v)-5 b(alue)30 b(for)g Fy(\014)35 b FK(is)30
b(1.0)h(or)f(\(1.0,0.0\).)136 868 y FJ(\017)46 b FK(F)-8
b(ortran)31 b(77)h(binding:)514 1093 y FD(SUBROUTINE)45
b(BLAS_xAXPBY\()f(N,)j(ALPHA,)f(X,)i(INCX,)e(BETA,)g(Y,)h(INCY)g(\))514
1205 y(INTEGER)570 b(INCX,)47 b(INCY,)f(N)514 1318 y(<type>)618
b(ALPHA,)47 b(BETA)514 1431 y(<type>)618 b(X\()48 b(*)f(\),)g(Y\()g(*)h
(\))136 1656 y FJ(\017)e FK(C)30 b(binding:)227 1881
y FD(void)47 b(BLAS_xaxpby\()d(int)j(n,)g(SCALAR_IN)f(alpha,)g(const)g
(ARRAY)h(x,)g(int)g(incx,)1086 1994 y(SCALAR_IN)f(beta,)g(ARRAY)g(y,)i
(int)e(incy)h(\);)p 0 2219 3900 6 v 0 2332 a FK(W)-10
b(AXPBY)31 b(\(Scaled)g(v)m(ector)h(addition\))1964 b
Fy(w)28 b FJ( )d Fy(\013x)c FK(+)f Fy(\014)5 b(y)141
2558 y FK(The)33 b(routine)f Fv(W)-8 b(AXPBY)32 b FK(scales)h(the)h(v)m
(ector)g Fy(x)f FK(b)m(y)g Fy(\013)h FK(and)f(the)g(v)m(ector)i
Fy(y)h FK(b)m(y)d Fy(\014)5 b FK(,)34 b(adds)e(these)i(t)m(w)m(o)g(v)m
(ectors)0 2671 y(to)d(one)f(another)h(and)e(stores)i(the)f(result)f(in)
g(the)h(v)m(ector)i Fy(w)r FK(.)41 b(If)30 b Fv(n)g FK(is)f(less)g
(than)h(or)g(equal)g(to)h(zero,)g(this)e(routine)0 2784
y(returns)i(immediately)-8 b(.)46 b(As)32 b(describ)s(ed)f(in)g
(section)i(2.5.3,)i(the)d(v)-5 b(alue)32 b Fv(incx)h
FK(or)f Fv(incy)h FK(or)f Fv(incw)h FK(less)e(than)i(zero)g(is)0
2897 y(p)s(ermitted.)39 b(Ho)m(w)m(ev)m(er,)31 b(if)c(either)h
Fv(incx)g FK(or)h Fv(incy)f FK(or)g Fv(incw)h FK(is)e(equal)h(to)h
(zero,)h(an)e(error)g(\015ag)h(is)f(set)h(and)e(passed)h(to)0
3010 y(the)j(error)f(handler.)136 3222 y FJ(\017)46 b
FK(F)-8 b(ortran)31 b(95)h(binding:)514 3472 y FD(SUBROUTINE)45
b(waxpby\()g(x,)j(y,)f(w)g([,)g(alpha])g([,)g(beta])f(\))609
3585 y(<type>\(<wp>\),)e(INTENT)i(\(IN\))h(::)g(x\(:\),)g(y\(:\))609
3698 y(<type>\(<wp>\),)d(INTENT)i(\(OUT\))h(::)g(w\(:\))609
3811 y(<type>\(<wp>\),)d(INTENT)i(\(IN\),)h(OPTIONAL)e(::)i(alpha,)g
(beta)514 3924 y(where)609 4037 y(x,)g(y)h(and)f(w)g(have)g(shape)f
(\(n\))227 4286 y FK(The)30 b(default)g(v)-5 b(alue)30
b(for)g Fy(\014)35 b FK(is)30 b(1.0)h(or)f(\(1.0,0.0\).)136
4474 y FJ(\017)46 b FK(F)-8 b(ortran)31 b(77)h(binding:)514
4699 y FD(SUBROUTINE)45 b(BLAS_xWAXPBY\()f(N,)j(ALPHA,)f(X,)h(INCX,)g
(BETA,)f(Y,)h(INCY,)g(W,)g(INCW)f(\))514 4812 y(INTEGER)570
b(INCW,)47 b(INCX,)f(INCY,)h(N)514 4925 y(<type>)618
b(ALPHA,)47 b(BETA)514 5038 y(<type>)618 b(W\()48 b(*)f(\),)g(X\()g(*)h
(\),)f(Y\()g(*)h(\))136 5263 y FJ(\017)e FK(C)30 b(binding:)4084
64 y FI(1)4084 177 y(2)4084 290 y(3)4084 403 y(4)4084
516 y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084 967
y(9)4069 1080 y(10)4069 1193 y(11)4069 1306 y(12)4069
1419 y(13)4069 1532 y(14)4069 1645 y(15)4069 1758 y(16)4069
1870 y(17)4069 1983 y(18)4069 2096 y(19)4069 2209 y(20)4069
2322 y(21)4069 2435 y(22)4069 2548 y(23)4069 2661 y(24)4069
2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
3677 y(33)4069 3790 y(34)4069 3903 y(35)4069 4016 y(36)4069
4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 49 59
49 58 bop 0 -165 a FA(2.8.)72 b(LANGUA)m(GE)32 b(BINDINGS)2578
b FK(49)227 91 y FD(void)47 b(BLAS_xwaxpby\()d(int)j(n,)g(SCALAR_IN)e
(alpha,)i(const)f(ARRAY)g(x,)h(int)g(incx,)1134 204 y(SCALAR_IN)e
(beta,)i(const)f(ARRAY)g(y,)i(int)f(incy,)f(ARRAY)g(w,)1134
317 y(int)h(incw)g(\);)p 0 542 3900 6 v 0 655 a FK(AXPY)p
271 655 28 4 v 33 w(DOT)30 b(\(Com)m(bined)f(AXPY)i(and)f(DOT\))1308
b(^)-63 b Fy(w)27 b FJ( )f Fy(w)c FJ(\000)e Fy(\013v)s(;)15
b(r)29 b FJ( )44 b FK(^)-64 b Fy(w)3792 622 y Fw(T)3848
655 y Fy(u)141 881 y FK(The)30 b(routine)g(com)m(bines)g(an)h(axp)m(y)g
(and)f(a)h(dot)g(pro)s(duct.)41 b Fy(w)33 b FK(is)d(decremen)m(ted)i(b)
m(y)e(a)h(m)m(ultiple)e(of)i Fy(v)s FK(.)42 b(A)31 b(dot)0
994 y(pro)s(duct)e(is)h(then)g(computed)g(with)f(the)h(decremen)m(ted)i
Fy(w)r FK(.)227 1206 y Fz(A)-5 b(dvic)g(e)39 b(to)h(implementors.)123
b FK(Note)39 b(that)56 b(^)-63 b Fy(w)39 b FK(ma)m(y)f(b)s(e)f(used)f
(to)i(up)s(date)e Fy(r)k FK(b)s(efore)d(it)g(is)f(written)g(bac)m(k)227
1319 y(to)43 b(memory)-8 b(.)76 b(This)41 b(optimization,)j(whic)m(h)d
(accelerates)j(algorithms)c(lik)m(e)i(mo)s(di\014ed)e(Gram-Sc)m(hmidt)
227 1432 y(orthogonalization,)29 b(is)e(the)i(justi\014cation)e(for)h
Fv(AXPY)p 2096 1432 V 31 w(DOT)p FK(,)g(whic)m(h)f(could)g(otherwise)h
(b)s(e)f(implemen)m(ted)227 1545 y(b)m(y)k(calls)e(to)i
Fv(AXPBY)e FK(and)h Fv(DOT)p FK(.)g(\()p Fz(End)j(of)g(advic)-5
b(e)33 b(to)g(implementors.)p FK(\))141 1758 y(If)26
b Fv(n)g FK(is)f(less)g(than)h(or)g(equal)g(to)h(zero,)h(this)d
(routine)g(returns)g(immediately)-8 b(.)38 b(As)26 b(describ)s(ed)e(in)
h(section)h(2.5.3,)0 1870 y(the)31 b(v)-5 b(alue)30 b
Fv(incw)h FK(or)g Fv(incv)g FK(or)g Fv(incu)g FK(less)f(than)g(zero)i
(is)e(p)s(ermitted.)40 b(Ho)m(w)m(ev)m(er,)34 b(if)29
b(either)i Fv(incw)g FK(or)f Fv(incv)h FK(or)g Fv(incu)g
FK(is)0 1983 y(equal)f(to)h(zero,)g(an)g(error)f(\015ag)g(is)g(set)h
(and)e(passed)h(to)h(the)g(error)f(handler.)136 2196
y FJ(\017)46 b FK(F)-8 b(ortran)31 b(95)h(binding:)514
2421 y FD(SUBROUTINE)45 b(axpy_dot\()g(w,)i(v,)g(u,)g(r)h([,)f(alpha])f
(\))609 2534 y(<type>\(<wp>\),)e(INTENT)i(\(IN\))h(::)g(v\(:\),)g
(u\(:\))609 2647 y(<type>\(<wp>\),)d(INTENT)i(\(INOUT\))g(::)h(w\(:\))
609 2760 y(<type>\(<wp>\),)d(INTENT)i(\(OUT\))h(::)g(r)609
2873 y(<type>\(<wp>\),)d(INTENT)i(\(IN\),)h(OPTIONAL)e(::)i(alpha)514
2985 y(where)609 3098 y(u,)g(v)h(and)f(w)g(have)g(shape)f(\(n\))136
3323 y FJ(\017)g FK(F)-8 b(ortran)31 b(77)h(binding:)514
3548 y FD(SUBROUTINE)45 b(BLAS_xAXPY_DOT\()e(N,)k(ALPHA,)g(W,)g(INCW,)f
(V,)h(INCV,)g(U,)g(INCU,)466 3661 y($)1288 b(R)48 b(\))514
3774 y(INTEGER)570 b(INCW,)47 b(INCV,)f(INCU,)h(N)514
3887 y(<type>)618 b(ALPHA,)47 b(R)514 4000 y(<type>)618
b(W\()48 b(*)f(\),)g(V\()g(*)h(\),)f(U\()g(*)h(\))136
4225 y FJ(\017)e FK(C)30 b(binding:)227 4450 y FD(void)47
b(BLAS_xaxpy_dot\()d(int)i(n,)i(SCALAR_IN)d(alpha,)h(ARRAY)g(w,)i(int)e
(incw,)1230 4563 y(const)g(ARRAY)g(v,)h(int)g(incv,)g(const)f(ARRAY)g
(u,)i(int)f(incu,)1230 4676 y(SCALAR_INOUT)d(r)j(\);)p
0 4901 3900 6 v 0 5014 a FK(APPL)-8 b(Y)p 314 5014 28
4 v 33 w(GR)m(OT)30 b(\(Apply)g(plane)f(rotation\))1468
b(\()42 b Fy(x)83 b(y)44 b FK(\))26 b FJ( )f FK(\()42
b Fy(x)83 b(y)44 b FK(\))p Fy(R)-214 64 y FI(1)-214 177
y(2)-214 290 y(3)-214 403 y(4)-214 516 y(5)-214 628 y(6)-214
741 y(7)-214 854 y(8)-214 967 y(9)-230 1080 y(10)-230
1193 y(11)-230 1306 y(12)-230 1419 y(13)-230 1532 y(14)-230
1645 y(15)-230 1758 y(16)-230 1870 y(17)-230 1983 y(18)-230
2096 y(19)-230 2209 y(20)-230 2322 y(21)-230 2435 y(22)-230
2548 y(23)-230 2661 y(24)-230 2774 y(25)-230 2887 y(26)-230
3000 y(27)-230 3112 y(28)-230 3225 y(29)-230 3338 y(30)-230
3451 y(31)-230 3564 y(32)-230 3677 y(33)-230 3790 y(34)-230
3903 y(35)-230 4016 y(36)-230 4129 y(37)-230 4242 y(38)-230
4354 y(39)-230 4467 y(40)-230 4580 y(41)-230 4693 y(42)-230
4806 y(43)-230 4919 y(44)-230 5032 y(45)-230 5145 y(46)-230
5258 y(47)-230 5371 y(48)p eop
%%Page: 50 60
50 59 bop 0 -165 a FK(50)1930 b FA(CHAPTER)30 b(2.)71
b(DENSE)30 b(AND)h(BANDED)h(BLAS)141 91 y FK(The)c(routine)f
Fv(APPL)-8 b(Y)p 921 91 28 4 v 33 w(GROT)27 b FK(applies)f(a)j(plane)e
(rotation)i(to)g(the)f(v)m(ectors)i Fy(x)e FK(and)f Fy(y)s
FK(.)40 b(When)28 b(the)g(v)m(ectors)i Fy(x)0 204 y FK(and)g
Fy(y)k FK(are)d(real)f(v)m(ectors,)j(the)e(scalars)f
Fy(c)h FK(and)g Fy(s)f FK(are)h(real)f(scalars.)42 b(When)31
b(the)g(v)m(ectors)h Fy(x)e FK(and)h Fy(y)i FK(are)e(complex)0
317 y(v)m(ectors,)h Fy(c)f FK(is)e(a)i(real)f(scalar)g(and)g
Fy(s)g FK(is)f(a)i(complex)f(scalar.)41 b(This)28 b(routine)i(computes)
961 561 y FJ(8)g Fy(i)c FJ(2)f FK([0)15 b Fy(:)g(:)g(:)i(n)j
FJ(\000)f FK(1])p Fy(;)1667 417 y Ft( )1776 504 y Fy(x)1828
518 y Fw(i)1780 617 y Fy(y)1825 631 y Fw(i)1897 417 y
Ft(!)1988 561 y FK(=)2084 417 y Ft( )2229 504 y Fy(c)120
b(s)2192 617 y FJ(\000)t FK(\026)-49 b Fy(s)84 b(c)2472
417 y Ft(!)2558 561 y FJ(\001)2603 417 y Ft( )2711 504
y Fy(x)2763 518 y Fw(i)2714 617 y Fy(y)2759 631 y Fw(i)2832
417 y Ft(!)2913 561 y Fy(:)0 805 y FK(If)38 b Fv(n)h
FK(is)f(less)g(than)h(or)g(equal)f(to)i(zero)g(or)f(if)e
Fy(c)j FK(is)e(one)h(and)f Fy(s)g FK(is)g(zero,)k(the)e(routine)d
Fv(APPL)-8 b(Y)p 3301 805 V 33 w(GROT)38 b FK(returns)0
918 y(immediately)-8 b(.)59 b(As)36 b(describ)s(ed)f(in)g(section)i
(2.5.3,)k(the)c(v)-5 b(alue)36 b(of)h Fv(incx)g FK(or)f
Fv(incy)h FK(less)f(than)h(zero)g(is)f(p)s(ermitted.)0
1030 y(Ho)m(w)m(ev)m(er,)d(if)c Fv(incx)h FK(or)h Fv(incy)f
FK(is)f(equal)h(to)h(zero,)h(an)e(error)g(\015ag)h(is)e(set)i(and)f
(passed)g(to)h(the)f(error)g(handler.)136 1222 y FJ(\017)46
b FK(F)-8 b(ortran)31 b(95)h(binding:)514 1426 y FD(SUBROUTINE)45
b(apply_grot\()f(c,)k(s,)f(x,)g(y)g(\))609 1539 y(REAL\(<wp>\),)e
(INTENT)h(\(IN\))h(::)g(c)609 1652 y(<type>\(<wp>\),)d(INTENT)i(\(IN\))
h(::)g(s)609 1765 y(<type>\(<wp>\),)d(INTENT)i(\(INOUT\))g(::)h
(x\(:\),)g(y\(:\))514 1878 y(where)609 1991 y(x)h(and)e(y)i(have)f
(shape)f(\(n\))136 2195 y FJ(\017)g FK(F)-8 b(ortran)31
b(77)h(binding:)514 2399 y FD(SUBROUTINE)45 b(BLAS_xAPPLY_GROT\()e(N,)k
(C,)g(S,)g(X,)g(INCX,)g(Y,)g(INCY)g(\))514 2512 y(INTEGER)570
b(INCX,)47 b(INCY,)f(N)514 2625 y(<rtype>)570 b(C)514
2738 y(<type>)618 b(S)514 2851 y(<type>)g(X\()48 b(*)f(\),)g(Y\()g(*)h
(\))136 3055 y FJ(\017)e FK(C)30 b(binding:)227 3259
y FD(void)47 b(BLAS_xapply_grot\()c(int)k(n,)g(RSCALAR_IN)e(c,)i
(SCALAR_IN)f(s,)h(ARRAY)f(x,)h(int)g(incx,)1325 3372
y(ARRAY)f(y,)i(int)e(incy)h(\);)p 0 3576 3900 6 v 0 3816
a Fx(2.8.5)97 b(Data)32 b(Movement)h(with)g(V)m(ecto)m(rs)0
3988 y FK(COPY)d(\(V)-8 b(ector)32 b(cop)m(y\))2823 b
Fy(y)28 b FJ( )d Fy(x)141 4214 y FK(The)31 b(routine)g
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(ector)i Fy(y)s FK(.)44 b(If)32 b Fv(n)f FK(is)g(less)g(than)h(or)g
(equal)f(to)i(zero,)g(the)0 4327 y(routine)f(returns)f(immediately)-8
b(.)46 b(As)32 b(describ)s(ed)f(in)g(section)i(2.5.3,)i(the)e(v)-5
b(alue)32 b Fv(incx)g FK(or)h Fv(incy)f FK(less)g(than)h(zero)g(is)0
4440 y(p)s(ermitted.)56 b(Ho)m(w)m(ev)m(er,)39 b(if)c(either)h
Fv(incx)f FK(or)h Fv(incy)g FK(is)f(equal)h(to)g(zero,)j(an)c(error)h
(\015ag)g(is)f(set)h(and)g(passed)f(to)i(the)0 4553 y(error)30
b(handler.)136 4744 y FJ(\017)46 b FK(F)-8 b(ortran)31
b(95)h(binding:)514 4948 y FD(SUBROUTINE)45 b(copy\()h(x,)h(y)h(\))609
5061 y(<type>\(<wp>\),)c(INTENT)i(\(IN\))h(::)g(x\(:\))609
5174 y(<type>\(<wp>\),)d(INTENT)i(\(OUT\))h(::)g(y\(:\))514
5287 y(where)609 5400 y(x)h(and)e(y)i(have)f(shape)f(\(n\))4084
64 y FI(1)4084 177 y(2)4084 290 y(3)4084 403 y(4)4084
516 y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084 967
y(9)4069 1080 y(10)4069 1193 y(11)4069 1306 y(12)4069
1419 y(13)4069 1532 y(14)4069 1645 y(15)4069 1758 y(16)4069
1870 y(17)4069 1983 y(18)4069 2096 y(19)4069 2209 y(20)4069
2322 y(21)4069 2435 y(22)4069 2548 y(23)4069 2661 y(24)4069
2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
3677 y(33)4069 3790 y(34)4069 3903 y(35)4069 4016 y(36)4069
4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 51 61
51 60 bop 0 -165 a FA(2.8.)72 b(LANGUA)m(GE)32 b(BINDINGS)2578
b FK(51)227 91 y(This)29 b(is)g(similar)f(to)j(the)g(F)-8
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275 y FJ(\017)46 b FK(F)-8 b(ortran)31 b(77)h(binding:)514
488 y FD(SUBROUTINE)45 b(BLAS_xCOPY\()f(N,)k(X,)f(INCX,)f(Y,)h(INCY)g
(\))514 601 y(INTEGER)570 b(INCX,)47 b(INCY,)f(N)514
714 y(<type>)618 b(X\()48 b(*)f(\),)g(Y\()g(*)h(\))136
927 y FJ(\017)e FK(C)30 b(binding:)227 1140 y FD(void)47
b(BLAS_xcopy\()e(int)i(n,)g(const)f(ARRAY)g(x,)i(int)f(incx,)f(ARRAY)g
(y,)h(int)g(incy)g(\);)p 0 1353 3900 6 v 0 1466 a FK(SW)-10
b(AP)30 b(\(Sw)m(ap\))3085 b Fy(y)28 b FJ($)d Fy(x)141
1691 y FK(The)39 b(routine)f Fv(SW)-8 b(AP)38 b FK(in)m(terc)m(hanges)i
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b Fv(n)g FK(is)f(less)g(than)h(or)g(equal)g(to)g(zero,)k(the)0
1804 y(routine)32 b(returns)f(immediately)-8 b(.)46 b(As)32
b(describ)s(ed)f(in)g(section)i(2.5.3,)i(the)e(v)-5 b(alue)32
b Fv(incx)g FK(or)h Fv(incy)f FK(less)g(than)h(zero)g(is)0
1917 y(p)s(ermitted.)56 b(Ho)m(w)m(ev)m(er,)39 b(if)c(either)h
Fv(incx)f FK(or)h Fv(incy)g FK(is)f(equal)h(to)g(zero,)j(an)c(error)h
(\015ag)g(is)f(set)h(and)g(passed)f(to)i(the)0 2030 y(error)30
b(handler.)136 2231 y FJ(\017)46 b FK(F)-8 b(ortran)31
b(95)h(binding:)514 2444 y FD(SUBROUTINE)45 b(swap\()h(x,)h(y)h(\))609
2556 y(<type>\(<wp>\),)c(INTENT)i(\(INOUT\))g(::)h(x\(:\),)g(y\(:\))514
2669 y(where)609 2782 y(x)h(and)e(y)i(have)f(shape)f(\(n\))136
2995 y FJ(\017)g FK(F)-8 b(ortran)31 b(77)h(binding:)514
3208 y FD(SUBROUTINE)45 b(BLAS_xSWAP\()f(N,)k(X,)f(INCX,)f(Y,)h(INCY)g
(\))514 3321 y(INTEGER)570 b(INCX,)47 b(INCY,)f(N)514
3434 y(<type>)618 b(X\()48 b(*)f(\),)g(Y\()g(*)h(\))136
3647 y FJ(\017)e FK(C)30 b(binding:)227 3860 y FD(void)47
b(BLAS_xswap\()e(int)i(n,)g(ARRAY)f(x,)h(int)g(incx,)g(ARRAY)f(y,)h
(int)g(incy)g(\);)p 0 4073 V 0 4186 a FK(SOR)-8 b(T)30
b(\(Sort)g(v)m(ector\))2647 b Fy(x)25 b FJ( )g FK(sort\()p
Fy(x)p FK(\))141 4412 y(The)39 b(routine)g Fv(SORT)f
FK(sorts)i(the)f(en)m(tries)g(of)h(a)g(real)f(v)m(ector)i
Fy(x)f FK(in)e(increasing)g(or)h(decreasing)h(order)f(and)0
4525 y(o)m(v)m(erwrites)h(this)f(v)m(ector)i Fy(x)e FK(with)g(the)h
(sorted)f(v)m(ector.)70 b(If)40 b Fv(n)f FK(is)g(less)g(than)g(or)h
(equal)f(to)h(zero,)j(the)d(function)0 4638 y(returns)h(immediately)-8
b(.)77 b(As)42 b(describ)s(ed)f(in)g(section)i(2.5.3,)k(the)c(v)-5
b(alue)42 b Fv(incx)h FK(less)f(than)g(zero)h(is)f(p)s(ermitted.)0
4750 y(Ho)m(w)m(ev)m(er,)33 b(if)c Fv(incx)h FK(is)g(equal)g(to)h
(zero,)g(an)f(error)g(\015ag)h(is)f(set)g(and)g(passed)g(to)h(the)g
(error)f(handler.)227 4951 y Fz(A)-5 b(dvic)g(e)39 b(to)f(users.)118
b FK(The)36 b(routine)g Fv(SORT)f FK(strictly)h(op)s(erates)h(on)f
(real)g(v)m(ectors.)61 b(This)35 b(routine)g(is)h(not)227
5064 y(de\014ned)29 b(for)i(complex)f(v)m(ectors.)42
b(\()p Fz(End)33 b(of)g(advic)-5 b(e)33 b(to)g(users.)p
FK(\))227 5264 y Fz(A)-5 b(dvic)g(e)33 b(to)g(implementors.)84
b FK(The)30 b(subroutine)f Fv(xLASRT)g FK(of)i(the)f(LAP)-8
b(A)m(CK)31 b([6)q(])f(soft)m(w)m(are)i(library)c(is)i(an)227
5377 y(example)g(of)h(suc)m(h)f(a)h(routine.)39 b(\()p
Fz(End)34 b(of)e(advic)-5 b(e)34 b(to)f(implementors.)p
FK(\))-214 64 y FI(1)-214 177 y(2)-214 290 y(3)-214 403
y(4)-214 516 y(5)-214 628 y(6)-214 741 y(7)-214 854 y(8)-214
967 y(9)-230 1080 y(10)-230 1193 y(11)-230 1306 y(12)-230
1419 y(13)-230 1532 y(14)-230 1645 y(15)-230 1758 y(16)-230
1870 y(17)-230 1983 y(18)-230 2096 y(19)-230 2209 y(20)-230
2322 y(21)-230 2435 y(22)-230 2548 y(23)-230 2661 y(24)-230
2774 y(25)-230 2887 y(26)-230 3000 y(27)-230 3112 y(28)-230
3225 y(29)-230 3338 y(30)-230 3451 y(31)-230 3564 y(32)-230
3677 y(33)-230 3790 y(34)-230 3903 y(35)-230 4016 y(36)-230
4129 y(37)-230 4242 y(38)-230 4354 y(39)-230 4467 y(40)-230
4580 y(41)-230 4693 y(42)-230 4806 y(43)-230 4919 y(44)-230
5032 y(45)-230 5145 y(46)-230 5258 y(47)-230 5371 y(48)p
eop
%%Page: 52 62
52 61 bop 0 -165 a FK(52)1930 b FA(CHAPTER)30 b(2.)71
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b FK(F)-8 b(ortran)31 b(95)h(binding:)37 b Fz(R)-5 b(efer)33
b(to)g(SOR)-7 b(TV)33 b(sp)-5 b(e)g(ci\014c)g(ation)136
279 y FJ(\017)46 b FK(F)-8 b(ortran)31 b(77)h(binding:)514
504 y FD(SUBROUTINE)45 b(BLAS_xSORT\()f(SORT,)j(N,)g(X,)g(INCX)g(\))514
617 y(INTEGER)570 b(INCX,)47 b(N,)g(SORT)514 730 y(<rtype>)570
b(X\()48 b(*)f(\))136 955 y FJ(\017)f FK(C)30 b(binding:)227
1180 y FD(void)47 b(BLAS_xsort\()e(enum)h(blas_sort_type)e(sort,)j(int)
f(n,)i(RARRAY)e(x,)h(int)g(incx)f(\);)p 0 1405 3900 6
v 0 1518 a FK(SOR)-8 b(TV)30 b(\(Sort)g(v)m(ector)i(&)e(return)g(index)
e(v)m(ector\))1525 b(\()p Fy(p;)15 b(x)p FK(\))26 b FJ( )f
FK(sort\()p Fy(x)p FK(\))141 1743 y(The)35 b(routine)g
Fv(SORTV)f FK(sorts)i(the)g(en)m(tries)f(of)h(a)g(real)g(v)m(ector)h
Fy(x)e FK(in)g(increasing)f(or)i(decreasing)f(order)h(and)0
1856 y(o)m(v)m(erwrites)d(this)f(v)m(ector)i Fy(x)f FK(with)f(the)h
(sorted)g(v)m(ector)h(\()p Fy(x)c FK(=)f Fy(P)34 b FJ(\003)23
b Fy(x)p FK(\).)48 b(If)32 b Fv(n)h FK(is)f(less)g(than)h(or)f(equal)h
(to)g(zero,)i(the)0 1969 y(routine)c(returns)g(immediately)-8
b(.)46 b(As)32 b(describ)s(ed)e(in)h(section)h(2.5.3,)j(the)e(v)-5
b(alue)31 b Fv(incx)i FK(or)f Fv(incp)g FK(less)g(than)g(zero)h(is)0
2082 y(p)s(ermitted.)55 b(Ho)m(w)m(ev)m(er,)39 b(if)c(either)g
Fv(incx)h FK(or)f Fv(incp)h FK(is)f(equal)g(to)h(zero,)i(an)e(error)f
(\015ag)h(is)f(set)h(and)f(passed)g(to)i(the)0 2195 y(error)30
b(handler.)141 2308 y(The)g(represen)m(tation)g(of)h(the)g(p)s(erm)m
(utation)e(v)m(ector)j Fy(p)e FK(is)f(describ)s(ed)g(in)g(section)h
(2.2.6.)227 2521 y Fz(A)-5 b(dvic)g(e)36 b(to)g(users.)100
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2633 y(de\014ned)c(for)i(complex)f(v)m(ectors.)42 b(\()p
Fz(End)33 b(of)g(advic)-5 b(e)33 b(to)g(users.)p FK(\))136
2846 y FJ(\017)46 b FK(F)-8 b(ortran)31 b(95)h(binding:)514
3096 y FD(SUBROUTINE)45 b(sortv\()h(x)h([,)g(sort])g([,)g(p])g(\))609
3209 y(REAL\(<wp>\),)e(INTENT)h(\(INOUT\))g(::)h(x\(:\))609
3322 y(TYPE)g(\(blas_sort_type\),)c(INTENT)j(\(IN\),)g(OPTIONAL)g(::)h
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514 3548 y(where)609 3660 y(x)g(and)e(p)i(have)f(shape)f(\(n\))227
3910 y FK(The)30 b(functionalit)m(y)f(of)i(SOR)-8 b(T)29
b(is)g(co)m(v)m(ered)j(b)m(y)f(SOR)-8 b(TV.)136 4098
y FJ(\017)46 b FK(F)-8 b(ortran)31 b(77)h(binding:)514
4323 y FD(SUBROUTINE)45 b(BLAS_xSORTV\()f(SORT,)i(N,)i(X,)f(INCX,)f(P,)
h(INCP)g(\))514 4436 y(INTEGER)570 b(INCP,)47 b(INCX,)f(N,)h(SORT)514
4549 y(INTEGER)570 b(P\()48 b(*)f(\))514 4662 y(<rtype>)570
b(X\()48 b(*)f(\))136 4887 y FJ(\017)f FK(C)30 b(binding:)227
5112 y FD(void)47 b(BLAS_xsortv\()d(enum)j(blas_sort_type)d(sort,)i
(int)h(n,)g(RARRAY)f(x,)i(int)f(incx,)1086 5225 y(int)g(*p,)g(int)g
(incp)g(\);)4084 64 y FI(1)4084 177 y(2)4084 290 y(3)4084
403 y(4)4084 516 y(5)4084 628 y(6)4084 741 y(7)4084 854
y(8)4084 967 y(9)4069 1080 y(10)4069 1193 y(11)4069 1306
y(12)4069 1419 y(13)4069 1532 y(14)4069 1645 y(15)4069
1758 y(16)4069 1870 y(17)4069 1983 y(18)4069 2096 y(19)4069
2209 y(20)4069 2322 y(21)4069 2435 y(22)4069 2548 y(23)4069
2661 y(24)4069 2774 y(25)4069 2887 y(26)4069 3000 y(27)4069
3112 y(28)4069 3225 y(29)4069 3338 y(30)4069 3451 y(31)4069
3564 y(32)4069 3677 y(33)4069 3790 y(34)4069 3903 y(35)4069
4016 y(36)4069 4129 y(37)4069 4242 y(38)4069 4354 y(39)4069
4467 y(40)4069 4580 y(41)4069 4693 y(42)4069 4806 y(43)4069
4919 y(44)4069 5032 y(45)4069 5145 y(46)4069 5258 y(47)4069
5371 y(48)p eop
%%Page: 53 63
53 62 bop 0 -165 a FA(2.8.)72 b(LANGUA)m(GE)32 b(BINDINGS)2578
b FK(53)p 0 91 3900 6 v 0 204 a(PERMUTE)30 b(\(P)m(erm)m(ute)i(v)m
(ector\))2407 b Fy(x)25 b FJ( )g Fy(P)13 b(x)141 430
y FK(The)29 b(routine)f Fv(PERMUTE)g FK(p)s(erm)m(utes)h(the)g(en)m
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m(utation)f(v)m(ector)0 543 y Fy(p)p FK(.)40 b(If)29
b Fv(n)g FK(is)f(less)h(than)g(or)g(equal)g(to)h(zero,)g(the)g(routine)
e(returns)g(immediately)-8 b(.)39 b(As)29 b(describ)s(ed)f(in)f
(section)j(2.5.3,)0 656 y(the)k(v)-5 b(alue)33 b Fv(incx)g
FK(or)h Fv(incp)f FK(less)g(than)g(zero)i(is)d(p)s(ermitted.)49
b(Ho)m(w)m(ev)m(er,)37 b(if)32 b(either)h Fv(incx)h FK(or)f
Fv(incp)h FK(is)f(equal)g(to)h(zero,)0 769 y(an)c(error)g(\015ag)h(is)e
(set)i(and)f(passed)g(to)h(the)g(error)f(handler.)141
882 y(The)35 b(enco)s(ding)g(of)h(the)f(p)s(erm)m(utation)g
Fy(P)48 b FK(in)35 b(the)h(v)m(ector)h Fy(p)e FK(follo)m(ws)g(the)h
(same)g(con)m(v)m(en)m(tions)g(as)g(the)g(ones)0 995
y(describ)s(ed)28 b(ab)s(o)m(v)m(e)k(for)e(the)h(routine)e
Fv(SORTV)p FK(.)g(Refer)i(to)g(section)f(2.2.6)i(for)e(complete)h
(details.)136 1205 y FJ(\017)46 b FK(F)-8 b(ortran)31
b(95)h(binding:)514 1427 y FD(SUBROUTINE)45 b(permute\()g(x,)i(p)h(\))
609 1540 y(<type>\(<wp>\),)c(INTENT)i(\(INOUT\))g(::)h(x\(:\))609
1653 y(INTEGER,)f(INTENT)g(\(IN\))g(::)i(p\(:\))514 1766
y(where)609 1879 y(x)g(and)e(p)i(have)f(shape)f(\(n\))136
2102 y FJ(\017)g FK(F)-8 b(ortran)31 b(77)h(binding:)514
2324 y FD(SUBROUTINE)45 b(BLAS_xPERMUTE\()f(N,)j(P,)g(INCP,)f(X,)h
(INCX)g(\))514 2437 y(INTEGER)570 b(INCP,)47 b(INCX,)f(N)514
2550 y(INTEGER)570 b(P\()48 b(*)f(\))514 2663 y(<type>)618
b(X\()48 b(*)f(\))227 2885 y FK(The)30 b(v)-5 b(alue)30
b(of)h FD(INCP)f FK(ma)m(y)h(b)s(e)f(p)s(ositiv)m(e)f(or)i(negativ)m
(e.)43 b(A)30 b(negativ)m(e)i(v)-5 b(alue)30 b(of)h FD(INCP)e
FK(applies)g(the)i(p)s(erm)m(u-)227 2998 y(tation)g(in)e(the)i(opp)s
(osite)e(direction.)136 3185 y FJ(\017)46 b FK(C)30 b(binding:)227
3408 y FD(void)47 b(BLAS_xpermute\()d(int)j(n,)g(const)f(int)h(*p,)g
(int)g(incp,)f(ARRAY)h(x,)g(int)g(incx)f(\);)227 3630
y FK(The)30 b(v)-5 b(alue)30 b(of)h FD(incp)f FK(ma)m(y)h(b)s(e)f(p)s
(ositiv)m(e)f(or)i(negativ)m(e.)43 b(A)30 b(negativ)m(e)i(v)-5
b(alue)30 b(of)h FD(incp)e FK(applies)g(the)i(p)s(erm)m(u-)227
3743 y(tation)g(in)e(the)i(opp)s(osite)e(direction.)0
3986 y Fx(2.8.6)97 b(Matrix-V)m(ecto)m(r)33 b(Op)s(erations)0
4158 y FK(In)d(the)g(follo)m(wing)f(section,)i Fy(op)p
FK(\()p Fy(X)7 b FK(\))31 b(denotes)g Fy(X)7 b FK(,)31
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4125 y Fw(H)2293 4158 y FK(where)g Fy(X)38 b FK(is)29
b(a)i(matrix.)0 4384 y FJ(f)p FK(GE,GB)p FJ(g)p FK(MV)i(\(Matrix)e(v)m
(ector)h(pro)s(duct\))1630 b Fy(y)29 b FJ( )c Fy(\013op)p
FK(\()p Fy(A)p FK(\))p Fy(x)c FK(+)f Fy(\014)5 b(y)141
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Fy(\013)h FK(and)f Fy(\014)38 b FK(are)33 b(scalars,)0
4723 y(and)i Fy(A)h FK(is)e(a)i(general)g(\(or)g(general)f(band\))g
(matrix.)56 b(If)35 b Fv(m)h FK(or)f Fv(n)h FK(is)e(less)h(than)h(or)f
(equal)g(to)h(zero)h(or)e(if)g Fv(b)s(eta)g FK(is)0 4835
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(this)d(routine)g(returns)f(immediately)-8 b(.)47 b(As)33
b(describ)s(ed)e(in)h(section)0 4948 y(2.5.3,)j(the)e(v)-5
b(alue)33 b Fv(incx)g FK(or)f Fv(incy)h FK(less)f(than)h(zero)g(is)f(p)
s(ermitted.)47 b(Ho)m(w)m(ev)m(er,)36 b(if)31 b(either)i
Fv(incx)f FK(or)h Fv(incy)g FK(is)f(equal)g(to)0 5061
y(zero,)f(an)f(error)g(\015ag)h(is)e(set)i(and)f(passed)f(to)i(the)g
(error)f(handler.)38 b(F)-8 b(or)31 b(the)g(routine)e
Fv(GEMV)p FK(,)h(if)f Fv(lda)g FK(is)h(less)f(than)0
5174 y(one,)37 b(or)e Fy(tr)s(ans)c FK(=)i Fy(bl)r(as)p
836 5174 28 4 v 32 w(no)p 967 5174 V 33 w(tr)s(ans)g
FK(and)i Fv(lda)f FK(is)g(less)g(than)h Fv(m)p FK(,)i(or)e
Fy(tr)s(ans)c FK(=)i Fy(bl)r(as)p 2837 5174 V 32 w(tr)s(ans)h
FK(and)g Fv(lda)h FK(is)f(less)g(than)0 5287 y Fv(n)p
FK(,)j(an)f(error)f(\015ag)h(is)e(set)j(and)e(passed)g(to)h(the)g
(error)f(handler.)55 b(F)-8 b(or)36 b(the)g(C)f(bindings)e(of)i
Fv(GEMV)p FK(,)g(if)g FD(order)46 b(=)0 5400 y(blas)p
198 5400 29 4 v 33 w(rowmajor)25 b FK(and)i(if)g Fv(lda)g
FK(is)f(less)h(than)g(one)h(or)f Fv(lda)g FK(is)g(less)f(than)i
Fv(n)p FK(,)g(an)f(error)g(\015ag)h(is)f(set)h(and)f(passed)g(to)h(the)
-214 64 y FI(1)-214 177 y(2)-214 290 y(3)-214 403 y(4)-214
516 y(5)-214 628 y(6)-214 741 y(7)-214 854 y(8)-214 967
y(9)-230 1080 y(10)-230 1193 y(11)-230 1306 y(12)-230
1419 y(13)-230 1532 y(14)-230 1645 y(15)-230 1758 y(16)-230
1870 y(17)-230 1983 y(18)-230 2096 y(19)-230 2209 y(20)-230
2322 y(21)-230 2435 y(22)-230 2548 y(23)-230 2661 y(24)-230
2774 y(25)-230 2887 y(26)-230 3000 y(27)-230 3112 y(28)-230
3225 y(29)-230 3338 y(30)-230 3451 y(31)-230 3564 y(32)-230
3677 y(33)-230 3790 y(34)-230 3903 y(35)-230 4016 y(36)-230
4129 y(37)-230 4242 y(38)-230 4354 y(39)-230 4467 y(40)-230
4580 y(41)-230 4693 y(42)-230 4806 y(43)-230 4919 y(44)-230
5032 y(45)-230 5145 y(46)-230 5258 y(47)-230 5371 y(48)p
eop
%%Page: 54 64
54 63 bop 0 -165 a FK(54)1930 b FA(CHAPTER)30 b(2.)71
b(DENSE)30 b(AND)h(BANDED)h(BLAS)0 91 y FK(error)e(handler;)g(if)g
FD(order)46 b(=)h(blas)p 1241 91 29 4 v 34 w(colmajor)28
b FK(and)i(if)g Fv(lda)g FK(is)g(less)g(than)h(one)g(or)g
Fv(lda)f FK(is)g(less)g(than)g Fv(m)p FK(,)i(an)e(error)0
204 y(\015ag)j(is)e(set)h(and)g(passed)g(to)h(the)f(error)g(handler.)44
b(F)-8 b(or)33 b(the)g(routine)e Fv(GBMV)p FK(,)f(if)i
Fv(kl)g FK(or)g Fv(ku)h FK(is)e(less)g(than)h(zero,)i(or)0
317 y(if)29 b Fv(lda)h FK(is)f(less)h(than)g Fv(kl)h
FK(plus)d Fv(ku)j FK(plus)d(one,)j(an)f(error)g(\015ag)h(is)f(set)g
(and)g(passed)g(to)h(the)g(error)f(handler.)136 530 y
FJ(\017)46 b FK(F)-8 b(ortran)31 b(95)h(binding:)418
755 y FD(SUBROUTINE)45 b(gbmv\()i(a,)g(m,)g(kl,)g(x,)g(y)g([,)h(trans])
e([,)h(alpha])f([,)h(beta])g(\))514 868 y(<type>\(<wp>\),)d
(INTENT\(IN\))h(::)i(a\(:,:\),)f(x\(:\))514 980 y(INTEGER,)f
(INTENT\(IN\))g(::)i(m,)h(kl)514 1093 y(<type>\(<wp>\),)c
(INTENT\(INOUT\))g(::)j(y\(:\))514 1206 y(TYPE)f(\(blas_trans_type\),)d
(INTENT\(IN\),)i(OPTIONAL)g(::)j(trans)514 1319 y(<type>\(<wp>\),)c
(INTENT\(IN\),)h(OPTIONAL)g(::)i(alpha,)f(beta)418 1432
y(where)514 1545 y(if)h(trans)f(=)i(blas_no_trans)c(then)657
1658 y(x)j(has)g(shape)g(\(n\))657 1771 y(y)g(has)g(shape)g(\(m\))514
1884 y(else)f(if)h(trans)g(=/)g(blas_no_trans)d(then)657
1997 y(x)j(has)g(shape)g(\(m\))657 2110 y(y)g(has)g(shape)g(\(n\))514
2222 y(end)g(if)227 2447 y FK(The)30 b(functionalit)m(y)f(of)i
Fv(gemv)g FK(is)e(co)m(v)m(ered)j(b)m(y)e Fv(gemm)p FK(.)136
2635 y FJ(\017)46 b FK(F)-8 b(ortran)31 b(77)h(binding:)227
2860 y FD(General:)514 2973 y(SUBROUTINE)45 b(BLAS_xGEMV\()f(TRANS,)i
(M,)i(N,)f(ALPHA,)f(A,)h(LDA,)g(X,)g(INCX,)f(BETA,)466
3086 y($)1097 b(Y,)48 b(INCY)e(\))227 3199 y(General)g(Band:)514
3312 y(SUBROUTINE)f(BLAS_xGBMV\()f(TRANS,)i(M,)i(N,)f(KL,)g(KU,)g
(ALPHA,)f(A,)h(LDA,)g(X,)466 3425 y($)1097 b(INCX,)47
b(BETA,)f(Y,)h(INCY)g(\))227 3538 y(all:)514 3650 y(INTEGER)570
b(INCX,)47 b(INCY,)f(KL,)h(KU,)g(LDA,)g(M,)g(N,)g(TRANS)514
3763 y(<type>)618 b(ALPHA,)47 b(BETA)514 3876 y(<type>)618
b(A\()48 b(LDA,)e(*)i(\),)f(X\()g(*)h(\),)f(Y\()g(*)g(\))136
4101 y FJ(\017)f FK(C)30 b(binding:)227 4326 y FD(General:)227
4439 y(void)47 b(BLAS_xgemv\()e(enum)h(blas_order_type)e(order,)i(enum)
h(blas_trans_type)c(trans,)1039 4552 y(int)k(m,)g(int)g(n,)g(SCALAR_IN)
e(alpha,)h(const)h(ARRAY)f(a,)h(int)g(lda,)1039 4665
y(const)f(ARRAY)g(x,)i(int)e(incx,)h(SCALAR_IN)e(beta,)h(ARRAY)h(y,)g
(int)g(incy)g(\);)227 4778 y(General)f(Band:)227 4891
y(void)h(BLAS_xgbmv\()e(enum)h(blas_order_type)e(order,)i(enum)h
(blas_trans_type)c(trans,)1039 5004 y(int)k(m,)g(int)g(n,)g(int)g(kl,)g
(int)g(ku,)f(SCALAR_IN)g(alpha,)g(const)g(ARRAY)h(a,)1039
5117 y(int)g(lda,)f(const)h(ARRAY)f(x,)h(int)g(incx,)f(SCALAR_IN)g
(beta,)1039 5230 y(ARRAY)g(y,)h(int)g(incy)g(\);)4084
64 y FI(1)4084 177 y(2)4084 290 y(3)4084 403 y(4)4084
516 y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084 967
y(9)4069 1080 y(10)4069 1193 y(11)4069 1306 y(12)4069
1419 y(13)4069 1532 y(14)4069 1645 y(15)4069 1758 y(16)4069
1870 y(17)4069 1983 y(18)4069 2096 y(19)4069 2209 y(20)4069
2322 y(21)4069 2435 y(22)4069 2548 y(23)4069 2661 y(24)4069
2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
3677 y(33)4069 3790 y(34)4069 3903 y(35)4069 4016 y(36)4069
4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 55 65
55 64 bop 0 -165 a FA(2.8.)72 b(LANGUA)m(GE)32 b(BINDINGS)2578
b FK(55)p 0 91 3900 6 v 0 204 a FJ(f)p FK(SY,SB,SP)p
FJ(g)p FK(MV)31 b(\(Symmetric)f(matrix)g(v)m(ector)i(pro)s(duct\))689
b Fy(y)28 b FJ( )d Fy(\013Ax)c FK(+)f Fy(\014)5 b(y)33
b FK(with)c Fy(A)d FK(=)f Fy(A)3845 171 y Fw(T)141 430
y FK(The)j(routines)f(m)m(ultiply)e(a)k(v)m(ector)h Fy(x)e
FK(b)m(y)g(a)g(real)g(or)g(complex)g(symmetric)g(matrix)f
Fy(A)p FK(,)i(scales)f(the)h(resulting)0 543 y(v)m(ector)g(and)f(adds)f
(it)g(to)i(the)f(scaled)f(v)m(ector)j(op)s(erand)c Fy(y)s
FK(.)40 b(If)27 b Fv(n)h FK(or)g Fv(k)g FK(is)f(less)g(than)h(or)g
(equal)f(to)h(zero)h(or)f(if)f Fv(b)s(eta)g FK(is)0 656
y(equal)32 b(to)i(one)f(and)g Fv(alpha)e FK(is)h(equal)h(to)g(zero,)i
(this)d(routine)g(returns)f(immediately)-8 b(.)47 b(As)33
b(describ)s(ed)e(in)h(section)0 769 y(2.5.3,)j(the)e(v)-5
b(alue)33 b Fv(incx)g FK(or)f Fv(incy)h FK(less)f(than)h(zero)g(is)f(p)
s(ermitted.)47 b(Ho)m(w)m(ev)m(er,)36 b(if)31 b(either)i
Fv(incx)f FK(or)h Fv(incy)g FK(is)f(equal)g(to)0 882
y(zero,)f(an)g(error)f(\015ag)h(is)e(set)i(and)f(passed)g(to)h(the)g
(error)f(handler.)39 b(F)-8 b(or)31 b(the)g(routine)e
Fv(SYMV)p FK(,)g(if)g Fv(lda)h FK(is)f(less)h(than)0
995 y(one)d(or)f Fv(lda)g FK(is)g(less)f(than)i Fv(n)p
FK(,)g(an)f(error)g(\015ag)h(is)f(set)h(and)f(passed)g(to)h(the)f
(error)h(handler.)37 b(F)-8 b(or)27 b(the)g(routine)e
Fv(SBMV)p FK(,)0 1108 y(if)k Fv(lda)h FK(is)f(less)h(than)g
Fv(k)h FK(plus)d(one,)j(an)g(error)f(\015ag)g(is)g(set)h(and)e(passed)h
(to)h(the)g(error)f(handler.)136 1320 y FJ(\017)46 b
FK(F)-8 b(ortran)31 b(95)h(binding:)227 1545 y FD(Symmetric)46
b(Band:)418 1658 y(SUBROUTINE)f(sbmv\()i(a,)g(x,)g(y)g([,)h(uplo])e([,)
h(alpha])f([,)h(beta])g(\))227 1771 y(Symmetric)f(Packed:)418
1884 y(SUBROUTINE)f(spmv\()i(ap,)f(x,)i(y)f([,)g(uplo])g([,)g(alpha])f
([,)h(beta])f(\))227 1997 y(all:)514 2110 y(<type>\(<wp>\),)e
(INTENT\(IN\))h(::)i(<aa>,)f(x\(:\))514 2222 y(<type>\(<wp>\),)e
(INTENT\(INOUT\))g(::)j(y\(:\))514 2335 y(TYPE)f(\(blas_uplo_type\),)d
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(INTENT\(IN\),)h(OPTIONAL)g(::)i(alpha,)f(beta)418 2561
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2787 y(and)514 2900 y(SB)95 b(a)47 b(has)g(shape)f(\(k+1,n\))514
3013 y(SP)95 b(ap)47 b(has)g(shape)f(\(n*\(n+1\)/2\))514
3126 y(x)h(and)g(y)g(have)g(shape)f(\(n\))418 3239 y(\(k=band)g
(width\))227 3464 y FK(The)30 b(fun)m(tionalit)m(y)f(of)i
Fv(symv)f FK(is)f(co)m(v)m(ered)j(b)m(y)e Fv(symm)p FK(.)136
3651 y FJ(\017)46 b FK(F)-8 b(ortran)31 b(77)h(binding:)227
3876 y FD(Symmetric:)514 3989 y(SUBROUTINE)45 b(BLAS_xSYMV\()f(UPLO,)j
(N,)g(ALPHA,)f(A,)h(LDA,)g(X,)g(INCX,)f(BETA,)h(Y,)466
4102 y($)1097 b(INCY)47 b(\))227 4215 y(Symmetric)f(Band:)514
4328 y(SUBROUTINE)f(BLAS_xSBMV\()f(UPLO,)j(N,)g(K,)g(ALPHA,)f(A,)h
(LDA,)g(X,)g(INCX,)g(BETA,)f(Y,)466 4441 y($)1097 b(INCY)47
b(\))227 4554 y(Symmetric)f(Packed:)514 4667 y(SUBROUTINE)f
(BLAS_xSPMV\()f(UPLO,)j(N,)g(ALPHA,)f(AP,)h(X,)g(INCX,)f(BETA,)h(Y,)g
(INCY)g(\))227 4780 y(all:)514 4892 y(INTEGER)570 b(INCX,)47
b(INCY,)f(K,)h(LDA,)g(N,)g(UPLO)514 5005 y(<type>)618
b(ALPHA,)47 b(BETA)514 5118 y(<type>)618 b(A\()48 b(LDA,)e(*)i(\))f(or)
g(AP\()g(*)h(\),)f(X\()g(*)h(\),)f(Y\()g(*)g(\))136 5343
y FJ(\017)f FK(C)30 b(binding:)-214 64 y FI(1)-214 177
y(2)-214 290 y(3)-214 403 y(4)-214 516 y(5)-214 628 y(6)-214
741 y(7)-214 854 y(8)-214 967 y(9)-230 1080 y(10)-230
1193 y(11)-230 1306 y(12)-230 1419 y(13)-230 1532 y(14)-230
1645 y(15)-230 1758 y(16)-230 1870 y(17)-230 1983 y(18)-230
2096 y(19)-230 2209 y(20)-230 2322 y(21)-230 2435 y(22)-230
2548 y(23)-230 2661 y(24)-230 2774 y(25)-230 2887 y(26)-230
3000 y(27)-230 3112 y(28)-230 3225 y(29)-230 3338 y(30)-230
3451 y(31)-230 3564 y(32)-230 3677 y(33)-230 3790 y(34)-230
3903 y(35)-230 4016 y(36)-230 4129 y(37)-230 4242 y(38)-230
4354 y(39)-230 4467 y(40)-230 4580 y(41)-230 4693 y(42)-230
4806 y(43)-230 4919 y(44)-230 5032 y(45)-230 5145 y(46)-230
5258 y(47)-230 5371 y(48)p eop
%%Page: 56 66
56 65 bop 0 -165 a FK(56)1930 b FA(CHAPTER)30 b(2.)71
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(blas_uplo_type)d(uplo,)1039 317 y(int)j(n,)g(SCALAR_IN)e(alpha,)h
(const)g(ARRAY)h(a,)g(int)g(lda,)1039 430 y(const)f(ARRAY)g(x,)i(int)e
(incx,)h(SCALAR_IN)e(beta,)h(ARRAY)h(y,)g(int)g(incy)g(\);)227
543 y(Symmetric)f(Band:)227 656 y(void)h(BLAS_xsbmv\()e(enum)h
(blas_order_type)e(order,)i(enum)h(blas_uplo_type)d(uplo,)1039
769 y(int)j(n,)g(int)g(k,)g(SCALAR_IN)e(alpha,)h(const)h(ARRAY)f(a,)h
(int)g(lda,)1039 882 y(const)f(ARRAY)g(x,)i(int)e(incx,)h(SCALAR_IN)e
(beta,)h(ARRAY)h(y,)g(int)g(incy)g(\);)227 995 y(Symmetric)f(Packed:)
227 1108 y(void)h(BLAS_xspmv\()e(enum)h(blas_order_type)e(order,)i
(enum)h(blas_uplo_type)d(uplo,)i(int)h(n,)1039 1220 y(SCALAR_IN)e
(alpha,)h(const)g(ARRAY)h(ap,)g(const)f(ARRAY)g(x,)i(int)e(incx,)1039
1333 y(SCALAR_IN)f(beta,)h(ARRAY)h(y,)g(int)g(incy)f(\);)p
0 1558 3900 6 v 0 1671 a FJ(f)p FK(HE,HB,HP)p FJ(g)p
FK(MV)33 b(\(Hermitian)c(matrix)h(v)m(ector)i(pro)s(duct\))656
b Fy(y)28 b FJ( )d Fy(\013Ax)c FK(+)f Fy(\014)5 b(y)33
b FK(with)c Fy(A)d FK(=)f Fy(A)3833 1638 y Fw(H)141 1897
y FK(The)i(routines)g(m)m(ultiply)e(a)j(v)m(ector)h Fy(x)f
FK(b)m(y)f(a)i(Hermitian)d(matrix)h Fy(A)p FK(,)i(scales)f(the)f
(resulting)f(v)m(ector)k(and)d(adds)0 2010 y(it)d(to)h(the)g(scaled)f
(v)m(ector)i(op)s(erand)d Fy(y)s FK(.)39 b(If)24 b Fv(n)g
FK(is)g(less)f(than)i(or)f(equal)g(to)h(zero)g(or)g(if)e
Fv(b)s(eta)h FK(is)f(equal)h(to)h(one)g(and)f Fv(alpha)0
2123 y FK(is)35 b(equal)g(to)h(zero,)i(this)d(routine)f(returns)h
(immediately)-8 b(.)55 b(The)35 b(imaginary)f(part)i(of)g(the)f
(diagonal)g(en)m(tries)h(of)0 2236 y(the)30 b(matrix)f(op)s(erand)g
(are)h(supp)s(osed)e(to)i(b)s(e)g(zero)g(and)f(should)f(not)i(b)s(e)f
(referenced.)41 b(As)30 b(describ)s(ed)d(in)i(section)0
2349 y(2.5.3,)35 b(the)e(v)-5 b(alue)33 b Fv(incx)g FK(or)f
Fv(incy)h FK(less)f(than)h(zero)g(is)f(p)s(ermitted.)47
b(Ho)m(w)m(ev)m(er,)36 b(if)31 b(either)i Fv(incx)f FK(or)h
Fv(incy)g FK(is)f(equal)g(to)0 2462 y(zero,)f(an)f(error)g(\015ag)g(is)
f(set)i(and)e(passed)h(to)h(the)f(error)f(handler.)39
b(F)-8 b(or)31 b(the)f(routine)f Fv(HEMV)p FK(,)h(if)f
Fv(lda)h FK(is)f(less)g(than)0 2575 y(one)d(or)g Fv(lda)f
FK(is)g(less)g(than)g Fv(n)p FK(,)i(an)f(error)f(\015ag)h(is)f(set)i
(and)e(passed)g(to)i(the)f(error)f(handler.)37 b(F)-8
b(or)27 b(the)f(routine)f Fv(HBMV)p FK(,)0 2687 y(if)k
Fv(lda)h FK(is)f(less)h(than)g Fv(k)h FK(plus)d(one,)j(an)g(error)f
(\015ag)g(is)g(set)h(and)e(passed)h(to)h(the)g(error)f(handler.)136
2900 y FJ(\017)46 b FK(F)-8 b(ortran)31 b(95)h(binding:)227
3125 y FD(Hermitian)46 b(Band:)418 3238 y(SUBROUTINE)f(hbmv\()i(a,)g
(x,)g(y)95 b([,)47 b(uplo])g([,)g(alpha])f([,)h(beta])f(\))227
3351 y(Hermitian)g(Packed:)418 3464 y(SUBROUTINE)f(hpmv\()i(ap,)f(x,)i
(y)f([,)g(uplo])g([,)g(alpha])f([,)h(beta])f(\))227 3577
y(all:)514 3689 y(COMPLEX\(<wp>\),)e(INTENT\(IN\))h(::)i(<aa>,)f
(x\(:\))514 3802 y(COMPLEX\(<wp>\),)e(INTENT\(INOUT\))g(::)j(y\(:\))514
3915 y(TYPE)f(\(blas_uplo_type\),)d(INTENT\(IN\),)i(OPTIONAL)h(::)h
(uplo)514 4028 y(COMPLEX\(<wp>\),)d(INTENT\(IN\),)g(OPTIONAL)i(::)h
(alpha,)f(beta)418 4141 y(where)514 4254 y(<aa>)94 b(::=)47
b(a\(:,:\))f(or)h(ap\(:\))418 4367 y(and)561 4480 y(HB)95
b(a)48 b(has)f(shape)f(\(k+1,n\))561 4593 y(HP)95 b(ap)47
b(has)g(shape)g(\(n*\(n+1\)/2\))561 4706 y(x)h(and)f(y)g(have)g(shape)f
(\(n\))418 4819 y(\(k=band)g(width\))227 5044 y FK(The)30
b(fun)m(tionalit)m(y)f(of)i Fv(hemv)f FK(is)g(co)m(v)m(ered)i(b)m(y)e
Fv(hemm)p FK(.)136 5231 y FJ(\017)46 b FK(F)-8 b(ortran)31
b(77)h(binding:)4084 64 y FI(1)4084 177 y(2)4084 290
y(3)4084 403 y(4)4084 516 y(5)4084 628 y(6)4084 741 y(7)4084
854 y(8)4084 967 y(9)4069 1080 y(10)4069 1193 y(11)4069
1306 y(12)4069 1419 y(13)4069 1532 y(14)4069 1645 y(15)4069
1758 y(16)4069 1870 y(17)4069 1983 y(18)4069 2096 y(19)4069
2209 y(20)4069 2322 y(21)4069 2435 y(22)4069 2548 y(23)4069
2661 y(24)4069 2774 y(25)4069 2887 y(26)4069 3000 y(27)4069
3112 y(28)4069 3225 y(29)4069 3338 y(30)4069 3451 y(31)4069
3564 y(32)4069 3677 y(33)4069 3790 y(34)4069 3903 y(35)4069
4016 y(36)4069 4129 y(37)4069 4242 y(38)4069 4354 y(39)4069
4467 y(40)4069 4580 y(41)4069 4693 y(42)4069 4806 y(43)4069
4919 y(44)4069 5032 y(45)4069 5145 y(46)4069 5258 y(47)4069
5371 y(48)p eop
%%Page: 57 67
57 66 bop 0 -165 a FA(2.8.)72 b(LANGUA)m(GE)32 b(BINDINGS)2578
b FK(57)227 91 y FD(Hermitian:)514 204 y(SUBROUTINE)45
b(BLAS_xHEMV\()f(UPLO,)j(N,)g(ALPHA,)f(A,)h(LDA,)g(X,)g(INCX,)f(BETA,)h
(Y,)466 317 y($)1097 b(INCY)47 b(\))227 430 y(Hermitian)f(Band:)514
543 y(SUBROUTINE)f(BLAS_xHBMV\()f(UPLO,)j(N,)g(K,)g(ALPHA,)f(A,)h(LDA,)
g(X,)g(INCX,)g(BETA,)466 656 y($)1097 b(Y,)48 b(INCY)e(\))227
769 y(Hermitian)g(Packed:)514 882 y(SUBROUTINE)f(BLAS_xHPMV\()f(UPLO,)j
(N,)g(ALPHA,)f(AP,)h(X,)g(INCX,)f(BETA,)h(Y,)g(INCY)g(\))227
995 y(all:)514 1108 y(INTEGER)570 b(INCX,)47 b(INCY,)f(K,)h(LDA,)g(N,)g
(UPLO)514 1220 y(<ctype>)570 b(ALPHA,)47 b(BETA)514 1333
y(<ctype>)570 b(A\()48 b(LDA,)e(*)i(\))f(or)g(AP\()g(*)h(\),)f(X\()g(*)
h(\),)f(Y\()g(*)g(\))136 1558 y FJ(\017)f FK(C)30 b(binding:)227
1783 y FD(Hermitian:)227 1896 y(void)47 b(BLAS_xhemv\()e(enum)h
(blas_order_type)e(order,)i(enum)h(blas_uplo_type)d(uplo,)1039
2009 y(int)j(n,)g(CSCALAR_IN)e(alpha,)h(const)g(CARRAY)g(a,)h(int)g
(lda,)1039 2122 y(const)f(CARRAY)g(x,)h(int)g(incx,)g(CSCALAR_IN)e
(beta,)h(CARRAY)g(y,)1039 2235 y(int)h(incy)f(\);)227
2348 y(Hermitian)g(Band:)227 2461 y(void)h(BLAS_xhbmv\()e(enum)h
(blas_order_type)e(order,)i(enum)h(blas_uplo_type)d(uplo,)1039
2574 y(int)j(n,)g(int)g(k,)g(CSCALAR_IN)e(alpha,)h(const)g(CARRAY)g(a,)
i(int)e(lda,)1039 2687 y(const)g(CARRAY)g(x,)h(int)g(incx,)g
(CSCALAR_IN)e(beta,)h(CARRAY)g(y,)1039 2800 y(int)h(incy)f(\);)227
2912 y(Hermitian)g(Packed:)227 3025 y(void)h(BLAS_xhpmv\()e(enum)h
(blas_order_type)e(order,)i(enum)h(blas_uplo_type)d(uplo,)1039
3138 y(int)j(n,)g(CSCALAR_IN)e(alpha,)h(const)g(CARRAY)g(ap,)h(const)g
(CARRAY)f(x,)1039 3251 y(int)h(incx,)f(CSCALAR_IN)f(beta,)h(CARRAY)g
(y,)i(int)e(incy)h(\);)p 0 3476 3900 6 v 0 3589 a FJ(f)p
FK(TR,TB,TP)p FJ(g)p FK(MV)31 b(\(T)-8 b(riangular)29
b(matrix)h(v)m(ector)i(pro)s(duct\))360 b Fy(x)25 b FJ( )g
Fy(\013T)13 b(x)p FK(,)31 b Fy(x)25 b FJ( )g Fy(\013T)3214
3556 y Fw(T)3270 3589 y Fy(x)30 b FK(or)g Fy(x)25 b FJ( )h
Fy(\013T)3781 3556 y Fw(H)3848 3589 y Fy(x)141 3815 y
FK(The)43 b(routines)g(m)m(ultiply)e(a)j(v)m(ector)h
Fy(x)f FK(b)m(y)g(a)g(general)g(triangular)e(matrix)h
Fy(T)56 b FK(or)44 b(its)f(transp)s(ose,)k(or)d(its)0
3928 y(conjugate)36 b(transp)s(ose,)f(and)f(copies)h(the)f(resulting)f
(v)m(ector)j(in)e(the)g(v)m(ector)j(op)s(erand)c Fy(x)p
FK(.)53 b(If)35 b Fv(n)f FK(is)g(less)g(than)g(or)0 4041
y(equal)h(to)g(zero,)j(this)c(routine)g(returns)g(immediately)-8
b(.)53 b(As)35 b(describ)s(ed)e(in)h(section)h(2.5.3,)k(the)c(v)-5
b(alue)35 b Fv(incx)g FK(less)0 4154 y(than)28 b(zero)g(is)f(p)s
(ermitted.)38 b(Ho)m(w)m(ev)m(er,)31 b(if)c Fv(incx)g
FK(is)g(equal)g(to)i(zero,)g(an)f(error)f(\015ag)h(is)f(set)h(and)g
(passed)f(to)h(the)g(error)0 4267 y(handler.)41 b(F)-8
b(or)32 b(the)f(routine)f Fv(TRMV)p FK(,)g(if)g Fv(ldt)g
FK(is)g(less)h(than)g(one)g(or)g Fv(ldt)f FK(is)g(less)h(than)g
Fv(n)p FK(,)g(an)g(error)g(\015ag)g(is)f(set)i(and)0
4379 y(passed)h(to)i(the)f(error)g(handler.)49 b(F)-8
b(or)35 b(the)f(routine)e Fv(TBMV)p FK(,)h(if)g Fv(ldt)g
FK(is)g(less)g(than)h Fv(k)g FK(plus)e(one,)j(an)f(error)g(\015ag)g(is)
0 4492 y(set)d(and)f(passed)g(to)h(the)f(error)g(handler.)136
4705 y FJ(\017)46 b FK(F)-8 b(ortran)31 b(95)h(binding:)227
4930 y FD(Triangular)45 b(Band:)418 5043 y(SUBROUTINE)g(tbmv\()i(t,)g
(x)95 b([,)47 b(uplo])f([,)i(trans])e([,)h(diag])f([,)h(alpha])g(\))227
5156 y(Triangular)e(Packed:)418 5269 y(SUBROUTINE)g(tpmv\()i(tp,)f(x)i
([,)f(uplo])f([,)i(trans])e([,)h(diag])f([,)h(alpha])g(\))227
5381 y(all:)-214 64 y FI(1)-214 177 y(2)-214 290 y(3)-214
403 y(4)-214 516 y(5)-214 628 y(6)-214 741 y(7)-214 854
y(8)-214 967 y(9)-230 1080 y(10)-230 1193 y(11)-230 1306
y(12)-230 1419 y(13)-230 1532 y(14)-230 1645 y(15)-230
1758 y(16)-230 1870 y(17)-230 1983 y(18)-230 2096 y(19)-230
2209 y(20)-230 2322 y(21)-230 2435 y(22)-230 2548 y(23)-230
2661 y(24)-230 2774 y(25)-230 2887 y(26)-230 3000 y(27)-230
3112 y(28)-230 3225 y(29)-230 3338 y(30)-230 3451 y(31)-230
3564 y(32)-230 3677 y(33)-230 3790 y(34)-230 3903 y(35)-230
4016 y(36)-230 4129 y(37)-230 4242 y(38)-230 4354 y(39)-230
4467 y(40)-230 4580 y(41)-230 4693 y(42)-230 4806 y(43)-230
4919 y(44)-230 5032 y(45)-230 5145 y(46)-230 5258 y(47)-230
5371 y(48)p eop
%%Page: 58 68
58 67 bop 0 -165 a FK(58)1930 b FA(CHAPTER)30 b(2.)71
b(DENSE)30 b(AND)h(BANDED)h(BLAS)514 91 y FD(<type>\(<wp>\),)44
b(INTENT\(IN\))h(::)i(<tt>)514 204 y(<type>\(<wp>\),)d(INTENT\(INOUT\))
g(::)95 b(x\(:\))514 317 y(<type>\(<wp>\),)44 b(INTENT\(IN\),)h
(OPTIONAL)g(::)i(alpha)514 430 y(TYPE)f(\(blas_diag_type\),)d
(INTENT\(IN\),)i(OPTIONAL)h(::)h(diag)514 543 y(TYPE)f
(\(blas_trans_type\),)d(INTENT\(IN\),)i(OPTIONAL)g(::)j(trans)514
656 y(TYPE)e(\(blas_uplo_type\),)d(INTENT\(IN\),)i(OPTIONAL)h(::)h
(uplo)418 769 y(where)514 882 y(<tt>)94 b(::=)47 b(t\(:,:\))f(or)h
(tp\(:\))418 995 y(and)561 1108 y(TB)95 b(t)48 b(has)f(shape)f
(\(k+1,n\))561 1220 y(TP)95 b(tp)47 b(has)g(shape)g(\(n*\(n+1\)/2\))561
1333 y(x)h(has)f(shape)f(\(n\))418 1446 y(\(k=band)g(width\))227
1671 y FK(The)30 b(fun)m(tionalit)m(y)f(of)i Fv(trmv)f
FK(is)f(co)m(v)m(ered)j(b)m(y)f Fv(trmm)p FK(.)136 1859
y FJ(\017)46 b FK(F)-8 b(ortran)31 b(77)h(binding:)227
2084 y FD(Triangular:)561 2197 y(SUBROUTINE)45 b(BLAS_xTRMV\()g(UPLO,)h
(TRANS,)h(DIAG,)f(N,)h(ALPHA,)f(T,)h(LDT,)g(X,)514 2310
y($)1097 b(INCX)47 b(\))227 2423 y(Triangular)e(Band:)561
2535 y(SUBROUTINE)g(BLAS_xTBMV\()g(UPLO,)h(TRANS,)h(DIAG,)f(N,)h(K,)g
(ALPHA,)f(T,)i(LDT,)514 2648 y($)1097 b(X,)47 b(INCX)g(\))227
2761 y(Triangular)e(Packed:)561 2874 y(SUBROUTINE)g(BLAS_xTPMV\()g
(UPLO,)h(TRANS,)h(DIAG,)f(N,)h(ALPHA,)f(TP,)h(X,)g(INCX)g(\))227
2987 y(all:)514 3100 y(INTEGER)570 b(DIAG,)47 b(INCX,)f(K,)h(LDT,)g(N,)
g(TRANS,)f(UPLO)514 3213 y(<type>)618 b(ALPHA)514 3326
y(<type>)g(T\()48 b(LDT,)e(*)i(\))f(or)g(TP\()g(*)h(\),)f(X\()g(*)h(\))
136 3551 y FJ(\017)e FK(C)30 b(binding:)227 3776 y FD(Triangular:)227
3889 y(void)47 b(BLAS_xtrmv\()e(enum)h(blas_order_type)e(order,)i(enum)
h(blas_uplo_type)d(uplo,)1039 4002 y(enum)i(blas_trans_type)e(trans,)i
(enum)h(blas_diag_type)d(diag,)i(int)h(n,)1039 4115 y(SCALAR_IN)e
(alpha,)h(const)g(ARRAY)h(t,)g(int)g(ldt,)f(ARRAY)h(x,)g(int)g(incx)g
(\);)227 4227 y(Triangular)e(Band:)227 4340 y(void)i(BLAS_xtbmv\()e
(enum)h(blas_order_type)e(order,)i(enum)h(blas_uplo_type)d(uplo,)1039
4453 y(enum)i(blas_trans_type)e(trans,)i(enum)h(blas_diag_type)d(diag,)
i(int)h(n,)1039 4566 y(int)g(k,)g(SCALAR_IN)e(alpha,)h(const)g(ARRAY)h
(t,)g(int)g(ldt,)g(ARRAY)f(x,)1039 4679 y(int)h(incx)f(\);)227
4792 y(Triangular)f(Packed:)227 4905 y(void)i(BLAS_xtpmv\()e(enum)h
(blas_order_type)e(order,)i(enum)h(blas_uplo_type)d(uplo,)1039
5018 y(enum)i(blas_trans_type)e(trans,)i(enum)h(blas_diag_type)d(diag,)
i(int)h(n,)1039 5131 y(SCALAR_IN)e(alpha,)h(const)g(ARRAY)h(tp,)g
(ARRAY)f(x,)h(int)g(incx)g(\);)p 0 5356 3900 6 v 4084
64 a FI(1)4084 177 y(2)4084 290 y(3)4084 403 y(4)4084
516 y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084 967
y(9)4069 1080 y(10)4069 1193 y(11)4069 1306 y(12)4069
1419 y(13)4069 1532 y(14)4069 1645 y(15)4069 1758 y(16)4069
1870 y(17)4069 1983 y(18)4069 2096 y(19)4069 2209 y(20)4069
2322 y(21)4069 2435 y(22)4069 2548 y(23)4069 2661 y(24)4069
2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
3677 y(33)4069 3790 y(34)4069 3903 y(35)4069 4016 y(36)4069
4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 59 69
59 68 bop 0 -165 a FA(2.8.)72 b(LANGUA)m(GE)32 b(BINDINGS)2578
b FK(59)0 91 y(GE)p 138 91 28 4 v 33 w(SUM)p 373 91 V
33 w(MV)31 b(\(Summed)e(matrix)g(v)m(ector)j(m)m(ultiplies\))1254
b Fy(y)28 b FJ( )e Fy(\013Ax)20 b FK(+)g Fy(\014)5 b(B)g(x)141
317 y FK(This)26 b(routine)h(adds)f(the)i(pro)s(duct)e(of)i(t)m(w)m(o)h
(scaled)e(matrix)g(v)m(ector)j(pro)s(ducts.)38 b(It)28
b(can)g(b)s(e)f(used)f(to)j(compute)0 430 y(the)37 b(residual)e(of)i
(an)f(appro)m(ximate)h(eigen)m(v)m(ector)i(and)d(eigen)m(v)-5
b(alue)37 b(of)g(the)g(generalized)g(eigen)m(v)-5 b(alue)37
b(problem)0 543 y Fy(A)23 b FJ(\003)h Fy(x)32 b FK(=)g
Fy(\025)23 b FJ(\003)g Fy(B)28 b FJ(\003)23 b Fy(x)p
FK(.)53 b(If)34 b Fv(m)h FK(or)g Fv(n)f FK(is)g(less)g(than)g(or)g
(equal)g(to)i(zero,)g(then)f(this)e(routine)h(returns)f(immediately)-8
b(.)0 656 y(As)35 b(describ)s(ed)f(in)g(section)i(2.5.3,)i(the)e(v)-5
b(alue)35 b Fv(incx)g FK(or)h Fv(incy)f FK(less)g(than)g(zero)h(is)f(p)
s(ermitted.)55 b(Ho)m(w)m(ev)m(er,)39 b(if)34 b Fv(incx)0
769 y FK(or)e Fv(incy)f FK(is)g(equal)g(to)i(zero,)g(an)e(error)h
(\015ag)g(is)e(set)j(and)e(passed)g(to)h(the)g(error)f(handler.)43
b(If)31 b Fv(lda)g FK(is)g(less)g(than)h(one)0 882 y(or)j
Fv(lda)f FK(is)f(less)h(than)h Fv(m)p FK(,)h(or)f Fv(ldb)f
FK(is)g(less)g(than)g(one)h(or)g Fv(ldb)f FK(is)g(less)g(than)g
Fv(m)p FK(,)i(an)f(error)f(\015ag)h(is)f(set)h(and)f(passed)0
995 y(to)d(the)e(error)h(handler.)39 b(F)-8 b(or)30 b(the)g(C)f
(bindings)e(for)j Fv(GE)p 1889 995 V 32 w(SUM)p 2115
995 V 31 w(MV)p FK(,)g(if)e FD(order)47 b(=)g(blas)p
2999 995 29 4 v 33 w(rowmajor)28 b FK(and)h(if)g Fv(lda)g
FK(is)0 1108 y(less)g(than)h(one)h(or)f Fv(lda)f FK(is)g(less)g(than)h
Fv(n)p FK(,)h(or)f(if)f Fv(ldb)g FK(is)g(less)h(than)g(one)g(or)g
Fv(ldb)g FK(is)f(less)g(than)h Fv(n)p FK(,)g(an)g(error)g(\015ag)g(is)f
(set)0 1220 y(and)f(passed)g(to)h(the)f(error)g(handler;)g(if)f
FD(order)46 b(=)i(blas)p 1960 1220 V 33 w(colmajor)26
b FK(and)i(if)f Fv(lda)h FK(is)f(less)h(than)g(one)g(or)h
Fv(lda)e FK(is)h(less)0 1333 y(than)k Fv(m)p FK(,)h(or)f(if)f
Fv(ldb)h FK(is)f(less)h(than)g(one)g(or)h Fv(ldb)e FK(is)h(less)f(than)
h Fv(m)p FK(,)h(an)f(error)g(\015ag)h(is)e(set)i(and)e(passed)h(to)h
(the)f(error)0 1446 y(handler.)136 1634 y FJ(\017)46
b FK(F)-8 b(ortran)31 b(95)h(binding:)514 1859 y FD(SUBROUTINE)45
b(ge_sum_mv\()g(a,)i(x,)g(b,)g(y)h([,)f(alpha])f([,)h(beta])f(\))609
1972 y(<type>\(<wp>\),)e(INTENT)i(\(IN\))h(::)g(a\(:,:\),)f(b\(:,:\))
609 2085 y(<type>\(<wp>\),)e(INTENT)i(\(IN\))h(::)g(x\(:\))609
2198 y(<type>\(<wp>\),)d(INTENT)i(\(OUT\))h(::)g(y\(:\))609
2311 y(<type>\(<wp>\),)d(INTENT)i(\(IN\),)h(OPTIONAL)e(::)i(alpha,)g
(beta)514 2423 y(where)609 2536 y(x)h(has)e(shape)h(\(n\);)609
2649 y(y)h(has)e(shape)h(\(m\);)609 2762 y(a)h(and)e(b)i(have)f(shape)f
(\(m,n\))g(for)h(general)f(matrices)136 2987 y FJ(\017)g
FK(F)-8 b(ortran)31 b(77)h(binding:)514 3212 y FD(SUBROUTINE)45
b(BLAS_xGE_SUM_MV\()e(M,)k(N,)g(ALPHA,)f(A,)i(LDA,)e(X,)h(INCX,)g
(BETA,)466 3325 y($)1336 b(B,)47 b(LDB,)g(Y,)g(INCY)g(\))514
3438 y(INTEGER)570 b(INCX,)47 b(INCY,)f(LDA,)h(LDB,)f(M,)i(N)514
3551 y(<type>)618 b(ALPHA,)47 b(BETA)514 3664 y(<type>)618
b(A\()48 b(LDA,)e(*)i(\),)f(B\()g(LDB,)g(*)g(\),)g(X\()h(*)f(\),)g(Y\()
g(*)h(\))136 3889 y FJ(\017)e FK(C)30 b(binding:)227
4114 y FD(void)47 b(BLAS_xge_sum_mv\()c(enum)k(blas_order_type)d
(order,)i(int)h(m,)g(int)g(n,)1277 4227 y(SCALAR_IN)f(alpha,)g(const)g
(ARRAY)g(a,)i(int)e(lda,)1277 4340 y(const)h(ARRAY)f(x,)h(int)g(incx,)f
(SCALAR_IN)g(beta,)1277 4452 y(const)h(ARRAY)f(B,)h(int)g(ldb,)g(ARRAY)
f(y,)h(int)g(incy)g(\);)p 0 4677 3900 6 v 0 4790 a FK(GEMVT)31
b(\(Multiple)d(matrix)i(v)m(ector)i(m)m(ultiplies\))1118
b Fy(x)25 b FJ( )g Fy(\014)5 b(A)3211 4757 y Fw(T)3267
4790 y Fy(y)23 b FK(+)d Fy(z)t(;)15 b(w)28 b FJ( )d Fy(\013Ax)141
5016 y FK(The)k(routine)g(com)m(bines)g(a)h(matrix)f(v)m(ector)i(and)e
(a)h(transp)s(osed)f(matrix)g(v)m(ector)i(m)m(ultiply)-8
b(.)38 b(It)30 b(m)m(ultiplies)d(a)0 5129 y(v)m(ector)35
b Fy(y)i FK(b)m(y)c(a)h(general)g(matrix)e Fy(A)1249
5096 y Fw(T)1305 5129 y FK(,)i(scales)g(the)g(resulting)d(v)m(ector)36
b(and)d(adds)f(the)i(result)f(to)h Fy(z)t FK(,)h(storing)e(the)0
5242 y(result)i(in)g(the)h(v)m(ector)h(op)s(erand)e Fy(x)p
FK(.)58 b(It)36 b(then)f(m)m(ultiplies)e(the)j(matrix)f
Fy(A)i FK(b)m(y)e Fy(x)p FK(,)j(scales)e(the)g(resulting)e(v)m(ector)0
5355 y(and)c(stores)h(it)f(in)f(the)h(v)m(ector)i(op)s(erand)d
Fy(w)r FK(.)-214 64 y FI(1)-214 177 y(2)-214 290 y(3)-214
403 y(4)-214 516 y(5)-214 628 y(6)-214 741 y(7)-214 854
y(8)-214 967 y(9)-230 1080 y(10)-230 1193 y(11)-230 1306
y(12)-230 1419 y(13)-230 1532 y(14)-230 1645 y(15)-230
1758 y(16)-230 1870 y(17)-230 1983 y(18)-230 2096 y(19)-230
2209 y(20)-230 2322 y(21)-230 2435 y(22)-230 2548 y(23)-230
2661 y(24)-230 2774 y(25)-230 2887 y(26)-230 3000 y(27)-230
3112 y(28)-230 3225 y(29)-230 3338 y(30)-230 3451 y(31)-230
3564 y(32)-230 3677 y(33)-230 3790 y(34)-230 3903 y(35)-230
4016 y(36)-230 4129 y(37)-230 4242 y(38)-230 4354 y(39)-230
4467 y(40)-230 4580 y(41)-230 4693 y(42)-230 4806 y(43)-230
4919 y(44)-230 5032 y(45)-230 5145 y(46)-230 5258 y(47)-230
5371 y(48)p eop
%%Page: 60 70
60 69 bop 0 -165 a FK(60)1930 b FA(CHAPTER)30 b(2.)71
b(DENSE)30 b(AND)h(BANDED)h(BLAS)227 91 y Fz(A)-5 b(dvic)g(e)32
b(to)h(implementors.)83 b FK(Note)31 b(that)f Fy(x)g
FK(and)f Fy(w)k FK(ma)m(y)d(b)s(e)f(computed)h(while)e(passing)h
Fy(A)h FK(through)f(the)227 204 y(top)f(of)g(the)g(memory)g(just)f
(once.)40 b(This)26 b(optimization,)i(whic)m(h)e(accelerates)k
(algorithms)c(lik)m(e)h(reducing)g(a)227 317 y(symmetric)i(matrix)g(to)
h(tridiagonal)e(form,)h(is)g(the)g(justi\014cation)f(for)h
Fv(GEMVT)p FK(,)g(whic)m(h)f(could)h(otherwise)227 430
y(b)s(e)h(implemen)m(ted)f(b)m(y)h(t)m(w)m(o)i(calls)d(to)j
Fv(GEMV)p FK(.)d(\()p Fz(End)k(of)g(advic)-5 b(e)33 b(to)g
(implementors.)p FK(\))141 610 y(If)25 b Fv(m)h FK(or)f
Fv(n)h FK(is)e(less)h(than)g(or)h(equal)f(to)h(zero,)i(this)c(function)
h(returns)f(immediately)-8 b(.)38 b(As)25 b(describ)s(ed)f(in)g
(section)0 723 y(2.5.3,)30 b(the)e(v)-5 b(alue)27 b Fv(incx)h
FK(or)g Fv(incy)f FK(or)h Fv(incw)g FK(or)g Fv(incz)f
FK(less)g(than)g(zero)i(is)e(p)s(ermitted.)38 b(Ho)m(w)m(ev)m(er,)30
b(if)d(either)g Fv(incx)p FK(,)i Fv(incy)p FK(,)0 836
y Fv(incw)p FK(,)h(or)f Fv(incz)g FK(is)f(equal)g(to)i(zero,)h(an)e
(error)g(\015ag)g(is)f(set)i(and)e(passed)h(to)h(the)f(error)g
(handler.)38 b(If)29 b Fv(lda)g FK(is)f(less)g(than)0
949 y(one)k(or)g Fv(lda)f FK(is)f(less)h(than)h Fv(m)p
FK(,)g(an)g(error)f(\015ag)h(is)f(set)h(and)f(passed)h(to)g(the)g
(error)f(handler.)43 b(F)-8 b(or)33 b(the)f(C)f(bindings,)0
1062 y(if)g FD(order)46 b(=)i(blas)p 665 1062 29 4 v
33 w(rowmajor)29 b FK(and)i(if)g Fv(lda)g FK(is)g(less)g(than)h(one)g
(or)g Fv(lda)f FK(is)f(less)h(than)h Fv(n)p FK(,)g(an)g(error)f(\015ag)
h(is)f(set)i(and)0 1175 y(passed)26 b(to)h(the)f(error)g(handler;)g(if)
g FD(order)46 b(=)i(blas)p 1774 1175 V 33 w(colmajor)24
b FK(and)i(if)f Fv(lda)h FK(is)f(less)h(than)g(one)g(or)h
Fv(lda)e FK(is)h(less)f(than)0 1288 y Fv(m)p FK(,)31
b(an)f(error)g(\015ag)h(is)e(set)i(and)f(passed)g(to)h(the)f(error)g
(handler.)136 1468 y FJ(\017)46 b FK(F)-8 b(ortran)31
b(95)h(binding:)514 1660 y FD(SUBROUTINE)45 b(gemvt\()h(a,)h(x,)g(y,)g
(w,)g(z)h([,)f(alpha])f([,)h(beta])g(\))609 1773 y(<type>\(<wp>\),)d
(INTENT)i(\(IN\))h(::)g(a\(:,:\))609 1886 y(<type>\(<wp>\),)d(INTENT)i
(\(IN\))h(::)g(y\(:\),)g(z\(:\))609 1999 y(<type>\(<wp>\),)d(INTENT)i
(\(OUT\))h(::)g(x\(:\),)f(w\(:\))609 2112 y(<type>\(<wp>\),)e(INTENT)i
(\(IN\),)h(OPTIONAL)e(::)i(alpha,)g(beta)514 2225 y(where)609
2338 y(w)h(and)e(y)i(have)f(shape)f(\(m\);)609 2451 y(x)i(and)e(z)i
(have)f(shape)f(\(n\);)609 2564 y(a)i(has)e(shape)h(\(m,n\))f(for)h
(general)f(matrix)136 2756 y FJ(\017)g FK(F)-8 b(ortran)31
b(77)h(binding:)514 2949 y FD(SUBROUTINE)45 b(BLAS_xGEMVT\()f(M,)j(N,)g
(ALPHA,)g(A,)g(LDA,)f(X,)i(INCX,)e(Y,)h(INCY,)466 3062
y($)1145 b(BETA,)46 b(W,)i(INCW,)e(Z,)h(INCZ)g(\))514
3174 y(INTEGER)570 b(INCW,)47 b(INCX,)f(INCY,)h(INCZ,)f(LDA,)h(M,)g(N)
514 3287 y(<type>)618 b(ALPHA,)47 b(BETA)514 3400 y(<type>)618
b(A\()48 b(LDA,)e(*)i(\),)f(X\()g(*)h(\),)f(Y\()g(*)g(\),)h(W\()f(*)g
(\),)g(Z\()h(*)f(\))136 3593 y FJ(\017)f FK(C)30 b(binding:)227
3785 y FD(void)47 b(BLAS_xgemvt\()d(enum)j(blas_order_type)d(order,)i
(int)h(m,)g(int)g(n,)g(SCALAR_IN)e(alpha,)1086 3898 y(const)i(ARRAY)f
(a,)h(int)g(lda,)g(ARRAY)f(x,)h(int)g(incx,)g(const)f(ARRAY)g(y,)1086
4011 y(int)h(incy,)g(SCALAR_IN)e(beta,)h(ARRAY)h(w,)g(int)g(incw,)f
(const)g(ARRAY)h(z,)1086 4124 y(int)g(incz)g(\);)p 0
4317 3900 6 v 0 4430 a FK(TRMVT)30 b(\(Multiple)f(triangular)f(matrix)i
(v)m(ector)i(pro)s(duct\))888 b Fy(x)25 b FJ( )g Fy(T)3269
4397 y Fw(T)3324 4430 y Fy(y)33 b FK(and)d Fy(w)e FJ( )d
Fy(T)13 b(z)141 4655 y FK(The)34 b(routine)g(com)m(bines)g(a)i(matrix)e
(v)m(ector)i(and)e(a)h(transp)s(osed)f(matrix)g(v)m(ector)j(m)m
(ultiply)-8 b(.)51 b(It)35 b(m)m(ultiplies)0 4768 y(a)d(v)m(ector)h
Fy(y)i FK(b)m(y)d(a)g(triangular)e(matrix)h Fy(T)1425
4735 y Fw(T)1480 4768 y FK(,)h(storing)f(the)h(result)f(as)g
Fy(x)p FK(.)45 b(It)32 b(also)g(m)m(ultiplies)c(the)k(matrix)f(b)m(y)h
(the)0 4881 y(v)m(ector)g Fy(z)t FK(,)f(storing)f(the)g(result)f(as)i
Fy(w)r FK(.)227 5061 y Fz(A)-5 b(dvic)g(e)33 b(to)f(implementors.)83
b FK(Note)31 b(that)g Fy(x)f FK(and)f Fy(w)k FK(ma)m(y)e(b)s(e)e
(computed)h(while)e(passing)h Fy(T)42 b FK(through)30
b(the)227 5174 y(top)e(of)g(the)g(memory)g(just)f(once.)40
b(This)26 b(optimization,)i(whic)m(h)e(accelerates)k(algorithms)c(lik)m
(e)h(reducing)g(a)227 5287 y(symmetric)i(matrix)f(to)h(tridiagonal)f
(form,)h(is)f(the)h(justi\014cation)e(for)i Fv(TRMVT)p
FK(,)f(whic)m(h)g(could)g(otherwise)227 5400 y(b)s(e)i(implemen)m(ted)f
(b)m(y)h(t)m(w)m(o)i(calls)d(to)j Fv(TRMV)p FK(.)d(\()p
Fz(End)k(of)g(advic)-5 b(e)33 b(to)g(implementors.)p
FK(\))4084 64 y FI(1)4084 177 y(2)4084 290 y(3)4084 403
y(4)4084 516 y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084
967 y(9)4069 1080 y(10)4069 1193 y(11)4069 1306 y(12)4069
1419 y(13)4069 1532 y(14)4069 1645 y(15)4069 1758 y(16)4069
1870 y(17)4069 1983 y(18)4069 2096 y(19)4069 2209 y(20)4069
2322 y(21)4069 2435 y(22)4069 2548 y(23)4069 2661 y(24)4069
2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
3677 y(33)4069 3790 y(34)4069 3903 y(35)4069 4016 y(36)4069
4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 61 71
61 70 bop 0 -165 a FA(2.8.)72 b(LANGUA)m(GE)32 b(BINDINGS)2578
b FK(61)141 91 y(If)37 b Fv(n)h FK(is)e(less)h(than)g(or)h(equal)f(to)h
(zero,)j(this)36 b(function)g(returns)h(immediately)-8
b(.)61 b(As)37 b(describ)s(ed)f(in)g(section)0 204 y(2.5.3,)30
b(the)e(v)-5 b(alue)27 b Fv(incx)h FK(or)g Fv(incy)f
FK(or)h Fv(incw)g FK(or)g Fv(incz)f FK(less)g(than)g(zero)i(is)e(p)s
(ermitted.)38 b(Ho)m(w)m(ev)m(er,)30 b(if)d(either)g
Fv(incx)p FK(,)i Fv(incy)p FK(,)0 317 y Fv(incw)p FK(,)h(or)g
Fv(incz)f FK(is)g(equal)g(to)h(zero,)h(an)f(error)f(\015ag)h(is)f(set)h
(and)f(passed)g(to)h(the)g(error)g(handler.)38 b(If)29
b Fv(ldt)h FK(is)e(less)h(than)0 430 y(one)i(or)f Fv(ldt)g
FK(is)f(less)h(than)g Fv(n)p FK(,)h(an)f(error)g(\015ag)h(is)e(set)i
(and)f(passed)g(to)h(the)f(error)g(handler.)136 639 y
FJ(\017)46 b FK(F)-8 b(ortran)31 b(95)h(binding:)514
885 y FD(SUBROUTINE)45 b(trmvt\()h(t,)h(x,)g(y,)g(w,)g(z)h([,)f(uplo])f
(\))609 998 y(<type>\(<wp>\),)e(INTENT)i(\(IN\))h(::)g(t\(:,:\))609
1111 y(<type>\(<wp>\),)d(INTENT)i(\(IN\))h(::)g(y\(:\),)g(z\(:\))609
1223 y(<type>\(<wp>\),)d(INTENT)i(\(OUT\))h(::)g(x\(:\),)f(w\(:\))609
1336 y(TYPE)h(\(blas_uplo_type\),)c(INTENT)j(\(IN\),)g(OPTIONAL)g(::)h
(uplo)514 1449 y(where)609 1562 y(w,)g(x,)g(y)h(and)f(z)g(have)g(shape)
f(\(n\);)609 1675 y(t)i(has)e(shape)h(\(n,n\).)136 1921
y FJ(\017)f FK(F)-8 b(ortran)31 b(77)h(binding:)561 2142
y FD(SUBROUTINE)45 b(BLAS_xTRMVT\()g(UPLO,)h(N,)h(T,)h(LDT,)e(X,)h
(INCX,)g(Y,)g(INCY,)f(W,)h(INCW,)514 2255 y($)1145 b(Z,)47
b(INCZ)g(\))561 2368 y(INTEGER)571 b(INCW,)47 b(INCX,)f(INCY,)g(INCZ,)h
(LDT,)f(N,)h(UPLO)561 2481 y(<type>)619 b(T\()47 b(LDT,)g(*)g(\),)h
(W\()f(*)g(\),)g(X\()h(*)f(\),)g(Y\()g(*)h(\),)f(Z\()g(*)h(\))136
2702 y FJ(\017)e FK(C)30 b(binding:)227 2924 y FD(void)47
b(BLAS_xtrmvt\()d(enum)j(blas_order_type)d(order,)i(enum)g
(blas_uplo_type)e(uplo,)1086 3037 y(int)j(n,)g(const)g(ARRAY)f(t,)h
(int)g(ldt,)g(ARRAY)f(x,)h(int)g(incx,)1086 3149 y(const)g(ARRAY)f(y,)h
(int)g(incy,)g(ARRAY)f(w,)h(int)g(incw,)f(const)h(ARRAY)f(z,)1086
3262 y(int)h(incz)g(\);)p 0 3484 3900 6 v 0 3597 a FK(GEMVER)31
b(\(Multiple)d(matrix)i(v)m(ector)i(m)m(ultiply)c(with)h(a)h(rank)g(2)h
(up)s(date\))1657 3758 y(^)1633 3781 y Fy(A)25 b FJ( )g
Fy(A)c FK(+)e Fy(u)2073 3795 y FC(1)2113 3781 y Fy(v)2160
3748 y Fw(T)2157 3804 y FC(1)2236 3781 y FK(+)g Fy(u)2378
3795 y FC(2)2418 3781 y Fy(v)2465 3748 y Fw(T)2462 3804
y FC(2)2551 3781 y FK(and)29 b Fy(x)d FJ( )f Fy(\014)3001
3758 y FK(^)2977 3781 y Fy(A)3045 3748 y Fw(T)3100 3781
y Fy(y)e FK(+)d Fy(z)35 b FK(and)29 b Fy(w)f FJ( )d Fy(\013)3804
3758 y FK(^)3779 3781 y Fy(A)q(x)141 3966 y FK(The)32
b(routine)f(precedes)i(a)g(com)m(bined)e(matrix)h(v)m(ector)i(and)e(a)h
(transp)s(osed)e(matrix)h(v)m(ector)i(m)m(ultiply)29
b(b)m(y)k(a)0 4079 y(rank)28 b(t)m(w)m(o)i(up)s(date.)40
b(A)29 b(matrix)f Fy(A)g FK(is)g(up)s(dated)g(b)m(y)g
Fy(u)1827 4093 y FC(1)1867 4079 y Fy(v)1914 4046 y Fw(T)1911
4102 y FC(1)1998 4079 y FK(and)g Fy(u)2225 4093 y FC(2)2264
4079 y Fy(v)2311 4046 y Fw(T)2308 4102 y FC(2)2367 4079
y FK(.)40 b(The)28 b(transp)s(ose)g(of)h(the)g(up)s(dated)f(matrix)0
4192 y(is)i(m)m(ultiplied)d(b)m(y)k(a)g(v)m(ector)i Fy(y)s
FK(.)42 b(The)30 b(resulting)f(v)m(ector)j(is)e(scaled)h(and)f(added)g
(to)i(the)f(v)m(ector)h(op)s(erand)e Fy(z)t FK(,)i(and)0
4305 y(stored)e(in)f Fy(x)h FK(.)41 b(The)30 b(op)s(erand)f
Fy(x)h FK(is)f(m)m(ultiplied)e(b)m(y)j(the)g(up)s(dated)f(matrix)g
Fy(A)p FK(.)41 b(The)30 b(resulting)e(v)m(ector)k(is)d(scaled)0
4418 y(and)h(stored)g(as)h Fy(w)r FK(.)227 4627 y Fz(A)-5
b(dvic)g(e)25 b(to)g(implementors.)77 b FK(Note)24 b(that)1671
4604 y(^)1647 4627 y Fy(A)p FK(,)g Fy(x)e FK(and)f Fy(w)j
FK(ma)m(y)e(b)s(e)g(computed)f(while)f(passing)h Fy(A)h
FK(through)f(the)227 4739 y(top)34 b(of)g(the)f(memory)g(just)g(once.)
51 b(This)31 b(optimization,)j(whic)m(h)e(accelerates)j(algorithms)e
(lik)m(e)f(reducing)227 4852 y(a)g(general)f(matrix)g(to)h(bidiagonal)d
(form,)i(is)f(the)i(justi\014cation)e(for)h Fv(GEMVER)p
FK(,)f(whic)m(h)g(could)h(otherwise)227 4965 y(b)s(e)f(implemen)m(ted)f
(b)m(y)h(calls)g(to)h(other)f(BLAS)h(routines.)39 b(\()p
Fz(End)33 b(of)g(advic)-5 b(e)33 b(to)h(implementors.)p
FK(\))141 5174 y(If)25 b Fv(m)h FK(or)f Fv(n)h FK(is)e(less)h(than)g
(or)h(equal)f(to)h(zero,)i(this)c(function)h(returns)f(immediately)-8
b(.)38 b(As)25 b(describ)s(ed)f(in)g(section)0 5287 y(2.5.3,)30
b(the)e(v)-5 b(alue)27 b Fv(incx)h FK(or)g Fv(incy)f
FK(or)h Fv(incw)g FK(or)g Fv(incz)f FK(less)g(than)g(zero)i(is)e(p)s
(ermitted.)38 b(Ho)m(w)m(ev)m(er,)30 b(if)d(either)g
Fv(incx)p FK(,)i Fv(incy)p FK(,)0 5400 y Fv(incw)p FK(,)h(or)f
Fv(incz)g FK(is)f(equal)g(to)i(zero,)h(an)e(error)g(\015ag)g(is)f(set)i
(and)e(passed)h(to)h(the)f(error)g(handler.)38 b(If)29
b Fv(lda)g FK(is)f(less)g(than)-214 64 y FI(1)-214 177
y(2)-214 290 y(3)-214 403 y(4)-214 516 y(5)-214 628 y(6)-214
741 y(7)-214 854 y(8)-214 967 y(9)-230 1080 y(10)-230
1193 y(11)-230 1306 y(12)-230 1419 y(13)-230 1532 y(14)-230
1645 y(15)-230 1758 y(16)-230 1870 y(17)-230 1983 y(18)-230
2096 y(19)-230 2209 y(20)-230 2322 y(21)-230 2435 y(22)-230
2548 y(23)-230 2661 y(24)-230 2774 y(25)-230 2887 y(26)-230
3000 y(27)-230 3112 y(28)-230 3225 y(29)-230 3338 y(30)-230
3451 y(31)-230 3564 y(32)-230 3677 y(33)-230 3790 y(34)-230
3903 y(35)-230 4016 y(36)-230 4129 y(37)-230 4242 y(38)-230
4354 y(39)-230 4467 y(40)-230 4580 y(41)-230 4693 y(42)-230
4806 y(43)-230 4919 y(44)-230 5032 y(45)-230 5145 y(46)-230
5258 y(47)-230 5371 y(48)p eop
%%Page: 62 72
62 71 bop 0 -165 a FK(62)1930 b FA(CHAPTER)30 b(2.)71
b(DENSE)30 b(AND)h(BANDED)h(BLAS)0 91 y FK(one)g(or)g
Fv(lda)f FK(is)f(less)h(than)h Fv(m)p FK(,)g(an)g(error)f(\015ag)h(is)f
(set)h(and)f(passed)h(to)g(the)g(error)f(handler.)43
b(F)-8 b(or)33 b(the)f(C)f(bindings,)0 204 y(if)g FD(order)46
b(=)i(blas)p 665 204 29 4 v 33 w(rowmajor)29 b FK(and)i(if)g
Fv(lda)g FK(is)g(less)g(than)h(one)g(or)g Fv(lda)f FK(is)f(less)h(than)
h Fv(n)p FK(,)g(an)g(error)f(\015ag)h(is)f(set)i(and)0
317 y(passed)26 b(to)h(the)f(error)g(handler;)g(if)g
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Fv(lda)e FK(is)h(less)f(than)0 430 y Fv(m)p FK(,)31 b(an)f(error)g
(\015ag)h(is)e(set)i(and)f(passed)g(to)h(the)f(error)g(handler.)136
643 y FJ(\017)46 b FK(F)-8 b(ortran)31 b(95)h(binding:)514
892 y FD(SUBROUTINE)45 b(gemver\()g(a,)j(u1,)f(v1,)f(u2,)h(v2,)g(x,)g
(y,)h(z,)f(w)g([,)g(alpha])g([,)g(beta])f(\))609 1005
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(INTENT)i(\(INOUT\))g(::)h(a\(:,:\),)f(x\(:\))609 1231
y(<type>\(<wp>\),)e(INTENT)i(\(OUT\))h(::)g(w\(:\))609
1344 y(<type>\(<wp>\),)d(INTENT)i(\(IN\),)h(OPTIONAL)e(::)i(alpha,)g
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(\(n\);)609 1796 y(a)h(has)e(shape)h(\(m,n\).)136 2046
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514 2609 y(INTEGER)570 b(INCW,)47 b(INCX,)f(INCY,)h(INCZ,)f(LDA,)h(M,)g
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y(<type>)618 b(U1\()47 b(*)h(\),)f(V1\()g(*)g(\),)h(U2\()e(*)i(\),)f
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4301 y Fy(x)p FK(,)31 b Fy(x)25 b FJ( )g Fy(\013T)3738
4268 y Fu(\000)p Fw(T)3848 4301 y Fy(x)141 4526 y FK(These)35
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4526 y Fy(x)h FK(or)h Fy(x)d FJ( )g Fy(\013T)3260 4493
y Fu(\000)p Fw(T)3370 4526 y Fy(x)p FK(,)k(where)e Fy(x)g
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Fv(n)g FK(is)e(less)i(than)f(or)h(equal)f(to)i(zero,)g(this)e(function)
f(returns)h(immediately)-8 b(.)39 b(As)0 4865 y(describ)s(ed)33
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b(F)-8 b(or)31 b Fv(TRSV)p FK(,)f(if)f Fv(ldt)h FK(is)f(less)h(than)g
(one)h(or)f Fv(ldt)g FK(is)0 5091 y(less)e(than)g Fv(n)p
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(error)f(handler.)38 b(F)-8 b(or)29 b Fv(TBSV)p FK(,)e(if)g
Fv(ldt)h FK(is)g(less)f(than)h(one)h(or)0 5204 y Fv(ldt)h
FK(is)f(less)h(than)g Fv(k)h FK(plus)d(one,)j(an)f(error)g(\015ag)h(is)
e(set)i(and)f(passed)g(to)h(the)g(error)f(handler.)4084
64 y FI(1)4084 177 y(2)4084 290 y(3)4084 403 y(4)4084
516 y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084 967
y(9)4069 1080 y(10)4069 1193 y(11)4069 1306 y(12)4069
1419 y(13)4069 1532 y(14)4069 1645 y(15)4069 1758 y(16)4069
1870 y(17)4069 1983 y(18)4069 2096 y(19)4069 2209 y(20)4069
2322 y(21)4069 2435 y(22)4069 2548 y(23)4069 2661 y(24)4069
2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
3677 y(33)4069 3790 y(34)4069 3903 y(35)4069 4016 y(36)4069
4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 63 73
63 72 bop 0 -165 a FA(2.8.)72 b(LANGUA)m(GE)32 b(BINDINGS)2578
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204 y(for)24 b(these)g(triangular)f(equation-solving)f(routines.)38
b(The)23 b(requiremen)m(ts)g(for)h(suc)m(h)g(a)g(test)h(dep)s(end)d(on)
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FK(\))136 634 y FJ(\017)46 b FK(F)-8 b(ortran)31 b(95)h(binding:)227
850 y FD(Triangular)45 b(Band:)418 963 y(SUBROUTINE)g(tbsv\()i(t,)g(x)g
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1076 y(Triangular)f(Packed:)418 1189 y(SUBROUTINE)g(tpsv\()i(tp,)f(x)i
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1302 y(all:)514 1415 y(<type>\(<wp>\),)d(INTENT\(IN\))h(::)i(<tt>)514
1528 y(<type>\(<wp>\),)d(INTENT\(INOUT\))g(::)j(x\(:\))514
1640 y(TYPE)f(\(blas_uplo_type\),)d(INTENT\(IN\),)i(OPTIONAL)h(::)h
(uplo)514 1753 y(TYPE)f(\(blas_trans_type\),)d(INTENT\(IN\),)i
(OPTIONAL)g(::)j(trans)514 1866 y(TYPE)e(\(blas_diag_type\),)d
(INTENT\(IN\),)i(OPTIONAL)h(::)h(diag)514 1979 y(<type>\(<wp>\),)d
(INTENT\(IN\),)h(OPTIONAL)g(::)i(alpha)418 2092 y(where)514
2205 y(<tt>)94 b(::=)47 b(t\(:,:\))f(or)h(tp\(:\))418
2318 y(and)514 2431 y(x)g(has)g(shape)f(\(n\))514 2544
y(TB)95 b(t)47 b(has)g(shape)f(\(k+1,n\))514 2657 y(TP)95
b(tp)47 b(has)g(shape)f(\(n*\(n+1\)/2\))418 2770 y(\(k=band)g(width\))
227 2986 y FK(The)30 b(fun)m(tionalit)m(y)f(of)i Fv(trsv)f
FK(is)f(co)m(v)m(ered)j(b)m(y)e Fv(trsm)p FK(.)136 3171
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3387 y FD(Triangular:)561 3500 y(SUBROUTINE)45 b(BLAS_xTRSV\()g(UPLO,)h
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(ALPHA,)f(T,)i(LDT,)514 3951 y($)1097 b(X,)47 b(INCX)g(\))227
4064 y(Triangular)e(Packed:)561 4177 y(SUBROUTINE)g(BLAS_xTPSV\()g
(UPLO,)h(TRANS,)h(DIAG,)f(N,)h(ALPHA,)f(TP,)h(X,)g(INCX)g(\))227
4290 y(all:)514 4403 y(INTEGER)570 b(DIAG,)47 b(INCX,)f(K,)h(LDT,)g(N,)
g(TRANS,)f(UPLO)514 4516 y(<type>)618 b(ALPHA)514 4629
y(<type>)g(T\()48 b(LDT,)e(*)i(\))f(or)g(TP\()g(*)h(\),)f(X\()g(*)h(\))
136 4845 y FJ(\017)e FK(C)30 b(binding:)227 5061 y FD(Triangular:)227
5174 y(void)47 b(BLAS_xtrsv\()e(enum)h(blas_order_type)e(order,)i(enum)
h(blas_uplo_type)d(uplo,)1039 5287 y(enum)i(blas_trans_type)e(trans,)i
(enum)h(blas_diag_type)d(diag,)1039 5400 y(int)j(n,)g(SCALAR_IN)e
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177 y(2)-214 290 y(3)-214 403 y(4)-214 516 y(5)-214 628
y(6)-214 741 y(7)-214 854 y(8)-214 967 y(9)-230 1080
y(10)-230 1193 y(11)-230 1306 y(12)-230 1419 y(13)-230
1532 y(14)-230 1645 y(15)-230 1758 y(16)-230 1870 y(17)-230
1983 y(18)-230 2096 y(19)-230 2209 y(20)-230 2322 y(21)-230
2435 y(22)-230 2548 y(23)-230 2661 y(24)-230 2774 y(25)-230
2887 y(26)-230 3000 y(27)-230 3112 y(28)-230 3225 y(29)-230
3338 y(30)-230 3451 y(31)-230 3564 y(32)-230 3677 y(33)-230
3790 y(34)-230 3903 y(35)-230 4016 y(36)-230 4129 y(37)-230
4242 y(38)-230 4354 y(39)-230 4467 y(40)-230 4580 y(41)-230
4693 y(42)-230 4806 y(43)-230 4919 y(44)-230 5032 y(45)-230
5145 y(46)-230 5258 y(47)-230 5371 y(48)p eop
%%Page: 64 74
64 73 bop 0 -165 a FK(64)1930 b FA(CHAPTER)30 b(2.)71
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656 y(ARRAY)f(x,)h(int)g(incx)g(\);)227 769 y(Triangular)e(Packed:)227
882 y(void)i(BLAS_xtpsv\()e(enum)h(blas_order_type)e(order,)i(enum)h
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(alpha,)h(const)g(ARRAY)h(tp,)g(ARRAY)f(x,)1039 1220
y(int)h(incx)f(\);)p 0 1437 3900 6 v 0 1550 a FK(GER)30
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b(R)1275 1514 y Fw(n)1318 1490 y FI(2)1357 1550 y Fy(;)15
b(A)25 b FJ( )h Fy(\013xy)1765 1517 y Fw(T)1838 1550
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1513 y Fw(n)2359 1489 y FI(2)2398 1550 y Fy(;)15 b(A)26
b FJ( )f Fy(\013xy)2806 1517 y Fw(T)2880 1550 y FK(+)18
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1517 y Fw(H)3686 1550 y FK(+)19 b Fy(\014)5 b(A)141 1775
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Fy(A)c FJ( )f Fy(\013xy)2261 1742 y Fw(T)2337 1775 y
FK(+)20 b Fy(\014)5 b(A)31 b FK(where)f Fy(\013)h FK(and)f
Fy(\014)36 b FK(are)31 b(scalars,)g Fy(x)g FK(and)0 1888
y Fy(y)36 b FK(are)d(v)m(ectors,)j(and)c(and)h Fy(A)g
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FK(is)f(less)g(than)h(or)g(equal)g(to)h(zero)g(or)f(if)f
Fv(b)s(eta)g FK(is)h(equal)f(to)0 2001 y(one)37 b(and)f
Fv(alpha)g FK(is)g(equal)h(to)g(zero,)j(this)c(function)f(returns)h
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2114 y(the)d(v)-5 b(alue)34 b Fv(incx)g FK(or)g Fv(incy)g
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b(if)c(either)h Fv(incx)g FK(or)g Fv(incy)g FK(is)f(equal)g(to)i(zero,)
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f Fv(lda)g FK(is)g(less)g(than)g Fv(m)p FK(,)h(an)0 2340
y(error)j(\015ag)h(is)f(set)h(and)f(passed)h(to)g(the)g(error)f
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y(if)f FD(order)47 b(=)g(blas)p 663 2566 V 34 w(colmajor)28
b FK(and)i(if)f Fv(lda)h FK(is)g(less)f(than)i(one)g(or)f
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(set)j(and)0 2679 y(passed)e(to)h(the)g(error)f(handler.)141
2792 y(The)e(op)s(erator)g(argumen)m(t)h Fv(conj)g FK(is)f(only)f
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(ectors.)41 b(When)28 b Fy(x)h FK(and)0 2904 y Fy(y)k
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FJ(\017)46 b FK(F)-8 b(ortran)31 b(77)h(binding:)561
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y FD(void)47 b(BLAS_xger\()e(enum)i(blas_order_type)c(order,)j(enum)h
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5400 y Fy(x)32 b FK(is)f(a)h(v)m(ector)h(and)f Fy(A)g
FK(is)e(a)j(symmetric)e(\(symmetric)g(pac)m(k)m(ed\))j(matrix.)44
b(This)30 b(routine)h(returns)g(immediately)4084 64 y
FI(1)4084 177 y(2)4084 290 y(3)4084 403 y(4)4084 516
y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084 967 y(9)4069
1080 y(10)4069 1193 y(11)4069 1306 y(12)4069 1419 y(13)4069
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2435 y(22)4069 2548 y(23)4069 2661 y(24)4069 2774 y(25)4069
2887 y(26)4069 3000 y(27)4069 3112 y(28)4069 3225 y(29)4069
3338 y(30)4069 3451 y(31)4069 3564 y(32)4069 3677 y(33)4069
3790 y(34)4069 3903 y(35)4069 4016 y(36)4069 4129 y(37)4069
4242 y(38)4069 4354 y(39)4069 4467 y(40)4069 4580 y(41)4069
4693 y(42)4069 4806 y(43)4069 4919 y(44)4069 5032 y(45)4069
5145 y(46)4069 5258 y(47)4069 5371 y(48)p eop
%%Page: 65 75
65 74 bop 0 -165 a FA(2.8.)72 b(LANGUA)m(GE)32 b(BINDINGS)2578
b FK(65)0 91 y(if)26 b Fv(n)h FK(is)f(less)g(than)h(or)g(equal)f(to)i
(zero)g(or)f(if)f Fv(b)s(eta)g FK(is)g(equal)h(to)g(one)g(and)g
Fv(alpha)f FK(is)g(equal)g(to)i(zero.)40 b(As)27 b(describ)s(ed)e(in)0
204 y(section)32 b(2.5.3,)i(the)e(v)-5 b(alue)31 b Fv(incx)g
FK(less)g(than)g(zero)i(is)d(p)s(ermitted.)43 b(Ho)m(w)m(ev)m(er,)35
b(if)30 b Fv(incx)i FK(is)e(equal)i(to)g(zero,)h(an)e(error)0
317 y(\015ag)f(is)f(set)h(and)f(passed)g(to)i(the)f(error)f(handler.)39
b(If)29 b Fv(lda)g FK(is)f(less)h(than)h(one)g(or)g Fv(lda)f
FK(is)f(less)h(than)h Fv(n)p FK(,)g(an)f(error)h(\015ag)0
430 y(is)f(set)i(and)f(passed)g(to)h(the)g(error)f(handler.)141
543 y(These)20 b(in)m(terfaces)h(encompass)g(the)g(Legacy)h(BLAS)e
(routines)g(xSYR)g(and)g(xSPR)f(with)h(added)f(functionalit)m(y)0
656 y(for)30 b(complex)g(symmetric)g(matrices.)136 861
y FJ(\017)46 b FK(F)-8 b(ortran)31 b(95)h(binding:)227
1079 y FD(Symmetric)46 b(Packed:)418 1191 y(SUBROUTINE)f(spr\()i(x,)g
(ap)g([,)g(uplo])g([,)g(trans])f([,)h(alpha])f([,)h(beta])g(\))514
1304 y(<type>\(<wp>\),)d(INTENT\(IN\))h(::)i(x\(:\))514
1417 y(<type>\(<wp>\),)d(INTENT\(INOUT\))g(::)j(ap\(:\))514
1530 y(TYPE)f(\(blas_uplo_type\),)d(INTENT\(IN\),)i(OPTIONAL)h(::)h
(uplo)514 1643 y(TYPE)f(\(blas_trans_type\),)d(INTENT\(IN\),)i
(OPTIONAL)g(::)j(trans)514 1756 y(<type>\(<wp>\),)c(INTENT\(IN\),)h
(OPTIONAL)g(::)i(alpha,)f(beta)418 1869 y(where)466 1982
y(x)h(has)g(shape)g(\(n\))466 2095 y(ap)g(has)g(shape)f
(\(n*\(n+1\)/2\))227 2312 y FK(The)30 b(functionalit)m(y)f(of)i
Fv(syr)f FK(is)f(co)m(v)m(ered)j(b)m(y)e Fv(syrk)p FK(.)136
2497 y FJ(\017)46 b FK(F)-8 b(ortran)31 b(77)h(binding:)227
2715 y FD(Symmetric:)514 2828 y(SUBROUTINE)45 b(BLAS_xSYR\()g(UPLO,)h
(N,)h(ALPHA,)f(X,)h(INCX,)g(BETA,)f(A,)h(LDA)g(\))227
2941 y(Symmetric)f(Packed:)514 3054 y(SUBROUTINE)f(BLAS_xSPR\()g(UPLO,)
h(N,)h(ALPHA,)f(X,)h(INCX,)g(BETA,)f(AP)h(\))227 3167
y(all:)514 3280 y(INTEGER)570 b(INCX,)47 b(LDA,)f(N,)i(UPLO)514
3392 y(<type>)618 b(ALPHA,)47 b(BETA)514 3505 y(<type>)618
b(A\()48 b(LDA,)e(*)i(\))f(or)g(AP\()g(*)h(\),)f(X\()g(*)h(\))136
3723 y FJ(\017)e FK(C)30 b(binding:)227 3940 y FD(Symmetric:)227
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(blas_uplo_type)d(uplo,)991 4166 y(int)j(n,)g(SCALAR_IN)e(alpha,)h
(const)h(ARRAY)f(x,)h(int)g(incx,)991 4279 y(SCALAR_IN)e(beta,)i(ARRAY)
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(const)h(ARRAY)f(x,)h(int)g(incx,)991 4731 y(SCALAR_IN)e(beta,)i(ARRAY)
f(ap)h(\);)p 0 4948 3900 6 v 0 5061 a FJ(f)p FK(HE,HP)p
FJ(g)p FK(R)31 b(\(Hermitian)f(Rank)g(One)g(Up)s(date\))961
b Fy(A)25 b FJ( )h Fy(\013xx)3035 5028 y Fw(H)3123 5061
y FK(+)19 b Fy(\014)5 b(A)31 b FK(with)e Fy(A)d FK(=)f
Fy(A)3833 5028 y Fw(H)141 5287 y FK(The)34 b(routine)g(p)s(erforms)f
(the)i(Hermitian)e(rank-1)i(up)s(date)e Fy(A)g FK(=)f
Fy(\013xx)2596 5254 y Fw(H)2687 5287 y FK(+)22 b Fy(\014)5
b(A)p FK(,)36 b(where)f Fy(\013)g FK(and)f Fy(\014)39
b FK(are)c(real)0 5400 y(scalars,)25 b Fy(x)d FK(is)g(a)i(complex)f(v)m
(ector)h(and)f Fy(A)g FK(is)f(a)h(Hermitian)f(\(Hermitian)g(pac)m(k)m
(ed\))i(matrix.)38 b(This)21 b(routine)h(returns)-214
64 y FI(1)-214 177 y(2)-214 290 y(3)-214 403 y(4)-214
516 y(5)-214 628 y(6)-214 741 y(7)-214 854 y(8)-214 967
y(9)-230 1080 y(10)-230 1193 y(11)-230 1306 y(12)-230
1419 y(13)-230 1532 y(14)-230 1645 y(15)-230 1758 y(16)-230
1870 y(17)-230 1983 y(18)-230 2096 y(19)-230 2209 y(20)-230
2322 y(21)-230 2435 y(22)-230 2548 y(23)-230 2661 y(24)-230
2774 y(25)-230 2887 y(26)-230 3000 y(27)-230 3112 y(28)-230
3225 y(29)-230 3338 y(30)-230 3451 y(31)-230 3564 y(32)-230
3677 y(33)-230 3790 y(34)-230 3903 y(35)-230 4016 y(36)-230
4129 y(37)-230 4242 y(38)-230 4354 y(39)-230 4467 y(40)-230
4580 y(41)-230 4693 y(42)-230 4806 y(43)-230 4919 y(44)-230
5032 y(45)-230 5145 y(46)-230 5258 y(47)-230 5371 y(48)p
eop
%%Page: 66 76
66 75 bop 0 -165 a FK(66)1930 b FA(CHAPTER)30 b(2.)71
b(DENSE)30 b(AND)h(BANDED)h(BLAS)0 91 y FK(immediately)f(if)h
Fv(n)h FK(is)f(less)g(than)h(or)g(equal)f(to)i(zero)f(or)g(if)f
Fv(b)s(eta)g FK(is)g(equal)h(to)g(one)h(and)e Fv(alpha)g
FK(is)g(equal)g(to)i(zero.)0 204 y(As)27 b(describ)s(ed)f(in)g(section)
h(2.5.3,)j(the)e(v)-5 b(alue)27 b Fv(incx)g FK(less)g(than)g(zero)h(is)
f(p)s(ermitted.)38 b(Ho)m(w)m(ev)m(er,)30 b(if)d Fv(incx)g
FK(is)f(equal)h(to)0 317 y(zero,)34 b(an)e(error)f(\015ag)i(is)e(set)h
(and)g(passed)g(to)g(the)h(error)e(handler.)44 b(If)32
b Fv(lda)f FK(is)h(less)f(than)h(one)g(or)g Fv(lda)g
FK(is)f(less)g(than)0 430 y Fv(n)p FK(,)g(an)f(error)g(\015ag)g(is)g
(set)h(and)f(passed)f(to)j(the)e(error)g(handler.)136
635 y FJ(\017)46 b FK(F)-8 b(ortran)31 b(95)h(binding:)227
853 y FD(Hermitian)46 b(Packed:)418 966 y(SUBROUTINE)f(hpr\()i(x,)g(ap)
g([,)g(uplo])g([,)g(trans])f([,)h(alpha])f([,)h(beta])g(\))514
1079 y(COMPLEX\(<wp>\),)d(INTENT\(IN\))h(::)i(x\(:\))514
1191 y(COMPLEX\(<wp>\),)d(INTENT\(INOUT\))g(::)j(ap\(:\))514
1304 y(TYPE)f(\(blas_uplo_type\),)d(INTENT\(IN\),)i(OPTIONAL)h(::)h
(uplo)514 1417 y(TYPE)f(\(blas_trans_type\),)d(INTENT\(IN\),)i
(OPTIONAL)g(::)j(trans)514 1530 y(REAL\(<wp>\),)c(INTENT\(IN\),)h
(OPTIONAL)h(::)h(alpha,)f(beta)418 1643 y(where)466 1756
y(x)h(has)g(shape)g(\(n\))466 1869 y(ap)g(has)g(shape)f
(\(n*\(n+1\)/2\))227 2086 y FK(The)30 b(functionalit)m(y)f(of)i
Fv(her)f FK(is)g(co)m(v)m(ered)i(b)m(y)e Fv(herk)p FK(.)136
2272 y FJ(\017)46 b FK(F)-8 b(ortran)31 b(77)h(binding:)227
2489 y FD(Hermitian:)514 2602 y(SUBROUTINE)45 b(BLAS_xHER\()g(UPLO,)h
(N,)h(ALPHA,)f(X,)h(INCX,)g(BETA,)f(A,)h(LDA)g(\))227
2715 y(Hermitian)f(Packed:)514 2828 y(SUBROUTINE)f(BLAS_xHPR\()g(UPLO,)
h(N,)h(ALPHA,)f(X,)h(INCX,)g(BETA,)f(AP)h(\))227 2941
y(all:)514 3054 y(INTEGER)570 b(INCX,)47 b(LDA,)f(N,)i(UPLO)514
3167 y(<rtype>)570 b(ALPHA,)47 b(BETA)514 3280 y(<ctype>)570
b(A\()48 b(LDA,)e(*)i(\))f(or)g(AP\()g(*)h(\),)f(X\()g(*)h(\))136
3497 y FJ(\017)e FK(C)30 b(binding:)227 3715 y FD(Hermitian:)227
3828 y(void)47 b(BLAS_xher\()e(enum)i(blas_order_type)c(order,)j(enum)h
(blas_uplo_type)d(uplo,)991 3940 y(int)j(n,)g(RSCALAR_IN)e(alpha,)h
(const)g(CARRAY)h(x,)g(int)g(incx,)991 4053 y(RSCALAR_IN)e(beta,)h
(CARRAY)g(a,)i(int)e(lda)h(\);)227 4166 y(Hermitian)f(Packed:)227
4279 y(void)h(BLAS_xhpr\()e(enum)i(blas_order_type)c(order,)j(enum)h
(blas_uplo_type)d(uplo,)991 4392 y(int)j(n,)g(RSCALAR_IN)e(alpha,)h
(const)g(CARRAY)h(x,)g(int)g(incx,)991 4505 y(RSCALAR_IN)e(beta,)h
(CARRAY)g(ap)i(\);)p 0 4723 3900 6 v 0 4835 a FJ(f)p
FK(SY,SP)p FJ(g)p FK(R2)31 b(\(Symmetric)f(Rank)g(t)m(w)m(o)h(up)s
(date\))661 b Fy(A)26 b FJ( )f Fy(\013xy)2735 4802 y
Fw(T)2810 4835 y FK(+)20 b Fy(\013y)s(x)3059 4802 y Fw(T)3135
4835 y FK(+)g Fy(\014)5 b(A)30 b FK(with)f Fy(A)d FK(=)f
Fy(A)3845 4802 y Fw(T)141 5061 y FK(The)35 b(routine)f(p)s(erforms)g
(the)i(symmetric)e(rank-2)i(up)s(date)e Fy(A)g FK(=)f
Fy(\013xy)2610 5028 y Fw(T)2689 5061 y FK(+)23 b Fy(\013y)s(x)2941
5028 y Fw(T)3020 5061 y FK(+)g Fy(\014)5 b(A)p FK(,)37
b(where)e Fy(\013)h FK(and)f Fy(\014)0 5174 y FK(are)g(scalars,)g
Fy(x)f FK(is)g(a)g(v)m(ector)i(and)e Fy(A)g FK(is)g(a)g(symmetric)g
(\(symmetric)g(pac)m(k)m(ed\))i(matrix.)51 b(This)33
b(routine)g(returns)0 5287 y(immediately)e(if)h Fv(n)h
FK(is)f(less)g(than)h(or)g(equal)f(to)i(zero)f(or)g(if)f
Fv(b)s(eta)g FK(is)g(equal)h(to)g(one)h(and)e Fv(alpha)g
FK(is)g(equal)g(to)i(zero.)0 5400 y(As)e(describ)s(ed)d(in)h(section)i
(2.5.3,)i(the)d(v)-5 b(alue)32 b Fv(incx)f FK(or)h Fv(incy)f
FK(less)g(than)g(zero)h(is)f(p)s(ermitted.)43 b(Ho)m(w)m(ev)m(er,)34
b(if)c(either)4084 64 y FI(1)4084 177 y(2)4084 290 y(3)4084
403 y(4)4084 516 y(5)4084 628 y(6)4084 741 y(7)4084 854
y(8)4084 967 y(9)4069 1080 y(10)4069 1193 y(11)4069 1306
y(12)4069 1419 y(13)4069 1532 y(14)4069 1645 y(15)4069
1758 y(16)4069 1870 y(17)4069 1983 y(18)4069 2096 y(19)4069
2209 y(20)4069 2322 y(21)4069 2435 y(22)4069 2548 y(23)4069
2661 y(24)4069 2774 y(25)4069 2887 y(26)4069 3000 y(27)4069
3112 y(28)4069 3225 y(29)4069 3338 y(30)4069 3451 y(31)4069
3564 y(32)4069 3677 y(33)4069 3790 y(34)4069 3903 y(35)4069
4016 y(36)4069 4129 y(37)4069 4242 y(38)4069 4354 y(39)4069
4467 y(40)4069 4580 y(41)4069 4693 y(42)4069 4806 y(43)4069
4919 y(44)4069 5032 y(45)4069 5145 y(46)4069 5258 y(47)4069
5371 y(48)p eop
%%Page: 67 77
67 76 bop 0 -165 a FA(2.8.)72 b(LANGUA)m(GE)32 b(BINDINGS)2578
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(error)g(handler.)41 b(If)30 b Fv(lda)h FK(is)f(less)g(than)0
204 y(one)h(or)f Fv(lda)g FK(is)f(less)h(than)g Fv(n)p
FK(,)g(an)h(error)f(\015ag)g(is)g(set)h(and)f(passed)f(to)j(the)e
(error)g(handler.)141 317 y(These)25 b(in)m(terfaces)h(encompass)f(the)
g(Legacy)i(BLAS)e(routines)f(xSYR2)h(and)g(xSPR2)g(with)e(added)i
(function-)0 430 y(alit)m(y)30 b(for)g(complex)g(symmetric)g(matrices.)
136 635 y FJ(\017)46 b FK(F)-8 b(ortran)31 b(95)h(binding:)227
853 y FD(Symmetric)46 b(Packed:)418 966 y(SUBROUTINE)f(spr2\()i(x,)g
(y,)g(ap)g([,)g(uplo])g([,)g(trans])f([,)h(alpha])f([,)h(beta])g(\))514
1079 y(<type>\(<wp>\),)d(INTENT\(IN\))h(::)i(x\(:\),)f(y\(:\))514
1191 y(<type>\(<wp>\),)e(INTENT\(INOUT\))g(::)j(ap\(:\))514
1304 y(TYPE)f(\(blas_uplo_type\),)d(INTENT\(IN\),)i(OPTIONAL)h(::)h
(uplo)514 1417 y(TYPE)f(\(blas_trans_type\),)d(INTENT\(IN\),)i
(OPTIONAL)g(::)j(trans)514 1530 y(<type>\(<wp>\),)c(INTENT\(IN\),)h
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y(x)h(and)g(y)h(have)e(shape)h(\(n\))466 1869 y(ap)g(has)g(shape)f
(\(n*\(n+1\)/2\))227 2086 y FK(The)30 b(functionalit)m(y)f(of)i
Fv(syr2)f FK(is)g(co)m(v)m(ered)i(b)m(y)e Fv(syr2k)p
FK(.)136 2272 y FJ(\017)46 b FK(F)-8 b(ortran)31 b(77)h(binding:)227
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(N,)g(ALPHA,)f(X,)h(INCX,)g(Y,)g(INCY,)f(BETA,)g(A,)466
2715 y($)1097 b(LDA)47 b(\))227 2828 y(Symmetric)f(Packed:)514
2941 y(SUBROUTINE)f(BLAS_xSPR2\()f(UPLO,)j(N,)g(ALPHA,)f(X,)h(INCX,)g
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3167 y(all:)514 3280 y(INTEGER)570 b(INCX,)47 b(LDA,)f(N,)i(UPLO)514
3392 y(<type>)618 b(ALPHA,)47 b(BETA)514 3505 y(<type>)618
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y FD(Symmetric:)227 4053 y(void)47 b(BLAS_xsyr2\()e(enum)h
(blas_order_type)e(order,)i(enum)h(blas_uplo_type)d(uplo,)1039
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(incx,)1039 4279 y(const)f(ARRAY)g(y,)i(int)e(incy,)h(SCALAR_IN)e
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(alpha,)h(const)g(ARRAY)h(x,)g(int)g(incx,)1039 4731
y(const)f(ARRAY)g(y,)i(int)e(incy,)h(SCALAR_IN)e(beta,)h(ARRAY)h(ap)g
(\);)p 0 4948 3900 6 v 0 5061 a FJ(f)p FK(HE,HP)p FJ(g)p
FK(R2)32 b(\(Hermitian)d(Rank)i(t)m(w)m(o)g(up)s(date\))621
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b(\026)-54 b Fy(\013y)s(x)2999 5254 y Fw(H)3093 5287
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b FK(is)40 b(a)j(real)e(scalar,)k Fy(x)c FK(and)h Fy(y)i
FK(are)e(complex)g(v)m(ectors)h(and)e Fy(A)h FK(is)f(a)h(Hermitian)-214
64 y FI(1)-214 177 y(2)-214 290 y(3)-214 403 y(4)-214
516 y(5)-214 628 y(6)-214 741 y(7)-214 854 y(8)-214 967
y(9)-230 1080 y(10)-230 1193 y(11)-230 1306 y(12)-230
1419 y(13)-230 1532 y(14)-230 1645 y(15)-230 1758 y(16)-230
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2322 y(21)-230 2435 y(22)-230 2548 y(23)-230 2661 y(24)-230
2774 y(25)-230 2887 y(26)-230 3000 y(27)-230 3112 y(28)-230
3225 y(29)-230 3338 y(30)-230 3451 y(31)-230 3564 y(32)-230
3677 y(33)-230 3790 y(34)-230 3903 y(35)-230 4016 y(36)-230
4129 y(37)-230 4242 y(38)-230 4354 y(39)-230 4467 y(40)-230
4580 y(41)-230 4693 y(42)-230 4806 y(43)-230 4919 y(44)-230
5032 y(45)-230 5145 y(46)-230 5258 y(47)-230 5371 y(48)p
eop
%%Page: 68 78
68 77 bop 0 -165 a FK(68)1930 b FA(CHAPTER)30 b(2.)71
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(ed\))i(matrix.)48 b(This)31 b(routine)h(returns)g(immediately)f(if)h
Fv(n)h FK(is)e(less)i(than)f(or)h(equal)g(to)g(zero)h(or)0
204 y(if)f Fv(b)s(eta)h FK(is)f(equal)h(to)h(one)g(and)f
Fv(alpha)f FK(is)g(equal)h(to)h(zero.)54 b(As)34 b(describ)s(ed)e(in)h
(section)i(2.5.3,)i(the)e(v)-5 b(alue)34 b Fv(incx)g
FK(or)0 317 y Fv(incy)d FK(less)f(than)g(zero)i(is)d(p)s(ermitted.)41
b(Ho)m(w)m(ev)m(er,)33 b(if)c(either)i Fv(incx)f FK(or)h
Fv(incy)f FK(is)g(equal)g(to)i(zero,)g(an)e(error)h(\015ag)g(is)e(set)0
430 y(and)g(passed)g(to)h(the)g(error)f(handler.)38 b(If)29
b Fv(lda)g FK(is)g(less)f(than)i(one)f(or)h Fv(lda)f
FK(is)f(less)h(than)g Fv(n)p FK(,)h(an)f(error)g(\015ag)h(is)f(set)h
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756 y FJ(\017)46 b FK(F)-8 b(ortran)31 b(95)h(binding:)227
980 y FD(Hermitian)46 b(Packed:)418 1093 y(SUBROUTINE)f(hpr2\()i(x,)g
(y,)g(ap)g([,)g(uplo])g([,)g(trans])f([,)h(alpha])f([,)h(beta])g(\))514
1206 y(COMPLEX\(<wp>\),)d(INTENT\(IN\))h(::)i(x\(:\),)f(y\(:\))514
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5371 y(48)p eop
%%Page: 69 79
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5371 y(48)p eop
%%Page: 70 80
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eop
%%Page: 71 81
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5371 y(48)p eop
%%Page: 72 82
72 81 bop 0 -165 a FK(72)1930 b FA(CHAPTER)30 b(2.)71
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5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 73 83
73 82 bop 0 -165 a FA(2.8.)72 b(LANGUA)m(GE)32 b(BINDINGS)2578
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5371 y(48)p eop
%%Page: 74 84
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(INCD,)e(A,)h(LDA)g(\))227 5242 y(Symmetric)f(Packed:)514
5355 y(SUBROUTINE)f(BLAS_xSP_LRSCALE\()e(UPLO,)j(N,)h(D,)g(INCD,)g(AP)g
(\))4084 64 y FI(1)4084 177 y(2)4084 290 y(3)4084 403
y(4)4084 516 y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084
967 y(9)4069 1080 y(10)4069 1193 y(11)4069 1306 y(12)4069
1419 y(13)4069 1532 y(14)4069 1645 y(15)4069 1758 y(16)4069
1870 y(17)4069 1983 y(18)4069 2096 y(19)4069 2209 y(20)4069
2322 y(21)4069 2435 y(22)4069 2548 y(23)4069 2661 y(24)4069
2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
3677 y(33)4069 3790 y(34)4069 3903 y(35)4069 4016 y(36)4069
4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 75 85
75 84 bop 0 -165 a FA(2.8.)72 b(LANGUA)m(GE)32 b(BINDINGS)2578
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1315 y(int)j(n,)g(int)g(k,)g(const)g(ARRAY)f(d,)h(int)g(incd,)f(ARRAY)h
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b(This)22 b(routine)h(returns)f(immediately)g(if)g Fv(n)i
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b(or)31 b(the)g(routines)e Fv(HE)p 1157 2909 V 34 w(LRSCALE)p
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3022 y(set)e(and)e(passed)h(to)h(the)f(error)g(handler.)38
b(F)-8 b(or)28 b(the)h(routine)e Fv(HB)p 2204 3022 V
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4257 y(all:)514 4370 y(COMPLEX\(<wp>\),)d(INTENT)i(\(IN\))g(::)h
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4934 y(\(k+1,n\))f(for)h(Hermitian)e(banded)h(\(k=band)g(width\))514
5047 y(ap)h(has)g(shape)f(\(n*\(n+1\)/2\).)514 5160 y(d)h(has)g(shape)f
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64 y FI(1)-214 177 y(2)-214 290 y(3)-214 403 y(4)-214
516 y(5)-214 628 y(6)-214 741 y(7)-214 854 y(8)-214 967
y(9)-230 1080 y(10)-230 1193 y(11)-230 1306 y(12)-230
1419 y(13)-230 1532 y(14)-230 1645 y(15)-230 1758 y(16)-230
1870 y(17)-230 1983 y(18)-230 2096 y(19)-230 2209 y(20)-230
2322 y(21)-230 2435 y(22)-230 2548 y(23)-230 2661 y(24)-230
2774 y(25)-230 2887 y(26)-230 3000 y(27)-230 3112 y(28)-230
3225 y(29)-230 3338 y(30)-230 3451 y(31)-230 3564 y(32)-230
3677 y(33)-230 3790 y(34)-230 3903 y(35)-230 4016 y(36)-230
4129 y(37)-230 4242 y(38)-230 4354 y(39)-230 4467 y(40)-230
4580 y(41)-230 4693 y(42)-230 4806 y(43)-230 4919 y(44)-230
5032 y(45)-230 5145 y(46)-230 5258 y(47)-230 5371 y(48)p
eop
%%Page: 76 86
76 85 bop 0 -165 a FK(76)1930 b FA(CHAPTER)30 b(2.)71
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882 y(INTEGER)570 b(INCD,)47 b(K,)g(LDA,)g(N,)g(UPLO)514
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1442 y FD(Hermitian:)227 1555 y(void)47 b(BLAS_xhe_lrscale\()c(enum)k
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(BLAS_xhb_lrscale\()c(enum)k(blas_order_type)c(order,)j(enum)h
(blas_uplo_type)d(uplo,)1325 2007 y(int)j(n,)g(int)g(k,)g(const)g
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2232 y(Hermitian)f(Packed:)227 2345 y(void)h(BLAS_xhp_lrscale\()c(enum)
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2458 y(int)j(n,)g(const)f(ARRAY)h(d,)g(int)g(incd,)f(ARRAY)h(ap)g(\);)p
0 2682 3900 6 v 0 2795 a FJ(f)p FK(GE,GB)p FJ(g)p 388
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999 2795 V 32 w(A)m(CC)30 b(\(Diagonal)h(scaling)e(and)h(accum)m
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b(is)f(less)g(than)h(or)g(equal)f(to)i(zero.)46 b(As)32
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(set)i(and)f(passed)g(to)h(the)f(error)g(handler.)54
b(F)-8 b(or)37 b(the)e(C)g(bindings)d(of)k Fv(GE)p 3037
3585 V 32 w(DIA)m(G)p 3279 3585 V 33 w(SCALE)p 3585 3585
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580 3698 29 4 v 33 w(rowmajor)29 b FK(and)h(if)f Fv(lda)h
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403 y(4)4084 516 y(5)4084 628 y(6)4084 741 y(7)4084 854
y(8)4084 967 y(9)4069 1080 y(10)4069 1193 y(11)4069 1306
y(12)4069 1419 y(13)4069 1532 y(14)4069 1645 y(15)4069
1758 y(16)4069 1870 y(17)4069 1983 y(18)4069 2096 y(19)4069
2209 y(20)4069 2322 y(21)4069 2435 y(22)4069 2548 y(23)4069
2661 y(24)4069 2774 y(25)4069 2887 y(26)4069 3000 y(27)4069
3112 y(28)4069 3225 y(29)4069 3338 y(30)4069 3451 y(31)4069
3564 y(32)4069 3677 y(33)4069 3790 y(34)4069 3903 y(35)4069
4016 y(36)4069 4129 y(37)4069 4242 y(38)4069 4354 y(39)4069
4467 y(40)4069 4580 y(41)4069 4693 y(42)4069 4806 y(43)4069
4919 y(44)4069 5032 y(45)4069 5145 y(46)4069 5258 y(47)4069
5371 y(48)p eop
%%Page: 77 87
77 86 bop 0 -165 a FA(2.8.)72 b(LANGUA)m(GE)32 b(BINDINGS)2578
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g(b,)i(int)f(ldb,)1659 3145 y(const)f(ARRAY)h(d,)g(int)g(incd,)f(ARRAY)
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b Fy(\014)5 b(B)141 3704 y FK(These)36 b(routines)f(scale)h(a)h(matrix)
e Fy(A)i FK(\(or)f(its)g(transp)s(ose\))g(and)f(scale)i(a)f(matrix)g
Fy(B)k FK(and)c(accum)m(ulate)h(the)0 3817 y(result)d(in)g(the)i
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Fy(B)40 b FK(ha)m(v)m(e)d(the)e(same)h(storage)h(format.)56
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(band)h(matrices\))g(is)g(less)f(than)h(or)g(equal)g(to)h(zero.)41
b(As)28 b(describ)s(ed)e(in)h(section)i(2.5.3,)0 4156
y(for)f(the)h(routine)f Fv(GE)p 724 4156 V 32 w(A)m(CC)p
FK(,)h(if)f Fv(lda)g FK(or)h Fv(ldb)f FK(is)f(less)h(than)h(one)g(or)f
Fv(lda)g FK(or)h Fv(ldb)f FK(is)f(less)h(than)h Fv(m)p
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FK(,)h(if)e FD(order)47 b(=)g(blas)p 3312 4269 29 4 v
33 w(rowmajor)31 b FK(and)0 4382 y(if)f Fv(lda)g FK(or)h
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FD(order)46 b(=)i(blas)p 1012 4495 V 33 w(colmajor)25
b FK(and)i(if)f Fv(lda)g FK(or)i Fv(ldb)f FK(is)f(less)g(than)h(one)h
(or)f Fv(lda)g FK(or)g Fv(ldb)g FK(is)f(less)h(than)g
Fv(m)p FK(,)h(an)0 4608 y(error)j(\015ag)h(is)e(set)i(and)f(passed)f
(to)i(the)g(error)f(handler.)42 b(F)-8 b(or)32 b(the)f(routine)g
Fv(SY)p 2713 4608 28 4 v 31 w(A)m(CC)p FK(,)h(if)e Fv(lda)h
FK(or)g Fv(ldb)g FK(is)g(less)f(than)0 4721 y(one)f(or)g
Fv(lda)g FK(or)g Fv(ldb)f FK(is)g(less)h(than)f Fv(n)p
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(error)g(handler.)38 b(F)-8 b(or)30 b(the)f(routine)0
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(handler.)136 5042 y FJ(\017)46 b FK(F)-8 b(ortran)31
b(95)h(binding:)227 5287 y FD(General:)418 5400 y(SUBROUTINE)45
b(ge_acc\()h(a,)h(b)h([,)f(trans])f([,)h(alpha])f([,)h(beta])g(\))-214
64 y FI(1)-214 177 y(2)-214 290 y(3)-214 403 y(4)-214
516 y(5)-214 628 y(6)-214 741 y(7)-214 854 y(8)-214 967
y(9)-230 1080 y(10)-230 1193 y(11)-230 1306 y(12)-230
1419 y(13)-230 1532 y(14)-230 1645 y(15)-230 1758 y(16)-230
1870 y(17)-230 1983 y(18)-230 2096 y(19)-230 2209 y(20)-230
2322 y(21)-230 2435 y(22)-230 2548 y(23)-230 2661 y(24)-230
2774 y(25)-230 2887 y(26)-230 3000 y(27)-230 3112 y(28)-230
3225 y(29)-230 3338 y(30)-230 3451 y(31)-230 3564 y(32)-230
3677 y(33)-230 3790 y(34)-230 3903 y(35)-230 4016 y(36)-230
4129 y(37)-230 4242 y(38)-230 4354 y(39)-230 4467 y(40)-230
4580 y(41)-230 4693 y(42)-230 4806 y(43)-230 4919 y(44)-230
5032 y(45)-230 5145 y(46)-230 5258 y(47)-230 5371 y(48)p
eop
%%Page: 78 88
78 87 bop 0 -165 a FK(78)1930 b FA(CHAPTER)30 b(2.)71
b(DENSE)30 b(AND)h(BANDED)h(BLAS)227 91 y FD(Symmetric:)418
204 y(SUBROUTINE)45 b(sy_acc\()h(a,)h(b)h([,)f(uplo])f([,)h(trans])f
([,)i(alpha])e([,)h(beta])f(\))227 317 y(Symmetric)g(Band:)418
430 y(SUBROUTINE)f(sb_acc\()h(a,)h(b)h([,)f(uplo])f([,)h(trans])f([,)i
(alpha])e([,)h(beta])f(\))227 543 y(Symmetric)g(Packed:)418
656 y(SUBROUTINE)f(sp_acc\()h(ap,)h(bp)g([,)g(uplo])g([,)g(trans])f([,)
h(alpha])f([,)h(beta])g(\))227 769 y(all:)514 882 y(<type>\(<wp>\),)d
(INTENT\(IN\))h(::)i(a\(:,:\))f(|)i(ap\(:\))514 995 y(<type>\(<wp>\),)c
(INTENT\(INOUT\))g(::)j(b\(:,:\))f(|)i(bp\(:\))514 1108
y(TYPE)e(\(blas_uplo_type\),)d(INTENT)j(\(IN\),)h(OPTIONAL)e(::)j(uplo)
514 1220 y(TYPE)e(\(blas_trans_type\),)d(INTENT)j(\(IN\),)h(OPTIONAL)e
(::)i(trans)514 1333 y(<type>\(<wp>\),)d(INTENT\(IN\),)h(OPTIONAL)g(::)
i(alpha,)f(beta)227 1583 y FK(The)30 b(default)g(v)-5
b(alue)30 b(for)g Fy(\014)35 b FK(is)30 b(1.0)h(or)f(\(1.0,0.0\).)136
1771 y FJ(\017)46 b FK(F)-8 b(ortran)31 b(77)h(binding:)227
1996 y FD(General:)514 2109 y(SUBROUTINE)45 b(BLAS_xGE_ACC\()f(TRANS,)i
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b(LDB)47 b(\))227 2335 y(Symmetric:)514 2447 y(SUBROUTINE)e
(BLAS_xSY_ACC\()f(UPLO,)i(TRANS,)g(N,)h(ALPHA,)g(A,)g(LDA,)f(BETA,)h
(B,)466 2560 y($)1193 b(LDB)47 b(\))227 2673 y(Symmetric)f(Band:)514
2786 y(SUBROUTINE)f(BLAS_xSB_ACC\()f(UPLO,)i(TRANS,)g(N,)h(K,)h(ALPHA,)
e(A,)h(LDA,)g(BETA,)466 2899 y($)1193 b(B,)47 b(LDB)g(\))227
3012 y(Symmetric)f(Packed:)514 3125 y(SUBROUTINE)f(BLAS_xSP_ACC\()f
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3238 y(all:)514 3351 y(INTEGER)570 b(K,)48 b(LDA,)e(LDB,)h(M,)g(N,)g
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(blas_trans_type)d(trans,)1134 4252 y(int)j(m,)g(int)g(n,)g(SCALAR_IN)f
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4591 y(void)g(BLAS_xsy_acc\()d(enum)j(blas_order_type)c(order,)j(enum)h
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(int)h(n,)h(SCALAR_IN)d(alpha,)1134 4817 y(const)h(ARRAY)h(a,)g(int)g
(lda,)g(SCALAR_IN)e(beta,)h(ARRAY)h(b,)g(int)g(ldb)g(\);)227
4930 y(Symmetric)f(Band:)227 5043 y(void)h(BLAS_xsb_acc\()d(enum)j
(blas_order_type)c(order,)j(enum)h(blas_uplo_type)d(uplo,)1134
5156 y(enum)j(blas_trans_type)c(trans,)j(int)h(n,)h(int)e(k,)i
(SCALAR_IN)d(alpha,)1134 5269 y(const)h(ARRAY)h(a,)g(int)g(lda,)g
(SCALAR_IN)e(beta,)h(ARRAY)h(b,)g(int)g(ldb)g(\);)227
5381 y(Symmetric)f(Packed:)4084 64 y FI(1)4084 177 y(2)4084
290 y(3)4084 403 y(4)4084 516 y(5)4084 628 y(6)4084 741
y(7)4084 854 y(8)4084 967 y(9)4069 1080 y(10)4069 1193
y(11)4069 1306 y(12)4069 1419 y(13)4069 1532 y(14)4069
1645 y(15)4069 1758 y(16)4069 1870 y(17)4069 1983 y(18)4069
2096 y(19)4069 2209 y(20)4069 2322 y(21)4069 2435 y(22)4069
2548 y(23)4069 2661 y(24)4069 2774 y(25)4069 2887 y(26)4069
3000 y(27)4069 3112 y(28)4069 3225 y(29)4069 3338 y(30)4069
3451 y(31)4069 3564 y(32)4069 3677 y(33)4069 3790 y(34)4069
3903 y(35)4069 4016 y(36)4069 4129 y(37)4069 4242 y(38)4069
4354 y(39)4069 4467 y(40)4069 4580 y(41)4069 4693 y(42)4069
4806 y(43)4069 4919 y(44)4069 5032 y(45)4069 5145 y(46)4069
5258 y(47)4069 5371 y(48)p eop
%%Page: 79 89
79 88 bop 0 -165 a FA(2.8.)72 b(LANGUA)m(GE)32 b(BINDINGS)2578
b FK(79)227 91 y FD(void)47 b(BLAS_xsp_acc\()d(enum)j(blas_order_type)c
(order,)j(enum)h(blas_uplo_type)d(uplo,)1134 204 y(enum)j
(blas_trans_type)c(trans,)j(int)h(n,)h(SCALAR_IN)d(alpha,)1134
317 y(const)h(ARRAY)h(ap,)g(SCALAR_IN)e(beta,)h(ARRAY)h(bp)g(\);)p
0 542 3900 6 v 0 655 a FJ(f)p FK(GB,TR,TB,TP)p FJ(g)p
696 655 28 4 v 34 w FK(A)m(CC)31 b(\(Matrix)f(accum)m(ulation)g(and)g
(scale\))1070 b Fy(B)29 b FJ( )c Fy(\013A)c FK(+)f Fy(\014)5
b(B)141 881 y FK(These)29 b(routines)f(scale)i(matrices)f
Fy(A)h FK(and)e Fy(B)34 b FK(and)29 b(accum)m(ulate)h(the)g(result)e
(in)g(the)h(matrix)g Fy(B)5 b FK(.)40 b(Matrices)30 b
Fy(A)0 994 y FK(and)j Fy(B)k FK(ha)m(v)m(e)e(the)e(same)h(storage)g
(format.)50 b(These)33 b(routines)f(return)g(immediately)g(if)g
Fv(alpha)g FK(is)g(equal)h(to)h(zero)0 1107 y(and)24
b Fv(b)s(eta)g FK(is)g(equal)g(to)h(one,)h(or)f(if)e
Fv(m)i FK(or)g Fv(kl)f FK(or)h Fv(ku)g FK(\(for)g(general)f(band)g
(matrices\))h(or)f Fv(n)h FK(or)f Fv(k)h FK(\(for)g(triangular)e(band)0
1220 y(matrices\))33 b(is)f(less)g(than)g(or)h(equal)g(to)g(zero.)49
b(F)-8 b(or)33 b(the)g(routine)f Fv(GB)p 2352 1220 V
32 w(A)m(CC)p FK(,)h(if)f Fv(lda)g FK(is)g(less)g(than)g
Fv(kl)h FK(plus)e Fv(ku)i FK(plus)0 1333 y(one,)e(an)f(error)f(\015ag)i
(is)e(set)h(and)g(passed)f(to)i(the)f(error)g(handler.)39
b(F)-8 b(or)31 b(the)f(routines)f Fv(TR)p 3057 1333 V
32 w(A)m(CC)h FK(and)g Fv(TP)p 3590 1333 V 32 w(A)m(CC)p
FK(,)h(if)0 1445 y Fv(lda)26 b FK(is)h(less)f(than)h(one)g(or)g
Fv(lda)g FK(is)f(less)g(than)h Fv(n)p FK(,)h(an)f(error)g(\015ag)g(is)f
(set)i(and)f(passed)f(to)i(the)f(error)g(handler.)38
b(F)-8 b(or)28 b(the)0 1558 y(routine)h Fv(TB)p 441 1558
V 33 w(A)m(CC)p FK(,)h(if)g Fv(lda)f FK(is)h(less)f(than)i
Fv(k)f FK(plus)f(one,)i(an)f(error)g(\015ag)h(is)e(set)i(and)f(passed)g
(to)h(the)f(error)g(handler.)136 1771 y FJ(\017)46 b
FK(F)-8 b(ortran)31 b(95)h(binding:)227 2021 y FD(General)46
b(Band:)418 2134 y(SUBROUTINE)f(gb_acc\()h(a,)h(m,)g(kl,)g(b)h([,)f
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2359 y(SUBROUTINE)e(tr_acc\()h(a,)h(b)h([,)f(uplo])f([,)h(diag])g([,)g
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2585 y(SUBROUTINE)g(tb_acc\()h(a,)h(b)h([,)f(uplo])f([,)h(diag])g([,)g
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(INTENT\(IN\))h(::)i(a\(:,:\))f(|)i(ap\(:\))514 3150
y(INTEGER,)d(INTENT)h(\(IN\))h(::)g(m,)g(kl)514 3263
y(<type>\(<wp>\),)d(INTENT\(INOUT\))g(::)j(b\(:,:\))f(|)i(bp\(:\))514
3376 y(TYPE)e(\(blas_uplo_type\),)d(INTENT)j(\(IN\),)h(OPTIONAL)e(::)j
(uplo)514 3489 y(TYPE)e(\(blas_diag_type\),)d(INTENT)j(\(IN\),)h
(OPTIONAL)e(::)j(diag)514 3601 y(<type>\(<wp>\),)c(INTENT\(IN\),)h
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4039 y FJ(\017)46 b FK(F)-8 b(ortran)31 b(77)h(binding:)227
4264 y FD(General)46 b(Band:)514 4377 y(SUBROUTINE)f(BLAS_xGB_ACC\()f
(M,)j(N,)g(KL,)g(KU,)g(ALPHA,)f(A,)h(LDA,)g(BETA,)f(B,)466
4490 y($)1193 b(LDB)47 b(\))227 4603 y(Triangular:)514
4716 y(SUBROUTINE)e(BLAS_xTR_ACC\()f(UPLO,)i(DIAG,)h(N,)g(ALPHA,)f(A,)h
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4941 y(Triangular)e(Band:)514 5054 y(SUBROUTINE)g(BLAS_xTB_ACC\()f
(UPLO,)i(DIAG,)h(N,)g(K,)g(ALPHA,)f(A,)h(LDA,)g(BETA,)f(B,)466
5167 y($)1193 b(LDB)47 b(\))227 5280 y(Triangular)e(Packed:)514
5393 y(SUBROUTINE)g(BLAS_xTP_ACC\()f(UPLO,)i(DIAG,)h(N,)g(ALPHA,)f(AP,)
h(BETA,)f(BP)h(\))-214 64 y FI(1)-214 177 y(2)-214 290
y(3)-214 403 y(4)-214 516 y(5)-214 628 y(6)-214 741 y(7)-214
854 y(8)-214 967 y(9)-230 1080 y(10)-230 1193 y(11)-230
1306 y(12)-230 1419 y(13)-230 1532 y(14)-230 1645 y(15)-230
1758 y(16)-230 1870 y(17)-230 1983 y(18)-230 2096 y(19)-230
2209 y(20)-230 2322 y(21)-230 2435 y(22)-230 2548 y(23)-230
2661 y(24)-230 2774 y(25)-230 2887 y(26)-230 3000 y(27)-230
3112 y(28)-230 3225 y(29)-230 3338 y(30)-230 3451 y(31)-230
3564 y(32)-230 3677 y(33)-230 3790 y(34)-230 3903 y(35)-230
4016 y(36)-230 4129 y(37)-230 4242 y(38)-230 4354 y(39)-230
4467 y(40)-230 4580 y(41)-230 4693 y(42)-230 4806 y(43)-230
4919 y(44)-230 5032 y(45)-230 5145 y(46)-230 5258 y(47)-230
5371 y(48)p eop
%%Page: 80 90
80 89 bop 0 -165 a FK(80)1930 b FA(CHAPTER)30 b(2.)71
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1216 y(ARRAY)h(b,)i(int)f(ldb)f(\);)227 1329 y(Triangular:)227
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3472 y(F)-8 b(or)28 b(the)g(routine)f Fv(GE)p 745 3472
V 33 w(ADD)p FK(,)g(if)f Fv(lda)h FK(or)h Fv(ldb)f FK(is)g(less)g(than)
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(set)h(and)f(passed)0 3585 y(to)k(the)g(error)e(handler.)39
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2831 3585 29 4 v 33 w(rowmajor)28 b FK(and)i(if)f Fv(lda)h
FK(or)g Fv(ldb)0 3698 y FK(is)i(less)g(than)h(one)g(or)g
Fv(lda)f FK(or)h Fv(ldb)f FK(is)g(less)g(than)h Fv(n)p
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(error)f(handler;)h(if)0 3811 y FD(order)46 b(=)i(blas)p
580 3811 V 33 w(colmajor)27 b FK(and)i(if)g Fv(lda)f
FK(or)i Fv(ldb)f FK(is)f(less)h(than)g(one)h(or)f Fv(lda)g
FK(or)h Fv(ldb)f FK(is)f(less)h(than)g Fv(m)p FK(,)h(an)g(error)f
(\015ag)0 3924 y(is)f(set)i(and)f(passed)f(to)i(the)g(error)f(handler.)
38 b(F)-8 b(or)30 b(the)g(routine)e Fv(GB)p 2302 3924
28 4 v 32 w(ADD)p FK(,)g(if)g Fv(lda)h FK(or)g Fv(ldb)g
FK(is)f(less)h(than)g Fv(kl)g FK(plus)f Fv(ku)0 4037
y FK(plus)h(one,)j(an)e(error)h(\015ag)g(is)f(set)i(and)e(passed)g(to)i
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Fv(SY)p 3255 4037 V 32 w(ADD)p FK(,)g Fv(TR)p 3656 4037
V 32 w(ADD)p FK(,)0 4150 y Fv(SP)p 114 4150 V 32 w(ADD)p
FK(,)g(and)g Fv(TP)p 691 4150 V 33 w(ADD)p FK(,)f(if)h
Fv(lda)g FK(or)g Fv(ldb)g FK(is)g(less)g(than)g(one)h(or)f
Fv(lda)g FK(or)h Fv(ldb)f FK(is)f(less)h(than)h Fv(n)p
FK(,)f(an)h(error)f(\015ag)h(is)e(set)0 4263 y(and)j(passed)g(to)h(the)
g(error)f(handler.)45 b(F)-8 b(or)33 b(the)f(routines)g
Fv(SB)p 2129 4263 V 32 w(ADD)f FK(and)h Fv(TB)p 2687
4263 V 32 w(ADD)p FK(,)f(if)h Fv(lda)g FK(or)g Fv(ldb)g
FK(is)f(less)h(than)0 4376 y Fv(k)f FK(plus)d(one,)j(an)f(error)g
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4835 y FD(General:)418 4948 y(SUBROUTINE)45 b(ge_add\()h(a,)h(b,)g(c)h
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(sy_add\()h(a,)h(b,)g(c)h([,)f(uplo])f([,)i(alpha])e([,)h(beta])f(\))
4084 64 y FI(1)4084 177 y(2)4084 290 y(3)4084 403 y(4)4084
516 y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084 967
y(9)4069 1080 y(10)4069 1193 y(11)4069 1306 y(12)4069
1419 y(13)4069 1532 y(14)4069 1645 y(15)4069 1758 y(16)4069
1870 y(17)4069 1983 y(18)4069 2096 y(19)4069 2209 y(20)4069
2322 y(21)4069 2435 y(22)4069 2548 y(23)4069 2661 y(24)4069
2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
3677 y(33)4069 3790 y(34)4069 3903 y(35)4069 4016 y(36)4069
4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 81 91
81 90 bop 0 -165 a FA(2.8.)72 b(LANGUA)m(GE)32 b(BINDINGS)2578
b FK(81)227 91 y FD(Symmetric)46 b(Band:)418 204 y(SUBROUTINE)f
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543 y(Triangular:)418 656 y(SUBROUTINE)f(tr_add\()h(a,)h(b,)g(c)h([,)f
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769 y(Triangular)e(Band:)418 882 y(SUBROUTINE)g(tb_add\()h(a,)h(b,)g(c)
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1559 y(<type>\(<wp>\),)d(INTENT\(IN\))h(::)i(b\(:,:\))f(|)i(bp\(:\))514
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3802 y(SUBROUTINE)45 b(BLAS_xGE_ADD\()f(M,)j(N,)g(ALPHA,)f(A,)h(LDA,)g
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4254 y($)1193 b(LDB,)46 b(C,)i(LDC)f(\))227 4367 y(Symmetric:)514
4480 y(SUBROUTINE)e(BLAS_xSY_ADD\()f(UPLO,)i(N,)h(ALPHA,)f(A,)i(LDA,)e
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4706 y(Symmetric)f(Band:)514 4819 y(SUBROUTINE)f(BLAS_xSB_ADD\()f
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4932 y($)1193 b(C,)47 b(LDC)g(\))227 5044 y(Symmetric)f(Packed:)514
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(BLAS_xTR_ADD\()f(UPLO,)i(DIAG,)h(N,)g(ALPHA,)f(A,)h(LDA,)g(BETA,)f(B,)
-214 64 y FI(1)-214 177 y(2)-214 290 y(3)-214 403 y(4)-214
516 y(5)-214 628 y(6)-214 741 y(7)-214 854 y(8)-214 967
y(9)-230 1080 y(10)-230 1193 y(11)-230 1306 y(12)-230
1419 y(13)-230 1532 y(14)-230 1645 y(15)-230 1758 y(16)-230
1870 y(17)-230 1983 y(18)-230 2096 y(19)-230 2209 y(20)-230
2322 y(21)-230 2435 y(22)-230 2548 y(23)-230 2661 y(24)-230
2774 y(25)-230 2887 y(26)-230 3000 y(27)-230 3112 y(28)-230
3225 y(29)-230 3338 y(30)-230 3451 y(31)-230 3564 y(32)-230
3677 y(33)-230 3790 y(34)-230 3903 y(35)-230 4016 y(36)-230
4129 y(37)-230 4242 y(38)-230 4354 y(39)-230 4467 y(40)-230
4580 y(41)-230 4693 y(42)-230 4806 y(43)-230 4919 y(44)-230
5032 y(45)-230 5145 y(46)-230 5258 y(47)-230 5371 y(48)p
eop
%%Page: 82 92
82 91 bop 0 -165 a FK(82)1930 b FA(CHAPTER)30 b(2.)71
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b(C,)i(LDC)f(\))227 204 y(Triangular)e(Band:)514 317
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543 y(Triangular)e(Packed:)514 656 y(SUBROUTINE)g(BLAS_xTP_ADD\()f
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b(ALPHA,)47 b(BETA)514 1108 y(<type>)618 b(A\()48 b(LDA,)e(*)i(\))f(or)
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1220 y(<type>)618 b(C\()48 b(LDC,)e(*)i(\))f(or)g(CP\()g(*)h(\))136
1445 y FJ(\017)e FK(C)30 b(binding:)227 1670 y FD(General:)227
1783 y(void)47 b(BLAS_xge_add\()d(enum)j(blas_order_type)c(order,)j
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2009 y(int)h(ldb,)g(ARRAY)f(c,)h(int)g(ldc)g(\);)227
2122 y(General)f(Band:)227 2235 y(void)h(BLAS_xgb_add\()d(enum)j
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y(void)g(BLAS_xsy_add\()d(enum)j(blas_order_type)c(order,)j(enum)h
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(const)h(ARRAY)f(a,)h(int)g(lda,)g(SCALAR_IN)e(beta,)1134
2912 y(const)h(ARRAY)h(b,)g(int)g(ldb,)g(ARRAY)f(c,)h(int)g(ldc)g(\);)
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(lda,)g(SCALAR_IN)e(beta,)h(const)h(ARRAY)f(b,)1134 4380
y(int)h(ldb,)g(ARRAY)f(c,)h(int)g(ldc)g(\);)227 4493
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(SCALAR_IN)e(beta,)h(const)h(ARRAY)f(bp,)4084 64 y FI(1)4084
177 y(2)4084 290 y(3)4084 403 y(4)4084 516 y(5)4084 628
y(6)4084 741 y(7)4084 854 y(8)4084 967 y(9)4069 1080
y(10)4069 1193 y(11)4069 1306 y(12)4069 1419 y(13)4069
1532 y(14)4069 1645 y(15)4069 1758 y(16)4069 1870 y(17)4069
1983 y(18)4069 2096 y(19)4069 2209 y(20)4069 2322 y(21)4069
2435 y(22)4069 2548 y(23)4069 2661 y(24)4069 2774 y(25)4069
2887 y(26)4069 3000 y(27)4069 3112 y(28)4069 3225 y(29)4069
3338 y(30)4069 3451 y(31)4069 3564 y(32)4069 3677 y(33)4069
3790 y(34)4069 3903 y(35)4069 4016 y(36)4069 4129 y(37)4069
4242 y(38)4069 4354 y(39)4069 4467 y(40)4069 4580 y(41)4069
4693 y(42)4069 4806 y(43)4069 4919 y(44)4069 5032 y(45)4069
5145 y(46)4069 5258 y(47)4069 5371 y(48)p eop
%%Page: 83 93
83 92 bop 0 -165 a FA(2.8.)72 b(LANGUA)m(GE)32 b(BINDINGS)2578
b FK(83)1134 91 y FD(ARRAY)46 b(cp)i(\);)p 0 316 3900
6 v 0 560 a Fx(2.8.8)97 b(Matrix-Matrix)31 b(Op)s(erations)0
731 y FK(In)f(the)g(follo)m(wing)f(section,)i Fy(op)p
FK(\()p Fy(X)7 b FK(\))31 b(denotes)g Fy(X)7 b FK(,)31
b(or)f Fy(X)1916 698 y Fw(T)2002 731 y FK(or)g Fy(X)2195
698 y Fw(H)2293 731 y FK(where)g Fy(X)38 b FK(is)29 b(a)i(matrix.)0
957 y(GEMM)g(\(General)g(Matrix)f(Matrix)g(Pro)s(duct\))1258
b Fy(C)32 b FJ( )25 b Fy(\013op)p FK(\()p Fy(A)p FK(\))p
Fy(op)p FK(\()p Fy(B)5 b FK(\))21 b(+)f Fy(\014)5 b(C)141
1183 y FK(The)32 b(routine)g(p)s(erforms)f(a)h(general)h(matrix)f
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FK(\()p Fy(A)p FK(\))p Fy(op)p FK(\()p Fy(B)5 b FK(\))23
b(+)e Fy(\014)5 b(C)40 b FK(where)32 b Fy(\013)h FK(and)0
1296 y Fy(\014)42 b FK(are)c(scalars,)h(and)e Fy(A)p
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Fv(alpha)0 1409 y FK(is)e(equal)h(to)g(zero)h(and)e Fv(b)s(eta)h
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Fv(n)h FK(or)g Fv(k)h FK(is)e(less)g(than)h(or)g(equal)f(to)i(zero.)55
b(If)35 b Fv(lda)f FK(is)0 1522 y(less)h(than)h(one,)h(or)f
Fy(tr)s(ansa)d FK(=)h Fy(bl)r(as)p 1279 1522 28 4 v 33
w(no)p 1411 1522 V 32 w(tr)s(ans)g FK(and)h Fv(lda)h
FK(is)e(less)i(than)f Fv(m)p FK(,)j(or)d Fy(tr)s(ansa)e
FJ(6)p FK(=)i Fy(bl)r(as)p 3338 1522 V 32 w(no)p 3469
1522 V 32 w(tr)s(ans)g FK(and)0 1635 y Fv(lda)k FK(is)g(less)h(than)g
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Fy(tr)s(ansb)g FK(=)h Fy(bl)r(as)p 2444 1635 V 33 w(no)p
2576 1635 V 32 w(tr)s(ans)e FK(and)g Fv(ldb)h FK(is)f(less)g(than)h
Fv(k)p FK(,)j(or)0 1748 y Fy(tr)s(ansb)27 b FJ(6)p FK(=)i
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Fv(ldc)h FK(is)e(less)h(than)g(one)h(or)g(less)e(than)i
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2186 y FJ(\017)46 b FK(F)-8 b(ortran)31 b(95)h(binding:)418
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418 2975 y(where)514 3088 y(<aa>)94 b(::=)47 b(a\(:,:\))f(or)h(a\(:\))
514 3201 y(<bb>)94 b(::=)47 b(b\(:,:\))f(or)h(b\(:\))514
3314 y(<cc>)94 b(::=)47 b(c\(:,:\))f(or)h(c\(:\))418
3427 y(and)514 3540 y(c,)g(rank)f(2,)i(has)f(shape)f(\(m,n\))752
3653 y(a)i(has)f(shape)f(\(m,k\))g(if)i(transa)e(=)h(blas_no_trans)d
(\(the)j(default\))1325 3766 y(\(k,m\))f(if)i(transa)e(/=)h
(blas_no_trans)1325 3879 y(\(m\))g(if)g(rank)g(1)752
3992 y(b)h(has)f(shape)f(\(k,n\))g(if)i(transb)e(=)h(blas_no_trans)d
(\(the)j(default\))1325 4105 y(\(n,k\))f(if)i(transb)e(/=)h
(blas_no_trans)1325 4217 y(\(n\))g(if)g(rank)g(1)514
4330 y(c,)g(rank)f(1,)i(has)f(shape)f(\(m\))752 4443
y(a)i(has)f(shape)f(\(m,n\))g(if)i(transa)e(=)h(blas_no_trans)d(\(the)j
(default\))1325 4556 y(\(n,m\))f(if)i(transa)e(/=)h(blas_no_trans)752
4669 y(b)h(has)f(shape)f(\(n\))-214 64 y FI(1)-214 177
y(2)-214 290 y(3)-214 403 y(4)-214 516 y(5)-214 628 y(6)-214
741 y(7)-214 854 y(8)-214 967 y(9)-230 1080 y(10)-230
1193 y(11)-230 1306 y(12)-230 1419 y(13)-230 1532 y(14)-230
1645 y(15)-230 1758 y(16)-230 1870 y(17)-230 1983 y(18)-230
2096 y(19)-230 2209 y(20)-230 2322 y(21)-230 2435 y(22)-230
2548 y(23)-230 2661 y(24)-230 2774 y(25)-230 2887 y(26)-230
3000 y(27)-230 3112 y(28)-230 3225 y(29)-230 3338 y(30)-230
3451 y(31)-230 3564 y(32)-230 3677 y(33)-230 3790 y(34)-230
3903 y(35)-230 4016 y(36)-230 4129 y(37)-230 4242 y(38)-230
4354 y(39)-230 4467 y(40)-230 4580 y(41)-230 4693 y(42)-230
4806 y(43)-230 4919 y(44)-230 5032 y(45)-230 5145 y(46)-230
5258 y(47)-230 5371 y(48)p eop
%%Page: 84 94
84 93 bop 0 -165 a FK(84)1930 b FA(CHAPTER)30 b(2.)71
b(DENSE)30 b(AND)h(BANDED)h(BLAS)p 244 3 3640 4 v 242
116 4 113 v 294 82 a FK(Rank)e FD(a)p 631 116 V 99 w
FK(Rank)h FD(b)p 1019 116 V 99 w FK(Rank)f FD(c)p 1408
116 V 99 w(transa)p 1794 116 V 98 w(transb)p 2180 116
V 98 w FK(Op)s(eration)p 3066 116 V 483 w(Argumen)m(ts)p
3881 116 V 244 120 3640 4 v 242 232 4 113 v 416 199 a(2)p
631 232 V 343 w(2)p 1019 232 V 344 w(2)p 1408 232 V 331
w(N)p 1794 232 V 318 w(N)p 2180 232 V 208 w Fy(C)i FJ( )25
b Fy(\013AB)h FK(+)20 b Fy(\014)5 b(C)p 3066 232 V 240
w FD(real)47 b(or)g(complex)p 3881 232 V 242 345 V 416
311 a FK(2)p 631 345 V 343 w(2)p 1019 345 V 344 w(2)p
1408 345 V 331 w(N)p 1794 345 V 319 w(T)p 2180 345 V
209 w Fy(C)32 b FJ( )25 b Fy(\013AB)2644 279 y Fw(T)2720
311 y FK(+)20 b Fy(\014)5 b(C)p 3066 345 V 185 w FD(real)47
b(or)g(complex)p 3881 345 V 242 458 V 416 424 a FK(2)p
631 458 V 343 w(2)p 1019 458 V 344 w(2)p 1408 458 V 331
w(N)p 1794 458 V 318 w(H)p 2180 458 V 208 w Fy(C)32 b
FJ( )25 b Fy(\013AB)2644 391 y Fw(H)2732 424 y FK(+)20
b Fy(\014)5 b(C)p 3066 458 V 173 w FD(complex)p 3881
458 V 242 571 V 416 537 a FK(2)p 631 571 V 343 w(2)p
1019 571 V 344 w(2)p 1408 571 V 332 w(T)p 1794 571 V
319 w(N)p 2180 571 V 208 w Fy(C)32 b FJ( )25 b Fy(\013A)2570
504 y Fw(T)2626 537 y Fy(B)g FK(+)20 b Fy(\014)5 b(C)p
3066 571 V 185 w FD(real)47 b(or)g(complex)p 3881 571
V 242 684 V 416 650 a FK(2)p 631 684 V 343 w(2)p 1019
684 V 344 w(2)p 1408 684 V 332 w(T)p 1794 684 V 320 w(T)p
2180 684 V 209 w Fy(C)32 b FJ( )25 b Fy(\013A)2570 617
y Fw(T)2626 650 y Fy(B)2700 617 y Fw(T)2775 650 y FK(+)20
b Fy(\014)5 b(C)p 3066 684 V 130 w FD(real)47 b(or)g(complex)p
3881 684 V 242 797 V 416 763 a FK(2)p 631 797 V 343 w(2)p
1019 797 V 344 w(2)p 1408 797 V 331 w(H)p 1794 797 V
318 w(N)p 2180 797 V 208 w Fy(C)32 b FJ( )25 b Fy(\013A)2570
730 y Fw(H)2638 763 y Fy(B)g FK(+)20 b Fy(\014)5 b(C)p
3066 797 V 173 w FD(complex)p 3881 797 V 242 910 V 416
876 a FK(2)p 631 910 V 343 w(2)p 1019 910 V 344 w(2)p
1408 910 V 331 w(H)p 1794 910 V 318 w(H)p 2180 910 V
208 w Fy(C)32 b FJ( )25 b Fy(\013A)2570 843 y Fw(H)2638
876 y Fy(B)2712 843 y Fw(H)2799 876 y FK(+)20 b Fy(\014)5
b(C)p 3066 910 V 106 w FD(complex)p 3881 910 V 242 1023
V 416 989 a FK(2)p 631 1023 V 343 w(1)p 1019 1023 V 344
w(1)p 1408 1023 V 331 w(N)p 1794 1023 V 336 w(-)p 2180
1023 V 228 w Fy(c)26 b FJ( )f Fy(\013Ab)c FK(+)f Fy(\014)5
b(c)p 3066 1023 V 333 w FD(real)47 b(or)g(complex)p 3881
1023 V 242 1136 V 416 1102 a FK(2)p 631 1136 V 343 w(1)p
1019 1136 V 344 w(1)p 1408 1136 V 332 w(T)p 1794 1136
V 337 w(-)p 2180 1136 V 228 w Fy(c)26 b FJ( )f Fy(\013A)2538
1069 y Fw(T)2594 1102 y Fy(b)20 b FK(+)g Fy(\014)5 b(c)p
3066 1136 V 278 w FD(real)47 b(or)g(complex)p 3881 1136
V 242 1249 V 416 1215 a FK(2)p 631 1249 V 343 w(1)p 1019
1249 V 344 w(1)p 1408 1249 V 331 w(H)p 1794 1249 V 336
w(-)p 2180 1249 V 228 w Fy(c)26 b FJ( )f Fy(\013A)2538
1182 y Fw(H)2606 1215 y Fy(b)20 b FK(+)g Fy(\014)5 b(c)p
3066 1249 V 266 w FD(complex)p 3881 1249 V 242 1362 V
416 1328 a FK(1)p 631 1362 V 343 w(1)p 1019 1362 V 344
w(2)p 1408 1362 V 350 w(-)p 1794 1362 V 355 w(-)p 2180
1362 V 228 w Fy(C)32 b FJ( )25 b Fy(\013ab)2589 1295
y Fw(T)2665 1328 y FK(+)20 b Fy(\014)5 b(C)p 3066 1362
V 240 w FD(real)47 b(or)g(complex)p 3881 1362 V 242 1474
V 416 1441 a FK(1)p 631 1474 V 343 w(1)p 1019 1474 V
344 w(2)p 1408 1474 V 350 w(-)p 1794 1474 V 337 w(H)p
2180 1474 V 208 w Fy(C)32 b FJ( )25 b Fy(\013ab)2589
1408 y Fw(H)2677 1441 y FK(+)20 b Fy(\014)5 b(C)p 3066
1474 V 228 w FD(complex)p 3881 1474 V 244 1478 3640 4
v 227 1686 a FK(The)32 b(functionalit)m(y)f(of)i(xGEMV,)g(xGER,)g(xGER)
m(U,)h(and)e(xGER)m(C)g(are)h(also)g(co)m(v)m(ered)h(b)m(y)f(this)e
(generic)227 1799 y(pro)s(cedure.)136 1987 y FJ(\017)46
b FK(F)-8 b(ortran)31 b(77)h(binding:)514 2212 y FD(SUBROUTINE)45
b(BLAS_xGEMM\()f(TRANSA,)i(TRANSB,)g(M,)h(N,)g(K,)h(ALPHA,)e(A,)h(LDA,)
466 2325 y($)1097 b(B,)48 b(LDB,)e(BETA,)h(C,)g(LDC)g(\))514
2438 y(INTEGER)570 b(K,)48 b(LDA,)e(LDB,)h(LDC,)g(M,)g(N,)g(TRANSA,)f
(TRANSB)514 2550 y(<type>)618 b(ALPHA,)47 b(BETA)514
2663 y(<type>)618 b(A\()48 b(LDA,)e(*)i(\),)f(B\()g(LDB,)g(*)g(\),)g
(C\()h(LDC,)e(*)i(\))136 2888 y FJ(\017)e FK(C)30 b(binding:)227
3113 y FD(void)47 b(BLAS_xgemm\()e(enum)h(blas_order_type)e(order,)i
(enum)h(blas_trans_type)c(transa,)1039 3226 y(enum)j(blas_trans_type)e
(transb,)i(int)h(m,)g(int)g(n,)g(int)g(k,)1039 3339 y(SCALAR_IN)e
(alpha,)h(const)g(ARRAY)h(a,)g(int)g(lda,)f(const)h(ARRAY)f(b,)1039
3452 y(int)h(ldb,)f(SCALAR_IN)f(beta,)i(ARRAY)f(c,)h(int)g(ldc)g(\);)p
0 3677 3900 6 v 0 3790 a FK(SYMM)31 b(\(Symmetric)e(Matrix)i(Matrix)f
(Pro)s(duct\))682 b Fy(C)31 b FJ( )25 b Fy(\013AB)h FK(+)20
b Fy(\014)5 b(C)37 b FK(or)30 b Fy(C)i FJ( )25 b Fy(\013B)5
b(A)20 b FK(+)g Fy(\014)5 b(C)141 4016 y FK(This)41 b(routine)h(p)s
(erforms)f(one)h(of)h(the)g(symmetric)f(matrix)g(matrix)g(op)s
(erations)g Fy(C)52 b FJ( )45 b Fy(\013AB)34 b FK(+)28
b Fy(\014)5 b(C)49 b FK(or)0 4129 y Fy(C)40 b FJ( )33
b Fy(\013B)5 b(A)24 b FK(+)f Fy(\014)5 b(C)42 b FK(where)35
b Fy(\013)g FK(and)g Fy(\014)40 b FK(are)c(scalars,)h
Fy(A)e FK(is)f(a)i(symmetric)f(matrix,)h(and)e Fy(B)40
b FK(and)35 b Fy(C)41 b FK(are)36 b(general)0 4242 y(matrices.)44
b(This)30 b(routine)h(returns)f(immediately)g(if)g Fv(alpha)h
FK(is)f(equal)i(to)g(zero)g(and)f Fv(b)s(eta)g FK(is)g(equal)g(to)h
(one,)g(or)g(if)0 4355 y Fv(m)c FK(or)f Fv(n)g FK(is)g(less)g(than)g
(or)g(equal)g(to)h(zero.)41 b(F)-8 b(or)28 b Fv(side)f
FK(equal)g(to)i Fv(blas)p 2255 4355 28 4 v 31 w(left)p
2409 4355 V 33 w(side)p FK(,)f(and)f(if)f Fv(lda)h FK(is)g(less)f(than)
h(one)h(or)g(less)0 4467 y(than)k Fv(m)p FK(,)i(or)e(if)f
Fv(ldb)h FK(is)g(less)g(than)g(one)g(or)h(less)f(than)g
Fv(m)p FK(,)h(or)f(if)g Fv(ldc)g FK(is)g(less)f(than)i(one)f(or)h(less)
e(than)i Fv(m)p FK(,)g(an)f(error)0 4580 y(\015ag)h(is)f(set)h(and)g
(passed)f(to)i(the)f(error)f(handler.)46 b(F)-8 b(or)34
b Fv(side)f FK(equal)f(to)i Fv(blas)p 2604 4580 V 32
w(right)p 2814 4580 V 32 w(side)p FK(,)g(and)e(if)g Fv(lda)g
FK(is)g(less)g(than)0 4693 y(one)g(or)f(less)g(than)h
Fv(n)p FK(,)g(or)f(if)g Fv(ldb)g FK(is)g(less)g(than)g(one)h(or)f(less)
g(than)h Fv(n)p FK(,)g(or)f(if)g Fv(ldc)g FK(is)g(less)g(than)g(one)h
(or)g(less)e(than)i Fv(n)p FK(,)0 4806 y(an)e(error)g(\015ag)h(is)e
(set)i(and)f(passed)g(to)h(the)g(error)f(handler.)141
4919 y(The)d(in)m(terfaces)h(encompass)g(the)g(Legacy)h(BLAS)f(routine)
e(xSYMM)i(with)f(added)g(functionalit)m(y)f(for)h(com-)0
5032 y(plex)i(symmetric)h(matrices.)136 5245 y FJ(\017)46
b FK(F)-8 b(ortran)31 b(95)h(binding:)4084 64 y FI(1)4084
177 y(2)4084 290 y(3)4084 403 y(4)4084 516 y(5)4084 628
y(6)4084 741 y(7)4084 854 y(8)4084 967 y(9)4069 1080
y(10)4069 1193 y(11)4069 1306 y(12)4069 1419 y(13)4069
1532 y(14)4069 1645 y(15)4069 1758 y(16)4069 1870 y(17)4069
1983 y(18)4069 2096 y(19)4069 2209 y(20)4069 2322 y(21)4069
2435 y(22)4069 2548 y(23)4069 2661 y(24)4069 2774 y(25)4069
2887 y(26)4069 3000 y(27)4069 3112 y(28)4069 3225 y(29)4069
3338 y(30)4069 3451 y(31)4069 3564 y(32)4069 3677 y(33)4069
3790 y(34)4069 3903 y(35)4069 4016 y(36)4069 4129 y(37)4069
4242 y(38)4069 4354 y(39)4069 4467 y(40)4069 4580 y(41)4069
4693 y(42)4069 4806 y(43)4069 4919 y(44)4069 5032 y(45)4069
5145 y(46)4069 5258 y(47)4069 5371 y(48)p eop
%%Page: 85 95
85 94 bop 0 -165 a FA(2.8.)72 b(LANGUA)m(GE)32 b(BINDINGS)2578
b FK(85)418 91 y FD(SUBROUTINE)45 b(symm\()i(a,)g(b,)g(c)g([,)h(side])e
([,)h(uplo])f([,)i(alpha])e([,)h(beta])f(\))514 204 y(<type>\(<wp>\),)e
(INTENT\(IN\))h(::)i(a\(:,:\),)f(<bb>)514 317 y(<type>\(<wp>\),)e
(INTENT\(INOUT\))g(::)j(<cc>)514 430 y(TYPE)f(\(blas_side_type\),)d
(INTENT\(IN\),)i(OPTIONAL)h(::)h(side)514 543 y(TYPE)f
(\(blas_uplo_type\),)d(INTENT\(IN\),)i(OPTIONAL)h(::)h(uplo)514
656 y(<type>\(<wp>\),)d(INTENT\(IN\),)h(OPTIONAL)g(::)i(alpha,)f(beta)
418 769 y(where)514 882 y(<bb>)94 b(::=)47 b(b\(:,:\))f(or)h(b\(:\))514
995 y(<cc>)94 b(::=)47 b(c\(:,:\))f(or)h(c\(:\))418 1108
y(and)466 1220 y(c,)g(rank)g(2,)g(has)g(shape)f(\(m,n\),)g(b)i(same)e
(shape)h(as)g(c)561 1333 y(SY)95 b(a)48 b(has)f(shape)f(\(m,m\))g(if)i
(side)e(=)i(blas_left_side)c(\(the)i(default\))752 1446
y(a)i(has)f(shape)f(\(n,n\))g(if)i(side)e(/=)h(blas_left_side)466
1559 y(c,)g(rank)g(1,)g(has)g(shape)f(\(m\),)h(b)g(same)g(shape)f(as)h
(c)561 1672 y(SY)95 b(a)48 b(has)f(shape)f(\(m,m\))p
1154 1801 1820 4 v 1152 1914 4 113 v 1204 1880 a FK(Rank)30
b FD(b)p 1541 1914 V 99 w FK(Rank)h FD(c)p 1929 1914
V 99 w(side)p 2220 1914 V 98 w FK(Op)s(eration)p 2972
1914 V 1154 1917 1820 4 v 1152 2030 4 113 v 1326 1996
a(2)p 1541 2030 V 343 w(2)p 1929 2030 V 289 w(L)p 2220
2030 V 166 w Fy(C)h FJ( )25 b Fy(\013AB)h FK(+)20 b Fy(\014)5
b(C)p 2972 2030 V 1152 2143 V 1326 2109 a FK(2)p 1541
2143 V 343 w(2)p 1929 2143 V 284 w(R)p 2220 2143 V 161
w Fy(C)32 b FJ( )25 b Fy(\013B)5 b(A)21 b FK(+)f Fy(\014)5
b(C)p 2972 2143 V 1152 2256 V 1326 2222 a FK(1)p 1541
2256 V 343 w(1)p 1929 2256 V 302 w(-)p 2220 2256 V 180
w Fy(c)26 b FJ( )f Fy(\013Ab)c FK(+)f Fy(\014)5 b(c)p
2972 2256 V 1154 2259 1820 4 v 227 2428 a FK(The)30 b(functionalit)m(y)
f(of)i(xSYMV)f(is)f(co)m(v)m(ered)j(b)m(y)f Fv(symm)p
FK(.)136 2604 y FJ(\017)46 b FK(F)-8 b(ortran)31 b(77)h(binding:)514
2795 y FD(SUBROUTINE)45 b(BLAS_xSYMM\()f(SIDE,)j(UPLO,)f(M,)h(N,)g
(ALPHA,)g(A,)g(LDA,)f(B,)i(LDB,)466 2908 y($)1097 b(BETA,)47
b(C,)g(LDC)g(\))514 3021 y(INTEGER)570 b(LDA,)47 b(LDB,)g(LDC,)f(M,)i
(N,)f(SIDE,)f(UPLO)514 3134 y(<type>)618 b(ALPHA,)47
b(BETA)514 3247 y(<type>)618 b(A\()48 b(LDA,)e(*)i(\),)f(B\()g(LDB,)g
(*)g(\),)g(C\()h(LDC,)e(*)i(\))136 3438 y FJ(\017)e FK(C)30
b(binding:)227 3628 y FD(void)47 b(BLAS_xsymm\()e(enum)h
(blas_order_type)e(order,)i(enum)h(blas_side_type)d(side,)1039
3741 y(enum)i(blas_uplo_type)e(uplo,)j(int)f(m,)i(int)f(n,)g(SCALAR_IN)
e(alpha,)1039 3854 y(const)h(ARRAY)g(a,)i(int)e(lda,)h(const)f(ARRAY)h
(b,)g(int)g(ldb,)1039 3967 y(SCALAR_IN)e(beta,)h(ARRAY)h(c,)g(int)g
(ldc)g(\);)p 0 4158 3900 6 v 0 4271 a FK(HEMM)31 b(\(Hermitian)e
(Matrix)i(Matrix)f(Pro)s(duct\))696 b Fy(C)31 b FJ( )25
b Fy(\013AB)h FK(+)20 b Fy(\014)5 b(C)37 b FK(or)30 b
Fy(C)i FJ( )25 b Fy(\013B)5 b(A)20 b FK(+)g Fy(\014)5
b(C)141 4497 y FK(This)42 b(routine)g(p)s(erforms)g(one)h(of)h(the)f
(Hermitian)f(matrix)h(matrix)f(op)s(erations)h Fy(C)53
b FJ( )47 b Fy(\013AB)34 b FK(+)28 b Fy(\014)5 b(C)50
b FK(or)0 4610 y Fy(C)41 b FJ( )34 b Fy(\013B)5 b(A)24
b FK(+)f Fy(\014)5 b(C)43 b FK(where)35 b Fy(\013)h FK(and)f
Fy(\014)41 b FK(are)36 b(scalars,)h Fy(A)f FK(is)f(a)h(Hermitian)f
(matrix,)h(and)f Fy(B)41 b FK(and)35 b Fy(C)42 b FK(are)36
b(general)0 4723 y(matrices.)44 b(This)30 b(routine)h(returns)f
(immediately)g(if)g Fv(alpha)h FK(is)f(equal)i(to)g(zero)g(and)f
Fv(b)s(eta)g FK(is)g(equal)g(to)h(one,)g(or)g(if)0 4835
y Fv(m)c FK(or)f Fv(n)g FK(is)g(less)g(than)g(or)g(equal)g(to)h(zero.)
41 b(F)-8 b(or)28 b Fv(side)f FK(equal)g(to)i Fv(blas)p
2255 4835 28 4 v 31 w(left)p 2409 4835 V 33 w(side)p
FK(,)f(and)f(if)f Fv(lda)h FK(is)g(less)f(than)h(one)h(or)g(less)0
4948 y(than)k Fv(m)p FK(,)i(or)e(if)f Fv(ldb)h FK(is)g(less)g(than)g
(one)g(or)h(less)f(than)g Fv(m)p FK(,)h(or)f(if)g Fv(ldc)g
FK(is)g(less)f(than)i(one)f(or)h(less)e(than)i Fv(m)p
FK(,)g(an)f(error)0 5061 y(\015ag)h(is)f(set)h(and)g(passed)f(to)i(the)
f(error)f(handler.)46 b(F)-8 b(or)34 b Fv(side)f FK(equal)f(to)i
Fv(blas)p 2604 5061 V 32 w(right)p 2814 5061 V 32 w(side)p
FK(,)g(and)e(if)g Fv(lda)g FK(is)g(less)g(than)0 5174
y(one)g(or)f(less)g(than)h Fv(n)p FK(,)g(or)f(if)g Fv(ldb)g
FK(is)g(less)g(than)g(one)h(or)f(less)g(than)h Fv(n)p
FK(,)g(or)f(if)g Fv(ldc)g FK(is)g(less)g(than)g(one)h(or)g(less)e(than)
i Fv(n)p FK(,)0 5287 y(an)e(error)g(\015ag)h(is)e(set)i(and)f(passed)g
(to)h(the)g(error)f(handler.)141 5400 y(The)g(in)m(terfaces)h
(encompass)f(the)h(Legacy)h(BLAS)e(routine)f(xHEMM.)-214
64 y FI(1)-214 177 y(2)-214 290 y(3)-214 403 y(4)-214
516 y(5)-214 628 y(6)-214 741 y(7)-214 854 y(8)-214 967
y(9)-230 1080 y(10)-230 1193 y(11)-230 1306 y(12)-230
1419 y(13)-230 1532 y(14)-230 1645 y(15)-230 1758 y(16)-230
1870 y(17)-230 1983 y(18)-230 2096 y(19)-230 2209 y(20)-230
2322 y(21)-230 2435 y(22)-230 2548 y(23)-230 2661 y(24)-230
2774 y(25)-230 2887 y(26)-230 3000 y(27)-230 3112 y(28)-230
3225 y(29)-230 3338 y(30)-230 3451 y(31)-230 3564 y(32)-230
3677 y(33)-230 3790 y(34)-230 3903 y(35)-230 4016 y(36)-230
4129 y(37)-230 4242 y(38)-230 4354 y(39)-230 4467 y(40)-230
4580 y(41)-230 4693 y(42)-230 4806 y(43)-230 4919 y(44)-230
5032 y(45)-230 5145 y(46)-230 5258 y(47)-230 5371 y(48)p
eop
%%Page: 86 96
86 95 bop 0 -165 a FK(86)1930 b FA(CHAPTER)30 b(2.)71
b(DENSE)30 b(AND)h(BANDED)h(BLAS)136 91 y FJ(\017)46
b FK(F)-8 b(ortran)31 b(95)h(binding:)227 316 y FD(Hermitian:)418
429 y(SUBROUTINE)45 b(hemm\()i(a,)g(b,)g(c)g([,)h(side])e([,)h(uplo])f
([,)i(alpha])e([,)h(beta])f(\))514 542 y(COMPLEX\(<wp>\),)e
(INTENT\(IN\))h(::)i(a\(:,:\),)f(<bb>)514 655 y(COMPLEX\(<wp>\),)e
(INTENT\(INOUT\))g(::)j(<cc>)514 768 y(TYPE)f(\(blas_side_type\),)d
(INTENT\(IN\),)i(OPTIONAL)h(::)h(side)514 881 y(TYPE)f
(\(blas_uplo_type\),)d(INTENT\(IN\),)i(OPTIONAL)h(::)h(uplo)514
994 y(COMPLEX\(<wp>\),)d(INTENT\(IN\),)g(OPTIONAL)i(::)h(alpha,)f(beta)
418 1107 y(where)514 1219 y(<bb>)94 b(::=)47 b(b\(:,:\))f(or)h(b\(:\))
514 1332 y(<cc>)94 b(::=)47 b(c\(:,:\))f(or)h(c\(:\))418
1445 y(and)466 1558 y(c,)g(rank)g(2,)g(has)g(shape)f(\(m,n\),)g(b)i
(same)e(shape)h(as)g(c)561 1671 y(HE)95 b(a)48 b(has)f(shape)f(\(m,m\))
g(if)i("side")e(=)h(blas_left_side)d(\(the)j(default\))752
1784 y(a)h(has)f(shape)f(\(n,n\))g(if)i("side")e(/=)h(blas_left_side)
466 1897 y(c,)g(rank)g(1,)g(has)g(shape)f(\(m\),)h(b)g(same)g(shape)f
(as)h(c)561 2010 y(HE)95 b(a)48 b(has)f(shape)f(\(m,m\))p
1154 2179 1820 4 v 1152 2291 4 113 v 1204 2258 a FK(Rank)30
b FD(b)p 1541 2291 V 99 w FK(Rank)h FD(c)p 1929 2291
V 99 w(side)p 2220 2291 V 98 w FK(Op)s(eration)p 2972
2291 V 1154 2295 1820 4 v 1152 2408 4 113 v 1326 2374
a(2)p 1541 2408 V 343 w(2)p 1929 2408 V 289 w(L)p 2220
2408 V 166 w Fy(C)h FJ( )25 b Fy(\013AB)h FK(+)20 b Fy(\014)5
b(C)p 2972 2408 V 1152 2521 V 1326 2487 a FK(2)p 1541
2521 V 343 w(2)p 1929 2521 V 284 w(R)p 2220 2521 V 161
w Fy(C)32 b FJ( )25 b Fy(\013B)5 b(A)21 b FK(+)f Fy(\014)5
b(C)p 2972 2521 V 1152 2633 V 1326 2600 a FK(1)p 1541
2633 V 343 w(1)p 1929 2633 V 302 w(-)p 2220 2633 V 180
w Fy(c)26 b FJ( )f Fy(\013Ab)c FK(+)f Fy(\014)5 b(c)p
2972 2633 V 1154 2637 1820 4 v 227 2845 a FK(The)30 b(functionalit)m(y)
f(of)i(xHEMV)f(is)g(co)m(v)m(ered)i(b)m(y)e Fv(hemm)p
FK(.)136 3033 y FJ(\017)46 b FK(F)-8 b(ortran)31 b(77)h(binding:)514
3258 y FD(SUBROUTINE)45 b(BLAS_xHEMM\()f(SIDE,)j(UPLO,)f(M,)h(N,)g
(ALPHA,)g(A,)g(LDA,)f(B,)i(LDB,)466 3370 y($)1097 b(BETA,)47
b(C,)g(LDC)g(\))514 3483 y(INTEGER)570 b(LDA,)47 b(LDB,)g(LDC,)f(M,)i
(N,)f(SIDE,)f(UPLO)514 3596 y(<ctype>)570 b(ALPHA,)47
b(BETA)514 3709 y(<ctype>)570 b(A\()48 b(LDA,)e(*)i(\),)f(B\()g(LDB,)g
(*)g(\),)g(C\()h(LDC,)e(*)i(\))136 3934 y FJ(\017)e FK(C)30
b(binding:)227 4159 y FD(void)47 b(BLAS_xhemm\()e(enum)h
(blas_order_type)e(order,)i(enum)h(blas_side_type)d(side,)1039
4272 y(enum)i(blas_uplo_type)e(uplo,)j(int)f(m,)i(int)f(n,)g
(CSCALAR_IN)e(alpha,)1039 4385 y(const)h(CARRAY)g(a,)h(int)g(lda,)g
(const)f(CARRAY)g(b,)h(int)g(ldb,)1039 4498 y(CSCALAR_IN)e(beta,)h
(CARRAY)g(c,)h(int)g(ldc)g(\);)p 0 4723 3900 6 v 0 4835
a FK(TRMM)31 b(\(T)-8 b(riangular)28 b(Matrix)j(Matrix)f(Multiply\))812
b Fy(B)30 b FJ( )25 b Fy(\013op)p FK(\()p Fy(T)13 b FK(\))p
Fy(B)35 b FK(or)c Fy(B)f FJ( )25 b Fy(\013B)5 b(op)p
FK(\()p Fy(T)13 b FK(\))141 5061 y(These)33 b(routines)g(p)s(erform)f
(one)i(of)g(the)g(matrix-matrix)e(op)s(erations)h Fy(B)i
FJ( )c Fy(\013op)p FK(\()p Fy(T)13 b FK(\))p Fy(B)38
b FK(or)c Fy(B)h FJ( )c Fy(\013B)5 b(op)p FK(\()p Fy(T)13
b FK(\))0 5174 y(where)31 b Fy(\013)h FK(is)f(a)h(scalar,)g
Fy(B)k FK(is)31 b(a)h(general)f(matrix,)h(and)f Fy(T)44
b FK(is)31 b(a)h(unit,)e(or)i(non-unit,)f(upp)s(er)e(or)j(lo)m(w)m(er)g
(triangular)0 5287 y(\(or)k(triangular)d(band\))i(matrix.)55
b(This)33 b(routine)h(returns)h(immediately)e(if)h Fv(m)p
FK(,)j Fv(n)p FK(,)g(or)e Fv(k)h FK(\(for)f(triangular)f(band)0
5400 y(matrices\),)i(is)e(less)g(than)g(or)h(equal)f(to)h(zero.)55
b(F)-8 b(or)35 b Fv(side)f FK(equal)h(to)g Fv(blas)p
2488 5400 28 4 v 32 w(left)p 2643 5400 V 32 w(side)p
FK(,)h(and)e(if)g Fv(ldt)g FK(is)f(less)h(than)h(one)4084
64 y FI(1)4084 177 y(2)4084 290 y(3)4084 403 y(4)4084
516 y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084 967
y(9)4069 1080 y(10)4069 1193 y(11)4069 1306 y(12)4069
1419 y(13)4069 1532 y(14)4069 1645 y(15)4069 1758 y(16)4069
1870 y(17)4069 1983 y(18)4069 2096 y(19)4069 2209 y(20)4069
2322 y(21)4069 2435 y(22)4069 2548 y(23)4069 2661 y(24)4069
2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
3677 y(33)4069 3790 y(34)4069 3903 y(35)4069 4016 y(36)4069
4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 87 97
87 96 bop 0 -165 a FA(2.8.)72 b(LANGUA)m(GE)32 b(BINDINGS)2578
b FK(87)0 91 y(or)30 b(less)g(than)h Fv(m)p FK(,)g(or)f(if)f
Fv(ldb)i FK(is)e(less)h(than)g(one)h(or)f(less)g(than)h
Fv(m)p FK(,)f(an)h(error)f(\015ag)h(is)e(set)i(and)f(passed)g(to)i(the)
e(error)0 204 y(handler.)47 b(F)-8 b(or)34 b Fv(side)f
FK(equal)g(to)h Fv(blas)p 1225 204 28 4 v 31 w(right)p
1434 204 V 33 w(side)p FK(,)g(and)f(if)f Fv(ldt)g FK(is)g(less)h(than)g
(one)g(or)g(less)g(than)g Fv(n)p FK(,)h(or)f(if)f Fv(ldb)g
FK(is)h(less)0 317 y(than)d(one)h(or)f(less)g(than)g
Fv(m)p FK(,)h(an)f(error)g(\015ag)h(is)e(set)i(and)f(passed)g(to)h(the)
f(error)g(handler.)141 430 y(These)g(in)m(terfaces)h(encompass)g(the)f
(Legacy)i(BLAS)e(routine)g(xTRMM.)136 643 y FJ(\017)46
b FK(F)-8 b(ortran)31 b(95)h(binding:)418 892 y FD(SUBROUTINE)45
b(trmm\()i(t,)g(b)g([,)g(side])g([,)g(uplo])f([,)h(transt])f([,)h
(diag])g([,)g(alpha])f(\))514 1005 y(<type>\(<wp>\),)e(INTENT\(IN\))h
(::)i(t\(:,:\))514 1118 y(<type>\(<wp>\),)d(INTENT\(INOUT\))g(::)j
(<bb>)514 1231 y(<type>\(<wp>\),)d(INTENT\(IN\),)h(OPTIONAL)g(::)i
(alpha)514 1344 y(TYPE)f(\(blas_diag_type\),)d(INTENT\(IN\),)i
(OPTIONAL)h(::)h(diag)514 1457 y(TYPE)f(\(blas_side_type\),)d
(INTENT\(IN\),)i(OPTIONAL)h(::)h(side)514 1570 y(TYPE)f
(\(blas_trans_type\),)d(INTENT\(IN\),)i(OPTIONAL)g(::)j(transt)514
1683 y(TYPE)e(\(blas_uplo_type\),)d(INTENT\(IN\),)i(OPTIONAL)h(::)h
(uplo)418 1796 y(where)514 1909 y(<bb>)94 b(::=)47 b(b\(:,:\))f(or)h
(b\(:\))418 2022 y(and)466 2134 y(b,)g(rank)g(2,)g(has)g(shape)f
(\(m,n\))561 2247 y(TR)95 b(t)48 b(has)f(shape)f(\(m,m\))g(if)i(side)e
(=)i(blas_left_side)c(\(the)i(default\))752 2360 y(t)i(has)f(shape)f
(\(n,n\))g(if)i(side)e(/=)h(blas_left_side)466 2473 y(b,)g(rank)g(1,)g
(has)g(shape)f(\(m\))561 2586 y(TR)95 b(t)48 b(has)f(shape)f(\(m,m\))p
1241 2755 1645 4 v 1239 2868 4 113 v 1291 2834 a FK(Rank)30
b FD(b)p 1628 2868 V 100 w(transt)p 2014 2868 V 98 w(side)p
2305 2868 V 98 w FK(Op)s(eration)p 2884 2868 V 1241 2871
1645 4 v 1239 2984 4 113 v 1413 2950 a(2)p 1628 2984
V 331 w(N)p 2014 2984 V 276 w(L)p 2305 2984 V 166 w Fy(B)g
FJ( )25 b Fy(\013T)13 b(B)p 2884 2984 V 1239 3097 V 1413
3063 a FK(2)p 1628 3097 V 332 w(T)p 2014 3097 V 277 w(L)p
2305 3097 V 166 w Fy(B)30 b FJ( )25 b Fy(\013T)2695 3030
y Fw(T)2750 3063 y Fy(B)p 2884 3097 V 1239 3210 V 1413
3176 a FK(2)p 1628 3210 V 331 w(H)p 2014 3210 V 276 w(L)p
2305 3210 V 166 w Fy(B)30 b FJ( )25 b Fy(\013T)2695 3143
y Fw(H)2763 3176 y Fy(B)p 2884 3210 V 1239 3323 V 1413
3289 a FK(2)p 1628 3323 V 331 w(N)p 2014 3323 V 271 w(R)p
2305 3323 V 161 w Fy(B)30 b FJ( )25 b Fy(\013B)5 b(T)p
2884 3323 V 1239 3436 V 1413 3402 a FK(2)p 1628 3436
V 332 w(T)p 2014 3436 V 272 w(R)p 2305 3436 V 161 w Fy(B)30
b FJ( )25 b Fy(\013B)5 b(T)2769 3369 y Fw(T)p 2884 3436
V 1239 3549 V 1413 3515 a FK(2)p 1628 3549 V 331 w(H)p
2014 3549 V 271 w(R)p 2305 3549 V 161 w Fy(B)30 b FJ( )25
b Fy(\013B)5 b(T)2769 3482 y Fw(H)p 2884 3549 V 1239
3662 V 1413 3628 a FK(1)p 1628 3662 V 331 w(N)p 2014
3662 V 289 w(-)p 2305 3662 V 180 w Fy(b)25 b FJ( )h Fy(\013T)13
b(b)p 2884 3662 V 1239 3774 V 1413 3741 a FK(1)p 1628
3774 V 332 w(T)p 2014 3774 V 290 w(-)p 2305 3774 V 180
w Fy(b)25 b FJ( )h Fy(\013T)2661 3708 y Fw(T)2716 3741
y Fy(b)p 2884 3774 V 1239 3887 V 1413 3853 a FK(1)p 1628
3887 V 331 w(H)p 2014 3887 V 289 w(-)p 2305 3887 V 180
w Fy(b)f FJ( )h Fy(\013T)2661 3821 y Fw(H)2728 3853 y
Fy(b)p 2884 3887 V 1241 3891 1645 4 v 227 4099 a FK(The)k(functionalit)
m(y)f(of)i(xTRMV)f(is)f(co)m(v)m(ered)j(b)m(y)f Fv(trmm)p
FK(.)136 4287 y FJ(\017)46 b FK(F)-8 b(ortran)31 b(77)h(binding:)514
4512 y FD(SUBROUTINE)45 b(BLAS_xTRMM\()f(SIDE,)j(UPLO,)f(TRANST,)g
(DIAG,)g(M,)h(N,)h(ALPHA,)e(T,)466 4625 y($)1097 b(LDT,)47
b(B,)g(LDB)g(\))514 4738 y(INTEGER)570 b(DIAG,)47 b(LDB,)f(LDT,)h(M,)g
(N,)g(SIDE,)g(TRANST,)f(UPLO)514 4850 y(<type>)618 b(ALPHA)514
4963 y(<type>)g(T\()48 b(LDT,)e(*)i(\),)f(B\()g(LDB,)g(*)g(\))136
5188 y FJ(\017)f FK(C)30 b(binding:)-214 64 y FI(1)-214
177 y(2)-214 290 y(3)-214 403 y(4)-214 516 y(5)-214 628
y(6)-214 741 y(7)-214 854 y(8)-214 967 y(9)-230 1080
y(10)-230 1193 y(11)-230 1306 y(12)-230 1419 y(13)-230
1532 y(14)-230 1645 y(15)-230 1758 y(16)-230 1870 y(17)-230
1983 y(18)-230 2096 y(19)-230 2209 y(20)-230 2322 y(21)-230
2435 y(22)-230 2548 y(23)-230 2661 y(24)-230 2774 y(25)-230
2887 y(26)-230 3000 y(27)-230 3112 y(28)-230 3225 y(29)-230
3338 y(30)-230 3451 y(31)-230 3564 y(32)-230 3677 y(33)-230
3790 y(34)-230 3903 y(35)-230 4016 y(36)-230 4129 y(37)-230
4242 y(38)-230 4354 y(39)-230 4467 y(40)-230 4580 y(41)-230
4693 y(42)-230 4806 y(43)-230 4919 y(44)-230 5032 y(45)-230
5145 y(46)-230 5258 y(47)-230 5371 y(48)p eop
%%Page: 88 98
88 97 bop 0 -165 a FK(88)1930 b FA(CHAPTER)30 b(2.)71
b(DENSE)30 b(AND)h(BANDED)h(BLAS)227 91 y FD(void)47
b(BLAS_xtrmm\()e(enum)h(blas_order_type)e(order,)i(enum)h
(blas_side_type)d(side,)1039 204 y(enum)i(blas_uplo_type)e(uplo,)j
(enum)f(blas_trans_type)e(transt,)1039 317 y(enum)i(blas_diag_type)e
(diag,)j(int)f(m,)i(int)f(n,)g(SCALAR_IN)e(alpha,)1039
430 y(const)h(ARRAY)g(t,)i(int)e(ldt,)h(ARRAY)f(b,)i(int)f(ldb)f(\);)p
0 611 3900 6 v 0 723 a FK(TRSM)30 b(\(T)-8 b(riangular)29
b(Solv)m(e\))1401 b Fy(B)30 b FJ( )25 b Fy(\013op)p FK(\()p
Fy(T)2887 690 y Fu(\000)p FC(1)2982 723 y FK(\))p Fy(B)35
b FK(or)30 b Fy(B)g FJ( )25 b Fy(\013B)5 b(op)p FK(\()p
Fy(T)3770 690 y Fu(\000)p FC(1)3865 723 y FK(\))141 949
y(This)23 b(routine)h(solv)m(es)i(one)f(of)g(the)g(matrix)f(equations)h
Fy(B)30 b FJ( )25 b Fy(\013op)p FK(\()p Fy(T)2471 916
y Fu(\000)p FC(1)2566 949 y FK(\))p Fy(B)30 b FK(or)25
b Fy(B)k FJ( )c Fy(\013B)5 b(op)p FK(\()p Fy(T)3343 916
y Fu(\000)p FC(1)3438 949 y FK(\))25 b(where)f Fy(\013)i
FK(is)0 1062 y(a)h(scalar,)g Fy(B)k FK(is)25 b(a)i(general)g(matrix,)f
(and)g Fy(T)39 b FK(is)26 b(a)h(unit,)f(or)g(non-unit,)g(upp)s(er)e(or)
j(lo)m(w)m(er)f(triangular)f(matrix.)39 b(This)0 1175
y(routine)31 b(returns)f(immediately)g(if)h Fv(m)h FK(or)f
Fv(n)h FK(is)f(less)g(than)g(or)h(equal)f(to)h(zero.)46
b(F)-8 b(or)32 b Fv(side)g FK(equal)f(to)h Fv(blas)p
3548 1175 28 4 v 32 w(left)p 3703 1175 V 33 w(side)p
FK(,)0 1288 y(and)27 b(if)g Fv(ldt)g FK(is)f(less)h(than)h(one)g(or)f
(less)g(than)h Fv(m)p FK(,)g(or)g(if)e Fv(ldb)i FK(is)e(less)h(than)h
(one)f(or)h(less)f(than)g Fv(m)p FK(,)i(an)e(error)h(\015ag)g(is)e(set)
0 1401 y(and)31 b(passed)g(to)h(the)g(error)f(handler.)42
b(F)-8 b(or)32 b Fv(side)f FK(equal)g(to)h Fv(blas)p
2174 1401 V 32 w(right)p 2384 1401 V 33 w(side)p FK(,)g(and)f(if)f
Fv(ldt)h FK(is)g(less)f(than)h(one)h(or)g(less)0 1514
y(than)c Fv(n)p FK(,)h(or)f(if)g Fv(ldb)f FK(is)h(less)f(than)i(one)f
(or)h(less)e(than)h Fv(m)p FK(,)h(an)g(error)f(\015ag)g(is)g(set)g(and)
g(passed)g(to)h(the)g(error)f(handler.)141 1627 y(These)i(in)m
(terfaces)h(encompass)g(the)f(Legacy)i(BLAS)e(routine)g(xTRSM.)227
1795 y Fz(A)-5 b(dvic)g(e)35 b(to)h(implementors.)97
b FK(Note)34 b(that)g(no)e(c)m(hec)m(k)j(for)e(singularit)m(y)-8
b(,)32 b(or)g(near)h(singularit)m(y)e(is)h(sp)s(eci\014ed)227
1908 y(for)24 b(these)g(triangular)f(equation-solving)f(routines.)38
b(The)23 b(requiremen)m(ts)g(for)h(suc)m(h)g(a)g(test)h(dep)s(end)d(on)
i(the)227 2021 y(application,)j(and)g(so)h(w)m(e)h(felt)e(that)i(this)d
(should)g(not)i(b)s(e)f(included,)f(but)h(should)f(instead)h(b)s(e)g(p)
s(erformed)227 2133 y(b)s(efore)j(calling)f(the)i(triangular)d(solv)m
(er.)41 b(\()p Fz(End)33 b(of)g(advic)-5 b(e)33 b(to)g(implementors.)p
FK(\))136 2301 y FJ(\017)46 b FK(F)-8 b(ortran)31 b(95)h(binding:)418
2499 y FD(SUBROUTINE)45 b(trsm\()i(t,)g(b)g([,)g(side])g([,)g(uplo])f
([,)h(transt])f([,)h(diag])g([,)g(alpha])f(\))514 2612
y(<type>\(<wp>\),)e(INTENT\(IN\))h(::)i(t\(:,:\))514
2725 y(<type>\(<wp>\),)d(INTENT\(INOUT\))g(::)j(<bb>)514
2838 y(TYPE)f(\(blas_side_type\),)d(INTENT\(IN\),)i(OPTIONAL)h(::)h
(side)514 2951 y(TYPE)f(\(blas_uplo_type\),)d(INTENT\(IN\),)i(OPTIONAL)
h(::)h(uplo)514 3064 y(TYPE)f(\(blas_trans_type\),)d(INTENT\(IN\),)i
(OPTIONAL)g(::)j(transt)514 3177 y(TYPE)e(\(blas_diag_type\),)d
(INTENT\(IN\),)i(OPTIONAL)h(::)h(diag)514 3290 y(<type>\(<wp>\),)d
(INTENT\(IN\),)h(OPTIONAL)g(::)i(alpha)418 3403 y(where)514
3516 y(<bb>)94 b(::=)47 b(b\(:,:\))f(or)h(b\(:\))418
3629 y(and)466 3741 y(b,)g(rank)g(2,)g(has)g(shape)f(\(m,n\))561
3854 y(TR)95 b(t)48 b(has)f(shape)f(\(m,m\))g(if)i(side)e(=)i
(blas_left_side)c(\(the)i(default\))752 3967 y(t)i(has)f(shape)f
(\(n,n\))g(if)i(side)e(/=)h(blas_left_side)466 4080 y(b,)g(rank)g(1,)g
(has)g(shape)f(\(m\))561 4193 y(TR)95 b(t)48 b(has)f(shape)f(\(m,m\))p
1214 4310 1700 4 v 1212 4423 4 113 v 1264 4389 a FK(Rank)30
b FD(b)p 1601 4423 V 99 w(transt)p 1987 4423 V 98 w(side)p
2277 4423 V 99 w FK(Op)s(eration)p 2912 4423 V 1214 4426
1700 4 v 1212 4539 4 113 v 1385 4505 a(2)p 1601 4539
V 331 w(N)p 1987 4539 V 276 w(L)p 2277 4539 V 167 w Fy(B)g
FJ( )25 b Fy(\013T)2668 4472 y Fu(\000)p FC(1)2762 4505
y Fy(B)p 2912 4539 V 1212 4652 V 1385 4618 a FK(2)p 1601
4652 V 333 w(T)p 1987 4652 V 276 w(L)p 2277 4652 V 167
w Fy(B)30 b FJ( )25 b Fy(\013T)2668 4585 y Fu(\000)p
Fw(T)2778 4618 y Fy(B)p 2912 4652 V 1212 4765 V 1385
4731 a FK(2)p 1601 4765 V 331 w(H)p 1987 4765 V 276 w(L)p
2277 4765 V 167 w Fy(B)30 b FJ( )25 b Fy(\013T)2668 4698
y Fu(\000)p Fw(H)2790 4731 y Fy(B)p 2912 4765 V 1212
4878 V 1385 4844 a FK(2)p 1601 4878 V 331 w(N)p 1987
4878 V 271 w(R)p 2277 4878 V 162 w Fy(B)30 b FJ( )25
b Fy(\013B)5 b(T)2742 4811 y Fu(\000)p FC(1)p 2912 4878
V 1212 4991 V 1385 4957 a FK(2)p 1601 4991 V 333 w(T)p
1987 4991 V 271 w(R)p 2277 4991 V 162 w Fy(B)30 b FJ( )25
b Fy(\013B)5 b(T)2742 4924 y Fu(\000)p Fw(T)p 2912 4991
V 1212 5104 V 1385 5070 a FK(2)p 1601 5104 V 331 w(H)p
1987 5104 V 271 w(R)p 2277 5104 V 162 w Fy(B)30 b FJ( )25
b Fy(\013B)5 b(T)2742 5037 y Fu(\000)p Fw(H)p 2912 5104
V 1212 5217 V 1385 5183 a FK(1)p 1601 5217 V 331 w(N)p
1987 5217 V 290 w(-)p 2277 5217 V 180 w Fy(b)25 b FJ( )g
Fy(\013T)2633 5150 y Fu(\000)p FC(1)2728 5183 y Fy(b)p
2912 5217 V 1212 5329 V 1385 5296 a FK(1)p 1601 5329
V 333 w(T)p 1987 5329 V 290 w(-)p 2277 5329 V 180 w Fy(b)g
FJ( )g Fy(\013T)2633 5263 y Fu(\000)p Fw(T)2743 5296
y Fy(b)p 2912 5329 V 1212 5442 V 1385 5408 a FK(1)p 1601
5442 V 331 w(H)p 1987 5442 V 290 w(-)p 2277 5442 V 180
w Fy(b)g FJ( )g Fy(\013T)2633 5375 y Fu(\000)p Fw(H)2756
5408 y Fy(b)p 2912 5442 V 1214 5446 1700 4 v 4084 64
a FI(1)4084 177 y(2)4084 290 y(3)4084 403 y(4)4084 516
y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084 967 y(9)4069
1080 y(10)4069 1193 y(11)4069 1306 y(12)4069 1419 y(13)4069
1532 y(14)4069 1645 y(15)4069 1758 y(16)4069 1870 y(17)4069
1983 y(18)4069 2096 y(19)4069 2209 y(20)4069 2322 y(21)4069
2435 y(22)4069 2548 y(23)4069 2661 y(24)4069 2774 y(25)4069
2887 y(26)4069 3000 y(27)4069 3112 y(28)4069 3225 y(29)4069
3338 y(30)4069 3451 y(31)4069 3564 y(32)4069 3677 y(33)4069
3790 y(34)4069 3903 y(35)4069 4016 y(36)4069 4129 y(37)4069
4242 y(38)4069 4354 y(39)4069 4467 y(40)4069 4580 y(41)4069
4693 y(42)4069 4806 y(43)4069 4919 y(44)4069 5032 y(45)4069
5145 y(46)4069 5258 y(47)4069 5371 y(48)p eop
%%Page: 89 99
89 98 bop 0 -165 a FA(2.8.)72 b(LANGUA)m(GE)32 b(BINDINGS)2578
b FK(89)227 91 y(The)30 b(functionalit)m(y)f(of)i(xTRSV)e(is)g(co)m(v)m
(ered)j(b)m(y)f Fv(trsm)p FK(.)136 270 y FJ(\017)46 b
FK(F)-8 b(ortran)31 b(77)h(binding:)514 470 y FD(SUBROUTINE)45
b(BLAS_xTRSM\()f(SIDE,)j(UPLO,)f(TRANST,)g(DIAG,)g(M,)h(N,)h(ALPHA,)466
583 y($)1097 b(T,)48 b(LDT,)e(B,)h(LDB)g(\))514 695 y(INTEGER)570
b(DIAG,)47 b(LDB,)f(LDT,)h(M,)g(N,)g(SIDE,)g(TRANST,)f(UPLO)514
808 y(<type>)618 b(ALPHA)514 921 y(<type>)g(T\()48 b(LDT,)e(*)i(\),)f
(B\()g(LDB,)g(*)g(\))136 1120 y FJ(\017)f FK(C)30 b(binding:)227
1320 y FD(void)47 b(BLAS_xtrsm\()e(enum)h(blas_order_type)e(order,)i
(enum)h(blas_side_type)d(side,)1039 1433 y(enum)i(blas_uplo_type)e
(uplo,)j(enum)f(blas_trans_type)e(transt,)1039 1546 y(enum)i
(blas_diag_type)e(diag,)j(int)f(m,)i(int)f(n,)g(SCALAR_IN)e(alpha,)1039
1658 y(const)h(ARRAY)g(t,)i(int)e(ldt,)h(ARRAY)f(b,)i(int)f(ldb)f(\);)p
0 1858 3900 6 v 0 1971 a FK(SYRK)30 b(\(Symmetric)f(Rank)h(K)g(up)s
(date\))1009 b Fy(C)32 b FJ( )25 b Fy(\013AA)2848 1938
y Fw(T)2924 1971 y FK(+)20 b Fy(\014)5 b(C)i FK(,)30
b Fy(C)i FJ( )25 b Fy(\013A)3537 1938 y Fw(T)3593 1971
y Fy(A)20 b FK(+)g Fy(\014)5 b(C)141 2196 y FK(This)41
b(routine)h(p)s(erforms)f(one)i(of)g(the)g(symmetric)f(rank)g(k)h(op)s
(erations)f Fy(C)52 b FJ( )46 b Fy(\013AA)3214 2163 y
Fw(T)3298 2196 y FK(+)29 b Fy(\014)5 b(C)49 b FK(or)43
b Fy(C)52 b FJ( )0 2309 y Fy(\013A)126 2276 y Fw(T)182
2309 y Fy(A)20 b FK(+)g Fy(\014)5 b(C)37 b FK(where)29
b Fy(\013)i FK(and)f Fy(\014)35 b FK(are)c(scalars,)f
Fy(C)37 b FK(is)29 b(a)i(symmetric)e(matrix,)h(and)g
Fy(A)g FK(is)g(a)g(general)h(matrix.)40 b(This)0 2422
y(routine)35 b(returns)f(immediately)g(if)g Fv(alpha)g
FK(is)h(equal)g(to)h(zero)h(and)d Fv(b)s(eta)h FK(is)g(equal)g(to)h
(one,)h(or)f(if)e Fv(n)i FK(or)f Fv(k)h FK(is)f(less)0
2535 y(than)e(or)h(equal)f(to)h(zero.)51 b(If)33 b Fv(ldc)g
FK(is)g(less)g(than)g(one)h(or)f(less)g(than)g Fv(n)p
FK(,)i(an)e(error)g(\015ag)h(is)f(set)h(and)e(passed)i(to)g(the)0
2648 y(error)g(handler.)49 b(F)-8 b(or)35 b Fv(trans)e
FK(equal)g(to)i Fv(blas)p 1502 2648 28 4 v 32 w(no)p
1626 2648 V 33 w(trans)p FK(,)f(and)g(if)f Fv(lda)g FK(is)g(less)g
(than)h(one)g(or)g(less)f(than)h Fv(n)p FK(,)h(an)e(error)0
2761 y(\015ag)e(is)f(set)h(and)f(passed)g(to)h(the)g(error)f(handler.)
40 b(F)-8 b(or)31 b Fv(trans)f FK(equal)h(to)g Fv(blas)p
2616 2761 V 32 w(trans)p FK(,)f(and)g(if)g Fv(lda)g FK(is)f(less)h
(than)h(one)0 2874 y(or)f(less)g(than)g Fv(k)p FK(,)h(an)f(error)g
(\015ag)h(is)f(set)g(and)g(passed)g(to)h(the)g(error)f(handler.)141
2987 y(These)43 b(in)m(terfaces)h(encompass)f(the)h(Legacy)h(BLAS)e
(routine)f(xSYRK)h(with)f(added)g(functionalit)m(y)g(for)0
3100 y(complex)30 b(symmetric)g(matrices.)136 3286 y
FJ(\017)46 b FK(F)-8 b(ortran)31 b(95)h(binding:)418
3506 y FD(SUBROUTINE)45 b(syrk\()i(a,)g(c)g([,)g(uplo])g([,)g(trans])f
([,)h(alpha])f([,)h(beta])g(\))514 3619 y(<type>\(<wp>\),)d
(INTENT\(IN\))h(::)i(<aa>)514 3732 y(<type>\(<wp>\),)d(INTENT\(INOUT\))
g(::)j(c\(:,:\))514 3845 y(TYPE)f(\(blas_uplo_type\),)d(INTENT\(IN\),)i
(OPTIONAL)h(::)h(uplo)514 3958 y(TYPE)f(\(blas_trans_type\),)d
(INTENT\(IN\),)i(OPTIONAL)g(::)j(trans)514 4071 y(<type>\(<wp>\),)c
(INTENT\(IN\),)h(OPTIONAL)g(::)i(alpha,)f(beta)418 4184
y(where)514 4297 y(<aa>)94 b(::=)47 b(a\(:,:\))f(or)h(a\(:\))418
4410 y(and)466 4523 y(c)g(has)g(shape)g(\(n,n\))466 4635
y(a)g(has)g(shape)g(\(n,k\))f(if)h(trans)g(=)g(blas_no_trans)d(\(the)j
(default\))1039 4748 y(\(k,n\))f(if)h(trans)g(/=)g(blas_no_trans)1039
4861 y(\(n\))g(if)g(rank)f(1)p 1300 4987 1528 4 v 1298
5100 4 113 v 1349 5066 a FK(Rank)31 b FD(a)p 1686 5100
V 99 w(trans)p 2025 5100 V 98 w FK(Op)s(eration)p 2826
5100 V 1300 5104 1528 4 v 1298 5217 4 113 v 1471 5183
a(2)p 1686 5217 V 307 w(N)p 2025 5217 V 185 w Fy(C)h
FJ( )25 b Fy(\013AA)2483 5150 y Fw(T)2559 5183 y FK(+)20
b Fy(\014)5 b(C)p 2826 5217 V 1298 5329 V 1471 5296 a
FK(2)p 1686 5329 V 308 w(T)p 2025 5329 V 186 w Fy(C)32
b FJ( )25 b Fy(\013A)2415 5263 y Fw(T)2471 5296 y Fy(A)20
b FK(+)g Fy(\014)5 b(C)p 2826 5329 V 1298 5442 V 1471
5408 a FK(1)p 1686 5442 V 326 w(-)p 2025 5442 V 204 w
Fy(C)32 b FJ( )25 b Fy(\013aa)2443 5375 y Fw(T)2519 5408
y FK(+)20 b Fy(\014)5 b(C)p 2826 5442 V 1300 5446 1528
4 v -214 64 a FI(1)-214 177 y(2)-214 290 y(3)-214 403
y(4)-214 516 y(5)-214 628 y(6)-214 741 y(7)-214 854 y(8)-214
967 y(9)-230 1080 y(10)-230 1193 y(11)-230 1306 y(12)-230
1419 y(13)-230 1532 y(14)-230 1645 y(15)-230 1758 y(16)-230
1870 y(17)-230 1983 y(18)-230 2096 y(19)-230 2209 y(20)-230
2322 y(21)-230 2435 y(22)-230 2548 y(23)-230 2661 y(24)-230
2774 y(25)-230 2887 y(26)-230 3000 y(27)-230 3112 y(28)-230
3225 y(29)-230 3338 y(30)-230 3451 y(31)-230 3564 y(32)-230
3677 y(33)-230 3790 y(34)-230 3903 y(35)-230 4016 y(36)-230
4129 y(37)-230 4242 y(38)-230 4354 y(39)-230 4467 y(40)-230
4580 y(41)-230 4693 y(42)-230 4806 y(43)-230 4919 y(44)-230
5032 y(45)-230 5145 y(46)-230 5258 y(47)-230 5371 y(48)p
eop
%%Page: 90 100
90 99 bop 0 -165 a FK(90)1930 b FA(CHAPTER)30 b(2.)71
b(DENSE)30 b(AND)h(BANDED)h(BLAS)227 91 y FK(The)e(functionalit)m(y)f
(of)i(xSYR)e(is)h(co)m(v)m(ered)i(b)m(y)e Fv(syrk)p FK(.)136
279 y FJ(\017)46 b FK(F)-8 b(ortran)31 b(77)h(binding:)514
504 y FD(SUBROUTINE)45 b(BLAS_xSYRK\()f(UPLO,)j(TRANS,)f(N,)h(K,)g
(ALPHA,)f(A,)h(LDA,)g(BETA,)466 617 y($)1097 b(C,)48
b(LDC)e(\))514 730 y(INTEGER)570 b(K,)48 b(LDA,)e(LDC,)h(N,)g(TRANS,)f
(UPLO)514 843 y(<type>)618 b(ALPHA,)47 b(BETA)514 956
y(<type>)618 b(A\()48 b(LDA,)e(*)i(\),)f(C\()g(LDC,)g(*)g(\))136
1181 y FJ(\017)f FK(C)30 b(binding:)227 1406 y FD(void)47
b(BLAS_xsyrk\()e(enum)h(blas_order_type)e(order,)i(enum)h
(blas_uplo_type)d(uplo,)1039 1518 y(enum)i(blas_trans_type)e(trans,)i
(int)h(n,)g(int)g(k,)g(SCALAR_IN)e(alpha,)1039 1631 y(const)h(ARRAY)g
(a,)i(int)e(lda,)h(SCALAR_IN)e(beta,)i(ARRAY)f(c,)h(int)g(ldc)g(\);)p
0 1856 3900 6 v 0 1969 a FK(HERK)30 b(\(Hermitian)f(Rank)i(K)f(up)s
(date\))998 b Fy(C)32 b FJ( )25 b Fy(\013AA)2824 1936
y Fw(H)2912 1969 y FK(+)20 b Fy(\014)5 b(C)i FK(,)30
b Fy(C)i FJ( )25 b Fy(\013A)3525 1936 y Fw(H)3593 1969
y Fy(A)20 b FK(+)g Fy(\014)5 b(C)141 2195 y FK(This)41
b(routine)h(p)s(erforms)f(one)i(of)g(the)f(Hermitian)g(rank)g(k)g(op)s
(erations)g Fy(C)53 b FJ( )45 b Fy(\013AA)3202 2162 y
Fw(H)3299 2195 y FK(+)28 b Fy(\014)5 b(C)49 b FK(or)43
b Fy(C)52 b FJ( )0 2308 y Fy(\013A)126 2275 y Fw(H)194
2308 y Fy(A)20 b FK(+)g Fy(\014)5 b(C)36 b FK(where)30
b Fy(\013)h FK(and)e Fy(\014)36 b FK(are)30 b(scalars,)h
Fy(C)36 b FK(is)29 b(a)i(Hermitian)e(matrix,)h(and)f
Fy(A)i FK(is)e(a)i(general)f(matrix.)40 b(This)0 2421
y(routine)35 b(returns)f(immediately)g(if)g Fv(alpha)g
FK(is)h(equal)g(to)h(zero)h(and)d Fv(b)s(eta)h FK(is)g(equal)g(to)h
(one,)h(or)f(if)e Fv(n)i FK(or)f Fv(k)h FK(is)f(less)0
2534 y(than)e(or)h(equal)f(to)h(zero.)51 b(If)33 b Fv(ldc)g
FK(is)g(less)g(than)g(one)h(or)f(less)g(than)g Fv(n)p
FK(,)i(an)e(error)g(\015ag)h(is)f(set)h(and)e(passed)i(to)g(the)0
2647 y(error)g(handler.)49 b(F)-8 b(or)35 b Fv(trans)e
FK(equal)g(to)i Fv(blas)p 1502 2647 28 4 v 32 w(no)p
1626 2647 V 33 w(trans)p FK(,)f(and)g(if)f Fv(lda)g FK(is)g(less)g
(than)h(one)g(or)g(less)f(than)h Fv(n)p FK(,)h(an)e(error)0
2760 y(\015ag)e(is)f(set)h(and)f(passed)g(to)h(the)g(error)f(handler.)
40 b(F)-8 b(or)31 b Fv(trans)f FK(equal)h(to)g Fv(blas)p
2616 2760 V 32 w(trans)p FK(,)f(and)g(if)g Fv(lda)g FK(is)f(less)h
(than)h(one)0 2873 y(or)f(less)g(than)g Fv(k)p FK(,)h(an)f(error)g
(\015ag)h(is)f(set)g(and)g(passed)g(to)h(the)g(error)f(handler.)141
2985 y(These)g(in)m(terfaces)h(encompass)g(the)f(Legacy)i(BLAS)e
(routine)g(xHERK.)136 3198 y FJ(\017)46 b FK(F)-8 b(ortran)31
b(95)h(binding:)418 3423 y FD(SUBROUTINE)45 b(herk\()i(a,)g(c)g([,)g
(uplo])g([,)g(trans])f([,)h(alpha])f([,)h(beta])g(\))514
3536 y(COMPLEX\(<wp>\),)d(INTENT\(IN\))h(::)i(<aa>)514
3649 y(COMPLEX\(<wp>\),)d(INTENT\(INOUT\))g(::)j(c\(:,:\))514
3762 y(TYPE)f(\(blas_uplo_type\),)d(INTENT\(IN\),)i(OPTIONAL)h(::)h
(uplo)514 3875 y(TYPE)f(\(blas_trans_type\),)d(INTENT\(IN\),)i
(OPTIONAL)g(::)j(trans)514 3988 y(REAL\(<wp>\),)c(INTENT\(IN\),)h
(OPTIONAL)h(::)h(alpha,)f(beta)418 4100 y(where)514 4213
y(<aa>)94 b(::=)47 b(a\(:,:\))f(or)h(a\(:\))418 4326
y(and)466 4439 y(c)g(has)g(shape)g(\(n,n\))466 4552 y(a)g(has)g(shape)g
(\(n,k\))f(if)h(trans)g(=)g(blas_no_trans)d(\(the)j(default\))1039
4665 y(\(k,n\))f(if)h(trans)g(/=)g(blas_no_trans)1039
4778 y(\(n\))g(if)g(rank)f(1)p 1294 4934 1541 4 v 1292
5047 4 113 v 1343 5013 a FK(Rank)31 b FD(a)p 1680 5047
V 99 w(trans)p 2019 5047 V 98 w FK(Op)s(eration)p 2832
5047 V 1294 5050 1541 4 v 1292 5163 4 113 v 1465 5129
a(2)p 1680 5163 V 307 w(N)p 2019 5163 V 185 w Fy(C)h
FJ( )25 b Fy(\013AA)2477 5096 y Fw(H)2565 5129 y FK(+)20
b Fy(\014)5 b(C)p 2832 5163 V 1292 5276 V 1465 5242 a
FK(2)p 1680 5276 V 308 w(T)p 2019 5276 V 186 w Fy(C)32
b FJ( )25 b Fy(\013A)2409 5209 y Fw(H)2477 5242 y Fy(A)20
b FK(+)g Fy(\014)5 b(C)p 2832 5276 V 1292 5389 V 1465
5355 a FK(1)p 1680 5389 V 326 w(-)p 2019 5389 V 204 w
Fy(C)32 b FJ( )25 b Fy(\013aa)2437 5322 y Fw(H)2525 5355
y FK(+)20 b Fy(\014)5 b(C)p 2832 5389 V 1294 5392 1541
4 v 4084 64 a FI(1)4084 177 y(2)4084 290 y(3)4084 403
y(4)4084 516 y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084
967 y(9)4069 1080 y(10)4069 1193 y(11)4069 1306 y(12)4069
1419 y(13)4069 1532 y(14)4069 1645 y(15)4069 1758 y(16)4069
1870 y(17)4069 1983 y(18)4069 2096 y(19)4069 2209 y(20)4069
2322 y(21)4069 2435 y(22)4069 2548 y(23)4069 2661 y(24)4069
2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
3677 y(33)4069 3790 y(34)4069 3903 y(35)4069 4016 y(36)4069
4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 91 101
91 100 bop 0 -165 a FA(2.8.)72 b(LANGUA)m(GE)32 b(BINDINGS)2578
b FK(91)227 91 y(The)30 b(functionalit)m(y)f(of)i(xHER)f(is)f(co)m(v)m
(ered)j(b)m(y)e Fv(herk)p FK(.)136 274 y FJ(\017)46 b
FK(F)-8 b(ortran)31 b(77)h(binding:)514 485 y FD(SUBROUTINE)45
b(BLAS_xHERK\()f(UPLO,)j(TRANS,)f(N,)h(K,)g(ALPHA,)f(A,)h(LDA,)g(BETA,)
f(C,)466 598 y($)1097 b(LDC)47 b(\))514 711 y(INTEGER)570
b(K,)48 b(LDA,)e(LDC,)h(N,)g(TRANS,)f(UPLO)514 824 y(<rtype>)570
b(ALPHA,)47 b(BETA)514 937 y(<ctype>)570 b(A\()48 b(LDA,)e(*)i(\),)f
(C\()g(LDC,)g(*)g(\))136 1147 y FJ(\017)f FK(C)30 b(binding:)227
1358 y FD(void)47 b(BLAS_xherk\()e(enum)h(blas_order_type)e(order,)i
(enum)h(blas_uplo_type)d(uplo,)1039 1471 y(enum)i(blas_trans_type)e
(trans,)i(int)h(n,)g(int)g(k,)g(RSCALAR_IN)e(alpha,)1039
1584 y(const)h(CARRAY)g(a,)h(int)g(lda,)g(RSCALAR_IN)e(beta,)h(CARRAY)g
(c,)h(int)g(ldc)g(\);)p 0 1794 3900 6 v 0 1907 a FK(SY)p
124 1907 28 4 v 32 w(TRIDIA)m(G)p 560 1907 V 34 w(RK)30
b(\(Symmetric)f(Rank)i(K)f(up)s(date)f(with)g(symmetric)h(tridiagonal)f
(matrix\))2323 2083 y Fy(C)j FJ( )25 b Fy(\013AJ)9 b(A)2789
2050 y Fw(T)2865 2083 y FK(+)20 b Fy(\014)5 b(C)i FK(,)30
b Fy(C)i FJ( )25 b Fy(\013A)3478 2050 y Fw(T)3534 2083
y Fy(J)9 b(A)20 b FK(+)g Fy(\014)5 b(C)141 2259 y FK(This)38
b(routine)g(p)s(erforms)g(one)i(of)g(the)g(symmetric)e(rank)h(k)h(op)s
(erations)f Fy(C)47 b FJ( )40 b Fy(\013AJ)9 b(A)3230
2226 y Fw(T)3312 2259 y FK(+)26 b Fy(\014)5 b(C)47 b
FK(or)39 b Fy(C)47 b FJ( )0 2372 y Fy(\013A)126 2339
y Fw(T)182 2372 y Fy(J)9 b(A)22 b FK(+)h Fy(\014)5 b(C)40
b FK(where)33 b Fy(\013)h FK(and)f Fy(\014)39 b FK(are)34
b(scalars,)h Fy(C)40 b FK(is)33 b(a)h(symmetric)f(matrix,)h
Fy(A)g FK(is)f(a)h(general)g(matrix,)g(and)f Fy(J)0 2485
y FK(is)f(a)i(symmetric)e(tridiagonal)g(matrix.)49 b(This)31
b(routine)i(returns)f(immediately)f(if)h Fv(alpha)g FK(is)h(equal)g(to)
g(zero)i(and)0 2597 y Fv(b)s(eta)30 b FK(is)g(equal)h(to)h(one,)f(or)g
(if)f Fv(n)h FK(or)g Fv(k)h FK(is)e(less)g(than)h(or)g(equal)f(to)i
(zero.)44 b(If)30 b Fv(ldc)h FK(is)f(less)h(than)f(one)i(or)f(less)f
(than)h Fv(n)p FK(,)0 2710 y(an)j(error)g(\015ag)g(is)f(set)i(and)e
(passed)h(to)g(the)h(error)e(handler.)50 b(F)-8 b(or)35
b Fv(trans)e FK(equal)h(to)h Fv(blas)p 3024 2710 V 31
w(no)p 3147 2710 V 34 w(trans)p FK(,)f(and)g(if)f Fv(lda)g
FK(is)0 2823 y(less)h(than)g(one)h(or)g(less)e(than)i
Fv(n)p FK(,)g(an)g(error)f(\015ag)h(is)f(set)h(and)f(passed)g(to)h(the)
g(error)f(handler.)51 b(F)-8 b(or)36 b Fv(trans)d FK(equal)0
2936 y(to)g Fv(blas)p 266 2936 V 32 w(trans)p FK(,)g(and)f(if)g
Fv(lda)g FK(is)g(less)g(than)g(one)h(or)g(less)f(than)g
Fv(k)p FK(,)i(an)f(error)f(\015ag)h(is)f(set)h(and)f(passed)g(to)h(the)
g(error)0 3049 y(handler.)136 3247 y FJ(\017)46 b FK(F)-8
b(ortran)31 b(95)h(binding:)418 3481 y FD(SUBROUTINE)45
b(sy_tridiag_rk\()f(a,)j(d,)g(e,)h(c)f([,)g(uplo])g([,)g(trans])f([,)h
(alpha])f(&)1659 3593 y([,)h(beta])g(\))514 3706 y(<type>\(<wp>\),)d
(INTENT\(IN\))h(::)i(a\(:,:\))514 3819 y(<type>\(<wp>\),)d
(INTENT\(IN\))h(::)i(d\(:\),)f(e\(:\))514 3932 y(<type>\(<wp>\),)e
(INTENT\(INOUT\))g(::)j(c\(:,:\))514 4045 y(TYPE)f(\(blas_uplo_type\),)
d(INTENT\(IN\),)i(OPTIONAL)h(::)h(uplo)514 4158 y(TYPE)f
(\(blas_trans_type\),)d(INTENT\(IN\),)i(OPTIONAL)g(::)j(trans)514
4271 y(<type>\(<wp>\),)c(INTENT\(IN\),)h(OPTIONAL)g(::)i(alpha,)f(beta)
418 4384 y(where)466 4497 y(c)h(has)g(shape)g(\(n,n\))514
4610 y(if)g(trans)f(=)i(blas_no_trans)c(\(the)i(default\))657
4723 y(a)h(has)g(shape)g(\(n,k\))657 4835 y(d)g(has)g(shape)g(\(k\))657
4948 y(e)g(has)g(shape)g(\(k-1\))514 5061 y(if)g(trans)f(/=)h
(blas_no_trans)657 5174 y(a)g(has)g(shape)g(\(k,n\))657
5287 y(d)g(has)g(shape)g(\(n\))657 5400 y(e)g(has)g(shape)g(\(n-1\))
-214 64 y FI(1)-214 177 y(2)-214 290 y(3)-214 403 y(4)-214
516 y(5)-214 628 y(6)-214 741 y(7)-214 854 y(8)-214 967
y(9)-230 1080 y(10)-230 1193 y(11)-230 1306 y(12)-230
1419 y(13)-230 1532 y(14)-230 1645 y(15)-230 1758 y(16)-230
1870 y(17)-230 1983 y(18)-230 2096 y(19)-230 2209 y(20)-230
2322 y(21)-230 2435 y(22)-230 2548 y(23)-230 2661 y(24)-230
2774 y(25)-230 2887 y(26)-230 3000 y(27)-230 3112 y(28)-230
3225 y(29)-230 3338 y(30)-230 3451 y(31)-230 3564 y(32)-230
3677 y(33)-230 3790 y(34)-230 3903 y(35)-230 4016 y(36)-230
4129 y(37)-230 4242 y(38)-230 4354 y(39)-230 4467 y(40)-230
4580 y(41)-230 4693 y(42)-230 4806 y(43)-230 4919 y(44)-230
5032 y(45)-230 5145 y(46)-230 5258 y(47)-230 5371 y(48)p
eop
%%Page: 92 102
92 101 bop 0 -165 a FK(92)1930 b FA(CHAPTER)30 b(2.)71
b(DENSE)30 b(AND)h(BANDED)h(BLAS)p 1270 3 1588 4 v 1268
116 4 113 v 1320 82 a FK(Rank)e FD(a)p 1657 116 V 99
w(trans)p 1995 116 V 99 w FK(Op)s(eration)p 2856 116
V 1270 120 1588 4 v 1268 232 4 113 v 1442 199 a(2)p 1657
232 V 307 w(N)p 1995 232 V 185 w Fy(C)h FJ( )26 b Fy(\013AJ)9
b(A)2513 166 y Fw(T)2589 199 y FK(+)20 b Fy(\014)5 b(C)p
2856 232 V 1268 345 V 1442 311 a FK(2)p 1657 345 V 308
w(T)p 1995 345 V 186 w Fy(C)31 b FJ( )26 b Fy(\013A)2386
279 y Fw(T)2441 311 y Fy(J)9 b(A)21 b FK(+)f Fy(\014)5
b(C)p 2856 345 V 1270 349 1588 4 v 136 550 a FJ(\017)46
b FK(F)-8 b(ortran)31 b(77)h(binding:)514 769 y FD(SUBROUTINE)45
b(BLAS_xSY_TRIDIAG_RK\()d(UPLO,)k(TRANS,)g(N,)i(K,)f(ALPHA,)f(A,)h
(LDA,)g(D,)466 881 y($)1527 b(E,)47 b(BETA,)f(C,)i(LDC)f(\))514
994 y(INTEGER)570 b(K,)48 b(LDA,)e(LDC,)h(N,)g(TRANS,)f(UPLO)514
1107 y(<type>)618 b(ALPHA,)47 b(BETA)514 1220 y(<type>)618
b(A\()48 b(LDA,)e(*)i(\),)f(C\()g(LDC,)g(*)g(\),)g(D\()h(*)f(\),)g(E\()
g(*)h(\))136 1439 y FJ(\017)e FK(C)30 b(binding:)227
1658 y FD(void)47 b(BLAS_xsy_tridiag_rk\()42 b(enum)47
b(blas_order_type)c(order,)k(enum)f(blas_uplo_type)e(uplo,)1468
1771 y(enum)j(blas_trans_type)c(trans,)k(int)f(n,)i(int)f(k,)1468
1884 y(SCALAR_IN)e(alpha,)i(const)f(ARRAY)g(a,)h(int)g(lda,)1468
1996 y(const)g(ARRAY)f(d,)h(const)f(ARRAY)h(e,)g(SCALAR_IN)e(beta,)1468
2109 y(ARRAY)i(c,)g(int)g(ldc)g(\);)p 0 2328 3900 6 v
0 2441 a FK(HE)p 135 2441 28 4 v 33 w(TRIDIA)m(G)p 572
2441 V 33 w(RK)30 b(\(Hermitian)g(Rank)g(K)g(up)s(date)f(with)g
(symmetric)h(tridiagonal)f(matrix\))2299 2623 y Fy(C)i
FJ( )25 b Fy(\013AJ)9 b(A)2764 2590 y Fw(H)2853 2623
y FK(+)20 b Fy(\014)5 b(C)i FK(,)30 b Fy(C)i FJ( )25
b Fy(\013A)3466 2590 y Fw(H)3534 2623 y Fy(J)9 b(A)20
b FK(+)g Fy(\014)5 b(C)141 2806 y FK(This)38 b(routine)g(p)s(erforms)g
(one)i(of)f(the)h(Hermitian)e(rank)h(k)g(op)s(erations)g
Fy(C)47 b FJ( )40 b Fy(\013AJ)9 b(A)3218 2773 y Fw(H)3313
2806 y FK(+)26 b Fy(\014)5 b(C)46 b FK(or)39 b Fy(C)47
b FJ( )0 2919 y Fy(\013A)126 2886 y Fw(H)194 2919 y Fy(J)9
b(A)23 b FK(+)f Fy(\014)5 b(C)40 b FK(where)33 b Fy(\013)h
FK(and)f Fy(\014)39 b FK(are)34 b(scalars,)h Fy(C)40
b FK(is)32 b(a)i(Hermitian)f(matrix,)h Fy(A)f FK(is)g(a)h(general)g
(matrix,)g(and)f Fy(J)0 3032 y FK(is)f(a)i(symmetric)e(tridiagonal)g
(matrix.)49 b(This)31 b(routine)i(returns)f(immediately)f(if)h
Fv(alpha)g FK(is)h(equal)g(to)g(zero)i(and)0 3145 y Fv(b)s(eta)30
b FK(is)g(equal)h(to)h(one,)f(or)g(if)f Fv(n)h FK(or)g
Fv(k)h FK(is)e(less)g(than)h(or)g(equal)f(to)i(zero.)44
b(If)30 b Fv(ldc)h FK(is)f(less)h(than)f(one)i(or)f(less)f(than)h
Fv(n)p FK(,)0 3257 y(an)j(error)g(\015ag)g(is)f(set)i(and)e(passed)h
(to)g(the)h(error)e(handler.)50 b(F)-8 b(or)35 b Fv(trans)e
FK(equal)h(to)h Fv(blas)p 3024 3257 V 31 w(no)p 3147
3257 V 34 w(trans)p FK(,)f(and)g(if)f Fv(lda)g FK(is)0
3370 y(less)h(than)g(one)h(or)g(less)e(than)i Fv(n)p
FK(,)g(an)g(error)f(\015ag)h(is)f(set)h(and)f(passed)g(to)h(the)g
(error)f(handler.)51 b(F)-8 b(or)36 b Fv(trans)d FK(equal)0
3483 y(to)g Fv(blas)p 266 3483 V 32 w(trans)p FK(,)g(and)f(if)g
Fv(lda)g FK(is)g(less)g(than)g(one)h(or)g(less)f(than)g
Fv(k)p FK(,)i(an)f(error)f(\015ag)h(is)f(set)h(and)f(passed)g(to)h(the)
g(error)0 3596 y(handler.)136 3802 y FJ(\017)46 b FK(F)-8
b(ortran)31 b(95)h(binding:)418 4045 y FD(SUBROUTINE)45
b(he_tridiag_rk\()f(a,)j(d,)g(e,)h(c)f([,)g(uplo])g([,)g(trans])f([,)h
(alpha])f(&)1659 4158 y([,)h(beta])g(\))514 4271 y(COMPLEX\(<wp>\),)d
(INTENT\(IN\))h(::)i(a\(:,:\))514 4384 y(COMPLEX\(<wp>\),)d
(INTENT\(IN\))h(::)i(d\(:\),)f(e\(:\))514 4497 y(COMPLEX\(<wp>\),)e
(INTENT\(INOUT\))g(::)j(c\(:,:\))514 4610 y(TYPE)f(\(blas_uplo_type\),)
d(INTENT\(IN\),)i(OPTIONAL)h(::)h(uplo)514 4723 y(TYPE)f
(\(blas_trans_type\),)d(INTENT\(IN\),)i(OPTIONAL)g(::)j(trans)514
4835 y(REAL\(<wp>\),)c(INTENT\(IN\),)h(OPTIONAL)h(::)h(alpha,)f(beta)
418 4948 y(where)466 5061 y(c)h(has)g(shape)g(\(n,n\))466
5174 y(if)g(trans)f(=)i(blas_no_trans)c(\(the)j(default\))609
5287 y(a)h(has)e(shape)h(\(n,k\))609 5400 y(d)h(has)e(shape)h(\(k\))
4084 64 y FI(1)4084 177 y(2)4084 290 y(3)4084 403 y(4)4084
516 y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084 967
y(9)4069 1080 y(10)4069 1193 y(11)4069 1306 y(12)4069
1419 y(13)4069 1532 y(14)4069 1645 y(15)4069 1758 y(16)4069
1870 y(17)4069 1983 y(18)4069 2096 y(19)4069 2209 y(20)4069
2322 y(21)4069 2435 y(22)4069 2548 y(23)4069 2661 y(24)4069
2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
3677 y(33)4069 3790 y(34)4069 3903 y(35)4069 4016 y(36)4069
4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 93 103
93 102 bop 0 -165 a FA(2.8.)72 b(LANGUA)m(GE)32 b(BINDINGS)2578
b FK(93)609 91 y FD(e)48 b(has)e(shape)h(\(k-1\))466
204 y(if)g(trans)f(/=)i(blas_no_trans)609 317 y(a)g(has)e(shape)h
(\(k,n\))609 430 y(d)h(has)e(shape)h(\(n\))609 543 y(e)h(has)e(shape)h
(\(n-1\))p 1264 712 1600 4 v 1262 825 4 113 v 1314 791
a FK(Rank)30 b FD(a)p 1651 825 V 99 w(trans)p 1989 825
V 99 w FK(Op)s(eration)p 2862 825 V 1264 828 1600 4 v
1262 941 4 113 v 1435 907 a(2)p 1651 941 V 308 w(N)p
1989 941 V 185 w Fy(C)h FJ( )25 b Fy(\013AJ)9 b(A)2506
874 y Fw(H)2595 907 y FK(+)20 b Fy(\014)5 b(C)p 2862
941 V 1262 1054 V 1435 1020 a FK(2)p 1651 1054 V 309
w(T)p 1989 1054 V 186 w Fy(C)31 b FJ( )25 b Fy(\013A)2379
987 y Fw(H)2447 1020 y Fy(J)9 b(A)21 b FK(+)f Fy(\014)5
b(C)p 2862 1054 V 1264 1057 1600 4 v 136 1266 a FJ(\017)46
b FK(F)-8 b(ortran)31 b(77)h(binding:)514 1491 y FD(SUBROUTINE)45
b(BLAS_xHE_TRIDIAG_RK\()d(UPLO,)k(TRANS,)g(N,)i(K,)f(ALPHA,)f(A,)h
(LDA,)466 1603 y($)1527 b(D,)47 b(E,)g(BETA,)g(C,)g(LDC)g(\))514
1716 y(INTEGER)570 b(K,)48 b(LDA,)e(LDC,)h(N,)g(TRANS,)f(UPLO)514
1829 y(<rtype>)570 b(ALPHA,)47 b(BETA)514 1942 y(<ctype>)570
b(A\()48 b(LDA,)e(*)i(\),)f(C\()g(LDC,)g(*)g(\),)g(D\()h(*)f(\),)g(E\()
g(*)h(\))136 2167 y FJ(\017)e FK(C)30 b(binding:)227
2392 y FD(void)47 b(BLAS_xhe_tridiag_rk\()42 b(enum)47
b(blas_order_type)c(order,)k(enum)f(blas_uplo_type)e(uplo,)1468
2505 y(enum)j(blas_trans_type)c(trans,)k(int)f(n,)i(int)f(k,)1468
2618 y(RSCALAR_IN)e(alpha,)h(const)h(CARRAY)f(a,)h(int)g(lda,)1468
2731 y(const)g(CARRAY)f(d,)h(const)f(CARRAY)g(e,)h(RSCALAR_IN)e(beta,)
1468 2844 y(CARRAY)h(c,)h(int)g(ldc)g(\);)p 0 3069 3900
6 v 0 3182 a FK(SYR2K)30 b(\(Symmetric)g(rank)g(2k)g(up)s(date\))1216
b Fy(C)32 b FJ( )25 b FK(\()p Fy(\013A)p FK(\))p Fy(B)3168
3149 y Fw(T)3244 3182 y FK(+)20 b Fy(B)5 b FK(\()p Fy(\013A)p
FK(\))3605 3149 y Fw(T)3681 3182 y FK(+)20 b Fy(\014)5
b(C)2685 3369 y(C)32 b FJ( )25 b FK(\()p Fy(\013A)p FK(\))3094
3336 y Fw(T)3151 3369 y Fy(B)f FK(+)c Fy(B)3409 3336
y Fw(T)3464 3369 y FK(\()p Fy(\013A)p FK(\))h(+)f Fy(\014)5
b(C)141 3557 y FK(These)39 b(routines)g(p)s(erform)f(the)i(symmetric)e
(rank)h(2k)h(op)s(eration)f Fy(C)47 b FJ( )40 b FK(\()p
Fy(\013A)p FK(\))p Fy(B)3023 3524 y Fw(T)3106 3557 y
FK(+)26 b Fy(B)5 b FK(\()p Fy(\013A)p FK(\))3473 3524
y Fw(T)3555 3557 y FK(+)26 b Fy(\014)5 b(C)46 b FK(or)0
3670 y Fy(C)33 b FJ( )26 b FK(\()p Fy(\013A)p FK(\))411
3637 y Fw(T)467 3670 y Fy(B)f FK(+)20 b Fy(B)726 3637
y Fw(T)781 3670 y FK(\()p Fy(\013A)p FK(\))i(+)e Fy(\014)5
b(C)37 b FK(where)31 b Fy(\013)g FK(and)f Fy(\014)36
b FK(are)c(scalars,)f Fy(C)37 b FK(is)30 b(a)h(symmetric)f(matrix,)h
(and)f Fy(A)h FK(and)f Fy(B)0 3783 y FK(are)k(general)f(matrices.)51
b(This)31 b(routine)i(returns)f(immediately)g(if)g Fv(alpha)h
FK(is)f(equal)i(to)g(zero)g(and)f Fv(b)s(eta)g FK(is)f(equal)0
3896 y(to)g(one,)g(or)f(if)f Fv(n)i FK(or)f Fv(k)h FK(is)e(less)g(than)
h(or)h(equal)e(to)i(zero.)45 b(If)30 b Fv(ldc)i FK(is)e(less)h(than)g
(one)g(or)g(less)g(than)g Fv(n)p FK(,)h(an)f(error)g(\015ag)0
4009 y(is)h(set)h(and)f(passed)h(to)g(the)g(error)g(handler.)46
b(F)-8 b(or)34 b Fv(trans)e FK(equal)g(to)i Fv(blas)p
2475 4009 28 4 v 32 w(no)p 2599 4009 V 33 w(trans)p FK(,)f(and)f(if)g
Fv(lda)g FK(is)g(less)g(than)h(one)0 4122 y(or)g(less)e(than)i
Fv(n)p FK(,)g(or)g(if)e Fv(ldb)h FK(is)g(less)g(than)g(one)h(or)f(less)
g(than)h Fv(n)p FK(,)g(an)f(error)h(\015ag)f(is)g(set)h(and)f(passed)g
(to)i(the)e(error)0 4234 y(handler.)38 b(F)-8 b(or)30
b Fv(trans)e FK(equal)g(to)h Fv(blas)p 1243 4234 V 32
w(trans)p FK(,)g(and)f(if)f Fv(lda)h FK(is)g(less)g(than)g(one)h(or)g
(less)f(than)g Fv(k)p FK(,)i(or)f(if)e Fv(ldb)i FK(is)e(less)h(than)0
4347 y(one)j(or)f(less)g(than)g Fv(k)p FK(,)h(an)f(error)g(\015ag)h(is)
e(set)i(and)f(passed)g(to)h(the)f(error)g(handler.)141
4460 y(These)39 b(in)m(terfaces)h(encompass)f(the)g(Legacy)i(BLAS)e
(routine)f(xSYR2K)h(with)f(added)h(functionalit)m(y)e(for)0
4573 y(complex)30 b(symmetric)g(matrices.)136 4786 y
FJ(\017)46 b FK(F)-8 b(ortran)31 b(95)h(binding:)418
5036 y FD(SUBROUTINE)45 b(syr2k\()h(a,)h(b,)h(c)f([,)g(uplo])g([,)g
(trans])f([,)h(alpha])f([,)h(beta])g(\))514 5149 y(<type>\(<wp>\),)d
(INTENT\(IN\))h(::)i(<aa>,)f(<bb>)514 5261 y(<type>\(<wp>\),)e
(INTENT\(INOUT\))g(::)j(c\(:,:\))514 5374 y(TYPE)f(\(blas_uplo_type\),)
d(INTENT\(IN\),)i(OPTIONAL)h(::)h(uplo)-214 64 y FI(1)-214
177 y(2)-214 290 y(3)-214 403 y(4)-214 516 y(5)-214 628
y(6)-214 741 y(7)-214 854 y(8)-214 967 y(9)-230 1080
y(10)-230 1193 y(11)-230 1306 y(12)-230 1419 y(13)-230
1532 y(14)-230 1645 y(15)-230 1758 y(16)-230 1870 y(17)-230
1983 y(18)-230 2096 y(19)-230 2209 y(20)-230 2322 y(21)-230
2435 y(22)-230 2548 y(23)-230 2661 y(24)-230 2774 y(25)-230
2887 y(26)-230 3000 y(27)-230 3112 y(28)-230 3225 y(29)-230
3338 y(30)-230 3451 y(31)-230 3564 y(32)-230 3677 y(33)-230
3790 y(34)-230 3903 y(35)-230 4016 y(36)-230 4129 y(37)-230
4242 y(38)-230 4354 y(39)-230 4467 y(40)-230 4580 y(41)-230
4693 y(42)-230 4806 y(43)-230 4919 y(44)-230 5032 y(45)-230
5145 y(46)-230 5258 y(47)-230 5371 y(48)p eop
%%Page: 94 104
94 103 bop 0 -165 a FK(94)1930 b FA(CHAPTER)30 b(2.)71
b(DENSE)30 b(AND)h(BANDED)h(BLAS)514 91 y FD(TYPE)46
b(\(blas_trans_type\),)d(INTENT\(IN\),)i(OPTIONAL)g(::)j(trans)514
204 y(<type>\(<wp>\),)c(INTENT\(IN\),)h(OPTIONAL)g(::)i(alpha,)f(beta)
418 317 y(where)514 430 y(<aa>)94 b(::=)47 b(a\(:,:\))f(or)h(a\(:\))514
543 y(<bb>)94 b(::=)47 b(b\(:,:\))f(or)h(b\(:\))418 656
y(and)466 769 y(c)g(has)g(shape)g(\(n,n\))466 882 y(if)g(trans)f(=)i
(blas_no_trans)c(\(the)j(default\))609 995 y(a)h(has)e(shape)h(\(n,k\))
609 1108 y(b)h(has)e(shape)h(\(n,k\))466 1220 y(if)g(trans)f(/=)i
(blas_no_trans)609 1333 y(a)g(has)e(shape)h(\(k,n\))609
1446 y(b)h(has)e(shape)h(\(k,n\))p 920 1594 2289 4 v
918 1707 4 113 v 969 1673 a FK(Rank)31 b FD(a)p 1306
1707 V 99 w FK(Rank)f FD(b)p 1695 1707 V 99 w(trans)p
2033 1707 V 99 w FK(Op)s(eration)p 3206 1707 V 920 1710
2289 4 v 918 1823 4 113 v 1091 1789 a(2)p 1306 1823 V
344 w(2)p 1695 1823 V 307 w(N)p 2033 1823 V 185 w Fy(C)h
FJ( )26 b Fy(\013AB)2498 1756 y Fw(T)2573 1789 y FK(+)20
b Fy(\013B)5 b(A)2864 1756 y Fw(T)2939 1789 y FK(+)20
b Fy(\014)5 b(C)p 3206 1823 V 918 1936 V 1091 1902 a
FK(2)p 1306 1936 V 344 w(2)p 1695 1936 V 308 w(T)p 2033
1936 V 186 w Fy(C)31 b FJ( )26 b Fy(\013A)2424 1869 y
Fw(T)2479 1902 y Fy(B)f FK(+)20 b Fy(\013B)2796 1869
y Fw(T)2851 1902 y Fy(A)g FK(+)g Fy(\014)5 b(C)p 3206
1936 V 918 2049 V 1091 2015 a FK(1)p 1306 2049 V 344
w(1)p 1695 2049 V 326 w(-)p 2033 2049 V 204 w Fy(C)31
b FJ( )26 b Fy(\013ab)2443 1982 y Fw(T)2518 2015 y FK(+)20
b Fy(\013ba)2754 1982 y Fw(T)2830 2015 y FK(+)g Fy(\014)5
b(C)p 3206 2049 V 920 2052 2289 4 v 227 2239 a FK(The)30
b(functionalit)m(y)f(of)i(xSYR2)f(is)f(co)m(v)m(ered)j(b)m(y)f
Fv(syr2k)p FK(.)136 2421 y FJ(\017)46 b FK(F)-8 b(ortran)31
b(77)h(binding:)514 2628 y FD(SUBROUTINE)45 b(BLAS_xSYR2K\()f(UPLO,)i
(TRANS,)h(N,)g(K,)g(ALPHA,)f(A,)h(LDA,)g(B,)g(LDB,)466
2741 y($)1145 b(BETA,)46 b(C,)i(LDC)f(\))514 2854 y(INTEGER)570
b(K,)48 b(LDA,)e(LDB,)h(LDC,)g(N,)g(TRANS,)f(UPLO)514
2967 y(<type>)618 b(ALPHA,)47 b(BETA)514 3080 y(<type>)618
b(A\()48 b(LDA,)e(*)i(\),)f(B\()g(LDB,)g(*)g(\),)g(C\()h(LDC,)e(*)i(\))
136 3286 y FJ(\017)e FK(C)30 b(binding:)227 3493 y FD(void)47
b(BLAS_xsyr2k\()d(enum)j(blas_order_type)d(order,)i(enum)g
(blas_uplo_type)e(uplo,)1086 3606 y(enum)j(blas_trans_type)d(trans,)i
(int)h(n,)g(int)g(k,)g(SCALAR_IN)e(alpha,)1086 3719 y(const)i(ARRAY)f
(a,)h(int)g(lda,)g(const)f(ARRAY)h(b,)g(int)g(ldb,)1086
3832 y(SCALAR_IN)f(beta,)g(ARRAY)g(c,)i(int)e(ldc)h(\);)p
0 4039 3900 6 v 0 4152 a FK(HER2K)30 b(\(Hermitian)g(rank)g(2k)g(up)s
(date\))1206 b Fy(C)32 b FJ( )25 b FK(\()p Fy(\013A)p
FK(\))p Fy(B)3144 4119 y Fw(H)3232 4152 y FK(+)20 b Fy(B)5
b FK(\()p Fy(\013A)p FK(\))3593 4119 y Fw(H)3681 4152
y FK(+)20 b Fy(\014)5 b(C)2661 4324 y(C)32 b FJ( )25
b FK(\()p Fy(\013A)p FK(\))3070 4291 y Fw(H)3138 4324
y Fy(B)g FK(+)20 b Fy(B)3397 4291 y Fw(H)3464 4324 y
FK(\()p Fy(\013A)p FK(\))h(+)f Fy(\014)5 b(C)141 4497
y FK(These)38 b(routines)g(p)s(erform)f(the)i(Hermitian)e(rank)h(2k)h
(op)s(eration)f Fy(C)46 b FJ( )38 b FK(\()p Fy(\013A)p
FK(\))p Fy(B)3002 4464 y Fw(H)3096 4497 y FK(+)26 b Fy(B)5
b FK(\()p Fy(\013A)p FK(\))3463 4464 y Fw(H)3556 4497
y FK(+)26 b Fy(\014)5 b(C)45 b FK(or)0 4610 y Fy(C)32
b FJ( )25 b FK(\()p Fy(\013A)p FK(\))409 4577 y Fw(H)478
4610 y Fy(B)f FK(+)c Fy(B)736 4577 y Fw(H)802 4610 y
FK(\()p Fy(\013A)p FK(\))i(+)d Fy(\014)5 b(C)37 b FK(where)30
b Fy(\013)h FK(and)e Fy(\014)36 b FK(are)30 b(scalars,)h
Fy(C)36 b FK(is)29 b(a)i(Hermitian)e(matrix,)h(and)g
Fy(A)g FK(and)f Fy(B)0 4723 y FK(are)34 b(general)f(matrices.)51
b(This)31 b(routine)i(returns)f(immediately)g(if)g Fv(alpha)h
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4835 y(to)g(one,)g(or)f(if)f Fv(n)i FK(or)f Fv(k)h FK(is)e(less)g(than)
h(or)h(equal)e(to)i(zero.)45 b(If)30 b Fv(ldc)i FK(is)e(less)h(than)g
(one)g(or)g(less)g(than)g Fv(n)p FK(,)h(an)f(error)g(\015ag)0
4948 y(is)h(set)h(and)f(passed)h(to)g(the)g(error)g(handler.)46
b(F)-8 b(or)34 b Fv(trans)e FK(equal)g(to)i Fv(blas)p
2475 4948 28 4 v 32 w(no)p 2599 4948 V 33 w(trans)p FK(,)f(and)f(if)g
Fv(lda)g FK(is)g(less)g(than)h(one)0 5061 y(or)g(less)e(than)i
Fv(n)p FK(,)g(or)g(if)e Fv(ldb)h FK(is)g(less)g(than)g(one)h(or)f(less)
g(than)h Fv(n)p FK(,)g(an)f(error)h(\015ag)f(is)g(set)h(and)f(passed)g
(to)i(the)e(error)0 5174 y(handler.)38 b(F)-8 b(or)30
b Fv(trans)e FK(equal)g(to)h Fv(blas)p 1243 5174 V 32
w(trans)p FK(,)g(and)f(if)f Fv(lda)h FK(is)g(less)g(than)g(one)h(or)g
(less)f(than)g Fv(k)p FK(,)i(or)f(if)e Fv(ldb)i FK(is)e(less)h(than)0
5287 y(one)j(or)f(less)g(than)g Fv(k)p FK(,)h(an)f(error)g(\015ag)h(is)
e(set)i(and)f(passed)g(to)h(the)f(error)g(handler.)141
5400 y(These)g(in)m(terfaces)h(encompass)g(the)f(Legacy)i(BLAS)e
(routine)g(xHER2K.)4084 64 y FI(1)4084 177 y(2)4084 290
y(3)4084 403 y(4)4084 516 y(5)4084 628 y(6)4084 741 y(7)4084
854 y(8)4084 967 y(9)4069 1080 y(10)4069 1193 y(11)4069
1306 y(12)4069 1419 y(13)4069 1532 y(14)4069 1645 y(15)4069
1758 y(16)4069 1870 y(17)4069 1983 y(18)4069 2096 y(19)4069
2209 y(20)4069 2322 y(21)4069 2435 y(22)4069 2548 y(23)4069
2661 y(24)4069 2774 y(25)4069 2887 y(26)4069 3000 y(27)4069
3112 y(28)4069 3225 y(29)4069 3338 y(30)4069 3451 y(31)4069
3564 y(32)4069 3677 y(33)4069 3790 y(34)4069 3903 y(35)4069
4016 y(36)4069 4129 y(37)4069 4242 y(38)4069 4354 y(39)4069
4467 y(40)4069 4580 y(41)4069 4693 y(42)4069 4806 y(43)4069
4919 y(44)4069 5032 y(45)4069 5145 y(46)4069 5258 y(47)4069
5371 y(48)p eop
%%Page: 95 105
95 104 bop 0 -165 a FA(2.8.)72 b(LANGUA)m(GE)32 b(BINDINGS)2578
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%%Page: 96 106
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177 y(2)4084 290 y(3)4084 403 y(4)4084 516 y(5)4084 628
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%%Page: 97 107
97 106 bop 0 -165 a FA(2.8.)72 b(LANGUA)m(GE)32 b(BINDINGS)2578
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1181 y Fy(C)i FJ( )26 b FK(\()p Fy(\013AJ)9 b FK(\))p
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%%Page: 98 108
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5145 y(46)4069 5258 y(47)4069 5371 y(48)p eop
%%Page: 99 109
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%%Page: 100 110
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%%Page: 101 111
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516 y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084 967
y(9)4069 1080 y(10)4069 1193 y(11)4069 1306 y(12)4069
1419 y(13)4069 1532 y(14)4069 1645 y(15)4069 1758 y(16)4069
1870 y(17)4069 1983 y(18)4069 2096 y(19)4069 2209 y(20)4069
2322 y(21)4069 2435 y(22)4069 2548 y(23)4069 2661 y(24)4069
2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
3677 y(33)4069 3790 y(34)4069 3903 y(35)4069 4016 y(36)4069
4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 105 115
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5258 y(47)-230 5371 y(48)p eop
%%Page: 106 116
106 115 bop 0 -165 a FK(106)2512 b FA(CHAPTER)30 b(3.)72
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3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
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eop
%%Page: 107 117
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%%Page: 117 127
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eop
%%Page: 118 128
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eop
%%Page: 120 130
120 129 bop 0 -165 a FK(120)2512 b FA(CHAPTER)30 b(3.)72
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3790 y(34)4069 3903 y(35)4069 4016 y(36)4069 4129 y(37)4069
4242 y(38)4069 4354 y(39)4069 4467 y(40)4069 4580 y(41)4069
4693 y(42)4069 4806 y(43)4069 4919 y(44)4069 5032 y(45)4069
5145 y(46)4069 5258 y(47)4069 5371 y(48)p eop
%%Page: 121 131
121 130 bop 0 -165 a FA(3.8.)72 b(LANGUA)m(GE)32 b(BINDINGS)2533
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%%Page: 122 132
122 131 bop 0 -165 a FK(122)2512 b FA(CHAPTER)30 b(3.)72
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5371 y(48)p eop
%%Page: 123 133
123 132 bop 0 -165 a FA(3.8.)72 b(LANGUA)m(GE)32 b(BINDINGS)2533
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%%Page: 124 134
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5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 125 135
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%%Page: 126 136
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%%Page: 127 137
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%%Page: 128 138
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1532 y(14)4069 1645 y(15)4069 1758 y(16)4069 1870 y(17)4069
1983 y(18)4069 2096 y(19)4069 2209 y(20)4069 2322 y(21)4069
2435 y(22)4069 2548 y(23)4069 2661 y(24)4069 2774 y(25)4069
2887 y(26)4069 3000 y(27)4069 3112 y(28)4069 3225 y(29)4069
3338 y(30)4069 3451 y(31)4069 3564 y(32)4069 3677 y(33)4069
3790 y(34)4069 3903 y(35)4069 4016 y(36)4069 4129 y(37)4069
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4693 y(42)4069 4806 y(43)4069 4919 y(44)4069 5032 y(45)4069
5145 y(46)4069 5258 y(47)4069 5371 y(48)p eop
%%Page: 129 139
129 138 bop 0 -165 a FA(3.8.)72 b(LANGUA)m(GE)32 b(BINDINGS)2533
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2096 y(19)-230 2209 y(20)-230 2322 y(21)-230 2435 y(22)-230
2548 y(23)-230 2661 y(24)-230 2774 y(25)-230 2887 y(26)-230
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5258 y(47)-230 5371 y(48)p eop
%%Page: 130 140
130 139 bop 0 -165 a FK(130)2512 b FA(CHAPTER)30 b(3.)72
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64 y FI(1)4084 177 y(2)4084 290 y(3)4084 403 y(4)4084
516 y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084 967
y(9)4069 1080 y(10)4069 1193 y(11)4069 1306 y(12)4069
1419 y(13)4069 1532 y(14)4069 1645 y(15)4069 1758 y(16)4069
1870 y(17)4069 1983 y(18)4069 2096 y(19)4069 2209 y(20)4069
2322 y(21)4069 2435 y(22)4069 2548 y(23)4069 2661 y(24)4069
2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
3677 y(33)4069 3790 y(34)4069 3903 y(35)4069 4016 y(36)4069
4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 131 141
131 140 bop 0 -165 a FA(3.8.)72 b(LANGUA)m(GE)32 b(BINDINGS)2533
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483 4015 V 34 w(X)h(are)f(represen)m(table)h(in)m(teger)g(v)-5
b(alues,)34 b(whereas)f(the)h(other)f(p)s(ossible)f(return)g(v)-5
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(table)g(in)f(an)m(y)h(user-declarable)g(format.)p 514
4257 2872 4 v 512 4370 4 113 v 564 4336 a(Floating)h(P)m(oin)m(t)p
1188 4370 V 100 w(Description)p 3384 4370 V 512 4483
V 564 4449 a(parameter)p 1188 4483 V 3384 4483 V 514
4486 2872 4 v 512 4599 4 113 v 564 4565 a(BASE)p 1188
4599 V 431 w(base)f(of)h(the)f(mac)m(hine)p 3384 4599
V 512 4712 V 564 4678 a(T)p 1188 4712 V 610 w(n)m(um)m(b)s(er)f(of)h
(\(BASE\))h(digits)e(in)g(the)i(man)m(tissa)p 3384 4712
V 512 4825 V 564 4791 a(RND)p 1188 4825 V 472 w(1)f(when)g(\\prop)s(er)
f(rounding")g(o)s(ccurs)h(in)f(addition,)p 3384 4825
V 512 4938 V 1188 4938 V 1240 4904 a(0)h(otherwise)p
3384 4938 V 512 5051 V 564 5017 a(IEEE)p 1188 5051 V
457 w(1)g(when)g(rounding)e(in)h(addition)f(o)s(ccurs)j(in)e(\\IEEE)h
(st)m(yle",)p 3384 5051 V 512 5164 V 1188 5164 V 1240
5130 a(0)g(otherwise)p 3384 5164 V 512 5277 V 564 5243
a(EMIN)p 1188 5277 V 430 w(minim)m(um)d(exp)s(onen)m(t)k(b)s(efore)f
(\(gradual\))g(under\015o)m(w)p 3384 5277 V 512 5389
V 564 5356 a(EMAX)p 1188 5389 V 395 w(largest)g(exp)s(onen)m(t)h(b)s
(efore)f(o)m(v)m(er\015o)m(w)p 3384 5389 V 514 5393 2872
4 v 4084 64 a FI(1)4084 177 y(2)4084 290 y(3)4084 403
y(4)4084 516 y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084
967 y(9)4069 1080 y(10)4069 1193 y(11)4069 1306 y(12)4069
1419 y(13)4069 1532 y(14)4069 1645 y(15)4069 1758 y(16)4069
1870 y(17)4069 1983 y(18)4069 2096 y(19)4069 2209 y(20)4069
2322 y(21)4069 2435 y(22)4069 2548 y(23)4069 2661 y(24)4069
2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
3677 y(33)4069 3790 y(34)4069 3903 y(35)4069 4016 y(36)4069
4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 137 147
137 146 bop 0 -165 a FA(4.3.)72 b(FUNCTIONALITY)2761
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b(able)35 b(from)h(the)h(v)-5 b(alues)0 204 y(returned)29
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(ulas)e(in)g(section)i(1.6:)136 381 y FJ(\017)46 b Fy(\017)264
411 y FK(PREC)553 381 y(is)27 b Fz(r)-5 b(elative)32
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493 y(PREC,)136 677 y FJ(\017)46 b Fy(\017)264 691 y
Fw(o)333 677 y FK(is)29 b(the)i(mac)m(hine)f(epsilon)e(for)i(the)h
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(the)f(form)1470 1867 y Fy(r)1511 1881 y Fw(tr)r(ue)1674
1867 y FK(=)25 b Fy(\013)20 b FJ(\001)h FK(\()1968 1762
y Fw(n)1929 1787 y Ft(X)1932 1969 y Fw(i)p FC(=1)2064
1867 y Fy(a)2112 1881 y Fw(i)2161 1867 y FJ(\001)f Fy(b)2245
1881 y Fw(i)2273 1867 y FK(\))h(+)f Fy(\014)25 b FJ(\001)c
Fy(c)51 b(;)227 2126 y FK(where)23 b(all)f(quan)m(tities)g(are)i
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(output)f(quan)m(tities,)227 2578 y(should)d(satisfy)554
2824 y FJ(j)p Fy(r)620 2839 y Fw(computed)942 2824 y
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2824 y FJ(j)f FK(+)g FJ(j)p Fy(\014)26 b FJ(\001)21 b
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3507 y FK(PREC)2902 3476 y(,)j(with)d(or)i(without)e(a)i(guard)227
3589 y(digit,)34 b(b)s(efore)f(rounding)e(the)j(\014nal)e(result)g(to)i
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(precision)f(PREC)i(is)f(less)h(than)g Fn(UN)3070 3733
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FJ(j)p Fy(r)1707 3830 y Fw(computed)2010 3815 y FJ(j)h
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3815 y FK(\(unless)f(its)g(exact)j(v)-5 b(alue)32 b(is)227
3928 y(zero\).)45 b(Similarly)-8 b(,)29 b(o)m(v)m(er\015o)m(w)k(is)d
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(quan)m(tit)m(y)h(in)e(precision)227 4041 y(PREC=)36
b(exceeds)i Fn(O)m(V)1072 4071 y FK(PREC)1369 4041 y(in)e(magnitude,)i
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y Fw(o)3442 4041 y FK(.)60 b(W)-8 b(e)38 b(a)m(v)m(oid)227
4154 y(sp)s(ecifying)26 b(what)j(happ)s(ens)d(with)h(under\015o)m(w,)h
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(ose)h(to)227 4266 y(compute)f Fy(r)i FK(using)c Fy(\013)15
b FJ(\001)g FK(\()1047 4202 y Ft(P)1150 4266 y Fy(a)1198
4280 y Fw(i)1241 4266 y FJ(\001)g Fy(b)1320 4280 y Fw(i)1348
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Fy(b)1878 4280 y Fw(i)1933 4266 y FK(or)2042 4202 y Ft(P)2145
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FK(\))28 b(dep)s(ending)d(on)i(dimensions,)f(and)h(the)227
4379 y(error)f(b)s(ounds)e(in)h(the)h(presence)h(of)f(under\015o)m(w)f
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Fy(n)g FK(trian-)227 4788 y(gular)f(system)g(of)h(equations)1895
4901 y Fy(T)13 b(x)25 b FK(=)g Fy(\013b)227 5061 y FK(where)32
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i(or)h(output)e(quan)m(tities,)227 5287 y(satis\014es)1387
5400 y(\()p Fy(T)33 b FK(+)20 b Fy(E)5 b FK(\)\()p Fy(x)1793
5415 y Fw(computed)2117 5400 y FK(+)20 b Fy(e)p FK(\))26
b(=)f Fy(\013)p FK(\()p Fy(b)c FK(+)e Fy(f)10 b FK(\))-214
64 y FI(1)-214 177 y(2)-214 290 y(3)-214 403 y(4)-214
516 y(5)-214 628 y(6)-214 741 y(7)-214 854 y(8)-214 967
y(9)-230 1080 y(10)-230 1193 y(11)-230 1306 y(12)-230
1419 y(13)-230 1532 y(14)-230 1645 y(15)-230 1758 y(16)-230
1870 y(17)-230 1983 y(18)-230 2096 y(19)-230 2209 y(20)-230
2322 y(21)-230 2435 y(22)-230 2548 y(23)-230 2661 y(24)-230
2774 y(25)-230 2887 y(26)-230 3000 y(27)-230 3112 y(28)-230
3225 y(29)-230 3338 y(30)-230 3451 y(31)-230 3564 y(32)-230
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4129 y(37)-230 4242 y(38)-230 4354 y(39)-230 4467 y(40)-230
4580 y(41)-230 4693 y(42)-230 4806 y(43)-230 4919 y(44)-230
5032 y(45)-230 5145 y(46)-230 5258 y(47)-230 5371 y(48)p
eop
%%Page: 138 148
138 147 bop 0 -165 a FK(138)1214 b FA(CHAPTER)30 b(4.)72
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122 y FK(PREC)2954 91 y FJ(j)p Fy(b)3018 105 y Fw(i)3046
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213 y(real,)31 b(and)e Fy(\032)d FK(=)f(6)20 b(+)g(4)976
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eop
%%Page: 139 149
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%%Page: 140 150
140 149 bop 0 -165 a FK(140)1214 b FA(CHAPTER)30 b(4.)72
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eop
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1419 y(13)4069 1532 y(14)4069 1645 y(15)4069 1758 y(16)4069
1870 y(17)4069 1983 y(18)4069 2096 y(19)4069 2209 y(20)4069
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2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
3677 y(33)4069 3790 y(34)4069 3903 y(35)4069 4016 y(36)4069
4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 143 153
143 152 bop 0 -165 a FA(4.5.)72 b(LANGUA)m(GE)32 b(BINDINGS)2533
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1667 y FG({)45 b FK(HERK)30 b(\(Hermitian)g(rank-k)g(up)s(date\))330
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Fy(y)28 b FK(=)d Fy(\014)5 b(r)23 b FK(+)d Fy(\013)2129
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2743 y Fy(y)2402 2757 y Fw(i)2461 2743 y FK(or)30 b Fy(r)e
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177 y(2)-214 290 y(3)-214 403 y(4)-214 516 y(5)-214 628
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1532 y(14)-230 1645 y(15)-230 1758 y(16)-230 1870 y(17)-230
1983 y(18)-230 2096 y(19)-230 2209 y(20)-230 2322 y(21)-230
2435 y(22)-230 2548 y(23)-230 2661 y(24)-230 2774 y(25)-230
2887 y(26)-230 3000 y(27)-230 3112 y(28)-230 3225 y(29)-230
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4693 y(42)-230 4806 y(43)-230 4919 y(44)-230 5032 y(45)-230
5145 y(46)-230 5258 y(47)-230 5371 y(48)p eop
%%Page: 144 154
144 153 bop 0 -165 a FK(144)1214 b FA(CHAPTER)30 b(4.)72
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204 y(argumen)m(ts)h(set)h(do)m(wn)e(in)f(section)i(4.3:)43
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1728 y(but)f(if)p 483 1728 29 4 v 64 w FD(a)p 566 1728
V 34 w(b)g FK(is)f(presen)m(t)i(then)p 1293 1728 V 64
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3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
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4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 145 155
145 154 bop 0 -165 a FA(4.5.)72 b(LANGUA)m(GE)32 b(BINDINGS)2533
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FD(alpha)p FK(,)227 5115 y FD(beta)29 b FK(and)h FD(y)p
FK(.)136 5303 y FJ(\017)46 b FK(F)-8 b(ortran)31 b(77)h(binding:)-214
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516 y(5)-214 628 y(6)-214 741 y(7)-214 854 y(8)-214 967
y(9)-230 1080 y(10)-230 1193 y(11)-230 1306 y(12)-230
1419 y(13)-230 1532 y(14)-230 1645 y(15)-230 1758 y(16)-230
1870 y(17)-230 1983 y(18)-230 2096 y(19)-230 2209 y(20)-230
2322 y(21)-230 2435 y(22)-230 2548 y(23)-230 2661 y(24)-230
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4129 y(37)-230 4242 y(38)-230 4354 y(39)-230 4467 y(40)-230
4580 y(41)-230 4693 y(42)-230 4806 y(43)-230 4919 y(44)-230
5032 y(45)-230 5145 y(46)-230 5258 y(47)-230 5371 y(48)p
eop
%%Page: 146 156
146 155 bop 0 -165 a FK(146)1214 b FA(CHAPTER)30 b(4.)72
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317 y(INTEGER)570 b(INCX,)47 b(INCY,)f(N)i([,)f(PREC])514
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850 y FK(The)36 b(t)m(yp)s(es)g(of)g FD(ALPHA)p FK(,)f
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963 y(argumen)m(ts)d(set)g(do)m(wn)f(in)f(section)i(4.3.)45
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1251 1076 V 71 w FD(a)g FK(is)f(the)i(t)m(yp)s(e)f(of)h
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V 64 w FD(X)g FK(m)m(ust)h(b)s(e)e(presen)m(t.)136 1366
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2093 y(argumen)m(ts)d(set)g(do)m(wn)f(in)f(section)i(4.3.)45
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487 2206 V 66 w FD(a)g FK(is)f(presen)m(t)i(then)p 1222
2206 V 66 w FD(a)f FK(is)g(the)g(t)m(yp)s(e)h(of)f(argumen)m(t)h
FD(x)p FK(.)47 b(The)32 b(su\016x)p 2861 2206 V 65 w
FD(x)g FK(is)g(presen)m(t)g(if)g(and)f(only)h(if)227
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2319 V 64 w FD(x)g FK(m)m(ust)g(b)s(e)g(presen)m(t.)p
0 2500 3900 6 v 0 2613 a(W)-10 b(AXPBY)31 b(\(Scaled)g(v)m(ector)h
(addition\))1964 b Fy(w)28 b FJ( )d Fy(\013x)c FK(+)f
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FK(less)e(than)i(zero)g(is)0 3178 y(p)s(ermitted.)39
b(Ho)m(w)m(ev)m(er,)31 b(if)c(either)h Fv(incx)g FK(or)h
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FK(,)227 5400 y FD(alpha)e FK(and)h FD(beta)p FK(.)4084
64 y FI(1)4084 177 y(2)4084 290 y(3)4084 403 y(4)4084
516 y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084 967
y(9)4069 1080 y(10)4069 1193 y(11)4069 1306 y(12)4069
1419 y(13)4069 1532 y(14)4069 1645 y(15)4069 1758 y(16)4069
1870 y(17)4069 1983 y(18)4069 2096 y(19)4069 2209 y(20)4069
2322 y(21)4069 2435 y(22)4069 2548 y(23)4069 2661 y(24)4069
2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
3677 y(33)4069 3790 y(34)4069 3903 y(35)4069 4016 y(36)4069
4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 147 157
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FK(or)f(its)h(transp)s(ose,)g(or)0 3835 y(its)g(conjugate)i(transp)s
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4174 y(Ho)m(w)m(ev)m(er,)33 b(if)c(either)h Fv(incx)g
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4286 y(F)-8 b(or)28 b(the)g(routine)f Fv(GEMV)p FK(,)g(if)g
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516 y(5)-214 628 y(6)-214 741 y(7)-214 854 y(8)-214 967
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4580 y(41)-230 4693 y(42)-230 4806 y(43)-230 4919 y(44)-230
5032 y(45)-230 5145 y(46)-230 5258 y(47)-230 5371 y(48)p
eop
%%Page: 148 158
148 157 bop 0 -165 a FK(148)1214 b FA(CHAPTER)30 b(4.)72
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1665 y FK(The)30 b(functionalit)m(y)f(of)i Fv(gemv)g
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y FJ(\017)46 b FK(F)-8 b(ortran)31 b(77)h(binding:)227
2068 y FD(General:)514 2181 y(SUBROUTINE)45 b(BLAS_xGEMV{_a_b}{_X}\()d
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2407 y(General)g(Band:)514 2520 y(SUBROUTINE)f(BLAS_xGBMV{_a_b}{_X}\()d
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3197 y(<type>)618 b(X\()48 b(*)f(\))514 3310 y(<type>)618
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(wn)f(in)f(section)i(4.3.)45 b(The)31 b(pre\014x)g FD(x)g
FK(is)g(the)g(\015oating)h(p)s(oin)m(t)e(t)m(yp)s(e)i(of)g(the)f
(argumen)m(ts,)227 3754 y(but)f(if)p 483 3754 29 4 v
64 w FD(a)p 566 3754 V 34 w(b)g FK(is)f(presen)m(t)i(then)p
1293 3754 V 64 w FD(a)f FK(is)g(the)g(t)m(yp)s(e)h(of)g
FD(A)f FK(and)p 2216 3754 V 64 w FD(b)g FK(is)f(the)i(t)m(yp)s(e)g(of)f
FD(X)p FK(.)h(The)f(su\016x)p 3416 3754 V 63 w FD(X)g
FK(is)g(presen)m(t)227 3867 y(if)g(and)f(only)h(if)f
FD(PREC)g FK(is)h(presen)m(t.)41 b(One)30 b(or)g(b)s(oth)g(of)g(the)h
(su\016xes)p 2535 3867 V 64 w FD(a)p 2618 3867 V 34 w(b)f
FK(and)p 2906 3867 V 64 w FD(X)g FK(m)m(ust)g(b)s(e)g(presen)m(t.)136
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4384 y(void)47 b(BLAS_xgemv{_a_b}{_x}\()42 b(enum)47
b(blas_order_type)c(order,)1516 4497 y(enum)k(blas_trans_type)c(trans,)
j(int)h(m,)g(int)g(n,)1516 4610 y(SCALAR_IN)e(alpha,)h(const)h(ARRAY)f
(a,)h(int)g(lda,)1516 4723 y(const)f(ARRAY)h(x,)g(int)g(incx,)f
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5061 y(void)h(BLAS_xgbmv{_a_b}{_x}\()42 b(enum)47 b(blas_order_type)c
(order,)1516 5174 y(enum)k(blas_trans_type)c(trans,)j(int)h(m,)g(int)g
(n,)1516 5287 y(int)g(kl,)g(int)g(ku,)g(SCALAR_IN)e(alpha,)1516
5400 y(const)h(ARRAY)h(a,)g(int)g(lda,)f(const)h(ARRAY)f(x,)h(int)g
(incx,)4084 64 y FI(1)4084 177 y(2)4084 290 y(3)4084
403 y(4)4084 516 y(5)4084 628 y(6)4084 741 y(7)4084 854
y(8)4084 967 y(9)4069 1080 y(10)4069 1193 y(11)4069 1306
y(12)4069 1419 y(13)4069 1532 y(14)4069 1645 y(15)4069
1758 y(16)4069 1870 y(17)4069 1983 y(18)4069 2096 y(19)4069
2209 y(20)4069 2322 y(21)4069 2435 y(22)4069 2548 y(23)4069
2661 y(24)4069 2774 y(25)4069 2887 y(26)4069 3000 y(27)4069
3112 y(28)4069 3225 y(29)4069 3338 y(30)4069 3451 y(31)4069
3564 y(32)4069 3677 y(33)4069 3790 y(34)4069 3903 y(35)4069
4016 y(36)4069 4129 y(37)4069 4242 y(38)4069 4354 y(39)4069
4467 y(40)4069 4580 y(41)4069 4693 y(42)4069 4806 y(43)4069
4919 y(44)4069 5032 y(45)4069 5145 y(46)4069 5258 y(47)4069
5371 y(48)p eop
%%Page: 149 159
149 158 bop 0 -165 a FA(4.5.)72 b(LANGUA)m(GE)32 b(BINDINGS)2533
b FK(149)1516 91 y FD(SCALAR_IN)45 b(beta,)i(ARRAY)f(y,)h(int)g(incy)
1516 204 y([,)g(enum)g(blas_prec_type)d(prec])i(\);)227
429 y FK(The)31 b(t)m(yp)s(es)g(of)g FD(alpha)p FK(,)g
FD(a)p FK(,)g FD(x)p FK(,)g FD(y)g FK(and)f FD(beta)g
FK(are)i(go)m(v)m(erned)g(according)f(to)h(the)g(rules)d(of)j(mixed)e
(precision)227 542 y(argumen)m(ts)i(set)g(do)m(wn)f(in)f(section)i
(4.3.)45 b(The)31 b(pre\014x)g FD(x)g FK(is)g(the)g(\015oating)h(p)s
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655 y(but)c(if)p 477 655 29 4 v 61 w FD(a)p 560 655 V
34 w(b)g FK(is)f(presen)m(t)h(then)p 1274 655 V 62 w
FD(a)g FK(is)f(the)i(t)m(yp)s(e)f(of)h(argumen)m(t)f
FD(a)g FK(and)p 2580 655 V 61 w FD(b)g FK(is)g(the)g(t)m(yp)s(e)h(of)f
(argumen)m(t)h FD(x)p FK(.)39 b(The)227 768 y(su\016x)p
470 768 V 60 w FD(x)27 b FK(is)f(presen)m(t)h(if)f(and)g(only)g(if)f
FD(prec)h FK(is)g(presen)m(t.)40 b(One)26 b(or)h(b)s(oth)f(of)h(the)g
(su\016xes)p 3238 768 V 60 w FD(a)p 3320 768 V 34 w(b)g
FK(and)p 3602 768 V 61 w FD(x)f FK(m)m(ust)227 881 y(b)s(e)k(presen)m
(t.)p 0 1093 3900 6 v 0 1206 a FJ(f)p FK(SY,SB,SP)p FJ(g)p
FK(MV)h(\(Symmetric)f(matrix)g(v)m(ector)i(m)m(ultiply\))665
b Fy(y)28 b FJ( )d Fy(\013Ax)c FK(+)f Fy(\014)5 b(y)33
b FK(with)c Fy(A)d FK(=)f Fy(A)3845 1173 y Fw(T)141 1432
y FK(The)j(routines)f(m)m(ultiply)e(a)k(v)m(ector)h Fy(x)e
FK(b)m(y)g(a)g(real)g(or)g(complex)g(symmetric)g(matrix)f
Fy(A)p FK(,)i(scales)f(the)h(resulting)0 1545 y(v)m(ector)36
b(and)d(adds)h(it)g(to)h(the)f(scaled)g(v)m(ector)i(op)s(erand)d
Fy(y)s FK(.)52 b(If)34 b Fv(n)68 b FK(is)33 b(less)h(than)g(or)g(equal)
g(to)h(zero)g(or)f(if)f Fv(b)s(eta)h FK(is)0 1658 y(equal)e(to)i(one)f
(and)g Fv(alpha)e FK(is)h(equal)h(to)g(zero,)i(this)d(routine)g
(returns)f(immediately)-8 b(.)47 b(As)33 b(describ)s(ed)e(in)h(section)
0 1771 y(2.5.3,)j(the)e(v)-5 b(alue)33 b Fv(incx)g FK(or)f
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b(Ho)m(w)m(ev)m(er,)36 b(if)31 b(either)i Fv(incx)f FK(or)h
Fv(incy)g FK(is)f(equal)g(to)0 1884 y(zero,)f(an)g(error)f(\015ag)h(is)
e(set)i(and)f(passed)g(to)h(the)g(error)f(handler.)39
b(F)-8 b(or)31 b(the)g(routine)e Fv(SYMV)p FK(,)g(if)g
Fv(lda)h FK(is)f(less)h(than)0 1997 y(one)d(or)f Fv(lda)g
FK(is)g(less)f(than)i Fv(n)p FK(,)g(an)f(error)g(\015ag)h(is)f(set)h
(and)f(passed)g(to)h(the)f(error)h(handler.)37 b(F)-8
b(or)27 b(the)g(routine)e Fv(SBMV)p FK(,)0 2110 y(if)k
Fv(lda)h FK(is)f(less)h(than)g Fv(k)h FK(plus)d(one,)j(an)g(error)f
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2222 y(Extended)g(precision)f(and)g(mixed)g(precision)g(are)i(p)s
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(precision)e(and)0 2448 y(mixed)29 b(precision)g(are)i(p)s(ermitted.)
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3337 y(<type>\(<wp>\),)e(INTENT\(IN\))h(::)i(<aa>)514
3450 y(<type>\(<wp>\),)d(INTENT\(IN\))h(::)i(x\(:\))514
3563 y(<type>\(<wp>\),)d(INTENT\(INOUT\))g(::)j(y\(:\))514
3676 y(TYPE)f(\(blas_uplo_type\),)d(INTENT\(IN\),)i(OPTIONAL)h(::)h
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b(a)47 b(has)g(shape)f(\(k+1,n\))514 4467 y(SP)95 b(ap)47
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h(mixed)f(precision)227 4917 y(argumen)m(ts)30 b(set)f(do)m(wn)g(in)e
(section)j(4.3:)41 b(the)29 b(t)m(yp)s(es)g(of)g FD(a)g
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(that)227 5030 y(of)j FD(y)p FK(,)f FD(alpha)f FK(and)h
FD(beta)p FK(.)227 5181 y(The)g(functionalit)m(y)f(of)i
Fv(symv)f FK(is)f(co)m(v)m(ered)j(b)m(y)e Fv(symm)p FK(.)136
5368 y FJ(\017)46 b FK(F)-8 b(ortran)31 b(77)h(binding:)-214
64 y FI(1)-214 177 y(2)-214 290 y(3)-214 403 y(4)-214
516 y(5)-214 628 y(6)-214 741 y(7)-214 854 y(8)-214 967
y(9)-230 1080 y(10)-230 1193 y(11)-230 1306 y(12)-230
1419 y(13)-230 1532 y(14)-230 1645 y(15)-230 1758 y(16)-230
1870 y(17)-230 1983 y(18)-230 2096 y(19)-230 2209 y(20)-230
2322 y(21)-230 2435 y(22)-230 2548 y(23)-230 2661 y(24)-230
2774 y(25)-230 2887 y(26)-230 3000 y(27)-230 3112 y(28)-230
3225 y(29)-230 3338 y(30)-230 3451 y(31)-230 3564 y(32)-230
3677 y(33)-230 3790 y(34)-230 3903 y(35)-230 4016 y(36)-230
4129 y(37)-230 4242 y(38)-230 4354 y(39)-230 4467 y(40)-230
4580 y(41)-230 4693 y(42)-230 4806 y(43)-230 4919 y(44)-230
5032 y(45)-230 5145 y(46)-230 5258 y(47)-230 5371 y(48)p
eop
%%Page: 150 160
150 159 bop 0 -165 a FK(150)1214 b FA(CHAPTER)30 b(4.)72
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430 y(Symmetric)g(Band:)514 543 y(SUBROUTINE)f(BLAS_xSBMV{_a_b}{_X}\()d
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y(<type>)618 b(Y\()48 b(*)f(\))227 1884 y FK(The)39 b(t)m(yp)s(es)g(of)
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(to)h(the)f(rules)f(of)h(mixed)227 1997 y(precision)c(argumen)m(ts)i
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227 2110 y(argumen)m(ts,)c(but)e(if)p 956 2110 29 4 v
65 w FD(a)p 1038 2110 V 34 w(b)h FK(is)f(presen)m(t)g(then)p
1771 2110 V 66 w FD(a)h FK(is)e(the)i(t)m(yp)s(e)g(of)g
FD(A)g FK(or)g FD(AP)p FK(,)f(and)p 2969 2110 V 66 w
FD(b)g FK(is)g(the)h(t)m(yp)s(e)g(of)g FD(X)p FK(.)f(The)227
2223 y(su\016x)p 470 2223 V 60 w FD(X)c FK(is)f(presen)m(t)h(if)f(and)g
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b(or)h(b)s(oth)f(of)h(the)g(su\016xes)p 3238 2223 V 60
w FD(a)p 3320 2223 V 34 w(b)g FK(and)p 3602 2223 V 61
w FD(X)f FK(m)m(ust)227 2336 y(b)s(e)k(presen)m(t.)136
2519 y FJ(\017)46 b FK(C)30 b(binding:)227 2731 y FD(Symmetric:)227
2844 y(void)47 b(BLAS_xsymv{_a_b}{_x}\()42 b(enum)47
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4198 y(const)g(ARRAY)h(x,)g(int)g(incx,)f(SCALAR_IN)f(beta,)i(ARRAY)f
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227 4523 y FK(The)37 b(t)m(yp)s(es)g(of)h FD(alpha)p
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4749 y(argumen)m(ts,)29 b(but)e(if)p 943 4749 V 60 w
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FK(is)f(the)i(t)m(yp)s(e)g(of)227 4862 y(argumen)m(t)f
FD(x)p FK(.)39 b(The)27 b(su\016x)p 1168 4862 V 60 w
FD(x)f FK(is)f(presen)m(t)i(if)f(and)g(only)f(if)h FD(prec)f
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227 4975 V 256 4975 a FD(a)p 310 4975 V 34 w(b)j FK(and)p
599 4975 V 64 w FD(x)g FK(m)m(ust)g(b)s(e)g(presen)m(t.)p
0 5174 3900 6 v 0 5287 a FJ(f)p FK(HE,HB,HP)p FJ(g)p
FK(MV)j(\(Hermitian)c(matrix)h(v)m(ector)i(pro)s(duct\))656
b Fy(y)28 b FJ( )d Fy(\013Ax)c FK(+)f Fy(\014)5 b(y)33
b FK(with)c Fy(A)d FK(=)f Fy(A)3833 5254 y Fw(H)4084
64 y FI(1)4084 177 y(2)4084 290 y(3)4084 403 y(4)4084
516 y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084 967
y(9)4069 1080 y(10)4069 1193 y(11)4069 1306 y(12)4069
1419 y(13)4069 1532 y(14)4069 1645 y(15)4069 1758 y(16)4069
1870 y(17)4069 1983 y(18)4069 2096 y(19)4069 2209 y(20)4069
2322 y(21)4069 2435 y(22)4069 2548 y(23)4069 2661 y(24)4069
2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
3677 y(33)4069 3790 y(34)4069 3903 y(35)4069 4016 y(36)4069
4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 151 161
151 160 bop 0 -165 a FA(4.5.)72 b(LANGUA)m(GE)32 b(BINDINGS)2533
b FK(151)141 91 y(The)27 b(routines)g(m)m(ultiply)e(a)j(v)m(ector)h
Fy(x)f FK(b)m(y)f(a)i(Hermitian)d(matrix)h Fy(A)p FK(,)i(scales)f(the)f
(resulting)f(v)m(ector)k(and)d(adds)0 204 y(it)d(to)h(the)g(scaled)f(v)
m(ector)i(op)s(erand)d Fy(y)s FK(.)39 b(If)24 b Fv(n)g
FK(is)g(less)f(than)i(or)f(equal)g(to)h(zero)g(or)g(if)e
Fv(b)s(eta)h FK(is)f(equal)h(to)h(one)g(and)f Fv(alpha)0
317 y FK(is)35 b(equal)g(to)h(zero,)i(this)d(routine)f(returns)h
(immediately)-8 b(.)55 b(The)35 b(imaginary)f(part)i(of)g(the)f
(diagonal)g(en)m(tries)h(of)0 430 y(the)30 b(matrix)f(op)s(erand)g(are)
h(supp)s(osed)e(to)i(b)s(e)g(zero)g(and)f(should)f(not)i(b)s(e)f
(referenced.)41 b(As)30 b(describ)s(ed)d(in)i(section)0
543 y(2.5.3,)35 b(the)e(v)-5 b(alue)33 b Fv(incx)g FK(or)f
Fv(incy)h FK(less)f(than)h(zero)g(is)f(p)s(ermitted.)47
b(Ho)m(w)m(ev)m(er,)36 b(if)31 b(either)i Fv(incx)f FK(or)h
Fv(incy)g FK(is)f(equal)g(to)0 656 y(zero,)f(an)f(error)g(\015ag)g(is)f
(set)i(and)e(passed)h(to)h(the)f(error)f(handler.)39
b(F)-8 b(or)31 b(the)f(routine)f Fv(HEMV)p FK(,)h(if)f
Fv(lda)h FK(is)f(less)g(than)0 769 y(one)d(or)g Fv(lda)f
FK(is)g(less)g(than)g Fv(n)p FK(,)i(an)f(error)f(\015ag)h(is)f(set)i
(and)e(passed)g(to)i(the)f(error)f(handler.)37 b(F)-8
b(or)27 b(the)f(routine)f Fv(HBMV)p FK(,)0 882 y(if)k
Fv(lda)h FK(is)f(less)h(than)g Fv(k)h FK(plus)d(one,)j(an)g(error)f
(\015ag)g(is)g(set)h(and)e(passed)h(to)h(the)g(error)f(handler.)141
995 y(Extended)g(precision)f(and)g(mixed)g(precision)g(are)i(p)s
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(eci\014cation)e(as)i(in)f(Chapter)g(2,)k(except)d(that)h(extended)f
(precision)e(and)0 1220 y(mixed)29 b(precision)g(are)i(p)s(ermitted.)
136 1433 y FJ(\017)46 b FK(F)-8 b(ortran)31 b(95)h(binding:)227
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(<aa>)514 2222 y(COMPLEX\(<wp>\),)d(INTENT\(IN\))h(::)i(x\(:\))514
2335 y(COMPLEX\(<wp>\),)d(INTENT\(INOUT\))g(::)j(y\(:\))514
2448 y(TYPE)f(\(blas_uplo_type\),)d(INTENT\(IN\),)i(OPTIONAL)h(::)h
(uplo)514 2561 y(COMPLEX\(<wp>\),)d(INTENT\(IN\),)g(OPTIONAL)i(::)h
(alpha,)f(beta)514 2674 y(TYPE)g(\(blas_prec_type\),)d(INTENT\(IN\),)i
(OPTIONAL)h(::)h(prec)418 2787 y(where)514 2900 y(<aa>)94
b(::=)47 b(a\(:,:\))f(or)h(ap\(:\))418 3013 y(and)514
3126 y(HB)95 b(a)47 b(has)g(shape)f(\(k+1,n\))514 3239
y(HP)95 b(ap)47 b(has)g(shape)f(\(n*\(n+1\)/2\))514 3352
y(x)h(and)g(y)g(have)g(shape)f(\(n\))227 3577 y FK(The)38
b(t)m(yp)s(es)g(of)g FD(alpha)p FK(,)h FD(a)f FK(or)g
FD(ap)p FK(,)h FD(x)p FK(,)h FD(beta)p FK(,)f(and)f FD(y)f
FK(are)i(go)m(v)m(erned)g(b)m(y)f(the)g(rules)f(of)h(mixed)f(precision)
227 3689 y(argumen)m(ts)30 b(set)f(do)m(wn)g(in)e(section)j(4.3:)41
b(the)29 b(t)m(yp)s(es)g(of)g FD(a)g FK(or)g FD(ap)f
FK(and)h FD(x)f FK(can)i(optionally)d(di\013er)h(from)g(that)227
3802 y(of)j FD(y)p FK(,)f FD(alpha)f FK(and)h FD(beta)p
FK(.)227 3953 y(The)g(functionalit)m(y)f(of)i Fv(hemv)f
FK(is)g(co)m(v)m(ered)i(b)m(y)e Fv(hemm)p FK(.)136 4140
y FJ(\017)46 b FK(F)-8 b(ortran)31 b(77)h(binding:)227
4365 y FD(Hermitian:)514 4478 y(SUBROUTINE)45 b(BLAS_xHEMV{_a_b}{_X}\()
d(UPLO,)k(N,)h(ALPHA,)f(A,)h(LDA,)g(X,)g(INCX,)466 4591
y($)1575 b(BETA,)46 b(Y,)h(INCY)g([,)g(PREC])f(\))227
4704 y(Hermitian)g(Band:)514 4817 y(SUBROUTINE)f
(BLAS_xHBMV{_a_b}{_X}\()d(UPLO,)k(N,)h(K,)g(ALPHA,)f(A,)i(LDA,)e(X,)h
(INCX,)466 4930 y($)1575 b(BETA,)46 b(Y,)h(INCY)g([,)g(PREC])f(\))227
5043 y(Hermitian)g(Packed:)514 5156 y(SUBROUTINE)f
(BLAS_xHPMV{_a_b}{_X}\()d(UPLO,)k(N,)h(ALPHA,)f(AP,)h(X,)g(INCX,)466
5269 y($)1575 b(BETA,)46 b(Y,)h(INCY)g([,)g(PREC])f(\))227
5381 y(all:)-214 64 y FI(1)-214 177 y(2)-214 290 y(3)-214
403 y(4)-214 516 y(5)-214 628 y(6)-214 741 y(7)-214 854
y(8)-214 967 y(9)-230 1080 y(10)-230 1193 y(11)-230 1306
y(12)-230 1419 y(13)-230 1532 y(14)-230 1645 y(15)-230
1758 y(16)-230 1870 y(17)-230 1983 y(18)-230 2096 y(19)-230
2209 y(20)-230 2322 y(21)-230 2435 y(22)-230 2548 y(23)-230
2661 y(24)-230 2774 y(25)-230 2887 y(26)-230 3000 y(27)-230
3112 y(28)-230 3225 y(29)-230 3338 y(30)-230 3451 y(31)-230
3564 y(32)-230 3677 y(33)-230 3790 y(34)-230 3903 y(35)-230
4016 y(36)-230 4129 y(37)-230 4242 y(38)-230 4354 y(39)-230
4467 y(40)-230 4580 y(41)-230 4693 y(42)-230 4806 y(43)-230
4919 y(44)-230 5032 y(45)-230 5145 y(46)-230 5258 y(47)-230
5371 y(48)p eop
%%Page: 152 162
152 161 bop 0 -165 a FK(152)1214 b FA(CHAPTER)30 b(4.)72
b(EXTENDED)30 b(AND)h(MIXED)g(PRECISION)e(BLAS)514 91
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(PREC])514 204 y(<ctype>)570 b(ALPHA,)47 b(BETA)514 317
y(<ctype>)570 b(A\()48 b(LDA,)e(*)i(\))f(or)g(AP\()g(*)h(\))514
430 y(<ctype>)570 b(X\()48 b(*)f(\))514 543 y(<ctype>)570
b(Y\()48 b(*)f(\))227 755 y FK(The)37 b(t)m(yp)s(es)h(of)g
FD(ALPHA)p FK(,)e FD(A)i FK(or)f FD(AP)p FK(,)h FD(X)p
FK(,)f FD(Y)p FK(,)h(and)f FD(BETA)f FK(are)i(go)m(v)m(erned)h
(according)f(to)g(the)g(rules)e(of)i(mixed)227 868 y(precision)d
(argumen)m(ts)i(set)g(do)m(wn)f(in)f(section)h(4.3.)60
b(The)36 b(pre\014x)g FD(x)g FK(is)f(the)i(\015oating)f(p)s(oin)m(t)g
(t)m(yp)s(e)g(of)h(the)227 981 y(argumen)m(ts,)d(but)f(if)p
959 981 29 4 v 66 w FD(a)p 1042 981 V 34 w(b)g FK(is)e(presen)m(t)i
(then)p 1779 981 V 67 w FD(a)g FK(is)f(the)h(t)m(yp)s(e)g(of)g
FD(A)g FK(or)g FD(AP)f FK(and)p 2962 981 V 67 w FD(b)g
FK(is)g(the)h(t)m(yp)s(e)h(of)f FD(X)p FK(.)f(The)227
1094 y(su\016x)p 470 1094 V 60 w FD(X)27 b FK(is)f(presen)m(t)h(if)f
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w FD(a)p 3320 1094 V 34 w(b)g FK(and)p 3602 1094 V 61
w FD(X)f FK(m)m(ust)227 1206 y(b)s(e)k(presen)m(t.)136
1390 y FJ(\017)46 b FK(C)30 b(binding:)227 1602 y FD(Hermitian:)227
1714 y(void)47 b(BLAS_xhemv{_a_b}{_x}\()42 b(enum)47
b(blas_order_type)c(order,)j(enum)h(blas_uplo_type)d(uplo,)1516
1827 y(int)j(n,)g(CSCALAR_IN)e(alpha,)h(const)g(CARRAY)h(a,)g(int)g
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(beta,)h(CARRAY)g(y,)1516 2053 y(int)h(incy)f([,)i(enum)e
(blas_prec_type)e(prec])j(\);)227 2166 y(Hermitian)f(Band:)227
2279 y(void)h(BLAS_xhbmv{_a_b}{_x}\()42 b(enum)47 b(blas_order_type)c
(order,)j(enum)h(blas_uplo_type)d(uplo,)1516 2392 y(int)j(n,)g(int)g
(k,)g(CSCALAR_IN)e(alpha,)h(const)h(CARRAY)f(a,)1516
2505 y(int)h(lda,)f(const)h(CARRAY)f(x,)h(int)g(incx,)f(CSCALAR_IN)f
(beta,)1516 2618 y(CARRAY)h(y,)h(int)g(incy)g([,)g(enum)g
(blas_prec_type)c(prec])k(\);)227 2731 y(Hermitian)f(Packed:)227
2844 y(void)h(BLAS_xhpmv{_a_b}{_x}\()42 b(enum)47 b(blas_order_type)c
(order,)j(enum)h(blas_uplo_type)d(uplo,)1516 2956 y(int)j(n,)g
(CSCALAR_IN)e(alpha,)h(const)g(CARRAY)h(ap,)1516 3069
y(const)f(CARRAY)g(x,)i(int)e(incx,)h(CSCALAR_IN)e(beta,)h(CARRAY)g(y,)
1516 3182 y(int)h(incy)f([,)i(enum)e(blas_prec_type)e(prec])j(\);)227
3394 y FK(The)37 b(t)m(yp)s(es)g(of)h FD(alpha)p FK(,)g
FD(a)f FK(or)g FD(ap)p FK(,)h FD(x)p FK(,)h FD(y)p FK(,)g(and)e
FD(beta)f FK(are)i(go)m(v)m(erned)g(according)f(to)h(the)g(rules)e(of)h
(mixed)227 3507 y(precision)e(argumen)m(ts)i(set)g(do)m(wn)f(in)f
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3620 y(argumen)m(ts,)29 b(but)e(if)p 943 3620 V 60 w
FD(a)p 1025 3620 V 35 w(b)g FK(is)f(presen)m(t)i(then)p
1741 3620 V 61 w FD(a)g FK(is)e(the)i(t)m(yp)s(e)f(of)h(argumen)m(t)g
FD(a)f FK(or)h FD(ap)e FK(and)p 3279 3620 V 62 w FD(b)h
FK(is)f(the)i(t)m(yp)s(e)g(of)227 3733 y(argumen)m(t)f
FD(x)p FK(.)39 b(The)27 b(su\016x)p 1168 3733 V 60 w
FD(x)f FK(is)f(presen)m(t)i(if)f(and)g(only)f(if)h FD(prec)f
FK(is)h(presen)m(t.)39 b(One)27 b(or)f(b)s(oth)g(of)h(the)g(su\016xes)p
227 3846 V 256 3846 a FD(a)p 310 3846 V 34 w(b)j FK(and)p
599 3846 V 64 w FD(x)g FK(m)m(ust)g(b)s(e)g(presen)m(t.)p
0 4045 3900 6 v 0 4158 a FJ(f)p FK(TR,TB,TP)p FJ(g)p
FK(MV)h(\(T)-8 b(riangular)29 b(matrix)h(v)m(ector)i(pro)s(duct\))360
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b FJ( )g Fy(\013T)3214 4125 y Fw(T)3270 4158 y Fy(x)30
b FK(or)g Fy(x)25 b FJ( )h Fy(\013T)3781 4125 y Fw(H)3848
4158 y Fy(x)141 4384 y FK(The)43 b(routines)g(m)m(ultiply)e(a)j(v)m
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Fy(T)56 b FK(or)44 b(its)f(transp)s(ose,)k(or)d(its)0
4497 y(conjugate)36 b(transp)s(ose,)f(and)f(copies)h(the)f(resulting)f
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FK(.)53 b(If)35 b Fv(n)f FK(is)g(less)g(than)g(or)0 4610
y(equal)h(to)g(zero,)j(this)c(routine)g(returns)g(immediately)-8
b(.)53 b(As)35 b(describ)s(ed)e(in)h(section)h(2.5.3,)k(the)c(v)-5
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(ermitted.)38 b(Ho)m(w)m(ev)m(er,)31 b(if)c Fv(incx)g
FK(is)g(equal)g(to)i(zero,)g(an)f(error)f(\015ag)h(is)f(set)h(and)g
(passed)f(to)h(the)g(error)0 4835 y(handler.)41 b(F)-8
b(or)32 b(the)f(routine)f Fv(TRMV)p FK(,)g(if)g Fv(ldt)g
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Fv(n)p FK(,)g(an)g(error)g(\015ag)g(is)f(set)i(and)0
4948 y(passed)h(to)i(the)f(error)g(handler.)49 b(F)-8
b(or)35 b(the)f(routine)e Fv(TBMV)p FK(,)h(if)g Fv(ldt)g
FK(is)g(less)g(than)h Fv(k)g FK(plus)e(one,)j(an)f(error)g(\015ag)g(is)
0 5061 y(set)d(and)f(passed)g(to)h(the)f(error)g(handler.)141
5174 y(Extended)g(precision)f(and)g(mixed)g(precision)g(are)i(p)s
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(eci\014cation)e(as)i(in)f(Chapter)g(2,)k(except)d(that)h(extended)f
(precision)e(and)0 5400 y(mixed)29 b(precision)g(are)i(p)s(ermitted.)
4084 64 y FI(1)4084 177 y(2)4084 290 y(3)4084 403 y(4)4084
516 y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084 967
y(9)4069 1080 y(10)4069 1193 y(11)4069 1306 y(12)4069
1419 y(13)4069 1532 y(14)4069 1645 y(15)4069 1758 y(16)4069
1870 y(17)4069 1983 y(18)4069 2096 y(19)4069 2209 y(20)4069
2322 y(21)4069 2435 y(22)4069 2548 y(23)4069 2661 y(24)4069
2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
3677 y(33)4069 3790 y(34)4069 3903 y(35)4069 4016 y(36)4069
4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 153 163
153 162 bop 0 -165 a FA(4.5.)72 b(LANGUA)m(GE)32 b(BINDINGS)2533
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514 994 y(<type>\(<wp>\),)d(INTENT\(IN\),)h(OPTIONAL)g(::)i(alpha)514
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1784 y(and)514 1897 y(x)g(has)g(shape)f(\(n\))514 2010
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227 2574 y(set)f(do)m(wn)f(in)f(section)i(4.3:)42 b(the)30
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FK(.)227 2724 y(The)g(functionalit)m(y)f(of)i Fv(trmv)f
FK(is)f(co)m(v)m(ered)j(b)m(y)f Fv(trmm)p FK(.)136 2912
y FJ(\017)46 b FK(F)-8 b(ortran)31 b(77)h(binding:)227
3137 y FD(Triangular:)561 3249 y(SUBROUTINE)45 b(BLAS_xTRMV{_a}{_X}\()e
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4379 y(<type>)618 b(ALPHA)514 4491 y(<type>)g(T\()48
b(LDT,)e(*)i(\))f(or)g(TP\()g(*)h(\))514 4604 y(<type>)618
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5055 y(but)f(if)p 483 5055 29 4 v 64 w FD(a)g FK(is)g(presen)m(t)h
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FD(T)f FK(or)g FD(TP)p FK(.)h(The)f(su\016x)p 2650 5055
V 64 w FD(X)g FK(is)g(presen)m(t)g(if)g(and)g(only)g(if)f
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2060 5168 V 64 w FD(X)g FK(m)m(ust)g(b)s(e)g(presen)m(t.)136
5356 y FJ(\017)46 b FK(C)30 b(binding:)-214 64 y FI(1)-214
177 y(2)-214 290 y(3)-214 403 y(4)-214 516 y(5)-214 628
y(6)-214 741 y(7)-214 854 y(8)-214 967 y(9)-230 1080
y(10)-230 1193 y(11)-230 1306 y(12)-230 1419 y(13)-230
1532 y(14)-230 1645 y(15)-230 1758 y(16)-230 1870 y(17)-230
1983 y(18)-230 2096 y(19)-230 2209 y(20)-230 2322 y(21)-230
2435 y(22)-230 2548 y(23)-230 2661 y(24)-230 2774 y(25)-230
2887 y(26)-230 3000 y(27)-230 3112 y(28)-230 3225 y(29)-230
3338 y(30)-230 3451 y(31)-230 3564 y(32)-230 3677 y(33)-230
3790 y(34)-230 3903 y(35)-230 4016 y(36)-230 4129 y(37)-230
4242 y(38)-230 4354 y(39)-230 4467 y(40)-230 4580 y(41)-230
4693 y(42)-230 4806 y(43)-230 4919 y(44)-230 5032 y(45)-230
5145 y(46)-230 5258 y(47)-230 5371 y(48)p eop
%%Page: 154 164
154 163 bop 0 -165 a FK(154)1214 b FA(CHAPTER)30 b(4.)72
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1559 y(int)j(n,)h(SCALAR_IN)d(alpha,)h(const)g(ARRAY)h(tp,)1420
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2236 y(only)c(if)f FD(prec)g FK(is)h(presen)m(t.)40 b(One)30
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609 4579 y(<type>\(<wp>\),)d(INTENT)i(\(OUT\))h(::)g(y\(:\))609
4692 y(<type>\(<wp>\),)d(INTENT)i(\(IN\),)h(OPTIONAL)e(::)i(alpha,)g
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y(a)h(and)e(b)i(have)f(shape)f(\(m,n\))g(for)h(general)f(matrices)4084
64 y FI(1)4084 177 y(2)4084 290 y(3)4084 403 y(4)4084
516 y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084 967
y(9)4069 1080 y(10)4069 1193 y(11)4069 1306 y(12)4069
1419 y(13)4069 1532 y(14)4069 1645 y(15)4069 1758 y(16)4069
1870 y(17)4069 1983 y(18)4069 2096 y(19)4069 2209 y(20)4069
2322 y(21)4069 2435 y(22)4069 2548 y(23)4069 2661 y(24)4069
2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
3677 y(33)4069 3790 y(34)4069 3903 y(35)4069 4016 y(36)4069
4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 155 165
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2322 y(21)-230 2435 y(22)-230 2548 y(23)-230 2661 y(24)-230
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5032 y(45)-230 5145 y(46)-230 5258 y(47)-230 5371 y(48)p
eop
%%Page: 156 166
156 165 bop 0 -165 a FK(156)1214 b FA(CHAPTER)30 b(4.)72
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%%Page: 157 167
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%%Page: 158 168
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b(BETA)514 5366 y(<type>)618 b(A\()48 b(LDA,)e(*)i(\))4084
64 y FI(1)4084 177 y(2)4084 290 y(3)4084 403 y(4)4084
516 y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084 967
y(9)4069 1080 y(10)4069 1193 y(11)4069 1306 y(12)4069
1419 y(13)4069 1532 y(14)4069 1645 y(15)4069 1758 y(16)4069
1870 y(17)4069 1983 y(18)4069 2096 y(19)4069 2209 y(20)4069
2322 y(21)4069 2435 y(22)4069 2548 y(23)4069 2661 y(24)4069
2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
3677 y(33)4069 3790 y(34)4069 3903 y(35)4069 4016 y(36)4069
4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 159 169
159 168 bop 0 -165 a FA(4.5.)72 b(LANGUA)m(GE)32 b(BINDINGS)2533
b FK(159)514 91 y FD(<type>)618 b(B\()48 b(LDB,)e(*)i(\))514
204 y(<type>)618 b(C\()48 b(LDC,)e(*)i(\))227 422 y FK(The)31
b(t)m(yp)s(es)g(of)h FD(ALPHA)p FK(,)e FD(A)p FK(,)h
FD(B)p FK(,)g FD(BETA)f FK(and)g FD(C)h FK(are)h(go)m(v)m(erned)g
(according)f(to)h(the)g(rules)d(of)j(mixed)e(precision)227
535 y(argumen)m(ts)i(set)g(do)m(wn)f(in)f(section)i(4.3.)45
b(The)31 b(pre\014x)g FD(x)g FK(is)g(the)g(\015oating)h(p)s(oin)m(t)e
(t)m(yp)s(e)i(of)g(the)f(argumen)m(ts,)227 648 y(but)f(if)p
483 648 29 4 v 64 w FD(a)p 566 648 V 34 w(b)g FK(is)f(presen)m(t)i
(then)p 1293 648 V 64 w FD(a)f FK(is)g(the)g(t)m(yp)s(e)h(of)g
FD(A)f FK(and)p 2216 648 V 64 w FD(b)g FK(is)f(the)i(t)m(yp)s(e)g(of)f
FD(B)p FK(.)h(The)f(su\016x)p 3416 648 V 63 w FD(X)g
FK(is)g(presen)m(t)227 761 y(if)g(and)f(only)h(if)f FD(PREC)g
FK(is)h(presen)m(t.)41 b(One)30 b(or)g(b)s(oth)g(of)g(the)h(su\016xes)p
2535 761 V 64 w FD(a)p 2618 761 V 34 w(b)f FK(and)p 2906
761 V 64 w FD(X)g FK(m)m(ust)g(b)s(e)g(presen)m(t.)136
947 y FJ(\017)46 b FK(C)30 b(binding:)227 1165 y FD(void)47
b(BLAS_xgemm{_a_b}{_x}\()42 b(enum)47 b(blas_order_type)c(order,)1516
1278 y(enum)k(blas_trans_type)c(transa,)1516 1391 y(enum)k
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1503 y(SCALAR_IN)e(alpha,)h(const)h(ARRAY)f(a,)h(int)g(lda,)1516
1616 y(const)f(ARRAY)h(b,)g(int)g(ldb,)1516 1729 y(SCALAR_IN)e(beta,)i
(ARRAY)f(c,)h(int)g(ldc)1516 1842 y([,)g(enum)g(blas_prec_type)d(prec])
i(\);)227 2060 y FK(The)31 b(t)m(yp)s(es)g(of)g FD(alpha)p
FK(,)g FD(a)p FK(,)g FD(b)p FK(,)g FD(beta)f FK(and)h
FD(c)f FK(are)i(go)m(v)m(erned)g(according)f(to)h(the)g(rules)d(of)j
(mixed)e(precision)227 2173 y(argumen)m(ts)i(set)g(do)m(wn)f(in)f
(section)i(4.3.)45 b(The)31 b(pre\014x)g FD(x)g FK(is)g(the)g
(\015oating)h(p)s(oin)m(t)e(t)m(yp)s(e)i(of)g(the)f(argumen)m(ts,)227
2286 y(but)c(if)p 477 2286 V 61 w FD(a)p 560 2286 V 34
w(b)g FK(is)f(presen)m(t)h(then)p 1274 2286 V 62 w FD(a)g
FK(is)f(the)i(t)m(yp)s(e)f(of)h(argumen)m(t)f FD(a)g
FK(and)p 2580 2286 V 61 w FD(b)g FK(is)g(the)g(t)m(yp)s(e)h(of)f
(argumen)m(t)h FD(b)p FK(.)39 b(The)227 2399 y(su\016x)p
470 2399 V 60 w FD(x)27 b FK(is)f(presen)m(t)h(if)f(and)g(only)g(if)f
FD(prec)h FK(is)g(presen)m(t.)40 b(One)26 b(or)h(b)s(oth)f(of)h(the)g
(su\016xes)p 3238 2399 V 60 w FD(a)p 3320 2399 V 34 w(b)g
FK(and)p 3602 2399 V 61 w FD(x)f FK(m)m(ust)227 2512
y(b)s(e)k(presen)m(t.)p 0 2718 3900 6 v 0 2831 a(SYMM)h(\(Symmetric)e
(Matrix)i(Matrix)f(Pro)s(duct\))682 b Fy(C)31 b FJ( )25
b Fy(\013AB)h FK(+)20 b Fy(\014)5 b(C)37 b FK(or)30 b
Fy(C)i FJ( )25 b Fy(\013B)5 b(A)20 b FK(+)g Fy(\014)5
b(C)141 3057 y FK(This)41 b(routine)h(p)s(erforms)f(one)h(of)h(the)g
(symmetric)f(matrix)g(matrix)g(op)s(erations)g Fy(C)52
b FJ( )45 b Fy(\013AB)34 b FK(+)28 b Fy(\014)5 b(C)49
b FK(or)0 3169 y Fy(C)40 b FJ( )33 b Fy(\013B)5 b(A)24
b FK(+)f Fy(\014)5 b(C)42 b FK(where)35 b Fy(\013)g FK(and)g
Fy(\014)40 b FK(are)c(scalars,)h Fy(A)e FK(is)f(a)i(symmetric)f
(matrix,)h(and)e Fy(B)40 b FK(and)35 b Fy(C)41 b FK(are)36
b(general)0 3282 y(matrices.)k(This)26 b(routine)h(returns)f
(immediately)g(if)h Fv(m)h FK(or)g Fv(n)f FK(is)g(less)g(than)h(or)f
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3395 y Fv(blas)p 153 3395 28 4 v 32 w(left)p 308 3395
V 32 w(side)p FK(,)32 b(and)f(if)g Fv(lda)g FK(is)f(less)h(than)g(one)h
(or)f(less)g(than)g Fv(m)p FK(,)i(or)e(if)g Fv(ldb)g
FK(is)f(less)h(than)g(one)h(or)g(less)e(than)i Fv(m)p
FK(,)g(or)0 3508 y(if)f Fv(ldc)h FK(is)f(less)g(than)h(one)g(or)g(less)
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(to)i(the)f(error)g(handler.)43 b(F)-8 b(or)33 b Fv(side)0
3621 y FK(equal)h(to)i Fv(blas)p 513 3621 V 32 w(right)p
723 3621 V 32 w(side)p FK(,)g(and)e(if)g Fv(lda)g FK(is)g(less)g(than)g
(one)h(or)g(less)f(than)g Fv(n)p FK(,)i(or)f(if)f Fv(ldb)g
FK(is)g(less)g(than)g(one)h(or)g(less)0 3734 y(than)29
b Fv(n)p FK(,)i(or)e(if)g Fv(ldc)h FK(is)e(less)h(than)h(one)g(or)g
(less)f(than)g Fv(n)p FK(,)h(an)g(error)f(\015ag)h(is)f(set)h(and)g
(passed)f(to)h(the)g(error)g(handler.)141 3847 y(The)d(in)m(terfaces)h
(encompass)g(the)g(Legacy)h(BLAS)f(routine)e(xSYMM)i(with)f(added)g
(functionalit)m(y)f(for)h(com-)0 3960 y(plex)i(symmetric)h(matrices.)
141 4073 y(Extended)g(precision)f(and)g(mixed)g(precision)g(are)i(p)s
(ermitted.)141 4186 y(This)36 b(routine)h(has)h(the)g(same)g(sp)s
(eci\014cation)e(as)i(in)f(Chapter)g(2,)k(except)d(that)h(extended)f
(precision)e(and)0 4299 y(mixed)29 b(precision)g(are)i(p)s(ermitted.)
136 4504 y FJ(\017)46 b FK(F)-8 b(ortran)31 b(95)h(binding:)418
4723 y FD(SUBROUTINE)45 b(symm\()i(a,)g(b,)g(c)g([,)h(side])e([,)h
(uplo])f([,)i(alpha])e([,)h(beta])f([,)h(prec])g(\))514
4835 y(<type>\(<wp>\),)d(INTENT\(IN\))h(::)i(a\(:,:\))514
4948 y(<type>\(<wp>\),)d(INTENT\(IN\))h(::)i(<bb>)514
5061 y(<type>\(<wp>\),)d(INTENT\(INOUT\))g(::)j(<cc>)514
5174 y(TYPE)f(\(blas_side_type\),)d(INTENT\(IN\),)i(OPTIONAL)h(::)h
(side)514 5287 y(TYPE)f(\(blas_uplo_type\),)d(INTENT\(IN\),)i(OPTIONAL)
h(::)h(uplo)514 5400 y(<type>\(<wp>\),)d(INTENT\(IN\),)h(OPTIONAL)g(::)
i(alpha,)f(beta)-214 64 y FI(1)-214 177 y(2)-214 290
y(3)-214 403 y(4)-214 516 y(5)-214 628 y(6)-214 741 y(7)-214
854 y(8)-214 967 y(9)-230 1080 y(10)-230 1193 y(11)-230
1306 y(12)-230 1419 y(13)-230 1532 y(14)-230 1645 y(15)-230
1758 y(16)-230 1870 y(17)-230 1983 y(18)-230 2096 y(19)-230
2209 y(20)-230 2322 y(21)-230 2435 y(22)-230 2548 y(23)-230
2661 y(24)-230 2774 y(25)-230 2887 y(26)-230 3000 y(27)-230
3112 y(28)-230 3225 y(29)-230 3338 y(30)-230 3451 y(31)-230
3564 y(32)-230 3677 y(33)-230 3790 y(34)-230 3903 y(35)-230
4016 y(36)-230 4129 y(37)-230 4242 y(38)-230 4354 y(39)-230
4467 y(40)-230 4580 y(41)-230 4693 y(42)-230 4806 y(43)-230
4919 y(44)-230 5032 y(45)-230 5145 y(46)-230 5258 y(47)-230
5371 y(48)p eop
%%Page: 160 170
160 169 bop 0 -165 a FK(160)1214 b FA(CHAPTER)30 b(4.)72
b(EXTENDED)30 b(AND)h(MIXED)g(PRECISION)e(BLAS)514 91
y FD(TYPE)46 b(\(blas_prec_type\),)d(INTENT)j(\(IN\),)h(OPTIONAL)e(::)j
(prec)418 204 y(where)514 317 y(<bb>)94 b(::=)47 b(b\(:,:\))f(or)h
(b\(:\))514 430 y(<cc>)94 b(::=)47 b(c\(:,:\))f(or)h(c\(:\))418
543 y(and)466 656 y(c,)g(rank)g(2,)g(has)g(shape)f(\(m,n\),)g(b)i(same)
e(shape)h(as)g(c)561 769 y(SY)95 b(a)48 b(has)f(shape)f(\(m,m\))g(if)i
(side)e(=)i(blas_left_side)c(\(the)i(default\))752 882
y(a)i(has)f(shape)f(\(n,n\))g(if)i(side)e(/=)h(blas_left_side)466
995 y(c,)g(rank)g(1,)g(has)g(shape)f(\(m\),)h(b)g(same)g(shape)f(as)h
(c)561 1108 y(SY)95 b(a)48 b(has)f(shape)f(\(m,m\))p
1154 1276 1820 4 v 1152 1389 4 113 v 1204 1355 a FK(Rank)30
b FD(b)p 1541 1389 V 99 w FK(Rank)h FD(c)p 1929 1389
V 99 w(side)p 2220 1389 V 98 w FK(Op)s(eration)p 2972
1389 V 1154 1393 1820 4 v 1152 1505 4 113 v 1326 1472
a(2)p 1541 1505 V 343 w(2)p 1929 1505 V 289 w(L)p 2220
1505 V 166 w Fy(C)h FJ( )25 b Fy(\013AB)h FK(+)20 b Fy(\014)5
b(C)p 2972 1505 V 1152 1618 V 1326 1585 a FK(2)p 1541
1618 V 343 w(2)p 1929 1618 V 284 w(R)p 2220 1618 V 161
w Fy(C)32 b FJ( )25 b Fy(\013B)5 b(A)21 b FK(+)f Fy(\014)5
b(C)p 2972 1618 V 1152 1731 V 1326 1697 a FK(1)p 1541
1731 V 343 w(1)p 1929 1731 V 302 w(-)p 2220 1731 V 180
w Fy(c)26 b FJ( )f Fy(\013Ab)c FK(+)f Fy(\014)5 b(c)p
2972 1731 V 1154 1735 1820 4 v 227 1943 a FK(The)44 b(table)h
(de\014ning)e(the)i(op)s(eration)f(as)h(a)g(function)e(of)i(the)g(op)s
(erator)g(argumen)m(ts)g(is)f(iden)m(tical)f(to)227 2056
y(Chapter)30 b(2.)227 2206 y(The)g(functionalit)m(y)f(of)i(xSYMV)f(is)f
(co)m(v)m(ered)j(b)m(y)f Fv(symm)p FK(.)227 2356 y(The)g(t)m(yp)s(es)g
(of)g FD(a)p FK(,)h FD(b)p FK(,)f FD(c)p FK(,)g FD(alpha)f
FK(and)g FD(beta)g FK(are)i(go)m(v)m(erned)g(according)f(to)h(the)g
(rules)d(of)j(mixed)e(precision)227 2469 y(argumen)m(ts)h(set)h(do)m
(wn)e(in)f(section)i(4.3:)43 b(the)31 b(t)m(yp)s(es)f(of)h
FD(a)g FK(and)f FD(b)g FK(can)h(optionally)e(di\013er)h(from)g(that)h
(of)g FD(c)p FK(,)227 2582 y FD(alpha)e FK(and)h FD(beta)p
FK(.)136 2770 y FJ(\017)46 b FK(F)-8 b(ortran)31 b(77)h(binding:)514
2995 y FD(SUBROUTINE)45 b(BLAS_xSYMM{_a_b}{_X}\()d(SIDE,)k(UPLO,)g(M,)i
(N,)f(ALPHA,)f(A,)h(LDA,)466 3108 y($)1575 b(B,)47 b(LDB,)f(BETA,)h(C,)
g(LDC)g([,)g(PREC])f(\))514 3221 y(INTEGER)570 b(LDA,)47
b(LDB,)g(LDC,)f(M,)i(N,)f(SIDE,)f(UPLO)h([,)g(PREC])514
3334 y(<type>)618 b(ALPHA,)47 b(BETA)514 3447 y(<type>)618
b(A\()48 b(LDA,)e(*)i(\))514 3559 y(<type>)618 b(B\()48
b(LDB,)e(*)i(\))514 3672 y(<type>)618 b(C\()48 b(LDC,)e(*)i(\))227
3897 y FK(The)31 b(t)m(yp)s(es)g(of)h FD(ALPHA)p FK(,)e
FD(A)p FK(,)h FD(B)p FK(,)g FD(BETA)f FK(and)g FD(C)h
FK(are)h(go)m(v)m(erned)g(according)f(to)h(the)g(rules)d(of)j(mixed)e
(precision)227 4010 y(argumen)m(ts)i(set)g(do)m(wn)f(in)f(section)i
(4.3.)45 b(The)31 b(pre\014x)g FD(x)g FK(is)g(the)g(\015oating)h(p)s
(oin)m(t)e(t)m(yp)s(e)i(of)g(the)f(argumen)m(ts,)227
4123 y(but)f(if)p 483 4123 29 4 v 64 w FD(a)p 566 4123
V 34 w(b)g FK(is)f(presen)m(t)i(then)p 1293 4123 V 64
w FD(a)f FK(is)g(the)g(t)m(yp)s(e)h(of)g FD(A)f FK(and)p
2216 4123 V 64 w FD(b)g FK(is)f(the)i(t)m(yp)s(e)g(of)f
FD(B)p FK(.)h(The)f(su\016x)p 3416 4123 V 63 w FD(X)g
FK(is)g(presen)m(t)227 4236 y(if)g(and)f(only)h(if)f
FD(PREC)g FK(is)h(presen)m(t.)41 b(One)30 b(or)g(b)s(oth)g(of)g(the)h
(su\016xes)p 2535 4236 V 64 w FD(a)p 2618 4236 V 34 w(b)f
FK(and)p 2906 4236 V 64 w FD(X)g FK(m)m(ust)g(b)s(e)g(presen)m(t.)136
4424 y FJ(\017)46 b FK(C)30 b(binding:)227 4649 y FD(void)47
b(BLAS_xsymm{_a_b}{_x}\()42 b(enum)47 b(blas_order_type)c(order,)1516
4762 y(enum)k(blas_side_type)c(side,)1516 4875 y(enum)k(blas_uplo_type)
c(uplo,)k(int)g(m,)g(int)g(n,)1516 4987 y(SCALAR_IN)e(alpha,)h(const)h
(ARRAY)f(a,)h(int)g(lda,)1516 5100 y(const)f(ARRAY)h(b,)g(int)g(ldb,)f
(SCALAR_IN)g(beta,)g(ARRAY)g(c,)1516 5213 y(int)h(ldc)g([,)g(enum)g
(blas_prec_type)c(prec])k(\);)4084 64 y FI(1)4084 177
y(2)4084 290 y(3)4084 403 y(4)4084 516 y(5)4084 628 y(6)4084
741 y(7)4084 854 y(8)4084 967 y(9)4069 1080 y(10)4069
1193 y(11)4069 1306 y(12)4069 1419 y(13)4069 1532 y(14)4069
1645 y(15)4069 1758 y(16)4069 1870 y(17)4069 1983 y(18)4069
2096 y(19)4069 2209 y(20)4069 2322 y(21)4069 2435 y(22)4069
2548 y(23)4069 2661 y(24)4069 2774 y(25)4069 2887 y(26)4069
3000 y(27)4069 3112 y(28)4069 3225 y(29)4069 3338 y(30)4069
3451 y(31)4069 3564 y(32)4069 3677 y(33)4069 3790 y(34)4069
3903 y(35)4069 4016 y(36)4069 4129 y(37)4069 4242 y(38)4069
4354 y(39)4069 4467 y(40)4069 4580 y(41)4069 4693 y(42)4069
4806 y(43)4069 4919 y(44)4069 5032 y(45)4069 5145 y(46)4069
5258 y(47)4069 5371 y(48)p eop
%%Page: 161 171
161 170 bop 0 -165 a FA(4.5.)72 b(LANGUA)m(GE)32 b(BINDINGS)2533
b FK(161)227 91 y(The)31 b(t)m(yp)s(es)g(of)g FD(alpha)p
FK(,)g FD(a)p FK(,)g FD(b)p FK(,)g FD(beta)f FK(and)h
FD(c)f FK(are)i(go)m(v)m(erned)g(according)f(to)h(the)g(rules)d(of)j
(mixed)e(precision)227 204 y(argumen)m(ts)i(set)g(do)m(wn)f(in)f
(section)i(4.3.)45 b(The)31 b(pre\014x)g FD(x)g FK(is)g(the)g
(\015oating)h(p)s(oin)m(t)e(t)m(yp)s(e)i(of)g(the)f(argumen)m(ts,)227
317 y(but)k(if)p 494 317 29 4 v 69 w FD(a)p 576 317 V
35 w(b)g FK(is)g(presen)m(t)h(then)p 1325 317 V 70 w
FD(a)f FK(is)g(the)h(t)m(yp)s(e)g(of)g(argumen)m(t)g
FD(a)p FK(,)h(and)p 2725 317 V 70 w FD(b)e FK(is)g(the)h(t)m(yp)s(e)g
(of)g(argumen)m(t)g FD(b)p FK(.)227 430 y(The)29 b(su\016x)p
657 430 V 62 w FD(x)f FK(is)g(presen)m(t)h(if)f(and)g(only)g(if)g
FD(prec)f FK(is)h(presen)m(t.)40 b(One)29 b(or)g(b)s(oth)f(of)h(the)g
(su\016xes)p 3456 430 V 62 w FD(a)p 3538 430 V 34 w(b)g
FK(and)p 3824 430 V 62 w FD(x)227 543 y FK(m)m(ust)i(b)s(e)e(presen)m
(t.)p 0 731 3900 6 v 0 844 a(HEMM)i(\(Hermitian)e(Matrix)i(Matrix)f
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b Fy(\014)5 b(C)37 b FK(or)30 b Fy(C)i FJ( )25 b Fy(\013B)5
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b Fy(\014)5 b(C)50 b FK(or)0 1183 y Fy(C)41 b FJ( )34
b Fy(\013B)5 b(A)24 b FK(+)f Fy(\014)5 b(C)43 b FK(where)35
b Fy(\013)h FK(and)f Fy(\014)41 b FK(are)36 b(scalars,)h
Fy(A)f FK(is)f(a)h(Hermitian)f(matrix,)h(and)f Fy(B)41
b FK(and)35 b Fy(C)42 b FK(are)36 b(general)0 1296 y(matrices.)k(This)
26 b(routine)h(returns)f(immediately)g(if)h Fv(m)h FK(or)g
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b(F)-8 b(or)28 b Fv(side)g FK(equal)f(to)0 1409 y Fv(blas)p
153 1409 28 4 v 32 w(left)p 308 1409 V 32 w(side)p FK(,)32
b(and)f(if)g Fv(lda)g FK(is)f(less)h(than)g(one)h(or)f(less)g(than)g
Fv(m)p FK(,)i(or)e(if)g Fv(ldb)g FK(is)f(less)h(than)g(one)h(or)g(less)
e(than)i Fv(m)p FK(,)g(or)0 1522 y(if)f Fv(ldc)h FK(is)f(less)g(than)h
(one)g(or)g(less)f(than)h Fv(m)p FK(,)h(an)f(error)f(\015ag)i(is)e(set)
h(and)g(passed)f(to)i(the)f(error)g(handler.)43 b(F)-8
b(or)33 b Fv(side)0 1635 y FK(equal)h(to)i Fv(blas)p
513 1635 V 32 w(right)p 723 1635 V 32 w(side)p FK(,)g(and)e(if)g
Fv(lda)g FK(is)g(less)g(than)g(one)h(or)g(less)f(than)g
Fv(n)p FK(,)i(or)f(if)f Fv(ldb)g FK(is)g(less)g(than)g(one)h(or)g(less)
0 1748 y(than)29 b Fv(n)p FK(,)i(or)e(if)g Fv(ldc)h FK(is)e(less)h
(than)h(one)g(or)g(less)f(than)g Fv(n)p FK(,)h(an)g(error)f(\015ag)h
(is)f(set)h(and)g(passed)f(to)h(the)g(error)g(handler.)141
1860 y(The)g(in)m(terfaces)h(encompass)f(the)h(Legacy)h(BLAS)e(routine)
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(extended)f(precision)e(and)0 2199 y(mixed)29 b(precision)g(are)i(p)s
(ermitted.)136 2388 y FJ(\017)46 b FK(F)-8 b(ortran)31
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514 3040 y(COMPLEX\(<wp>\),)d(INTENT\(INOUT\))g(::)j(<cc>)514
3153 y(TYPE)f(\(blas_side_type\),)d(INTENT\(IN\),)i(OPTIONAL)h(::)h
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h(::)h(uplo)514 3379 y(COMPLEX\(<wp>\),)d(INTENT\(IN\),)g(OPTIONAL)i
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3718 y(<bb>)94 b(::=)47 b(b\(:,:\))f(or)h(b\(:\))514
3830 y(<cc>)94 b(::=)47 b(c\(:,:\))f(or)h(c\(:\))418
3943 y(and)466 4056 y(c,)g(rank)g(2,)g(has)g(shape)f(\(m,n\),)g(b)i
(same)e(shape)h(as)g(c)561 4169 y(HE)95 b(a)48 b(has)f(shape)f(\(m,m\))
g(if)i("side")e(=)h(blas_left_side)d(\(the)j(default\))752
4282 y(a)h(has)f(shape)f(\(n,n\))g(if)i("side")e(/=)h(blas_left_side)
466 4395 y(c,)g(rank)g(1,)g(has)g(shape)f(\(m\),)h(b)g(same)g(shape)f
(as)h(c)561 4508 y(HE)95 b(a)48 b(has)f(shape)f(\(m,m\))p
1154 4649 1820 4 v 1152 4761 4 113 v 1204 4728 a FK(Rank)30
b FD(b)p 1541 4761 V 99 w FK(Rank)h FD(c)p 1929 4761
V 99 w(side)p 2220 4761 V 98 w FK(Op)s(eration)p 2972
4761 V 1154 4765 1820 4 v 1152 4878 4 113 v 1326 4844
a(2)p 1541 4878 V 343 w(2)p 1929 4878 V 289 w(L)p 2220
4878 V 166 w Fy(C)h FJ( )25 b Fy(\013AB)h FK(+)20 b Fy(\014)5
b(C)p 2972 4878 V 1152 4991 V 1326 4957 a FK(2)p 1541
4991 V 343 w(2)p 1929 4991 V 284 w(R)p 2220 4991 V 161
w Fy(C)32 b FJ( )25 b Fy(\013B)5 b(A)21 b FK(+)f Fy(\014)5
b(C)p 2972 4991 V 1152 5104 V 1326 5070 a FK(1)p 1541
5104 V 343 w(1)p 1929 5104 V 302 w(-)p 2220 5104 V 180
w Fy(c)26 b FJ( )f Fy(\013Ab)c FK(+)f Fy(\014)5 b(c)p
2972 5104 V 1154 5107 1820 4 v 227 5287 a FK(The)44 b(table)h
(de\014ning)e(the)i(op)s(eration)f(as)h(a)g(function)e(of)i(the)g(op)s
(erator)g(argumen)m(ts)g(is)f(iden)m(tical)f(to)227 5400
y(Chapter)30 b(2.)-214 64 y FI(1)-214 177 y(2)-214 290
y(3)-214 403 y(4)-214 516 y(5)-214 628 y(6)-214 741 y(7)-214
854 y(8)-214 967 y(9)-230 1080 y(10)-230 1193 y(11)-230
1306 y(12)-230 1419 y(13)-230 1532 y(14)-230 1645 y(15)-230
1758 y(16)-230 1870 y(17)-230 1983 y(18)-230 2096 y(19)-230
2209 y(20)-230 2322 y(21)-230 2435 y(22)-230 2548 y(23)-230
2661 y(24)-230 2774 y(25)-230 2887 y(26)-230 3000 y(27)-230
3112 y(28)-230 3225 y(29)-230 3338 y(30)-230 3451 y(31)-230
3564 y(32)-230 3677 y(33)-230 3790 y(34)-230 3903 y(35)-230
4016 y(36)-230 4129 y(37)-230 4242 y(38)-230 4354 y(39)-230
4467 y(40)-230 4580 y(41)-230 4693 y(42)-230 4806 y(43)-230
4919 y(44)-230 5032 y(45)-230 5145 y(46)-230 5258 y(47)-230
5371 y(48)p eop
%%Page: 162 172
162 171 bop 0 -165 a FK(162)1214 b FA(CHAPTER)30 b(4.)72
b(EXTENDED)30 b(AND)h(MIXED)g(PRECISION)e(BLAS)227 91
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(mixed)e(precision)227 353 y(argumen)m(ts)h(set)h(do)m(wn)e(in)f
(section)i(4.3:)43 b(the)31 b(t)m(yp)s(es)f(of)h FD(a)g
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(LDC)g([,)g(PREC])f(\))514 1092 y(INTEGER)570 b(LDA,)47
b(LDB,)g(LDC,)f(M,)i(N,)f(SIDE,)f(UPLO)h([,)g(PREC])514
1205 y(<ctype>)570 b(ALPHA,)47 b(BETA)514 1317 y(<ctype>)570
b(A\()48 b(LDA,)e(*)i(\))514 1430 y(<ctype>)570 b(B\()48
b(LDB,)e(*)i(\))514 1543 y(<ctype>)570 b(C\()48 b(LDC,)e(*)i(\))227
1759 y FK(The)31 b(t)m(yp)s(es)g(of)h FD(ALPHA)p FK(,)e
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FK(are)h(go)m(v)m(erned)g(according)f(to)h(the)g(rules)d(of)j(mixed)e
(precision)227 1872 y(argumen)m(ts)i(set)g(do)m(wn)f(in)f(section)i
(4.3.)45 b(The)31 b(pre\014x)g FD(x)g FK(is)g(the)g(\015oating)h(p)s
(oin)m(t)e(t)m(yp)s(e)i(of)g(the)f(argumen)m(ts,)227
1985 y(but)f(if)p 483 1985 29 4 v 64 w FD(a)p 566 1985
V 34 w(b)g FK(is)f(presen)m(t)i(then)p 1293 1985 V 64
w FD(a)f FK(is)g(the)g(t)m(yp)s(e)h(of)g FD(A)f FK(and)p
2216 1985 V 64 w FD(b)g FK(is)f(the)i(t)m(yp)s(e)g(of)f
FD(B)p FK(.)h(The)f(su\016x)p 3416 1985 V 63 w FD(X)g
FK(is)g(presen)m(t)227 2097 y(if)g(and)f(only)h(if)f
FD(PREC)g FK(is)h(presen)m(t.)41 b(One)30 b(or)g(b)s(oth)g(of)g(the)h
(su\016xes)p 2535 2097 V 64 w FD(a)p 2618 2097 V 34 w(b)f
FK(and)p 2906 2097 V 64 w FD(X)g FK(m)m(ust)g(b)s(e)g(presen)m(t.)136
2282 y FJ(\017)46 b FK(C)30 b(binding:)227 2497 y FD(void)47
b(BLAS_xhemm{_a_b}{_x}\()42 b(enum)47 b(blas_order_type)c(order,)1516
2610 y(enum)k(blas_side_type)c(side,)1516 2723 y(enum)k(blas_uplo_type)
c(uplo,)k(int)g(m,)g(int)g(n,)1516 2836 y(CSCALAR_IN)e(alpha,)h(const)g
(CARRAY)g(a,)i(int)f(lda,)1516 2949 y(const)f(CARRAY)g(b,)i(int)e(ldb,)
h(CSCALAR_IN)e(beta,)h(CARRAY)h(c,)1516 3062 y(int)g(ldc)g([,)g(enum)g
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FD(alpha)p FK(,)g FD(a)p FK(,)g FD(b)p FK(,)g FD(beta)f
FK(and)h FD(c)f FK(are)i(go)m(v)m(erned)g(according)f(to)h(the)g(rules)
d(of)j(mixed)e(precision)227 3390 y(argumen)m(ts)i(set)g(do)m(wn)f(in)f
(section)i(4.3.)45 b(The)31 b(pre\014x)g FD(x)g FK(is)g(the)g
(\015oating)h(p)s(oin)m(t)e(t)m(yp)s(e)i(of)g(the)f(argumen)m(ts,)227
3503 y(but)k(if)p 494 3503 V 69 w FD(a)p 576 3503 V 35
w(b)g FK(is)g(presen)m(t)h(then)p 1325 3503 V 70 w FD(a)f
FK(is)g(the)h(t)m(yp)s(e)g(of)g(argumen)m(t)g FD(a)p
FK(,)h(and)p 2725 3503 V 70 w FD(b)e FK(is)g(the)h(t)m(yp)s(e)g(of)g
(argumen)m(t)g FD(b)p FK(.)227 3616 y(The)29 b(su\016x)p
657 3616 V 62 w FD(x)f FK(is)g(presen)m(t)h(if)f(and)g(only)g(if)g
FD(prec)f FK(is)h(presen)m(t.)40 b(One)29 b(or)g(b)s(oth)f(of)h(the)g
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FK(and)p 3824 3616 V 62 w FD(x)227 3729 y FK(m)m(ust)i(b)s(e)e(presen)m
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b(Matrix)j(Matrix)f(Multiply\))812 b Fy(B)30 b FJ( )25
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Fy(B)f FJ( )25 b Fy(\013B)5 b(op)p FK(\()p Fy(T)13 b
FK(\))141 4271 y(These)33 b(routines)g(p)s(erform)f(one)i(of)g(the)g
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b(F)-8 b(or)32 b Fv(side)f FK(equal)g(to)0 4610 y Fv(blas)p
153 4610 28 4 v 32 w(left)p 308 4610 V 32 w(side)p FK(,)h(and)f(if)f
Fv(ldt)h FK(is)f(less)h(than)g(one)h(or)f(less)g(than)g
Fv(m)p FK(,)h(or)f(if)f Fv(ldb)h FK(is)g(less)f(than)h(one)h(or)f(less)
g(than)g Fv(m)p FK(,)h(an)0 4723 y(error)g(\015ag)i(is)e(set)h(and)f
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b Fv(side)g FK(equal)g(to)g Fv(blas)p 2829 4723 V 32
w(right)p 3039 4723 V 33 w(side)p FK(,)g(and)g(if)e Fv(ldt)i
FK(is)f(less)0 4835 y(than)f(one)h(or)g(less)f(than)g
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g(than)h Fv(m)p FK(,)g(an)f(error)h(\015ag)f(is)g(set)h(and)f(passed)g
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(eci\014cation)e(as)i(in)f(Chapter)g(2,)k(except)d(that)h(extended)f
(precision)e(and)0 5400 y(mixed)29 b(precision)g(are)i(p)s(ermitted.)
4084 64 y FI(1)4084 177 y(2)4084 290 y(3)4084 403 y(4)4084
516 y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084 967
y(9)4069 1080 y(10)4069 1193 y(11)4069 1306 y(12)4069
1419 y(13)4069 1532 y(14)4069 1645 y(15)4069 1758 y(16)4069
1870 y(17)4069 1983 y(18)4069 2096 y(19)4069 2209 y(20)4069
2322 y(21)4069 2435 y(22)4069 2548 y(23)4069 2661 y(24)4069
2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
3677 y(33)4069 3790 y(34)4069 3903 y(35)4069 4016 y(36)4069
4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 163 173
163 172 bop 0 -165 a FA(4.5.)72 b(LANGUA)m(GE)32 b(BINDINGS)2533
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655 y(<type>\(<wp>\),)d(INTENT\(INOUT\))g(::)j(<bb>)514
768 y(<type>\(<wp>\),)d(INTENT\(IN\),)h(OPTIONAL)g(::)i(alpha)514
881 y(TYPE)f(\(blas_diag_type\),)d(INTENT\(IN\),)i(OPTIONAL)h(::)h
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(OPTIONAL)g(::)j(transt)514 1220 y(TYPE)e(\(blas_uplo_type\),)d
(INTENT\(IN\),)i(OPTIONAL)h(::)h(uplo)514 1333 y(TYPE)f
(\(blas_prec_type\),)d(INTENT)j(\(IN\),)h(OPTIONAL)e(::)j(prec)418
1445 y(where)514 1558 y(<bb>)94 b(::=)47 b(b\(:,:\))f(or)h(b\(:\))418
1671 y(and)466 1784 y(b,)g(rank)g(2,)g(has)g(shape)f(\(m,n\))561
1897 y(TR)95 b(t)48 b(has)f(shape)f(\(m,m\))g(if)i(side)e(=)i
(blas_left_side)c(\(the)i(default\))752 2010 y(t)i(has)f(shape)f
(\(n,n\))g(if)i(side)e(/=)h(blas_left_side)466 2123 y(b,)g(rank)g(1,)g
(has)g(shape)f(\(m\))561 2236 y(TR)95 b(t)48 b(has)f(shape)f(\(m,m\))p
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2305 2518 V 98 w FK(Op)s(eration)p 2884 2518 V 1241 2521
1645 4 v 1239 2634 4 113 v 1413 2600 a(2)p 1628 2634
V 331 w(N)p 2014 2634 V 276 w(L)p 2305 2634 V 166 w Fy(B)g
FJ( )25 b Fy(\013T)13 b(B)p 2884 2634 V 1239 2747 V 1413
2713 a FK(2)p 1628 2747 V 332 w(T)p 2014 2747 V 277 w(L)p
2305 2747 V 166 w Fy(B)30 b FJ( )25 b Fy(\013T)2695 2680
y Fw(T)2750 2713 y Fy(B)p 2884 2747 V 1239 2860 V 1413
2826 a FK(2)p 1628 2860 V 331 w(H)p 2014 2860 V 276 w(L)p
2305 2860 V 166 w Fy(B)30 b FJ( )25 b Fy(\013T)2695 2793
y Fw(H)2763 2826 y Fy(B)p 2884 2860 V 1239 2972 V 1413
2939 a FK(2)p 1628 2972 V 331 w(N)p 2014 2972 V 271 w(R)p
2305 2972 V 161 w Fy(B)30 b FJ( )25 b Fy(\013B)5 b(T)p
2884 2972 V 1239 3085 V 1413 3052 a FK(2)p 1628 3085
V 332 w(T)p 2014 3085 V 272 w(R)p 2305 3085 V 161 w Fy(B)30
b FJ( )25 b Fy(\013B)5 b(T)2769 3019 y Fw(T)p 2884 3085
V 1239 3198 V 1413 3164 a FK(2)p 1628 3198 V 331 w(H)p
2014 3198 V 271 w(R)p 2305 3198 V 161 w Fy(B)30 b FJ( )25
b Fy(\013B)5 b(T)2769 3131 y Fw(H)p 2884 3198 V 1239
3311 V 1413 3277 a FK(1)p 1628 3311 V 331 w(N)p 2014
3311 V 289 w(-)p 2305 3311 V 180 w Fy(b)25 b FJ( )h Fy(\013T)13
b(b)p 2884 3311 V 1239 3424 V 1413 3390 a FK(1)p 1628
3424 V 332 w(T)p 2014 3424 V 290 w(-)p 2305 3424 V 180
w Fy(b)25 b FJ( )h Fy(\013T)2661 3357 y Fw(T)2716 3390
y Fy(b)p 2884 3424 V 1239 3537 V 1413 3503 a FK(1)p 1628
3537 V 331 w(H)p 2014 3537 V 289 w(-)p 2305 3537 V 180
w Fy(b)f FJ( )h Fy(\013T)2661 3470 y Fw(H)2728 3503 y
Fy(b)p 2884 3537 V 1241 3540 1645 4 v 227 3749 a FK(The)44
b(table)h(de\014ning)e(the)i(op)s(eration)f(as)h(a)g(function)e(of)i
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3862 y(Chapter)30 b(2.)227 4012 y(The)g(functionalit)m(y)f(of)i(xTRMV)f
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y(set)31 b(do)m(wn)f(in)f(section)i(4.3:)42 b(the)30
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y FJ(\017)46 b FK(F)-8 b(ortran)31 b(77)h(binding:)514
4688 y FD(SUBROUTINE)45 b(BLAS_xTRMM{_a}{_X}\()d(SIDE,)47
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4914 y(INTEGER)570 b(DIAG,)47 b(LDT,)f(LDB,)h(M,)g(N,)g(SIDE,)g
(TRANST,)f(UPLO)466 5026 y($)906 b([,)48 b(PREC])514
5139 y(<type>)618 b(ALPHA)514 5252 y(<type>)g(T\()48
b(LDT,)e(*)i(\))514 5365 y(<type>)618 b(B\()48 b(LDB,)e(*)i(\))-214
64 y FI(1)-214 177 y(2)-214 290 y(3)-214 403 y(4)-214
516 y(5)-214 628 y(6)-214 741 y(7)-214 854 y(8)-214 967
y(9)-230 1080 y(10)-230 1193 y(11)-230 1306 y(12)-230
1419 y(13)-230 1532 y(14)-230 1645 y(15)-230 1758 y(16)-230
1870 y(17)-230 1983 y(18)-230 2096 y(19)-230 2209 y(20)-230
2322 y(21)-230 2435 y(22)-230 2548 y(23)-230 2661 y(24)-230
2774 y(25)-230 2887 y(26)-230 3000 y(27)-230 3112 y(28)-230
3225 y(29)-230 3338 y(30)-230 3451 y(31)-230 3564 y(32)-230
3677 y(33)-230 3790 y(34)-230 3903 y(35)-230 4016 y(36)-230
4129 y(37)-230 4242 y(38)-230 4354 y(39)-230 4467 y(40)-230
4580 y(41)-230 4693 y(42)-230 4806 y(43)-230 4919 y(44)-230
5032 y(45)-230 5145 y(46)-230 5258 y(47)-230 5371 y(48)p
eop
%%Page: 164 174
164 173 bop 0 -165 a FK(164)1214 b FA(CHAPTER)30 b(4.)72
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227 1519 y FK(The)23 b(t)m(yp)s(es)h(of)g FD(alpha)p
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1632 y(set)36 b(do)m(wn)f(in)f(section)i(4.3.)56 b(The)35
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FK(is)227 1858 y(presen)m(t.)41 b(One)30 b(or)g(b)s(oth)g(of)h(the)f
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3900 6 v 0 2183 a(TRSM)h(\(T)-8 b(riangular)29 b(Solv)m(e\))1401
b Fy(B)30 b FJ( )25 b Fy(\013op)p FK(\()p Fy(T)2887 2150
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2861 y(and)31 b(passed)g(to)h(the)g(error)f(handler.)42
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Fv(B)f FK(in)m(ternally)f(to)j(higher)e(precision.)227
4127 y(\()p Fz(End)h(of)g(advic)-5 b(e)33 b(to)h(implementors.)p
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4915 y FD(SUBROUTINE)45 b(trsm\()i(t,)g(b)g([,)g(side])g([,)g(uplo])f
([,)h(transt])f([,)h(diag])g(&)1230 5028 y([,)g(alpha])f([,)h(prec])f
(\))514 5141 y(<type>\(<wp>\),)e(INTENT\(IN\))h(::)i(t\(:,:\))514
5254 y(<type>\(<wp>\),)d(INTENT\(INOUT\))g(::)j(<bb>)514
5367 y(TYPE)f(\(blas_side_type\),)d(INTENT\(IN\),)i(OPTIONAL)h(::)h
(side)4084 64 y FI(1)4084 177 y(2)4084 290 y(3)4084 403
y(4)4084 516 y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084
967 y(9)4069 1080 y(10)4069 1193 y(11)4069 1306 y(12)4069
1419 y(13)4069 1532 y(14)4069 1645 y(15)4069 1758 y(16)4069
1870 y(17)4069 1983 y(18)4069 2096 y(19)4069 2209 y(20)4069
2322 y(21)4069 2435 y(22)4069 2548 y(23)4069 2661 y(24)4069
2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
3677 y(33)4069 3790 y(34)4069 3903 y(35)4069 4016 y(36)4069
4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 165 175
165 174 bop 0 -165 a FA(4.5.)72 b(LANGUA)m(GE)32 b(BINDINGS)2533
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(\(blas_diag_type\),)d(INTENT\(IN\),)i(OPTIONAL)h(::)h(diag)514
430 y(<type>\(<wp>\),)d(INTENT\(IN\),)h(OPTIONAL)g(::)i(alpha)514
543 y(TYPE)f(\(blas_prec_type\),)d(INTENT)j(\(IN\),)h(OPTIONAL)e(::)j
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561 1108 y(TR)95 b(t)48 b(has)f(shape)f(\(m,m\))g(if)i(side)e(=)i
(blas_left_side)c(\(the)i(default\))752 1220 y(t)i(has)f(shape)f
(\(n,n\))g(if)i(side)e(/=)h(blas_left_side)466 1333 y(b,)g(rank)g(1,)g
(has)g(shape)f(\(m\))561 1446 y(TR)95 b(t)48 b(has)f(shape)f(\(m,m\))p
1214 1615 1700 4 v 1212 1728 4 113 v 1264 1694 a FK(Rank)30
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2277 1728 V 99 w FK(Op)s(eration)p 2912 1728 V 1214 1731
1700 4 v 1212 1844 4 113 v 1385 1810 a(2)p 1601 1844
V 331 w(N)p 1987 1844 V 276 w(L)p 2277 1844 V 167 w Fy(B)g
FJ( )25 b Fy(\013T)2668 1777 y Fu(\000)p FC(1)2762 1810
y Fy(B)p 2912 1844 V 1212 1957 V 1385 1923 a FK(2)p 1601
1957 V 333 w(T)p 1987 1957 V 276 w(L)p 2277 1957 V 167
w Fy(B)30 b FJ( )25 b Fy(\013T)2668 1890 y Fu(\000)p
Fw(T)2778 1923 y Fy(B)p 2912 1957 V 1212 2070 V 1385
2036 a FK(2)p 1601 2070 V 331 w(H)p 1987 2070 V 276 w(L)p
2277 2070 V 167 w Fy(B)30 b FJ( )25 b Fy(\013T)2668 2003
y Fu(\000)p Fw(H)2790 2036 y Fy(B)p 2912 2070 V 1212
2183 V 1385 2149 a FK(2)p 1601 2183 V 331 w(N)p 1987
2183 V 271 w(R)p 2277 2183 V 162 w Fy(B)30 b FJ( )25
b Fy(\013B)5 b(T)2742 2116 y Fu(\000)p FC(1)p 2912 2183
V 1212 2296 V 1385 2262 a FK(2)p 1601 2296 V 333 w(T)p
1987 2296 V 271 w(R)p 2277 2296 V 162 w Fy(B)30 b FJ( )25
b Fy(\013B)5 b(T)2742 2229 y Fu(\000)p Fw(T)p 2912 2296
V 1212 2409 V 1385 2375 a FK(2)p 1601 2409 V 331 w(H)p
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b Fy(\013B)5 b(T)2742 2342 y Fu(\000)p Fw(H)p 2912 2409
V 1212 2522 V 1385 2488 a FK(1)p 1601 2522 V 331 w(N)p
1987 2522 V 290 w(-)p 2277 2522 V 180 w Fy(b)25 b FJ( )g
Fy(\013T)2633 2455 y Fu(\000)p FC(1)2728 2488 y Fy(b)p
2912 2522 V 1212 2635 V 1385 2601 a FK(1)p 1601 2635
V 333 w(T)p 1987 2635 V 290 w(-)p 2277 2635 V 180 w Fy(b)g
FJ( )g Fy(\013T)2633 2568 y Fu(\000)p Fw(T)2743 2601
y Fy(b)p 2912 2635 V 1212 2747 V 1385 2714 a FK(1)p 1601
2747 V 331 w(H)p 1987 2747 V 290 w(-)p 2277 2747 V 180
w Fy(b)g FJ( )g Fy(\013T)2633 2681 y Fu(\000)p Fw(H)2756
2714 y Fy(b)p 2912 2747 V 1214 2751 1700 4 v 227 2959
a FK(The)44 b(table)h(de\014ning)e(the)i(op)s(eration)f(as)h(a)g
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3373 y(The)25 b(t)m(yp)s(es)h(of)f FD(t)p FK(,)h FD(x)f
FK(and)g FD(alpha)f FK(are)i(go)m(v)m(erned)g(according)g(to)g(the)f
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y(set)31 b(do)m(wn)f(in)f(section)i(4.3:)42 b(the)30
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4350 y(<type>)618 b(ALPHA)514 4463 y(<type>)g(T\()48
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4801 y FK(The)24 b(t)m(yp)s(es)g(of)g FD(ALPHA)p FK(,)e
FD(T)p FK(,)i(and)f FD(B)h FK(are)g(go)m(v)m(erned)h(according)f(to)g
(the)g(rules)f(of)h(mixed)f(precision)f(argumen)m(ts)227
4914 y(set)32 b(do)m(wn)e(in)g(section)g(4.3.)44 b(The)30
b(pre\014x)g FD(x)g FK(is)g(the)h(\015oating)g(p)s(oin)m(t)f(t)m(yp)s
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29 4 v 64 w FD(a)h FK(is)227 5026 y(presen)m(t)d(then)p
752 5026 V 62 w FD(a)g FK(is)f(the)h(t)m(yp)s(e)g(of)g
FD(T)p FK(.)g(The)f(su\016x)p 1931 5026 V 61 w FD(X)h
FK(is)f(presen)m(t)h(if)f(and)g(only)g(if)g FD(PREC)g
FK(is)g(presen)m(t.)39 b(One)28 b(or)227 5139 y(b)s(oth)i(of)g(the)h
(su\016xes)p 1024 5139 V 64 w FD(a)f FK(and)p 1314 5139
V 64 w FD(X)g FK(m)m(ust)g(b)s(e)g(presen)m(t.)136 5327
y FJ(\017)46 b FK(C)30 b(binding:)-214 64 y FI(1)-214
177 y(2)-214 290 y(3)-214 403 y(4)-214 516 y(5)-214 628
y(6)-214 741 y(7)-214 854 y(8)-214 967 y(9)-230 1080
y(10)-230 1193 y(11)-230 1306 y(12)-230 1419 y(13)-230
1532 y(14)-230 1645 y(15)-230 1758 y(16)-230 1870 y(17)-230
1983 y(18)-230 2096 y(19)-230 2209 y(20)-230 2322 y(21)-230
2435 y(22)-230 2548 y(23)-230 2661 y(24)-230 2774 y(25)-230
2887 y(26)-230 3000 y(27)-230 3112 y(28)-230 3225 y(29)-230
3338 y(30)-230 3451 y(31)-230 3564 y(32)-230 3677 y(33)-230
3790 y(34)-230 3903 y(35)-230 4016 y(36)-230 4129 y(37)-230
4242 y(38)-230 4354 y(39)-230 4467 y(40)-230 4580 y(41)-230
4693 y(42)-230 4806 y(43)-230 4919 y(44)-230 5032 y(45)-230
5145 y(46)-230 5258 y(47)-230 5371 y(48)p eop
%%Page: 166 176
166 175 bop 0 -165 a FK(166)1214 b FA(CHAPTER)30 b(4.)72
b(EXTENDED)30 b(AND)h(MIXED)g(PRECISION)e(BLAS)227 91
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(blas_uplo_type)d(uplo,)i(enum)h(blas_trans_type)d(transt,)1420
317 y(enum)j(blas_diag_type)d(diag,)i(int)h(m,)g(int)g(n,)1420
430 y(SCALAR_IN)f(alpha,)g(const)g(ARRAY)h(t,)g(int)g(ldt,)f(ARRAY)h
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747 y FK(The)23 b(t)m(yp)s(es)h(of)g FD(alpha)p FK(,)g
FD(t)p FK(,)h(and)e FD(b)g FK(are)h(go)m(v)m(erned)h(according)f(to)g
(the)g(rules)e(of)i(mixed)f(precision)f(argumen)m(ts)227
860 y(set)36 b(do)m(wn)f(in)f(section)i(4.3.)56 b(The)35
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4 v 68 w FD(a)227 973 y FK(is)f(presen)m(t)h(then)p 861
973 V 69 w FD(a)f FK(is)g(the)h(t)m(yp)s(e)g(of)g(argumen)m(t)g
FD(t)p FK(.)53 b(The)35 b(su\016x)p 2525 973 V 68 w FD(x)f
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V 64 w FD(x)g FK(m)m(ust)h(b)s(e)e(presen)m(t.)p 0 1277
3900 6 v 0 1390 a(SYRK)h(\(Symmetric)f(Rank)h(K)g(up)s(date\))1009
b Fy(C)32 b FJ( )25 b Fy(\013AA)2848 1357 y Fw(T)2924
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b Fy(\013A)3537 1357 y Fw(T)3593 1390 y Fy(A)20 b FK(+)g
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g(the)g(symmetric)f(rank)g(k)h(op)s(erations)f Fy(C)52
b FJ( )46 b Fy(\013AA)3214 1583 y Fw(T)3298 1616 y FK(+)29
b Fy(\014)5 b(C)49 b FK(or)43 b Fy(C)52 b FJ( )0 1729
y Fy(\013A)126 1696 y Fw(T)182 1729 y Fy(A)20 b FK(+)g
Fy(\014)5 b(C)37 b FK(where)29 b Fy(\013)i FK(and)f Fy(\014)35
b FK(are)c(scalars,)f Fy(C)37 b FK(is)29 b(a)i(symmetric)e(matrix,)h
(and)g Fy(A)g FK(is)g(a)g(general)h(matrix.)40 b(This)0
1842 y(routine)35 b(returns)g(immediately)f(if)h Fv(n)h
FK(or)g Fv(k)h FK(is)e(less)g(than)h(or)g(equal)f(to)i(zero.)58
b(If)36 b Fv(ldc)g FK(is)f(less)h(than)f(one)i(or)f(less)0
1955 y(than)30 b Fv(n)p FK(,)g(an)g(error)g(\015ag)h(is)e(set)i(and)e
(passed)h(to)h(the)g(error)e(handler.)39 b(F)-8 b(or)31
b Fv(trans)f FK(equal)f(to)i Fv(blas)p 3273 1955 28 4
v 32 w(no)p 3397 1955 V 34 w(trans)p FK(,)e(and)h(if)0
2068 y Fv(lda)k FK(is)g(less)g(than)g(one)h(or)f(less)g(than)h
Fv(n)p FK(,)h(an)e(error)g(\015ag)h(is)f(set)h(and)f(passed)g(to)i(the)
e(error)h(handler.)51 b(F)-8 b(or)36 b Fv(trans)0 2181
y FK(equal)31 b(to)i Fv(blas)p 507 2181 V 32 w(trans)p
FK(,)f(and)f(if)g Fv(lda)g FK(is)g(less)h(than)f(one)h(or)g(less)g
(than)f Fv(k)p FK(,)i(an)f(error)g(\015ag)g(is)f(set)h(and)g(passed)f
(to)i(the)0 2293 y(error)d(handler.)141 2406 y(These)43
b(in)m(terfaces)h(encompass)f(the)h(Legacy)h(BLAS)e(routine)f(xSYRK)h
(with)f(added)g(functionalit)m(y)g(for)0 2519 y(complex)30
b(symmetric)g(matrices.)141 2632 y(Extended)g(precision)f(and)g(mixed)g
(precision)g(are)i(p)s(ermitted.)141 2745 y(This)36 b(routine)h(has)h
(the)g(same)g(sp)s(eci\014cation)e(as)i(in)f(Chapter)g(2,)k(except)d
(that)h(extended)f(precision)e(and)0 2858 y(mixed)29
b(precision)g(are)i(p)s(ermitted.)136 3050 y FJ(\017)46
b FK(F)-8 b(ortran)31 b(95)h(binding:)418 3275 y FD(SUBROUTINE)45
b(syrk\()i(a,)g(c)g([,)g(uplo])g([,)g(trans])f([,)h(alpha])f([,)h
(beta])g(&)1230 3388 y([,)g(prec])f(\))514 3501 y(<type>\(<wp>\),)e
(INTENT\(IN\))h(::)i(<aa>)514 3614 y(<type>\(<wp>\),)d(INTENT\(INOUT\))
g(::)j(c\(:,:\))514 3727 y(TYPE)f(\(blas_uplo_type\),)d(INTENT\(IN\),)i
(OPTIONAL)h(::)h(uplo)514 3839 y(TYPE)f(\(blas_trans_type\),)d
(INTENT\(IN\),)i(OPTIONAL)g(::)j(trans)514 3952 y(<type>\(<wp>\),)c
(INTENT\(IN\),)h(OPTIONAL)g(::)i(alpha,)f(beta)514 4065
y(TYPE)g(\(blas_prec_type\),)d(INTENT)j(\(IN\),)h(OPTIONAL)e(::)j(prec)
418 4178 y(where)514 4291 y(<aa>)94 b(::=)47 b(a\(:,:\))f(or)h(a\(:\))
418 4404 y(and)466 4517 y(c)g(has)g(shape)g(\(n,n\))466
4630 y(a)g(has)g(shape)g(\(n,k\))f(if)h(trans)g(=)g(blas_no_trans)d
(\(the)j(default\))1039 4743 y(\(k,n\))f(if)h(trans)g(/=)g
(blas_no_trans)1039 4856 y(\(n\))g(if)g(rank)f(1)p 1300
4987 1528 4 v 1298 5100 4 113 v 1349 5066 a FK(Rank)31
b FD(a)p 1686 5100 V 99 w(trans)p 2025 5100 V 98 w FK(Op)s(eration)p
2826 5100 V 1300 5104 1528 4 v 1298 5217 4 113 v 1471
5183 a(2)p 1686 5217 V 307 w(N)p 2025 5217 V 185 w Fy(C)h
FJ( )25 b Fy(\013AA)2483 5150 y Fw(T)2559 5183 y FK(+)20
b Fy(\014)5 b(C)p 2826 5217 V 1298 5329 V 1471 5296 a
FK(2)p 1686 5329 V 308 w(T)p 2025 5329 V 186 w Fy(C)32
b FJ( )25 b Fy(\013A)2415 5263 y Fw(T)2471 5296 y Fy(A)20
b FK(+)g Fy(\014)5 b(C)p 2826 5329 V 1298 5442 V 1471
5408 a FK(1)p 1686 5442 V 326 w(-)p 2025 5442 V 204 w
Fy(C)32 b FJ( )25 b Fy(\013aa)2443 5375 y Fw(T)2519 5408
y FK(+)20 b Fy(\014)5 b(C)p 2826 5442 V 1300 5446 1528
4 v 4084 64 a FI(1)4084 177 y(2)4084 290 y(3)4084 403
y(4)4084 516 y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084
967 y(9)4069 1080 y(10)4069 1193 y(11)4069 1306 y(12)4069
1419 y(13)4069 1532 y(14)4069 1645 y(15)4069 1758 y(16)4069
1870 y(17)4069 1983 y(18)4069 2096 y(19)4069 2209 y(20)4069
2322 y(21)4069 2435 y(22)4069 2548 y(23)4069 2661 y(24)4069
2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
3677 y(33)4069 3790 y(34)4069 3903 y(35)4069 4016 y(36)4069
4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 167 177
167 176 bop 0 -165 a FA(4.5.)72 b(LANGUA)m(GE)32 b(BINDINGS)2533
b FK(167)227 91 y(The)44 b(table)h(de\014ning)e(the)i(op)s(eration)f
(as)h(a)g(function)e(of)i(the)g(op)s(erator)g(argumen)m(ts)g(is)f(iden)
m(tical)f(to)227 204 y(Chapter)30 b(2.)227 353 y(The)37
b(t)m(yp)s(es)h(of)f FD(alpha)p FK(,)h FD(a)p FK(,)i
FD(beta)c FK(and)h FD(c)g FK(are)h(go)m(v)m(erned)g(according)g(to)g
(the)g(rules)e(of)h(mixed)g(precision)227 466 y(argumen)m(ts)30
b(set)g(do)m(wn)f(in)g(section)g(4.3:)42 b(the)30 b(t)m(yp)s(e)f(of)h
FD(a)g FK(can)f(optionally)f(di\013er)h(from)g(those)h(of)g
FD(c)p FK(,)f FD(alpha)227 579 y FK(and)h FD(beta)p FK(.)136
765 y FJ(\017)46 b FK(F)-8 b(ortran)31 b(77)h(binding:)514
984 y FD(SUBROUTINE)45 b(BLAS_xSYRK{_a}{_X}\()d(UPLO,)47
b(TRANS,)f(N,)h(K,)g(ALPHA,)f(A,)h(LDA,)g(BETA,)466 1097
y($)1479 b(C,)47 b(LDC)g([,)g(PREC])g(\))514 1210 y(INTEGER)570
b(K,)48 b(LDA,)e(LDC,)h(N,)g(TRANS,)f(UPLO)h([,)g(PREC])514
1322 y(<type>)618 b(ALPHA,)47 b(BETA)514 1435 y(<type>)618
b(A\()48 b(LDA,)e(*)i(\))514 1548 y(<type>)618 b(C\()48
b(LDC,)e(*)i(\))227 1767 y FK(The)37 b(t)m(yp)s(es)h(of)g
FD(ALPHA)p FK(,)f FD(A)p FK(,)g FD(BETA)g FK(and)g FD(C)g
FK(are)h(go)m(v)m(erned)h(according)f(to)g(the)g(rules)e(of)i(mixed)f
(precision)227 1880 y(argumen)m(ts)32 b(set)g(do)m(wn)f(in)f(section)i
(4.3.)45 b(The)31 b(pre\014x)g FD(x)g FK(is)g(the)g(\015oating)h(p)s
(oin)m(t)e(t)m(yp)s(e)i(of)g(the)f(argumen)m(ts,)227
1993 y(but)37 b(if)p 497 1993 29 4 v 70 w FD(a)g FK(is)g(presen)m(t)g
(then)p 1251 1993 V 71 w FD(a)g FK(is)f(the)i(t)m(yp)s(e)f(of)h
FD(A)p FK(.)f(The)f(su\016x)p 2505 1993 V 71 w FD(X)h
FK(is)f(presen)m(t)h(if)g(and)f(only)h(if)f FD(PREC)g
FK(is)227 2106 y(presen)m(t.)41 b(One)30 b(or)g(b)s(oth)g(of)h(the)f
(su\016xes)p 1679 2106 V 64 w FD(a)g FK(and)p 1969 2106
V 64 w FD(X)g FK(m)m(ust)h(b)s(e)e(presen)m(t.)136 2291
y FJ(\017)46 b FK(C)30 b(binding:)227 2510 y FD(void)47
b(BLAS_xsyrk{_a}{_x}\()42 b(enum)47 b(blas_order_type)d(order,)i(enum)g
(blas_uplo_type)e(uplo,)1420 2623 y(enum)j(blas_trans_type)d(trans,)i
(int)h(n,)g(int)g(k,)1420 2736 y(SCALAR_IN)f(alpha,)g(const)g(ARRAY)h
(a,)g(int)g(lda,)1420 2849 y(SCALAR_IN)f(beta,)g(ARRAY)g(c,)i(int)f
(ldc)1420 2962 y([,)h(enum)e(blas_prec_type)e(prec])j(\);)227
3181 y FK(The)37 b(t)m(yp)s(es)h(of)f FD(alpha)p FK(,)h
FD(a)p FK(,)i FD(beta)c FK(and)h FD(c)g FK(are)h(go)m(v)m(erned)g
(according)g(to)g(the)g(rules)e(of)h(mixed)g(precision)227
3294 y(argumen)m(ts)32 b(set)g(do)m(wn)f(in)f(section)i(4.3.)45
b(The)31 b(pre\014x)g FD(x)g FK(is)g(the)g(\015oating)h(p)s(oin)m(t)e
(t)m(yp)s(e)i(of)g(the)f(argumen)m(ts,)227 3407 y(but)h(if)p
487 3407 V 66 w FD(a)g FK(is)f(presen)m(t)i(then)p 1222
3407 V 66 w FD(a)f FK(is)g(the)g(t)m(yp)s(e)h(of)f(argumen)m(t)h
FD(a)p FK(.)47 b(The)32 b(su\016x)p 2861 3407 V 65 w
FD(x)g FK(is)g(presen)m(t)g(if)g(and)f(only)h(if)227
3519 y FD(prec)d FK(is)h(presen)m(t.)41 b(One)30 b(or)g(b)s(oth)g(of)g
(the)h(su\016xes)p 1992 3519 V 64 w FD(a)f FK(and)p 2281
3519 V 64 w FD(x)g FK(m)m(ust)g(b)s(e)g(presen)m(t.)p
0 3726 3900 6 v 0 3839 a(HERK)g(\(Hermitian)f(Rank)i(K)f(up)s(date\))
998 b Fy(C)32 b FJ( )25 b Fy(\013AA)2824 3806 y Fw(H)2912
3839 y FK(+)20 b Fy(\014)5 b(C)i FK(,)30 b Fy(C)i FJ( )25
b Fy(\013A)3525 3806 y Fw(H)3593 3839 y Fy(A)20 b FK(+)g
Fy(\014)5 b(C)141 4065 y FK(This)41 b(routine)h(p)s(erforms)f(one)i(of)
g(the)f(Hermitian)g(rank)g(k)g(op)s(erations)g Fy(C)53
b FJ( )45 b Fy(\013AA)3202 4032 y Fw(H)3299 4065 y FK(+)28
b Fy(\014)5 b(C)49 b FK(or)43 b Fy(C)52 b FJ( )0 4177
y Fy(\013A)126 4144 y Fw(H)194 4177 y Fy(A)20 b FK(+)g
Fy(\014)5 b(C)36 b FK(where)30 b Fy(\013)h FK(and)e Fy(\014)36
b FK(are)30 b(scalars,)h Fy(C)36 b FK(is)29 b(a)i(Hermitian)e(matrix,)h
(and)f Fy(A)i FK(is)e(a)i(general)f(matrix.)40 b(This)0
4290 y(routine)35 b(returns)g(immediately)f(if)h Fv(n)h
FK(or)g Fv(k)h FK(is)e(less)g(than)h(or)g(equal)f(to)i(zero.)58
b(If)36 b Fv(ldc)g FK(is)f(less)h(than)f(one)i(or)f(less)0
4403 y(than)30 b Fv(n)p FK(,)g(an)g(error)g(\015ag)h(is)e(set)i(and)e
(passed)h(to)h(the)g(error)e(handler.)39 b(F)-8 b(or)31
b Fv(trans)f FK(equal)f(to)i Fv(blas)p 3273 4403 28 4
v 32 w(no)p 3397 4403 V 34 w(trans)p FK(,)e(and)h(if)0
4516 y Fv(lda)k FK(is)g(less)g(than)g(one)h(or)f(less)g(than)h
Fv(n)p FK(,)h(an)e(error)g(\015ag)h(is)f(set)h(and)f(passed)g(to)i(the)
e(error)h(handler.)51 b(F)-8 b(or)36 b Fv(trans)0 4629
y FK(equal)31 b(to)i Fv(blas)p 507 4629 V 32 w(trans)p
FK(,)f(and)f(if)g Fv(lda)g FK(is)g(less)h(than)f(one)h(or)g(less)g
(than)f Fv(k)p FK(,)i(an)f(error)g(\015ag)g(is)f(set)h(and)g(passed)f
(to)i(the)0 4742 y(error)d(handler.)141 4855 y(These)g(in)m(terfaces)h
(encompass)g(the)f(Legacy)i(BLAS)e(routine)g(xHERK.)141
4968 y(Extended)g(precision)f(and)g(mixed)g(precision)g(are)i(p)s
(ermitted.)141 5081 y(This)36 b(routine)h(has)h(the)g(same)g(sp)s
(eci\014cation)e(as)i(in)f(Chapter)g(2,)k(except)d(that)h(extended)f
(precision)e(and)0 5194 y(mixed)29 b(precision)g(are)i(p)s(ermitted.)
136 5400 y FJ(\017)46 b FK(F)-8 b(ortran)31 b(95)h(binding:)-214
64 y FI(1)-214 177 y(2)-214 290 y(3)-214 403 y(4)-214
516 y(5)-214 628 y(6)-214 741 y(7)-214 854 y(8)-214 967
y(9)-230 1080 y(10)-230 1193 y(11)-230 1306 y(12)-230
1419 y(13)-230 1532 y(14)-230 1645 y(15)-230 1758 y(16)-230
1870 y(17)-230 1983 y(18)-230 2096 y(19)-230 2209 y(20)-230
2322 y(21)-230 2435 y(22)-230 2548 y(23)-230 2661 y(24)-230
2774 y(25)-230 2887 y(26)-230 3000 y(27)-230 3112 y(28)-230
3225 y(29)-230 3338 y(30)-230 3451 y(31)-230 3564 y(32)-230
3677 y(33)-230 3790 y(34)-230 3903 y(35)-230 4016 y(36)-230
4129 y(37)-230 4242 y(38)-230 4354 y(39)-230 4467 y(40)-230
4580 y(41)-230 4693 y(42)-230 4806 y(43)-230 4919 y(44)-230
5032 y(45)-230 5145 y(46)-230 5258 y(47)-230 5371 y(48)p
eop
%%Page: 168 178
168 177 bop 0 -165 a FK(168)1214 b FA(CHAPTER)30 b(4.)72
b(EXTENDED)30 b(AND)h(MIXED)g(PRECISION)e(BLAS)418 91
y FD(SUBROUTINE)45 b(herk\()i(a,)g(c)g([,)g(uplo])g([,)g(trans])f([,)h
(alpha])f([,)h(beta])g(&)1230 204 y([,)g(prec])f(\))514
317 y(COMPLEX\(<wp>\),)e(INTENT\(IN\))h(::)i(<aa>)514
430 y(COMPLEX\(<wp>\),)d(INTENT\(INOUT\))g(::)j(c\(:,:\))514
543 y(TYPE)f(\(blas_uplo_type\),)d(INTENT\(IN\),)i(OPTIONAL)h(::)h
(uplo)514 656 y(TYPE)f(\(blas_trans_type\),)d(INTENT\(IN\),)i(OPTIONAL)
g(::)j(trans)514 769 y(REAL\(<wp>\),)c(INTENT\(IN\),)h(OPTIONAL)h(::)h
(alpha,)f(beta)514 882 y(TYPE)g(\(blas_prec_type\),)d(INTENT)j(\(IN\),)
h(OPTIONAL)e(::)j(prec)418 995 y(where)514 1108 y(<aa>)94
b(::=)47 b(a\(:,:\))f(or)h(a\(:\))418 1220 y(and)466
1333 y(c)g(has)g(shape)g(\(n,n\))466 1446 y(a)g(has)g(shape)g(\(n,k\))f
(if)h(trans)g(=)g(blas_no_trans)d(\(the)j(default\))1039
1559 y(\(k,n\))f(if)h(trans)g(/=)g(blas_no_trans)1039
1672 y(\(n\))g(if)g(rank)f(1)p 1294 1828 1541 4 v 1292
1941 4 113 v 1343 1907 a FK(Rank)31 b FD(a)p 1680 1941
V 99 w(trans)p 2019 1941 V 98 w FK(Op)s(eration)p 2832
1941 V 1294 1944 1541 4 v 1292 2057 4 113 v 1465 2024
a(2)p 1680 2057 V 307 w(N)p 2019 2057 V 185 w Fy(C)h
FJ( )25 b Fy(\013AA)2477 1991 y Fw(H)2565 2024 y FK(+)20
b Fy(\014)5 b(C)p 2832 2057 V 1292 2170 V 1465 2136 a
FK(2)p 1680 2170 V 308 w(T)p 2019 2170 V 186 w Fy(C)32
b FJ( )25 b Fy(\013A)2409 2103 y Fw(H)2477 2136 y Fy(A)20
b FK(+)g Fy(\014)5 b(C)p 2832 2170 V 1292 2283 V 1465
2249 a FK(1)p 1680 2283 V 326 w(-)p 2019 2283 V 204 w
Fy(C)32 b FJ( )25 b Fy(\013aa)2437 2216 y Fw(H)2525 2249
y FK(+)20 b Fy(\014)5 b(C)p 2832 2283 V 1294 2287 1541
4 v 227 2495 a FK(The)44 b(table)h(de\014ning)e(the)i(op)s(eration)f
(as)h(a)g(function)e(of)i(the)g(op)s(erator)g(argumen)m(ts)g(is)f(iden)
m(tical)f(to)227 2608 y(Chapter)30 b(2.)227 2758 y(The)37
b(t)m(yp)s(es)h(of)f FD(alpha)p FK(,)h FD(a)p FK(,)i
FD(beta)c FK(and)h FD(c)g FK(are)h(go)m(v)m(erned)g(according)g(to)g
(the)g(rules)e(of)h(mixed)g(precision)227 2871 y(argumen)m(ts)30
b(set)g(do)m(wn)f(in)g(section)g(4.3:)42 b(the)30 b(t)m(yp)s(e)f(of)h
FD(a)g FK(can)f(optionally)f(di\013er)h(from)g(those)h(of)g
FD(c)p FK(,)f FD(alpha)227 2984 y FK(and)h FD(beta)p
FK(.)136 3172 y FJ(\017)46 b FK(F)-8 b(ortran)31 b(77)h(binding:)514
3397 y FD(SUBROUTINE)45 b(BLAS_xHERK{_a}{_X}\()d(UPLO,)47
b(TRANS,)f(N,)h(K,)g(ALPHA,)f(A,)h(LDA,)g(BETA,)466 3509
y($)1479 b(C,)47 b(LDC)g([,)g(PREC])g(\))514 3622 y(INTEGER)570
b(K,)48 b(LDA,)e(LDC,)h(N,)g(TRANS,)f(UPLO)h([,)g(PREC])514
3735 y(<rtype>)570 b(ALPHA,)47 b(BETA)514 3848 y(<ctype>)570
b(A\()48 b(LDA,)e(*)i(\))514 3961 y(<ctype>)570 b(C\()48
b(LDC,)e(*)i(\))227 4186 y FK(The)37 b(t)m(yp)s(es)h(of)g
FD(ALPHA)p FK(,)f FD(A)p FK(,)g FD(BETA)g FK(and)g FD(C)g
FK(are)h(go)m(v)m(erned)h(according)f(to)g(the)g(rules)e(of)i(mixed)f
(precision)227 4299 y(argumen)m(ts)32 b(set)g(do)m(wn)f(in)f(section)i
(4.3.)45 b(The)31 b(pre\014x)g FD(x)g FK(is)g(the)g(\015oating)h(p)s
(oin)m(t)e(t)m(yp)s(e)i(of)g(the)f(argumen)m(ts,)227
4412 y(but)37 b(if)p 497 4412 29 4 v 70 w FD(a)g FK(is)g(presen)m(t)g
(then)p 1251 4412 V 71 w FD(a)g FK(is)f(the)i(t)m(yp)s(e)f(of)h
FD(A)p FK(.)f(The)f(su\016x)p 2505 4412 V 71 w FD(X)h
FK(is)f(presen)m(t)h(if)g(and)f(only)h(if)f FD(PREC)g
FK(is)227 4525 y(presen)m(t.)41 b(One)30 b(or)g(b)s(oth)g(of)h(the)f
(su\016xes)p 1679 4525 V 64 w FD(a)g FK(and)p 1969 4525
V 64 w FD(X)g FK(m)m(ust)h(b)s(e)e(presen)m(t.)136 4712
y FJ(\017)46 b FK(C)30 b(binding:)227 4937 y FD(void)47
b(BLAS_xherk{_a}{_x}\()42 b(enum)47 b(blas_order_type)d(order,)i(enum)g
(blas_uplo_type)e(uplo,)1420 5050 y(enum)j(blas_trans_type)d(trans,)i
(int)h(n,)g(int)g(k,)1420 5163 y(RSCALAR_IN)e(alpha,)i(const)f(CARRAY)g
(a,)h(int)g(lda,)1420 5276 y(RSCALAR_IN)e(beta,)i(CARRAY)f(c,)h(int)g
(ldc)1420 5389 y([,)h(enum)e(blas_prec_type)e(prec])j(\);)4084
64 y FI(1)4084 177 y(2)4084 290 y(3)4084 403 y(4)4084
516 y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084 967
y(9)4069 1080 y(10)4069 1193 y(11)4069 1306 y(12)4069
1419 y(13)4069 1532 y(14)4069 1645 y(15)4069 1758 y(16)4069
1870 y(17)4069 1983 y(18)4069 2096 y(19)4069 2209 y(20)4069
2322 y(21)4069 2435 y(22)4069 2548 y(23)4069 2661 y(24)4069
2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
3677 y(33)4069 3790 y(34)4069 3903 y(35)4069 4016 y(36)4069
4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 169 179
169 178 bop 0 -165 a FA(4.5.)72 b(LANGUA)m(GE)32 b(BINDINGS)2533
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2289 4 v 918 5217 4 113 v 1091 5183 a(2)p 1306 5217 V
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%%Page: 170 180
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3716 y(but)c(if)p 477 3716 V 61 w FD(a)p 560 3716 V 34
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%%Page: 171 181
171 180 bop 0 -165 a FA(4.5.)72 b(LANGUA)m(GE)32 b(BINDINGS)2533
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(lo)m(w)m(er)h(case,)k(and)0 4299 y(adding)29 b(the)i(pre\014x)e
FD(cblas)p 956 4299 29 4 v 33 w FK(.)41 b(Therefore,)30
b(the)g(routine)g FD(DGEMM)f FK(b)s(ecomes)h FD(cblas)p
2832 4299 V 33 w(dgemm)p FK(.)0 4539 y Fv(Considered)h(metho)s(ds)367
4710 y Fz(V)-7 b(arious)37 b(other)h(naming)f(schemes)h(have)f(b)-5
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FD(C)p 3136 4710 V 71 w Fz(or)f FD(c)p 3376 4710 V 71
w Fz(to)g(the)227 4823 y(name.)49 b(Most)35 b(of)g(these)g(schemes)h
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h(of)f(the)f FD(blas)f Fz(pr)-5 b(e\014x)32 b(uni\014es)227
5049 y(the)h(naming)g(scheme)g(in)f(a)h(lo)-5 b(gic)g(al)34
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b(p)-5 b(ossible)34 b(futur)-5 b(e)32 b(interfac)-5 b(es.)4084
64 y FI(1)4084 177 y(2)4084 290 y(3)4084 403 y(4)4084
516 y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084 967
y(9)4069 1080 y(10)4069 1193 y(11)4069 1306 y(12)4069
1419 y(13)4069 1532 y(14)4069 1645 y(15)4069 1758 y(16)4069
1870 y(17)4069 1983 y(18)4069 2096 y(19)4069 2209 y(20)4069
2322 y(21)4069 2435 y(22)4069 2548 y(23)4069 2661 y(24)4069
2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
3677 y(33)4069 3790 y(34)4069 3903 y(35)4069 4016 y(36)4069
4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 181 191
181 190 bop 0 -165 a FA(B.2.)72 b(C)30 b(INTERF)-10 b(A)m(CE)30
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b FK(\(where)35 b Fy(N)45 b FK(is)34 b(the)h(n)m(um)m(b)s(er)e(of)i(en)
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602 y(The)f(C)g(in)m(terface)h(therefore)g(returns)e(indices)f(in)h
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FD(I)p 2661 715 29 4 v 34 w(AMAX)p FK(.)h(This)f(function)g(is)g
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773 827 V 33 w(INDEX)p FK(,)e(whic)m(h)g(is)h(guaran)m(teed)h(to)g(b)s
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1518 y Fx(B.2.3)97 b(Cha)m(racter)34 b(a)m(rguments)0
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283 b({CblasLeft=141,)44 b(CblasRight=142};)0 3011 y
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b(an)35 b(to)g(have)227 3635 y FD(DIAG='H')p Fz(,)27
b(for)i(instanc)-5 b(e\).)41 b(If)29 b FD(char)e Fz(was)j(chosen,)g
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5400 y(con)m(tains)31 b(the)f(real)g(comp)s(onen)m(t,)h(and)f(the)g
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s(er.)-214 64 y FI(1)-214 177 y(2)-214 290 y(3)-214 403
y(4)-214 516 y(5)-214 628 y(6)-214 741 y(7)-214 854 y(8)-214
967 y(9)-230 1080 y(10)-230 1193 y(11)-230 1306 y(12)-230
1419 y(13)-230 1532 y(14)-230 1645 y(15)-230 1758 y(16)-230
1870 y(17)-230 1983 y(18)-230 2096 y(19)-230 2209 y(20)-230
2322 y(21)-230 2435 y(22)-230 2548 y(23)-230 2661 y(24)-230
2774 y(25)-230 2887 y(26)-230 3000 y(27)-230 3112 y(28)-230
3225 y(29)-230 3338 y(30)-230 3451 y(31)-230 3564 y(32)-230
3677 y(33)-230 3790 y(34)-230 3903 y(35)-230 4016 y(36)-230
4129 y(37)-230 4242 y(38)-230 4354 y(39)-230 4467 y(40)-230
4580 y(41)-230 4693 y(42)-230 4806 y(43)-230 4919 y(44)-230
5032 y(45)-230 5145 y(46)-230 5258 y(47)-230 5371 y(48)p
eop
%%Page: 182 192
182 191 bop 0 -165 a FK(182)2590 b FA(ANNEX)31 b(B.)61
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2310 V 34 w(PORTABLE)p 1129 2310 V 32 w(COMPLEX)g FJ(f)p
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b(use)e(of)g(such)g(a)227 3552 y(structur)-5 b(e)35 b(turns)f(out)g(to)
h(not)f(o\013er)g(much)h(in)e(the)i(way)f(of)g(r)-5 b(e)g(al)36
b(advantage,)f(as)g(discusse)-5 b(d)35 b(in)e(the)227
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4983 y(F)-8 b(urther,)47 b(the)c(name)h(is)e(su\016xed)h(b)m(y)p
1532 4983 V 77 w FD(sub)p FK(.)79 b(There)43 b(are)h(t)m(w)m(o)h(main)d
(reasons)i(for)f(this)f(name)i(c)m(hange.)0 5096 y(First,)28
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64 y FI(1)4084 177 y(2)4084 290 y(3)4084 403 y(4)4084
516 y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084 967
y(9)4069 1080 y(10)4069 1193 y(11)4069 1306 y(12)4069
1419 y(13)4069 1532 y(14)4069 1645 y(15)4069 1758 y(16)4069
1870 y(17)4069 1983 y(18)4069 2096 y(19)4069 2209 y(20)4069
2322 y(21)4069 2435 y(22)4069 2548 y(23)4069 2661 y(24)4069
2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
3677 y(33)4069 3790 y(34)4069 3903 y(35)4069 4016 y(36)4069
4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 183 193
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2887 y(26)-230 3000 y(27)-230 3112 y(28)-230 3225 y(29)-230
3338 y(30)-230 3451 y(31)-230 3564 y(32)-230 3677 y(33)-230
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4242 y(38)-230 4354 y(39)-230 4467 y(40)-230 4580 y(41)-230
4693 y(42)-230 4806 y(43)-230 4919 y(44)-230 5032 y(45)-230
5145 y(46)-230 5258 y(47)-230 5371 y(48)p eop
%%Page: 184 194
184 193 bop 0 -165 a FK(184)2590 b FA(ANNEX)31 b(B.)61
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b(age,)227 2124 y(and)34 b FK(3)p Fy(n)e Fz(sign)h(changes.)367
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%%Page: 185 195
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%%Page: 186 196
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%%Page: 187 197
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Fk(\013A)1529 4296 y Fi(T)1582 4326 y Fk(x)c Fm(+)f Fk(\014)t(y)191
4426 y Fm(F77)27 b(call)99 b Fl(CSYMV\('L',)39 b(n,)k
Fk(\013)p Fl(,)h(A,)f(lda,)e(x,)i(incx,)f Fk(\014)t Fl(,)h(y,)g(incy\))
0 4754 y Fv(HEMV)0 4926 y FK(HEMV)31 b(routine)e(requires)g(3)p
Fy(n)h FK(conjugations,)h(and)f Fy(n)g FK(extra)h(storage.)191
5021 y Fm(C)d(call)176 b Fl(cblas)p 805 5021 V 29 w(chemv\(CblasRowMaj)
o(or)o(,)38 b(CblasUpper,)h(n,)j Fk(\013)p Fl(,)i(A,)f(lda,)f(x,)g
(incx,)g Fk(\014)t Fl(,)h(y,)g(incy\))191 5142 y Fm(op)301
b Fk(y)26 b Fj( )d Fk(\013Ax)c Fm(+)f Fk(\014)t(y)27
b Fj(\))c Fk(y)i Fj( )e Fk(\013A)1529 5112 y Fi(H)1593
5142 y Fk(x)c Fm(+)f Fk(\014)t(y)26 b Fj(\))p 1966 5058
650 4 v 23 w Fm(\()p 1998 5096 44 4 v Fk(y)g Fj( )p 2171
5096 54 4 v 23 w Fk(\013)q(A)2287 5118 y Fi(T)p 2339
5096 48 4 v 2339 5142 a Fk(x)19 b Fm(+)p 2488 5075 52
4 v 18 w Fk(\014)p 2540 5096 44 4 v 5 w(y)r Fm(\))191
5246 y(F77)27 b(call)99 b Fl(CHEMV\('L',)39 b(n,)p 1190
5201 54 4 v 43 w Fk(\013)q Fl(,)k(A,)g(lda,)p 1679 5201
48 4 v 41 w Fk(x)q Fl(,)g(incx,)p 2076 5179 52 4 v 42
w Fk(\014)t Fl(,)p 2214 5201 44 4 v 43 w Fk(y)s Fl(,)g(incy\))4084
64 y FI(1)4084 177 y(2)4084 290 y(3)4084 403 y(4)4084
516 y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084 967
y(9)4069 1080 y(10)4069 1193 y(11)4069 1306 y(12)4069
1419 y(13)4069 1532 y(14)4069 1645 y(15)4069 1758 y(16)4069
1870 y(17)4069 1983 y(18)4069 2096 y(19)4069 2209 y(20)4069
2322 y(21)4069 2435 y(22)4069 2548 y(23)4069 2661 y(24)4069
2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
3677 y(33)4069 3790 y(34)4069 3903 y(35)4069 4016 y(36)4069
4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 189 199
189 198 bop 0 -165 a FA(B.2.)72 b(C)30 b(INTERF)-10 b(A)m(CE)30
b(TO)g(THE)g(LEGA)m(CY)h(BLAS)1816 b FK(189)0 91 y Fv(TRMV/TRSV)70
251 y Fm(C)28 b(call)176 b Fl(cblas)p 684 251 27 4 v
29 w(ctrmv\(CblasRowMaj)o(or,)37 b(CblasUpper,)i(CblasNoTrans,)f(diag,)
j(n,)i(A,)g(lda,)f(x,)h(incx\))70 350 y Fm(op)301 b Fk(x)24
b Fj( )f Fk(Ax)70 450 y Fm(F77)k(call)99 b Fl(CTRMV\('L',)40
b('T',)h(diag,)h(n,)h(A,)f(lda,)g(x,)h(incx\))70 649
y Fm(C)28 b(call)176 b Fl(cblas)p 684 649 V 29 w(ctrmv\(CblasRowMaj)o
(or,)37 b(CblasUpper,)i(CblasTrans,)g(diag,)i(n,)i(A,)g(lda,)f(x,)g
(incx\))70 749 y Fm(op)301 b Fk(x)24 b Fj( )f Fk(A)698
719 y Fi(T)750 749 y Fk(x)70 849 y Fm(F77)k(call)99 b
Fl(CTRMV\('L',)40 b('N',)h(diag,)h(n,)h(A,)f(lda,)g(x,)h(incx\))70
1048 y Fm(C)28 b(call)176 b Fl(cblas)p 684 1048 V 29
w(ctrmv\(CblasRowMaj)o(or,)37 b(CblasUpper,)i(CblasConjTrans,)e(diag,)
42 b(n,)g(A,)h(lda,)f(x,)h(incx\))70 1158 y Fm(op)301
b Fk(x)24 b Fj( )f Fk(A)698 1128 y Fi(H)761 1158 y Fk(x)g
Fj(\))p 937 1084 385 4 v 23 w Fm(\()p 969 1112 48 4 v
Fk(x)h Fm(=)f Fk(A)1190 1134 y Fi(T)p 1242 1112 V 1242
1158 a Fk(x)q Fm(\))70 1258 y(F77)k(call)99 b Fl(CTRMV\('L',)40
b('N',)h(diag,)h(n,)h(A,)f(lda,)p 1897 1212 V 42 w Fk(x)q
Fl(,)h(incx\))141 1508 y FK(Again,)e(w)m(e)f(see)g(that)f(w)m(e)h(will)
c(need)j(some)h(extra)f(op)s(erations)g(when)f(w)m(e)h(are)h(handling)c
(the)k(conjugate)0 1621 y(transp)s(ose.)g(W)-8 b(e)29
b(conjugate)h Fy(x)e FK(b)s(efore)g(the)h(call,)g(giving)e(us)h(the)g
(conjugate)i(of)f(the)g(answ)m(er)f(w)m(e)h(seek.)41
b(W)-8 b(e)29 b(then)0 1734 y(conjugate)f(this)e(again)h(to)h(return)d
(the)j(correct)g(answ)m(er.)39 b(This)25 b(routine)h(therefore)i(needs)
e(2)p Fy(n)h FK(extra)h(op)s(erations)0 1847 y(for)i(the)h(complex)f
(conjugate)h(case.)141 1960 y(The)36 b(calls)f(with)g(the)h(C)f(arra)m
(y)i(b)s(eing)e FD(Lower)f FK(are)j(merely)e(the)h(re\015ection)g(of)g
(these)h(calls,)f(and)g(th)m(us)g(are)0 2073 y(not)j(sho)m(wn.)64
b(The)38 b(analysis)f(for)h(TRMV)g(is)g(the)g(same,)j(since)d(it)g(in)m
(v)m(olv)m(es)g(the)h(same)g(principle)c(of)j(what)h(a)0
2186 y(transp)s(ose)30 b(of)g(a)h(triangular)e(matrix)h(is.)0
2426 y Fv(GER/GERU)0 2598 y FK(This)g(is)h(our)g(\014rst)g(routine)g
(that)i(has)e(a)i(matrix)e(as)h(the)g(solution.)44 b(Recalling)30
b(that)j(this)d(means)i(w)m(e)h(solv)m(e)f(the)0 2711
y(transp)s(ose)e(of)g(the)h(original)d(problem,)i(w)m(e)g(get:)50
2806 y Fm(C)d(call)177 b Fl(cblas)p 664 2806 27 4 v 29
w(cgeru\(CblasRowMaj)o(or)o(,)37 b(m,)43 b(n,)g Fk(\013)p
Fl(,)h(x,)e(incx,)g(y,)h(incy,)e(A,)i(lda\))50 2906 y
Fm(C)27 b(op)214 b Fk(A)23 b Fj( )g Fk(\013xy)774 2876
y Fi(T)846 2906 y Fm(+)18 b Fk(A)50 3006 y Fm(F77)27
b(op)136 b Fk(A)501 2976 y Fi(T)576 3006 y Fj( )24 b
Fk(\013y)s(x)827 2976 y Fi(T)898 3006 y Fm(+)18 b Fk(A)1043
2976 y Fi(T)50 3105 y Fm(F77)27 b(call)99 b Fl(CGERU\(n,)40
b(m,)j Fk(\013)p Fl(,)g(y,)g(incy,)f(x,)h(incx,)e(A,)i(lda\))141
3306 y FK(No)31 b(extra)g(storage)h(or)e(op)s(erations)g(are)h
(required.)0 3546 y Fv(GERC)50 3683 y Fm(C)c(call)177
b Fl(cblas)p 664 3683 V 29 w(cgerc\(CblasRowMaj)o(or)o(,)37
b(m,)43 b(n,)g Fk(\013)p Fl(,)h(x,)e(incx,)g(y,)h(incy,)e(A,)i(lda\))50
3783 y Fm(C)27 b(op)214 b Fk(A)23 b Fj( )g Fk(\013xy)774
3753 y Fi(H)856 3783 y Fm(+)18 b Fk(A)50 3883 y Fm(F77)27
b(op)136 b Fk(A)501 3853 y Fi(T)576 3883 y Fj( )24 b
Fk(\013)p Fm(\()p Fk(xy)859 3853 y Fi(H)922 3883 y Fm(\))954
3853 y Fi(T)1025 3883 y Fm(+)18 b Fk(A)1170 3853 y Fi(T)1246
3883 y Fm(=)23 b Fk(\013)p 1387 3837 44 4 v(y)s(x)1478
3853 y Fi(T)1549 3883 y Fm(+)18 b Fk(A)1694 3853 y Fi(T)50
3982 y Fm(F77)27 b(call)99 b Fl(CGERU\(n,)40 b(m,)j Fk(\013)p
Fl(,)p 1102 3937 V 43 w Fk(y)s Fl(,)g(incy,)f(x,)h(incx,)e(A,)i(lda\))
141 4183 y FK(Note)30 b(that)e(w)m(e)h(need)f(to)h(allo)s(cate)f
Fy(n)p FK(-elemen)m(t)h(w)m(orkspace)g(to)g(hold)d(the)j(conjugated)g
Fy(y)s FK(,)f(and)g(w)m(e)g(call)g FD(GERU)p FK(,)0 4296
y(not)j FD(GERC)p FK(.)0 4536 y Fv(HER)50 4673 y Fm(C)c(call)177
b Fl(cblas)p 664 4673 27 4 v 29 w(cher\(CblasRowMajo)o(r,)37
b(CblasUpper,)i(n,)k Fk(\013)p Fl(,)g(x,)g(incx,)f(A,)g(lda\))50
4773 y Fm(C)27 b(op)214 b Fk(A)23 b Fj( )g Fk(\013xx)777
4743 y Fi(H)860 4773 y Fm(+)18 b Fk(A)50 4872 y Fm(F77)27
b(op)136 b Fk(A)501 4842 y Fi(T)576 4872 y Fj( )24 b
Fk(\013)p 736 4827 48 4 v(xx)830 4842 y Fi(T)902 4872
y Fm(+)18 b Fk(A)1047 4842 y Fi(T)50 4972 y Fm(F77)27
b(call)99 b Fl(CHER\('L',)40 b(n,)i Fk(\013)p Fl(,)p
1146 4926 V 44 w Fk(x)q Fl(,)h(1,)f(A,)h(lda\))141 5173
y FK(Again,)31 b(w)m(e)f(ha)m(v)m(e)i(an)e Fy(n)p FK(-elemen)m(t)h(w)m
(orkspace)g(and)f Fy(n)g FK(extra)h(op)s(erations.)-214
64 y FI(1)-214 177 y(2)-214 290 y(3)-214 403 y(4)-214
516 y(5)-214 628 y(6)-214 741 y(7)-214 854 y(8)-214 967
y(9)-230 1080 y(10)-230 1193 y(11)-230 1306 y(12)-230
1419 y(13)-230 1532 y(14)-230 1645 y(15)-230 1758 y(16)-230
1870 y(17)-230 1983 y(18)-230 2096 y(19)-230 2209 y(20)-230
2322 y(21)-230 2435 y(22)-230 2548 y(23)-230 2661 y(24)-230
2774 y(25)-230 2887 y(26)-230 3000 y(27)-230 3112 y(28)-230
3225 y(29)-230 3338 y(30)-230 3451 y(31)-230 3564 y(32)-230
3677 y(33)-230 3790 y(34)-230 3903 y(35)-230 4016 y(36)-230
4129 y(37)-230 4242 y(38)-230 4354 y(39)-230 4467 y(40)-230
4580 y(41)-230 4693 y(42)-230 4806 y(43)-230 4919 y(44)-230
5032 y(45)-230 5145 y(46)-230 5258 y(47)-230 5371 y(48)p
eop
%%Page: 190 200
190 199 bop 0 -165 a FK(190)2590 b FA(ANNEX)31 b(B.)61
b(LEGA)m(CY)31 b(BLAS)0 91 y Fv(HER2)50 228 y Fm(C)c(call)177
b Fl(cblas)p 664 228 27 4 v 29 w(cher2\(CblasRowMaj)o(or)o(,)37
b(CblasUpper,)j(n,)i Fk(\013)p Fl(,)i(x,)f(incx,)e(y,)i(incy,)e(A,)i
(lda\))50 328 y Fm(C)27 b(op)214 b Fk(A)23 b Fj( )g Fk(\013xy)774
298 y Fi(H)856 328 y Fm(+)18 b Fk(y)s Fm(\()p Fk(\013x)p
Fm(\))1147 298 y Fi(H)1230 328 y Fm(+)g Fk(A)50 428 y
Fm(F77)27 b(op)136 b Fk(A)501 397 y Fi(T)576 428 y Fj( )24
b Fk(\013)p 736 382 44 4 v(y)s(x)827 397 y Fi(T)898 428
y Fm(+)p 981 382 54 4 v 18 w Fk(\013)p 1034 382 48 4
v(x)q(y)1126 397 y Fi(T)1196 428 y Fm(+)18 b Fk(A)1341
397 y Fi(T)1417 428 y Fm(=)k Fk(\013)p 1557 382 44 4
v(y)t Fm(\()p 1634 382 48 4 v Fk(x)p Fm(\))1713 397 y
Fi(H)1795 428 y Fm(+)p 1878 382 V 18 w Fk(x)p Fm(\()p
Fk(\013)p 2010 382 44 4 v(y)t Fm(\))2087 397 y Fi(H)2169
428 y Fm(+)c Fk(A)2314 397 y Fi(T)50 527 y Fm(F77)27
b(call)99 b Fl(CHER2\('L',)39 b(n,)k Fk(\013)p Fl(,)p
1190 481 V 44 w Fk(y)r Fl(,)h(1,)p 1451 481 48 4 v 42
w Fk(x)q Fl(,)f(1,)g(A,)f(lda\))141 728 y FK(So)30 b(w)m(e)h(need)f(2)p
Fy(n)h FK(extra)g(w)m(orkspace)g(and)f(op)s(erations)f(to)i(form)f(the)
h(conjugates)g(of)g Fy(x)f FK(and)g Fy(y)s FK(.)0 968
y Fv(SYR)50 1105 y Fm(C)d(call)177 b Fl(cblas)p 664 1105
27 4 v 29 w(ssyr\(CblasRowMajo)o(r,)37 b(CblasUpper,)i(n,)k
Fk(\013)p Fl(,)g(x,)g(incx,)f(A,)g(lda\))50 1205 y Fm(C)27
b(op)214 b Fk(A)23 b Fj( )g Fk(\013xx)777 1175 y Fi(T)849
1205 y Fm(+)18 b Fk(A)50 1304 y Fm(F77)27 b(op)136 b
Fk(A)501 1274 y Fi(T)576 1304 y Fj( )24 b Fk(\013xx)830
1274 y Fi(T)902 1304 y Fm(+)18 b Fk(A)1047 1274 y Fi(T)50
1404 y Fm(F77)27 b(call)99 b Fl(SSYR\('L',)40 b(n,)i
Fk(\013)p Fl(,)i(x,)f(incx,)e(A,)i(lda\))141 1605 y FK(No)31
b(extra)g(storage)h(or)e(op)s(erations)g(required.)0
1845 y Fv(SYR2)50 1982 y Fm(C)d(call)177 b Fl(cblas)p
664 1982 V 29 w(ssyr2\(CblasRowMaj)o(or)o(,)37 b(CblasUpper,)j(n,)i
Fk(\013)p Fl(,)i(x,)f(incx,)e(y,)i(incy,)e(A,)i(lda\))50
2082 y Fm(C)27 b(op)214 b Fk(A)23 b Fj( )g Fk(\013xy)774
2051 y Fi(T)846 2082 y Fm(+)18 b Fk(\013y)s(x)1073 2051
y Fi(T)1144 2082 y Fm(+)g Fk(A)50 2181 y Fm(F77)27 b(op)136
b Fk(A)501 2151 y Fi(T)576 2181 y Fj( )24 b Fk(\013y)s(x)827
2151 y Fi(T)898 2181 y Fm(+)18 b Fk(\013xy)1125 2151
y Fi(T)1196 2181 y Fm(+)g Fk(A)1341 2151 y Fi(T)50 2281
y Fm(F77)27 b(call)99 b Fl(SSYR2\('L',)39 b(n,)k Fk(\013)p
Fl(,)h(y,)e(incy,)g(x,)h(incx,)e(A,)i(lda\))141 2482
y FK(No)31 b(extra)g(storage)h(or)e(op)s(erations)g(required.)4084
64 y FI(1)4084 177 y(2)4084 290 y(3)4084 403 y(4)4084
516 y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084 967
y(9)4069 1080 y(10)4069 1193 y(11)4069 1306 y(12)4069
1419 y(13)4069 1532 y(14)4069 1645 y(15)4069 1758 y(16)4069
1870 y(17)4069 1983 y(18)4069 2096 y(19)4069 2209 y(20)4069
2322 y(21)4069 2435 y(22)4069 2548 y(23)4069 2661 y(24)4069
2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
3677 y(33)4069 3790 y(34)4069 3903 y(35)4069 4016 y(36)4069
4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 191 201
191 200 bop 0 -165 a FA(B.2.)72 b(C)30 b(INTERF)-10 b(A)m(CE)30
b(TO)g(THE)g(LEGA)m(CY)h(BLAS)1816 b FK(191)0 91 y Fv(Level)31
b(3)g(BLAS)0 263 y(GEMM)50 394 y FB(C)26 b(call)172 b
Fh(cblas)p 617 394 24 4 v 30 w(cgemm\(CblasRowMajor,)43
b(CblasNoTrans,)f(CblasNoTrans,)h(m,)c(n,)h(k,)g Fs(\013)p
Fh(,)f(A,)h(lda,)g(B,)g(ldb,)g Fs(\014)t Fh(,)g(C,)f(ldc\))50
485 y FB(C)26 b(op)205 b Fs(C)27 b Fr( )21 b Fs(\013AB)f
FB(+)d Fs(\014)t(C)50 578 y FB(F77)26 b(op)134 b Fs(C)477
547 y Fq(T)547 578 y Fr( )21 b Fs(\013B)756 547 y Fq(T)805
578 y Fs(A)863 547 y Fq(T)928 578 y FB(+)c Fs(\014)t(C)1112
547 y Fq(T)50 670 y FB(F77)26 b(call)101 b Fh(CGEMM\('N',)42
b('N',)e(n,)f(m,)h(k,)g Fs(\013)p Fh(,)g(B,)f(ldb,)h(A,)g(lda,)g
Fs(\014)t Fh(,)g(C,)g(ldc\))50 852 y FB(C)26 b(call)172
b Fh(cblas)p 617 852 V 30 w(cgemm\(CblasRowMajor,)43
b(CblasNoTrans,)f(CblasTrans,)g(m,)e(n,)g(k,)f Fs(\013)p
Fh(,)h(A,)g(lda,)g(B,)f(ldb,)i Fs(\014)t Fh(,)e(C,)h(ldc\))50
946 y FB(C)26 b(op)205 b Fs(C)27 b Fr( )21 b Fs(\013AB)766
914 y Fq(T)831 946 y FB(+)c Fs(\014)t(C)50 1039 y FB(F77)26
b(op)134 b Fs(C)477 1007 y Fq(T)547 1039 y Fr( )21 b
Fs(\013B)t(A)814 1007 y Fq(T)880 1039 y FB(+)c Fs(\014)t(C)1064
1007 y Fq(T)50 1130 y FB(F77)26 b(call)101 b Fh(CGEMM\('T',)42
b('N',)e(n,)f(m,)h(k,)g Fs(\013)p Fh(,)g(B,)f(ldb,)h(A,)g(lda,)g
Fs(\014)t Fh(,)g(C,)g(ldc\))50 1313 y FB(C)26 b(call)172
b Fh(cblas)p 617 1313 V 30 w(cgemm\(CblasRowMajor,)43
b(CblasNoTrans,)f(CblasConjTrans,)h(m,)d(n,)f(k,)h Fs(\013)p
Fh(,)g(A,)g(lda,)g(B,)f(ldb,)i Fs(\014)t Fh(,)e(C,)h(ldc\))50
1406 y FB(C)26 b(op)205 b Fs(C)27 b Fr( )21 b Fs(\013AB)766
1374 y Fq(H)840 1406 y FB(+)c Fs(\014)t(C)50 1501 y FB(F77)26
b(op)134 b Fs(C)477 1469 y Fq(T)547 1501 y Fr( )21 b
Fs(\013)p 694 1440 62 4 v(B)t(A)814 1469 y Fq(T)880 1501
y FB(+)c Fs(\014)t(C)1064 1469 y Fq(T)50 1592 y FB(F77)26
b(call)101 b Fh(CGEMM\('C',)42 b('N',)e(n,)f(m,)h(k,)g
Fs(\013)p Fh(,)g(B,)f(ldb,)h(A,)g(lda,)g Fs(\014)t Fh(,)g(C,)g(ldc\))50
1775 y FB(C)26 b(call)172 b Fh(cblas)p 617 1775 24 4
v 30 w(cgemm\(CblasRowMajor,)43 b(CblasTrans,)f(CblasNoTrans,)g(m,)e
(n,)g(k,)f Fs(\013)p Fh(,)h(A,)g(lda,)g(B,)f(ldb,)i Fs(\014)t
Fh(,)e(C,)h(ldc\))50 1868 y FB(C)26 b(op)205 b Fs(C)27
b Fr( )21 b Fs(\013A)704 1836 y Fq(T)752 1868 y Fs(B)g
FB(+)c Fs(\014)t(C)50 1961 y FB(F77)26 b(op)134 b Fs(C)477
1930 y Fq(T)547 1961 y Fr( )21 b Fs(\013B)756 1930 y
Fq(T)805 1961 y Fs(A)c FB(+)g Fs(\014)t(C)1064 1930 y
Fq(T)50 2053 y FB(F77)26 b(call)101 b Fh(CGEMM\('N',)42
b('T',)e(n,)f(m,)h(k,)g Fs(\013)p Fh(,)g(B,)f(ldb,)h(A,)g(lda,)g
Fs(\014)t Fh(,)g(C,)g(ldc\))50 2235 y FB(C)26 b(call)172
b Fh(cblas)p 617 2235 V 30 w(cgemm\(CblasRowMajor,)43
b(CblasTrans,)f(CblasTrans,)g(m,)d(n,)h(k,)g Fs(\013)p
Fh(,)g(A,)f(lda,)h(B,)g(ldb,)g Fs(\014)t Fh(,)g(C,)f(ldc\))50
2328 y FB(C)26 b(op)205 b Fs(C)27 b Fr( )21 b Fs(\013A)704
2297 y Fq(T)752 2328 y Fs(B)814 2297 y Fq(T)880 2328
y FB(+)c Fs(\014)t(C)50 2422 y FB(F77)26 b(op)134 b Fs(C)477
2390 y Fq(T)547 2422 y Fr( )21 b Fs(\013B)t(A)c FB(+)g
Fs(\014)t(C)1015 2390 y Fq(T)50 2513 y FB(F77)26 b(call)101
b Fh(CGEMM\('T',)42 b('T',)e(n,)f(m,)h(k,)g Fs(\013)p
Fh(,)g(B,)f(ldb,)h(A,)g(lda,)g Fs(\014)t Fh(,)g(C,)g(ldc\))50
2696 y FB(C)26 b(call)172 b Fh(cblas)p 617 2696 V 30
w(cgemm\(CblasRowMajor,)43 b(CblasTrans,)f(CblasConjTrans,)h(m,)c(n,)h
(k,)g Fs(\013)p Fh(,)f(A,)h(lda,)g(B,)g(ldb,)g Fs(\014)t
Fh(,)g(C,)f(ldc\))50 2789 y FB(C)26 b(op)205 b Fs(C)27
b Fr( )21 b Fs(\013A)704 2757 y Fq(T)752 2789 y Fs(B)814
2757 y Fq(H)889 2789 y FB(+)c Fs(\014)t(C)50 2884 y FB(F77)26
b(op)134 b Fs(C)477 2852 y Fq(T)547 2884 y Fr( )21 b
Fs(\013)p 694 2823 62 4 v(B)t(A)c FB(+)g Fs(\014)t(C)1015
2852 y Fq(T)50 2975 y FB(F77)26 b(call)101 b Fh(CGEMM\('C',)42
b('T',)e(n,)f(m,)h(k,)g Fs(\013)p Fh(,)g(B,)f(ldb,)h(A,)g(lda,)g
Fs(\014)t Fh(,)g(C,)g(ldc\))50 3158 y FB(C)26 b(call)172
b Fh(cblas)p 617 3158 24 4 v 30 w(cgemm\(CblasRowMajor,)43
b(CblasConjTrans,)g(CblasNoTrans,)f(m,)e(n,)f(k,)h Fs(\013)p
Fh(,)g(A,)g(lda,)g(B,)f(ldb,)i Fs(\014)t Fh(,)e(C,)h(ldc\))50
3251 y FB(C)26 b(op)205 b Fs(C)27 b Fr( )21 b Fs(\013A)704
3219 y Fq(H)761 3251 y Fs(B)g FB(+)c Fs(\014)t(C)50 3346
y FB(F77)26 b(op)134 b Fs(C)477 3314 y Fq(T)547 3346
y Fr( )21 b Fs(\013B)756 3314 y Fq(T)p 805 3285 58 4
v 805 3346 a Fs(A)c FB(+)g Fs(\014)t(C)1064 3314 y Fq(T)50
3437 y FB(F77)26 b(call)101 b Fh(CGEMM\('N',)42 b('C',)e(n,)f(m,)h(k,)g
Fs(\013)p Fh(,)g(B,)f(ldb,)h(A,)g(lda,)g Fs(\014)t Fh(,)g(C,)g(ldc\))50
3620 y FB(C)26 b(call)172 b Fh(cblas)p 617 3620 24 4
v 30 w(cgemm\(CblasRowMajor,)43 b(CblasConjTrans,)g(CblasTrans,)f(m,)d
(n,)h(k,)g Fs(\013)p Fh(,)f(A,)h(lda,)g(B,)g(ldb,)g Fs(\014)t
Fh(,)g(C,)f(ldc\))50 3713 y FB(C)26 b(op)205 b Fs(C)27
b Fr( )21 b Fs(\013A)704 3681 y Fq(H)761 3713 y Fs(B)823
3681 y Fq(T)889 3713 y FB(+)c Fs(\014)t(C)50 3808 y FB(F77)26
b(op)134 b Fs(C)477 3776 y Fq(T)547 3808 y Fr( )21 b
Fs(\013B)p 756 3747 58 4 v 4 w(A)c FB(+)g Fs(\014)t(C)1015
3776 y Fq(T)50 3900 y FB(F77)26 b(call)101 b Fh(CGEMM\('T',)42
b('C',)e(n,)f(m,)h(k,)g Fs(\013)p Fh(,)g(B,)f(ldb,)h(A,)g(lda,)g
Fs(\014)t Fh(,)g(C,)g(ldc\))50 4082 y FB(C)26 b(call)172
b Fh(cblas)p 617 4082 24 4 v 30 w(cgemm\(CblasRowMajor,)43
b(CblasConjTrans,)g(CblasConjTrans,)g(m,)c(n,)h(k,)g
Fs(\013)p Fh(,)f(A,)h(lda,)g(B,)g(ldb,)g Fs(\014)t Fh(,)g(C,)f(ldc\))50
4175 y FB(C)26 b(op)205 b Fs(C)27 b Fr( )21 b Fs(\013A)704
4144 y Fq(H)761 4175 y Fs(B)823 4144 y Fq(H)898 4175
y FB(+)c Fs(\014)t(C)50 4270 y FB(F77)26 b(op)134 b Fs(C)477
4239 y Fq(T)547 4270 y Fr( )21 b Fs(\013)p 694 4209 62
4 v(B)p 756 4209 58 4 v 4 w(A)c FB(+)g Fs(\014)t(C)1015
4239 y Fq(T)50 4362 y FB(F77)26 b(call)101 b Fh(CGEMM\('C',)42
b('C',)e(n,)f(m,)h(k,)g Fs(\013)p Fh(,)g(B,)f(ldb,)h(A,)g(lda,)g
Fs(\014)t Fh(,)g(C,)g(ldc\))-214 64 y FI(1)-214 177 y(2)-214
290 y(3)-214 403 y(4)-214 516 y(5)-214 628 y(6)-214 741
y(7)-214 854 y(8)-214 967 y(9)-230 1080 y(10)-230 1193
y(11)-230 1306 y(12)-230 1419 y(13)-230 1532 y(14)-230
1645 y(15)-230 1758 y(16)-230 1870 y(17)-230 1983 y(18)-230
2096 y(19)-230 2209 y(20)-230 2322 y(21)-230 2435 y(22)-230
2548 y(23)-230 2661 y(24)-230 2774 y(25)-230 2887 y(26)-230
3000 y(27)-230 3112 y(28)-230 3225 y(29)-230 3338 y(30)-230
3451 y(31)-230 3564 y(32)-230 3677 y(33)-230 3790 y(34)-230
3903 y(35)-230 4016 y(36)-230 4129 y(37)-230 4242 y(38)-230
4354 y(39)-230 4467 y(40)-230 4580 y(41)-230 4693 y(42)-230
4806 y(43)-230 4919 y(44)-230 5032 y(45)-230 5145 y(46)-230
5258 y(47)-230 5371 y(48)p eop
%%Page: 192 202
192 201 bop 0 -165 a FK(192)2590 b FA(ANNEX)31 b(B.)61
b(LEGA)m(CY)31 b(BLAS)0 91 y Fv(SYMM/HEMM)50 251 y Fm(C)c(call)177
b Fl(cblas)p 664 251 27 4 v 29 w(chemm\(CblasRowMaj)o(or)o(,)37
b(CblasLeft,)j(CblasUpper,)f(m,)k(n,)f Fk(\013)p Fl(,)i(A,)f(lda,)f(B,)
h(ldb,)e Fk(\014)t Fl(,)j(C,)f(ldc\))50 350 y Fm(C)27
b(op)214 b Fk(C)29 b Fj( )23 b Fk(\013AB)h Fm(+)18 b
Fk(\014)t(C)50 450 y Fm(F77)27 b(op)136 b Fk(C)504 420
y Fi(T)580 450 y Fj( )23 b Fk(\013B)806 420 y Fi(T)858
450 y Fk(A)920 420 y Fi(T)991 450 y Fm(+)18 b Fk(\014)t(C)1190
420 y Fi(T)50 550 y Fm(F77)27 b(call)99 b Fl(CHEMM\('R',)39
b('L',)j(n,)h(m,)g Fk(\013)p Fl(,)g(A,)g(lda,)f(B,)h(ldb,)f
Fk(\014)t Fl(,)h(C,)g(ldc\))50 749 y Fm(C)27 b(call)177
b Fl(cblas)p 664 749 V 29 w(chemm\(CblasRowMaj)o(or)o(,)37
b(CblasRight,)j(CblasUpper,)f(m,)j(n,)h Fk(\013)p Fl(,)h(A,)e(lda,)g
(B,)h(ldb,)f Fk(\014)t Fl(,)i(C,)e(ldc\))50 849 y Fm(C)27
b(op)214 b Fk(C)29 b Fj( )23 b Fk(\013B)t(A)d Fm(+)e
Fk(\014)t(C)50 948 y Fm(F77)27 b(op)136 b Fk(C)504 918
y Fi(T)580 948 y Fj( )23 b Fk(\013A)801 918 y Fi(T)854
948 y Fk(B)921 918 y Fi(T)991 948 y Fm(+)18 b Fk(\014)t(C)1190
918 y Fi(T)50 1048 y Fm(F77)27 b(call)99 b Fl(CHEMM\('L',)39
b('L',)j(n,)h(m,)g Fk(\013)p Fl(,)g(A,)g(lda,)f(B,)h(ldb,)f
Fk(\014)t Fl(,)h(C,)g(ldc\))0 1426 y Fv(SYRK)50 1563
y Fm(C)27 b(call)177 b Fl(cblas)p 664 1563 V 29 w(csyrk\(CblasRowMaj)o
(or)o(,)37 b(CblasUpper,)j(CblasNoTrans,)e(n,)k(k,)h
Fk(\013)p Fl(,)h(A,)f(lda,)f Fk(\014)t Fl(,)h(C,)g(ldc\))50
1662 y Fm(C)27 b(op)214 b Fk(C)29 b Fj( )23 b Fk(\013AA)810
1632 y Fi(T)882 1662 y Fm(+)18 b Fk(\014)t(C)50 1762
y Fm(F77)27 b(op)136 b Fk(C)504 1732 y Fi(T)580 1762
y Fj( )23 b Fk(\013AA)863 1732 y Fi(T)934 1762 y Fm(+)18
b Fk(\014)t(C)1133 1732 y Fi(T)50 1862 y Fm(F77)27 b(call)99
b Fl(CSYRK\('L',)39 b('T',)j(n,)h(k,)g Fk(\013)p Fl(,)g(A,)g(lda,)f(B,)
h(ldb,)f Fk(\014)t Fl(,)h(C,)g(ldc\))50 2061 y Fm(C)27
b(call)177 b Fl(cblas)p 664 2061 V 29 w(csyrk\(CblasRowMaj)o(or)o(,)37
b(CblasUpper,)j(CblasTrans,)f(n,)j(k,)h Fk(\013)p Fl(,)h(A,)e(lda,)g
Fk(\014)t Fl(,)i(C,)f(ldc\))50 2161 y Fm(C)27 b(op)214
b Fk(C)29 b Fj( )23 b Fk(\013A)748 2131 y Fi(T)801 2161
y Fk(A)c Fm(+)f Fk(\014)t(C)50 2261 y Fm(F77)27 b(op)136
b Fk(C)504 2230 y Fi(T)580 2261 y Fj( )23 b Fk(\013A)801
2230 y Fi(T)854 2261 y Fk(A)18 b Fm(+)g Fk(\014)t(C)1133
2230 y Fi(T)50 2360 y Fm(F77)27 b(call)99 b Fl(CSYRK\('L',)39
b('N',)j(n,)h(k,)g Fk(\013)p Fl(,)g(A,)g(lda,)f(B,)h(ldb,)f
Fk(\014)t Fl(,)h(C,)g(ldc\))141 2611 y FK(In)20 b(reading)g(the)i(ab)s
(o)m(v)m(e)g(descriptions,)f(it)f(is)g(imp)s(ortan)m(t)g(to)i(remem)m
(b)s(er)e(a)i(few)f(things.)36 b(First,)22 b(the)g(symmetric)0
2724 y(matrix)34 b(is)g Fy(C)7 b FK(,)36 b(and)e(th)m(us)g(w)m(e)h(c)m
(hange)h FD(UPLO)e FK(to)i(accommo)s(date)g(the)f(di\013ering)e
(storage)j(of)f Fy(C)7 b FK(.)54 b FD(TRANSPOSE)32 b
FK(is)0 2837 y(then)e(v)-5 b(aried)30 b(to)h(handle)e(the)h(storage)i
(e\013ects)g(on)e Fy(A)p FK(.)0 3077 y Fv(HERK)50 3214
y Fm(C)d(call)177 b Fl(cblas)p 664 3214 V 29 w(cherk\(CblasRowMaj)o(or)
o(,)37 b(CblasUpper,)j(CblasNoTrans,)e(n,)k(k,)h Fk(\013)p
Fl(,)h(A,)f(lda,)f Fk(\014)t Fl(,)h(C,)g(ldc\))50 3313
y Fm(C)27 b(op)214 b Fk(C)29 b Fj( )23 b Fk(\013AA)810
3283 y Fi(H)893 3313 y Fm(+)18 b Fk(\014)t(C)50 3416
y Fm(F77)27 b(op)136 b Fk(C)504 3386 y Fi(T)580 3416
y Fj( )23 b Fk(\013)p 739 3350 63 4 v(AA)863 3386 y Fi(T)934
3416 y Fm(+)18 b Fk(\014)t(C)1133 3386 y Fi(T)50 3516
y Fm(F77)27 b(call)99 b Fl(CHERK\('L',)39 b('C',)j(n,)h(k,)g
Fk(\013)p Fl(,)g(A,)g(lda,)f(B,)h(ldb,)f Fk(\014)t Fl(,)h(C,)g(ldc\))50
3715 y Fm(C)27 b(call)177 b Fl(cblas)p 664 3715 27 4
v 29 w(cherk\(CblasRowMaj)o(or)o(,)37 b(CblasUpper,)j(CblasConjTrans,)d
(n,)43 b(k,)f Fk(\013)p Fl(,)i(A,)f(lda,)f Fk(\014)t
Fl(,)h(C,)g(ldc\))50 3815 y Fm(C)27 b(op)214 b Fk(C)29
b Fj( )23 b Fk(\013A)748 3785 y Fi(H)812 3815 y Fk(A)c
Fm(+)f Fk(\014)t(C)50 3918 y Fm(F77)27 b(op)136 b Fk(C)504
3888 y Fi(T)580 3918 y Fj( )23 b Fk(\013A)801 3888 y
Fi(T)p 854 3852 63 4 v 854 3918 a Fk(A)18 b Fm(+)g Fk(\014)t(C)1133
3888 y Fi(T)50 4018 y Fm(F77)27 b(call)99 b Fl(CHERK\('L',)39
b('N',)j(n,)h(k,)g Fk(\013)p Fl(,)g(A,)g(lda,)f(B,)h(ldb,)f
Fk(\014)t Fl(,)h(C,)g(ldc\))0 4396 y Fv(SYR2K)50 4527
y FB(C)26 b(call)172 b Fh(cblas)p 617 4527 24 4 v 30
w(csyr2k\(CblasRowMajor,)44 b(CblasUpper,)d(CblasNoTrans,)h(n,)e(k,)g
Fs(\013)p Fh(,)g(A,)f(lda,)h(B,)g(ldb,)g Fs(\014)t Fh(,)g(C,)f(ldc\))50
4620 y FB(C)26 b(op)205 b Fs(C)27 b Fr( )21 b Fs(\013AB)766
4588 y Fq(T)831 4620 y FB(+)c Fs(\013B)t(A)1077 4588
y Fq(T)1142 4620 y FB(+)g Fs(\014)t(C)50 4713 y FB(F77)26
b(op)134 b Fs(C)477 4681 y Fq(T)547 4713 y Fr( )21 b
Fs(\013B)t(A)814 4681 y Fq(T)880 4713 y FB(+)c Fs(\013AB)1126
4681 y Fq(T)1191 4713 y FB(+)g Fs(\014)t(C)1375 4681
y Fq(T)1445 4713 y FB(=)k Fs(\013AB)1695 4681 y Fq(T)1761
4713 y FB(+)16 b Fs(\013B)t(A)2006 4681 y Fq(T)2072 4713
y FB(+)g Fs(\014)t(C)2255 4681 y Fq(T)50 4805 y FB(F77)26
b(call)101 b Fh(CSYR2K\('L',)42 b('T',)e(n,)g(k,)f Fs(\013)p
Fh(,)h(A,)g(lda,)g(B,)g(ldb,)g Fs(\014)t Fh(,)f(C,)h(ldc\))50
4987 y FB(C)26 b(call)172 b Fh(cblas)p 617 4987 V 30
w(csyr2k\(CblasRowMajor,)44 b(CblasUpper,)d(CblasTrans,)h(n,)e(k,)f
Fs(\013)p Fh(,)h(A,)g(lda,)g(B,)g(ldb,)g Fs(\014)t Fh(,)f(C,)h(ldc\))50
5080 y FB(C)26 b(op)205 b Fs(C)27 b Fr( )21 b Fs(\013A)704
5049 y Fq(T)752 5080 y Fs(B)g FB(+)c Fs(\013B)1019 5049
y Fq(T)1068 5080 y Fs(A)f FB(+)h Fs(\014)t(C)50 5174
y FB(F77)26 b(op)134 b Fs(C)477 5142 y Fq(T)547 5174
y Fr( )21 b Fs(\013B)756 5142 y Fq(T)805 5174 y Fs(A)c
FB(+)g Fs(\013A)1064 5142 y Fq(T)1112 5174 y Fs(B)k FB(+)c
Fs(\014)t(C)1375 5142 y Fq(T)1445 5174 y FB(=)k Fs(\013A)1633
5142 y Fq(T)1682 5174 y Fs(B)g FB(+)16 b Fs(\013B)1948
5142 y Fq(T)1997 5174 y Fs(A)h FB(+)f Fs(\014)t(C)2255
5142 y Fq(T)50 5265 y FB(F77)26 b(call)101 b Fh(CSYR2K\('L',)42
b('N',)e(n,)g(k,)f Fs(\013)p Fh(,)h(A,)g(lda,)g(B,)g(ldb,)g
Fs(\014)t Fh(,)f(C,)h(ldc\))4084 64 y FI(1)4084 177 y(2)4084
290 y(3)4084 403 y(4)4084 516 y(5)4084 628 y(6)4084 741
y(7)4084 854 y(8)4084 967 y(9)4069 1080 y(10)4069 1193
y(11)4069 1306 y(12)4069 1419 y(13)4069 1532 y(14)4069
1645 y(15)4069 1758 y(16)4069 1870 y(17)4069 1983 y(18)4069
2096 y(19)4069 2209 y(20)4069 2322 y(21)4069 2435 y(22)4069
2548 y(23)4069 2661 y(24)4069 2774 y(25)4069 2887 y(26)4069
3000 y(27)4069 3112 y(28)4069 3225 y(29)4069 3338 y(30)4069
3451 y(31)4069 3564 y(32)4069 3677 y(33)4069 3790 y(34)4069
3903 y(35)4069 4016 y(36)4069 4129 y(37)4069 4242 y(38)4069
4354 y(39)4069 4467 y(40)4069 4580 y(41)4069 4693 y(42)4069
4806 y(43)4069 4919 y(44)4069 5032 y(45)4069 5145 y(46)4069
5258 y(47)4069 5371 y(48)p eop
%%Page: 193 203
193 202 bop 0 -165 a FA(B.2.)72 b(C)30 b(INTERF)-10 b(A)m(CE)30
b(TO)g(THE)g(LEGA)m(CY)h(BLAS)1816 b FK(193)141 91 y(Note)36
b(that)e(w)m(e)h(once)g(again)f(wind)e(up)h(with)g(an)h(op)s(eration)f
(that)i(lo)s(oks)f(the)g(same)g(from)g(C)g(and)f(F)-8
b(ortran)0 204 y(77,)29 b(sa)m(ving)e(that)h(the)g(C)f(op)s(erations)f
(wishes)g(to)i(form)f Fy(C)1972 171 y Fw(T)2027 204 y
FK(,)h(instead)f(of)g Fy(C)7 b FK(.)39 b(So)27 b(once)h(again)g(w)m(e)g
(\015ip)d(the)j(setting)0 317 y(of)34 b FD(UPLO)e FK(to)j(handle)d(the)
i(di\013erence)f(in)f(the)i(storage)h(of)f Fy(C)7 b FK(.)50
b(W)-8 b(e)35 b(then)e(\015ip)f(the)i(setting)g(of)g
FD(TRANS)e FK(to)i(handle)0 430 y(the)d(storage)g(e\013ects)h(for)e
Fy(A)h FK(and)f Fy(B)5 b FK(.)0 670 y Fv(HER2K)50 801
y FB(C)26 b(call)172 b Fh(cblas)p 617 801 24 4 v 30 w
(cher2k\(CblasRowMajor,)44 b(CblasUpper,)d(CblasNoTrans,)h(n,)e(k,)g
Fs(\013)p Fh(,)g(A,)f(lda,)h(B,)g(ldb,)g Fs(\014)t Fh(,)g(C,)f(ldc\))50
894 y FB(C)26 b(op)205 b Fs(C)27 b Fr( )21 b Fs(\013AB)766
863 y Fq(H)840 894 y FB(+)p 917 852 50 4 v 17 w Fs(\013B)t(A)1086
863 y Fq(H)1160 894 y FB(+)c Fs(\014)t(C)50 989 y FB(F77)26
b(op)134 b Fs(C)477 958 y Fq(T)547 989 y Fr( )21 b Fs(\013)p
694 928 62 4 v(B)t(A)814 958 y Fq(T)880 989 y FB(+)p
957 947 50 4 v 17 w Fs(\013)p 1006 928 58 4 v(A)o(B)1125
958 y Fq(T)1191 989 y FB(+)c Fs(\014)t(C)1375 958 y Fq(T)1445
989 y FB(=)p 1526 947 50 4 v 21 w Fs(\013)p 1575 928
58 4 v(AB)1695 958 y Fq(T)1761 989 y FB(+)f Fs(\013)p
1886 928 62 4 v(B)t(A)2006 958 y Fq(T)2072 989 y FB(+)g
Fs(\014)t(C)2255 958 y Fq(T)50 1081 y FB(F77)26 b(call)101
b Fh(CHER2K\('L',)42 b('C',)e(n,)g(k,)p 1319 1039 50
4 v 39 w Fs(\013)q Fh(,)f(A,)h(lda,)g(B,)g(ldb,)g Fs(\014)t
Fh(,)f(C,)h(ldc\))50 1263 y FB(C)26 b(call)172 b Fh(cblas)p
617 1263 24 4 v 30 w(cher2k\(CblasRowMajor,)44 b(CblasUpper,)d
(CblasConjTrans,)i(n,)d(k,)f Fs(\013)p Fh(,)h(A,)g(lda,)g(B,)f(ldb,)i
Fs(\014)t Fh(,)e(C,)h(ldc\))50 1357 y FB(C)26 b(op)205
b Fs(C)27 b Fr( )21 b Fs(\013A)704 1325 y Fq(H)761 1357
y Fs(B)g FB(+)p 917 1314 50 4 v 17 w Fs(\013B)1028 1325
y Fq(H)1086 1357 y Fs(A)16 b FB(+)h Fs(\014)t(C)50 1452
y FB(F77)26 b(op)134 b Fs(C)477 1420 y Fq(T)547 1452
y Fr( )21 b Fs(\013B)756 1420 y Fq(T)p 805 1391 58 4
v 805 1452 a Fs(A)c FB(+)p 957 1409 50 4 v 17 w Fs(\013A)1064
1420 y Fq(T)p 1112 1391 62 4 v 1112 1452 a Fs(B)k FB(+)c
Fs(\014)t(C)1375 1420 y Fq(T)1445 1452 y FB(=)p 1526
1409 50 4 v 21 w Fs(\013A)1633 1420 y Fq(T)p 1682 1391
62 4 v 1682 1452 a Fs(B)k FB(+)16 b Fs(\013B)1948 1420
y Fq(T)p 1997 1391 58 4 v 1997 1452 a Fs(A)h FB(+)f Fs(\014)t(C)2255
1420 y Fq(T)50 1543 y FB(F77)26 b(call)101 b Fh(CHER2K\('L',)42
b('N',)e(n,)g(k,)p 1319 1501 50 4 v 39 w Fs(\013)q Fh(,)f(A,)h(lda,)g
(B,)g(ldb,)g Fs(\014)t Fh(,)f(C,)h(ldc\))0 1910 y Fv(TRMM/TRSM)0
2082 y FK(Because)29 b(of)e(their)g(iden)m(tical)f(use)h(of)g(the)h
FD(SIDE)p FK(,)e FD(UPLO)p FK(,)g(and)h FD(TRANSA)f FK(parameters,)i
(TRMM)g(and)f(TRSM)f(share)0 2195 y(the)32 b(same)g(general)g
(analysis.)43 b(Remem)m(b)s(er)31 b(that)h(A)g(is)f(a)h(triangular)e
(matrix,)h(and)g(th)m(us)h(when)e(w)m(e)i(handle)f(its)0
2307 y(storage)40 b(b)m(y)d(\015ipping)e FD(UPLO)p FK(,)i(w)m(e)i
(implicitly)34 b(c)m(hange)39 b(its)f FD(TRANS)e FK(setting)i(as)h(w)m
(ell.)62 b(With)38 b(this)f(in)f(mind,)i(w)m(e)0 2420
y(ha)m(v)m(e:)50 2493 y FB(C)26 b(call)172 b Fh(cblas)p
617 2493 24 4 v 30 w(ctrmm\(CblasRowMajor,)43 b(CblasLeft,)f
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eop
%%Page: 194 204
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%%Page: 195 205
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(the)f(L)1299 4525 y Fw(th)1400 4558 y FK(cac)m(he.)p
3325 4592 V 573 4596 2754 4 v 571 4709 4 113 v 623 4675
a(The)g(access)i(time)e(to)h(get)g(data)h(from)d(the)i(L)2184
4642 y Fw(th)2284 4675 y FK(cac)m(he)h(divided)c(b)m(y)i(the)p
3325 4709 V 571 4821 V 623 4788 a(time)g(to)h(cop)m(y)h(one)e
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3325 4821 V 573 4825 2754 4 v 571 4938 4 113 v 623 4904
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5167 V 573 5170 2754 4 v 4084 64 a FI(1)4084 177 y(2)4084
290 y(3)4084 403 y(4)4084 516 y(5)4084 628 y(6)4084 741
y(7)4084 854 y(8)4084 967 y(9)4069 1080 y(10)4069 1193
y(11)4069 1306 y(12)4069 1419 y(13)4069 1532 y(14)4069
1645 y(15)4069 1758 y(16)4069 1870 y(17)4069 1983 y(18)4069
2096 y(19)4069 2209 y(20)4069 2322 y(21)4069 2435 y(22)4069
2548 y(23)4069 2661 y(24)4069 2774 y(25)4069 2887 y(26)4069
3000 y(27)4069 3112 y(28)4069 3225 y(29)4069 3338 y(30)4069
3451 y(31)4069 3564 y(32)4069 3677 y(33)4069 3790 y(34)4069
3903 y(35)4069 4016 y(36)4069 4129 y(37)4069 4242 y(38)4069
4354 y(39)4069 4467 y(40)4069 4580 y(41)4069 4693 y(42)4069
4806 y(43)4069 4919 y(44)4069 5032 y(45)4069 5145 y(46)4069
5258 y(47)4069 5371 y(48)p eop
%%Page: 199 209
199 208 bop 0 -165 a FA(C.1.)95 b(ENVIR)m(ONMENT)-8 b(AL)21
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237 V 713 241 2474 4 v 713 257 V 711 370 4 113 v 763
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3185 1416 V 713 1420 2474 4 v 711 1533 4 113 v 763 1499
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1536 2474 4 v 711 1649 4 113 v 763 1615 a(F)-8 b(used)30
b(\015oating)h(p)s(oin)m(t)e(ops;)h(m)m(ultiply/add)p
3185 1649 V 713 1652 2474 4 v 711 1765 4 113 v 763 1731
a(Cycles)g(from)g(memory)g(to)h(stages)h(in)d(the)h(cac)m(he)p
3185 1765 V 713 1768 2474 4 v 711 1881 4 113 v 763 1847
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3185 1881 V 713 1885 2474 4 v 711 1998 4 113 v 763 1964
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3185 2114 V 713 2117 2474 4 v 711 2230 4 113 v 763 2196
a(Num)m(b)s(er)f(of)i(instructions)d(issued)h(p)s(er)g(cycle)p
3185 2230 V 713 2233 2474 4 v 262 2645 3376 4 v 260 2758
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3636 3120 V 262 3123 3376 4 v 260 3236 4 113 v 312 3202
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3236 V 262 3240 3376 4 v 260 3353 4 113 v 312 3319 a(T)-8
b(ransfer)30 b(bandwidth:)38 b(Units)29 b(\(b)m(ytes\))j(p)s(er)d
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3636 3353 V 262 3356 3376 4 v 260 3469 4 113 v 312 3435
a(Unit)g(of)g(transfer:)41 b(Num)m(b)s(er)29 b(of)h(units)f(mo)m(v)m
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(mo)m(v)m(e.)p 3636 3469 V 262 3472 3376 4 v 565 3884
2770 4 v 563 3997 4 113 v 615 3963 a(Memory)i(Hierarc)m(h)m(y)p
3333 3997 V 565 4000 2770 4 v 565 4017 V 563 4130 4 113
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(non-v)m(olatile)p 3333 4130 V 565 4133 2770 4 v 563
4246 4 113 v 615 4212 a(Actual)g(Registers,)h(cac)m(he,)h(DRAM,)g
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V 565 4830 2770 4 v 563 4943 4 113 v 615 4909 a(T)-8
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3333 5060 V 565 5063 2770 4 v 563 5176 4 113 v 615 5142
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(non-v)m(olatile)p 3333 5176 V 565 5179 2770 4 v -214
64 a FI(1)-214 177 y(2)-214 290 y(3)-214 403 y(4)-214
516 y(5)-214 628 y(6)-214 741 y(7)-214 854 y(8)-214 967
y(9)-230 1080 y(10)-230 1193 y(11)-230 1306 y(12)-230
1419 y(13)-230 1532 y(14)-230 1645 y(15)-230 1758 y(16)-230
1870 y(17)-230 1983 y(18)-230 2096 y(19)-230 2209 y(20)-230
2322 y(21)-230 2435 y(22)-230 2548 y(23)-230 2661 y(24)-230
2774 y(25)-230 2887 y(26)-230 3000 y(27)-230 3112 y(28)-230
3225 y(29)-230 3338 y(30)-230 3451 y(31)-230 3564 y(32)-230
3677 y(33)-230 3790 y(34)-230 3903 y(35)-230 4016 y(36)-230
4129 y(37)-230 4242 y(38)-230 4354 y(39)-230 4467 y(40)-230
4580 y(41)-230 4693 y(42)-230 4806 y(43)-230 4919 y(44)-230
5032 y(45)-230 5145 y(46)-230 5258 y(47)-230 5371 y(48)p
eop
%%Page: 200 210
200 209 bop 0 -165 a FK(200)1882 b FA(ANNEX)31 b(C.)61
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407 y(nical)25 b(F)-8 b(orum)26 b(concerning)f(the)h
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967 y(9)4069 1080 y(10)4069 1193 y(11)4069 1306 y(12)4069
1419 y(13)4069 1532 y(14)4069 1645 y(15)4069 1758 y(16)4069
1870 y(17)4069 1983 y(18)4069 2096 y(19)4069 2209 y(20)4069
2322 y(21)4069 2435 y(22)4069 2548 y(23)4069 2661 y(24)4069
2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
3677 y(33)4069 3790 y(34)4069 3903 y(35)4069 4016 y(36)4069
4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 201 211
201 210 bop 0 -165 a FA(C.2.)71 b(DISTRIBUTED-MEMOR)-8
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%%Page: 205 215
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%%Page: 206 216
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%%Page: 207 217
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1143 V 1082 1109 a(blas)p 1245 1109 28 4 v 31 w(trans)p
1759 1143 4 113 v 336 w(op)s(erate)h(with)f(transp)s(ose)f(x)p
3259 1143 V 512 w(TRANSx)g(=)h('T')p 1030 1256 V 1082
1222 a(blas)p 1245 1222 28 4 v 31 w(conj)p 1759 1256
4 113 v 375 w(op)s(erate)h(with)f(conjugate)h(x)p 3259
1256 V 508 w(TRANSx)e(=)h('C')p 1030 1369 V 1082 1335
a(blas)p 1245 1335 28 4 v 31 w(conj)p 1440 1335 V 33
w(trans)p 1759 1369 4 113 v 139 w(op)s(erate)h(with)f(conjugate-transp)
s(ose)h(x)p 3259 1369 V 100 w(TRANSx)e(=)h('H')277 1448
y(lo)m(w)m(er)p 1030 1482 V 598 w Fz(not)j(use)-5 b(d)p
1759 1482 V 399 w FK(reference)31 b(upp)s(er)e(triangle)g(only)p
3259 1482 V 355 w(UPLO)g(=)h('U')p 1030 1595 V 1082 1561
a(blas)p 1245 1561 28 4 v 31 w(lo)m(w)m(er)p 1759 1595
4 113 v 332 w(reference)h(lo)m(w)m(er)g(triangle)e(only)p
3259 1595 V 378 w(UPLO)g(=)h('L')277 1674 y(righ)m(t)p
472 1674 28 4 v 32 w(side)p 1030 1708 4 113 v 430 w Fz(not)j(use)-5
b(d)p 1759 1708 V 399 w FK(op)s(erate)31 b(on)g(the)f(left-hand)g(side)
p 3259 1708 V 352 w(SIDE)g(=)g('L')p 1030 1821 V 1082
1787 a(blas)p 1245 1787 28 4 v 31 w(righ)m(t)p 1759 1821
4 113 v 349 w(op)s(erate)h(on)g(the)f(righ)m(t-hand)f(side)p
3259 1821 V 292 w(SIDE)h(=)g('R')277 1900 y(unit)p 445
1900 28 4 v 31 w(diag)p 1030 1934 4 113 v 444 w Fz(not)j(use)-5
b(d)p 1759 1934 V 399 w FK(non-unit)29 b(triangular)p
3259 1934 V 736 w(DIA)m(G)i(=)f('N')p 1030 2046 V 1082
2013 a(blas)p 1245 2013 28 4 v 31 w(unit)p 1439 2013
V 32 w(diag)p 1759 2046 4 113 v 177 w(unit)f(triangular)p
3259 2046 V 913 w(DIA)m(G)i(=)f('U')0 2261 y Fx(C.3.3)98
b(Interfaces)33 b(fo)m(r)g(Real)f(Data)0 2433 y FK(The)e(primary)e(aim)
i(of)h(this)e(pap)s(er)g(is)h(to)h(con)m(v)m(ey)h(the)e(\015a)m(v)m
(our)h(of)g(the)f(di\013eren)m(t)g(generic)g(in)m(terfaces.)141
2545 y(Therefore)k(w)m(e)g(\014rst)g(describ)s(e)e(the)i(in)m(terfaces)
h(as)f(they)g(apply)f(to)i Fz(r)-5 b(e)g(al)35 b FK(data.)53
b(The)33 b(extra)i(complications)0 2658 y(whic)m(h)29
b(arise)h(when)f(they)i(apply)e(to)i(complex)f(data)h(will)d(b)s(e)i
(considered)f(in)g(Section)h(C.3.4.)141 2771 y(W)-8 b(e)27
b(summarize)d(eac)m(h)i(in)m(terface)g(in)e(the)h(form)g(of)g(a)h
FD(subroutine)c FK(statemen)m(t)27 b(\(or)f(in)e(one)h(case)i(a)e
FD(function)0 2884 y FK(statemen)m(t\),)40 b(in)35 b(whic)m(h)g(all)g
(the)h(argumen)m(ts)g(migh)m(t)g(app)s(ear.)57 b(\(This)35
b(is)g(a)i(con)m(v)m(enien)m(t)g(w)m(a)m(y)g(to)g(think)d(of)j(the)0
2997 y(in)m(terface,)d(although)d(suc)m(h)h(a)h(statemen)m(t)h(using)d
(the)i(generic)f(in)m(terface)h(name)f(nev)m(er)h(app)s(ears)f(in)f
(the)h(co)s(de.\))0 3110 y(Argumen)m(ts)e(whic)m(h)g(need)g(not)g(b)s
(e)g(supplied)d(are)k(enclosed)f(in)f(square)h(brac)m(k)m(ets,)i(for)e
(example:)0 3323 y FD(subroutine)45 b(trmm\()h([alpha,])g(a,)h([op_a,])
f(b,)h([lower,])f([right_side,])e([unit_diag])h(\))141
3535 y FK(This)30 b(is)g(follo)m(w)m(ed)h(b)m(y)g(a)h(table)f(whic)m(h)
g(lists)f(the)h(di\013eren)m(t)g(v)-5 b(arian)m(ts)31
b(of)h(the)f(op)s(eration,)h(dep)s(ending)c(either)0
3648 y(on)i(the)h(ranks)f(of)g(some)h(of)f(the)h(argumen)m(ts)g(or)f
(on)g(the)h(k)m(ey)g(argumen)m(ts.)141 3761 y(The)e(follo)m(wing)e
(table)i(sho)m(ws)g(the)g(v)-5 b(alues)28 b(used)g(in)g(the)h(tables)g
(and)f(the)h(related)g(named)g(constan)m(t)h(for)f(the)0
3874 y(k)m(ey)i(argumen)m(ts.)914 4078 y(dumm)m(y)f(argumen)m(t)p
1667 4112 V 100 w(v)-5 b(alue)30 b(in)f(table)p 2305
4112 V 99 w(named)h(constan)m(t)p 865 4116 2171 4 v 914
4195 a(op)p 1015 4195 28 4 v 33 w(x)p 1667 4229 4 113
v 628 w('T')p 2305 4229 V 521 w(blas)p 2519 4195 28 4
v 32 w(trans)p 1667 4342 4 113 v 1719 4308 a('C')p 2305
4342 V 521 w(blas)p 2519 4308 28 4 v 32 w(conj)p 1667
4454 4 113 v 1719 4421 a('C/T')p 2305 4454 V 410 w(blas)p
2519 4421 28 4 v 32 w(conj)p 2715 4421 V 33 w(trans)914
4533 y(righ)m(t)p 1109 4533 V 33 w(side)p 1667 4567 4
113 v 429 w('R')p 2305 4567 V 520 w(blas)p 2519 4533
28 4 v 32 w(righ)m(t)0 4915 y Fv(Routines)g(using)g(conventional)h(sto)
m(rage)h(fo)m(r)f(matrices)0 5087 y FK(By)g(con)m(v)m(en)m(tional)g
(storage,)h(w)m(e)f(mean)f(storing)g(a)h(matrix)f(in)f(a)h
(2-dimensional)f(arra)m(y)-8 b(,)0 5300 y FD(subroutine)45
b(gemm\()h([alpha,])g(a,)h([op_a,])f(b,)h([op_b],)f([beta,])g(c)h(\))
-214 64 y FI(1)-214 177 y(2)-214 290 y(3)-214 403 y(4)-214
516 y(5)-214 628 y(6)-214 741 y(7)-214 854 y(8)-214 967
y(9)-230 1080 y(10)-230 1193 y(11)-230 1306 y(12)-230
1419 y(13)-230 1532 y(14)-230 1645 y(15)-230 1758 y(16)-230
1870 y(17)-230 1983 y(18)-230 2096 y(19)-230 2209 y(20)-230
2322 y(21)-230 2435 y(22)-230 2548 y(23)-230 2661 y(24)-230
2774 y(25)-230 2887 y(26)-230 3000 y(27)-230 3112 y(28)-230
3225 y(29)-230 3338 y(30)-230 3451 y(31)-230 3564 y(32)-230
3677 y(33)-230 3790 y(34)-230 3903 y(35)-230 4016 y(36)-230
4129 y(37)-230 4242 y(38)-230 4354 y(39)-230 4467 y(40)-230
4580 y(41)-230 4693 y(42)-230 4806 y(43)-230 4919 y(44)-230
5032 y(45)-230 5145 y(46)-230 5258 y(47)-230 5371 y(48)p
eop
%%Page: 208 218
208 217 bop 0 -165 a FK(208)1882 b FA(ANNEX)31 b(C.)61
b(JOURNAL)30 b(OF)g(DEVELOPMENT)341 79 y FK(rank)g(of)g
FD(a)p 750 113 4 113 v 99 w FK(rank)g(of)h FD(b)p 1211
113 V 99 w FK(rank)f(of)h FD(c)p 1671 113 V 99 w(op)p
1825 79 29 4 v 34 w(a)p 1949 113 4 113 v 99 w(op)p 2102
79 29 4 v 34 w(b)p 2226 113 4 113 v 99 w FK(op)s(eration)p
3087 113 V 485 w(F77)g(BLAS)p 291 116 3319 4 v 499 195
a(2)p 750 229 4 113 v 415 w(2)p 1211 229 V 416 w(2)p
1671 229 V 1949 229 V 2226 229 V 812 w Fy(C)h FJ( )25
b Fy(\013AB)h FK(+)19 b Fy(\014)5 b(C)p 3087 229 V 3145
195 29 4 v 251 w FD(GEMM)499 308 y FK(2)p 750 342 4 113
v 415 w(2)p 1211 342 V 416 w(2)p 1671 342 V 1949 342
V 566 w('T')p 2226 342 V 130 w Fy(C)32 b FJ( )25 b Fy(\013AB)2690
275 y Fw(T)2766 308 y FK(+)19 b Fy(\014)5 b(C)p 3087
342 V 3145 308 29 4 v 196 w FD(GEMM)499 421 y FK(2)p
750 455 4 113 v 415 w(2)p 1211 455 V 416 w(2)p 1671 455
V 289 w('T')p 1949 455 V 2226 455 V 407 w Fy(C)32 b FJ( )25
b Fy(\013A)2616 388 y Fw(T)2672 421 y Fy(B)g FK(+)19
b Fy(\014)5 b(C)p 3087 455 V 3145 421 29 4 v 196 w FD(GEMM)499
534 y FK(2)p 750 568 4 113 v 415 w(2)p 1211 568 V 416
w(2)p 1671 568 V 289 w('T')p 1949 568 V 161 w('T')p 2226
568 V 130 w Fy(C)32 b FJ( )25 b Fy(\013A)2616 501 y Fw(T)2672
534 y Fy(B)2746 501 y Fw(T)2821 534 y FK(+)20 b Fy(\014)5
b(C)p 3087 568 V 3145 534 29 4 v 140 w FD(GEMM)499 647
y FK(2)p 750 681 4 113 v 415 w(1)p 1211 681 V 416 w(1)p
1671 681 V 1949 681 V 2226 681 V 812 w Fy(c)26 b FJ( )f
Fy(\013Ab)c FK(+)f Fy(\014)5 b(c)p 3087 681 V 3145 647
29 4 v 343 w FD(GEMV)499 760 y FK(2)p 750 794 4 113 v
415 w(1)p 1211 794 V 416 w(1)p 1671 794 V 289 w('T')p
1949 794 V 2226 794 V 407 w Fy(c)26 b FJ( )f Fy(\013A)2584
727 y Fw(T)2640 760 y Fy(b)20 b FK(+)g Fy(\014)5 b(c)p
3087 794 V 3145 760 29 4 v 288 w FD(GEMV)499 873 y FK(1)p
750 907 4 113 v 415 w(1)p 1211 907 V 416 w(2)p 1671 907
V 1949 907 V 2226 907 V 812 w Fy(C)32 b FJ( )25 b Fy(\013ab)2635
840 y Fw(T)2711 873 y FK(+)20 b Fy(\014)5 b(C)p 3087
907 V 3145 873 29 4 v 250 w FD(GER)p 3323 873 V 0 1075
a(subroutine)45 b(symm\()h([alpha,])g(a,)h(b,)g([beta,])f(c,)h
([lower,])f([right_side])e(\))0 1188 y(subroutine)h(hemm\()h([alpha,])g
(a,)h(b,)g([beta,])f(c,)h([lower,])f([right_side])e(\))622
1393 y FK(rank)29 b(of)i FD(b)p 1031 1427 4 113 v 99
w FK(rank)f(of)h FD(c)p 1492 1427 V 99 w(right)p 1789
1393 29 4 v 33 w(side)p 2055 1427 4 113 v 99 w FK(op)s(eration)p
2807 1427 V 374 w(F77)h(BLAS)p 572 1430 2757 4 v 779
1509 a(2)p 1031 1543 4 113 v 416 w(2)p 1492 1543 V 2055
1543 V 822 w Fy(C)f FJ( )25 b Fy(\013AB)h FK(+)20 b Fy(\014)5
b(C)p 2807 1543 V 2864 1509 29 4 v 140 w FD(SYMM)779
1622 y FK(2)p 1031 1656 4 113 v 416 w(2)p 1492 1656 V
431 w('R')p 2055 1656 V 274 w Fy(C)31 b FJ( )25 b Fy(\013B)5
b(A)21 b FK(+)f Fy(\014)5 b(C)p 2807 1656 V 2864 1622
29 4 v 140 w FD(SYMM)779 1735 y FK(1)p 1031 1769 4 113
v 416 w(1)p 1492 1769 V 2055 1769 V 822 w Fy(c)25 b FJ( )g
Fy(\013Ab)c FK(+)f Fy(\014)5 b(c)p 2807 1769 V 2864 1735
29 4 v 233 w FD(SYMV)141 1937 y FK(where)30 b Fy(A)h
FK(is)e(a)i(symmetric)e(matrix.)0 2147 y FD(subroutine)45
b(syrk\()h([alpha,])g(a,)h([op_a,])f([beta,])g(c,)h([lower])f(\))0
2260 y(subroutine)f(herk\()h([alpha,])g(a,)h([op_a,])f([beta,])g(c,)h
([lower])f(\))970 2465 y FK(rank)30 b(of)h FD(a)p 1379
2499 4 113 v 99 w(op)p 1533 2465 29 4 v 34 w(a)p 1657
2499 4 113 v 99 w FK(op)s(eration)p 2458 2499 V 424 w(F77)h(BLAS)p
920 2502 2060 4 v 1128 2581 a(2)p 1379 2615 4 113 v 1657
2615 V 535 w Fy(C)g FJ( )25 b Fy(\013AA)2115 2548 y Fw(T)2191
2581 y FK(+)20 b Fy(\014)5 b(C)p 2458 2615 V 2515 2581
29 4 v 141 w FD(SYRK)1128 2694 y FK(2)p 1379 2728 4 113
v 289 w('T')p 1657 2728 V 130 w Fy(C)32 b FJ( )25 b Fy(\013A)2047
2661 y Fw(T)2103 2694 y Fy(A)20 b FK(+)g Fy(\014)5 b(C)p
2458 2728 V 2515 2694 29 4 v 141 w FD(SYRK)1128 2807
y FK(1)p 1379 2841 4 113 v 1657 2841 V 535 w Fy(C)32
b FJ( )25 b Fy(\013aa)2075 2774 y Fw(T)2151 2807 y FK(+)20
b Fy(\014)5 b(C)p 2458 2841 V 2515 2807 29 4 v 181 w
FD(SYR1)141 3010 y FK(where)30 b Fy(C)37 b FK(is)29 b(a)i(symmetric)f
(matrix.)0 3220 y FD(subroutine)45 b(syr2k\()h([alpha,])g(a,)h([op_a,])
f(b,)h([beta,])f(c,)h([lower])f(\))0 3333 y(subroutine)f(he2rk\()h
([alpha,])g(a,)h([op_a,])f(b,)h([beta,])f(c,)h([lower])f(\))554
3537 y FK(rank)30 b(of)g FD(a)p 963 3571 4 113 v 100
w FK(rank)g(of)g FD(b)p 1424 3571 V 99 w(op)p 1577 3537
29 4 v 34 w(a)p 1701 3571 4 113 v 100 w FK(op)s(eration)p
2874 3571 V 796 w(F77)h(BLAS)p 504 3574 2892 4 v 712
3653 a(2)p 963 3687 4 113 v 416 w(2)p 1424 3687 V 1701
3687 V 535 w Fy(C)g FJ( )26 b Fy(\013AB)2166 3620 y Fw(T)2241
3653 y FK(+)20 b Fy(\013B)5 b(A)2532 3620 y Fw(T)2607
3653 y FK(+)20 b Fy(\014)5 b(C)p 2874 3687 V 2931 3653
29 4 v 141 w FD(SYR2K)712 3766 y FK(2)p 963 3800 4 113
v 416 w(2)p 1424 3800 V 288 w('T')p 1701 3800 V 131 w
Fy(C)31 b FJ( )26 b Fy(\013A)2092 3733 y Fw(T)2147 3766
y Fy(B)f FK(+)20 b Fy(\013B)2464 3733 y Fw(T)2519 3766
y Fy(A)g FK(+)g Fy(\014)5 b(C)p 2874 3800 V 2931 3766
29 4 v 141 w FD(SYR2K)712 3879 y FK(1)p 963 3913 4 113
v 416 w(1)p 1424 3913 V 1701 3913 V 535 w Fy(C)31 b FJ( )26
b Fy(\013ab)2111 3846 y Fw(T)2186 3879 y FK(+)20 b Fy(\013ba)2422
3846 y Fw(T)2498 3879 y FK(+)g Fy(\014)5 b(C)p 2874 3913
V 2931 3879 29 4 v 250 w FD(SYR2)141 4082 y FK(where)30
b Fy(C)37 b FK(is)29 b(a)i(symmetric)f(matrix.)0 4292
y FD(subroutine)45 b(trmm\()h([alpha,])g(a,)h([op_a,])f(b,)h([lower,])f
([right_side,])e([unit_diag])h(\))804 4497 y FK(rank)30
b(of)h FD(b)p 1213 4530 4 113 v 99 w(op)p 1367 4497 29
4 v 34 w(a)p 1491 4530 4 113 v 99 w(right)p 1788 4497
29 4 v 33 w(side)p 2054 4530 4 113 v 99 w FK(op)s(eration)p
2624 4530 V 192 w(F77)h(BLAS)p 754 4534 2392 4 v 962
4613 a(2)p 1213 4647 4 113 v 1491 4647 V 2054 4647 V
1099 w Fy(B)d FJ( )d Fy(\013AB)p 2624 4647 V 2681 4613
29 4 v 194 w FD(TRMM)962 4726 y FK(2)p 1213 4760 4 113
v 289 w('T')p 1491 4760 V 2054 4760 V 694 w Fy(B)j FJ( )d
Fy(\013A)2447 4693 y Fw(T)2502 4726 y Fy(B)p 2624 4760
V 2681 4726 29 4 v 139 w FD(TRMM)962 4839 y FK(2)p 1213
4872 4 113 v 1491 4872 V 708 w('R')p 2054 4872 V 274
w Fy(B)j FJ( )d Fy(\013B)5 b(A)p 2624 4872 V 2681 4839
29 4 v 189 w FD(TRMM)962 4952 y FK(2)p 1213 4985 4 113
v 289 w('T')p 1491 4985 V 303 w('R')p 2054 4985 V 274
w Fy(B)29 b FJ( )d Fy(\013B)5 b(A)2521 4919 y Fw(T)p
2624 4985 V 2681 4952 29 4 v 2710 4952 a FD(TRMM)962
5064 y FK(1)p 1213 5098 4 113 v 1491 5098 V 2054 5098
V 1099 w Fy(b)25 b FJ( )g Fy(\013Ab)p 2624 5098 V 2681
5064 29 4 v 259 w FD(TRMV)962 5177 y FK(1)p 1213 5211
4 113 v 289 w('T')p 1491 5211 V 2054 5211 V 694 w Fy(b)g
FJ( )g Fy(\013A)2412 5144 y Fw(T)2468 5177 y Fy(b)p 2624
5211 V 2681 5177 29 4 v 203 w FD(TRMV)0 5380 y(subroutine)45
b(trsm\()h([alpha,])g(a,)h([op_a,])f(b,)h([lower,])f([right_side,])e
([unit_diag])h(\))4084 64 y FI(1)4084 177 y(2)4084 290
y(3)4084 403 y(4)4084 516 y(5)4084 628 y(6)4084 741 y(7)4084
854 y(8)4084 967 y(9)4069 1080 y(10)4069 1193 y(11)4069
1306 y(12)4069 1419 y(13)4069 1532 y(14)4069 1645 y(15)4069
1758 y(16)4069 1870 y(17)4069 1983 y(18)4069 2096 y(19)4069
2209 y(20)4069 2322 y(21)4069 2435 y(22)4069 2548 y(23)4069
2661 y(24)4069 2774 y(25)4069 2887 y(26)4069 3000 y(27)4069
3112 y(28)4069 3225 y(29)4069 3338 y(30)4069 3451 y(31)4069
3564 y(32)4069 3677 y(33)4069 3790 y(34)4069 3903 y(35)4069
4016 y(36)4069 4129 y(37)4069 4242 y(38)4069 4354 y(39)4069
4467 y(40)4069 4580 y(41)4069 4693 y(42)4069 4806 y(43)4069
4919 y(44)4069 5032 y(45)4069 5145 y(46)4069 5258 y(47)4069
5371 y(48)p eop
%%Page: 209 219
209 218 bop 0 -165 a FA(C.3.)71 b(F)m(OR)-8 b(TRAN)31
b(95)h(THIN)e(BLAS)2419 b FK(209)821 79 y(rank)30 b(of)h
FD(b)p 1231 113 4 113 v 99 w(op)p 1384 79 29 4 v 34 w(a)p
1508 113 4 113 v 99 w FK(righ)m(t)p 1754 79 28 4 v 33
w(side)p 1982 113 4 113 v 98 w(op)s(eration)p 2607 113
V 248 w(F77)h(BLAS)p 772 116 2357 4 v 979 195 a(2)p 1231
229 4 113 v 1508 229 V 1982 229 V 1009 w Fy(B)e FJ( )25
b Fy(\013A)2374 162 y Fu(\000)p FC(1)2469 195 y Fy(B)p
2607 229 V 2664 195 29 4 v 154 w FD(TRSM)979 308 y FK(2)p
1231 342 4 113 v 289 w('T')p 1508 342 V 1982 342 V 604
w Fy(B)30 b FJ( )25 b Fy(\013A)2374 275 y Fu(\000)p Fw(T)2485
308 y Fy(B)p 2607 342 V 2664 308 29 4 v 138 w FD(TRSM)979
421 y FK(2)p 1231 455 4 113 v 1508 455 V 664 w('R')p
1982 455 V 228 w Fy(B)30 b FJ( )25 b Fy(\013B)5 b(A)2448
388 y Fu(\000)p FC(1)p 2607 455 V 2664 421 29 4 v 2692
421 a FD(TRSM)979 534 y FK(2)p 1231 568 4 113 v 289 w('T')p
1508 568 V 259 w('R')p 1982 568 V 228 w Fy(B)30 b FJ( )25
b Fy(\013B)5 b(A)2448 501 y Fu(\000)p Fw(T)p 2607 568
V 2664 534 29 4 v 2692 534 a FD(TRSM)979 647 y FK(1)p
1231 681 4 113 v 1508 681 V 1982 681 V 1009 w Fy(b)26
b FJ( )f Fy(\013A)2340 614 y Fu(\000)p FC(1)2435 647
y Fy(b)p 2607 681 V 2664 647 29 4 v 218 w FD(TRSV)979
760 y FK(1)p 1231 794 4 113 v 289 w('T')p 1508 794 V
1982 794 V 604 w Fy(b)h FJ( )f Fy(\013A)2340 727 y Fu(\000)p
Fw(T)2450 760 y Fy(b)p 2607 794 V 2664 760 29 4 v 203
w FD(TRSV)0 991 y Fv(Routines)30 b(using)g(pack)m(ed)i(sto)m(rage)g(fo)
m(r)f(matrices)0 1162 y FK(By)26 b Fz(p)-5 b(acke)g(d)28
b FK(storage,)g(w)m(e)f(mean)e(storing)h(the)g(upp)s(er)e(or)i(lo)m(w)m
(er)g(triangle)f(of)h(a)g(symmetric)f(or)h(triangular)f(matrix)0
1275 y(in)k(a)i(1-dimensional)d(arra)m(y)j(\(i.e.)41
b(a)31 b(v)m(ector\).)0 1478 y FD(subroutine)45 b(spmv\()h([alpha,])g
(a,)h(b,)g([beta,])f(c,)h([lower])f(\))0 1591 y(subroutine)f(hpmv\()h
([alpha,])g(a,)h(b,)g([beta,])f(c,)h([lower])f(\))1413
1789 y FK(op)s(eration)p 2015 1823 4 113 v 276 w(F77)32
b(BLAS)p 1364 1826 1173 4 v 1413 1905 a Fy(c)26 b FJ( )f
Fy(\013Ab)c FK(+)f Fy(\014)5 b(c)p 2015 1939 4 113 v
2072 1905 29 4 v 135 w FD(SPMV)141 2100 y FK(where)30
b Fy(A)h FK(is)e(a)i(symmetric)e(matrix.)0 2303 y FD(subroutine)45
b(spr1\()h([alpha,])g(a,)h([beta,])f(c,)h([lower])f(\))0
2416 y(subroutine)f(hpr1\()h([alpha,])g(a,)h([beta,])f(c,)h([lower])f
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4184 V 124 w(F77)31 b(BLAS)p 1301 4188 1299 4 v 1576
4301 4 113 v 1628 4267 a Fy(b)25 b FJ( )g Fy(\013Ab)p
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4347 y Fw(T)1990 4380 y Fy(b)p 2077 4414 V 2134 4380
29 4 v 134 w FD(TPMV)141 4575 y FK(where)30 b Fy(A)h
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1323 4976 y(op)p 1425 4976 V 34 w(a)p 1549 5009 4 113
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y Fy(b)p 2105 5126 V 2162 5092 29 4 v 150 w FD(TPSV)1354
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2105 5239 V 2162 5205 29 4 v 134 w FD(TPSV)141 5400 y
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64 y FI(1)-214 177 y(2)-214 290 y(3)-214 403 y(4)-214
516 y(5)-214 628 y(6)-214 741 y(7)-214 854 y(8)-214 967
y(9)-230 1080 y(10)-230 1193 y(11)-230 1306 y(12)-230
1419 y(13)-230 1532 y(14)-230 1645 y(15)-230 1758 y(16)-230
1870 y(17)-230 1983 y(18)-230 2096 y(19)-230 2209 y(20)-230
2322 y(21)-230 2435 y(22)-230 2548 y(23)-230 2661 y(24)-230
2774 y(25)-230 2887 y(26)-230 3000 y(27)-230 3112 y(28)-230
3225 y(29)-230 3338 y(30)-230 3451 y(31)-230 3564 y(32)-230
3677 y(33)-230 3790 y(34)-230 3903 y(35)-230 4016 y(36)-230
4129 y(37)-230 4242 y(38)-230 4354 y(39)-230 4467 y(40)-230
4580 y(41)-230 4693 y(42)-230 4806 y(43)-230 4919 y(44)-230
5032 y(45)-230 5145 y(46)-230 5258 y(47)-230 5371 y(48)p
eop
%%Page: 210 220
210 219 bop 0 -165 a FK(210)1882 b FA(ANNEX)31 b(C.)61
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29 4 v 34 w(a)p 1457 504 4 113 v 99 w FK(op)s(eration)p
2197 504 V 363 w(F77)32 b(BLAS)p 1181 507 1538 4 v 1457
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699 y FK('T')p 1457 733 4 113 v 130 w Fy(C)32 b FJ( )25
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1230 y(subroutine)f(hbmv\()h([alpha,])g(a,)h(b,)g([beta,])f(c,)h
([lower])f(\))1413 1437 y FK(op)s(eration)p 2015 1471
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2212 V 124 w(F77)31 b(BLAS)p 1301 2215 1299 4 v 1576
2328 4 113 v 1628 2294 a Fy(b)25 b FJ( )g Fy(\013Ab)p
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29 4 v 134 w FD(TBMV)141 2612 y FK(where)30 b Fy(A)h
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b(swap\()h(x,)i(y)f(\))141 4515 y FK(Op)s(eration:)40
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f(c,)g(s)g(\))4084 64 y FI(1)4084 177 y(2)4084 290 y(3)4084
403 y(4)4084 516 y(5)4084 628 y(6)4084 741 y(7)4084 854
y(8)4084 967 y(9)4069 1080 y(10)4069 1193 y(11)4069 1306
y(12)4069 1419 y(13)4069 1532 y(14)4069 1645 y(15)4069
1758 y(16)4069 1870 y(17)4069 1983 y(18)4069 2096 y(19)4069
2209 y(20)4069 2322 y(21)4069 2435 y(22)4069 2548 y(23)4069
2661 y(24)4069 2774 y(25)4069 2887 y(26)4069 3000 y(27)4069
3112 y(28)4069 3225 y(29)4069 3338 y(30)4069 3451 y(31)4069
3564 y(32)4069 3677 y(33)4069 3790 y(34)4069 3903 y(35)4069
4016 y(36)4069 4129 y(37)4069 4242 y(38)4069 4354 y(39)4069
4467 y(40)4069 4580 y(41)4069 4693 y(42)4069 4806 y(43)4069
4919 y(44)4069 5032 y(45)4069 5145 y(46)4069 5258 y(47)4069
5371 y(48)p eop
%%Page: 211 221
211 220 bop 0 -165 a FA(C.3.)71 b(F)m(OR)-8 b(TRAN)31
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v 415 w(2)p 1149 844 V 416 w(2)p 1610 844 V 1936 844
V 640 w('T')p 2263 844 V 156 w Fy(C)32 b FJ( )25 b Fy(\013AB)2728
777 y Fw(T)2803 810 y FK(+)20 b Fy(\014)5 b(C)p 3149
844 V 3206 810 29 4 v 220 w FD(GEMM)437 923 y FK(2)p
688 956 4 113 v 415 w(2)p 1149 956 V 416 w(2)p 1610 956
V 1936 956 V 585 w('C/T')p 2263 956 V 100 w Fy(C)32 b
FJ( )25 b Fy(\013AB)2728 890 y Fw(H)2815 923 y FK(+)20
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1035 y FK(2)p 688 1069 4 113 v 415 w(2)p 1149 1069 V
416 w(2)p 1610 1069 V 314 w('T')p 1936 1069 V 2263 1069
V 482 w Fy(C)32 b FJ( )25 b Fy(\013A)2654 1002 y Fw(T)2709
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4 113 v 415 w(2)p 1149 1182 V 416 w(2)p 1610 1182 V 314
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1182 V 3206 1148 29 4 v 165 w FD(GEMM)437 1261 y FK(2)p
688 1295 4 113 v 415 w(2)p 1149 1295 V 416 w(2)p 1610
1295 V 314 w('T')p 1936 1295 V 155 w('C/T')p 2263 1295
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1261 y Fy(B)2783 1228 y Fw(H)2870 1261 y FK(+)20 b Fy(\014)5
b(C)p 3149 1295 V 3206 1261 29 4 v 153 w FD(GEMM)437
1374 y FK(2)p 688 1408 4 113 v 415 w(2)p 1149 1408 V
416 w(2)p 1610 1408 V 258 w('C/T')p 1936 1408 V 2263
1408 V 427 w Fy(C)32 b FJ( )25 b Fy(\013A)2654 1341 y
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V 3206 1374 29 4 v 208 w FD(GEMM)437 1487 y FK(2)p 688
1521 4 113 v 415 w(2)p 1149 1521 V 416 w(2)p 1610 1521
V 258 w('C/T')p 1936 1521 V 155 w('T')p 2263 1521 V 156
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1487 y Fy(B)2796 1454 y Fw(T)2870 1487 y FK(+)20 b Fy(\014)5
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1600 y FK(2)p 688 1634 4 113 v 415 w(2)p 1149 1634 V
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y Fw(H)2722 1600 y Fy(B)2796 1567 y Fw(H)2883 1600 y
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v 141 w FD(GEMM)437 1713 y FK(2)p 688 1747 4 113 v 415
w(1)p 1149 1747 V 416 w(1)p 1610 1747 V 1936 1747 V 2263
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1826 y FK(2)p 688 1860 4 113 v 415 w(1)p 1149 1860 V
416 w(1)p 1610 1860 V 314 w('T')p 1936 1860 V 2263 1860
V 482 w Fy(c)25 b FJ( )h Fy(\013A)2622 1793 y Fw(T)2677
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1826 29 4 v 313 w FD(GEMV)437 1939 y FK(2)p 688 1973
4 113 v 415 w(1)p 1149 1973 V 416 w(1)p 1610 1973 V 258
w('C/T')p 1936 1973 V 2263 1973 V 427 w Fy(c)25 b FJ( )h
Fy(\013A)2622 1906 y Fw(H)2689 1939 y Fy(b)21 b FK(+)f
Fy(\014)5 b(c)p 3149 1973 V 3206 1939 29 4 v 300 w FD(GEMV)437
2052 y FK(1)p 688 2086 4 113 v 415 w(1)p 1149 2086 V
416 w(2)p 1610 2086 V 1936 2086 V 2263 2086 V 912 w Fy(C)32
b FJ( )25 b Fy(\013ab)2673 2019 y Fw(T)2748 2052 y FK(+)20
b Fy(\014)5 b(C)p 3149 2086 V 3206 2052 29 4 v 275 w
FD(GERU)437 2165 y FK(1)p 688 2198 4 113 v 415 w(1)p
1149 2198 V 416 w(2)p 1610 2198 V 1936 2198 V 640 w('C')p
2263 2198 V 156 w Fy(C)32 b FJ( )25 b Fy(\013ab)2673
2132 y Fw(H)2761 2165 y FK(+)20 b Fy(\014)5 b(C)p 3149
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i(follo)m(wing:)227 3953 y FD(SWAP)227 4066 y(ROT)227
4179 y(NRM2)227 4292 y(ROTG)141 4504 y(ROT)f FK(and)f
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(routines:)141 5367 y(W)-8 b(e)32 b(prop)s(ose)d(adding)g(one)i(new)f
(routine:)-214 64 y FI(1)-214 177 y(2)-214 290 y(3)-214
403 y(4)-214 516 y(5)-214 628 y(6)-214 741 y(7)-214 854
y(8)-214 967 y(9)-230 1080 y(10)-230 1193 y(11)-230 1306
y(12)-230 1419 y(13)-230 1532 y(14)-230 1645 y(15)-230
1758 y(16)-230 1870 y(17)-230 1983 y(18)-230 2096 y(19)-230
2209 y(20)-230 2322 y(21)-230 2435 y(22)-230 2548 y(23)-230
2661 y(24)-230 2774 y(25)-230 2887 y(26)-230 3000 y(27)-230
3112 y(28)-230 3225 y(29)-230 3338 y(30)-230 3451 y(31)-230
3564 y(32)-230 3677 y(33)-230 3790 y(34)-230 3903 y(35)-230
4016 y(36)-230 4129 y(37)-230 4242 y(38)-230 4354 y(39)-230
4467 y(40)-230 4580 y(41)-230 4693 y(42)-230 4806 y(43)-230
4919 y(44)-230 5032 y(45)-230 5145 y(46)-230 5258 y(47)-230
5371 y(48)p eop
%%Page: 212 222
212 221 bop 0 -165 a FK(212)1882 b FA(ANNEX)31 b(C.)61
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b(auxiliary)d(routine)h(xLAR)-8 b(TG.)141 486 y(The)39
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b(On)28 b(the)g(other)g(hand,)f(man)m(y)h(of)h(the)f(F)-8
b(ortran)28 b(77)h(Lev)m(el)f(1)h(BLAS)e(can)i(b)s(e)0
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%%Page: 213 223
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%%Page: 214 224
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%%Page: 215 225
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%%Page: 216 226
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Fw(\013)h FC(if)f(di\013eren)n(t)h(from)e(one.)213 5275
y Fc(Note:)35 b FC(if)23 b Fw(\013)h FC(is)f(exactly)i(one,)f(y)n(ou)g
(need)h(not)f(supply)g(this)g(argumen)n(t.)4084 64 y
FI(1)4084 177 y(2)4084 290 y(3)4084 403 y(4)4084 516
y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084 967 y(9)4069
1080 y(10)4069 1193 y(11)4069 1306 y(12)4069 1419 y(13)4069
1532 y(14)4069 1645 y(15)4069 1758 y(16)4069 1870 y(17)4069
1983 y(18)4069 2096 y(19)4069 2209 y(20)4069 2322 y(21)4069
2435 y(22)4069 2548 y(23)4069 2661 y(24)4069 2774 y(25)4069
2887 y(26)4069 3000 y(27)4069 3112 y(28)4069 3225 y(29)4069
3338 y(30)4069 3451 y(31)4069 3564 y(32)4069 3677 y(33)4069
3790 y(34)4069 3903 y(35)4069 4016 y(36)4069 4129 y(37)4069
4242 y(38)4069 4354 y(39)4069 4467 y(40)4069 4580 y(41)4069
4693 y(42)4069 4806 y(43)4069 4919 y(44)4069 5032 y(45)4069
5145 y(46)4069 5258 y(47)4069 5371 y(48)p eop
%%Page: 217 227
217 226 bop 0 -165 a FA(C.3.)71 b(F)m(OR)-8 b(TRAN)31
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580 197 22 4 v 26 w(a)i FC(is)f(supplied,)h(it)f(sp)r(eci\014es)i
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457 y Fg(blas)p 357 457 V 26 w(trans)p FC(:)33 b(if)22
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537 y Fq(H)2432 560 y FC(rather)e(than)i(the)g(matrix)d
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b FC(for)23 b(real)h(matrices,)e Fg(blas)p 1106 766 V
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b Fg(op)p 697 869 V 26 w(a)21 b Fa(must)j(not)k FC(b)r(e)21
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1123 y Fd(a\()p Fw(m)p Fd(\))j(/)h(a\()p Fw(p;)10 b(q)r
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w(a)i FC(is)f(supplied,)g(the)i(shap)r(e)f(of)g Fg(a)g
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1712 y Fd(op)p 91 1712 25 4 v 29 w(b)24 b FC(|)f(a)h(\\k)n(ey")h
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b FC(if)22 b Fg(op)p 576 1817 22 4 v 26 w(b)i FC(is)f(supplied)h(and)g
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(eration)h(in)n(v)n(olv)n(es)f(the)g(transp)r(ose)h Fw(B)3324
1794 y Fq(T)3396 1817 y FC(or)e(its)g(conjugate-)213
1896 y(transp)r(ose)h Fw(B)585 1872 y Fq(H)667 1896 y
FC(\(=)c Fw(B)825 1872 y Fq(T)898 1896 y FC(if)j Fw(B)k
FC(is)d(real\).)31 b(In)25 b(this)f(case)g Fg(op)p 1757
1896 V 26 w(b)g FC(m)n(ust)f(ha)n(v)n(e)i(one)g(of)e(the)i(follo)n
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(dule)e Fg(blas)p FC(\):)213 2078 y Fg(blas)p 357 2078
V 26 w(trans)p FC(:)33 b(if)22 b(the)j(op)r(eration)f(in)n(v)n(olv)n
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2078 y FC(rather)g(than)h(the)f(matrix)f Fw(B)s FC(;)213
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Fw(b)3060 2284 y Fq(T)3158 2307 y FC(\()p Fw(b)3215 2284
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(t)h(to)g Fg(blas)p 2108 2671 V 27 w(trans)p FC(.)31
b(F)-6 b(or)20 b(real)g(arra)n(ys)g Fg(blas)p 2967 2671
V 26 w(conj)i FC(do)r(es)e(not)h(ha)n(v)n(e)h(an)n(y)f(e\013ect.)213
2774 y Fc(Constrain)n(ts:)35 b Fg(op)p 697 2774 V 26
w(b)26 b Fa(must)i(not)k FC(b)r(e)26 b(supplied)g(if)e(the)j(op)r
(eration)g(do)r(es)f(not)g(in)n(v)n(olv)n(e)h(the)f(conjugate)i(of)d
Fw(b)p FC(,)h(the)h(transp)r(ose)f(of)g Fw(B)j FC(or)c(the)213
2853 y(conjugate-transp)r(ose)h(of)d Fw(B)s FC(.)0 3028
y Fd(b\()p Fw(r)r Fd(\))j(/)h(b\()p Fw(r)n(;)11 b(s)p
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Fc(wp)p FC(\),)f(in)n(ten)n(t\(in\))213 3133 y Fc(Input:)36
b FC(the)24 b(matrix)f Fw(B)k FC(or)c(v)n(ector)i Fw(b)p
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3315 y(if)f Fg(a)i FC(is)f(rank-1,)g(the)i(shap)r(e)f(of)g
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y(if)e Fg(a)i FC(is)f(rank-2,)g(the)i(shap)r(e)f(of)g
Fg(b)f FC(m)n(ust)g(b)r(e)h Fg(SIZE\(op)p 1721 3418 V
28 w(a\(a\),2\))p FC(.)213 3521 y(If)f Fg(b)h FC(is)f(rank-2)g(then:)
307 3624 y(if)f Fg(op)p 445 3624 V 26 w(b)i FC(is)f(not)i(supplied,)e
(the)h(shap)r(e)h(of)e Fg(b)h FC(m)n(ust)f(b)r(e)h(\()p
Fw(k)r(;)11 b(n)p FC(\);)307 3726 y(if)22 b Fg(op)p 445
3726 V 26 w(b)i FC(is)f(supplied,)g(the)i(shap)r(e)f(of)g
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(t\(inout\))213 4414 y Fc(Input:)36 b FC(the)24 b(matrix)f
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(initialized.)213 4517 y Fc(Output:)36 b FC(the)24 b(matrix)f
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FC(use)24 b(the)h(call:)141 5227 y Fg(CALL)37 b(gemm)f
(\(alpha,a,blas_conj_tran)q(s,b,)q(c\))0 5400 y FC(T)-6
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177 y(2)-214 290 y(3)-214 403 y(4)-214 516 y(5)-214 628
y(6)-214 741 y(7)-214 854 y(8)-214 967 y(9)-230 1080
y(10)-230 1193 y(11)-230 1306 y(12)-230 1419 y(13)-230
1532 y(14)-230 1645 y(15)-230 1758 y(16)-230 1870 y(17)-230
1983 y(18)-230 2096 y(19)-230 2209 y(20)-230 2322 y(21)-230
2435 y(22)-230 2548 y(23)-230 2661 y(24)-230 2774 y(25)-230
2887 y(26)-230 3000 y(27)-230 3112 y(28)-230 3225 y(29)-230
3338 y(30)-230 3451 y(31)-230 3564 y(32)-230 3677 y(33)-230
3790 y(34)-230 3903 y(35)-230 4016 y(36)-230 4129 y(37)-230
4242 y(38)-230 4354 y(39)-230 4467 y(40)-230 4580 y(41)-230
4693 y(42)-230 4806 y(43)-230 4919 y(44)-230 5032 y(45)-230
5145 y(46)-230 5258 y(47)-230 5371 y(48)p eop
%%Page: 218 228
218 227 bop 0 -165 a FK(218)1882 b FA(ANNEX)31 b(C.)61
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Fw(c)d Fu( )g Fw(\013A)609 960 y Fq(T)658 984 y Fw(b)d
FC(+)f Fw(\014)s(c)23 b FC(use)h(the)h(call:)141 1162
y Fg(CALL)37 b(gemm)f(\(alpha,blas_trans,a,b,b)q(eta,)q(c\))0
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b FC(use)23 b(the)i(call:)141 1519 y Fg(CALL)37 b(gemm)f
(\(a,b,blas_conj,beta,c\))4084 64 y FI(1)4084 177 y(2)4084
290 y(3)4084 403 y(4)4084 516 y(5)4084 628 y(6)4084 741
y(7)4084 854 y(8)4084 967 y(9)4069 1080 y(10)4069 1193
y(11)4069 1306 y(12)4069 1419 y(13)4069 1532 y(14)4069
1645 y(15)4069 1758 y(16)4069 1870 y(17)4069 1983 y(18)4069
2096 y(19)4069 2209 y(20)4069 2322 y(21)4069 2435 y(22)4069
2548 y(23)4069 2661 y(24)4069 2774 y(25)4069 2887 y(26)4069
3000 y(27)4069 3112 y(28)4069 3225 y(29)4069 3338 y(30)4069
3451 y(31)4069 3564 y(32)4069 3677 y(33)4069 3790 y(34)4069
3903 y(35)4069 4016 y(36)4069 4129 y(37)4069 4242 y(38)4069
4354 y(39)4069 4467 y(40)4069 4580 y(41)4069 4693 y(42)4069
4806 y(43)4069 4919 y(44)4069 5032 y(45)4069 5145 y(46)4069
5258 y(47)4069 5371 y(48)p eop
%%Page: 219 229
219 228 bop 0 -165 a FA(C.4.)71 b(INTER)-10 b(V)g(AL)30
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1558 y(interval)26 b FK([)p Fy(a)399 1525 y Fu(\003)439
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(in)m(terv)-5 b(al)32 b([)p Fy(a)1440 1751 y Fu(\003)1480
1784 y Fy(;)15 b(b)1559 1751 y Fu(\003)1599 1784 y FK(])33
b(is)f(a)h Fz(tight)j(r)-5 b(epr)g(esentation)35 b FK(of)e(a)h
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5400 y(triangular)29 b(in)m(terv)-5 b(al)29 b(matricies.)40
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y(2)4084 290 y(3)4084 403 y(4)4084 516 y(5)4084 628 y(6)4084
741 y(7)4084 854 y(8)4084 967 y(9)4069 1080 y(10)4069
1193 y(11)4069 1306 y(12)4069 1419 y(13)4069 1532 y(14)4069
1645 y(15)4069 1758 y(16)4069 1870 y(17)4069 1983 y(18)4069
2096 y(19)4069 2209 y(20)4069 2322 y(21)4069 2435 y(22)4069
2548 y(23)4069 2661 y(24)4069 2774 y(25)4069 2887 y(26)4069
3000 y(27)4069 3112 y(28)4069 3225 y(29)4069 3338 y(30)4069
3451 y(31)4069 3564 y(32)4069 3677 y(33)4069 3790 y(34)4069
3903 y(35)4069 4016 y(36)4069 4129 y(37)4069 4242 y(38)4069
4354 y(39)4069 4467 y(40)4069 4580 y(41)4069 4693 y(42)4069
4806 y(43)4069 4919 y(44)4069 5032 y(45)4069 5145 y(46)4069
5258 y(47)4069 5371 y(48)p eop
%%Page: 221 231
221 230 bop 0 -165 a FA(C.4.)71 b(INTER)-10 b(V)g(AL)30
b(BLAS)2793 b FK(221)0 91 y(Sections)28 b(C.4.2)i({)58
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444 y Fv(Interval)h(V)m(ecto)m(r)i(Op)s(erations)0 616
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b(v)m(ector)k(reduction)c(op)s(erations.)37 b(T)-8 b(able)22
b(C.3)h(lists)e(in)m(terv)-5 b(al)22 b(v)m(ector)i(op)s(erations.)37
b(T)-8 b(able)0 729 y(C.4)31 b(lists)e(in)m(terv)-5 b(al)29
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4 113 v 313 962 V 364 929 a(Dot)h(pro)s(duct)p 1612 962
V 807 w FG(r)25 b FJ( )g Fy(\014)5 b FG(r)21 b FK(+)f
Fy(\013)p FG(x)2172 896 y Fw(T)2227 929 y FG(y)p 2915
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4 113 v 3601 962 V 296 1075 V 313 1075 V 364 1041 a(V)-8
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V 3584 1075 V 3601 1075 V 296 1188 V 313 1188 V 1612
1188 V 1664 1154 a Fy(r)i FJ( )d(jj)p FG(x)p FJ(jj)2004
1168 y Fu(1)p 2915 1188 V 2967 1154 a FK(NORM)p 3261
1154 28 4 v 33 w(I)p 3584 1188 4 113 v 3601 1188 V 296
1301 V 313 1301 V 364 1267 a(Sum)p 1612 1301 V 1122 w
FG(r)g FJ( )1848 1203 y Ft(P)1936 1290 y Fw(i)1979 1267
y FG(x)2034 1281 y Fw(i)p 2915 1301 V 2967 1267 a FK(SUM)p
3174 1267 28 4 v 32 w(I)p 3584 1301 4 113 v 3601 1301
V 296 1414 V 313 1414 V 364 1380 a(Max)31 b(magnitude)f(&)g(lo)s
(cation)p 1612 1414 V 226 w Fy(k)s(;)15 b FG(x)1809 1395
y Fw(k)1852 1380 y FK(;)31 b Fy(k)d FK(=)d(arg)46 b(max)2420
1394 y Fw(i)2448 1380 y FJ(fj)p Fy(x)p 2518 1393 52 4
v 2571 1401 a Fw(i)2599 1380 y FJ(j)p Fy(;)15 b FJ(j)p
2689 1331 V Fy(x)2742 1394 y Fw(i)2770 1380 y FJ(jg)p
2915 1414 4 113 v 127 w FK(AMAX)p 3259 1380 28 4 v 33
w(V)-10 b(AL)p 3475 1380 V 33 w(I)p 3584 1414 4 113 v
3601 1414 V 296 1527 V 313 1527 V 364 1493 a(Min)29 b(absolute)i(v)-5
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b FG(x)1809 1508 y Fw(k)1852 1493 y FK(;)31 b Fy(k)d
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Fy(x)p 2501 1506 52 4 v 21 x Fw(i)2582 1493 y FJ(j)p
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1527 4 113 v 3601 1527 V 296 1640 4 114 v 313 1640 V
364 1607 a(Sum)29 b(of)i(squares)p 1612 1640 V 697 w(\()p
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1570 y FC(2)2546 1607 y FK(=)2641 1542 y Ft(P)2729 1630
y Fw(i)2772 1607 y FG(x)2828 1574 y FC(2)2828 1631 y
Fw(i)p 2915 1640 V 2967 1607 a FK(SUMSQ)p 3296 1607 28
4 v 32 w(I)p 3584 1640 4 114 v 3601 1640 V 298 1644 3305
4 v 1287 1898 a(T)-8 b(able)30 b(C.2:)41 b(Reduction)30
b(Op)s(erations)p 530 2118 2841 4 v 528 2231 4 113 v
545 2231 V 596 2197 a(Recipro)s(cal)g(scale)p 2057 2231
V 876 w FG(x)c FJ( )f FG(x)p Fy(=\013)p 2709 2231 V 298
w FK(RSCALE)p 3137 2197 28 4 v 31 w(I)p 3352 2231 4 113
v 3369 2231 V 528 2344 V 545 2344 V 596 2310 a(Scaled)30
b(in)m(terv)-5 b(al)30 b(v)m(ector)i(accum)m(ulation)p
2057 2344 V 99 w FG(y)26 b FJ( )f Fy(\013)p FG(x)c FK(+)e
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2310 28 4 v 33 w(I)p 3352 2344 4 113 v 3369 2344 V 528
2457 V 545 2457 V 596 2423 a(Scaled)30 b(in)m(terv)-5
b(al)30 b(v)m(ector)i(accum)m(ulation)p 2057 2457 V 99
w FG(w)25 b FJ( )g Fy(\013)p FG(x)c FK(+)f Fy(\014)5
b FG(y)p 2709 2457 V 100 w FK(W)-10 b(AXPBY)p 3179 2423
28 4 v 34 w(I)p 3352 2457 4 113 v 3369 2457 V 528 2570
V 545 2570 V 596 2536 a(Scaled)30 b(in)m(terv)-5 b(al)30
b(v)m(ector)i(cancellation)p 2057 2570 V 157 w FG(y)26
b FJ( )f Fy(\013)p FG(x)c FJ(\011)e Fy(\014)5 b FG(y)p
2709 2570 V 121 w FK(CANCEL)p 3153 2536 28 4 v 32 w(I)p
3352 2570 4 113 v 3369 2570 V 528 2683 V 545 2683 V 596
2649 a(Scaled)30 b(in)m(terv)-5 b(al)30 b(v)m(ector)i(cancellation)p
2057 2683 V 157 w FG(w)25 b FJ( )g Fy(\013)p FG(x)c FJ(\011)f
Fy(\014)5 b FG(y)p 2709 2683 V 100 w FK(W)m(CANCEL)p
3243 2649 28 4 v 33 w(I)p 3352 2683 4 113 v 3369 2683
V 530 2686 2841 4 v 1193 2940 a(T)-8 b(able)30 b(C.3:)41
b(In)m(terv)-5 b(al)30 b(V)-8 b(ector)32 b(Op)s(erations)p
1051 3160 1798 4 v 1049 3273 4 113 v 1066 3273 V 1117
3239 a(Cop)m(y)p 1773 3273 V 501 w FG(y)25 b FJ( )g FG(x)p
2196 3273 V 171 w FK(COPY)p 2519 3239 28 4 v 32 w(I)p
2831 3273 4 113 v 2848 3273 V 1049 3386 V 1066 3386 V
1117 3352 a(Sw)m(ap)p 1773 3386 V 498 w FG(y)g FJ($)g
FG(x)p 2196 3386 V 171 w FK(SW)-10 b(AP)p 2516 3352 28
4 v 33 w(I)p 2831 3386 4 113 v 2848 3386 V 1049 3499
V 1066 3499 V 1117 3465 a(P)m(erm)m(ute)32 b(v)m(ector)p
1773 3499 V 101 w FG(x)25 b FJ( )g Fy(P)13 b FG(x)p 2196
3499 V 100 w FK(PERMUTE)p 2722 3465 28 4 v 33 w(I)p 2831
3499 4 113 v 2848 3499 V 1051 3502 1798 4 v 756 3756
a(T)-8 b(able)30 b(C.4:)41 b(Data)32 b(Mo)m(v)m(emen)m(t)h(with)c(In)m
(terv)-5 b(al)30 b(V)-8 b(ector)32 b(Op)s(erations)-214
64 y FI(1)-214 177 y(2)-214 290 y(3)-214 403 y(4)-214
516 y(5)-214 628 y(6)-214 741 y(7)-214 854 y(8)-214 967
y(9)-230 1080 y(10)-230 1193 y(11)-230 1306 y(12)-230
1419 y(13)-230 1532 y(14)-230 1645 y(15)-230 1758 y(16)-230
1870 y(17)-230 1983 y(18)-230 2096 y(19)-230 2209 y(20)-230
2322 y(21)-230 2435 y(22)-230 2548 y(23)-230 2661 y(24)-230
2774 y(25)-230 2887 y(26)-230 3000 y(27)-230 3112 y(28)-230
3225 y(29)-230 3338 y(30)-230 3451 y(31)-230 3564 y(32)-230
3677 y(33)-230 3790 y(34)-230 3903 y(35)-230 4016 y(36)-230
4129 y(37)-230 4242 y(38)-230 4354 y(39)-230 4467 y(40)-230
4580 y(41)-230 4693 y(42)-230 4806 y(43)-230 4919 y(44)-230
5032 y(45)-230 5145 y(46)-230 5258 y(47)-230 5371 y(48)p
eop
%%Page: 222 232
222 231 bop 0 -165 a FK(222)1882 b FA(ANNEX)31 b(C.)61
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384 3263 4 v 317 496 4 113 v 334 496 V 385 463 a(Matrix)e(v)m(ector)i
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FG(Ax)20 b FK(+)g Fy(\014)5 b FG(y)p 2431 496 V 499 w
FK(GE,GB,SY,SB,SP)p 3246 496 V 101 w(MV)p 3454 463 28
4 v 33 w(I)p 3563 496 4 113 v 3580 496 V 317 612 4 116
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3454 578 28 4 v 33 w(I)p 3563 612 4 116 v 3580 612 V
317 727 V 334 727 V 1320 727 V 1372 693 a FG(x)25 b FJ( )h
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3246 727 V 314 w(MV)p 3454 693 28 4 v 33 w(I)p 3563 727
4 116 v 3580 727 V 317 843 V 334 843 V 385 809 a(T)-8
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b(TB,)h(TP)p 3246 843 V 314 w(SV)p 3422 809 28 4 v 32
w(I)p 3563 843 4 116 v 3580 843 V 317 955 4 113 v 334
955 V 385 922 a(Rank)f(one)h(up)s(dates)p 1320 955 V
267 w FG(A)25 b FJ( )g Fy(\013)p FG(x)q(y)1761 889 y
Fw(T)1836 922 y FK(+)20 b Fy(\014)5 b FG(A)p 2431 955
V 420 w FK(GE,SY,SP)p 3246 955 V 401 w(R)p 3370 922 28
4 v 32 w(I)p 3563 955 4 113 v 3580 955 V 319 959 3263
4 v 1049 1213 a(T)-8 b(able)30 b(C.5:)41 b(In)m(terv)-5
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1837 y(\015oating)k(p)s(oin)m(t)g(op)s(erations.)53 b(The)34
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b(al)27 b(matrix.)40 b(T)-8 b(able)27 b(C.7)i(lists)d(the)j(in)m(terv)
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2392 V 186 w FK(GE,GB,SY,SB,)p 3038 2392 V 3095 2358
28 4 v 134 w(NORM)p 3416 2358 V 33 w(I)p 3811 2392 4
113 v 3828 2392 V 69 2505 V 86 2505 V 1255 2505 V 1306
2471 a Fy(r)j FJ( )d(jj)p FG(A)q FJ(jj)1671 2485 y Fu(1)1746
2471 y Fy(;)15 b(r)28 b FJ( )d(jj)p FG(A)q FJ(jj)2151
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V 137 2584 a(Diagonal)31 b(scaling)p 1255 2618 V 517
w FG(A)25 b FJ( )h FG(DA)p Fy(;)15 b FG(A)25 b FJ( )h
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3703 2584 V 32 w(I)p 3811 2618 4 113 v 3828 2618 V 69
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278 w(LRSCALE)p 3555 2809 V 32 w(I)p 3811 2843 4 113
v 3828 2843 V 69 2956 V 86 2956 V 1255 2956 V 1306 2922
a FG(A)25 b FJ( )h FG(A)20 b FK(+)g FG(BD)p 2335 2956
V 515 w FK(GE,)31 b(GB)p 3038 2956 V 3811 2956 V 3828
2956 V 69 3069 V 86 3069 V 137 3035 a(Matrix)g(acc)g(and)f(scale)p
1255 3069 V 345 w FG(B)c FJ( )f Fy(\013)p FG(A)c FK(+)e
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3038 3069 V 3095 3035 28 4 v 134 w(A)m(CC)p 3324 3035
V 33 w(I)p 3811 3069 4 113 v 3828 3069 V 69 3184 4 116
v 86 3184 V 1255 3184 V 1306 3151 a FG(B)26 b FJ( )f
Fy(\013)p FG(A)1659 3115 y Fw(T)1735 3151 y FK(+)20 b
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3038 3184 V 3811 3184 V 3828 3184 V 69 3297 4 113 v 86
3297 V 137 3264 a(Matrix)31 b(add)e(and)h(scale)p 1255
3297 V 325 w FG(C)25 b FJ( )g Fy(\013)p FG(A)c FK(+)f
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3038 3297 V 3095 3264 28 4 v 134 w(ADD)p 3333 3264 V
34 w(I)p 3811 3297 4 113 v 3828 3297 V 69 3410 V 86 3410
V 1255 3410 V 2335 3410 V 2386 3376 a(SP)-8 b(,TR,TB,TP)p
3038 3410 V 3811 3410 V 3828 3410 V 71 3414 3759 4 v
678 3680 a(T)g(able)30 b(C.6:)41 b(Matrix)30 b(Op)s(erations)f({)i
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4021 V 101 w(MM)p 3680 3987 28 4 v 34 w(I)p 3790 4021
4 116 v 3807 4021 V 90 4136 V 107 4136 V 1116 4136 V
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b FG(C)25 b FJ( )g Fy(\013)p FG(A)2305 4066 y Fw(T)2360
4102 y FG(B)2434 4066 y Fw(T)2509 4102 y FK(+)20 b Fy(\014)5
b FG(C)p 2780 4136 V 3458 4136 V 3790 4136 V 3807 4136
V 90 4252 V 107 4252 V 1116 4252 V 1168 4218 a(C)25 b
FJ( )g Fy(\013)p FG(B)q(A)20 b FK(+)g Fy(\014)5 b FG(C)p
FK(,)30 b FG(C)25 b FJ( )g Fy(\013)p FG(B)2245 4182 y
Fw(T)2300 4218 y FG(A)20 b FK(+)g Fy(\014)5 b FG(C)p
FK(,)p 2780 4252 V 184 w(GB)p 3458 4252 V 543 w(MM)p
3680 4218 28 4 v 34 w(I)p 3790 4252 4 116 v 3807 4252
V 90 4367 V 107 4367 V 1116 4367 V 1168 4333 a FG(C)25
b FJ( )g Fy(\013)p FG(B)q(A)1597 4297 y Fw(T)1672 4333
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4297 y Fw(T)2509 4333 y FK(+)20 b Fy(\014)5 b FG(C)p
2780 4367 V 3458 4367 V 3790 4367 V 3807 4367 V 90 4480
4 113 v 107 4480 V 158 4446 a FK(T)-8 b(riangular)29
b(m)m(ultiply)p 1116 4480 V 226 w FG(B)c FJ( )h Fy(\013)p
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3680 4446 28 4 v 34 w(I)p 3790 4480 4 113 v 3807 4480
V 90 4595 4 116 v 107 4595 V 1116 4595 V 1168 4561 a
FG(B)25 b FJ( )h Fy(\013)p FG(T)1515 4525 y Fw(T)1570
4561 y FG(B)p FK(,)31 b FG(B)25 b FJ( )h Fy(\013)p FG(BT)2121
4525 y Fw(T)p 2780 4595 V 3458 4595 V 3790 4595 V 3806
4595 V 90 4708 4 113 v 107 4708 V 158 4674 a FK(T)-8
b(riangular)29 b(solv)m(e)p 1116 4708 V 370 w FG(B)c
FJ( )h Fy(\013)p FG(T)1515 4638 y Fu(\000)p FC(1)1609
4674 y FG(B)q FK(,)k FG(B)c FJ( )f Fy(\013)p FG(B)q(T)2160
4638 y Fu(\000)p FC(1)p 2780 4708 V 2831 4674 a FK(TR,)31
b(TB)p 3458 4708 V 359 w(SM)p 3648 4674 28 4 v 33 w(I)p
3790 4708 4 113 v 3807 4708 V 90 4824 4 116 v 107 4824
V 1116 4824 V 1168 4790 a FG(B)25 b FJ( )h Fy(\013)p
FG(T)1515 4754 y Fu(\000)p Fw(T)1625 4790 y FG(B)p FK(,)31
b FG(B)25 b FJ( )h Fy(\013)p FG(BT)2176 4754 y Fu(\000)p
Fw(T)p 2780 4824 V 3458 4824 V 3790 4824 V 3806 4824
V 92 4827 3717 4 v 678 5094 a FK(T)-8 b(able)30 b(C.7:)41
b(Matrix)30 b(Op)s(erations)f({)i Fy(O)s FK(\()p Fy(n)2139
5061 y FC(3)2178 5094 y FK(\))g(\015oating)f(p)s(oin)m(t)g(op)s
(erations)4084 64 y FI(1)4084 177 y(2)4084 290 y(3)4084
403 y(4)4084 516 y(5)4084 628 y(6)4084 741 y(7)4084 854
y(8)4084 967 y(9)4069 1080 y(10)4069 1193 y(11)4069 1306
y(12)4069 1419 y(13)4069 1532 y(14)4069 1645 y(15)4069
1758 y(16)4069 1870 y(17)4069 1983 y(18)4069 2096 y(19)4069
2209 y(20)4069 2322 y(21)4069 2435 y(22)4069 2548 y(23)4069
2661 y(24)4069 2774 y(25)4069 2887 y(26)4069 3000 y(27)4069
3112 y(28)4069 3225 y(29)4069 3338 y(30)4069 3451 y(31)4069
3564 y(32)4069 3677 y(33)4069 3790 y(34)4069 3903 y(35)4069
4016 y(36)4069 4129 y(37)4069 4242 y(38)4069 4354 y(39)4069
4467 y(40)4069 4580 y(41)4069 4693 y(42)4069 4806 y(43)4069
4919 y(44)4069 5032 y(45)4069 5145 y(46)4069 5258 y(47)4069
5371 y(48)p eop
%%Page: 223 233
223 232 bop 0 -165 a FA(C.4.)71 b(INTER)-10 b(V)g(AL)30
b(BLAS)2793 b FK(223)p 131 3 3638 4 v 129 116 4 113 v
146 116 V 198 82 a(Matrix)30 b(cop)m(y)p 927 116 V 296
w FG(B)c FJ( )f FG(A)p 1809 116 V 587 w FK(GE,GB,SY,SB,SP)-8
b(,TR,TB,TP)p 3083 116 V 3140 82 28 4 v 134 w(COPY)p
3439 82 V 32 w(I)p 3750 116 4 113 v 3767 116 V 129 232
4 116 v 146 232 V 927 232 V 978 198 a FG(B)26 b FJ( )f
FG(A)1273 162 y Fw(T)p 1809 232 V 1860 198 a FK(GE,)31
b(GB)p 3083 232 V 3140 198 28 4 v 983 w(COPY)p 3439 198
V 32 w(I)p 3750 232 4 116 v 3767 232 V 129 347 V 146
347 V 198 313 a(Matrix)f(transp)s(ose)p 927 347 V 99
w FG(A)c FJ( )f FG(A)1278 277 y Fw(T)p 1809 347 V 1860
313 a FK(GE)p 3083 347 V 3140 313 28 4 v 1174 w(TRANS)p
3492 313 V 32 w(I)p 3750 347 4 116 v 3767 347 V 129 460
4 113 v 146 460 V 198 426 a(P)m(erm)m(ute)31 b(matrix)p
927 460 V 149 w FG(A)26 b FJ( )f FG(PA)p Fy(;)15 b FG(A)26
b FJ( )f FG(AP)p 1809 460 V 100 w FK(GE)p 3083 460 V
3140 426 28 4 v 1174 w(PERMUTE)p 3642 426 V 32 w(I)p
3750 460 4 113 v 3767 460 V 131 463 3638 4 v 948 717
a(T)-8 b(able)30 b(C.8:)41 b(Data)32 b(Mo)m(v)m(emen)m(t)h(with)c(In)m
(terv)-5 b(al)30 b(Matrices)0 975 y Fv(Set)g(Op)s(erations)g(Involving)
g(Interval)h(V)m(ecto)m(rs)0 1146 y FK(T)-8 b(able)30
b(C.9)h(lists)e(set)h(op)s(erations)g(for)g(in)m(terv)-5
b(al)30 b(v)m(ectors.)p 415 1267 3070 4 v 413 1380 4
113 v 430 1380 V 482 1346 a(Enclosed)p 995 1380 V 214
w FG(x)g FK(is)g(enclosed)g(in)f FG(y)h FK(if)g FG(x)25
b FJ(\022)g FG(y)p 2380 1380 V 342 w FK(ENCV)p 2700 1346
28 4 v 33 w(I)p 3466 1380 4 113 v 3483 1380 V 413 1493
V 430 1493 V 482 1459 a(In)m(terior)p 995 1493 V 266
w FG(x)30 b FK(is)g(enclosed)g(in)f(the)h(in)m(terior)g(of)g
FG(y)p 2380 1493 V 106 w FK(INTERIOR)-10 b(V)p 2961 1459
28 4 v 32 w(I)p 3466 1493 4 113 v 3483 1493 V 413 1606
V 430 1606 V 482 1572 a(Disjoin)m(t)p 995 1606 V 252
w FG(x)30 b FK(and)g FG(y)h FK(are)f(disjoin)m(t)f(if)g
FG(x)21 b FJ(\\)f FG(y)25 b FK(=)g FJ(;)p 2380 1606 V
100 w FK(DISJV)p 2704 1572 28 4 v 32 w(I)p 3466 1606
4 113 v 3483 1606 V 413 1718 V 430 1718 V 482 1685 a(In)m(tersection)p
995 1718 V 100 w FG(y)g FJ( )g FG(x)c FJ(\\)f FG(y)p
Fy(;)15 b FG(z)26 b FJ( )f FG(x)20 b FJ(\\)g FG(y)p 2380
1718 V 537 w FK(INTER)-10 b(V)p 2790 1685 28 4 v 32 w(I,)31
b(WINTER)-10 b(V)p 3358 1685 V 32 w(I)p 3466 1718 4 113
v 3483 1718 V 413 1831 V 430 1831 V 482 1798 a(Hull)p
995 1831 V 394 w(the)30 b(con)m(v)m(ex)i(h)m(ull)d(of)h
FG(x)h FK(and)e FG(y)p 2380 1831 V 330 w FK(HULL)-10
b(V)p 2744 1798 28 4 v 33 w(I,)30 b(WHULL)-10 b(V)p 3266
1798 V 33 w(I)p 3466 1831 4 113 v 3483 1831 V 415 1835
3070 4 v 1027 2089 a(T)i(able)30 b(C.9:)41 b(Set)31 b(Op)s(erations)e
(for)h(In)m(terv)-5 b(al)30 b(V)-8 b(ectors)0 2429 y
Fv(Set)30 b(Op)s(erations)g(Involving)g(Interval)h(Matrices)0
2600 y FK(T)-8 b(able)30 b(C.10)h(lists)e(set)i(op)s(erations)f(for)g
(in)m(terv)-5 b(al)29 b(matrices.)p 191 2721 3519 4 v
189 2834 4 113 v 206 2834 V 257 2800 a(Enclosed)p 771
2834 V 214 w FG(A)h FK(is)g(enclosed)g(in)f FG(B)i FK(if)e
FG(A)c FJ(\022)g FG(B)p 2241 2834 V 342 w FK(GE,GB,SY,SB,)p
2944 2834 V 3001 2800 28 4 v 134 w(ENCM)p 3312 2800 V
33 w(I)p 3691 2834 4 113 v 3708 2834 V 189 2947 V 206
2947 V 771 2947 V 2241 2947 V 2292 2913 a(SP)-8 b(,TR,TB,TP)p
2944 2947 V 3691 2947 V 3708 2947 V 189 3060 V 206 3060
V 257 3026 a(In)m(terior)p 771 3060 V 266 w FG(A)30 b
FK(is)g(enclosed)g(in)f(the)h(in)m(terior)g(of)g FG(B)p
2241 3060 V 149 w FK(GE,GB,SY,SB,)p 2944 3060 V 3001
3026 28 4 v 134 w(INTERIORM)p 3583 3026 V 32 w(I)p 3691
3060 4 113 v 3708 3060 V 189 3172 V 206 3172 V 771 3172
V 2241 3172 V 2292 3139 a(SP)-8 b(,TR,TB,TP)p 2944 3172
V 3691 3172 V 3708 3172 V 189 3285 V 206 3285 V 257 3251
a(Disjoin)m(t)p 771 3285 V 252 w FG(A)30 b FK(and)g FG(B)h
FK(are)g(disjoin)m(t)d(if)i FG(A)20 b FJ(\\)g FG(B)25
b FK(=)g FJ(;)p 2241 3285 V 100 w FK(GE,GB,SY,SB,)p 2944
3285 V 3001 3251 28 4 v 134 w(DISJM)p 3316 3251 V 33
w(I)p 3691 3285 4 113 v 3708 3285 V 189 3398 V 206 3398
V 771 3398 V 2241 3398 V 2292 3364 a(SP)-8 b(,TR,TB,TP)p
2944 3398 V 3691 3398 V 3708 3398 V 189 3511 V 206 3511
V 257 3477 a(In)m(tersection)p 771 3511 V 100 w FG(B)26
b FJ( )f FG(A)20 b FJ(\\)g FG(B)p FK(,)31 b FG(C)25 b
FJ( )g FG(A)20 b FJ(\\)g FG(B)p 2241 3511 V 473 w FK(GE,GB,SY,SB,)p
2944 3511 V 3001 3477 28 4 v 134 w(INTERM)p 3412 3477
V 33 w(I,)p 3691 3511 4 113 v 3708 3511 V 189 3624 V
206 3624 V 771 3624 V 2241 3624 V 2292 3590 a(SP)-8 b(,TR,TB,TP)p
2944 3624 V 3001 3590 28 4 v 165 w(WINTERM)p 3505 3590
V 33 w(I)p 3691 3624 4 113 v 3708 3624 V 189 3737 V 206
3737 V 257 3703 a(Hull)p 771 3737 V 394 w(the)31 b(con)m(v)m(ex)h(h)m
(ull)c(of)i FG(A)h FK(and)e FG(B)p 2241 3737 V 373 w
FK(GE,GB,SY,SB,)p 2944 3737 V 3001 3703 28 4 v 134 w(HULLM)p
3366 3703 V 33 w(I,)p 3691 3737 4 113 v 3708 3737 V 189
3850 V 206 3850 V 771 3850 V 2241 3850 V 2292 3816 a(SP)-8
b(,TR,TB,TP)p 2944 3850 V 3001 3816 28 4 v 165 w(WHULLM)p
3459 3816 V 34 w(I)p 3691 3850 4 113 v 3708 3850 V 191
3853 3519 4 v 981 4107 a(T)g(able)30 b(C.10:)41 b(Set)31
b(Op)s(erations)e(for)h(In)m(terv)-5 b(al)30 b(Matrices)0
4447 y Fv(Utilit)m(y)f(F)m(unctions)i(Involving)f(Interval)h(V)m(ecto)m
(rs)0 4619 y FK(T)-8 b(able)30 b(C.11)h(lists)e(some)i(utilit)m(y)e(op)
s(erations)g(for)h(in)m(terv)-5 b(al)30 b(v)m(ectors.)0
4859 y Fv(Utilit)m(y)f(F)m(unctions)i(Involving)f(Interval)h(Matrices)0
5030 y FK(T)-8 b(able)30 b(C.12)h(lists)e(some)i(utilit)m(y)e(op)s
(erations)g(for)h(in)m(terv)-5 b(al)30 b(matrices.)-214
64 y FI(1)-214 177 y(2)-214 290 y(3)-214 403 y(4)-214
516 y(5)-214 628 y(6)-214 741 y(7)-214 854 y(8)-214 967
y(9)-230 1080 y(10)-230 1193 y(11)-230 1306 y(12)-230
1419 y(13)-230 1532 y(14)-230 1645 y(15)-230 1758 y(16)-230
1870 y(17)-230 1983 y(18)-230 2096 y(19)-230 2209 y(20)-230
2322 y(21)-230 2435 y(22)-230 2548 y(23)-230 2661 y(24)-230
2774 y(25)-230 2887 y(26)-230 3000 y(27)-230 3112 y(28)-230
3225 y(29)-230 3338 y(30)-230 3451 y(31)-230 3564 y(32)-230
3677 y(33)-230 3790 y(34)-230 3903 y(35)-230 4016 y(36)-230
4129 y(37)-230 4242 y(38)-230 4354 y(39)-230 4467 y(40)-230
4580 y(41)-230 4693 y(42)-230 4806 y(43)-230 4919 y(44)-230
5032 y(45)-230 5145 y(46)-230 5258 y(47)-230 5371 y(48)p
eop
%%Page: 224 234
224 233 bop 0 -165 a FK(224)1882 b FA(ANNEX)31 b(C.)61
b(JOURNAL)30 b(OF)g(DEVELOPMENT)p 767 3 2367 4 v 765
116 4 113 v 782 116 V 833 82 a FK(Empt)m(y)g(elemen)m(t)p
1486 116 V 101 w Fy(k)j FK(if)c FG(x)1757 97 y Fw(k)1824
82 y FK(=)c FJ(;)p FK(;)31 b(or)g FJ(\000)p FK(1)p 2297
116 V 100 w(EMPTYELEV)p 2944 82 28 4 v 32 w(I)p 3115
116 4 113 v 3132 116 V 765 229 V 782 229 V 833 195 a(Left)g(endp)s(oin)
m(t)p 1486 229 V 164 w Fy(v)d FJ( )d Fy(x)p 1726 208
52 4 v 2297 229 4 113 v 571 w FK(INFV)p 2582 195 28 4
v 33 w(I)p 3115 229 4 113 v 3132 229 V 765 342 V 782
342 V 833 308 a(Righ)m(t)30 b(endp)s(oin)m(t)p 1486 342
V 104 w Fy(v)e FJ( )p 1726 259 52 4 v 25 w Fy(x)p 2297
342 4 113 v 571 w FK(SUPV)p 2603 308 28 4 v 32 w(I)p
3115 342 4 113 v 3132 342 V 765 455 V 782 455 V 833 421
a(Midp)s(oin)m(t)p 1486 455 V 337 w Fy(v)g FJ( )d FK(\()p
Fy(x)p 1761 434 52 4 v 21 w FK(+)p 1925 372 V 20 w Fy(x)p
FK(\))p Fy(=)p FK(2)p 2297 455 4 113 v 247 w(MID)m(V)p
2604 421 28 4 v 34 w(I)p 3115 455 4 113 v 3132 455 V
765 568 V 782 568 V 833 534 a(Width)p 1486 568 V 449
w Fy(v)j FJ( )p 1726 485 52 4 v 25 w Fy(x)20 b FJ(\000)g
Fy(x)p 1889 547 V 2297 568 4 113 v 408 w FK(WIDTHV)p
2751 534 28 4 v 33 w(I)p 3115 568 4 113 v 3132 568 V
765 681 V 782 681 V 833 647 a(Construct)p 1486 681 V
310 w FG(x)25 b FJ( )g Fy(u;)15 b(v)p 2297 681 V 479
w FK(CONSTR)m(UCTV)p 3008 647 28 4 v 31 w(I)p 3115 681
4 113 v 3132 681 V 767 684 2367 4 v 938 938 a(T)-8 b(able)30
b(C.11:)41 b(Utilit)m(y)30 b(Op)s(erations)e(for)j(In)m(terv)-5
b(al)30 b(V)-8 b(ectors)p 50 1059 3800 4 v 48 1172 4
113 v 65 1172 V 117 1138 a(Empt)m(y)30 b(elemen)m(t)p
770 1172 V 100 w(if)g FG(A)g FK(has)g(an)g(empt)m(y)h(in)m(terv)-5
b(al)30 b(elemen)m(t)p 2262 1172 V 100 w(GE,GB,SY,SB,)p
2965 1172 V 3022 1138 28 4 v 134 w(EMPTYELEM)p 3660 1138
V 32 w(I)p 3831 1172 4 113 v 3848 1172 V 48 1285 V 65
1285 V 770 1285 V 2262 1285 V 2314 1251 a(SP)-8 b(,TR,TB,TP)p
2965 1285 V 3831 1285 V 3848 1285 V 48 1398 V 65 1398
V 117 1364 a(Left)30 b(endp)s(oin)m(t)p 770 1398 V 164
w Fy(C)i FJ( )25 b Fy(A)p 1034 1377 69 4 v 2262 1398
4 113 v 1212 w FK(GE,GB,SY,SB,)p 2965 1398 V 3022 1364
28 4 v 134 w(INFM)p 3298 1364 V 33 w(I)p 3831 1398 4
113 v 3848 1398 V 48 1510 V 65 1510 V 770 1510 V 2262
1510 V 2314 1477 a(SP)-8 b(,TR,TB,TP)p 2965 1510 V 3831
1510 V 3848 1510 V 48 1623 V 65 1623 V 117 1589 a(Righ)m(t)30
b(endp)s(oin)m(t)p 770 1623 V 103 w Fy(C)i FJ( )p 1034
1517 69 4 v 25 w Fy(A)p 2262 1623 4 113 v 1212 w FK(GE,GB,SY,SB,)p
2965 1623 V 3022 1589 28 4 v 134 w(SUPM)p 3319 1589 V
32 w(I)p 3831 1623 4 113 v 3848 1623 V 48 1736 V 65 1736
V 770 1736 V 2262 1736 V 2314 1702 a(SP)-8 b(,TR,TB,TP)p
2965 1736 V 3831 1736 V 3848 1736 V 48 1849 V 65 1849
V 117 1815 a(Midp)s(oin)m(t)p 770 1849 V 336 w Fy(C)32
b FJ( )25 b FK(\()p Fy(A)p 1069 1828 69 4 v 21 w FK(+)p
1249 1743 V 20 w Fy(A)p FK(\))p Fy(=)p FK(2)p 2262 1849
4 113 v 872 w(GE,GB,SY,SB,)p 2965 1849 V 3022 1815 28
4 v 134 w(MIDM)p 3323 1815 V 33 w(I)p 3831 1849 4 113
v 3848 1849 V 48 1962 V 65 1962 V 770 1962 V 2262 1962
V 2314 1928 a(SP)-8 b(,TR,TB,TP)p 2965 1962 V 3831 1962
V 3848 1962 V 48 2075 V 65 2075 V 117 2041 a(Width)p
770 2075 V 448 w Fy(C)32 b FJ( )p 1034 1969 69 4 v 25
w Fy(A)21 b FJ(\000)e Fy(A)p 1213 2054 V 2262 2075 4
113 v 1033 w FK(GE,GB,SY,SB,)p 2965 2075 V 3022 2041
28 4 v 134 w(WIDTHM)p 3467 2041 V 33 w(I)p 3831 2075
4 113 v 3848 2075 V 48 2188 V 65 2188 V 117 2154 a(Construct)p
770 2188 V 309 w FG(A)26 b FJ( )f Fy(B)5 b(;)15 b(C)p
2262 2188 V 1093 w FK(GE,GB,SY,SB,)p 2965 2188 V 3022
2154 28 4 v 134 w(CONSTR)m(UCTM)p 3724 2154 V 31 w(I)p
3831 2188 4 113 v 3848 2188 V 48 2301 V 65 2301 V 770
2301 V 2262 2301 V 2314 2267 a(SP)-8 b(,TR,TB,TP)p 2965
2301 V 3831 2301 V 3848 2301 V 50 2304 3800 4 v 1337
2558 a(T)g(able)30 b(C.12:)42 b(Utilit)m(y)29 b(Op)s(erations)0
2833 y Fx(C.4.3)98 b(Interface)33 b(Issues)0 3005 y Fv(Naming)e
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(the)g(same)g(as)g(describ)s(ed)e(in)h(section)h(2.3.1)h(except)g(that)
f(the)g(su\016x)p 3569 3177 28 4 v 63 w(I)g(\(or)p 3812
3177 V 63 w(i\))0 3289 y(is)e(added)h(to)h(indicate)f(an)g(in)m(terv)-5
b(al)29 b(BLAS)i(routine.)0 3530 y Fv(Interface)g(Issues)g(fo)m(r)g(F)m
(o)m(rtran)g(95)0 3701 y(Design)f(of)h(the)f(F)m(o)m(rtran)h(95)h
(Interfaces)0 3873 y FK(The)24 b(F)-8 b(ortran)26 b(95)f(binding)d(is)h
(de\014ned)h(in)f(a)i(mo)s(dule.)37 b(The)25 b(sp)s(eci\014c)e(in)m
(terfaces)i(in)f(this)f(mo)s(dule)g(should)g(declare)0
3986 y(the)31 b(default)e(in)m(terv)-5 b(al)30 b(data)h(t)m(yp)s(e)f
(as)h FD(TYPE\(INTERVAL\).)227 4198 y Fz(A)-5 b(dvic)g(e)38
b(to)g(implementors:)53 b FK(In)35 b(the)h(F)-8 b(ortran)36
b(95)h(in)m(terfaces,)h(it)d(is)g(assumed)g(that)h FD(INTERVAL)e
FK(is)227 4311 y(a)43 b(deriv)m(ed)f(t)m(yp)s(e.)77 b(Ho)m(w)m(ev)m
(er,)47 b(in)41 b(compilers)g(that)i(supp)s(ort)e(an)h(in)m(trinsic)e
(in)m(terv)-5 b(al)42 b(t)m(yp)s(e,)k(it)c(is)227 4424
y(recommended)35 b(that)g(an)g(alternate)g(mo)s(dule)e(that)j(con)m
(tains)f(appropriately)e(mo)s(di\014ed)f(declara-)227
4537 y(tions)g(also)g(b)s(e)g(supplied.)43 b(F)-8 b(or)33
b(example,)f FD(TYPE\(INTERVAL\),)44 b(INTENT\(IN\))h(::)95
b(ALPHA)31 b FK(could)227 4650 y(b)s(ecome)g FD(INTERVAL,)45
b(INTENT\(IN\))g(::)95 b(ALPHA)29 b FK(in)g(a)i(recommended)f
(alternate)h(mo)s(dule.)0 4862 y(The)h(F)-8 b(ortran)33
b(95)g(in)m(terv)-5 b(al)31 b(BLAS)h(routines)f(are)i(consisten)m(t)g
(with)e(regard)h(to)h(generic)f(in)m(terfaces,)i(precision,)0
4975 y(rank,)f(assumed-shap)s(e)f(arra)m(ys,)i(deriv)m(ed)f(t)m(yp)s
(es,)g(op)s(erator)h(argumen)m(ts)f(and)f FD(CMACH)g
FK(v)-5 b(alues,)33 b(and)g(error)f(han-)0 5088 y(dling)i(as)j(describ)
s(ed)d(in)h(section)i(2.4)g(of)g(this)e(do)s(cumen)m(t.)59
b(Ho)m(w)m(ev)m(er,)40 b(in)35 b(the)h(in)m(terv)-5 b(al)36
b(BLAS,)g Fy(\013)h FK(and)f Fy(\014)42 b FK(are)0 5201
y(in)m(terv)-5 b(als;)30 b(and)f(their)h(default)f(v)-5
b(alues)30 b(are)h FD(alpha)46 b(=)i([1,1],)e(beta)g(=)i([0,0])p
FK(.)0 5314 y(Error)29 b(handling)f(is)i(as)g(de\014ned)f(in)g(section)
i(2.4.6.)4084 64 y FI(1)4084 177 y(2)4084 290 y(3)4084
403 y(4)4084 516 y(5)4084 628 y(6)4084 741 y(7)4084 854
y(8)4084 967 y(9)4069 1080 y(10)4069 1193 y(11)4069 1306
y(12)4069 1419 y(13)4069 1532 y(14)4069 1645 y(15)4069
1758 y(16)4069 1870 y(17)4069 1983 y(18)4069 2096 y(19)4069
2209 y(20)4069 2322 y(21)4069 2435 y(22)4069 2548 y(23)4069
2661 y(24)4069 2774 y(25)4069 2887 y(26)4069 3000 y(27)4069
3112 y(28)4069 3225 y(29)4069 3338 y(30)4069 3451 y(31)4069
3564 y(32)4069 3677 y(33)4069 3790 y(34)4069 3903 y(35)4069
4016 y(36)4069 4129 y(37)4069 4242 y(38)4069 4354 y(39)4069
4467 y(40)4069 4580 y(41)4069 4693 y(42)4069 4806 y(43)4069
4919 y(44)4069 5032 y(45)4069 5145 y(46)4069 5258 y(47)4069
5371 y(48)p eop
%%Page: 225 235
225 234 bop 0 -165 a FA(C.4.)71 b(INTER)-10 b(V)g(AL)30
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eop
%%Page: 228 238
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eop
%%Page: 230 240
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y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084 967 y(9)4069
1080 y(10)4069 1193 y(11)4069 1306 y(12)4069 1419 y(13)4069
1532 y(14)4069 1645 y(15)4069 1758 y(16)4069 1870 y(17)4069
1983 y(18)4069 2096 y(19)4069 2209 y(20)4069 2322 y(21)4069
2435 y(22)4069 2548 y(23)4069 2661 y(24)4069 2774 y(25)4069
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5145 y(46)4069 5258 y(47)4069 5371 y(48)p eop
%%Page: 231 241
231 240 bop 0 -165 a FA(C.4.)71 b(INTER)-10 b(V)g(AL)30
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Fu(\024)p Fw(i<n)967 3637 y FJ(fj)p Fy(x)p 1037 3650
52 4 v 1090 3658 a Fw(i)1118 3637 y FJ(j)p Fy(;)15 b
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V Fy(x)2896 3652 y Fw(k)2939 3637 y FJ(jg)26 b FK(=)f
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3651 y Fw(i)3829 3637 y FJ(jg)0 3863 y FK(The)21 b(routine)f
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5287 y(where)609 5400 y(x)h(has)e(shape)h(\(n\))-214
64 y FI(1)-214 177 y(2)-214 290 y(3)-214 403 y(4)-214
516 y(5)-214 628 y(6)-214 741 y(7)-214 854 y(8)-214 967
y(9)-230 1080 y(10)-230 1193 y(11)-230 1306 y(12)-230
1419 y(13)-230 1532 y(14)-230 1645 y(15)-230 1758 y(16)-230
1870 y(17)-230 1983 y(18)-230 2096 y(19)-230 2209 y(20)-230
2322 y(21)-230 2435 y(22)-230 2548 y(23)-230 2661 y(24)-230
2774 y(25)-230 2887 y(26)-230 3000 y(27)-230 3112 y(28)-230
3225 y(29)-230 3338 y(30)-230 3451 y(31)-230 3564 y(32)-230
3677 y(33)-230 3790 y(34)-230 3903 y(35)-230 4016 y(36)-230
4129 y(37)-230 4242 y(38)-230 4354 y(39)-230 4467 y(40)-230
4580 y(41)-230 4693 y(42)-230 4806 y(43)-230 4919 y(44)-230
5032 y(45)-230 5145 y(46)-230 5258 y(47)-230 5371 y(48)p
eop
%%Page: 232 242
232 241 bop 0 -165 a FK(232)1882 b FA(ANNEX)31 b(C.)61
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b FJ( )c FK(max)p FJ(fj)p Fy(x)p 2658 1619 52 4 v 2711
1626 a Fw(k)2753 1606 y FJ(j)p Fy(;)15 b FJ(j)p 2843
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1620 y Fw(i)3829 1606 y FJ(jg)0 1832 y FK(The)44 b(routine)g
FD(AMAX)p 727 1832 29 4 v 33 w(VAL)p 904 1832 V 34 w(I)g
FK(\014nds)f(the)i(index)e(of)i(the)g(comp)s(onen)m(t)g(of)g(an)g(in)m
(terv)-5 b(al)44 b(v)m(ector)i(suc)m(h)e(that)i(the)0
1944 y(absolute)38 b(v)-5 b(alue)38 b(of)h(the)f(lo)m(w)m(er)h(or)g
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(and)f(passed)f(to)j(the)e(error)g(handler.)136 2609
y FJ(\017)46 b FK(F)-8 b(ortran)31 b(95)h(binding:)514
2858 y FD(SUBROUTINE)45 b(amax_val_i\()f(x,)k(k,)f(r)g(\))609
2971 y(TYPE\(INTERVAL\)\(<wp>\),)42 b(INTENT\(IN\))j(::)i(x\(:\))609
3084 y(INTEGER,)f(INTENT\(OUT\))e(::)k(k)609 3197 y(REAL)f(\(<wp>\),)f
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3923 y FD(SUBROUTINE)45 b(BLAS_AMAX_VAL_I\()e(N,)k(X,)g(INCX,)g(K,)g(R)
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y(<type>)571 b(X\()47 b(2,)g(*)h(\))514 4262 y(<type>)571
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y FD(void)47 b(BLAS_xamax_val_i\()c(int)k(n,)g(const)f
(<interval_array>)e(x,)j(int)g(incx,)f(int)h(k,)1325
4849 y(SCALAR_INOUT)92 b(r)48 b(\);)p 0 5048 3900 4 v
0 5195 a FK(SUMSQ)p 329 5195 28 4 v 32 w(I)30 b(\(Sum)g(of)g(squares\))
2118 b(\()p Fy(scl)r(;)15 b(ssq)s FK(\))25 b FJ( )3703
5131 y Ft(P)3805 5195 y FG(x)3861 5162 y FC(2)3861 5219
y Fw(i)4084 64 y FI(1)4084 177 y(2)4084 290 y(3)4084
403 y(4)4084 516 y(5)4084 628 y(6)4084 741 y(7)4084 854
y(8)4084 967 y(9)4069 1080 y(10)4069 1193 y(11)4069 1306
y(12)4069 1419 y(13)4069 1532 y(14)4069 1645 y(15)4069
1758 y(16)4069 1870 y(17)4069 1983 y(18)4069 2096 y(19)4069
2209 y(20)4069 2322 y(21)4069 2435 y(22)4069 2548 y(23)4069
2661 y(24)4069 2774 y(25)4069 2887 y(26)4069 3000 y(27)4069
3112 y(28)4069 3225 y(29)4069 3338 y(30)4069 3451 y(31)4069
3564 y(32)4069 3677 y(33)4069 3790 y(34)4069 3903 y(35)4069
4016 y(36)4069 4129 y(37)4069 4242 y(38)4069 4354 y(39)4069
4467 y(40)4069 4580 y(41)4069 4693 y(42)4069 4806 y(43)4069
4919 y(44)4069 5032 y(45)4069 5145 y(46)4069 5258 y(47)4069
5371 y(48)p eop
%%Page: 233 243
233 242 bop 0 -165 a FA(C.4.)71 b(INTER)-10 b(V)g(AL)30
b(BLAS)2793 b FK(233)0 91 y(The)30 b(routine)f FD(SUMSQ)p
746 91 29 4 v 33 w(I)h FK(returns)f(the)i(in)m(terv)-5
b(als)29 b Fy(scl)k FK(and)c Fy(ssq)k FK(suc)m(h)d(that)1223
335 y Fy(scl)1334 298 y FC(2)1394 335 y FJ(\003)21 b
Fy(ssq)27 b FK(=)e Fy(scal)r(e)1911 298 y FC(2)1971 335
y FJ(\003)20 b Fy(sumsq)j FK(+)2409 229 y Fw(n)p Fu(\000)p
FC(1)2415 254 y Ft(X)2418 437 y Fw(i)p FC(=0)2557 335
y FG(x)2612 298 y FC(2)2612 358 y Fw(i)2651 335 y Fy(:)0
577 y FK(The)36 b(v)-5 b(alue)36 b(of)g Fy(sumsq)j FK(is)c(assumed)h
(to)h(b)s(e)f(at)h(least)g(unit)m(y)e(and)h(the)h(v)-5
b(alue)36 b(of)g Fy(ssq)j FK(will)34 b(then)i(satisfy)g(1)p
Fy(:)p FK(0)g FJ(\024)0 690 y Fy(ssq)27 b FJ(\024)e FK(\()p
Fy(sumsq)e FK(+)d Fy(n)p FK(\).)40 b(It)31 b(is)e(assumed)h(that)h
Fy(scal)r(e)f FK(is)g(to)h(b)s(e)f(non-negativ)m(e,)h(and)f
Fy(scl)i FK(returns)d(the)i(v)-5 b(alue)1492 916 y Fy(scl)27
b FK(=)47 b(max)1724 974 y FC(0)p Fu(\024)p Fw(i<n)1936
916 y FK(\()p Fy(scal)r(e;)15 b FJ(j)p FG(x)2294 930
y Fw(i)2322 916 y FJ(j)p FK(\))p Fy(:)0 1104 y(scal)r(e)21
b FK(and)g Fy(sumsq)h FK(m)m(ust)f(b)s(e)g(supplied)c(on)k(en)m(try)h
(in)d FD(scl)h FK(and)h FD(ssq)f FK(resp)s(ectiv)m(ely)-8
b(.)37 b FD(scl)21 b FK(and)f FD(ssq)g FK(are)h(o)m(v)m(erwritten)0
1217 y(b)m(y)28 b Fy(scl)h FK(and)e Fy(ssq)j FK(resp)s(ectiv)m(ely)-8
b(.)39 b(If)28 b FD(n)f FK(is)g(less)g(than)g(or)h(equal)f(to)h(zero,)i
(this)c(routine)h(returns)f(immediately)g(with)0 1330
y FD(scl)32 b FK(and)g FD(ssq)g FK(unc)m(hanged.)49 b(As)33
b(describ)s(ed)d(in)i(section)h(2.5.3,)j(the)d(v)-5 b(alue)32
b Fv(incx)h FK(less)g(than)f(zero)i(is)e(p)s(ermitted.)0
1443 y(Ho)m(w)m(ev)m(er,)h(if)c Fv(incx)h FK(is)g(equal)g(to)h(zero,)g
(an)f(error)g(\015ag)h(is)f(set)g(and)g(passed)g(to)h(the)g(error)f
(handler.)136 1625 y FJ(\017)46 b FK(F)-8 b(ortran)31
b(95)h(binding:)514 1840 y FD(SUBROUTINE)45 b(sumsq_i\()g(x,)i(ssq,)g
(scl)g(\))609 1952 y(TYPE\(INTERVAL\)\(<wp>\),)42 b(INTENT\(IN\))j(::)i
(x\(:\))609 2065 y(TYPE\(INTERVAL\)\(<wp>\),)42 b(INTENT\(INOUT\))i(::)
j(ssq,)g(scl)514 2178 y(where)609 2291 y(x)h(has)e(shape)h(\(n\))136
2506 y FJ(\017)f FK(F)-8 b(ortran)31 b(77)h(binding:)514
2720 y FD(SUBROUTINE)45 b(BLAS_xSUMSQ_I\()f(N,)j(X,)g(INCX,)f(SSQ,)h
(SCL)g(\))514 2833 y(INTEGER)523 b(INCX,)46 b(N)514 2946
y(<type>)571 b(X\()47 b(2,)g(*)h(\))514 3059 y(<type>)571
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FK(C)30 b(binding:)227 3488 y FD(void)47 b(BLAS_xsumsq_i\()d(int)j(n,)g
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3601 y(<interval>)g(scl)i(\);)0 3815 y Fv(Interval)30
b(V)m(ecto)m(r)i(Op)s(erations)0 3987 y FK(RSCALE)p 376
3987 28 4 v 32 w(I)e(\(Recipro)s(cal)g(Scale)g(of)h(an)f(in)m(terv)-5
b(al)29 b(v)m(ector\))1528 b FG(x)26 b FJ( )f FG(x)p
Fy(=\013)0 4213 y FK(The)h(routine)g FD(RSCALE)p 787
4213 29 4 v 33 w(I)g FK(up)s(dates)g(the)h(en)m(tries)g(of)g(an)f(in)m
(terv)-5 b(al)26 b(v)m(ector)j FG(x)d FK(b)m(y)h(the)g(scale)g(in)m
(terv)-5 b(al)26 b(1)p Fy(=\013)i FK(pro)m(vided)0 4326
y(that)37 b(0)e FJ(62)f Fy(\013)p FK(.)59 b(If)35 b Fv(n)h
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4439 y(section)e(2.5.3,)i(the)e(v)-5 b(alue)31 b Fv(incx)g
FK(less)g(than)g(zero)i(is)d(p)s(ermitted.)43 b(Ho)m(w)m(ev)m(er,)35
b(if)30 b Fv(incx)i FK(is)e(equal)i(to)g(zero,)h(an)e(error)0
4552 y(\015ag)g(is)e(set)i(and)f(passed)g(to)h(the)f(error)g(handler.)
136 4734 y FJ(\017)46 b FK(F)-8 b(ortran)31 b(95)h(binding:)514
4948 y FD(SUBROUTINE)45 b(rscale_i\()g(alpha,)h(x)h(\))609
5061 y(TYPE\(INTERVAL\)\(<wp>\),)42 b(INTENT\(INOUT\))i(::)j(x\(:\))609
5174 y(TYPE\(INTERVAL\)\(<wp>\),)42 b(INTENT\(IN\))j(::)i(alpha)514
5287 y(where)609 5400 y(x)h(has)e(shape)h(\(n\))-214
64 y FI(1)-214 177 y(2)-214 290 y(3)-214 403 y(4)-214
516 y(5)-214 628 y(6)-214 741 y(7)-214 854 y(8)-214 967
y(9)-230 1080 y(10)-230 1193 y(11)-230 1306 y(12)-230
1419 y(13)-230 1532 y(14)-230 1645 y(15)-230 1758 y(16)-230
1870 y(17)-230 1983 y(18)-230 2096 y(19)-230 2209 y(20)-230
2322 y(21)-230 2435 y(22)-230 2548 y(23)-230 2661 y(24)-230
2774 y(25)-230 2887 y(26)-230 3000 y(27)-230 3112 y(28)-230
3225 y(29)-230 3338 y(30)-230 3451 y(31)-230 3564 y(32)-230
3677 y(33)-230 3790 y(34)-230 3903 y(35)-230 4016 y(36)-230
4129 y(37)-230 4242 y(38)-230 4354 y(39)-230 4467 y(40)-230
4580 y(41)-230 4693 y(42)-230 4806 y(43)-230 4919 y(44)-230
5032 y(45)-230 5145 y(46)-230 5258 y(47)-230 5371 y(48)p
eop
%%Page: 234 244
234 243 bop 0 -165 a FK(234)1882 b FA(ANNEX)31 b(C.)61
b(JOURNAL)30 b(OF)g(DEVELOPMENT)136 91 y FJ(\017)46 b
FK(F)-8 b(ortran)31 b(77)h(binding:)514 317 y FD(SUBROUTINE)45
b(BLAS_xRSCALE_I\()e(N,)k(ALPHA,)g(X,)g(INCX)f(\))514
429 y(INTEGER)523 b(INCX,)46 b(N)514 542 y(<type>)571
b(ALPHA\()46 b(2)h(\))514 655 y(<type>)571 b(X\()47 b(2,)g(*)h(\))136
880 y FJ(\017)e FK(C)30 b(binding:)227 1084 y FD(void)47
b(BLAS_xrscale_i\()d(int)i(n,)i(<interval>)d(alpha,)h(<interval_array>)
d(x,)k(int)g(incx)g(\);)p 0 1270 3900 4 v 0 1409 a FK(AXPBY)p
335 1409 28 4 v 34 w(I)30 b(\(Scaled)g(v)m(ector)i(accum)m(ulation\))
1786 b FG(y)26 b FJ( )f Fy(\013)p FG(x)c FK(+)f Fy(\014)5
b FG(y)0 1634 y FK(The)31 b(routine)g FD(AXPBY)p 749
1634 29 4 v 33 w(I)g FK(scales)h(the)g(in)m(terv)-5 b(al)31
b(v)m(ector)i FG(x)f FK(b)m(y)f(the)h(in)m(terv)-5 b(al)31
b Fy(\013)h FK(and)f(the)h(in)m(terv)-5 b(al)31 b(v)m(ector)i
FG(y)f FK(b)m(y)g Fy(\014)5 b FK(,)0 1747 y(adds)36 b(these)h(t)m(w)m
(o)h(v)m(ectors)g(to)g(one)f(another)g(and)f(stores)h(the)g(result)f
(in)f(the)i(v)m(ector)h FG(y)p FK(.)60 b(If)36 b FD(n)h
FK(is)e(less)h(than)h(or)0 1860 y(equal)e(to)i(zero,)h(or)e(if)f
Fy(\013)h FK(is)f(equal)g(to)i([0,0])h(and)d Fy(\014)41
b FK(equal)35 b(to)i([1,1],)i(this)c(routine)f(returns)h(immediately)-8
b(.)56 b(As)0 1973 y(describ)s(ed)27 b(in)g(section)i(2.5.3,)j(the)d(v)
-5 b(alue)28 b Fv(incx)h FK(or)g Fv(incy)f FK(less)g(than)h(zero)h(is)e
(p)s(ermitted.)38 b(Ho)m(w)m(ev)m(er,)32 b(if)c(either)g
Fv(incx)0 2086 y FK(or)i Fv(incy)h FK(is)e(equal)h(to)h(zero,)h(an)e
(error)g(\015ag)g(is)g(set)h(and)f(passed)f(to)j(the)e(error)g
(handler.)136 2277 y FJ(\017)46 b FK(F)-8 b(ortran)31
b(95)h(binding:)561 2503 y FD(SUBROUTINE)45 b(axpby_i\()h(x,)h(y)h([,)f
(alpha])f([,)h(beta])f(\))609 2616 y(<type>\(<wp>\),)e(INTENT)i(\(IN\))
h(::)g(x)h(\(:\))609 2728 y(<type>\(<wp>\),)c(INTENT)i(\(INOUT\))g(::)h
(y)h(\(:\))609 2841 y(<type>\(<wp>\),)c(INTENT)i(\(IN\),)h(OPTIONAL)e
(::)i(alpha,)g(beta)514 2954 y(where)609 3067 y(x)h(and)e(y)i(have)f
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b(77)h(binding:)514 3518 y FD(SUBROUTINE)45 b(BLAS_xAXPBY_I\()f(N,)j
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y(INTEGER)570 b(INCX,)47 b(INCY,)f(N)514 3743 y(<type>)618
b(ALPHA\()47 b(2)g(\),)g(BETA\()g(2)g(\))514 3856 y(<type>)618
b(X\()48 b(2,)f(*)g(\),)g(Y\()h(2,)f(*)g(\))136 4081
y FJ(\017)f FK(C)30 b(binding:)227 4285 y FD(void)47
b(BLAS_xaxpby_i\()d(int)j(n,)g(<interval>)e(alpha,)h(<interval_array>)d
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e(y,)j(int)g(incy)f(\);)p 0 4583 3900 4 v 0 4723 a FK(W)-10
b(AXPBY)p 418 4723 28 4 v 34 w(I)30 b(\(Scaled)g(v)m(ector)i
(addition\))1881 b FG(w)25 b FJ( )g Fy(\013)p FG(x)c
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FD(WAXPBY)p 805 4948 29 4 v 32 w(I)g FK(scales)h(the)g(in)m(terv)-5
b(al)35 b(v)m(ector)i FG(x)e FK(b)m(y)h(the)f(in)m(terv)-5
b(al)35 b Fy(\013)h FK(and)f(the)h(in)m(terv)-5 b(al)34
b(v)m(ector)j FG(y)f FK(b)m(y)0 5061 y Fy(\014)5 b FK(,)31
b(adds)f(these)h(t)m(w)m(o)h(v)m(ectors)g(to)g(one)f(another)g(and)f
(stores)h(the)g(result)f(in)f(the)i(v)m(ector)h FG(w)p
FK(.)41 b(If)30 b FD(n)h FK(is)f(less)f(than)i(or)0 5174
y(equal)c(to)h(zero,)h(this)e(routine)f(returns)h(immediately)-8
b(.)38 b(As)28 b(describ)s(ed)d(in)h(section)i(2.5.3,)i(the)e(v)-5
b(alue)27 b Fv(incx)g FK(or)h Fv(incy)0 5287 y FK(or)h
Fv(incw)f FK(less)g(than)h(zero)g(is)f(p)s(ermitted.)39
b(Ho)m(w)m(ev)m(er,)31 b(if)d(either)g Fv(incx)h FK(or)f
Fv(incy)h FK(or)g Fv(incw)f FK(is)g(equal)g(to)i(zero,)g(an)e(error)0
5400 y(\015ag)j(is)e(set)i(and)f(passed)g(to)h(the)f(error)g(handler.)
4084 64 y FI(1)4084 177 y(2)4084 290 y(3)4084 403 y(4)4084
516 y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084 967
y(9)4069 1080 y(10)4069 1193 y(11)4069 1306 y(12)4069
1419 y(13)4069 1532 y(14)4069 1645 y(15)4069 1758 y(16)4069
1870 y(17)4069 1983 y(18)4069 2096 y(19)4069 2209 y(20)4069
2322 y(21)4069 2435 y(22)4069 2548 y(23)4069 2661 y(24)4069
2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
3677 y(33)4069 3790 y(34)4069 3903 y(35)4069 4016 y(36)4069
4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 235 245
235 244 bop 0 -165 a FA(C.4.)71 b(INTER)-10 b(V)g(AL)30
b(BLAS)2793 b FK(235)136 91 y FJ(\017)46 b FK(F)-8 b(ortran)31
b(95)h(binding:)561 325 y FD(SUBROUTINE)45 b(waxpby_i\()h(x,)h(y,)g(w)g
([,)h(alpha])e([,)h(beta])f(\))609 437 y(<type>\(<wp>\),)e(INTENT)i
(\(IN\))h(::)g(x\(:\),)g(y\(:\))609 550 y(<type>\(<wp>\),)d(INTENT)i
(\(OUT\))h(::)g(w\(:\))609 663 y(<type>\(<wp>\),)d(INTENT)i(\(IN\),)h
(OPTIONAL)e(::)i(alpha,)g(beta)514 776 y(where)609 889
y(x,)g(y)h(and)f(w)g(have)g(shape)f(\(n\))136 1122 y
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y FD(SUBROUTINE)45 b(BLAS_xWAXPBY_I\()e(N,)k(ALPHA,)g(X,)g(INCX,)f
(BETA,)g(Y,)i(INCY,)e(W,)466 1469 y($)1288 b(INCW)47
b(\))514 1581 y(INTEGER)570 b(INCW,)47 b(INCX,)f(INCY,)h(N)514
1694 y(<type>)618 b(ALPHA\()47 b(2)g(\),)g(BETA\()g(2)g(\))514
1807 y(<type>)618 b(W\()48 b(2,)f(*)g(\),)g(X\()h(2,)f(*)g(\),)g(Y\()h
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2251 y FD(void)47 b(BLAS_wxaxpby_i\()d(int)i(n,)i(<interval>)d(alpha,)h
(const)g(<interval_array>)d(x,)1230 2364 y(int)j(incx,)h(<interval>)e
(beta,)h(const)h(<interval_array>)c(y,)1230 2477 y(int)j(incy,)h
(<interval_array>)c(w,)k(int)g(incw)g(\);)p 0 2669 3900
4 v 0 2808 a FK(CANCEL)p 392 2808 28 4 v 32 w(I)30 b(\(Scaled)g
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FG(a)27 b FJ(\011)f FG(b)43 b FK(=)e([)p Fy(a)p 3317
3047 49 4 v 28 w FJ(\000)26 b Fy(b)p 3490 3047 40 4 v(;)p
3569 2985 49 4 v 15 w(a)i FJ(\000)p 3742 2961 40 4 v
26 w Fy(b)p FK(])41 b(if)0 3147 y(\()p Fy(a)p 35 3160
49 4 v 16 w FJ(\000)15 b Fy(b)p 185 3160 40 4 v 1 w FK(\))25
b FJ(\024)g FK(\()p 416 3098 49 4 v Fy(a)16 b FJ(\000)p
567 3074 40 4 v 16 w Fy(b)p FK(\);)29 b(Otherwise,)e
FJ(;)p FK(.)41 b(The)27 b(routine)h FD(CANCEL)p 2049
3147 29 4 v 32 w(I)g FK(scales)g(the)h(in)m(terv)-5 b(al)27
b(v)m(ector)j FG(x)e FK(b)m(y)g(the)g(in)m(terv)-5 b(al)28
b Fy(\013)0 3260 y FK(and)g(the)i(in)m(terv)-5 b(al)28
b(v)m(ector)i FG(y)f FK(b)m(y)g Fy(\014)5 b FK(,)30 b(up)s(dates)e
FG(y)1644 3282 y Fw(i)1701 3260 y FK(with)g Fy(\013)p
FG(x)2020 3274 y Fw(i)2066 3260 y FJ(\011)17 b Fy(\014)5
b FG(y)2266 3282 y Fw(i)2294 3260 y FK(,)29 b FJ(8)p
FK(0)c FJ(\024)g Fy(i)h(<)f(n)p FK(.)40 b(If)28 b FD(n)h
FK(is)f(less)g(than)h(or)g(equal)f(to)0 3373 y(zero,)g(this)c(routine)h
(returns)f(immediately)-8 b(.)38 b(As)26 b(describ)s(ed)d(in)h(section)
i(2.5.3,)j(the)d(v)-5 b(alue)25 b Fv(incx)g FK(or)h Fv(incy)f
FK(less)g(than)0 3486 y(zero)31 b(is)e(p)s(ermitted.)39
b(Ho)m(w)m(ev)m(er,)32 b(if)d(either)g Fv(incx)h FK(or)g
Fv(incy)g FK(is)f(equal)h(to)g(zero,)h(an)f(error)g(\015ag)g(is)f(set)h
(and)g(passed)f(to)0 3599 y(the)i(error)f(handler.)136
3797 y FJ(\017)46 b FK(F)-8 b(ortran)31 b(95)h(binding:)561
4030 y FD(SUBROUTINE)45 b(cancel_i\()h(x,)h(y)g([,)g(alpha])g([,)g
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(\(:\))609 4256 y(<type>\(<wp>\),)c(INTENT)i(\(INOUT\))g(::)h(y)h
(\(:\))609 4369 y(<type>\(<wp>\),)c(INTENT)i(\(IN\),)h(OPTIONAL)e(::)i
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b(INCY,)f(N)514 5287 y(<type>)618 b(ALPHA\()47 b(2)g(\),)g(BETA\()g(2)g
(\))514 5400 y(<type>)618 b(X\()48 b(2,)f(*)g(\),)g(Y\()h(2,)f(*)g(\))
-214 64 y FI(1)-214 177 y(2)-214 290 y(3)-214 403 y(4)-214
516 y(5)-214 628 y(6)-214 741 y(7)-214 854 y(8)-214 967
y(9)-230 1080 y(10)-230 1193 y(11)-230 1306 y(12)-230
1419 y(13)-230 1532 y(14)-230 1645 y(15)-230 1758 y(16)-230
1870 y(17)-230 1983 y(18)-230 2096 y(19)-230 2209 y(20)-230
2322 y(21)-230 2435 y(22)-230 2548 y(23)-230 2661 y(24)-230
2774 y(25)-230 2887 y(26)-230 3000 y(27)-230 3112 y(28)-230
3225 y(29)-230 3338 y(30)-230 3451 y(31)-230 3564 y(32)-230
3677 y(33)-230 3790 y(34)-230 3903 y(35)-230 4016 y(36)-230
4129 y(37)-230 4242 y(38)-230 4354 y(39)-230 4467 y(40)-230
4580 y(41)-230 4693 y(42)-230 4806 y(43)-230 4919 y(44)-230
5032 y(45)-230 5145 y(46)-230 5258 y(47)-230 5371 y(48)p
eop
%%Page: 236 246
236 245 bop 0 -165 a FK(236)1882 b FA(ANNEX)31 b(C.)61
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426 y(<interval>)e(beta,)h(<interval_array>)d(y,)k(int)g(incy)g(\);)p
0 629 3900 4 v 0 768 a FK(W)m(CANCEL)p 482 768 28 4 v
33 w(I)30 b(\(Scaled)g(cancellation\))1951 b FG(w)25
b FJ( )g Fy(\013)p FG(x)c FJ(\011)f Fy(\014)5 b FG(y)0
994 y FK(The)40 b(op)s(eration)g(cancel,)k FJ(\011)p
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b FG(a)g FK(and)g FG(b)g FK(is)g(de\014ned)f(as)i FG(a)27
b FJ(\011)f FG(b)43 b FK(=)e([)p Fy(a)p 3317 1007 49
4 v 28 w FJ(\000)26 b Fy(b)p 3490 1007 40 4 v(;)p 3569
945 49 4 v 15 w(a)i FJ(\000)p 3742 921 40 4 v 26 w Fy(b)p
FK(])41 b(if)0 1107 y(\()p Fy(a)p 35 1120 49 4 v 20 w
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40 4 v 19 w Fy(b)p FK(\);)31 b(Otherwise,)e FJ(;)p FK(.)41
b(The)30 b(routine)f FD(WCANCEL)p 2120 1107 29 4 v 32
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FG(x)g FK(b)m(y)e(the)i(in)m(terv)-5 b(al)0 1220 y Fy(\013)30
b FK(and)f(the)h(in)m(terv)-5 b(al)28 b(v)m(ector)k FG(y)d
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1234 y Fw(i)1759 1220 y FJ(\011)19 b Fy(\014)5 b FG(y)1960
1241 y Fw(i)2018 1220 y FK(in)28 b FG(w)2198 1234 y Fw(i)2256
1220 y FK(for)h(0)d FJ(\024)f Fy(i)h(<)f(n)p FK(.)39
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1333 y(zero,)i(this)e(routine)g(returns)g(immediately)-8
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1445 y FK(less)g(than)h(zero)h(is)f(p)s(ermitted.)41
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(\015ag)i(is)0 1558 y(set)f(and)f(passed)g(to)h(the)f(error)g(handler.)
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j(int)g(incw)f(\);)0 4455 y Fv(Data)29 b(Movement)i(with)f(Interval)g
(V)m(ecto)m(rs)0 4626 y FK(COPY)p 272 4626 28 4 v 32
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b FG(y)26 b FJ( )f FG(x)0 4852 y FK(The)j(routine)f FD(COPY)p
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64 b(Ho)m(w)m(ev)m(er,)43 b(if)38 b(either)g Fv(incx)h
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5400 y FJ(\017)46 b FK(F)-8 b(ortran)31 b(95)h(binding:)4084
64 y FI(1)4084 177 y(2)4084 290 y(3)4084 403 y(4)4084
516 y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084 967
y(9)4069 1080 y(10)4069 1193 y(11)4069 1306 y(12)4069
1419 y(13)4069 1532 y(14)4069 1645 y(15)4069 1758 y(16)4069
1870 y(17)4069 1983 y(18)4069 2096 y(19)4069 2209 y(20)4069
2322 y(21)4069 2435 y(22)4069 2548 y(23)4069 2661 y(24)4069
2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
3677 y(33)4069 3790 y(34)4069 3903 y(35)4069 4016 y(36)4069
4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 237 247
237 246 bop 0 -165 a FA(C.4.)71 b(INTER)-10 b(V)g(AL)30
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(y\(:\))514 430 y(where)609 543 y(x)h(and)e(y)i(have)f(shape)f(\(n\))
136 762 y FJ(\017)g FK(F)-8 b(ortran)31 b(77)h(binding:)514
981 y FD(SUBROUTINE)45 b(BLAS_xCOPY_I\()f(N,)j(X,)g(INCX,)g(Y,)g(INCY)f
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1207 y(<type>)618 b(X\()48 b(2,)f(*)g(\),)g(Y\()h(2,)f(*)g(\))136
1425 y FJ(\017)f FK(C)30 b(binding:)227 1624 y FD(void)47
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0 1917 3900 4 v 0 2056 a FK(SW)-10 b(AP)p 269 2056 28
4 v 33 w(I)30 b(\(In)m(terv)-5 b(al)30 b(v)m(ector)i(sw)m(ap\))2414
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0 4696 3900 4 v 0 4835 a FK(PERMUTE)p 475 4835 28 4 v
32 w(I)31 b(\(P)m(erm)m(ute)g(in)m(terv)-5 b(al)30 b(v)m(ector\))2006
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5174 y(v)m(ector)27 b Fy(P)13 b FK(.)40 b(If)25 b FD(n)g
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b(Ho)m(w)m(ev)m(er,)35 b(if)c(either)h Fv(incx)g FK(or)h
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64 y FI(1)-214 177 y(2)-214 290 y(3)-214 403 y(4)-214
516 y(5)-214 628 y(6)-214 741 y(7)-214 854 y(8)-214 967
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3225 y(29)-230 3338 y(30)-230 3451 y(31)-230 3564 y(32)-230
3677 y(33)-230 3790 y(34)-230 3903 y(35)-230 4016 y(36)-230
4129 y(37)-230 4242 y(38)-230 4354 y(39)-230 4467 y(40)-230
4580 y(41)-230 4693 y(42)-230 4806 y(43)-230 4919 y(44)-230
5032 y(45)-230 5145 y(46)-230 5258 y(47)-230 5371 y(48)p
eop
%%Page: 238 248
238 247 bop 0 -165 a FK(238)1882 b FA(ANNEX)31 b(C.)61
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2982 y(routine)32 b(returns)f(immediately)-8 b(.)46 b(As)32
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b Fv(incx)g FK(or)h Fv(incy)f FK(less)g(than)h(zero)g(is)0
3095 y(p)s(ermitted.)56 b(Ho)m(w)m(ev)m(er,)39 b(if)c(either)h
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1485 3208 V 31 w(I)p FK(,)i(if)e Fv(lda)g FK(is)g(less)g(than)h(one)g
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g(is)0 3321 y(set)h(and)f(passed)f(to)i(the)g(error)f(handler.)41
b(F)-8 b(or)32 b(the)g(routine)e Fv(GBMV)p 2374 3321
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3611 y FJ(\017)46 b FK(F)-8 b(ortran)31 b(95)h(binding:)227
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y(General)g(Band:)514 4158 y(SUBROUTINE)f(gbmv_i\()g(a,)j(m,)f(kl,)g
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4271 y(all:)609 4384 y(TYPE\(INTERVAL\))e(\(<wp>\),)i(INTENT\(IN\))f
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%%Page: 239 249
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5145 y(46)-230 5258 y(47)-230 5371 y(48)p eop
%%Page: 240 250
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%%Page: 241 251
241 250 bop 0 -165 a FA(C.4.)71 b(INTER)-10 b(V)g(AL)30
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5371 y(48)p eop
%%Page: 242 252
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eop
%%Page: 246 256
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eop
%%Page: 247 257
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eop
%%Page: 248 258
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33 w(LRSCALE)p 2621 5400 V 32 w(I)p FK(,)i(if)e Fv(lda)h
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64 y FI(1)4084 177 y(2)4084 290 y(3)4084 403 y(4)4084
516 y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084 967
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2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
3677 y(33)4069 3790 y(34)4069 3903 y(35)4069 4016 y(36)4069
4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 249 259
249 258 bop 0 -165 a FA(C.4.)71 b(INTER)-10 b(V)g(AL)30
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5258 y(47)-230 5371 y(48)p eop
%%Page: 250 260
250 259 bop 0 -165 a FK(250)1882 b FA(ANNEX)31 b(C.)61
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5145 y(46)4069 5258 y(47)4069 5371 y(48)p eop
%%Page: 251 261
251 260 bop 0 -165 a FA(C.4.)71 b(INTER)-10 b(V)g(AL)30
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5145 y(46)-230 5258 y(47)-230 5371 y(48)p eop
%%Page: 252 262
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w(I)p FK(,)h(if)g Fv(lda)f FK(is)g(less)g(than)h Fv(kl)h
FK(plus)d Fv(ku)i FK(plus)e(one,)k(an)e(error)f(\015ag)i(is)e(set)i
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FK(is)g(less)h(than)g(one)g(or)g Fv(lda)g FK(is)f(less)g(than)h
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Fv(TB)p 2325 4859 V 32 w(A)m(CC)p 2531 4859 V 33 w(I)p
FK(,)i(if)e Fv(lda)h FK(is)f(less)g(than)h Fv(k)h FK(plus)d(one,)j(an)0
4971 y(error)e(\015ag)h(is)e(set)i(and)f(passed)g(to)h(the)f(error)g
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64 y FI(1)4084 177 y(2)4084 290 y(3)4084 403 y(4)4084
516 y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084 967
y(9)4069 1080 y(10)4069 1193 y(11)4069 1306 y(12)4069
1419 y(13)4069 1532 y(14)4069 1645 y(15)4069 1758 y(16)4069
1870 y(17)4069 1983 y(18)4069 2096 y(19)4069 2209 y(20)4069
2322 y(21)4069 2435 y(22)4069 2548 y(23)4069 2661 y(24)4069
2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
3677 y(33)4069 3790 y(34)4069 3903 y(35)4069 4016 y(36)4069
4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 253 263
253 262 bop 0 -165 a FA(C.4.)71 b(INTER)-10 b(V)g(AL)30
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%%Page: 254 264
254 263 bop 0 -165 a FK(254)1882 b FA(ANNEX)31 b(C.)61
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b(F)-8 b(or)35 b(the)g(routine)e Fv(GE)p 1119 2480 V
33 w(ADD)p 1345 2480 V 32 w(I)p FK(,)h(if)g Fv(lda)f
FK(is)h(less)f(than)h(one)h(or)f(less)g(than)g Fv(m)p
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f(error)g(handler.)49 b(F)-8 b(or)35 b(the)f(routine)f
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Fv(lda)g FK(is)g(less)h(than)f Fv(kl)h FK(plus)e Fv(ku)j
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3379 2706 V 32 w(I)p FK(,)g Fv(SP)p 3598 2706 V 32 w(ADD)p
3823 2706 V 31 w(I)p FK(,)0 2819 y(and)35 b Fv(TP)p 307
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FK(is)f(less)h(than)h(one)g(or)f Fv(lda)g FK(is)g(less)g(than)g
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Fv(SB)p 1357 2932 V 31 w(ADD)p 1581 2932 V 32 w(I)h FK(and)f
Fv(TB)p 1961 2932 V 32 w(ADD)p 2186 2932 V 32 w(I)p FK(,)h(if)e
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64 y FI(1)4084 177 y(2)4084 290 y(3)4084 403 y(4)4084
516 y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084 967
y(9)4069 1080 y(10)4069 1193 y(11)4069 1306 y(12)4069
1419 y(13)4069 1532 y(14)4069 1645 y(15)4069 1758 y(16)4069
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2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
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4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 255 265
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%%Page: 256 266
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%%Page: 257 267
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%%Page: 258 268
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(one)h(or)f(less)g(than)g Fv(m)p FK(,)h(an)f(error)g(\015ag)g(is)g(set)
g(and)g(passed)g(to)h(the)g(error)e(handler.)42 b(F)-8
b(or)32 b Fv(side)f FK(equal)0 4503 y(to)g Fv(blas)p
264 4503 V 32 w(right)p 474 4503 V 33 w(side)p FK(,)g(and)f(if)g
Fv(ldt)g FK(is)g(less)g(than)g(one)h(or)g(less)f(than)g
Fv(n)p FK(,)h(or)g(if)f Fv(ldb)g FK(is)g(less)g(than)g(one)h(or)g(less)
f(than)h Fv(m)p FK(,)0 4616 y(an)f(error)g(\015ag)h(is)e(set)i(and)f
(passed)g(to)h(the)g(error)f(handler.)136 4820 y FJ(\017)46
b FK(F)-8 b(ortran)31 b(95)h(binding:)514 5061 y FD(SUBROUTINE)45
b(trmm_i\()g(t,)j(b)f([,)g(side])g([,)g(uplo])f([,)h(transt])f([,)h
(diag])g(&)1420 5174 y([,)h(alpha])e(\))514 5287 y(TYPE\(INTERVAL\))e
(\(<wp>\),)h(INTENT\(INOUT\))g(::)i(b\(:,:\))514 5400
y(TYPE\(INTERVAL\))d(\(<wp>\),)h(INTENT\(IN\))g(::)j(t\(:,:\))4084
64 y FI(1)4084 177 y(2)4084 290 y(3)4084 403 y(4)4084
516 y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084 967
y(9)4069 1080 y(10)4069 1193 y(11)4069 1306 y(12)4069
1419 y(13)4069 1532 y(14)4069 1645 y(15)4069 1758 y(16)4069
1870 y(17)4069 1983 y(18)4069 2096 y(19)4069 2209 y(20)4069
2322 y(21)4069 2435 y(22)4069 2548 y(23)4069 2661 y(24)4069
2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
3677 y(33)4069 3790 y(34)4069 3903 y(35)4069 4016 y(36)4069
4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 259 269
259 268 bop 0 -165 a FA(C.4.)71 b(INTER)-10 b(V)g(AL)30
b(BLAS)2793 b FK(259)514 91 y FD(TYPE\(blas_side_type\),)89
b(INTENT\(IN\),)45 b(OPTIONAL)h(::)h(side)514 204 y
(TYPE\(blas_trans_type\),)41 b(INTENT\(IN\),)k(OPTIONAL)h(::)h(transt)
514 317 y(TYPE\(blas_diag_type\),)89 b(INTENT\(IN\),)45
b(OPTIONAL)h(::)h(diag)514 430 y(TYPE\(blas_uplo_type\),)89
b(INTENT\(IN\),)45 b(OPTIONAL)h(::)h(uplo)514 543 y(TYPE\(INTERVAL\))d
(\(<wp>\),)h(INTENT\(IN\),)g(OPTIONAL)h(::)h(alpha,)f(beta)418
656 y(where)514 769 y(b)h(has)g(shape)f(\(m,n\))561 882
y(TR)95 b(t)48 b(has)f(shape)f(\(m,m\))g(if)i(side)e(=)i
(blas_left_side)c(\(the)i(default\))752 995 y(t)i(has)f(shape)f
(\(n,n\))g(if)i(side)e(/=)h(blas_left_side)136 1238 y
FJ(\017)f FK(F)-8 b(ortran)31 b(77)h(binding:)514 1482
y FD(SUBROUTINE)45 b(BLAS_xTRMM_I\()f(SIDE,)i(UPLO,)h(TRANST,)e(DIAG,)i
(M,)g(N,)g(ALPHA,)466 1595 y($)1193 b(T,)47 b(LDT,)g(B,)g(LDB)g(\))514
1707 y(INTEGER)570 b(DIAG,)47 b(LDA,)f(LDB,)h(M,)g(N,)g(SIDE,)g
(TRANST,)f(UPLO)514 1820 y(<type>)618 b(ALPHA\()47 b(2)g(\))514
1933 y(<type>)618 b(T\()48 b(2,)f(LDA,)f(*)i(\),)f(B\()g(2,)g(LDB,)g(*)
h(\))136 2177 y FJ(\017)e FK(C)30 b(binding:)227 2420
y FD(void)47 b(BLAS_xtrmm_i\()d(enum)j(blas_order_type)c(order,)j(enum)
h(blas_side_type)d(side,)1134 2533 y(enum)j(blas_uplo_type)d(uplo,)i
(enum)h(blas_trans_type)c(transt,)1134 2646 y(enum)k(blas_diag_type)d
(diag,)i(int)h(m,)g(int)g(n,)g(<interval>)e(alpha,)1134
2759 y(const)h(<interval_array>)e(t,)j(int)g(ldt,)g(<interval_array>)c
(b,)1134 2872 y(int)k(ldb)g(\);)p 0 3089 3900 4 v 0 3228
a FK(TRSM)p 272 3228 28 4 v 32 w(I)30 b(\(In)m(terv)-5
b(al)31 b(triangular)d(solv)m(e\))1333 3411 y FG(B)e
FJ( )f Fy(\013)p FG(T)1680 3375 y Fu(\000)p FC(1)1774
3411 y FG(B)q FK(,)30 b FG(B)c FJ( )f Fy(\013)p FK(\()p
FG(T)2287 3375 y Fu(\000)p FC(1)2381 3411 y FK(\))2416
3378 y Fw(T)2471 3411 y FG(B)q FK(,)30 b FG(B)c FJ( )f
Fy(\013)p FG(B)q(T)3023 3375 y Fu(\000)p FC(1)3147 3411
y FK(or)31 b FG(B)25 b FJ( )g Fy(\013)p FG(B)q FK(\()p
FG(T)3715 3375 y Fu(\000)p FC(1)3810 3411 y FK(\))3845
3378 y Fw(T)0 3595 y FK(These)35 b(routines)f(b)s(ound)e(one)k(of)f
(the)g(matrix)f(equations)h FG(B)e FJ( )g Fy(\013)p FG(T)2421
3558 y Fu(\000)p FC(1)2515 3595 y FG(B)q FK(,)j FG(B)d
FJ( )g Fy(\013)p FK(\()p FG(T)3049 3558 y Fu(\000)p FC(1)3143
3595 y FK(\))3178 3562 y Fw(T)3233 3595 y FG(B)q FK(,)j
FG(B)d FJ( )g Fy(\013)p FG(B)q(T)3806 3558 y Fu(\000)p
FC(1)0 3707 y FK(or)j FG(B)g FJ( )f Fy(\013)p FG(B)q
FK(\()p FG(T)594 3671 y Fu(\000)p FC(1)688 3707 y FK(\))723
3674 y Fw(T)815 3707 y FK(where)h Fy(\013)h FK(is)e(an)h(in)m(terv)-5
b(al,)38 b FG(B)e FK(is)g(a)g(general)h(in)m(terv)-5
b(al)35 b(matrix,)j(and)d FG(T)h FK(is)g(a)h(a)f(unit,)h(or)0
3820 y(non-unit,)31 b(upp)s(er)e(or)j(lo)m(w)m(er)g(triangular)e(in)m
(terv)-5 b(al)31 b(matrix.)44 b(This)30 b(routine)h(returns)g
(immediately)f(if)h Fv(m)g FK(or)h Fv(n)g FK(is)0 3933
y(less)i(than)g(or)g(equal)g(to)h(zero.)53 b(F)-8 b(or)35
b Fv(side)f FK(equal)g(to)h Fv(blas)p 1958 3933 V 32
w(left)p 2113 3933 V 33 w(side)p FK(,)g(and)f(if)f Fv(ldT)h
FK(is)f(less)h(than)g(one)g(or)h(less)e(than)0 4046 y
Fv(m)p FK(,)d(or)e(if)g Fv(ldb)h FK(is)f(less)g(than)h(one)g(or)g(less)
f(than)g Fv(m)p FK(,)i(an)f(error)f(\015ag)i(is)d(set)j(and)e(passed)h
(to)g(the)g(error)g(handler.)38 b(F)-8 b(or)0 4159 y
Fv(side)27 b FK(equal)g(to)h Fv(blas)p 669 4159 V 32
w(right)p 879 4159 V 33 w(side)p FK(,)g(and)f(if)g Fv(ldt)f
FK(is)h(less)g(than)g(one)h(or)f(less)g(than)g Fv(n)p
FK(,)h(or)g(if)e Fv(ldb)h FK(is)g(less)f(than)h(one)h(or)g(less)0
4272 y(than)i Fv(m)p FK(,)h(an)f(error)g(\015ag)h(is)e(set)i(and)f
(passed)g(to)h(the)g(error)f(handler.)136 4479 y FJ(\017)46
b FK(F)-8 b(ortran)31 b(95)h(binding:)514 4723 y FD(SUBROUTINE)45
b(trsm_i\()g(t,)j(b)f([,)g(side])g([,)g(uplo])f([,)h(transt])f([,)h
(diag])g([,)g(alpha])f(\))514 4835 y(TYPE\(INTERVAL\))e(\(<wp>\),)h
(INTENT\(INOUT\))g(::)i(b\(:,:\))514 4948 y(TYPE\(INTERVAL\))d
(\(<wp>\),)h(INTENT\(IN\))g(::)j(t\(:,:\))514 5061 y
(TYPE\(blas_side_type\),)89 b(INTENT\(IN\),)45 b(OPTIONAL)h(::)h(side)
514 5174 y(TYPE\(blas_trans_type\),)41 b(INTENT\(IN\),)k(OPTIONAL)h(::)
h(transt)514 5287 y(TYPE\(blas_diag_type\),)89 b(INTENT\(IN\),)45
b(OPTIONAL)h(::)h(diag)514 5400 y(TYPE\(blas_uplo_type\),)89
b(INTENT\(IN\),)45 b(OPTIONAL)h(::)h(uplo)-214 64 y FI(1)-214
177 y(2)-214 290 y(3)-214 403 y(4)-214 516 y(5)-214 628
y(6)-214 741 y(7)-214 854 y(8)-214 967 y(9)-230 1080
y(10)-230 1193 y(11)-230 1306 y(12)-230 1419 y(13)-230
1532 y(14)-230 1645 y(15)-230 1758 y(16)-230 1870 y(17)-230
1983 y(18)-230 2096 y(19)-230 2209 y(20)-230 2322 y(21)-230
2435 y(22)-230 2548 y(23)-230 2661 y(24)-230 2774 y(25)-230
2887 y(26)-230 3000 y(27)-230 3112 y(28)-230 3225 y(29)-230
3338 y(30)-230 3451 y(31)-230 3564 y(32)-230 3677 y(33)-230
3790 y(34)-230 3903 y(35)-230 4016 y(36)-230 4129 y(37)-230
4242 y(38)-230 4354 y(39)-230 4467 y(40)-230 4580 y(41)-230
4693 y(42)-230 4806 y(43)-230 4919 y(44)-230 5032 y(45)-230
5145 y(46)-230 5258 y(47)-230 5371 y(48)p eop
%%Page: 260 270
260 269 bop 0 -165 a FK(260)1882 b FA(ANNEX)31 b(C.)61
b(JOURNAL)30 b(OF)g(DEVELOPMENT)514 91 y FD(TYPE\(INTERVAL\))44
b(\(<wp>\),)h(INTENT\(IN\),)g(OPTIONAL)h(::)h(alpha,)f(beta)418
204 y(where)514 317 y(b)h(has)g(shape)f(\(m,n\))561 430
y(TR)95 b(t)48 b(has)f(shape)f(\(m,m\))g(if)i(side)e(=)i
(blas_left_side)c(\(the)i(default\))752 543 y(t)i(has)f(shape)f
(\(n,n\))g(if)i(side)e(/=)h(blas_left_side)136 793 y
FJ(\017)f FK(F)-8 b(ortran)31 b(77)h(binding:)514 1043
y FD(SUBROUTINE)45 b(BLAS_xTRSM_I\()f(SIDE,)i(UPLO,)h(TRANST,)e(DIAG,)i
(M,)g(N,)g(ALPHA,)466 1156 y($)1050 b(ALPHA,)46 b(T,)h(LDT,)g(B,)g(LDB)
g(\))514 1269 y(INTEGER)570 b(DIAG,)47 b(LDB,)f(LDT,)h(M,)g(N,)g(SIDE,)
g(TRANST,)f(UPLO)514 1381 y(<type>)618 b(ALPHA\()47 b(2)g(\))514
1494 y(<type>)618 b(T\()48 b(2,)f(LDA,)f(*)i(\),)f(B\()g(2,)g(LDB,)g(*)
h(\))136 1744 y FJ(\017)e FK(C)30 b(binding:)227 1994
y FD(void)47 b(BLAS_xtrsm_i\()d(enum)j(blas_order_type)c(order,)j(enum)
h(blas_side_type)d(side,)1134 2107 y(enum)j(blas_uplo_type)d(uplo,)i
(enum)h(blas_trans_type)c(transt,)1134 2220 y(enum)k(blas_diag_type)d
(diag,)i(int)h(m,)g(int)g(n,)g(<interval>)e(alpha,)1134
2333 y(const)h(<interval_array>)e(t,)j(int)g(ldt,)g(<interval_array>)c
(b,)1134 2446 y(int)k(ldb)g(\);)0 2696 y Fv(Data)29 b(Movement)i(with)f
(Interval)g(Matrices)0 2867 y FJ(f)p FK(GE,GB,SY,SB,SP)-8
b(,TR,TB,TP)p FJ(g)p 1268 2867 28 4 v 35 w FK(COPY)p
1570 2867 V 32 w(I)30 b(\(Matrix)h(cop)m(y\))1000 b FG(B)26
b FJ( )f FG(A)p Fy(;)15 b FG(B)26 b FJ( )f FG(A)3845
2831 y Fw(T)0 3093 y FK(This)20 b(routine)i(copies)g(an)g(in)m(terv)-5
b(al)22 b(matrix)f(\(or)i(its)e(transp)s(ose\))i FG(A)f
FK(and)g(stores)g(the)h(result)e(in)g(an)h(in)m(terv)-5
b(al)22 b(matrix)0 3206 y FG(B)p FK(.)44 b(Matrices)32
b Fy(A)f FK(\(or)h FG(A)842 3170 y Fw(T)897 3206 y FK(\))f(and)g
Fy(B)36 b FK(ha)m(v)m(e)c(the)f(same)h(storage)h(format.)44
b(This)29 b(routine)h(returns)g(immediately)g(if)0 3319
y Fv(m)j FK(\(for)f(nonsymmetric)g(matrices\),)h Fv(n)p
FK(,)h Fv(k)f FK(\(for)f(symmetric)g(band)g(matrices\),)h(or)g
Fv(kl)f FK(or)h Fv(ku)g FK(\(for)f(general)h(band)0 3432
y(matrices\),)e(is)f(less)f(than)i(or)f(equal)g(to)h(zero.)42
b(F)-8 b(or)32 b(the)e(routine)g Fv(GE)p 2341 3432 V
32 w(COPY)p 2617 3432 V 33 w(I)p FK(,)h(if)e Fv(trans)h
FK(equal)g(to)h Fv(blas)p 3533 3432 V 32 w(no)p 3657
3432 V 33 w(trans)p FK(,)0 3545 y(and)h(if)g Fv(lda)g
FK(is)g(less)g(than)g(one)h(or)g(less)f(than)h Fv(m)p
FK(,)g(or)g(if)f Fv(ldb)g FK(is)g(less)g(than)h(one)g(or)f(less)g(than)
h Fv(m)p FK(,)h(an)e(error)h(\015ag)g(is)0 3658 y(set)d(and)g(passed)f
(to)i(the)f(error)f(handler.)39 b(F)-8 b(or)30 b(the)g(routine)f
Fv(GE)p 2210 3658 V 33 w(COPY)p 2487 3658 V 32 w(I)p
FK(,)h(if)f Fv(trans)g FK(equal)h(to)g Fv(blas)p 3399
3658 V 32 w(trans)p FK(,)g(and)f(if)0 3771 y Fv(lda)i
FK(is)f(less)h(than)g(one)h(or)f(less)g(than)g Fv(m)p
FK(,)h(or)g(if)e Fv(ldb)h FK(is)g(less)g(than)g(one)h(or)f(less)g(than)
g Fv(n)p FK(,)h(an)f(error)g(\015ag)h(is)f(set)h(and)0
3884 y(passed)g(to)h(the)f(error)g(handler.)44 b(F)-8
b(or)33 b(the)g(routine)e Fv(GB)p 1922 3884 V 32 w(COPY)p
2198 3884 V 32 w(I)p FK(,)i(if)e Fv(lda)h FK(is)f(less)g(than)h
Fv(kl)h FK(plus)d Fv(ku)i FK(plus)f(one,)i(or)0 3996
y(if)e Fv(ldb)h FK(is)f(less)g(than)h Fv(kl)g FK(plus)e
Fv(ku)j FK(plus)d(one,)j(an)f(error)f(\015ag)i(is)e(set)h(and)g(passed)
f(to)i(the)f(error)g(handler.)44 b(F)-8 b(or)33 b(the)0
4109 y(routines)28 b Fv(SY)p 465 4109 V 32 w(COPY)p 741
4109 V 33 w(I)h FK(and)g Fv(TR)p 1125 4109 V 32 w(COPY)p
1401 4109 V 33 w(I)p FK(,)h(if)e Fv(lda)h FK(is)f(less)h(than)g(one)h
(or)g(less)e(than)h Fv(n)p FK(,)h(or)g(if)e Fv(ldb)h
FK(is)g(less)f(than)i(one)0 4222 y(or)d(less)f(than)h
Fv(n)p FK(,)h(an)f(error)g(\015ag)g(is)g(set)g(and)g(passed)f(to)i(the)
f(error)g(handler.)38 b(F)-8 b(or)28 b(the)f(routines)f
Fv(SB)p 3398 4222 V 32 w(COPY)p 3674 4222 V 32 w(I)i
FK(and)0 4335 y Fv(TB)p 128 4335 V 32 w(COPY)p 404 4335
V 33 w(I)p FK(,)33 b(if)f Fv(lda)g FK(is)g(less)g(than)h
Fv(k)g FK(plus)e(one,)j(or)f(if)f Fv(ldb)g FK(is)g(less)h(than)f
Fv(k)i FK(plus)c(one,)35 b(an)d(error)h(\015ag)g(is)f(set)i(and)0
4448 y(passed)c(to)h(the)g(error)f(handler.)136 4661
y FJ(\017)46 b FK(F)-8 b(ortran)31 b(95)h(binding:)227
4911 y FD(General:)514 5023 y(SUBROUTINE)45 b(ge_copy_i\()g(a,)i(b)g
([,)g(transa])f(\))227 5136 y(General)g(Band:)514 5249
y(SUBROUTINE)f(gb_copy_i\()g(a,)i(kl,)g(b)g([,)g(transa])f(\))227
5362 y(Symmetric:)4084 64 y FI(1)4084 177 y(2)4084 290
y(3)4084 403 y(4)4084 516 y(5)4084 628 y(6)4084 741 y(7)4084
854 y(8)4084 967 y(9)4069 1080 y(10)4069 1193 y(11)4069
1306 y(12)4069 1419 y(13)4069 1532 y(14)4069 1645 y(15)4069
1758 y(16)4069 1870 y(17)4069 1983 y(18)4069 2096 y(19)4069
2209 y(20)4069 2322 y(21)4069 2435 y(22)4069 2548 y(23)4069
2661 y(24)4069 2774 y(25)4069 2887 y(26)4069 3000 y(27)4069
3112 y(28)4069 3225 y(29)4069 3338 y(30)4069 3451 y(31)4069
3564 y(32)4069 3677 y(33)4069 3790 y(34)4069 3903 y(35)4069
4016 y(36)4069 4129 y(37)4069 4242 y(38)4069 4354 y(39)4069
4467 y(40)4069 4580 y(41)4069 4693 y(42)4069 4806 y(43)4069
4919 y(44)4069 5032 y(45)4069 5145 y(46)4069 5258 y(47)4069
5371 y(48)p eop
%%Page: 261 271
261 270 bop 0 -165 a FA(C.4.)71 b(INTER)-10 b(V)g(AL)30
b(BLAS)2793 b FK(261)514 91 y FD(SUBROUTINE)45 b(sy_copy_i\()g(a,)i(b)g
([,)g(uplo])g(\))227 204 y(Symmetric)f(Band:)514 317
y(SUBROUTINE)f(sb_copy_i\()g(a,)i(b)g([,)g(uplo])g(\))227
430 y(Symmetric)f(Packed:)514 543 y(SUBROUTINE)f(sp_copy_i\()g(ap,)i
(bp)g([,)g(uplo])f(\))227 656 y(Triangular:)514 769 y(SUBROUTINE)f
(tr_copy_i\()g(a,)i(b)g([,)g(uplo],)g([,)g(trans])f([,)h(diag])f(\))227
882 y(Triangular)f(Band:)514 995 y(SUBROUTINE)g(tb_copy_i\()g(a,)i(b)g
([,)g(uplo],)g([,)g(trans])f([,)h(diag])f(\))227 1108
y(Triangular)f(Packed:)514 1220 y(SUBROUTINE)g(tp_copy_i\()g(ap,)i(bp)g
([,)g(uplo],)f([,)h(trans])f([,)h(diag])g(\))227 1333
y(all:)514 1446 y(TYPE\(INTERVAL\))d(\(<wp>\),)h(INTENT\(OUT\))g(::)i
(b\(:,:\))f(|)i(bp\(:\))514 1559 y(TYPE\(INTERVAL\))c(\(<wp>\),)h
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y(INTEGER,)e(INTENT\(IN\))g(::)i(kl)514 1785 y
(TYPE\(blas_trans_type\),I)o(NTEN)o(T\(I)o(N\),)41 b(OPTIONAL)46
b(::)h(trans)514 1898 y(TYPE\(blas_uplo_type\),)42 b(INTENT\(IN\),)i
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b(INTENT\(IN\),)i(OPTIONAL)i(::)h(diag)418 2124 y(where)466
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2350 y(a,)g(b)h(have)e(shape)h(\(m,n\))f(for)h(general)f(matrix)1373
2462 y(\(l,n\))g(for)h(general)f(banded)g(matrix)g(\(l)h(>)h(kl\))1373
2575 y(\(n,n\))e(for)h(symmetric)e(or)i(triangular)1373
2688 y(\(k+1,n\))f(for)g(symmetric)g(banded)g(or)h(triangular)1755
2801 y(banded)f(\(k=band)f(width\))609 2914 y(ap)i(and)g(bp)g(have)g
(shape)f(\(n*\(n+1\)/2\).)466 3140 y(If)h(trans)f(\\=)i(blas_no_trans)
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f(for)h(general)f(matrix)1182 3366 y(\(l,n\))g(and)h(b)h(has)e(shape)h
(\(l,m\))f(for)h(general)f(banded)g(matrix)g(\(l>kl\))609
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5371 y(48)p eop
%%Page: 262 272
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%%Page: 263 273
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%%Page: 264 274
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2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
3677 y(33)4069 3790 y(34)4069 3903 y(35)4069 4016 y(36)4069
4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 265 275
265 274 bop 0 -165 a FA(C.4.)71 b(INTER)-10 b(V)g(AL)30
b(BLAS)2793 b FK(265)136 91 y FJ(\017)46 b FK(F)-8 b(ortran)31
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1905 y FD(int)47 b(BLAS_xinteriorv_i\()c(int)k(n,)g(const)f
(<interval_array>)e(x,)j(int)g(incx,)1325 2018 y(const)f
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4 v 0 2389 a FK(DISJV)p 273 2389 28 4 v 32 w(I)31 b(\(Chec)m(ks)f(if)g
(t)m(w)m(o)i(in)m(terv)-5 b(al)29 b(v)m(ectors)j(disjoin)m(t\))1294
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FJ(;)0 2615 y FK(This)31 b(routine)h(c)m(hec)m(ks)i(if)d(t)m(w)m(o)j
(in)m(terv)-5 b(al)32 b(v)m(ectors)i FG(x)f FK(and)f
FG(y)h FK(are)g(disjoin)m(t,)f(whic)m(h)f(means)i(that)g
FG(x)3369 2629 y Fw(i)3418 2615 y FJ(\\)22 b FG(y)3556
2636 y Fw(i)3613 2615 y FK(=)29 b FJ(;)k FK(for)0 2727
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b(alue)28 b Fv(incx)g FK(or)h Fv(incy)g FK(less)e(than)i(zero)g(is)f(p)
s(ermitted.)39 b(Ho)m(w)m(ev)m(er,)31 b(if)c Fv(incx)i
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(N,)j(X,)g(INCX,)g(Y,)g(INCY)f(\))514 4367 y(INTEGER)570
b(N,)48 b(INCX,)e(INCY)514 4480 y(<type>)618 b(X\()48
b(2,)f(*)g(\),)g(Y\()h(2,)f(*)g(\))136 4730 y FJ(\017)f
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(const)g(<interval_array>)c(x,)k(int)g(incx,)1134 5093
y(const)f(<interval_array>)e(y,)j(int)g(incy)g(\);)-214
64 y FI(1)-214 177 y(2)-214 290 y(3)-214 403 y(4)-214
516 y(5)-214 628 y(6)-214 741 y(7)-214 854 y(8)-214 967
y(9)-230 1080 y(10)-230 1193 y(11)-230 1306 y(12)-230
1419 y(13)-230 1532 y(14)-230 1645 y(15)-230 1758 y(16)-230
1870 y(17)-230 1983 y(18)-230 2096 y(19)-230 2209 y(20)-230
2322 y(21)-230 2435 y(22)-230 2548 y(23)-230 2661 y(24)-230
2774 y(25)-230 2887 y(26)-230 3000 y(27)-230 3112 y(28)-230
3225 y(29)-230 3338 y(30)-230 3451 y(31)-230 3564 y(32)-230
3677 y(33)-230 3790 y(34)-230 3903 y(35)-230 4016 y(36)-230
4129 y(37)-230 4242 y(38)-230 4354 y(39)-230 4467 y(40)-230
4580 y(41)-230 4693 y(42)-230 4806 y(43)-230 4919 y(44)-230
5032 y(45)-230 5145 y(46)-230 5258 y(47)-230 5371 y(48)p
eop
%%Page: 266 276
266 275 bop 0 -165 a FK(266)1882 b FA(ANNEX)31 b(C.)61
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b(routine)i(\014nds)e(the)j(in)m(tersection)f(of)g(t)m(w)m(o)i(in)m
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FK(,)i(and)f(stores)h(the)f(result)f(in)g FG(y)p FK(.)41
b(This)0 569 y(routine)36 b(returns)f(immediately)g(if)g
Fv(n)i FK(is)e(less)h(than)g(or)h(equal)f(to)h(zero.)60
b(As)36 b(describ)s(ed)f(in)g(section)i(2.5.3,)j(the)0
682 y(v)-5 b(alue)28 b Fv(incx)h FK(or)g Fv(incy)g FK(less)f(than)g
(zero)i(is)e(p)s(ermitted.)39 b(Ho)m(w)m(ev)m(er,)31
b(if)d Fv(incx)h FK(or)g Fv(incy)f FK(is)g(equal)h(to)g(zero,)h(an)f
(error)g(\015ag)0 795 y(is)g(set)i(and)f(passed)g(to)h(the)g(error)f
(handler.)136 981 y FJ(\017)46 b FK(F)-8 b(ortran)31
b(95)h(binding:)561 1199 y FD(SUBROUTINE)45 b(interv_i\()h(x,)h(y)g(\))
561 1312 y(TYPE\(INTERVAL\))d(\(<wp>\),)i(INTENT\(IN\))f(::)i(x\(:\))
561 1425 y(TYPE\(INTERVAL\))d(\(<wp>\),)i(INTENT\(INOUT\))e(::)j
(y\(:\))466 1538 y(where)561 1651 y(x)h(and)f(y)g(have)g(shape)f(\(n\))
136 1870 y FJ(\017)g FK(F)-8 b(ortran)31 b(77)h(binding:)514
2088 y FD(SUBROUTINE)45 b(BLAS_xINTERV_I\()e(N,)k(X,)h(INCX,)e(Y,)h
(INCY)g(\))514 2201 y(INTEGER)570 b(N,)48 b(INCX,)e(INCY)514
2314 y(<type>)618 b(X\()48 b(2,)f(*)g(\),)g(Y\()h(2,)f(*)g(\))136
2533 y FJ(\017)f FK(C)30 b(binding:)227 2751 y FD(void)47
b(BLAS_xinterv_i\()d(int)i(n,)i(const)e(<interval_array>)d(x,)48
b(int)e(incx,)1230 2864 y(<interval_array>)d(y,)k(int)g(incy)g(\);)p
0 3064 3900 4 v 0 3203 a FK(WINTER)-10 b(V)p 452 3203
28 4 v 33 w(I)30 b(\(In)m(tersection)h(of)f(t)m(w)m(o)i(in)m(terv)-5
b(al)30 b(v)m(ectors\))1486 b FG(z)25 b FJ( )g FG(x)c
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(another)0 3542 y(in)m(terv)-5 b(al)30 b(v)m(ector)i
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Fv(incz)f FK(is)f(equal)h(to)h(zero,)h(an)e(error)g(\015ag)h(is)e(set)i
(and)f(passed)g(to)h(the)f(error)g(handler.)136 3954
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4172 y FD(SUBROUTINE)45 b(winterv_i\(x,)f(y,)j(z)h(\))514
4285 y(TYPE\(INTERVAL\))c(\(<wp>\),)h(INTENT\(IN\))g(::)j(x\(:\),)e
(y\(:\))514 4398 y(TYPE\(INTERVAL\))e(\(<wp>\),)h(INTENT\(OUT\))g(::)i
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b(LDA,)f(M,)i(N)514 5287 y(INTEGER)570 b(N,)48 b(INCX,)e(INCY,)g(INCZ)
514 5400 y(<type>)618 b(X\()48 b(2,)f(*)g(\),)g(Y\()h(2,*)f(\),)g(Z\()g
(2,)g(*)h(\))4084 64 y FI(1)4084 177 y(2)4084 290 y(3)4084
403 y(4)4084 516 y(5)4084 628 y(6)4084 741 y(7)4084 854
y(8)4084 967 y(9)4069 1080 y(10)4069 1193 y(11)4069 1306
y(12)4069 1419 y(13)4069 1532 y(14)4069 1645 y(15)4069
1758 y(16)4069 1870 y(17)4069 1983 y(18)4069 2096 y(19)4069
2209 y(20)4069 2322 y(21)4069 2435 y(22)4069 2548 y(23)4069
2661 y(24)4069 2774 y(25)4069 2887 y(26)4069 3000 y(27)4069
3112 y(28)4069 3225 y(29)4069 3338 y(30)4069 3451 y(31)4069
3564 y(32)4069 3677 y(33)4069 3790 y(34)4069 3903 y(35)4069
4016 y(36)4069 4129 y(37)4069 4242 y(38)4069 4354 y(39)4069
4467 y(40)4069 4580 y(41)4069 4693 y(42)4069 4806 y(43)4069
4919 y(44)4069 5032 y(45)4069 5145 y(46)4069 5258 y(47)4069
5371 y(48)p eop
%%Page: 267 277
267 276 bop 0 -165 a FA(C.4.)71 b(INTER)-10 b(V)g(AL)30
b(BLAS)2793 b FK(267)136 91 y FJ(\017)46 b FK(C)30 b(binding:)227
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(<interval_array>)d(y,)k(int)g(incy,)1230 548 y(<interval_array>)c(z,)k
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(in)m(terv)-5 b(al)29 b(v)m(ector)j(with)d(another\))37
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(in)m(terv)-5 b(al)32 b(v)m(ectors)i FG(x)f FK(and)f
FG(y)q FK(,)h(and)f(o)m(v)m(erwrites)0 1238 y(the)k(input)d(in)m(terv)
-5 b(al)35 b(v)m(ector)i FG(y)e FK(with)f(the)i(result.)55
b(This)33 b(routine)i(returns)f(immediately)g(if)g Fv(n)i
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b(As)40 b(describ)s(ed)e(in)h(section)h(2.5.3,)45 b(the)40
b(v)-5 b(alue)40 b Fv(incx)g FK(or)g Fv(incy)g FK(less)f(than)h(zero)h
(is)e(p)s(ermitted.)0 1464 y(Ho)m(w)m(ev)m(er,)33 b(if)c
Fv(incx)h FK(or)h Fv(incy)f FK(is)f(equal)h(to)h(zero,)h(an)e(error)g
(\015ag)h(is)e(set)i(and)f(passed)g(to)h(the)f(error)g(handler.)136
1660 y FJ(\017)46 b FK(F)-8 b(ortran)31 b(95)h(binding:)514
1891 y FD(SUBROUTINE)45 b(hullv_i\()g(x,)i(y)h(\))514
2004 y(TYPE\(INTERVAL\))c(\(<wp>\),)h(INTENT\(IN\))g(::)j(x\(:\))514
2117 y(TYPE\(INTERVAL\))c(\(<wp>\),)h(INTENT\(INOUT\))g(::)i(y\(:\))418
2230 y(where)514 2343 y(x)g(and)g(y)g(have)g(shape)f(\(n\))136
2574 y FJ(\017)g FK(F)-8 b(ortran)31 b(77)h(binding:)514
2805 y FD(SUBROUTINE)45 b(BLAS_xHULLV_I\()f(N,)j(X,)g(INCX,)f(Y,)h
(INCY)g(\))514 2918 y(INTEGER)570 b(N,)48 b(INCX,)e(INCY)514
3030 y(<type>)618 b(X\()48 b(2,)f(*)g(\),)g(Y\()h(2,)f(*)g(\))136
3261 y FJ(\017)f FK(C)30 b(binding:)227 3492 y FD(void)47
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28 4 v 33 w(I)30 b(\(Con)m(v)m(ex)i(h)m(ull)c(of)j(t)m(w)m(o)h(in)m
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(con)m(v)m(ex)i(h)m(ull)c(of)i(t)m(w)m(o)i(in)m(terv)-5
b(al)33 b(v)m(ectors)j FG(x)e FK(and)f FG(y)p FK(,)j(and)d(stores)i
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(v)-5 b(alue)31 b Fv(incx)h(incy)p FK(,)g(or)f Fv(incz)h
FK(less)f(than)g(zero)h(is)f(p)s(ermitted.)43 b(Ho)m(w)m(ev)m(er,)35
b(if)30 b Fv(incx)i FK(or)f Fv(incy)h FK(or)0 4521 y
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(and)f(passed)g(to)h(the)f(error)g(handler.)136 4717
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5061 y(TYPE\(INTERVAL\))c(\(<wp>\),)h(INTENT\(IN\))g(::)j(x\(:\),)e
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(\(n\))-214 64 y FI(1)-214 177 y(2)-214 290 y(3)-214
403 y(4)-214 516 y(5)-214 628 y(6)-214 741 y(7)-214 854
y(8)-214 967 y(9)-230 1080 y(10)-230 1193 y(11)-230 1306
y(12)-230 1419 y(13)-230 1532 y(14)-230 1645 y(15)-230
1758 y(16)-230 1870 y(17)-230 1983 y(18)-230 2096 y(19)-230
2209 y(20)-230 2322 y(21)-230 2435 y(22)-230 2548 y(23)-230
2661 y(24)-230 2774 y(25)-230 2887 y(26)-230 3000 y(27)-230
3112 y(28)-230 3225 y(29)-230 3338 y(30)-230 3451 y(31)-230
3564 y(32)-230 3677 y(33)-230 3790 y(34)-230 3903 y(35)-230
4016 y(36)-230 4129 y(37)-230 4242 y(38)-230 4354 y(39)-230
4467 y(40)-230 4580 y(41)-230 4693 y(42)-230 4806 y(43)-230
4919 y(44)-230 5032 y(45)-230 5145 y(46)-230 5258 y(47)-230
5371 y(48)p eop
%%Page: 268 278
268 277 bop 0 -165 a FK(268)1882 b FA(ANNEX)31 b(C.)61
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454 y(INTEGER)570 b(N,)48 b(INCX,)e(INCY,)g(INCZ)514
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1293 y(int)j(incz)h(\);)p 0 1516 3900 4 v 0 1778 a Fv(Set)30
b(Op)s(erations)g(Involving)g(Interval)h(Matrices)0 1949
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1949 28 4 v 35 w FK(ENCM)p 1582 1949 V 33 w(I)30 b(\(If)g(an)g(in)m
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2401 y(an)j(in)m(terv)-5 b(al)34 b(matrix)h FG(A)g FK(is)f(enclosed)h
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b FG(b)310 2528 y Fw(i;j)421 2514 y FJ(8)p Fy(i)30 b
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2726 y FJ(\017)46 b FK(F)-8 b(ortran)31 b(95)h(binding:)227
2976 y FD(General:)514 3089 y(LOGICAL)45 b(FUNCTION)h(ge_encm_i\()f(a,)
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(gb_encm_i\()f(a,)i(m,)g(kl,)g(b)h(\))227 3428 y(Symmetric:)514
3541 y(LOGICAL)d(FUNCTION)h(sy_encm_i\()f(a,)i(b)h([,)f(uplo])f(\))227
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5371 y(48)p eop
%%Page: 269 279
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eop
%%Page: 270 280
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5258 y(47)4069 5371 y(48)p eop
%%Page: 271 281
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eop
%%Page: 272 282
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516 y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084 967
y(9)4069 1080 y(10)4069 1193 y(11)4069 1306 y(12)4069
1419 y(13)4069 1532 y(14)4069 1645 y(15)4069 1758 y(16)4069
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2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
3677 y(33)4069 3790 y(34)4069 3903 y(35)4069 4016 y(36)4069
4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 273 283
273 282 bop 0 -165 a FA(C.4.)71 b(INTER)-10 b(V)g(AL)30
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y(9)-230 1080 y(10)-230 1193 y(11)-230 1306 y(12)-230
1419 y(13)-230 1532 y(14)-230 1645 y(15)-230 1758 y(16)-230
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4580 y(41)-230 4693 y(42)-230 4806 y(43)-230 4919 y(44)-230
5032 y(45)-230 5145 y(46)-230 5258 y(47)-230 5371 y(48)p
eop
%%Page: 274 284
274 283 bop 0 -165 a FK(274)1882 b FA(ANNEX)31 b(C.)61
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516 y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084 967
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2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
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4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 275 285
275 284 bop 0 -165 a FA(C.4.)71 b(INTER)-10 b(V)g(AL)30
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1870 y(17)-230 1983 y(18)-230 2096 y(19)-230 2209 y(20)-230
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5032 y(45)-230 5145 y(46)-230 5258 y(47)-230 5371 y(48)p
eop
%%Page: 276 286
276 285 bop 0 -165 a FK(276)1882 b FA(ANNEX)31 b(C.)61
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3564 y(32)4069 3677 y(33)4069 3790 y(34)4069 3903 y(35)4069
4016 y(36)4069 4129 y(37)4069 4242 y(38)4069 4354 y(39)4069
4467 y(40)4069 4580 y(41)4069 4693 y(42)4069 4806 y(43)4069
4919 y(44)4069 5032 y(45)4069 5145 y(46)4069 5258 y(47)4069
5371 y(48)p eop
%%Page: 281 291
281 290 bop 0 -165 a FA(C.4.)71 b(INTER)-10 b(V)g(AL)30
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5032 y(45)-230 5145 y(46)-230 5258 y(47)-230 5371 y(48)p
eop
%%Page: 282 292
282 291 bop 0 -165 a FK(282)1882 b FA(ANNEX)31 b(C.)61
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y(6)4084 741 y(7)4084 854 y(8)4084 967 y(9)4069 1080
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1532 y(14)4069 1645 y(15)4069 1758 y(16)4069 1870 y(17)4069
1983 y(18)4069 2096 y(19)4069 2209 y(20)4069 2322 y(21)4069
2435 y(22)4069 2548 y(23)4069 2661 y(24)4069 2774 y(25)4069
2887 y(26)4069 3000 y(27)4069 3112 y(28)4069 3225 y(29)4069
3338 y(30)4069 3451 y(31)4069 3564 y(32)4069 3677 y(33)4069
3790 y(34)4069 3903 y(35)4069 4016 y(36)4069 4129 y(37)4069
4242 y(38)4069 4354 y(39)4069 4467 y(40)4069 4580 y(41)4069
4693 y(42)4069 4806 y(43)4069 4919 y(44)4069 5032 y(45)4069
5145 y(46)4069 5258 y(47)4069 5371 y(48)p eop
%%Page: 283 293
283 292 bop 0 -165 a FA(C.4.)71 b(INTER)-10 b(V)g(AL)30
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4467 y(40)-230 4580 y(41)-230 4693 y(42)-230 4806 y(43)-230
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5371 y(48)p eop
%%Page: 284 294
284 293 bop 0 -165 a FK(284)1882 b FA(ANNEX)31 b(C.)61
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4919 y(44)4069 5032 y(45)4069 5145 y(46)4069 5258 y(47)4069
5371 y(48)p eop
%%Page: 285 295
285 294 bop 0 -165 a FA(C.4.)71 b(INTER)-10 b(V)g(AL)30
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4467 y(40)-230 4580 y(41)-230 4693 y(42)-230 4806 y(43)-230
4919 y(44)-230 5032 y(45)-230 5145 y(46)-230 5258 y(47)-230
5371 y(48)p eop
%%Page: 286 296
286 295 bop 0 -165 a FK(286)1882 b FA(ANNEX)31 b(C.)61
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3677 y(33)4069 3790 y(34)4069 3903 y(35)4069 4016 y(36)4069
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eop
%%Page: 287 297
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1306 y(12)-230 1419 y(13)-230 1532 y(14)-230 1645 y(15)-230
1758 y(16)-230 1870 y(17)-230 1983 y(18)-230 2096 y(19)-230
2209 y(20)-230 2322 y(21)-230 2435 y(22)-230 2548 y(23)-230
2661 y(24)-230 2774 y(25)-230 2887 y(26)-230 3000 y(27)-230
3112 y(28)-230 3225 y(29)-230 3338 y(30)-230 3451 y(31)-230
3564 y(32)-230 3677 y(33)-230 3790 y(34)-230 3903 y(35)-230
4016 y(36)-230 4129 y(37)-230 4242 y(38)-230 4354 y(39)-230
4467 y(40)-230 4580 y(41)-230 4693 y(42)-230 4806 y(43)-230
4919 y(44)-230 5032 y(45)-230 5145 y(46)-230 5258 y(47)-230
5371 y(48)p eop
%%Page: 288 298
288 297 bop 0 -165 a FK(288)1882 b FA(ANNEX)31 b(C.)61
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5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 289 299
289 298 bop 0 -165 a FA(C.4.)71 b(INTER)-10 b(V)g(AL)30
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5371 y(48)p eop
%%Page: 290 300
290 299 bop 0 -165 a FK(290)1882 b FA(ANNEX)31 b(C.)61
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5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 291 301
291 300 bop 0 -165 a FA(C.4.)71 b(INTER)-10 b(V)g(AL)30
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177 y(2)-214 290 y(3)-214 403 y(4)-214 516 y(5)-214 628
y(6)-214 741 y(7)-214 854 y(8)-214 967 y(9)-230 1080
y(10)-230 1193 y(11)-230 1306 y(12)-230 1419 y(13)-230
1532 y(14)-230 1645 y(15)-230 1758 y(16)-230 1870 y(17)-230
1983 y(18)-230 2096 y(19)-230 2209 y(20)-230 2322 y(21)-230
2435 y(22)-230 2548 y(23)-230 2661 y(24)-230 2774 y(25)-230
2887 y(26)-230 3000 y(27)-230 3112 y(28)-230 3225 y(29)-230
3338 y(30)-230 3451 y(31)-230 3564 y(32)-230 3677 y(33)-230
3790 y(34)-230 3903 y(35)-230 4016 y(36)-230 4129 y(37)-230
4242 y(38)-230 4354 y(39)-230 4467 y(40)-230 4580 y(41)-230
4693 y(42)-230 4806 y(43)-230 4919 y(44)-230 5032 y(45)-230
5145 y(46)-230 5258 y(47)-230 5371 y(48)p eop
%%Page: 292 302
292 301 bop 0 -165 a FK(292)1882 b FA(ANNEX)31 b(C.)61
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5258 y(47)4069 5371 y(48)p eop
%%Page: 293 303
293 302 bop 0 -165 a FA(C.4.)71 b(INTER)-10 b(V)g(AL)30
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5371 y(48)p eop
%%Page: 294 304
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5371 y(48)p eop
%%Page: 295 305
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eop
%%Page: 296 306
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Fw(i;j)995 682 y FJ(g)p Fy(;)15 b FK(max)q FJ(f)p Fy(b)1334
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682 y FJ(g)p FK(])38 b FJ(8)p Fy(i)e FJ(2)f(f)p FK(0)p
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48 b(N,)f(KL,)g(KU,)g(A,)g(LDA,)f(B,)i(LDB,)e(C,)h(LDC)g(\))4084
64 y FI(1)4084 177 y(2)4084 290 y(3)4084 403 y(4)4084
516 y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084 967
y(9)4069 1080 y(10)4069 1193 y(11)4069 1306 y(12)4069
1419 y(13)4069 1532 y(14)4069 1645 y(15)4069 1758 y(16)4069
1870 y(17)4069 1983 y(18)4069 2096 y(19)4069 2209 y(20)4069
2322 y(21)4069 2435 y(22)4069 2548 y(23)4069 2661 y(24)4069
2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
3677 y(33)4069 3790 y(34)4069 3903 y(35)4069 4016 y(36)4069
4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 297 307
297 306 bop 0 -165 a FA(C.4.)71 b(INTER)-10 b(V)g(AL)30
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5400 y(int)h(ldb,)f(RARRAY)g(c,)h(int)g(ldc)g(\);)-214
64 y FI(1)-214 177 y(2)-214 290 y(3)-214 403 y(4)-214
516 y(5)-214 628 y(6)-214 741 y(7)-214 854 y(8)-214 967
y(9)-230 1080 y(10)-230 1193 y(11)-230 1306 y(12)-230
1419 y(13)-230 1532 y(14)-230 1645 y(15)-230 1758 y(16)-230
1870 y(17)-230 1983 y(18)-230 2096 y(19)-230 2209 y(20)-230
2322 y(21)-230 2435 y(22)-230 2548 y(23)-230 2661 y(24)-230
2774 y(25)-230 2887 y(26)-230 3000 y(27)-230 3112 y(28)-230
3225 y(29)-230 3338 y(30)-230 3451 y(31)-230 3564 y(32)-230
3677 y(33)-230 3790 y(34)-230 3903 y(35)-230 4016 y(36)-230
4129 y(37)-230 4242 y(38)-230 4354 y(39)-230 4467 y(40)-230
4580 y(41)-230 4693 y(42)-230 4806 y(43)-230 4919 y(44)-230
5032 y(45)-230 5145 y(46)-230 5258 y(47)-230 5371 y(48)p
eop
%%Page: 298 308
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y(2)4084 290 y(3)4084 403 y(4)4084 516 y(5)4084 628 y(6)4084
741 y(7)4084 854 y(8)4084 967 y(9)4069 1080 y(10)4069
1193 y(11)4069 1306 y(12)4069 1419 y(13)4069 1532 y(14)4069
1645 y(15)4069 1758 y(16)4069 1870 y(17)4069 1983 y(18)4069
2096 y(19)4069 2209 y(20)4069 2322 y(21)4069 2435 y(22)4069
2548 y(23)4069 2661 y(24)4069 2774 y(25)4069 2887 y(26)4069
3000 y(27)4069 3112 y(28)4069 3225 y(29)4069 3338 y(30)4069
3451 y(31)4069 3564 y(32)4069 3677 y(33)4069 3790 y(34)4069
3903 y(35)4069 4016 y(36)4069 4129 y(37)4069 4242 y(38)4069
4354 y(39)4069 4467 y(40)4069 4580 y(41)4069 4693 y(42)4069
4806 y(43)4069 4919 y(44)4069 5032 y(45)4069 5145 y(46)4069
5258 y(47)4069 5371 y(48)p eop
%%Page: 299 309
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516 y(5)-214 628 y(6)-214 741 y(7)-214 854 y(8)-214 967
y(9)-230 1080 y(10)-230 1193 y(11)-230 1306 y(12)-230
1419 y(13)-230 1532 y(14)-230 1645 y(15)-230 1758 y(16)-230
1870 y(17)-230 1983 y(18)-230 2096 y(19)-230 2209 y(20)-230
2322 y(21)-230 2435 y(22)-230 2548 y(23)-230 2661 y(24)-230
2774 y(25)-230 2887 y(26)-230 3000 y(27)-230 3112 y(28)-230
3225 y(29)-230 3338 y(30)-230 3451 y(31)-230 3564 y(32)-230
3677 y(33)-230 3790 y(34)-230 3903 y(35)-230 4016 y(36)-230
4129 y(37)-230 4242 y(38)-230 4354 y(39)-230 4467 y(40)-230
4580 y(41)-230 4693 y(42)-230 4806 y(43)-230 4919 y(44)-230
5032 y(45)-230 5145 y(46)-230 5258 y(47)-230 5371 y(48)p
eop
%%Page: 300 310
300 309 bop 0 -165 a FK(300)3038 b FA(BIBLIOGRAPHY)0
91 y FK([13])47 b(R.)35 b(Bren)m(t)h(and)f(P)-8 b(.)36
b(Strazdins.)54 b(Implemen)m(tation)34 b(of)i(BLAS)f(Lev)m(el)g(3)h
(and)f(LINP)-8 b(A)m(CK)35 b(Benc)m(hmark)h(on)187 204
y(the)30 b(AP1000.)43 b Fz(F)-7 b(ujitsu)32 b(Scienti\014c)h(and)g(T)-7
b(e)i(chnic)g(al)34 b(Journal)p FK(,)e(5\(1\):61{70,)j(1993.)0
392 y([14])47 b(D.)142 b(Chiriaev)e(and)h(G.)h(W.)g(W)-8
b(alster.)373 b(In)m(terv)-5 b(al)142 b(arithmetic)f(sp)s
(eci\014cation.)187 505 y FD(http://www.mscs.mu.edu/)p
FJ(\030)o FD(glo)o(bsol)o(/wal)o(ste)o(r-pa)o(pers)o(.ht)o(ml)p
FK(.)0 692 y([15])47 b(J.)35 b(Choi,)g(J.)g(Dongarra,)j(S.)c(Ostrouc)m
(ho)m(v,)k(A.)d(P)m(etitet,)j(D.)e(W)-8 b(alk)m(er,)37
b(and)e(R.)g(C.)g(Whaley)-8 b(.)55 b(A)35 b(Prop)s(osal)187
805 y(for)41 b(a)g(Set)g(of)g(P)m(arallel)f(Basic)h(Linear)f(Algebra)g
(Subprograms.)70 b(In)41 b(J.)f(Dongarra,)45 b(K.)c(Masden,)j(and)187
918 y(J.)d(W)-8 b(a)j(\023)-41 b(sniewski,)45 b(editors,)e
Fz(Applie)-5 b(d)44 b(Par)-5 b(al)5 b(lel)44 b(Computing)p
FK(,)i(pages)c(107{114.)j(Springer)39 b(V)-8 b(erlag,)45
b(1995.)187 1031 y(\(also)31 b(LAP)-8 b(A)m(CK)30 b(W)-8
b(orking)31 b(Note)g(No.100\).)0 1219 y([16])47 b(J.)24
b(Choi,)h(J.)f(Dongarra,)j(and)c(D.)i(W)-8 b(alk)m(er.)32
b(PUMMA:)25 b(P)m(arallel)f(Univ)m(ersal)f(Matrix)h(Multiplication)d
(Algo-)187 1332 y(rithms)f(on)h(Distributed)f(Memory)i(Concurren)m(t)f
(Computers.)26 b Fz(Concurr)-5 b(ency:)38 b(Pr)-5 b(actic)g(e)26
b(and)f(Exp)-5 b(erienc)g(e)p FK(,)187 1445 y(6\(7\):543{570,)35
b(1994.)43 b(\(also)31 b(LAP)-8 b(A)m(CK)30 b(W)-8 b(orking)31
b(Note)g(No.57\).)0 1632 y([17])47 b(J.)27 b(Choi,)h(J.)f(Dongarra,)j
(and)d(D.)h(W)-8 b(alk)m(er.)37 b(PB-BLAS:)28 b(A)g(Set)g(of)g(P)m
(arallel)e(Blo)s(c)m(k)j(Basic)f(Linear)e(Algebra)187
1745 y(Subroutines.)38 b Fz(Concurr)-5 b(ency:)43 b(Pr)-5
b(actic)g(e)33 b(and)h(Exp)-5 b(erienc)g(e)p FK(,)31
b(8\(7\):517{535,)k(1996.)0 1933 y([18])47 b(A.)40 b(Ch)m(tc)m(helk)-5
b(ano)m(v)g(a,)45 b(J.)40 b(Gunnels,)h(G.)g(Morro)m(w,)i(J.)d(Ov)m
(erfelt,)j(and)c(R.)i(v)-5 b(an)40 b(de)g(Geijn.)69 b(P)m(arallel)39
b(Im-)187 2046 y(plemen)m(tation)g(of)h(BLAS:)f(General)h(T)-8
b(ec)m(hniques)39 b(for)g(Lev)m(el)h(3)g(BLAS.)68 b(T)-8
b(ec)m(hnical)39 b(Rep)s(ort)g(TR95-49,)187 2159 y(Departmen)m(t)h(of)g
(Computer)f(Sciences,)i(UT-Austin,)g(1995.)69 b(Submitted)37
b(to)k(Concurrency:)57 b(Practice)187 2271 y(and)30 b(Exp)s(erience.)0
2459 y([19])47 b(J.)30 b(Demmel.)41 b Fz(Applie)-5 b(d)33
b(Numeric)-5 b(al)34 b(Line)-5 b(ar)33 b(A)n(lgebr)-5
b(a)p FK(.)41 b(SIAM,)30 b(1997.)0 2647 y([20])47 b(D.)34
b(S.)e(Do)s(dson.)48 b(Corrigendum:)c(Remark)33 b(on)g(\\Algorithm)f
(539:)47 b(Basic)34 b(Linear)e(Algebra)h(Subroutines)187
2760 y(for)d(F)m(OR)-8 b(TRAN)31 b(usage".)42 b Fz(A)n(CM)31
b(T)-7 b(r)i(ans.)34 b(Math.)f(Softwar)-5 b(e)p FK(,)33
b(9:140,)f(1983.)43 b(\(See)31 b(also)f([39)q(])h(and)e([21)r(]\).)0
2947 y([21])47 b(D.)24 b(S.)f(Do)s(dson)g(and)g(R.)h(G.)g(Grimes.)k
(Remark)c(on)f(algorithm)g(539:)38 b(Basic)24 b(Linear)f(Algebra)g
(Subprograms)187 3060 y(for)30 b(F)-8 b(ortran)31 b(usage.)41
b Fz(A)n(CM)32 b(T)-7 b(r)i(ans.)34 b(Math.)f(Softwar)-5
b(e)p FK(,)32 b(8:403{404,)j(1982.)42 b(\(See)31 b(also)f([39)q(])h
(and)f([20)q(]\).)0 3248 y([22])47 b(D.)39 b(S.)g(Do)s(dson,)i(R.)e(G.)
h(Grimes,)g(and)f(J.)g(G.)g(Lewis.)65 b(Sparse)39 b(extensions)f(to)i
(the)f(F)m(OR)-8 b(TRAN)40 b(Basic)187 3361 y(Linear)f(Algebra)h
(Subprograms.)69 b Fz(A)n(CM)40 b(T)-7 b(r)i(ans.)43
b(Math.)f(Softwar)-5 b(e)p FK(,)45 b(17:253{272,)j(1991.)72
b(\(Algorithm)187 3474 y(692\).)0 3661 y([23])47 b(J.)23
b(J.)g(Dongarra,)i(J.)e(R.)h(Bunc)m(h,)g(C.)f(B.)h(Moler,)g(and)f(G.)g
(W.)h(Stew)m(art.)30 b Fz(LINP)-7 b(A)n(CK)24 b(Users')i(Guide)p
FK(.)j(So)s(ciet)m(y)187 3774 y(for)h(Industrial)d(and)j(Applied)e
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3962 y([24])47 b(J.)35 b(J.)h(Dongarra,)i(J.)d(Du)g(Croz,)i(I.)f(S.)f
(Du\013,)i(and)e(S.)g(Hammarling.)54 b(A)36 b(prop)s(osal)e(for)h(a)h
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(Subprograms.)44 b(In)31 b(G.)h(Ro)s(drigue,)g(editor,)g
Fz(Par)-5 b(al)5 b(lel)35 b(Pr)-5 b(o)g(c)g(essing)36
b(for)e(Scienti\014c)187 4188 y(Computing)p FK(,)46 b(pages)d(40{44.)h
(SIAM,)e(Philadelphia,)g(P)-8 b(A,)42 b(USA,)g(1989.)78
b(\(Pro)s(ceedings)41 b(of)h(the)g(Third)187 4301 y(SIAM)30
b(Conference\).)0 4488 y([25])47 b(J.)38 b(J.)h(Dongarra,)i(J.)d(Du)h
(Croz,)h(I.)f(S.)f(Du\013,)j(and)c(S.)h(Hammarling.)64
b(A)38 b(set)h(of)g(Lev)m(el)f(3)h(Basic)g(Linear)187
4601 y(Algebra)30 b(Subprograms.)39 b Fz(A)n(CM)31 b(T)-7
b(r)i(ans.)34 b(Math.)f(Softwar)-5 b(e)p FK(,)33 b(16:1{28,)g(1990.)43
b(\(Algorithm)29 b(679\).)0 4789 y([26])47 b(J.)39 b(J.)g(Dongarra,)j
(J.)d(Du)g(Croz,)i(S.)e(Hammarling,)h(and)f(R.)g(J.)g(Hanson.)66
b(An)38 b(extended)i(set)f(of)g(F)m(OR-)187 4902 y(TRAN)31
b(Basic)h(Linear)f(Algebra)g(Subprograms.)43 b Fz(A)n(CM)33
b(T)-7 b(r)i(ans.)35 b(Math.)f(Softwar)-5 b(e)p FK(,)34
b(14:1{32,)h(399,)f(1988.)187 5015 y(\(Algorithm)29 b(656\).)0
5202 y([27])47 b(I.)25 b(S.)f(Du\013,)i(M.)f(Marrone,)i(G.)e(Radicati,)
h(and)e(C.)h(Vittoli.)30 b(Lev)m(el)25 b(3)g(Basic)g(Linear)f(Algebra)h
(Subprograms)187 5315 y(for)30 b(sparse)g(matrics:)40
b(A)31 b(user-lev)m(el)f(in)m(terface.)41 b Fz(A)n(CM)31
b(T)-7 b(r)i(ans.)34 b(Math.)f(Softwar)-5 b(e)p FK(,)33
b(23:379{401,)i(1997.)4084 64 y FI(1)4084 177 y(2)4084
290 y(3)4084 403 y(4)4084 516 y(5)4084 628 y(6)4084 741
y(7)4084 854 y(8)4084 967 y(9)4069 1080 y(10)4069 1193
y(11)4069 1306 y(12)4069 1419 y(13)4069 1532 y(14)4069
1645 y(15)4069 1758 y(16)4069 1870 y(17)4069 1983 y(18)4069
2096 y(19)4069 2209 y(20)4069 2322 y(21)4069 2435 y(22)4069
2548 y(23)4069 2661 y(24)4069 2774 y(25)4069 2887 y(26)4069
3000 y(27)4069 3112 y(28)4069 3225 y(29)4069 3338 y(30)4069
3451 y(31)4069 3564 y(32)4069 3677 y(33)4069 3790 y(34)4069
3903 y(35)4069 4016 y(36)4069 4129 y(37)4069 4242 y(38)4069
4354 y(39)4069 4467 y(40)4069 4580 y(41)4069 4693 y(42)4069
4806 y(43)4069 4919 y(44)4069 5032 y(45)4069 5145 y(46)4069
5258 y(47)4069 5371 y(48)p eop
%%Page: 301 311
301 310 bop 0 -165 a FA(BIBLIOGRAPHY)3038 b FK(301)0
91 y([28])47 b(A.)39 b(Elster.)64 b(Basic)39 b(Matrix)f(Subprograms)f
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Fz(Pr)-5 b(o)g(c)g(e)g(e)g(dings)37 b(of)d(the)h(Fifth)g(Distribute)-5
b(d)34 b(Memory)h(Computing)h(Confer)-5 b(enc)g(e)p FK(,)33
b(pages)187 317 y(311{316.)h(IEEE)29 b(Press,)h(1990.)0
498 y([29])47 b(R.)39 b(F)-8 b(algout,)42 b(A.)d(Skjellum,)g(S.)f
(Smith,)h(and)g(C.)f(Still.)63 b(The)39 b(Multicomputer)e(T)-8
b(o)s(olb)s(o)m(x)38 b(Approac)m(h)h(to)187 611 y(Concurren)m(t)e(BLAS)
h(and)g(LA)m(CS.)63 b(In)38 b Fz(Pr)-5 b(o)g(c)g(e)g(e)g(dings)41
b(of)f(the)g(Sc)-5 b(alable)41 b(High)f(Performanc)-5
b(e)41 b(Computing)187 724 y(Confer)-5 b(enc)g(e)33 b(SHPCC-92)p
FK(.)e(IEEE)f(Computer)f(So)s(ciet)m(y)i(Press,)f(1992.)0
905 y([30])47 b(Message)31 b(P)m(assing)d(In)m(terface)i(F)-8
b(orum.)39 b(MPI:)29 b(A)g(Message)i(P)m(assing)d(In)m(terface)i
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b(er)g(c)g(omputer)36 b(Applic)-5 b(ations)34 b(and)g(High)e
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1198 y([31])47 b(G.)37 b(F)-8 b(o)m(x,)41 b(S.)36 b(Otto,)k(and)c(A.)h
(Hey)-8 b(.)61 b(Matrix)36 b(Algorithms)g(on)h(a)g(Hyp)s(ercub)s(e)e
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b(lel)34 b(Computing)p FK(,)e(3:17{31,)h(1987.)0 1492
y([32])47 b(B.)31 b(S.)g(Garb)s(o)m(w,)g(J.)g(M.)g(Bo)m(yle,)h(J.)f(J.)
g(Dongarra,)h(and)e(C.)h(B.)g(Moler.)42 b Fz(Matrix)33
b(Eigensystem)g(R)-5 b(outines)35 b({)187 1605 y(EISP)-7
b(A)n(CK)24 b(Guide)i(Extension)p FK(,)f(v)m(olume)e(51)g(of)g
Fz(L)-5 b(e)g(ctur)g(e)27 b(Notes)e(in)h(Computer)h(Scienc)-5
b(e)p FK(.)28 b(Springer-V)-8 b(erlag,)187 1718 y(Berlin,)29
b(1977.)0 1899 y([33])47 b(G.)34 b(Golub)f(and)g(C.)h(v)-5
b(an)34 b(Loan.)51 b Fz(Matrix)36 b(Computations)p FK(.)54
b(Johns-Hopkins,)33 b(Baltimore,)i(third)d(edition,)187
2011 y(1996.)0 2192 y([34])47 b(M.)30 b(Heath)g(and)f(C.)g(Romine.)38
b(P)m(arallel)28 b(Solution)g(T)-8 b(riangular)27 b(Systems)i(on)g
(Distributed)f(Memory)i(Mul-)187 2305 y(tipro)s(cessors.)40
b Fz(SIAM)31 b(Journal)j(on)f(Scienti\014c)f(and)i(Statistic)-5
b(al)34 b(Computing)p FK(,)e(9:558{588,)j(1988.)0 2486
y([35])47 b(N.)24 b(J.)g(Higham.)30 b Fz(A)-5 b(c)g(cur)g(acy)27
b(and)h(Stability)f(of)g(Numeric)-5 b(al)27 b(Algorithms)p
FK(.)32 b(SIAM,)24 b(Philadelphia,)d(P)-8 b(A,)25 b(1996.)0
2667 y([36])47 b(S.)33 b(Huss-Lederman,)h(E.)g(Jacobson,)h(A.)f(Tsao,)h
(and)e(G.)h(Zhang.)50 b(Matrix)34 b(Multiplication)d(on)i(the)h(In)m
(tel)187 2780 y(T)-8 b(ouc)m(hstone)31 b(DEL)-8 b(T)g(A.)42
b Fz(Concurr)-5 b(ency:)42 b(Pr)-5 b(actic)g(e)34 b(and)f(Exp)-5
b(erienc)g(e)p FK(,)31 b(6\(7\):571{594,)36 b(1994.)0
2960 y([37])47 b(IEEE.)27 b Fz(ANSI/IEEE)c(Standar)-5
b(d)29 b(for)c(Binary)h(Flo)-5 b(ating)27 b(Point)e(A)n(rithmetic:)39
b(Std)25 b(754-1985)p FK(.)31 b(IEEE)21 b(Press,)187
3073 y(New)30 b(Y)-8 b(ork,)32 b(NY,)f(USA,)f(1985.)0
3254 y([38])47 b(ISO/IEC.)199 b Fz(C9X)81 b(F)n(CD)h(Standar)-5
b(d)84 b(\(Dr)-5 b(aft\))p FK(,)99 b(x3j11/98-049,)j(wg14/n843)86
b(edition,)96 b(1998.)187 3367 y(h)m(ttp://h)m(ttp://www)m
(old.dkuug.dk/JTC1/SC22/W)m(G14/.)0 3548 y([39])47 b(C.)27
b(L.)f(La)m(wson,)i(R.)f(J.)g(Hanson,)h(D.)f(Kincaid,)f(and)g(F.)i(T.)f
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3661 y(for)f(F)m(OR)-8 b(TRAN)26 b(usage.)35 b Fz(A)n(CM)27
b(T)-7 b(r)i(ans.)30 b(Math.)f(Softwar)-5 b(e)p FK(,)29
b(5:308{323,)i(1979.)k(\(Algorithm)25 b(539.)j(See)e(also)187
3774 y([21)q(])31 b(and)e([20)r(]\).)0 3954 y([40])47
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b(1988.)0 4248 y([41])47 b(G.)g(Li)g(and)f(T.)h(Coleman.)90
b(A)47 b(New)g(Metho)s(d)g(for)g(Solving)f(T)-8 b(riangular)45
b(Systems)i(on)g(Distributed-)187 4361 y(Memory)37 b(Message-P)m
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4474 y(puting)p FK(,)31 b(10\(2\):382{396,)36 b(1989.)0
4655 y([42])47 b(X.)32 b(Li,)g(J.)f(Demmel,)i(D.)g(Bailey)-8
b(,)32 b(G.)h(Henry)-8 b(,)32 b(Y.)g(Hida,)g(J.)g(Isk)-5
b(andar,)32 b(W.)g(Kahan,)g(A.)h(Kapur,)e(M.)h(Mar-)187
4768 y(tin,)53 b(T.)48 b(T)-8 b(ung,)53 b(and)c(D.)g(Y)-8
b(o)s(o.)97 b(Design,)53 b(implemen)m(tation)48 b(and)g(testing)h(of)g
(extended)g(and)f(mixed)187 4880 y(precision)41 b(blas.)79
b(T)-8 b(ec)m(hnical)43 b(Rep)s(ort)g(CS-00-451,)49 b(Departmen)m(t)c
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y(of)52 b(T)-8 b(ennessee,)59 b(1122)54 b(V)-8 b(olun)m(teer)52
b(Boulev)-5 b(ard,)58 b(Kno)m(xville,)e(TN)c(37996-3450,)62
b(USA,)52 b(2000.)108 b(URL:)187 5106 y(h)m(ttp://www.netlib.org/lapac)
m(k/la)m(wns/.)0 5287 y([43])47 b(W.)36 b(Lic)m(h)m(tenstein)e(and)h
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b(1993.)-214 64 y FI(1)-214 177 y(2)-214 290 y(3)-214
403 y(4)-214 516 y(5)-214 628 y(6)-214 741 y(7)-214 854
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y(12)-230 1419 y(13)-230 1532 y(14)-230 1645 y(15)-230
1758 y(16)-230 1870 y(17)-230 1983 y(18)-230 2096 y(19)-230
2209 y(20)-230 2322 y(21)-230 2435 y(22)-230 2548 y(23)-230
2661 y(24)-230 2774 y(25)-230 2887 y(26)-230 3000 y(27)-230
3112 y(28)-230 3225 y(29)-230 3338 y(30)-230 3451 y(31)-230
3564 y(32)-230 3677 y(33)-230 3790 y(34)-230 3903 y(35)-230
4016 y(36)-230 4129 y(37)-230 4242 y(38)-230 4354 y(39)-230
4467 y(40)-230 4580 y(41)-230 4693 y(42)-230 4806 y(43)-230
4919 y(44)-230 5032 y(45)-230 5145 y(46)-230 5258 y(47)-230
5371 y(48)p eop
%%Page: 302 312
302 311 bop 0 -165 a FK(302)3038 b FA(BIBLIOGRAPHY)0
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392 y([45])47 b(O.)c(McBry)m(an)i(and)e(E.)h(v)-5 b(an)44
b(de)f(V)-8 b(elde.)81 b(Matrix)43 b(and)g(V)-8 b(ector)46
b(Op)s(erations)c(on)i(Hyp)s(ercub)s(e)e(P)m(arallel)187
505 y(Pro)s(cessors.)e Fz(Par)-5 b(al)5 b(lel)34 b(Computing)p
FK(,)e(5:117{126,)i(1987.)0 692 y([46])47 b(D.)36 b(Priest.)57
b(Algorithms)35 b(for)g(arbitrary)g(precision)f(\015oating)i(p)s(oin)m
(t)f(arithmetic.)57 b(In)35 b(P)-8 b(.)36 b(Kornerup)f(and)187
805 y(D.)f(Matula,)g(editors,)g Fz(Pr)-5 b(o)g(c)g(e)g(e)g(dings)37
b(of)f(the)f(10th)i(Symp)-5 b(osium)38 b(on)d(Computer)i(A)n(rithmetic)
p FK(,)d(pages)g(132{)187 918 y(145,)e(Grenoble,)e(F)-8
b(rance,)32 b(June)d(26-28)j(1991.)h(IEEE)c(Computer)h(So)s(ciet)m(y)h
(Press.)0 1106 y([47])47 b(Jonathan)c(Ric)m(hard)e(Shew)m(c)m(h)m(uk.)
78 b(Adaptiv)m(e)43 b(Precision)e(Floating-Poin)m(t)i(Arithmetic)f(and)
h(Fast)g(Ro-)187 1219 y(bust)33 b(Geometric)i(Predicates.)52
b(T)-8 b(ec)m(hnical)33 b(Rep)s(ort)h(CMU-CS-96-140,)k(Sc)m(ho)s(ol)33
b(of)i(Computer)e(Science,)187 1332 y(Carnegie)39 b(Mellon)g(Univ)m
(ersit)m(y)-8 b(,)42 b(Pittsburgh,)e(P)m(ennsylv)-5 b(ania,)41
b(Ma)m(y)g(1996.)70 b(to)41 b(app)s(ear)e(in)f(Discrete)i(&)187
1445 y(Computational)29 b(Geometry)-8 b(.)0 1632 y([48])47
b(B.)35 b(T.)g(Smith,)g(J.)g(M.)h(Bo)m(yle,)h(J.)e(J.)g(Dongarra,)i(B.)
f(S.)f(Garb)s(o)m(w,)h(Y.)f(Ik)m(eb)s(e,)i(V.)e(C.)g(Klema,)h(and)e(C.)
h(B.)187 1745 y(Moler.)44 b Fz(Matrix)34 b(Eigensystem)g(R)-5
b(outines)35 b({)f(EISP)-7 b(A)n(CK)32 b(Guide)p FK(,)h(v)m(olume)e(6)h
(of)g Fz(L)-5 b(e)g(ctur)g(e)34 b(Notes)g(in)g(Com-)187
1858 y(puter)f(Scienc)-5 b(e)p FK(.)40 b(Springer-V)-8
b(erlag,)30 b(Berlin,)f(1976.)0 2046 y([49])47 b(P)-8
b(.)23 b(Strazdins.)k(A)c(High)f(P)m(erformance,)j(P)m(ortable)f
(Distributed)c(BLAS)j(Implemen)m(tation.)28 b(In)22 b
Fz(Pr)-5 b(o)g(c)g(e)g(e)g(dings)187 2159 y(of)33 b(the)g(Sixth)g(Par)
-5 b(al)5 b(lel)34 b(Computing)g(Workshop)p FK(,)e(F)-8
b(ujitsu)30 b(P)m(arallel)f(Computing)g(Cen)m(ter,)i(1996.)0
2346 y([50])47 b(Thinking)27 b(Mac)m(hines)k(Corp)s(oration.)39
b Fz(CMSSL)32 b(for)i(F)-7 b(ortr)i(an)p FK(,)33 b(1990.)0
2534 y([51])47 b(R.)33 b(v)-5 b(an)32 b(de)g(Geijn.)47
b Fz(Using)34 b(PLAP)-7 b(A)n(CK:)32 b(Par)-5 b(al)5
b(lel)36 b(Line)-5 b(ar)36 b(A)n(lgebr)-5 b(a)35 b(Package)p
FK(.)47 b(The)32 b(MIT)g(Press,)h(Cam-)187 2647 y(bridge,)c(Massac)m(h)
m(usetts,)k(1997.)0 2834 y([52])47 b(R.)29 b(v)-5 b(an)28
b(de)h(Geijn)f(and)g(J.)g(W)-8 b(atts.)40 b(SUMMA:)29
b(Scalable)f(Univ)m(ersal)g(Matrix)g(Multiplication)e(Algorithm.)187
2947 y(T)-8 b(ec)m(hnical)42 b(Rep)s(ort)h(UT)f(CS-95-286,)48
b(LAP)-8 b(A)m(CK)43 b(Working)f(Note)i(No.96,)k(Univ)m(ersit)m(y)42
b(of)g(T)-8 b(ennessee,)187 3060 y(1995.)4084 64 y FI(1)4084
177 y(2)4084 290 y(3)4084 403 y(4)4084 516 y(5)4084 628
y(6)4084 741 y(7)4084 854 y(8)4084 967 y(9)4069 1080
y(10)4069 1193 y(11)4069 1306 y(12)4069 1419 y(13)4069
1532 y(14)4069 1645 y(15)4069 1758 y(16)4069 1870 y(17)4069
1983 y(18)4069 2096 y(19)4069 2209 y(20)4069 2322 y(21)4069
2435 y(22)4069 2548 y(23)4069 2661 y(24)4069 2774 y(25)4069
2887 y(26)4069 3000 y(27)4069 3112 y(28)4069 3225 y(29)4069
3338 y(30)4069 3451 y(31)4069 3564 y(32)4069 3677 y(33)4069
3790 y(34)4069 3903 y(35)4069 4016 y(36)4069 4129 y(37)4069
4242 y(38)4069 4354 y(39)4069 4467 y(40)4069 4580 y(41)4069
4693 y(42)4069 4806 y(43)4069 4919 y(44)4069 5032 y(45)4069
5145 y(46)4069 5258 y(47)4069 5371 y(48)p eop
%%Page: 303 313
303 312 bop 0 559 a FH(Index)0 982 y FK(AMAX)p 292 982
28 4 v 34 w(V)-10 b(AL,)30 b(9,)h(42)0 1095 y(AMIN)p
257 1095 V 33 w(V)-10 b(AL,)31 b(9,)g(40)0 1208 y(APPL)-8
b(Y)p 314 1208 V 33 w(GR)m(OT,)31 b(9,)g(49)0 1321 y(AXPBY,)g(9,)g(47)0
1434 y(AXPBY)p 335 1434 V 34 w(a,)g(9,)g(145)0 1547 y(AXPBY)p
335 1547 V 34 w(a)p 414 1547 V 33 w(X,)f(9,)h(145)0 1659
y(AXPBY)p 335 1659 V 34 w(X,)f(9,)h(145)0 1772 y(AXPY)p
271 1772 V 33 w(DOT,)g(9,)g(49)0 1968 y(COPY,)f(9,)h(50)0
2164 y(DOT,)f(9,)h(38)0 2277 y(DOT)p 211 2277 V 33 w(a)p
289 2277 V 33 w(b,)f(9,)h(143)0 2390 y(DOT)p 211 2390
V 33 w(a)p 289 2390 V 33 w(b)p 373 2390 V 32 w(X,)g(9,)g(143)0
2503 y(DOT)p 211 2503 V 33 w(X,)f(9,)h(143)0 2699 y(FPINF)m(O,)g(13,)h
(103)0 2812 y(FPINF)m(O)p 354 2812 V 33 w(X,)f(13,)h(172)0
3008 y(GB)p 140 3008 V 33 w(A)m(CC,)f(11,)g(79)0 3121
y(GB)p 140 3121 V 33 w(ADD,)h(11,)g(80)0 3234 y(GB)p
140 3234 V 33 w(COPY,)e(11,)i(98)0 3346 y(GB)p 140 3346
V 33 w(DIA)m(G)p 411 3346 V 34 w(SCALE,)e(11,)i(72)0
3459 y(GB)p 140 3459 V 33 w(DIA)m(G)p 411 3459 V 34 w(SCALE)p
749 3459 V 32 w(A)m(CC,)f(11,)g(76)0 3572 y(GB)p 140
3572 V 33 w(LRSCALE,)f(11,)h(73)0 3685 y(GB)p 140 3685
V 33 w(NORM,)g(11,)h(69)0 3798 y(GBMV,)g(10,)f(53,)h(147)0
3911 y(GBMV)p 291 3911 V 34 w(a)p 370 3911 V 33 w(b,)e(10,)i(147)0
4024 y(GBMV)p 291 4024 V 34 w(a)p 370 4024 V 33 w(b)p
454 4024 V 32 w(X,)f(10,)h(147)0 4137 y(GBMV)p 291 4137
V 34 w(X,)f(10,)g(147)0 4250 y(GE)p 138 4250 V 33 w(A)m(CC,)f(11,)i(77)
0 4363 y(GE)p 138 4363 V 33 w(ADD,)g(11,)f(80)0 4476
y(GE)p 138 4476 V 33 w(COPY,)f(11,)h(98)0 4588 y(GE)p
138 4588 V 33 w(DIA)m(G)p 409 4588 V 34 w(SCALE,)f(11,)h(72)0
4701 y(GE)p 138 4701 V 33 w(DIA)m(G)p 409 4701 V 34 w(SCALE)p
747 4701 V 32 w(A)m(CC,)f(11,)i(76)0 4814 y(GE)p 138
4814 V 33 w(LRSCALE,)d(11,)j(73)0 4927 y(GE)p 138 4927
V 33 w(NORM,)f(11,)g(69)0 5040 y(GE)p 138 5040 V 33 w(PERMUTE,)f(11,)i
(102)0 5153 y(GE)p 138 5153 V 33 w(SUM)p 373 5153 V 33
w(MV,)f(10,)g(59)0 5266 y(GE)p 138 5266 V 33 w(SUM)p
373 5266 V 33 w(MV)p 557 5266 V 33 w(a)p 635 5266 V 33
w(b,)f(10,)i(154)0 5379 y(GE)p 138 5379 V 33 w(SUM)p
373 5379 V 33 w(MV)p 557 5379 V 33 w(a)p 635 5379 V 33
w(b)p 719 5379 V 32 w(X,)f(10,)h(154)2095 982 y(GE)p
2233 982 V 33 w(SUM)p 2468 982 V 33 w(MV)p 2652 982 V
33 w(X,)f(10,)g(154)2095 1095 y(GE)p 2233 1095 V 33 w(TRANS,)f(11,)i
(101)2095 1208 y(GEMM,)g(11,)f(83)2095 1321 y(GEMM)p
2399 1321 V 34 w(a)p 2478 1321 V 33 w(b,)f(11,)i(157)2095
1434 y(GEMM)p 2399 1434 V 34 w(a)p 2478 1434 V 33 w(b)p
2562 1434 V 32 w(X,)f(11,)h(157)2095 1547 y(GEMM)p 2399
1547 V 34 w(X,)f(11,)g(157)2095 1659 y(GEMV,)h(10,)f(53)2095
1772 y(GEMV)p 2384 1772 V 34 w(a)p 2463 1772 V 33 w(b,)f(10,)h(147)2095
1885 y(GEMV)p 2384 1885 V 34 w(a)p 2463 1885 V 33 w(b)p
2547 1885 V 32 w(X,)g(10,)g(147)2095 1998 y(GEMV)p 2384
1998 V 34 w(X,)f(10,)i(147)2095 2111 y(GEMVER,)f(10,)h(61)2095
2224 y(GEMVT,)f(10,)h(59)2095 2337 y(GEN)p 2301 2337
V 33 w(GR)m(OT,)f(9,)g(43)2095 2450 y(GEN)p 2301 2450
V 33 w(HOUSE,)f(9,)h(45)2095 2563 y(GEN)p 2301 2563 V
33 w(JR)m(OT,)f(9,)h(45)2095 2676 y(GER,)g(10,)g(64)2095
2872 y(HB)p 2232 2872 V 34 w(COPY,)f(11,)h(100)2095 2984
y(HB)p 2232 2984 V 34 w(LRSCALE,)e(11,)i(75)2095 3097
y(HB)p 2232 3097 V 34 w(NORM,)f(11,)i(69)2095 3210 y(HBMV,)g(10,)f(56)
2095 3323 y(HBMV)p 2383 3323 V 34 w(a)p 2462 3323 V 33
w(b,)f(10,)i(150)2095 3436 y(HBMV)p 2383 3436 V 34 w(a)p
2462 3436 V 33 w(b)p 2546 3436 V 33 w(X,)e(10,)i(150)2095
3549 y(HBMV)p 2383 3549 V 34 w(X,)f(10,)g(150)2095 3662
y(HE)p 2230 3662 V 33 w(COPY,)f(11,)i(100)2095 3775 y(HE)p
2230 3775 V 33 w(LRSCALE,)d(11,)j(75)2095 3888 y(HE)p
2230 3888 V 33 w(NORM,)f(11,)g(69)2095 4001 y(HE)p 2230
4001 V 33 w(TRIDIA)m(G)p 2667 4001 V 33 w(R2K,)g(11,)h(97)2095
4114 y(HE)p 2230 4114 V 33 w(TRIDIA)m(G)p 2667 4114 V
33 w(RK,)f(11,)g(92)2095 4226 y(HEMM,)h(85)2095 4339
y(HEMM)p 2396 4339 V 34 w(a)p 2475 4339 V 33 w(b,)e(11,)h(161)2095
4452 y(HEMM)p 2396 4452 V 34 w(a)p 2475 4452 V 33 w(b)p
2559 4452 V 32 w(X,)g(11,)g(161)2095 4565 y(HEMM)p 2396
4565 V 34 w(X,)f(11,)i(161)2095 4678 y(HEMV,)f(10,)h(56)2095
4791 y(HEMV)p 2381 4791 V 34 w(a)p 2460 4791 V 33 w(b,)e(10,)h(150)2095
4904 y(HEMV)p 2381 4904 V 34 w(a)p 2460 4904 V 33 w(b)p
2544 4904 V 32 w(X,)g(10,)g(150)2095 5017 y(HEMV)p 2381
5017 V 34 w(X,)f(10,)i(150)2095 5130 y(HER,)f(10,)g(65)2095
5243 y(HER2,)g(10,)h(67)2095 5356 y(HER2K,)f(11,)g(94)1882
5628 y(303)p eop
%%Page: 304 314
304 313 bop 0 -165 a FK(304)3464 b FA(INDEX)0 91 y FK(HER2K)p
318 91 28 4 v 33 w(a,)31 b(11,)g(170)0 204 y(HER2K)p
318 204 V 33 w(a)p 396 204 V 33 w(X,)g(11,)g(170)0 317
y(HER2K)p 318 317 V 33 w(X,)g(11,)g(170)0 430 y(HERK,)f(11,)i(90)0
543 y(HERK)p 273 543 V 32 w(a,)f(11,)h(167)0 656 y(HERK)p
273 656 V 32 w(a)p 350 656 V 34 w(X,)e(11,)i(167)0 769
y(HERK)p 273 769 V 32 w(X,)f(11,)h(167)0 882 y(HP)p 135
882 V 33 w(COPY,)e(11,)h(100)0 995 y(HP)p 135 995 V 33
w(LRSCALE,)e(11,)j(75)0 1108 y(HP)p 135 1108 V 33 w(NORM,)e(11,)i(69)0
1220 y(HPMV,)f(10,)h(56)0 1333 y(HPMV)p 286 1333 V 33
w(a)p 364 1333 V 33 w(b,)f(10,)g(150)0 1446 y(HPMV)p
286 1446 V 33 w(a)p 364 1446 V 33 w(b)p 448 1446 V 33
w(X,)f(10,)i(150)0 1559 y(HPMV)p 286 1559 V 33 w(X,)f(10,)g(150)0
1672 y(HPR,)g(10,)g(65)0 1785 y(HPR2,)g(10,)g(67)0 1981
y(MAX)p 224 1981 V 33 w(V)-10 b(AL,)31 b(9,)g(41)0 2094
y(MIN)p 189 2094 V 33 w(V)-10 b(AL,)31 b(9,)g(40)0 2290
y(NORM,)g(9,)g(39)0 2486 y(PERMUTE,)f(9,)h(53)0 2682
y(RSCALE,)f(9,)h(47)0 2878 y(SB)p 120 2878 V 33 w(A)m(CC,)f(11,)i(77)0
2990 y(SB)p 120 2990 V 33 w(ADD,)f(11,)h(80)0 3103 y(SB)p
120 3103 V 33 w(COPY,)e(11,)h(98)0 3216 y(SB)p 120 3216
V 33 w(LRSCALE,)e(11,)i(74)0 3329 y(SB)p 120 3329 V 33
w(NORM,)f(11,)i(69)0 3442 y(SBMV,)f(10,)g(55)0 3555 y(SBMV)p
271 3555 V 33 w(a)p 349 3555 V 33 w(b,)f(10,)i(149)0
3668 y(SBMV)p 271 3668 V 33 w(a)p 349 3668 V 33 w(b)p
433 3668 V 33 w(X,)e(10,)i(149)0 3781 y(SBMV)p 271 3781
V 33 w(X,)f(10,)g(149)0 3894 y(SOR)-8 b(T,)30 b(9,)h(51)0
4007 y(SOR)-8 b(TV,)30 b(9,)h(52)0 4120 y(SP)p 118 4120
V 32 w(A)m(CC,)g(11,)g(77)0 4232 y(SP)p 118 4232 V 32
w(ADD,)h(11,)f(80)0 4345 y(SP)p 118 4345 V 32 w(COPY,)f(11,)i(98)0
4458 y(SP)p 118 4458 V 32 w(LRSCALE,)d(11,)j(74)0 4571
y(SP)p 118 4571 V 32 w(NORM,)f(11,)g(69)0 4684 y(SPMV,)f(10,)i(55)0
4797 y(SPMV)p 269 4797 V 33 w(a)p 347 4797 V 33 w(b,)e(10,)h(149)0
4910 y(SPMV)p 269 4910 V 33 w(a)p 347 4910 V 33 w(b)p
431 4910 V 32 w(X,)g(10,)g(149)0 5023 y(SPMV)p 269 5023
V 33 w(X,)f(10,)i(149)0 5136 y(SPR,)e(10,)h(64)0 5249
y(SPR2,)f(10,)i(66)0 5362 y(SUM,)f(9,)g(39)2095 91 y(SUM)p
2302 91 V 33 w(X,)g(9,)g(144)2095 204 y(SUMSQ,)f(9,)h(42)2095
317 y(SW)-10 b(AP)i(,)31 b(9,)g(51)2095 430 y(SY)p 2219
430 V 33 w(A)m(CC,)f(11,)i(77)2095 543 y(SY)p 2219 543
V 33 w(ADD,)f(11,)h(80)2095 656 y(SY)p 2219 656 V 33
w(COPY,)e(11,)h(98)2095 769 y(SY)p 2219 769 V 33 w(LRSCALE,)e(11,)i(74)
2095 882 y(SY)p 2219 882 V 33 w(NORM,)f(11,)i(69)2095
995 y(SY)p 2219 995 V 33 w(TRIDIA)m(G)p 2656 995 V 33
w(R2K,)f(11,)g(95)2095 1108 y(SY)p 2219 1108 V 33 w(TRIDIA)m(G)p
2656 1108 V 33 w(RK,)f(11,)i(91)2095 1220 y(SYMM,)f(84)2095
1333 y(SYMM)p 2385 1333 V 33 w(a)p 2463 1333 V 34 w(b,)f(11,)h(159)2095
1446 y(SYMM)p 2385 1446 V 33 w(a)p 2463 1446 V 34 w(b)p
2548 1446 V 32 w(X,)g(11,)g(159)2095 1559 y(SYMM)p 2385
1559 V 33 w(X,)g(11,)h(159)2095 1672 y(SYMV,)f(10,)h(55)2095
1785 y(SYMV)p 2370 1785 V 33 w(a)p 2448 1785 V 33 w(b,)e(10,)i(149)2095
1898 y(SYMV)p 2370 1898 V 33 w(a)p 2448 1898 V 33 w(b)p
2532 1898 V 33 w(X,)e(10,)i(149)2095 2011 y(SYMV)p 2370
2011 V 33 w(X,)f(10,)g(149)2095 2124 y(SYR,)f(10,)i(64)2095
2237 y(SYR2,)f(10,)g(66)2095 2350 y(SYR2K,)g(11,)g(93)2095
2462 y(SYR2K)p 2402 2462 V 33 w(a,)g(11,)g(169)2095 2575
y(SYR2K)p 2402 2575 V 33 w(a)p 2480 2575 V 33 w(X,)g(11,)g(169)2095
2688 y(SYR2K)p 2402 2688 V 33 w(X,)g(11,)g(169)2095 2801
y(SYRK,)f(11,)i(89)2095 2914 y(SYRK)p 2357 2914 V 32
w(a,)f(11,)h(166)2095 3027 y(SYRK)p 2357 3027 V 32 w(a)p
2434 3027 V 34 w(X,)e(11,)i(166)2095 3140 y(SYRK)p 2357
3140 V 32 w(X,)f(11,)h(166)2095 3336 y(TB)p 2230 3336
V 33 w(A)m(CC,)f(11,)g(79)2095 3449 y(TB)p 2230 3449
V 33 w(ADD,)h(11,)f(80)2095 3562 y(TB)p 2230 3562 V 33
w(COPY,)f(11,)i(98)2095 3675 y(TB)p 2230 3675 V 33 w(NORM,)f(11,)g(69)
2095 3787 y(TBMV,)g(10,)h(57)2095 3900 y(TBMV)p 2381
3900 V 34 w(a,)f(10,)g(152)2095 4013 y(TBMV)p 2381 4013
V 34 w(a)p 2460 4013 V 33 w(X,)g(10,)g(152)2095 4126
y(TBMV)p 2381 4126 V 34 w(X,)f(10,)i(152)2095 4239 y(TBSV,)f(10,)g(62)
2095 4352 y(TBSV)p 2349 4352 V 33 w(a,)g(10,)g(155)2095
4465 y(TBSV)p 2349 4465 V 33 w(a)p 2427 4465 V 33 w(X,)g(10,)g(155)2095
4578 y(TBSV)p 2349 4578 V 33 w(X,)f(10,)i(155)2095 4691
y(TP)p 2228 4691 V 33 w(A)m(CC,)e(11,)i(79)2095 4804
y(TP)p 2228 4804 V 33 w(ADD,)f(11,)h(80)2095 4917 y(TP)p
2228 4917 V 33 w(COPY,)e(11,)h(98)2095 5029 y(TP)p 2228
5029 V 33 w(NORM,)f(11,)i(69)2095 5142 y(TPMV,)f(10,)g(57)2095
5255 y(TPMV)p 2379 5255 V 33 w(a,)g(10,)h(152)2095 5368
y(TPMV)p 2379 5368 V 33 w(a)p 2457 5368 V 33 w(X,)f(10,)g(152)4084
64 y FI(1)4084 177 y(2)4084 290 y(3)4084 403 y(4)4084
516 y(5)4084 628 y(6)4084 741 y(7)4084 854 y(8)4084 967
y(9)4069 1080 y(10)4069 1193 y(11)4069 1306 y(12)4069
1419 y(13)4069 1532 y(14)4069 1645 y(15)4069 1758 y(16)4069
1870 y(17)4069 1983 y(18)4069 2096 y(19)4069 2209 y(20)4069
2322 y(21)4069 2435 y(22)4069 2548 y(23)4069 2661 y(24)4069
2774 y(25)4069 2887 y(26)4069 3000 y(27)4069 3112 y(28)4069
3225 y(29)4069 3338 y(30)4069 3451 y(31)4069 3564 y(32)4069
3677 y(33)4069 3790 y(34)4069 3903 y(35)4069 4016 y(36)4069
4129 y(37)4069 4242 y(38)4069 4354 y(39)4069 4467 y(40)4069
4580 y(41)4069 4693 y(42)4069 4806 y(43)4069 4919 y(44)4069
5032 y(45)4069 5145 y(46)4069 5258 y(47)4069 5371 y(48)p
eop
%%Page: 305 315
305 314 bop 0 -165 a FA(INDEX)3464 b FK(305)0 91 y(TPMV)p
284 91 28 4 v 33 w(X,)31 b(10,)g(152)0 204 y(TPSV,)f(10,)h(62)0
317 y(TPSV)p 252 317 V 32 w(a,)g(10,)g(155)0 430 y(TPSV)p
252 430 V 32 w(a)p 329 430 V 33 w(X,)g(10,)g(155)0 543
y(TPSV)p 252 543 V 32 w(X,)g(10,)g(155)0 656 y(TR)p 138
656 V 32 w(A)m(CC,)g(11,)g(79)0 769 y(TR)p 138 769 V
32 w(ADD,)h(11,)f(80)0 882 y(TR)p 138 882 V 32 w(COPY,)f(11,)i(98)0
995 y(TR)p 138 995 V 32 w(NORM,)f(11,)g(69)0 1108 y(TRMM,)g(11,)g(86)0
1220 y(TRMM)p 304 1220 V 33 w(a,)g(11,)g(162)0 1333 y(TRMM)p
304 1333 V 33 w(a)p 382 1333 V 33 w(X,)g(11,)g(162)0
1446 y(TRMM)p 304 1446 V 33 w(X,)g(11,)g(162)0 1559 y(TRMV,)g(10,)g(57)
0 1672 y(TRMV)p 289 1672 V 33 w(a,)g(10,)g(152)0 1785
y(TRMV)p 289 1785 V 33 w(a)p 367 1785 V 33 w(X,)g(10,)g(152)0
1898 y(TRMV)p 289 1898 V 33 w(X,)g(10,)g(152)0 2011 y(TRMVT,)f(10,)i
(60)0 2124 y(TRSM,)e(11,)h(88)0 2237 y(TRSM)p 272 2237
V 32 w(a,)g(11,)h(164)0 2350 y(TRSM)p 272 2350 V 32 w(a)p
349 2350 V 33 w(X,)f(11,)h(164)0 2462 y(TRSM)p 272 2462
V 32 w(X,)f(11,)g(164)0 2575 y(TRSV,)f(10,)h(62)0 2688
y(TRSV)p 257 2688 V 32 w(a,)g(10,)g(155)0 2801 y(TRSV)p
257 2801 V 32 w(a)p 334 2801 V 33 w(X,)g(10,)g(155)0
2914 y(TRSV)p 257 2914 V 32 w(X,)g(10,)g(155)0 3110 y(USAXPY,)g(9,)g
(118)0 3223 y(USCR)p 257 3223 V 32 w(BEGIN,)g(123)0 3336
y(USCR)p 257 3336 V 32 w(BLOCK)p 618 3336 V 32 w(BEGIN,)g(124)0
3449 y(USCR)p 257 3449 V 32 w(END,)g(129)0 3562 y(USCR)p
257 3562 V 32 w(INSER)-8 b(T)p 628 3562 V 32 w(BLOCK,)30
b(128)0 3675 y(USCR)p 257 3675 V 32 w(INSER)-8 b(T)p
628 3675 V 32 w(CLIQUE,)30 b(128)0 3787 y(USCR)p 257
3787 V 32 w(INSER)-8 b(T)p 628 3787 V 32 w(COL,)30 b(126)0
3900 y(USCR)p 257 3900 V 32 w(INSER)-8 b(T)p 628 3900
V 32 w(ENTRIES,)29 b(126)0 4013 y(USCR)p 257 4013 V 32
w(INSER)-8 b(T)p 628 4013 V 32 w(ENTR)g(Y,)31 b(125)0
4126 y(USCR)p 257 4126 V 32 w(INSER)-8 b(T)p 628 4126
V 32 w(R)m(O)m(W,)32 b(127)0 4239 y(USDOT,)e(9,)h(117)0
4352 y(USDS,)f(131)0 4465 y(USGA,)h(9,)g(118)0 4578 y(USGP)-8
b(,)31 b(130)0 4691 y(USGZ,)f(9,)h(119)0 4804 y(USMM,)g(11,)g(122)0
4917 y(USMV,)g(10,)g(120)0 5029 y(USSC,)e(9,)i(119)0
5142 y(USSM,)f(11,)i(122)0 5255 y(USSP)-8 b(,)30 b(130)0
5368 y(USSV,)g(10,)h(121)2095 91 y(W)-10 b(AXPBY,)32
b(9,)f(48)2095 204 y(W)-10 b(AXPBY)p 2513 204 V 34 w(a)p
2592 204 V 33 w(b,)30 b(9,)h(146)2095 317 y(W)-10 b(AXPBY)p
2513 317 V 34 w(a)p 2592 317 V 33 w(b)p 2676 317 V 33
w(X,)30 b(9,)h(146)2095 430 y(W)-10 b(AXPBY)p 2513 430
V 34 w(X,)31 b(9,)g(146)-214 64 y FI(1)-214 177 y(2)-214
290 y(3)-214 403 y(4)-214 516 y(5)-214 628 y(6)-214 741
y(7)-214 854 y(8)-214 967 y(9)-230 1080 y(10)-230 1193
y(11)-230 1306 y(12)-230 1419 y(13)-230 1532 y(14)-230
1645 y(15)-230 1758 y(16)-230 1870 y(17)-230 1983 y(18)-230
2096 y(19)-230 2209 y(20)-230 2322 y(21)-230 2435 y(22)-230
2548 y(23)-230 2661 y(24)-230 2774 y(25)-230 2887 y(26)-230
3000 y(27)-230 3112 y(28)-230 3225 y(29)-230 3338 y(30)-230
3451 y(31)-230 3564 y(32)-230 3677 y(33)-230 3790 y(34)-230
3903 y(35)-230 4016 y(36)-230 4129 y(37)-230 4242 y(38)-230
4354 y(39)-230 4467 y(40)-230 4580 y(41)-230 4693 y(42)-230
4806 y(43)-230 4919 y(44)-230 5032 y(45)-230 5145 y(46)-230
5258 y(47)-230 5371 y(48)p eop
%%Trailer
end
userdict /end-hook known{end-hook}if
%%EOF