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x Shift sub y Shift sub moveto
gsave
curveticks
{ y yOld sub x xOld sub Atan 180 sub /rotAngle ED
x y translate rotAngle rotate
0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
SymbolLinewidth setlinewidth stroke
}
{
x Shift sub y Shift sub moveto
rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
Symbol show
}
ifelse
grestore
}
pathforall
% curveticks
% { gsave
% x y translate rotAngle rotate
% 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
% SymbolLinewidth setlinewidth stroke grestore
% } if
z
} def
%
/OpenSymbolCurve {
OpenCurve
0.1 setflat
/Shift Symbol stringwidth pop 2 div def
CurvePath
} def
%
/AltCurve {
{ false NArray n 2 mul 2 roll
[ n 2 mul 3 sub 1 roll ] aload
/Points ED
n 2 mul -2 roll }
{ false NArray } ifelse
n 4 lt { n { pop pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse
} def
%
/AltOpenSymbolCurve {
AltCurve
0.1 setflat
/Shift Symbol stringwidth pop 2 div def
CurvePath
} def
%
/ClosedCurve {
NArray n 3 lt
{ n { pop pop } repeat }
{ n 3 gt { CheckClosed } if
6 copy n 2 mul 6 add 6 roll
IC CC x y moveto n { NC } repeat
closepath pop pop
} ifelse
} def
%
/ClosedSymbolCurve {
ClosedCurve
0.1 setflat
/Shift Symbol stringwidth pop 2 div def
CurvePath
} def
%
/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def
/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def
/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } def
%
/FontDot {
DS 2 mul dup
matrix scale matrix concatmatrix exch matrix
rotate matrix concatmatrix exch
findfont exch makefont setfont
} def
%
/Rect {
x1 y1 y2 add 2 div moveto
x1 y2 lineto
x2 y2 lineto
x2 y1 lineto
x1 y1 lineto
closepath
} def
%
/OvalFrame {
x1 x2 eq y1 y2 eq or
{ pop pop x1 y1 moveto x2 y2 L }
{ y1 y2 sub abs x1 x2 sub abs 2 copy gt
{ exch pop } { pop } ifelse
2 div exch { dup 3 1 roll mul exch } if
2 copy lt { pop } { exch pop } ifelse
/b ED
x1 y1 y2 add 2 div moveto
x1 y2 x2 y2 b arcto
x2 y2 x2 y1 b arcto
x2 y1 x1 y1 b arcto
x1 y1 x1 y2 b arcto
16 { pop } repeat
closepath
} ifelse
} def
%
/Frame {
CLW mul /a ED
3 -1 roll
2 copy gt { exch } if
a sub /y2 ED
a add /y1 ED
2 copy gt { exch } if
a sub /x2 ED
a add /x1 ED
1 index 0 eq { pop pop Rect } { OvalFrame } ifelse
} def
%
/BezierNArray {
/f ED
counttomark 2 div dup cvi /n ED
n eq not { exch pop } if
n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat
f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse
} def
%
/OpenBezier {
BezierNArray
n 1 eq
{ pop pop }
{ ArrowA n 4 sub 3 idiv
{ 6 2 roll 4 2 roll curveto } repeat
6 2 roll 4 2 roll ArrowB curveto } ifelse
} def
%
/OpenSymbolBezier {
OpenBezier
0.1 setflat
/Shift Symbol stringwidth pop 2 div def
CurvePath
} def
%
/ClosedBezier {
BezierNArray
n 1 eq
{ pop pop }
{ moveto n 1 sub 3 idiv
{ 6 2 roll 4 2 roll curveto } repeat
closepath } ifelse
} def
%
/ClosedSymbolBezier {
/f ED % save showpoints value
2 copy /yEnd ED /xEnd ED
counttomark -2 roll 2 copy /yStart ED /xStart ED
counttomark 2 roll
f
ClosedBezier
0.1 setflat
/Shift Symbol stringwidth pop 2 div def
CurvePath
[ xEnd yEnd xStart yStart SymbolLine
} def
%
/BezierShowPoints {
gsave
Points aload length 2 div cvi /n ED
moveto
n 1 sub { lineto } repeat
CLW 2 div SLW [ 4 4 ] 0 setdash stroke
grestore
} def
%
/Parab {
/y0 ED /x0 ED /y1 ED /x1 ED
/dx x0 x1 sub 3 div def
/dy y0 y1 sub 3 div def
x0 dx sub y0 dy add x1 y1 ArrowA
x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB
curveto
/Points [ x1 y1 x0 y0 x0 2 mul x1 sub y1 ] def
} def
%
/Parab1 { % 1 end | 0 SP
/ySP ED /xSP ED /y1 ED /x1 ED
/dx xSP x1 sub 3 div def
/dy ySP y1 sub 3 div def
newpath x1 y1 moveto xSP y1 lineto xSP ySP lineto
x1 ySP lineto closepath clip
currentpoint
newpath moveto
xSP dx sub ySP dy add x1 y1 ArrowA
xSP dx add ySP dy add xSP 2 mul x1 sub y1 ArrowB
curveto
/Points [ x1 y1 xSP ySP xSP 2 mul x1 sub y1 ] def
} def
%
/Grid {
newpath
/a 4 string def
/b ED % psk@gridlabels in pt
/c ED % { \pst@usecolor\psgridlabelcolor }
/n ED % psk@griddots
cvi dup 1 lt { pop 1 } if
/s ED % \psk@subgriddiv
s div dup 0 eq { pop 1 } if
/dy ED s div dup 0 eq { pop 1 } if % \pst@number\psyunit abs
/dx ED dy div round dy mul % \pst@number\psxunit abs
/y0 ED dx div round dx mul
/x0 ED dy div round cvi
/y2 ED dx div round cvi
/x2 ED dy div round cvi
/y1 ED dx div round cvi
/x1 ED
/h y2 y1 sub 0 gt { 1 } { -1 } ifelse def
/w x2 x1 sub 0 gt { 1 } { -1 } ifelse def
b 0 gt {
/z1 b 4 div CLW 2 div add def
% /Helvetica findfont b scalefont setfont
/b b .95 mul CLW 2 div add def } if
systemdict /setstrokeadjust known
{ true setstrokeadjust /t { } def }
{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add
exch itransform } bind def } ifelse
gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse
/i x1 def
/f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def
/g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def
x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if
{ i dx mul dup y0 moveto
b 0 gt
{ gsave c i a cvs dup stringwidth pop
/z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse
h 0 gt {b neg}{z1} ifelse
rmoveto show grestore } if
dup t f moveto
g t L stroke
/i i w add def
} repeat
grestore
gsave
n 0 gt
% DG/SR modification begin - Nov. 7, 1997 - Patch 1
%{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }
{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
% DG/SR modification end
{ 2 setlinecap } ifelse
/i y1 def
/f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def
/g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def
y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if
{ newpath i dy mul dup x0 exch moveto
b 0 gt { gsave c i a cvs dup stringwidth pop
/z2 ED
w 0 gt {z1 z2 add neg} {z1} ifelse
h 0 gt {z1} {b neg} ifelse
rmoveto show grestore } if
dup f exch t moveto
g exch t L stroke
/i i h add def
} repeat
grestore
} def
%
/ArcArrow {
/d ED /b ED /a ED
gsave
newpath 0 -1000 moveto clip
newpath
0 1 0 0 b
grestore
c mul
/e ED
pop pop pop r a e d PtoC y add exch x add
exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
mul neg d
} def
%
/Ellipse {
/rotAngle ED
/mtrx CM def
T
rotAngle rotate
scale 0 0 1 5 3 roll arc
mtrx setmatrix
} def
%
/ArcAdjust { %%%% Vincent Guirardel
% given a target length (targetLength) and an initial angle (angle0) [in the stack],
% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
% This computes an angle t such that (x0,y0) is at distance
% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
% contrary to TvZ's code.
% To achieve, this, one iterates the following process: start with some angle t,
% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
%
% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
% the value of d = add/sub is used to know on which side we have to move.
% It is only used in the initialisation of the angle before the iteration.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Input stack: 1: target length 2: initial angle
% variables used : rx, ry, d (=add/sub)
%
/targetLength ED /angle0 ED
/x0 rx angle0 cos mul def
/y0 ry angle0 sin mul def
% we are looking for an angle t such that (x0,y0) is at distance targetLength
% from the point M(t)=(rx*cos(t),ry*sin(t)))
%initialisation of angle (using 1st order approx = TvZ's code)
targetLength 57.2958 mul
angle0 sin rx mul dup mul
angle0 cos ry mul dup mul
add sqrt div
% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
% (if the ellipse is very curved at the point where we draw the arrow, %
% the value can be much more than 360 degrees !)
% this should avoid going on the wrong side (more than 180 degrees) or go near
% a bad attractive point (at 180 degrees)
dup 90 ge { pop 90 } if
angle0 exch d % add or sub
% maximum number of times to iterate the iterative procedure:
% iterative procedure: takes an angle t on top of stack, computes a
% better angle (and put it on top of stack)
30 { dup
% compute distance D between (x0,y0) and M(t)
dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
% if D almost equals targetLength, we stop
dup targetLength sub abs 1e-5 le { pop exit } if
% stack now contains D t
% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
exch dup cos rx mul x0 sub exch sin ry mul y0 sub
% stack contains: y(t)-y0, x(t)-x0, d
2 index Div targetLength mul y0 add ry Div exch
2 index Div targetLength mul x0 add rx Div
% stack contains x(t')/rx , y(t')/ry , d
% now compute t', and remove D from stack
atan exch pop
} repeat
% we don't look at what happened... in particular, if targetLength is greater
% than the diameter of the ellipse...
% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
% to give back the result as a an angle relative to angle0 we could add the following line:
% angle0 sub 0 exch d
%
% begin bug fix 2006-01-11
% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180
%(we don't want to make the ellipse turn more or less than it should)...
dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
% end bug fix
} def
%
/EllipticArcArrow {
/d ED % is add or sub
/b ED % arrow procedure
/a1 ED % angle
gsave
newpath
0 -1000 moveto
clip % Set clippath far from arrow.
newpath
0 1 0 0 b % Draw arrow to determine length.
grestore
% Length of arrow is on top of stack. Next 3 numbers are junk.
%
a1 exch ArcAdjust % Angular position of base of arrow.
/a2 ED
pop pop pop
a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig
a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig
a1 cos rx mul xOrig add %
a1 sin ry mul yOrig add %
% Now arrow tip coor and base coor are on stack.
b pop pop pop pop % Draw arrow, and discard coordinates.
a2 CLW 8 div
% change value of d (test it by looking if `` 1 1 d '' gives 2 or not )
1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
ArcAdjust
% resets original value of d
1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap.
} def
%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
%
/Rot { CP CP translate 3 -1 roll neg rotate NET } def
%
/RotBegin {
tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
/TMatrix [ TMatrix CM ] cvx def
/a ED
a Rot /RAngle [ RAngle dup a add ] cvx def
} def
%
/RotEnd {
/TMatrix [ TMatrix setmatrix ] cvx def
/RAngle [ RAngle pop ] cvx def
} def
%
/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
%
/Uput {
/a ED
add 2 div /h ED 2
div /w ED
/s a sin def
/c a cos def
/b s abs c abs 2 copy gt dup
/q ED
{ pop } { exch pop } ifelse def
/w1 c b div w mul def
/h1 s b div h mul def
q { w1 abs w sub dup c mul abs }{ h1 abs h sub dup s mul abs } ifelse
} def
%
/UUput {
/z ED
abs /y ED
/x ED
q { x s div c mul abs y gt }{ x c div s mul abs y gt } ifelse
{ x x mul y y mul sub z z mul add sqrt z add }
{ q { x s div } { x c div } ifelse abs
} ifelse
a PtoC
h1 add exch
w1 add exch
} def
%
/BeginOL {
dup (all) eq exch TheOL eq or
{ IfVisible not { Visible /IfVisible true def } if }
{ IfVisible { Invisible /IfVisible false def } if } ifelse
} def
%
/InitOL {
/OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
/Visible { CP OLUnit idtransform T moveto } def
/Invisible { CP OLUnit neg exch neg exch idtransform T moveto } def
/BOL { BeginOL } def
/IfVisible true def
} def
%
end
%-----------------------------------------------------------------------------%
%
% END pstricks.pro
%%EndProcSet
%%BeginProcSet: pst-algparser.pro 0 0
% $Id: pst-algparser.pro 594 2011-10-31 18:13:18Z herbert $
%%
%% PostScript prologue for PSTricks algorithm parser
%% Version 0.04, 2011/10/21
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%%
%%-----------------------------------------------------------------------------%
%
/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez
%
/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
%
% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.13
%
% 09/2011 DR factorial with ! added
%
% E->T|E+T
% T->FS|T*FS
% FS -> F | +FS | -FS
% F->P|F^SF|P!
% P->(E)|literal
% literal->number|var|var[E]|func(params)
% params->E|E,param
% number->TOBEFINISHED
%
%% E expression, T term, SF signed factor, F factor, P power
%
%% parser
%
%% str
%
%% C->E<condition_operators>E
%% STR index -> STR index+lenExpr
/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def
%
%% analyze Expression List (separator , or | )
%% STR index -> STR index+lenExpr
%% /AnalyzeListOfE {
%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
%% NextNonBlankChar dup 0 eq { pop exit } if
%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
%% AnalyzeListOfEPostHook
%% } def
/AnalyzeListOfE {
/NotFirst false def
{ NextNonBlankChar pop AnalyzeExpr
NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
dup Strlen eq { exit } if NextNonBlankChar
dup 44 ne 1 index 124 ne and
{ dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
if pop 1 add } loop
AnalyzeListOfEPostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% E->T|E+T
%% STR index -> STR index+lenExpr
/AnalyzeExpr {
AnalyzePreHook AnalyzeTerm IsEndingExpr
{ dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
{ { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
ifelse
AnalyzePostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% T->FS|T*FS
%% STR index
/AnalyzeTerm {
AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
{ dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
{ { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
ifelse
AnalyzePostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% FS -> F | +FS | -FS
%% STR index
/AnalyzeSignedFactor {
AnalyzePreHook 2 copy get dup IsUnaryOp
{ RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
{ pop AnalyzeFactor }
ifelse AnalyzePostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% F->P|F^P|P!
%% STR index
/AnalyzeFactor {
AnalyzePreHook AnalyzePower IsEndingFactor
{ dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
{ { dup 33 eq%% is there a ! DR 09/2011
{ pop 1 add NextNonBlankChar pop EvalFactorial }
{ RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower }
ifelse
IsEndingFactor { pop exit } if } loop }
ifelse AnalyzePostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% P->(E)|literal
%% STR index
/AnalyzePower {
%% depending of first char either a number, or a literal
2 copy get dup 40 eq%%an open par
{ pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
{ AnalyzeLiteral }
ifelse
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% STR index STR[index] -> STR index
%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% recognize + or -
%% chr -> T/F
/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% a number can contain only : 0123456789.
%% chr -> T/F
/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% STR index -> STR index number
%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
%% STR index -> STR index' number
/ReadNumber {
exch dup 3 -1 roll dup 3 1 roll
%%read mantissa
{ 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
dup 101 eq exch 69 eq or
%%% there is a "e" or "E" -> read exponant
{ 1 add 2 copy get dup IsUnaryOp
{ pop 1 add 2 copy get } if
{ IsNumber not { exit } if 1 add 2 copy get } loop }
if
dup 4 1 roll
3 -1 roll exch 1 index sub getinterval
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% a number can contain only : 0123456789.
%% chr -> T/F
/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% STR index -> STR index number
%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
%% STR index -> STR index' number
/ReadCondOp {
NextNonBlankChar 1 index 4 1 roll
{ IsCondOp not { exit } if 1 add 2 copy get } loop
2 copy 5 -1 roll
exch 1 index sub getinterval 3 1 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% a literal can contain only : 0123456789.
%% chr -> T/F
/IsLiteral {%
dup 48 ge exch dup 57 le 3 -1 roll and exch
dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch
dup 97 ge exch 122 le and or } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
%% STR index -> literal STR index' nextchr
/ReadLiteral {
exch dup 3 -1 roll dup 3 1 roll
%%read literal core
{ 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% expr is ended by end of str or a clpar
%% STR index -> STR index STR[index] T/F
/IsEndingExpr {%
2 copy dup Strlen eq
%% if end of str is reached -> end !
{ pop pop 0 true }
%% ending chr -> clpar, comma, |, <, >, =, !,
{get dup dup 41 eq
exch dup 124 eq
exch dup 93 eq
exch dup 44 eq
exch dup 30 eq
exch dup 60 ge exch 62 le and or or or or or}
ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% expr is ended by end of str or a +-
%% STR index -> STR index STR[index] T/F
/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% expr is ended by end of str or */
%% STR index -> STR index STR[index] T/F
/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% expr is ended by end of str or ^
%% STR index -> STR index STR[index] T/F
/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% STR index -> STR index STR[index]
/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
%%%%%%%%%%%%%%%%%%%%%%%%
%% DEBUG
/BRK {false} def
/BRKtrue {/BRK true def} def
/BRKStop {BRK {BRKtoto} if } def
/BRKEvalStop {BRK exch if } def
/BRKBRK2true {BRK {BRK2true} if } def
/BRK2 {false} def
/BRK2true {/BRK2 true def} def
/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
end
%
%-------------------------------------------------------------------------------%
%
/tx@AlgToPs 12 dict def tx@AlgToPs begin
%
%% algExpr -> PSVector
/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
/Strlen 0 def
/EvalListOfExpr {} def%
/EvalNumber {%
ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
exch 1 add array astore def NextNonBlankChar pop } def
/EvalAddSub {%
/ExpressionVector ExpressionVector aload length dup 5 add -1 roll
43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
} def
/EvalMulDiv {%
/ExpressionVector ExpressionVector aload length dup 5 add -1 roll
42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
} def
/EvalPower {%
/ExpressionVector ExpressionVector aload length dup 5 add -1 roll
pop /exp cvx exch 1 add array astore def
} def
/EvalFactorial {% DR 09/2011
/ExpressionVector ExpressionVector aload length
/fact cvx exch 1 add array astore def
} def
/EvalLiteral {%
ReadLiteral
dup 40 eq%%% there is an open par -> function call
{ pop 2 index
dup (Sum) eq { EvalSum }
{ dup (IfTE) eq { EvalCond }
{ dup (Derive) eq { pop EvalDerive }
{ pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
/ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
{ /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
dup 91 eq%%% there is an open bracket -> vector element
{ pop 1 add NextNonBlankChar pop AnalyzeExpr
/ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
{ pop NextNonBlankChar pop }
ifelse}
ifelse
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% the derive function : Derive(n,f(x))
%% firstparindex lastparindex ->
/EvalDerive {
%% manage the function descripiton
1 add ReadNumber 3 1 roll NextNonBlankChar
44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
1 add NextNonBlankChar pop
3 -1 roll cvi
dup 0 eq
{ pop AnalyzeExpr 3 -1 roll pop 1 add }
{ 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll
{ (x) tx@Derive begin Derive end } repeat
ExpressionVector exch /ExpressionVector [] def
AlgToPs aload length
/ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def
l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
1 index length /Strlen exch def } ifelse
} def
/EvalSum {%
pop 1 add NextNonBlankChar pop
%% read the variable name
ReadLiteral pop NextNonBlankChar
44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
%% read the initial value
1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
%% read the increment value
1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
%% read the limit value
1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
/ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
5 -1 roll 4 add array astore def
%% keep ExpressionVector for later and create a new one for internal Sum computation
ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
1 add NextNonBlankChar pop AnalyzeExpr
%% add each term
/ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
/ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
array astore def 3 -1 roll pop 1 add
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Convert to radians if trigo function call
%% (name) ->
/TrigoFunc {
dup (cos) eq 1 index (sin) eq or exch (tan) eq or
{ /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
array astore def
} if
} def
/EvalCond {%
pop 1 add AnalyzeCond NextNonBlankChar
44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
ExpressionVector 3 1 roll /ExpressionVector [] def
1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
1 add AnalyzeExpr
NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
ExpressionVector
/ExpressionVector 6 -1 roll aload length dup
6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
1 add 3 -1 roll pop
} def
%% CondOp STR index
/EvalCondOp {%
3 -1 roll
dup (=) eq { /eq } {%
dup (<) eq { /lt } {%
dup (>) eq { /gt } {%
dup (>=) eq { /ge } {%
dup (<=) eq { /ge } {%
dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
cvx exch pop
/ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
/EvalUnaryOp {
3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% H O O K S
/AnalyzePreHook {} bind def
/PreEvalHook {} bind def
/AnalyzeListOfEPostHook {} bind def
/AnalyzePostHook {} def
/RollOp { 3 1 roll } bind def
end %tx@CoreAnalyzerDict
%
%--------------------------------------------------------------------%
%
/tx@Derive 41 dict def tx@Derive begin
%%increase ^^ for each function added
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% algExpr variable -> PSVector
/Derive {%
10240 string 3 1 roll 0 3 1 roll
/Variable exch def
tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
} def
/Strlen 0 def
/InitParser { dup length /Strlen exch def 0 } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% algExpr variable index -> PSVector
/DeriveIndexed {%
3 1 roll 10240 string 3 1 roll 0 3 1 roll
/Variable exch def
tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u,v)'=-(u',v')
/EvalListOfExpr {%
4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
2 copy 7 -1 roll dup length 4 1 roll putinterval add
6 -2 roll pop pop
2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (-u)'=-(u')
/EvalUnaryOp {
4 -2 roll 4 index (0) eq
{ (0) StrConcat 7 -1 roll pop }
{ 7 -1 roll 45 eq
{ AddSub AddOpPar true } { false } ifelse
3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
2 copy pop 0 6 2 roll GetIntervalNewStr
7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (number)'=0
/EvalNumber { ReadNumber (0) 6 2 roll } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u+v)'=u'+v'
/EvalAddSub {%
7 index dup (0) eq
{ pop true }%% du=0 nothing added
{ dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
ifelse
5 index dup (0) eq
{ pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0
{ exch
{ 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
{ 5 -2 roll 7 index 43 eq%%something yet added
{ AddAdd false } { AddSub AddOpPar true } ifelse }
ifelse 11 1 roll
3 -1 roll StrConcat 10 -1 roll { AddClPar } if
2 copy pop 0 6 2 roll GetIntervalNewStr }
ifelse
mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u*v)' or (u/v)'
/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u*v)'=u'*v+u*v'
/EvalMul {%
4 -2 roll 7 index dup (0) eq
{ pop false }%%du=0
{ (1) eq%%du=1
{ false }
{ AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
true }%%du!=0
ifelse
5 1 roll 5 index (0) eq
{ 5 -1 roll not { (0) StrConcat } if }%%dv=0
{ 5 -1 roll { AddAdd } if
4 index (1) eq
{ 8 index StrConcat }
{ AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
ifelse
}%%dv!=0
ifelse
2 copy pop 0 6 2 roll GetIntervalNewStr
mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u/v)'=(u'*v-u*v')/v^2
/EvalDiv {%
4 -2 roll
4 index (0) eq%%dv=0 -> u'/v
{ 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
{ 7 index dup (0) eq
{ pop }%%du=0
{ (1) eq%%du=1
{ false }
{ AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
ifelse
AddSub
4 index (1) eq
{ 8 index StrConcat }
{ AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
ifelse
%}%%dv!=0
2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
ifelse
2 copy pop 0 6 2 roll GetIntervalNewStr
mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% str1 index str2 -> str1 index
/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
/EvalPower {%
4 -2 roll 7 index (0) eq
{%%if du=0 then (u^v)'=v'ln(u)u^v
4 index (0) eq
{ (0) StrConcat }%%if dv=0 then (u^v)'=0
{ 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
}
{%%du!=0
4 index (0) eq
{%%if dv=0 then (u^v)'=vu'u^(v-1)
5 index dup IsStrNumber
{ dup (0) eq
{ StrConcat }
{ dup dup (1) eq exch (1.0) eq or
{ StrConcat }
{ StrConcat
7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1
{ (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006
(*\() StrConcat 8 index StrConcat (\)) StrConcat
5 index dup dup (2) eq exch (2.0) eq or
{ pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse }
{ pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat
5 index StrConcat (-1\)) StrConcat } ifelse
}
{%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if
AddOpPar 5 index StrConcat (\)*\() StrConcat
8 index StrConcat (\)^\() StrConcat
5 index StrConcat (-1\)+\() StrConcat
4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if
8 index StrConcat (\)^\() StrConcat
5 index StrConcat (\)*ln\() StrConcat
8 index StrConcat AddClPar
} ifelse
} ifelse
2 copy pop 0 6 2 roll GetIntervalNewStr
mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% No derivative for factorial ! only cst => null derivative
/EvalFactorial {% DR 09/2011
4 index (0) eq
{ (0) mark 8 -2 roll cleartomark 2 index 7 index dup 4 index exch sub getinterval exch 6 2 roll }
{ DERIVATIVE_ENGINE_ERROR_no_variable_in_factorial } ifelse
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% str -> true/false
/IsStrNumber {%
true exch
{ dup 48 lt exch dup 57 gt 3 -1 roll or
exch dup 46 ne%%.
exch dup 43 ne%%+
exch 45 ne%%-
and and and { pop false } if } forall
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% literal switch -> func call, vector, variables
/EvalLiteral {%
ReadLiteral dup 40 eq%%% there is an open par -> function call
{ pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec }
{ dup 91 eq%%% there is an open bracket -> vector element
{ DERIVATIVE_ENGINE_ERROR_vector_not_yet_implemented }
{ pop EvalVariable }
ifelse }
ifelse
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% first last parpos Expr[first:parpos-1] ->
/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (f(u))'=u'f'(u)
/EvalFunc {
4 2 roll 4 index (1) ne
{ AddOpPar 4 index StrConcat (\)*) StrConcat } if
(Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec
2 copy pop 0 6 2 roll GetIntervalNewStr
mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Func derivative -> Eval<func>
/EvalFunc_sin {%
PreCommonFunc
{ (cos\() StrConcat 5 index StrConcat AddClPar } if
PostCommonFunc } def
/EvalFunc_cos {%
PreCommonFunc
{ (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
PostCommonFunc } def
/EvalFunc_tan {%
PreCommonFunc
{ dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
PostCommonFunc } def
/EvalFunc_asin {%
PreCommonFunc
{ (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
PostCommonFunc } def
/EvalFunc_acos {%
PreCommonFunc
{ (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
PostCommonFunc } def
/EvalFunc_atg {%
PreCommonFunc
{ (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
PostCommonFunc } def
/EvalFunc_ln {%
PreCommonFunc
{ dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
PostCommonFunc } def
/EvalFunc_exp {%
PreCommonFunc
{ (exp\() StrConcat 5 index StrConcat AddClPar } if
PostCommonFunc } def
/EvalFunc_EXP {%
PreCommonFunc
{ (EXP\() StrConcat 5 index StrConcat AddClPar } if
PostCommonFunc } def
/EvalFunc_sqrt {%
PreCommonFunc
{ dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
PostCommonFunc } def
/EvalFunc_Fact {%
PreCommonFunc { DERIVATIVE_ENGINE_ERROR_no_variable_expression_in_Fact } if
PostCommonFunc } def
/EvalFunc_sh {%
PreCommonFunc
{ (ch\() StrConcat 5 index StrConcat AddClPar } if
PostCommonFunc } def
/EvalFunc_ch {%
PreCommonFunc
{ (sh\() StrConcat 5 index StrConcat AddClPar } if
PostCommonFunc } def
/EvalFunc_th {%
PreCommonFunc
{ dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
PostCommonFunc } def
/EvalFunc_Argsh {%
PreCommonFunc
{ (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
PostCommonFunc } def
/EvalFunc_Argch {%
PreCommonFunc
{ (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if
PostCommonFunc } def
/EvalFunc_Argth {%
PreCommonFunc
{ (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
PostCommonFunc } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
/PreCommonFunc {
1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop
4 2 roll 4 index (0) eq
{ (0) StrConcat false }
{ 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse
} def
/PostCommonFunc {
2 copy pop 0 6 2 roll GetIntervalNewStr
mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
/EvalFunc_Derive {%
1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs
4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add
4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar
2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval
exch 6 2 roll } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% literal switch -> func call, vector, variables
/EvalFunc_Sum {%
1 add NextNonBlankChar pop
%% read the variable name
ReadLiteral pop 3 -1 roll pop NextNonBlankChar
44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
%% read the initial value
1 add NextNonBlankChar pop ReadNumber pop
2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
%% read the increment value
1 add NextNonBlankChar pop ReadNumber pop
2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if
%% read the limit value
1 add NextNonBlankChar pop ReadNumber pop
2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if
1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop
4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat
4 index StrConcat AddClPar
2 copy pop 0 6 2 roll GetIntervalNewStr
mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% literal switch -> func call, vector, variables
/EvalFunc_IfTE {%
3 -1 roll pop 1 add NextNonBlankChar pop SkipCond
NextNonBlankChar
44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
1 add NextNonBlankChar pop dup 5 1 roll
AnalyzeExpr NextNonBlankChar
44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
1 add NextNonBlankChar pop
AnalyzeExpr 1 add NextNonBlankChar pop
4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat
6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar
2 copy pop 0 6 2 roll GetIntervalNewStr
mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% advance in str until a comma is found (no error detection!)
%% str index -> str index'
/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Convert to radians if trigo function call
%% (name) ->
/TrigoFunc {
dup (cos) eq 1 index (sin) eq or exch (tan) eq or
{ /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
array astore def
} if
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% No derivative for condition....
/EvalCondOp { 3 -1 roll pop } bind def
/PutIntervalOneAdd {putinterval 1 add} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add open parenthesis in string at the given index
%% str index -> str index+1
/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add close parenthesis in string at the given index
%% str index -> str index+1
/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add 0 in string at the given index
%% str index -> str index+1
/AddZero {2 copy (0) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add open parenthesis in string at the given index
%% str index -> str index+1
/AddMul {2 copy (*) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add open parenthesis in string at the given index
%% str index -> str index+1
/AddDiv {2 copy (/) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add a plus sign in string at the given index
%% str index -> str index+1
/AddAdd {2 copy (+) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add a minus sign in string at the given index
%% str index -> str index+1
/AddSub {2 copy (-) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add a pipe sign in string at the given index
%% str index -> str index+1
/AddPipe {2 copy (|) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% H O O K S
/AnalyzePreHook { dup 5 1 roll } bind def
/PreEvalHook {} def
/AnalyzePostHook { 7 -1 roll pop } bind def
/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def
/RollOp { 5 1 roll } bind def
end%%%tx@CoreAnalyzerDict
/tx@AddMathFunc 12 dict def tx@AddMathFunc begin
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% NEW FUNC
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2))
%% x -> theta
/asin {%
dup abs 1 gt { EQDFasinrangeerror } if
dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad
} def
%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x)
%% x -> theta
/acos {%
dup abs 1 gt { EQDFacosrangeerror } if
dup dup mul 1 exch sub sqrt exch atan DegtoRad
} def
%% function arctangent in radians
%% x -> theta
/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def
%% HYPERBOLIC FUNCTIONS
/sh { dup Ex exch neg Ex sub 2 div } def
/ch { dup Ex exch neg Ex add 2 div } def
/th { dup sh exch ch div } def
/Argsh { dup dup mul 1 add sqrt add ln } def
/Argch { dup dup mul 1 sub sqrt add ln } def
/Argth { dup 1 add exch 1 exch sub div ln 2 div } def
%% modified exponential funtion for 0
%% x n -> x^n
/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def
%% modified exponential funtion for 0
%% x -> e^x
/Ex { Euler exch exp } bind def
%%
%% factorial function
%% n -> n!
/Fact { 1 exch 2 exch 1 exch { mul } for } bind def
/fact { Fact } bind def
/! { Fact } bind def
end
%
% END pst-algparser.pro
%%EndProcSet
%%BeginProcSet: pst-tools.pro 0 0
% $Id: pst-tools.pro 713 2012-10-16 14:25:00Z herbert $
%
%% PostScript tools prologue for pstricks.tex.
%% Version 0.03, 2012/10/16
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%
%
/Pi2 1.57079632679489661925640 def
/factorial { % n on stack, returns n!
dup 0 eq { 1 }{
dup 1 gt { dup 1 sub factorial mul } if }
ifelse } def
%
/MoverN { % m n on stack, returns the binomial coefficient m over n
2 dict begin
/n exch def /m exch def
n 0 eq { 1 }{
m n eq { 1 }{
m factorial n factorial m n sub factorial mul div } ifelse } ifelse
end
} def
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% subroutines for complex numbers, given as an array [a b]
% which is a+bi = Real+i Imag
%
/cxadd { % [a1 b1] [a2 b2] = [a1+a2 b1+b2]
dup 0 get % [a1 b1] [a2 b2] a2
3 -1 roll % [a2 b2] a2 [a1 b1]
dup 0 get % [a2 b2] a2 [a1 b1] a1
3 -1 roll % [a2 b2] [a1 b1] a1 a2
add % [a2 b2] [a1 b1] a1+a2
3 1 roll % a1+a2 [a2 b2] [a1 b1]
1 get % a1+a2 [a2 b2] b1
exch 1 get % a1+a2 b1 b2
add 2 array astore
} def
%
/cxneg { % [a b]
dup 1 get % [a b] b
exch 0 get % b a
neg exch neg % -a -b
2 array astore
} def
%
/cxsub { cxneg cxadd } def % same as negative addition
%
% [a1 b1][a2 b2] = [a1a2-b1b2 a1b2+b1a2] = [a3 b3]
/cxmul { % [a1 b1] [a2 b2]
dup 0 get % [a1 b1] [a2 b2] a2
exch 1 get % [a1 b1] a2 b2
3 -1 roll % a2 b2 [a1 b1]
dup 0 get % a2 b2 [a1 b1] a1
exch 1 get % a2 b2 a1 b1
dup % a2 b2 a1 b1 b1
5 -1 roll dup % b2 a1 b1 b1 a2 a2
3 1 roll mul % b2 a1 b1 a2 b1a2
5 -2 roll dup % b1 a2 b1a2 b2 a1 a1
3 -1 roll dup % b1 a2 b1a2 a1 a1 b2 b2
3 1 roll mul % b1 a2 b1a2 a1 b2 a1b2
4 -1 roll add % b1 a2 a1 b2 b3
4 2 roll mul % b1 b2 b3 a1a2
4 2 roll mul sub % b3 a3
exch 2 array astore
} def
%
% [a b]^2 = [a^2-b^2 2ab] = [a2 b2]
/cxsqr { % [a b] square root
dup 0 get exch 1 get % a b
dup dup mul % a b b^2
3 -1 roll % b b^2 a
dup dup mul % b b^2 a a^2
3 -1 roll sub % b a a2
3 1 roll mul 2 mul % a2 b2
2 array astore
} def
%
/cxsqrt { % [a b]
% dup cxnorm sqrt /r exch def
% cxarg 2 div RadtoDeg dup cos r mul exch sin r mul cxmake2
cxlog % log[a b]
2 cxrdiv % log[a b]/2
aload pop exch % b a
2.781 exch exp % b exp(a)
exch cxconv exch % [Re +iIm] exp(a)
cxrmul %
} def
%
/cxarg { % [a b]
aload pop % a b
exch atan % arctan b/a
DegtoRad % arg(z)=atan(b/a)
} def
%
% log[a b] = [a^2-b^2 2ab] = [a2 b2]
/cxlog { % [a b]
dup % [a b][a b]
cxnorm % [a b] |z|
log % [a b] log|z|
exch % log|z|[a b]
cxarg % log|z| Theta
cxmake2 % [log|z| Theta]
} def
%
% square of magnitude of complex number
/cxnorm2 { % [a b]
dup 0 get exch 1 get % a b
dup mul % a b^2
exch dup mul add % a^2+b^2
} def
%
/cxnorm { % [a b]
cxnorm2 sqrt
} def
%
/cxconj { % conjugent complex
dup 0 get exch 1 get % a b
neg 2 array astore % [a -b]
} def
%
/cxre { 0 get } def % real value
/cxim { 1 get } def % imag value
%
% 1/[a b] = ([a -b]/(a^2+b^2)
/cxrecip { % [a b]
dup cxnorm2 exch % n2 [a b]
dup 0 get exch 1 get % n2 a b
3 -1 roll % a b n2
dup % a b n2 n2
4 -1 roll exch div % b n2 a/n2
3 1 roll div % a/n2 b/n2
neg 2 array astore
} def
%
/cxmake1 { 0 2 array astore } def % make a complex number, real given
/cxmake2 { 2 array astore } def % dito, both given
%
/cxdiv { cxrecip cxmul } def
%
% multiplikation by a real number
/cxrmul { % [a b] r
exch aload pop % r a b
3 -1 roll dup % a b r r
3 1 roll mul % a r b*r
3 1 roll mul % b*r a*r
exch 2 array astore % [a*r b*r]
} def
%
% division by a real number
/cxrdiv { % [a b] r
1 exch div % [a b] 1/r
cxrmul
} def
%
% exp(i theta) = cos(theta)+i sin(theta) polar<->cartesian
/cxconv { % theta
RadtoDeg dup sin exch cos cxmake2
} def
%%%%% ### bubblesort ###
%% syntax : array bubblesort --> array2 trie par ordre croissant
%% code de Bill Casselman
%%
http://www.math.ubc.ca/people/faculty/cass/graphics/text/www/
/bubblesort { % on stack must be an array [ ... ]
4 dict begin
/a exch def
/n a length 1 sub def
n 0 gt {
% at this point only the n+1 items in the bottom of a remain to
% the sorted largest item in that blocks is to be moved up into
% position n
n {
0 1 n 1 sub {
/i exch def
a i get a i 1 add get gt {
% if a[i] > a[i+1] swap a[i] and a[i+1]
a i 1 add
a i get
a i a i 1 add get
% set new a[i] = old a[i+1]
put
% set new a[i+1] = old a[i]
put
} if
} for
/n n 1 sub def
} repeat
} if
a % return the sorted array
end
} def
%
/concatstringarray{ % [(a) (b) ... (z)] --> (ab...z) 20100422
0 1 index { length add } forall
string
0 3 2 roll
{ 3 copy putinterval length add }forall
pop
} bind def
%
/dot2comma {% on stack a string (...)
2 dict begin
/Output exch def
0 1 Output length 1 sub {
/Index exch def
Output Index get 46 eq { Output Index 44 put } if
} for
Output
end
} def
%
/rightTrim {
dup
length 1 sub -1 0 {
/i exch def dup i get 32 ne { exit } if
} for
0 i 1 add getinterval
dup length string copy
} bind def
/psStringwidth /stringwidth load def
/psShow /show load def
%/stringwidth{ rightTrim psStringwidth } bind def
%/show { rightTrim psShow } bind def
%-----------------------------------------------------------------------------%
% END pst-tools.pro
%%EndProcSet
%%BeginProcSet: pst-dots.pro 0 0
% $Id: pst-dots.pro 130 2009-08-27 08:55:03Z herbert $
%
%% PostScript prologue for pstricks.tex.
%% Version 2.02, 2009/06/16
%%
%% For distribution, see pstricks.tex.
%%
%% Timothy Van Zandt <
[email protected]>
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%%
%% Modified by Etienne Riga - Dec. 16, 1999
%% Modified by Etienne Riga - 2005/01/01 (er)
%% to add /Diamond, /SolidDiamond and /BoldDiamond
%% Modified by Herbert Voss (hv) - 2008/04/17
%
10 dict dup begin % hold local
/FontType 3 def
/FontMatrix [.001 0 0 .001 0 0] def
% /FontBBox [-571.5 -742.5 571.5 742.5] def % changed to next line 20060616 hv
/FontBBox [-1000 -1000 1000 1000] def % See end of file in /BuildGlyph
/Encoding 256 array def
0 1 255 {Encoding exch /.notdef put} for % fill the array with /.notdef
Encoding % replace with given dot names
dup (b) 0 get /Bullet put % get the numerical position of b in ASCII
% % and save /Bullet at this place in Encoding
dup (c) 0 get /Circle put
dup (C) 0 get /BoldCircle put % 67
dup (u) 0 get /SolidTriangle put
dup (t) 0 get /Triangle put
dup (T) 0 get /BoldTriangle put
dup (r) 0 get /SolidSquare put
dup (s) 0 get /Square put
dup (S) 0 get /BoldSquare put
dup (q) 0 get /SolidPentagon put
dup (p) 0 get /Pentagon put
dup (P) 0 get /BoldPentagon put
%%%
dup (k) 0 get /Asterisk put
dup (K) 0 get /BoldAsterisk put
dup (J) 0 get /SolidAsterisk put
dup (h) 0 get /Hexagon put
dup (H) 0 get /BoldHexagon put
dup (G) 0 get /SolidHexagon put
dup (f) 0 get /Octogon put % 2008-04-18 hv
dup (F) 0 get /BoldOctogon put % 2008-04-18 hv
dup (g) 0 get /SolidOctogon put % 2008-04-18 hv
dup (a) 0 get /Add put
dup (A) 0 get /BoldAdd put % 65
dup (x) 0 get /Mul put
dup (X) 0 get /BoldMul put
dup (m) 0 get /Oplus put
dup (M) 0 get /BOplus put
dup (e) 0 get /SolidOplus put
dup (n) 0 get /Otimes put
dup (N) 0 get /BOtimes put
dup (E) 0 get /SolidOtimes put
dup (i) 0 get /Bar put
dup (I) 0 get /BoldBar put
dup (l) 0 get /SolidDiamond put
dup (d) 0 get /Diamond put
(D) 0 get /BoldDiamond put
%%%
/CharProcs 47 dict def
CharProcs begin
/CirclePath {0 0 500 0 360 arc closepath} def
/Bullet {CirclePath fill} def
/Circle {CirclePath .9 .9 scale CirclePath eofill} def
/BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def
/TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath} def
/SolidTriangle {TrianglePath fill} def
/Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def
/BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def
/SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath} def
/SolidSquare {SquarePath fill} def
/Square {SquarePath .89 .89 scale SquarePath eofill} def
/BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def
/PentagonPath {
-337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto
0 574.7 lineto -546.6 177.6 lineto closepath
} def
/SolidPentagon {PentagonPath fill} def
/Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def
/BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def
%-------------- hv begin 2004/07/25 from: er 2003/03/24
/HexagonPath {
0 550 moveto -476 275 lineto -476 -275 lineto
0 -550 lineto 476 -275 lineto 476 275 lineto closepath
} def
/SolidHexagon {HexagonPath fill} def
/Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def
/BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def
% 2008-04-18 hv
/OctogonPath {
550 dup 22.5 tan mul dup neg dup add /xMove exch def
exch moveto 7 { xMove 0 rlineto 45 rotate } repeat closepath } def
/SolidOctogon { OctogonPath fill } def
/Octogon { OctogonPath .89 .89 scale OctogonPath eofill } def
/BoldOctogon { OctogonPath .79 .79 scale OctogonPath eofill } def
%
/AsteriskPath {
20 0 moveto 10 250 180 500 0 500 curveto
-180 500 -10 250 -20 0 curveto closepath
} def
/Asterisk {
AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath
60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath fill
} def
%
/Basterp {50 250 220 500 0 500 curveto -220 500 -50 250 -50 30 cos 100 mul curveto} def
/BoldAsteriskPath {
50 30 cos 100 mul moveto Basterp
60 rotate Basterp 60 rotate Basterp
60 rotate Basterp 60 rotate Basterp
60 rotate Basterp closepath
} def
/BoldAsterisk {BoldAsteriskPath fill} def
/SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def
/CrossPath {
40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto
-550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto
40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath
} def
/BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto
-550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto
80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath
} def
/Add {CrossPath fill} def
/Mul {45 rotate CrossPath fill} def
/BoldAdd {BoldCrossPath fill} def
/BoldMul {45 rotate BoldCrossPath fill} def
/Oplus {CirclePath .9 .9 scale CirclePath eofill .775 .775 scale CrossPath fill } def
/SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def
/BOplus {CirclePath .8 .8 scale CirclePath eofill .775 .775 scale BoldCrossPath fill} def
/Otimes {CirclePath .9 .9 scale CirclePath eofill 45 rotate .775 .775 scale CrossPath fill} def
/BOtimes {CirclePath .8 .8 scale CirclePath eofill 45 rotate .775 .775 scale BoldCrossPath fill } def
/SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def
/BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto closepath} def
/Bar {BarPath fill} def
/BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto closepath} def
/BoldBar {BoldBarPath fill} def
/DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto 428.5 0 lineto closepath} def
/SolidDiamond {DiamondPath fill} def
/Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def
/BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def
%%%
/.notdef { } def
end
%
/BuildGlyph {
exch
begin
% Metrics 1 index get exec 0
0 0
% BBoxes 3 index get exec
-1000 -1000 1000 1000
% -571.5 -742.5 571.5 742.5
setcachedevice
CharProcs begin load exec end
end
} def
%
/BuildChar {
1 index /Encoding get exch get
1 index /BuildGlyph get exec
} bind def
%
end
/PSTricksDotFont exch definefont pop
%
%% end
%%EndProcSet
%%BeginProcSet: pst-coil.pro 0 0
%!ps
% PostScript prologue for pst-coil.tex.
% Version 1.03, 2010/02/01
% For distribution, see pstricks.tex.
%
/tx@CoilDict 40 dict def tx@CoilDict begin
/CoilLoop {
/t ED
t sin AspectSin mul t 180 div AspectCos mul add t cos lineto } def
/Coil {
/Inc ED
dup sin /AspectSin ED
cos /AspectCos ED
/ArmB ED
/ArmA ED
/h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED
x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth
/TotalLength ED
Atan rotate
/BeginAngle ArmA AspectCos Div w h mul Div 360 mul def
/EndAngle TotalLength ArmB sub AspectCos Div
w h mul Div 360 mul def
1 0 0 0 ArrowA ArmA 0 lineto
/mtrx CM def
w h mul 2 Div w 2 Div scale BeginAngle Inc
EndAngle { CoilLoop } for
EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP
% DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis)
% TotalLength 0 ArrowB lineto } def
TotalLength 0 ArrowB lineto
pop pop pop pop } def
% DG/SR modification end
%
/Sin {
/Func ED
/PointsPerPeriod ED
/ArmB ED
/ArmA ED
/Amplitude ED
/roundValue ED
/relativePeriod ED
/Periods ED
/y1 ED /x1 ED /y0 ED /x0 ED
x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth
dup /TotalLength ED
ArmA sub ArmB sub /SinLength ED
Atan rotate
1 0 0 0 ArrowA ArmA 0 lineto
/mtrx CM def
relativePeriod
{}
{ SinLength Periods div roundValue { cvi } if
/Periods ED } ifelse
/dxStep SinLength 360 div def % the default step for x pos
/xStep 360 PointsPerPeriod div def % the step for the for loop
1 xStep 360 { % PointsPerPeriod times
dup dxStep mul ArmA add exch % x pos and value for the func
Periods mul Func Amplitude mul lineto
} for
mtrx setmatrix TotalLength ArmB sub 0 lineto CP
TotalLength 0 ArrowB lineto
pop pop pop pop
} def
%
/AltCoil {
/Inc ED
dup sin /AspectSin ED
cos /AspectCos ED /h ED /w ED /EndAngle ED /BeginAngle ED
/mtrx CM def
w h mul 2 Div w 2 Div scale BeginAngle sin AspectSin mul
BeginAngle 180 div AspectCos mul add BeginAngle cos
/lineto load stopped { moveto } if
BeginAngle Inc EndAngle { CoilLoop } for
EndAngle CoilLoop mtrx setmatrix } def
/ZigZag {
/ArmB ED /ArmA ED
2 div /w ED
w mul /h ED /y1 ED /x1 ED /y0 ED /x0 ED
x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth
/TotalLength ED
Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul
sub 2 div dup ArmA add
/ArmA ED ArmB add
/ArmB ED
/x ArmB h 2 div add def
mark 0 0 ArmB 0
n { x w /w w neg def /x x h add def } repeat
TotalLength ArmA sub 0 TotalLength 0 } def
%
end
% END pst-coil.pro
%%EndProcSet
%%BeginProcSet: pst-node.pro 0 0
% $Id: pst-node.pro 805 2013-07-11 13:18:11Z herbert $
%%
%% PostScript prologue for pst-node.tex.
%% Version 1.14, 2012/09/18.
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%
tx@Dict begin % from main pstricks dict
/T /translate load def
/CP /currentpoint load def
% /startGlobal { true setglobal globaldict begin } bind def
% /endGlobal { end false setglobal } bind def
end
/tx@NodeDict 400 dict def tx@NodeDict begin
/NewNode { % on stack: { x y } boolean N@name type InitXnode
gsave
NodeScale % a bugfix for xelatex, it's empty for dvips
/next exch def % { x y } boolean N@name type
dict dup % { x y } boolean N@name dict dict
3 1 roll def % { x y } boolean dict N@name dict def
exch { dup 3 1 roll def } if % { x y } dict boolean
begin % { x y } dict begin
tx@Dict begin
STV CP T exec % set scaling
end
/NodeMtrx CM def % save CM
next % InitXNode
end
grestore
} def
%
/InitPnode {
/Y ED /X ED
/NodePos { NodeSep Cos mul NodeSep Sin mul } def
} def
%
/InitCnode {
/r ED /Y ED /X ED
/NodePos { NodeSep r add dup Cos mul exch Sin mul } def
} def
%
/GetRnodePos {
Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def } ifelse
Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } ifelse
dx Sin mul abs dy
Cos mul abs gt { dy Cos mul Sin div dy } { dx dup Sin mul Cos Div } ifelse
} def
%
/InitRnode {
/Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub /u ED
/NodePos { GetRnodePos } def
} def
%
/DiaNodePos {
w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup
Cos mul exch Sin mul
} def
%
/TriNodePos {
Sin s lt
{ d NodeSep sub dup Cos mul Sin Div exch }
{ w h mul w Sin mul h Cos abs mul add Div
NodeSep add dup Cos mul exch Sin mul
} ifelse
} def
%
/InitTriNode {
sub 2 div exch
2 div exch
2 copy T
2 copy 4 index index /d ED
pop pop pop pop
-90 mul rotate
/NodeMtrx CM def
/X 0 def /Y 0 def
d sub abs neg /d ED
d add /h ED
2 div h mul h d sub Div /w ED
/s d w Atan sin def
/NodePos { TriNodePos } def
} def
%
/OvalNodePos {
/ww w NodeSep add def
/hh h NodeSep add def
Sin ww mul Cos hh mul Atan dup cos ww mul exch sin hh mul
} def
%
/GetCenter { begin X Y NodeMtrx transform CM itransform end } def
%
/XYPos {
dup sin exch cos Do
/Cos ED /Sin ED /Dist ED
Cos 0 gt
{ Dist Dist Sin mul Cos div }
{ Cos 0 lt
{ Dist neg Dist Sin mul Cos div neg }
{ 0 Dist Sin mul } ifelse
} ifelse
Do
} def
%
/GetEdge {
dup 0 eq
{ pop begin 1 0 NodeMtrx dtransform
CM idtransform
exch atan sub
dup
sin /Sin ED
cos /Cos ED
/NodeSep ED
NodePos NodeMtrx dtransform CM idtransform end }
{ 1 eq {{exch}} {{}} ifelse /Do ED pop XYPos } ifelse
} def
%
/AddOffset {
1 index 0 eq
{ pop pop }
{ 2 copy 5 2 roll cos mul add 4 1 roll sin mul sub exch } ifelse
} def
%
/GetEdgeA {
NodeSepA AngleA NodeA NodeSepTypeA GetEdge
OffsetA AngleA AddOffset
yA add /yA1 ED
xA add /xA1 ED
} def
%
/GetEdgeB {
NodeSepB AngleB NodeB NodeSepTypeB GetEdge
OffsetB AngleB AddOffset
yB add /yB1 ED
xB add /xB1 ED
} def
%
/GetArmA {
ArmTypeA 0 eq
{ /xA2 ArmA AngleA cos mul xA1 add def
/yA2 ArmA AngleA sin mul yA1 add def }
{ ArmTypeA 1 eq {{exch}} {{}} ifelse
/Do ED
ArmA AngleA XYPos OffsetA AngleA AddOffset
yA add /yA2 ED
xA add /xA2 ED } ifelse
} def
%
/GetArmB {
ArmTypeB 0 eq
{ /xB2 ArmB AngleB cos mul xB1 add def
/yB2 ArmB AngleB sin mul yB1 add def }
{ ArmTypeB 1 eq {{exch}} {{}} ifelse
/Do ED
ArmB AngleB XYPos OffsetB AngleB AddOffset
yB add /yB2 ED
xB add /xB2 ED } ifelse
} def
%
/InitNC {
/b ED /a ED % second and first node
/NodeSepTypeB ED /NodeSepTypeA ED
/NodeSepB ED /NodeSepA ED
/OffsetB ED /OffsetA ED
tx@NodeDict a known tx@NodeDict b known and dup {
/NodeA a load def
/NodeB b load def
NodeA GetCenter /yA ED /xA ED
NodeB GetCenter /yB ED /xB ED } if
} def
%
/LPutLine {
4 copy
3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED
1 t sub mul
3 1 roll 1 t sub mul
4 1 roll t mul add /Y ED
t mul add /X ED
} def
%
/LPutLines {
mark LPutVar counttomark 2 div 1 sub /n ED
% t floor dup n gt
t floor dup n ge % to allow npos<= hv 2008-08-14
{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse
cvi 2 mul { pop } repeat
LPutLine
cleartomark
} def
%
/BezierMidpoint {
/y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED /t ED
/cx x1 x0 sub 3 mul def
/cy y1 y0 sub 3 mul def
/bx x2 x1 sub 3 mul cx sub def
/by y2 y1 sub 3 mul cy sub def
/ax x3 x0 sub cx sub bx sub def
/ay y3 y0 sub cy sub by sub def
ax t 3 exp mul bx t t mul mul add
cx t mul add x0 add ay t 3 exp mul
by t t mul mul add cy t mul add
y0 add 3 ay t t mul mul mul 2
by t mul mul add cy add 3 ax t t mul mul mul
2 bx t mul mul add cx add atan /NAngle ED
/Y ED /X ED
} def
%
/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def
} def
/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def
/NAngle yyB yyA sub xxB xxA sub Atan def } def
/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def
/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def
} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit
} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd
} def
/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def
} def
/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def
/NAngle yyB yyA sub xxB xxA sub Atan def } def
/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def
/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def
} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check {
exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark
VPosEnd } def
/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2
roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx
def grestore exec /LPutVar /SaveLPutVar load def } def
/NCCoor {
/AngleA yB yA sub xB xA sub Atan def
/AngleB AngleA 180 add def
GetEdgeA GetEdgeB
/LPutVar [ xB1 yB1 xA1 yA1 ] cvx def
/LPutPos { LPutVar LPutLine } def
/HPutPos { LPutVar HPutLine } def
/VPutPos { LPutVar VPutLine } def
LPutVar
} def
%
/NCLine {
NCCoor
tx@Dict begin
ArrowA CP 4 2 roll
ArrowB
lineto pop pop
end
} def
%
/NCLines {
false NArray
n 0 eq
{ NCLine }
{ 2 copy yA sub exch xA sub Atan /AngleA ED
n 2 mul dup index exch index yB sub exch xB sub
Atan /AngleB ED
GetEdgeA GetEdgeB
/LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 yA1 ] cvx def
mark LPutVar
tx@Dict begin false Line end
/LPutPos { LPutLines } def
/HPutPos { HPutLines } def
/VPutPos { VPutLines } def
} ifelse
} def
%
/NCCurve {
GetEdgeA
GetEdgeB
xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1
roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA
GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict
begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ]
cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines
} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def
%
/NCAngles {
GetEdgeA GetEdgeB GetArmA GetArmB
/mtrx AngleA matrix rotate def
xA2 yA2 mtrx transform pop
xB2 yB2 mtrx transform exch pop
mtrx itransform
/y0 ED /x0 ED
mark ArmB 0 ne { xB1 yB1 } if
xB2 yB2 x0 y0 xA2 yA2
ArmA 0 ne { xA1 yA1 } if
tx@Dict begin false Line end
/LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def
/LPutPos { LPutLines } def
/HPutPos { HPutLines } def
/VPutPos { VPutLines } def } def
%
/NCAngle {
GetEdgeA GetEdgeB GetArmB
/mtrx AngleA matrix rotate def
xB2 yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform
/y0 ED /x0 ED
mark
ArmB 0 ne { xB1 yB1 } if
xB2 yB2 x0 y0 xA1 yA1
tx@Dict begin false Line end
/LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] cvx def
/LPutPos { LPutLines } def
/HPutPos { HPutLines } def
/VPutPos { VPutLines } def
} def
%
/NCBar {
GetEdgeA GetEdgeB GetArmA GetArmB
/mtrx AngleA matrix rotate def
xA2 yA2 mtrx itransform pop
xB2 yB2 mtrx itransform pop
sub dup 0 mtrx transform
3 -1 roll 0 gt
{ /yB2 exch yB2 add def /xB2 exch xB2 add def }
{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse
mark
ArmB 0 ne { xB1 yB1 } if
xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if
tx@Dict begin false Line end
/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
/LPutPos { LPutLines } def
/HPutPos { HPutLines } def
/VPutPos { VPutLines } def
} def
%
/NCDiag {
/lineAngle ED
GetEdgeA GetEdgeB GetArmA GetArmB mark
lineAngle abs 0 gt {
/xTemp xA2 10 add def
/yTemp yA2 lineAngle dup sin exch cos div 10 mul add def
/dY1 yTemp yA2 sub def
/dX1 xTemp xA2 sub def
/dY2 yB2 yB1 sub def
/dX2 xB2 xB1 sub def
dX1 abs 0.01 lt {
/m2 dY2 dX2 div def
/xB2 xA2 def
/yB2 xA2 xB1 sub m2 mul yB1 add def
}{
dX2 abs 0.01 lt {
/m1 dY1 dX1 div def
/xB2 xB1 def
/yB2 xB1 xA2 sub m1 mul yA2 add def
}{%
/m1 dY1 dX1 div def
/m2 dY2 dX2 div def
/xB2 m1 xA2 mul m2 xB1 mul sub yA2 sub yB1 add m1 m2 sub div def
/yB2 xB2 xA2 sub m1 mul yA2 add def
} ifelse
} ifelse
} if
ArmB 0 ne { xB1 yB1 } if
xB2 yB2 xA2 yA2
ArmA 0 ne { xA1 yA1 } if
tx@Dict begin false Line end
/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
/LPutPos { LPutLines } def
/HPutPos { HPutLines } def
/VPutPos { VPutLines } def
%
% GetEdgeA GetEdgeB GetArmA GetArmB mark
% ArmB 0 ne { xB1 yB1 } if
% xB2 yB2 xA2 yA2
% ArmA 0 ne { xA1 yA1 } if
% tx@Dict begin false Line end
% /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
% /LPutPos { LPutLines } def
% /HPutPos { HPutLines } def
% /VPutPos { VPutLines } def
} def
%
/NCDiagg {
/lineAngle ED
GetEdgeA GetArmA
lineAngle abs 0 gt
{ lineAngle }
{ yB yA2 sub xB xA2 sub Atan 180 add } ifelse
/AngleB ED
GetEdgeB mark
lineAngle abs 0 gt {
/dY2 yA2 yA1 sub def
/dX2 xA2 xA1 sub def
lineAngle abs 90 eq {
/m2 dY2 dX2 div def
/yA2 xB xA2 sub m2 mul yA2 add def
/xA2 xB def
}{
/m1 lineAngle dup sin exch cos div def % tan alpha
dX2 abs 0.01 lt {
/yA2 xA1 xB sub m1 mul yB add def
/xA2 xA1 def
}{%
/m2 dY2 dX2 div def
/xA2 m1 xB mul m2 xA2 mul sub yA2 add yB sub m1 m2 sub div def
/yA2 xA2 xB sub m1 mul yB add def
} ifelse
} ifelse
} if
xB1 yB1 xA2 yA2
ArmA 0 ne { xA1 yA1 } if
tx@Dict begin false Line end
/LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def
/LPutPos { LPutLines } def
/HPutPos { HPutLines } def
/VPutPos { VPutLines } def
%
% GetEdgeA GetArmA
% yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED
% GetEdgeB
% mark
% xB1 yB1 xA2 yA2
% ArmA 0 ne { xA1 yA1 } if
% tx@Dict begin false Line end
% /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def
% /LPutPos { LPutLines } def
% /HPutPos { HPutLines } def
% /VPutPos { VPutLines } def
} def
%
/NCLoop {
GetEdgeA GetEdgeB GetArmA GetArmB
/mtrx AngleA matrix rotate def
xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED
/xB3 xB2 yB2 mtrx transform pop def
xB3 yA3 mtrx itransform /yB3 ED /xB3 ED
xA3 yA3 mtrx itransform /yA3 ED /xA3 ED
mark ArmB 0 ne { xB1 yB1 } if
xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if
tx@Dict begin false Line end
/LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] cvx def
/LPutPos { LPutLines } def
/HPutPos { HPutLines } def
/VPutPos { VPutLines } def
} def
%
% DG/SR modification begin - May 9, 1997 - Patch 1
%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r
%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add
%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360
%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED
%
/NCCircle {
NodeSepA 0 NodeA 0 GetEdge pop
2 div dup 2 exp r r mul sub abs sqrt
atan 2 mul /a ED
r AngleA 90 add PtoC yA add exch xA add
exch 2 copy
/LPutVar [ 4 2 roll r AngleA ] cvx def
/LPutPos {
LPutVar t 360 mul add dup 5 1 roll 90 sub PtoC
3 -1 roll add
/Y ED add /X ED /NAngle ED
% DG/SR modification end
} def
/HPutPos { LPutPos } def
/VPutPos { LPutPos } def
r AngleA 90 sub a add AngleA 270 add a sub
tx@Dict begin
/angleB ED /angleA ED /r ED
/c 57.2957 r Div def
/y ED /x ED
} def
%
/NCBox {
/d ED /h ED
/AngleB yB yA sub xB xA sub Atan def
/AngleA AngleB 180 add def
GetEdgeA GetEdgeB
/dx d AngleB sin mul def
/dy d AngleB cos mul neg def
/hx h AngleB sin mul neg def
/hy h AngleB cos mul def
/LPutVar [
xA1 hx add yA1 hy add xB1 hx add yB1 hy add
xB1 dx add yB1 dy add xA1 dx add yA1 dy add ] cvx def
/LPutPos { LPutLines } def
/HPutPos { xB yB xA yA LPutLine } def
/VPutPos { HPutPos } def
mark
LPutVar tx@Dict begin false Polygon end
} def
%
/NCArcBox {
/l ED neg /d ED /h ED /a ED
/AngleA yB yA sub xB xA sub Atan def
/AngleB AngleA 180 add def
/tA AngleA a sub 90 add def
/tB tA a 2 mul add def
/r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def
/x0 xA r tA cos mul add def
/y0 yA r tA sin mul add def
/c 57.2958 r div def
/AngleA AngleA a sub 180 add def
/AngleB AngleB a add 180 add def
GetEdgeA GetEdgeB
/AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul sub def
/AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def
l 0 eq {
x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn
}{
x0 y0 translate
/tA AngleA l c mul add def
/tB AngleB l c mul sub def
0 0 r h add tA tB arc r h add
AngleB PtoC r d add
AngleB PtoC 2 copy
6 2 roll l arcto 4 { pop } repeat
r d add tB PtoC l arcto 4 { pop } repeat
0 0 r d add tB tA arcn r d add
AngleA PtoC r h add
AngleA PtoC 2 copy 6 2 roll
l arcto 4 { pop } repeat
r h add tA PtoC l arcto 4 { pop } repeat
} ifelse
closepath
/LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def
/LPutPos {
LPutVar /d ED /h ED
/AngleB ED /AngleA ED
/r ED /y0 ED /x0 ED
t 1 le {
r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC
}{t 2 lt {
/NAngle AngleB 180 add def r 2 t sub
h mul t 1 sub d mul add add AngleB PtoC
}{
t 3 lt {
r d add AngleB 3 t sub mul AngleA 2 t sub
mul add dup 90 sub /NAngle ED PtoC
}{
/NAngle AngleA 180 add def
r 4 t sub d mul t 3 sub h mul add add AngleA PtoC
} ifelse
} ifelse
} ifelse
y0 add /Y ED x0 add /X ED
} def
/HPutPos { LPutPos } def
/VPutPos { LPutPos } def
} def
%
/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB
sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1
ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB
w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos
{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop }
{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine }
def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin
/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def
%
/LPutCoor {
NAngle
tx@Dict begin /NAngle ED end
gsave
CM STV
CP Y sub neg exch X sub neg exch moveto
setmatrix CP
grestore
} def
%
/LPut {
tx@NodeDict /LPutPos known
{ LPutPos } { CP /Y ED /X ED /NAngle 0 def } ifelse
LPutCoor
} def
%
/HPutAdjust {
Sin Cos mul 0 eq
{ 0 }
{ d Cos mul Sin div flag not { neg } if
h Cos mul Sin div flag { neg } if
2 copy gt { pop } { exch pop } ifelse
} ifelse
s add flag { r add neg }{ l add } ifelse
X add /X ED
} def
%
/VPutAdjust {
Sin Cos mul
0 eq
{ 0 }
{ l Sin mul Cos div flag { neg } if
r Sin mul Cos div flag not { neg } if
2 copy gt { pop } { exch pop } ifelse
} ifelse
s add flag { d add } { h add neg } ifelse
Y add /Y ED
} def
%
%
end
%
% END pst-node.pro
%%EndProcSet
%%BeginProcSet: pst-math.pro 0 0
% -*- Mode: Postscript -*-
% pst-math.pro --- PostScript header file pst-math.pro
%
% Author : Christophe JORSSEN
% Author : Herbert Voß <
[email protected]>
% Created the : Sat 20 March 2004
% Last Mod : $Date: 2010/10/02 $
% Version : 0.62 $
%
/PI 3.14159265359 def
/ENeperian 2.71828182846 def
%
/DegToRad {PI mul 180 div} bind def
/RadToDeg {180 mul PI div} bind def
%
/COS {RadToDeg cos} bind def
/SIN {RadToDeg sin} bind def
/TAN {dup SIN exch COS Div} bind def
/tan {dup sin exch cos Div} bind def
/ATAN {neg -1 atan 180 sub DegToRad} bind def
/ACOS {dup dup mul neg 1 add sqrt exch atan DegToRad} bind def
/acos {dup dup mul neg 1 add sqrt exch atan} bind def
/ASIN {neg dup dup mul neg 1 add sqrt neg atan 180 sub DegToRad} bind def
/asin {neg dup dup mul neg 1 add sqrt neg atan 180 sub} bind def
%
/EXP {ENeperian exch exp} bind def
%
/COSH {dup EXP exch neg EXP add 2 div} bind def
/SINH {dup EXP exch neg EXP sub 2 div} bind def
/TANH {dup SINH exch COSH div} bind def
/ACOSH {dup dup mul 1 sub sqrt add ln} bind def
/ASINH {dup dup mul 1 add sqrt add ln} bind def
/ATANH {dup 1 add exch neg 1 add Div ln 2 div} bind def
%
%/SINC {dup SIN exch Div} bind def
/SINC { dup 0 eq { pop 1 } { dup SIN exch div } ifelse } bind def
/GAUSS {dup mul 2 mul dup 4 -2 roll sub dup mul exch div neg EXP exch PI mul sqrt div} bind def
%
/GAMMA { 2 dict begin % hv 2007-08-30
/z exch def
1.000000000190015 % p(0)
0 1 5 { % on stack is 0 1 2 3 4 5
dup % n-1 n-1
[ 76.18009172947146
-86.50532032941677
24.0140982483091
-1.231739572450155
0.1208650973866179E-2
-0.5395239384953E-5 ] exch get exch % p(n) n-1
1 add z add div % p(n)/(z+n)
add % build the sum
} for
Pi 2 mul sqrt z div mul
z 5.5 add z 0.5 add exp mul ENeperian z 5.5 add neg exp mul
end } bind def
%
/GAMMALN {dup dup dup 5.5 add dup ln 3 -1 roll .5 add mul sub neg 1.000000000190015
0 1 5 {
[76.18009172947146 -86.50532032941677 24.0140982483091 -1.231739572450155
.1208650973866179E-2 -.5395239384953E-5 2.5066282746310005] exch get
4 -1 roll 1 add dup 5 1 roll div add} for
4 -1 roll div 2.5066282746310005 mul ln add exch pop} bind def
/BETA {2 copy add GAMMALN neg exch GAMMALN 3 -1 roll GAMMALN EXP} bind def
%
/HORNER {aload length
dup 2 add -1 roll
exch 1 sub {
dup 4 1 roll
mul add exch
} repeat
pop
} bind def
%
/BESSEL_J0 {dup abs 8 lt {
dup mul dup [57568490574 -13362590354 651619640.7 -11214424.18 77392.33017 -184.9052456] HORNER
exch [57568490411 1029532985 9494680.718 59272.64853 267.8532712 1] HORNER
Div}
{abs dup .636619772 exch div sqrt exch dup .785398164 sub exch 8 exch div dup dup mul dup
[1 -1.098628627E-2 .2734510407E-4 -.2073370639E-5 .2093887211E-6] HORNER
3 index COS mul
exch [-.1562499995E-1 .1430488765E-3 -.6911147651E-5 .7621095161E-6 -.934945152E-7] HORNER
4 -1 roll SIN mul 3 -1 roll mul neg add mul}
ifelse} bind def
%
/BESSEL_Y0 {dup 8 lt {
dup dup mul dup [-2957821389 7062834065 -512359803.6 10879881.29 -86327.92757 228.4622733] HORNER
exch [40076544269 745249964.8 7189466.438 47447.26470 226.1030244 1] HORNER
Div exch dup ln exch BESSEL_J0 .636619772 mul mul add}
{dup .636619772 exch div sqrt exch dup .785398164 sub exch 8 exch div dup dup mul dup
[1 -.1098628627E-2 .2734510407E-4 -.2073370639E-5 .2093887211E-6] HORNER
3 index SIN mul
exch [-.1562499995E-1 .1430488765E-3 -.6911147651E-5 .7621095161E-6 -.934945152E-7] HORNER
4 -1 roll COS mul 3 -1 roll mul add mul}
ifelse} bind def
%
/BESSEL_J1 {dup abs 8 lt {
dup dup mul dup 3 -2 roll [72362614232 -7895059235 242396853.1 -2972611.439 15704.48260 -30.16036606] HORNER mul
exch [144725228442 2300535178 18583304.74 99447.43394 376.9991397 1] HORNER
Div}
{dup abs dup .636619772 exch div sqrt exch dup 2.356194491 sub exch 8 exch div dup dup mul dup
[1 .183105E-2 -.3516396496E-4 .2457520174E-5 -.240337019E-6] HORNER
3 index COS mul
exch [.04687499995 6.2002690873E-3 .8449199096E-5 -.88228987E-6 .105787412E-6] HORNER
4 -1 roll SIN mul 3 -1 roll mul neg add mul exch dup abs Div mul}
ifelse} bind def
%
/BESSEL_Y1 {dup 8 lt {
dup dup dup mul dup [-.4900604943E13 .1275274390E13 -.5153428139E11 .7349264551E9 -.4237922726E7 .8511937935E4] HORNER
exch [.2499580570E14 .4244419664E12 .3733650367E10 .2245904002E8 .1020426050E6 .3549632885E3 1] HORNER
Div mul exch dup dup ln exch BESSEL_J1 mul exch 1 exch div sub .636619772 mul add}
{dup .636619772 exch div sqrt exch dup 2.356194491 sub exch 8 exch div dup dup mul dup
[1 .183105E-2 -.3516396496E-4 .2457520174E-5 -.240337019E-6] HORNER
3 index SIN mul
exch [.04687499995 -.2002690873E-3 .8449199096E-5 6.88228987E-6 .105787412E-6] HORNER
4 -1 roll COS mul 3 -1 roll mul add mul}
ifelse} bind def
%
% En cours...
/BESSEL_Yn {dup 0 eq {pop BESSEL_Y0}{dup 1 eq {pop BESSEL_Y1}{
exch dup BESSEL_Y0 exch dup BESSEL_Y1 exch 2 exch Div {
mul 3 -1 roll mul 2 index sub pstack} for
} ifelse } ifelse } bind def
%
/SIMPSON { 1 dict begin %% on stack a b var f ierr Dominik Rodriguez
3 index 5 index sub % compute h
1 % a b var f ierr h n
4 index 7 index def 3 index exec % a b var f ierr h n f(a)
5 index 7 index def 4 index exec add % a b var f ierr h n f(a)+f(b)
5 index 8 index 4 index 2 div add def 4 index exec % a b var f ierr h n f(a)+f(b) f(a+h/2)
exch 1 index 4 mul add 0 % a b var f ierr h n old=f(a+h/2) Estim=f(a)+f(b)+4f(a+h/2) NbLoop
{ % a b var f ierr h n old Estim NbLoop
5 -1 roll 2 div dup 6 1 roll % h<-h/2
5 -1 roll 2 mul 5 1 roll % n<-2n
% a b var f ierr h n old Estim NbLoop h
2 div 10 index add 0 % a b var f ierr h n old Estim NbLoop a+h/2 Cumul
5 index {
1 index 10 index exch def 8 index exec add exch 6 index add exch
} repeat % a b var f ierr h n old Estim NbLoop a+nh/2 Cumul
exch pop % a b var f ierr h n old Estim NbLoop New
2 index 1 index 4 mul 6 -1 roll 2 mul sub sub % a b var f ierr h n Estim NbLoop New Diff
4 -1 roll 2 mul 1 index sub 4 1 roll % a b var f ierr h n Estim NbLoop New Diff
exch 4 1 roll % a b var f ierr h n old Estim NbLoop Diff
5 index 6 div mul abs 6 index lt { exit } if
1 add dup 9 eq { exit } if
} loop % a b var f ierr h n old Estim NbLoop
exch 5 -1 roll 6 div mul mark 10 2 roll cleartomark
end
} def
% ------------------------------------ math stuff ----------------------------------
%
% Matrix A in arrays of rows A[[row1][row2]...]
% with [row1]=[a11 a12 ... b1]
% returns on stack solution vector X=[x1 x2 ... xn]
/SolveLinEqSystem { % on stack matrix M=[A,b] (A*x=b)
10 dict begin % hold all ocal
/A exch def
/Rows A length def % Rows = number of rows
/Cols A 0 get length def % Cols = number of columns
/Index [ 0 1 Rows 1 sub { } for ] def % Index = [0 1 2 ... Rows-1]
/col 0 def
/row 0 def
/PR Rows array def % PR[c] = pivot row for row row
{ % starts the loop, find pivot entry in row r
col Cols ge row Rows ge or { exit } if % col < Cols and row < Rows else exit
/pRow row def % pRow = pivot row
/max A row get col get abs def % get A[row[col]], first A[0,0]
row 1 add 1 Rows 1 sub { % starts for loop 1 1 Rows-1
/j exch def % index counter
/x A j get col get abs def % get A[j[r]]
x max gt { % x>max, then save position
/pRow j def
/max x def
} if
} for % now we have the row with biggest A[0,1]
% with pRow = the pivot row
max 0 gt { % swap entries pRow and row in i
/tmp Index row get def
Index row Index pRow get put
Index pRow tmp put % and columns pRow and row in A
/tmp A row get def
A row A pRow get put
A pRow tmp put % pivot
/row0 A row get def % the pivoting row
/p0 row0 col get def % the pivot value
row 1 add 1 Rows 1 sub { % start for loop
/j exch def
/c1 A j get def
/p c1 col get p0 div def
c1 col p put % subtract (p1/p0)*row[i] from row[j]
col 1 add 1 Cols 1 sub { % start for loop
/i exch def
c1 dup i exch % c1 i c1
i get row0 i get p mul sub put
} for
} for
PR row col put
/col col 1 add def
/row row 1 add def
}{ % all zero entries
/row row 1 add def % continue loop with same row
} ifelse
} loop
/X A def % solution vector
A Rows 1 sub get dup
Cols 1 sub get exch
Cols 2 sub get div
X Rows 1 sub 3 -1 roll put % X[n]
Rows 2 sub -1 0 { % for loop to calculate X[i]
/xi exch def % current index
A xi get % i-th row
/Axi exch def
/sum 0 def
Cols 2 sub -1 xi 1 add {
/n exch def
/sum sum Axi n get X n get mul add def
} for
Axi Cols 1 sub get % b=Axi[Cols-1]
sum sub % b-sum
Axi xi get div % b-sum / Axi[xi]
X xi 3 -1 roll put % X[xi]
} for
X
end
} def
%
/c@_0 2.515517 def
/c@_1 0.802853 def
/c@_2 0.010328 def
/d@_1 1.432788 def
/d@_2 0.189269 def
/d@_3 0.001308 def
/norminv {
5 dict begin
neg 1 add 1 exch div ln 2 mul sqrt
/t exch def
/t2 t dup mul def
/t3 t2 t mul def
c@_0 c@_1 t mul add c@_2 t2 mul add 1 d@_1 t mul add
d@_2 t2 mul add d@_3 t3 mul add div neg t add
end
} def
%end{norminv Michael Sharpe}
%
%
% END pst-math.pro
%%EndProcSet
%%BeginProcSet: pst-3d.pro 0 0
%% $Id: pst-3d.pro 247 2010-01-04 22:45:42Z herbert $
% PostScript prologue for pst-3d.tex.
% Version 0.01, 2010/01/01
%
/tx@3Ddict 300 dict def
tx@3Ddict begin
%
/SetMatrixThreeD {
dup sin /e ED cos /f ED
/p3 ED /p2 ED /p1 ED
p1 0 eq
{ /a 0 def /b p2 0 le { 1 } { -1 } ifelse def
p3 p2 abs
}
{ p2 0 eq
{ /a p1 0 lt { -1 } { 1 } ifelse def /b 0 def
p3 p1 abs
}
{ p1 dup mul p2 dup mul add sqrt dup
p1 exch div /a ED
p2 exch div neg /b ED
p3 p1 a div
}
ifelse
}
ifelse
atan dup sin /c ED cos /d ED
/Matrix3D
[
b f mul c a mul e mul sub
a f mul c b mul e mul add
d e mul
b e mul neg c a mul f mul sub
a e mul neg c b mul f mul add
d f mul
] def
} def
%
/ProjThreeD {
/z ED /y ED /x ED
Matrix3D aload pop
z mul exch y mul add exch x mul add
4 1 roll
z mul exch y mul add exch x mul add
exch
} def
%
/SetMatrixEmbed {
SetMatrixThreeD
Matrix3D aload pop
/z3 ED /z2 ED /z1 ED /x3 ED /x2 ED /x1 ED
SetMatrixThreeD
[
Matrix3D aload pop
z3 mul exch z2 mul add exch z1 mul add 4 1 roll
z3 mul exch z2 mul add exch z1 mul add
Matrix3D aload pop
x3 mul exch x2 mul add exch x1 mul add 4 1 roll
x3 mul exch x2 mul add exch x1 mul add
3 -1 roll 3 -1 roll 4 -1 roll 8 -3 roll 3 copy
x3 mul exch x2 mul add exch x1 mul add 4 1 roll
z3 mul exch z2 mul add exch z1 mul add
]
concat
} def
%
/TMSave {
tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
/TMatrix [ TMatrix CM ] cvx def
} def
%
/TMRestore { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
%
/TMChange {
TMSave
/cp [ currentpoint ] cvx def % ??? Check this later.
CM
CP T STV
CM matrix invertmatrix % Inv(M')
matrix concatmatrix % M Inv(M')
exch exec
concat cp moveto
} def
%
end % of tx@3Ddict
%%
%% End of file `pst-3d.pro'.
%%EndProcSet
%%BeginProcSet: pstricks-add.pro 0 0
%% $Id: pstricks-add.pro 328 2010-05-24 15:56:43Z herbert $
% PostScript prologue for pstricks-add.tex.
% Version 0.23, 2009/12/17
%
/tx@addDict 410 dict def tx@addDict begin
%%
realtime srand % set random generator
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
/GTriangle {
gsave
/mtrx CM def
/colorA ED /colorB ED /colorC ED % save the colors
/yA ED /xA ED % save the origin
xA yA translate
rotate % \psk@gangle
/yB ED /xB ED /yC ED /xC ED % save other coordinates
/ds [ % save data in a array
0 0 0 colorA aload pop % fd x y xr xg xb
0 xB xA sub yB yA sub colorB aload pop
0 xC xA sub yC yA sub colorC aload pop
% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD
] def
newpath
<<
/ShadingType 4 % single Gouraud
/ColorSpace [ /DeviceRGB ]
/DataSource ds
>>
shfill
closepath
mtrx
setmatrix grestore} def
%
/RGBtoCMYK { % on stack r g b -> C M Y K
3 dict begin
/Blue ED /Green ED /Red ED
1 Red sub % Cyan
1 Green sub % Magenta
1 Blue sub % Yellow
0 % Black
end
} def
%
/CMYKtoGRAY { % on stack c m y k -> gray
exch 0.11 mul add
exch 0.59 mul add
exch 0.3 mul add
dup 1 gt { pop 1 } if
neg 1 add
} def
%
/RGBtoGRAY { % on stack r g b -> gray
0.11 mul
exch 0.59 mul add
exch 0.3 mul add
} def
%
/HSBtoGRAY {
6 dict begin
/b exch def
/s exch def 6 mul dup cvi dup
/i exch def sub
/f exch def
/F [[0 1 f sub 1][f 0 1][1 0 1 f sub][1 f 0][1 f sub 1 0][0 1 f][0 1 1]] def
F i get { s mul neg 1 add b mul} forall
0.11 mul
exch 0.59 mul add
exch 0.3 mul add
end
} def
%
%% convertisseur longueur d'onde ->R,G,B Manuel Luque
%% lambda max=780 nanometres
%% lambda min=380 nanometres
%% adaptation de :
%%
http://www.physics.sfasu.edu/astro/color.html
%% www.efg2.com/lab
%
/Gamma 0.8 def
/calculateRGB {
lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if
lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if
lambda 380 ge {lambda 439 le {
/R {lambda 440 sub neg 440 380 sub div} def
/Red R factor mul Gamma exp def
/G 0 def
/Green G factor mul Gamma exp def
/B 1 def
/Blue B factor mul Gamma exp def} if
} if
lambda 440 ge { lambda 489 le {
/G {lambda 440 sub 490 440 sub div} def
/Green G factor mul Gamma exp def
/R 0 def /Red 0 def
/B 1 def
/Blue B factor mul Gamma exp def } if
} if
lambda 490 ge {lambda 509 le {
/B {lambda 510 sub neg 510 490 sub div} def
/Blue B factor mul Gamma exp def
/R 0 def /Red 0 def
/G 1 def
/Green G factor mul Gamma exp def } if
} if
lambda 510 ge {lambda 579 le {
/R {lambda 510 sub 580 510 sub div } def
/Red R factor mul Gamma exp def
/Blue 0 def
/G 1 def
/Green G factor mul Gamma exp def } if
} if
lambda 580 ge {lambda 644 le {
/G {lambda 645 sub neg 645 580 sub div } def
/Green G factor mul Gamma exp def
/Blue 0 def
/R 1 def
/Red R factor mul Gamma exp def } if
} if
lambda 645 ge { lambda 780 le {
/Red 1 factor mul Gamma exp def
/Blue 0 def
/Green 0 def } if
} if
} def
%
/factor {
lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if
lambda 420 ge {lambda 700 le { 1 } if } if
lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if
} def
%
/wavelengthToRGB { % the wavelength in nm must be on top of the stack
cvi /lambda exch def % no floating point here
calculateRGB
} def % now the colors are saved in Red Green Blue
%
/wavelengthToGRAY { % the wavelength in nm must be on top of the stack
cvi /lambda exch def % no floating point here
calculateRGB
Red Green Blue RGBtoGRAY
} def % now the gray color is on the stack
%
/wavelengthToCMYK { % the wavelength in nm must be on top of the stack
cvi /lambda exch def % no floating point here
gsave
calculateRGB Red Green Blue RGBtoCMYK
/Black ED /Yellow ED /Magenta ED /Cyan ED
grestore
} def % now the colors are saved in Cyan Magenta Yellow Black
%
/axfill {
8 dict begin
/xw exch def /nl exch def
/C1 exch def /y1 exch def/x1 exch def
/C0 exch def /y0 exch def/x0 exch def
<< /ShadingType 2
/ColorSpace /DeviceRGB
/Coords [ x0 y0 x1 y1 ]
/EmulatorHints [ xw 2 div dup ]
/Function <<
/FunctionType 2
/Domain [0 1]
/C0 C0
/C1 C1
/N 1
>>
>> shfill
end
} bind def
%
%/amplHand {.8} def
%/dtHand 2 def
/varHand { rand sin amplHand mul add } def
/MovetoByHand { moveto } def
%/MovetoByHand { /y0 ED /x0 ED x0 y0 moveto } def
/LinetoByHand { 4 dict begin
/y1 ED /x1 ED
currentpoint /y0 ED /x0 ED
x0 x1 sub dup mul y0 y1 sub dup mul add sqrt /dEnd ED
0 dtHand dEnd { dup
x1 x0 sub mul dEnd div x0 add varHand exch
y1 y0 sub mul dEnd div y0 add varHand lineto
} for
% /x0 x1 def /y0 y1 def
end
} def
%
end
%
% END pstricks-add.pro
%%EndProcSet
%%BeginProcSet: pst-func.pro 0 0
%% $Id: pst-func.pro 355 2010-06-21 10:02:44Z herbert $
%%
%% This is file `pst-func.pro',
%%
%% IMPORTANT NOTICE:
%%
%% Package `pst-func'
%%
%% Herbert Voss <
[email protected]>
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%%
%% DESCRIPTION:
%% `pst-func' is a PSTricks package to plot special math functions
%%
%%
%% version 0.13 / 2010-06-21 Herbert Voss
%
/tx@FuncDict 100 dict def
tx@FuncDict begin
%
/eps1 1.0e-05 def
/eps2 1.0e-04 def
/eps8 1.0e-08 def
/Pi2 1.57079632679489661925640 def
/CEuler 0.5772156649 def % Euler-Mascheroni constant
%
/factorial { % n on stack, returns n!
dup 0 eq { 1 }{
dup 1 gt { dup 1 sub factorial mul } if }
ifelse } def
%
/MoverN { % m n on stack, returns the binomial coefficient m over n
2 dict begin
/n exch def /m exch def
n 0 eq { 1 }{
m n eq { 1 }{
m factorial n factorial m n sub factorial mul div } ifelse } ifelse
end
} def
%
/Pascal [
[ 1 ] % 0
[ 1 1 ] % 1
[ 1 2 1 ] % 2
[ 1 3 3 1 ] % 3
[ 1 4 6 4 1 ] % 4
[ 1 5 10 10 5 1 ] % 5
[ 1 6 15 20 15 6 1 ] % 6
[ 1 7 21 35 35 21 7 1 ] % 7
[ 1 8 28 56 70 56 28 8 1 ] % 8
[ 1 9 36 84 126 126 84 36 9 1 ] % 9
] def
%
/GetBezierCoor { % t on stack
10 dict begin % hold all local
/t ED
/t1 1 t sub def % t1=1-t
/Coeff Pascal BezierType get def % get the coefficients
0 0 % initial values for x y
BezierType -1 0 { % BezierType,...,2,1,0
/I ED % I=BezierType,...,2,1,0
/J BezierType I sub def % J=0,1,2,...,BezierType
/T t I exp Coeff J get mul def % coeff(J)*t^I
/T1 t1 J exp def % t1^J
Points I dup add 1 add get % y(2*I+1)
T mul T1 mul add % the y coordinate
exch % y x
Points I dup add get % x(2*I)
T mul T1 mul add % the x coordinate
exch % x y
} for % x y on stack
end
} def
%
/BezierCurve { % on stack [ coors psk@plotpoints BezierType
% 10 dict begin
/BezierType ED
1 exch div /epsilon ED
] /Points ED % yi xi ... y3 x3 y2 x2 y1 x1 y0 x0
epsilon GetBezierCoor % next Bezier point
Points 0 get Points 1 get % starting point
ArrowA moveto
epsilon epsilon 1 {
/t ED
t GetBezierCoor
t 0.9999 lt { lineto }{ 1 epsilon sub GetBezierCoor 4 2 roll ArrowB pop pop pop pop } ifelse
} for
% end
} def
%
/Bernstein { % on stack tStart tEnd plotpoints i n
12 dict begin % hold all local
/envelope ED % plot envelope?
/n ED
/i ED
/ni n i sub def
/epsilon ED % step=1/plotpoints
/tEnd ED
/tStart ED
%
% B_{i,n}(t)=\binom{n}{i}t^i(1-t)^{n-i} (Bernstein)
% f_n(x)=\frac{1}{\sqrt{\pi n\cdot x(1-x)}} (envelope)
%
n i MoverN /noveri ED % \binom{n}{i}
[ % for the array of points
tStart epsilon tEnd {
dup dup /t ED % leave one on stack
neg 1 add /t1 ED % t1=1-t
envelope
{ t t1 mul 4 mul Pi2 mul n mul sqrt 1 exch Div } % envelope
{ noveri t i exp mul t1 ni exp mul } ifelse % t f(t)
ScreenCoor % convert to screen coor
} for
end
false /Lineto /lineto load def Line
} def
%
/Si { % integral sin from 0 to x (arg on stack)
/arg exch def
/Sum arg def
/sign -1 def
/index 3 def
{
arg index exp index div index factorial div sign mul
dup abs eps8 lt { pop exit } if
Sum add /Sum exch def
/sign sign neg def
/index index 2 add def
} loop
Sum
} def
/si { % integral sin from x to infty -> si(x)=Si(x)-pi/2
Si Pi2 sub
} def
/Ci { % integral cosin from x to infty (arg on stack)
abs /arg exch def
arg 0 eq { 0 } {
/argExp 1 def
/fact 1 def
/Sum CEuler arg ln add def
/sign -1 def
/index 2 def
{
/argExp argExp arg arg mul mul def
/fact fact index 1 sub index mul mul def
argExp index div fact div sign mul
dup abs exch Sum add /Sum exch def
eps8 lt { exit } if
/sign sign neg def
/index index 2 add def
} loop
Sum
} ifelse
} def
/ci { % integral cosin from x to infty -> ci(x)=-Ci(x)+ln(x)+CEuler
dup Ci neg exch abs ln add CEuler add
} def
%
/MaxIter 255 def
/func { coeff Derivation FuncValue } def
/func' { coeff Derivation 1 add FuncValue } def
/func'' { coeff Derivation 2 add FuncValue } def
%
/NewtonMehrfach {% the start value must be on top of the stack
/Nx exch def
/Iter 0 def
{
/Iter Iter 1 add def
Nx func /F exch def % f(Nx)
F abs eps2 lt { exit } if
Nx func' /FS exch def % f'(Nx)
FS 0 eq { /FS 1.0e-06 def } if
Nx func'' /F2S exch def % f''(Nx)
1.0 1.0 F F2S mul FS dup mul div sub div /J exch def
J F mul FS div /Diff exch def
/Nx Nx Diff sub def
Diff abs eps1 lt Iter MaxIter gt or { exit } if
} loop
Nx % the returned value ist the zero point
} def
/Steffensen {% the start value must be on top of the stack
/y0 exch def % the start value
/Iter 0 def
{
y0 func /F exch def
F abs eps2 lt { exit } if
y0 F sub /Phi exch def
Phi func /F2 exch def
F2 abs eps2 le { exit }{
Phi y0 sub dup mul Phi F2 sub 2 Phi mul sub y0 add Div /Diff exch def
y0 Diff sub /y0 exch def
Diff abs eps1 le { exit } if
} ifelse
/Iter Iter 1 add def
Iter MaxIter gt { exit } if
} loop
y0 % the returned value ist the zero point
} def
%
/Horner {% x [coeff] must be on top of the stack
aload length
dup 2 add -1 roll
exch 1 sub {
dup 4 1 roll
mul add exch
} repeat
pop % the y value is on top of the stack
} def
%
/FuncValue {% x [coeff] Derivation must be on top of the stack
{
aload % a0 a1 a2 ... a(n-1) [array]
length % a0 a1 a2 ... a(n-1) n
1 sub /grad exch def % a0 a1 a2 ... a(n-1)
grad -1 1 { % for n=grad step -1 until 1
/n exch def % Laufvariable speichern
n % a0 a1 a2 ... a(n-1) n
mul % a0 a1 a2 ... a(n-1)*n
grad 1 add % a0 a1 a2 ... a(n-1)*n grad+1
1 roll % an*na0 a1 a2 ... a(n-2)
} for
pop % loesche a0
grad array astore % [ a1 a2 ... a(n-2)]
} repeat
Horner
} def
%
/FindZeros { % dxN dxZ must be on top of the stack (x0..x1 the intervall) => []
12 dict begin
/dxZ exch def /dxN exch def
/pstZeros [] def
x0 dxZ x1 { % suche Nullstellen
/xWert exch def
xWert NewtonMehrfach
%xWert Steffensen
/xNull exch def
pstZeros aload length /Laenge exch def % now test if value is a new one
Laenge 0 eq
{ xNull 1 }
{ /newZero true def
Laenge {
xNull sub abs dxN lt { /newZero false def } if
} repeat
pstZeros aload pop
newZero { xNull Laenge 1 add } { Laenge } ifelse } ifelse
array astore
/pstZeros exch def
} for
pstZeros % the end array is now on the stack
end
} def
%
/Simpson { % on stack must be a b M --- simple version ---
% /SFunc must be defined
/M ED /b ED /a ED
/h b a sub M 2 mul div def
/s1 0 def
/s2 0 def
1 1 M {
/k exch def
/x k 2 mul 1 sub h mul a add def
/s1 s1 x SFunc add def
} for
1 1 M 1 sub {
/k exch def
/x k 2 mul h mul a add def
/s2 s2 x SFunc add def
} for
/I a SFunc b SFunc add s1 4 mul add s2 2 mul add 3 div h mul def
} def
%
/LogGamma { 5 dict begin % z on stack
/z ED
/sum 0 def
/k 1 def
{
z k div dup 1 add ln sub dup
abs eps8 lt { pop exit } if
sum add /sum exch def
/k k 1 add def
} loop
sum z ln sub CEuler z mul sub
end
} def
%
/ChebyshevT { 5 dict begin % z on stack
/xtmp exch def
/n exch def
0 0 1 n .5 mul floor {
/k exch def
xtmp xtmp mul 1 sub k exp
xtmp n 2 k mul sub exp mul
n 2 k mul MoverN mul
add
} for
end
} def
%
/ChebyshevU {5 dict begin % z on stack
/xtmp exch def
/n exch def
0 0 1 n .5 mul floor {
/k exch def
xtmp xtmp mul 1 sub k exp
xtmp n 2 k mul sub exp mul
n 1 add 2 k mul 1 add MoverN mul
add
} for
end
} def
%
% subroutines for complex numbers, given as an array [a b]
% which is a+bi = Real+i Imag
%
/cxadd { % [a1 b1] [a2 b2] = [a1+a2 b1+b2]
dup 0 get % [a1 b1] [a2 b2] a2
3 -1 roll % [a2 b2] a2 [a1 b1]
dup 0 get % [a2 b2] a2 [a1 b1] a1
3 -1 roll % [a2 b2] [a1 b1] a1 a2
add % [a2 b2] [a1 b1] a1+a2
3 1 roll % a1+a2 [a2 b2] [a1 b1]
1 get % a1+a2 [a2 b2] b1
exch 1 get % a1+a2 b1 b2
add 2 array astore
} def
%
/cxneg { % [a b]
dup 1 get % [a b] b
exch 0 get % b a
neg exch neg % -a -b
2 array astore
} def
%
/cxsub { cxneg cxadd } def % same as negative addition
%
% [a1 b1][a2 b2] = [a1a2-b1b2 a1b2+b1a2] = [a3 b3]
/cxmul { % [a1 b1] [a2 b2]
dup 0 get % [a1 b1] [a2 b2] a2
exch 1 get % [a1 b1] a2 b2
3 -1 roll % a2 b2 [a1 b1]
dup 0 get % a2 b2 [a1 b1] a1
exch 1 get % a2 b2 a1 b1
dup % a2 b2 a1 b1 b1
5 -1 roll dup % b2 a1 b1 b1 a2 a2
3 1 roll mul % b2 a1 b1 a2 b1a2
5 -2 roll dup % b1 a2 b1a2 b2 a1 a1
3 -1 roll dup % b1 a2 b1a2 a1 a1 b2 b2
3 1 roll mul % b1 a2 b1a2 a1 b2 a1b2
4 -1 roll add % b1 a2 a1 b2 b3
4 2 roll mul % b1 b2 b3 a1a2
4 2 roll mul sub % b3 a3
exch 2 array astore
} def
%
% [a b]^2 = [a^2-b^2 2ab] = [a2 b2]
/cxsqr { % [a b] square root
dup 0 get exch 1 get % a b
dup dup mul % a b b^2
3 -1 roll % b b^2 a
dup dup mul % b b^2 a a^2
3 -1 roll sub % b a a2
3 1 roll mul 2 mul % a2 b2
2 array astore
} def
%
/cxsqrt { % [a b]
% dup cxnorm sqrt /r exch def
% cxarg 2 div RadtoDeg dup cos r mul exch sin r mul cxmake2
cxlog % log[a b]
2 cxrdiv % log[a b]/2
aload pop exch % b a
2.781 exch exp % b exp(a)
exch cxconv exch % [Re +iIm] exp(a)
cxrmul %
} def
%
/cxarg { % [a b]
aload pop % a b
exch atan % arctan b/a
DegtoRad % arg(z)=atan(b/a)
} def
%
% log[a b] = [a^2-b^2 2ab] = [a2 b2]
/cxlog { % [a b]
dup % [a b][a b]
cxnorm % [a b] |z|
log % [a b] log|z|
exch % log|z|[a b]
cxarg % log|z| Theta
cxmake2 % [log|z| Theta]
} def
%
% square of magnitude of complex number
/cxnorm2 { % [a b]
dup 0 get exch 1 get % a b
dup mul % a b^2
exch dup mul add % a^2+b^2
} def
%
/cxnorm { % [a b]
cxnorm2 sqrt
} def
%
/cxconj { % conjugent complex
dup 0 get exch 1 get % a b
neg 2 array astore % [a -b]
} def
%
/cxre { 0 get } def % real value
/cxim { 1 get } def % imag value
%
% 1/[a b] = ([a -b]/(a^2+b^2)
/cxrecip { % [a b]
dup cxnorm2 exch % n2 [a b]
dup 0 get exch 1 get % n2 a b
3 -1 roll % a b n2
dup % a b n2 n2
4 -1 roll exch div % b n2 a/n2
3 1 roll div % a/n2 b/n2
neg 2 array astore
} def
%
/cxmake1 { 0 2 array astore } def % make a complex number, real given
/cxmake2 { 2 array astore } def % dito, both given
%
/cxdiv { cxrecip cxmul } def
%
% multiplikation by a real number
/cxrmul { % [a b] r
exch aload pop % r a b
3 -1 roll dup % a b r r
3 1 roll mul % a r b*r
3 1 roll mul % b*r a*r
exch 2 array astore % [a*r b*r]
} def
%
% division by a real number
/cxrdiv { % [a b] r
1 exch div % [a b] 1/r
cxrmul
} def
%
% exp(i theta) = cos(theta)+i sin(theta) polar<->cartesian
/cxconv { % theta
RadtoDeg dup sin exch cos cxmake2
} def
%
end
%%EndProcSet
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@endspecial @beginspecial
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@endspecial @beginspecial @setspecial
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@endspecial
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end
@endspecial @beginspecial
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@endspecial @beginspecial @setspecial
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@endspecial
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@endspecial @beginspecial
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@endspecial @beginspecial @setspecial
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@endspecial @beginspecial @setspecial
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@endspecial
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end
@endspecial @beginspecial @setspecial
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end
@endspecial
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} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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end
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pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat
} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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end
@endspecial @beginspecial
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end
@endspecial @beginspecial @setspecial
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end
@endspecial
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} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
end
@endspecial @beginspecial
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end
@endspecial @beginspecial @setspecial
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end
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@endspecial @beginspecial @setspecial
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@endspecial @beginspecial @setspecial
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end
@endspecial
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end
@endspecial @beginspecial
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end
@endspecial @beginspecial @setspecial
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end
@endspecial
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end
@endspecial @beginspecial
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@endspecial @beginspecial @setspecial
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tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def
/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
{ } def /ArrowInside { } def [ 144.0 65.13135 -24.0 65.13135 /Lineto
/lineto load def 0 setlinejoin false NArray n 0 eq not { n 1 eq {
0 0 /n 2 def } if () length 0 gt { 1.5 2. CLW mul add dup 1.4 mul
exch 0.4 mul neg add /arrowlength exch def 4 copy /y1 ED /x1 ED /y2
ED /x2 ED /Alpha y2 y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength
mul add y1 Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy
/y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub x2 x1
sub Atan def /ArrowPos 0. def /dArrowPos 0.5 abs def 1. cvi { /ArrowPos
ArrowPos dArrowPos add def x1 Alpha cos ArrowPos mul add y1 Alpha sin
ArrowPos mul add ArrowInside pop pop } repeat }{ /ArrowPos 0. def
/dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi {
/ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add
y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse
pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat
} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
end
@endspecial @beginspecial
@setspecial
tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def
/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
{ } def /ArrowInside { } def [ 144.0 67.41687 -24.0 67.41687 /Lineto
/lineto load def 0 setlinejoin false NArray n 0 eq not { n 1 eq {
0 0 /n 2 def } if () length 0 gt { 1.5 2. CLW mul add dup 1.4 mul
exch 0.4 mul neg add /arrowlength exch def 4 copy /y1 ED /x1 ED /y2
ED /x2 ED /Alpha y2 y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength
mul add y1 Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy
/y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub x2 x1
sub Atan def /ArrowPos 0. def /dArrowPos 0.5 abs def 1. cvi { /ArrowPos
ArrowPos dArrowPos add def x1 Alpha cos ArrowPos mul add y1 Alpha sin
ArrowPos mul add ArrowInside pop pop } repeat }{ /ArrowPos 0. def
/dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi {
/ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add
y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse
pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat
} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
end
@endspecial @beginspecial @setspecial
tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def
/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
{ } def /ArrowInside { } def [ 144.0 69.7024 -24.0 69.7024 /Lineto
/lineto load def 0 setlinejoin false NArray n 0 eq not { n 1 eq {
0 0 /n 2 def } if () length 0 gt { 1.5 2. CLW mul add dup 1.4 mul
exch 0.4 mul neg add /arrowlength exch def 4 copy /y1 ED /x1 ED /y2
ED /x2 ED /Alpha y2 y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength
mul add y1 Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy
/y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub x2 x1
sub Atan def /ArrowPos 0. def /dArrowPos 0.5 abs def 1. cvi { /ArrowPos
ArrowPos dArrowPos add def x1 Alpha cos ArrowPos mul add y1 Alpha sin
ArrowPos mul add ArrowInside pop pop } repeat }{ /ArrowPos 0. def
/dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi {
/ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add
y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse
pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat
} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
end
@endspecial
@beginspecial @setspecial
tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def
/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
{ } def /ArrowInside { } def [ 144.0 71.98792 -24.0 71.98792 /Lineto
/lineto load def 0 setlinejoin false NArray n 0 eq not { n 1 eq {
0 0 /n 2 def } if () length 0 gt { 1.5 2. CLW mul add dup 1.4 mul
exch 0.4 mul neg add /arrowlength exch def 4 copy /y1 ED /x1 ED /y2
ED /x2 ED /Alpha y2 y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength
mul add y1 Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy
/y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub x2 x1
sub Atan def /ArrowPos 0. def /dArrowPos 0.5 abs def 1. cvi { /ArrowPos
ArrowPos dArrowPos add def x1 Alpha cos ArrowPos mul add y1 Alpha sin
ArrowPos mul add ArrowInside pop pop } repeat }{ /ArrowPos 0. def
/dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi {
/ArrowPos ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add
y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse
pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat
} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
end
@endspecial @beginspecial
@setspecial
tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def
/ArrowInside { } def 0.5 SLW 1 setgray /ArrowA { moveto } def /ArrowB
{ } def /ArrowInside { } def /t 0 def /t1 1 def /dt t1 t sub 199
div def /F@pstplot (15*t^2*(1-t)^3+30*t^3*(1-t)^2+25*t^4*(1-t)+5*t^5|7.5*t*(1-t)^4+(1.1)*10*t^2*(1-t)^3+(1.4)*20*t^3*(1-t)^2+7.5*t^4*(1-t))
tx@AlgToPs begin AlgToPs end cvx def /xy { F@pstplot 24.0 mul exch
24.0 mul exch } def /ps@Exit false def xy moveto 199 1 sub { /t t
dt add def xy dup 1.e30 24.0 mul gt { moveto }{ dup -1.e30 24.0 mul
lt { moveto }{ L } ifelse } ifelse ps@Exit { exit } if } repeat ps@Exit
not { /t t1 def xy dup 1.e30 24.0 mul gt { moveto }{ dup -1.e30 24.0
mul lt { moveto }{ L } ifelse } ifelse } if gsave 0.5 SLW 1 setgray
1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
end
@endspecial @beginspecial @setspecial
tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def
/ArrowInside { } def 0.5 SLW 1 setgray /ArrowA { moveto } def /ArrowB
{ } def /ArrowInside { } def /t 0 def /t1 1 def /dt t1 t sub 199
div def /F@pstplot (5*(1-t)^5+25*t*(1-t)^4+35*t^2*(1-t)^3+20*t^3*(1-t)^2|(-7.5)*t*(1-t)^4+(1.2)*(-10)*t^2*(1-t)^3+(1.5)*(-20)*t^3*(1-t)^2+(-7.5)*t^4*(1-t))
tx@AlgToPs begin AlgToPs end cvx def /xy { F@pstplot 24.0 mul exch
24.0 mul exch } def /ps@Exit false def xy moveto 199 1 sub { /t t
dt add def xy dup 1.e30 24.0 mul gt { moveto }{ dup -1.e30 24.0 mul
lt { moveto }{ L } ifelse } ifelse ps@Exit { exit } if } repeat ps@Exit
not { /t t1 def xy dup 1.e30 24.0 mul gt { moveto }{ dup -1.e30 24.0
mul lt { moveto }{ L } ifelse } ifelse } if gsave 0.5 SLW 1 setgray
1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
end
@endspecial
0 TeXcolorgray 0 TeXcolorgray eop end
%%Trailer
userdict /end-hook known{end-hook}if
%%EOF
