;; variation on runge-kutta (rk) routine in complex_dynamics.lisp by
[email protected]
;; this one with changed by
[email protected]
#| rkfun may be much faster than rk because it calls compiled programs.
rkfun (this file) should also be compiled to speed it up.
how to use:
first, read and understand the documentation for rk().
next, define the ODE right hand sides as functions as shown below
fun1(y,x,x0):= x0$
fun2(y,x,x0):= block([], mode_declare([y, x0,x],float),(1-x^2)*x0-x);
compile(fun1)$
compile(fun2)$
showtime:all$
last(rkfun([fun1,fun2],[x,xdot],[0.0,0.6],[t,0,50,0.01]));
/* which is, in one test, 18 times faster than */
last(rk([xdot,(1-x^2)*xdot -x],[x,xdot],[0.0,0.6],[t,0,50,0.01]));
|#
(defun $rkfun (funs vars initial domain ;; taken from complex_dynamics.lisp
&aux d u funlist k1 k2 k3 k4 r1 r2 r3 traj r
(it (mapcar #'coerce-float (cddr domain))))
(unless ($listp funs) (setq funs `((mlist) ,funs)))
(unless ($listp initial) (setq initial `((mlist) ,initial)))
(unless ($listp vars) (setq vars `((mlist) ,vars)))
(dolist (var (cdr vars))
(unless (symbolp var)
(merror (intl:gettext "rk: variable name expected; found: ~M") var)))
(unless (symbolp (cadr domain))
(merror (intl:gettext "rk: variable name expected; found: ~M")
(cadr domain)))
(setq vars (append '((mlist)) (list (cadr domain)) (cdr vars)))
(setq r (append `(,(car it)) (mapcar #'coerce-float (cdr initial))))
(setq funlist (cdr funs))
(setq d (/ (- (cadr it) (car it)) (caddr it)))
(setq traj (list (cons '(mlist) r)))
(do ((m 1 (1+ m))) ((> m d))
(progn ;;; was ignore-errors
(setq k1 (mapcar #'(lambda (x) (apply x r)) funlist))
(setq r1 (map 'list #'+ (cdr r) (mapcar #'(lambda (x) (* 0.5d0 (caddr it) x)) k1)))
(push (+ (car r) (/ (caddr it) 2)) r1)
(setq k2 (mapcar #'(lambda (x) (apply x r1)) funlist))
(setq r2 (map 'list #'+ (cdr r) (mapcar #'(lambda (x) (* 0.5d0(caddr it) x)) k2)))
(push (+ (car r) (/ (caddr it) 2)) r2)
(setq k3 (mapcar #'(lambda (x) (apply x r2)) funlist))
(setq r3 (map 'list #'+ (cdr r) (mapcar #'(lambda (x) (* (caddr it) x)) k3)))
(push (+ (car r) (caddr it)) r3)
(setq k4 (mapcar #'(lambda (x) (apply x r3)) funlist))
(setq u (map 'list #'+
(mapcar #'(lambda (x) (* #.(/ 1.0 6.0d0) x)) k1)
(mapcar #'(lambda (x) (* #.(/ 1.0 3.0d0) x)) k2)
(mapcar #'(lambda (x) (* #.(/ 1.0 3.0d0) x)) k3)
(mapcar #'(lambda (x) (* #.(/ 1.0 6.0d0) x)) k4)))
(setq r
(append
`(,(+ (car it) (* m (caddr it))))
(map 'list #'+ (cdr r) (mapcar #'(lambda (x) (* (caddr it) x)) u))))
(push (cons '(mlist) r) traj)))
(when (< (car r) (cadr it))
(let ((s (- (cadr it) (car r))) )
(declare(double-float s)(special s)(optimize (speed 3)(safety 0)))
(progn ;; was ignore-errors
(setq k1 (mapcar #'(lambda (x) (mapply x r nil)) funlist))
(setq r1 (map 'list #'+ (cdr r) (mapcar #'(lambda (x)
(declare(double-float x))
(* s 0.5d0 x)) k1)))
(push (+ (car r) (* 0.5d0 s)) r1)
(setq k2 (mapcar #'(lambda (x) (mapply x r1 nil)) funlist))
(setq r2 (map 'list #'+ (cdr r) (mapcar #'(lambda (x)(declare(double-float x))
(* s 0.5d0 x)) k2)))
(push (+ (car r) (* 0.5d0 s)) r2)
(setq k3 (mapcar #'(lambda (x) (mapply x r2 nil)) funlist))
(setq r3 (map 'list #'+ (cdr r) (mapcar #'(lambda (x)(declare(double-float x))
(* s x)) k3)))
(push (+ (car r) s) r3)
(setq k4 (mapcar #'(lambda (x) (mapply x r3 nil)) funlist))
(setq u (map 'list #'+
(mapcar #'(lambda (x)(declare(double-float x))
(* #.(/ 1.0d0 6.0d0) x)) k1)
(mapcar #'(lambda (x)(declare(double-float x))
(* #.(/ 1.0d0 3.0d0) x)) k2)
(mapcar #'(lambda (x) (declare(double-float x))
(* #.(/ 1.0d0 3.0d0) x)) k3)
(mapcar #'(lambda (x)(declare(double-float x))
(* #.(/ 1.0d0 6.0d0) x)) k4)))
(setq r
(append
`(,(cadr it))
(map 'list #'+ (cdr r) (mapcar #'(lambda (x)(declare(double-float x))
(* s x)) u))))
(push (cons '(mlist) r) traj))))
(cons '(mlist) (nreverse traj)))
