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;; plotdf.mac - Adds a function plotdf() to Maxima, which draws a Direction
;; Field for an ordinary 1st order differential equation,
;; or for a system of two autonomous 1st order equations.
;;
;; Copyright (C) 2004, 2008 Jaime E. Villate <villate@gnu.org>
;;
;; This program is free software; you can redistribute it and/or modify
;; it under the terms of the GNU General Public License as published by
;; the Free Software Foundation; either version 2 of the License, or
;; (at your option) any later version.
;;
;; This program is distributed in the hope that it will be useful,
;; but WITHOUT ANY WARRANTY; without even the implied warranty of
;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
;; GNU General Public License for more details.
;;
;; You should have received a copy of the GNU General Public License
;; along with this program; if not, write to the Free Software
;; Foundation, Inc., 59 Temple Place, Suite 330, Boston,
;; MA 02111-1307 USA
;;
;; See plotdf.usg (which should come together with this program) for
;; a usage summary
;;
;; $Id: plotdf.lisp,v 1.11 2009/04/10 13:46:28 villate Exp $
(in-package :maxima)
;; parses a plotdf option into a command-line option for tcl scripts
(defun plotdf-option-to-tcl (value s1 s2)
(let (vv)
(unless (and ($listp value)
(symbolp (setq name (second value))))
(merror "~M is not a plotdf option. Must be [symbol,..data]" value))
(setq value
(case name
(($xradius $yradius $xcenter $ycenter $tinitial $tstep)
(check-list-items name (rest (rest value)) 'number 1))
(($width $height $nsteps $versus_t)
(check-list-items name (rest (rest value)) 'fixnum 1))
($trajectory_at
(check-list-items name (rest (rest value)) 'number 2))
($bbox (check-list-items name (rest (rest value)) 'number 4))
(($xfun $parameters $sliders $vectors $fieldlines $curves
$windowtitle $xaxislabel $yaxislabel $psfile) value)
($axes
(if (not (third value))
(setq value '((mlist simp) $axes 0))
(case (third value)
($x (setq value '((mlist simp) $axes "x")))
($y (setq value '((mlist simp) $axes "y")))
(t (setq value '((mlist simp) $axes "xy"))))))
($box
(if (not (third value))
(setq value '((mlist simp) $nobox 1))
(setq value '((mlist simp) $nobox 0))))
($direction
(or (member (third value) '($forward $backward $both))
(merror "direction: choose one of [forward,backward,both]"))
value)
(t (cond
((eql name s1)
(setq value (check-range value))
(check-list-items '$x (rest (rest value)) 'number 2))
((eql name s2)
(setq value (check-range value))
(check-list-items '$y (rest (rest value)) 'number 2))
(t (merror "Unknown option ~M" name))))))
(setq vv (mapcar #'stripdollar (rest value)))
(with-output-to-string (st)
(cond ((or (eql (first vv) 'x) (eql (first vv) 'y))
(format st "-~(~a~)center " (first vv))
(format st "{~a} " (/ (+ (third vv) (second vv)) 2))
(format st "-~(~a~)radius " (first vv))
(format st "{~a}" (/ (- (third vv) (second vv)) 2)))
(t
(format st "-~(~a~) " (first vv))
(format st "{~{~a~^ ~}}" (rest vv)))))))
;; applies float(ev(expression, numer)) to an expression, and returns a string
(defun expr_to_str (fun)
(mstring (mfuncall '$float (mfuncall '$ev fun '$numer))))
;; plots the direction field for an ODE dy/dx = f(x,y), or for an autonomous
;; system of 2 equations dx/dt = f(x,y), dy/dt = g(x,y)
;;
(defun $plotdf (ode &rest options)
(let (cmd (opts " ") (s1 '$x) (s2 '$y))
(unless ($listp ode) (setf ode `((mlist) ,ode)))
;; parse arguments and prepare string cmd with the equation(s)
(unless
(member (second (first options))
'($xradius $yradius $xcenter $ycenter $tinitial $tstep
$width $height $nsteps $versus_t $xfun $parameters
$sliders $vector $trajectory $orthogonal))
(if (and (listp (first options)) (= (length (first options)) 3)
(symbolp (second (first options)))
(symbolp (third (first options))))
(progn
(setf s1 (second (first options)))
(setf s2 (third (first options)))
(defun subxy (expr)
(if (listp expr)
(mapcar #'subxy expr)
(cond ((eq expr s1) '$x) ((eq expr s2) '$y) (t expr))))
(setf ode (mapcar #'subxy ode))
(setf options (cdr options)))))
;; the next two lines should take into account parameters given in the options
;; (if (delete '$y (delete '$x (rest (mfuncall '$listofvars ode))))
;; (merror "The equation(s) can depend only on 2 variable which must be specified!"))
(case (length ode)
(3 (setq cmd (concatenate 'string " -dxdt \""
(expr_to_str (second ode)) "\" -dydt \""
(expr_to_str (third ode)) "\"")))
(2 (setq cmd (concatenate 'string " -dydx \""
(expr_to_str (second ode)) "\"")))
(t (merror "Argument must be either dydx or [dxdt, dydt]")))
;; parse options and copy them to string opts
(cond (options
(dolist (v options)
(setq opts (concatenate 'string opts " "
(plotdf-option-to-tcl v s1 s2))))))
(unless (search "-xaxislabel " opts)
(setq opts (concatenate 'string opts " -xaxislabel " (ensure-string s1))))
(unless (search "-yaxislabel " opts)
(setq opts (concatenate 'string opts " -yaxislabel " (ensure-string s2))))
(show-open-plot
(with-output-to-string (st)
(cond ($show_openplot (format st "plotdf ~a ~a~%" cmd opts))
(t (format st "{plotdf ~a ~a}" cmd opts)))))))
;; plot equipotential curves for a scalar field f(x,y)
(defun $ploteq (fun &rest options)
(let (cmd mfun (opts " ") (s1 '$x) (s2 '$y))
(setf mfun `((mtimes) -1 ,fun))
;; parse arguments and prepare string cmd with the equation(s)
(unless
(member (second (first options))
'($xradius $yradius $xcenter $ycenter $tinitial $tstep
$width $height $nsteps $versus_t $xfun $parameters
$sliders $vector $trajectory $orthogonal))
(if (and (listp (first options)) (= (length (first options)) 3)
(symbolp (second (first options)))
(symbolp (third (first options))))
(progn
(setf s1 (second (first options)))
(setf s2 (third (first options)))
(defun subxy (expr)
(if (listp expr)
(mapcar #'subxy expr)
(cond ((eq expr s1) '$x) ((eq expr s2) '$y) (t expr))))
(setf mfun (mapcar #'subxy mfun))
(setf options (cdr options)))))
;; the next two lines should take into account parameters given in the options
;; (if (delete '$y (delete '$x (rest (mfuncall '$listofvars ode))))
;; (merror "The equation(s) can depend only on 2 variable which must be specified!"))
(setq cmd (concatenate 'string " -dxdt \""
(expr_to_str (mfuncall '$diff mfun '$x))
"\" -dydt \""
(expr_to_str (mfuncall '$diff mfun '$y))
"\" "))
;; parse options and copy them to string opts
(cond (options
(dolist (v options)
(setq opts (concatenate 'string opts " "
(plotdf-option-to-tcl v s1 s2))))))
(unless (search "-vectors " opts)
(setq opts (concatenate 'string opts " -vectors {}")))
(unless (search "-fieldlines " opts)
(setq opts (concatenate 'string opts " -fieldlines {}")))
(unless (search "-curves " opts)
(setq opts (concatenate 'string opts " -curves {red}")))
(unless (search "-windowtitle " opts)
(setq opts (concatenate 'string opts " -windowtitle {Ploteq}")))
(unless (search "-xaxislabel " opts)
(setq opts (concatenate 'string opts " -xaxislabel " (ensure-string s1))))
(unless (search "-yaxislabel " opts)
(setq opts (concatenate 'string opts " -yaxislabel " (ensure-string s2))))
(show-open-plot
(with-output-to-string (st)
(cond ($show_openplot (format st "plotdf ~a ~a~%" cmd opts))
(t (format st "{plotdf ~a ~a}" cmd opts)))))))
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