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1 | ;;; calcalg3.el --- more algebraic functions for Calc |
2 | ||
58ba2f8f | 3 | ;; Copyright (C) 1990, 1991, 1992, 1993, 2001, 2002, 2003, 2004, |
8b72699e | 4 | ;; 2005, 2006, 2007, 2008 Free Software Foundation, Inc. |
3132f345 CW |
5 | |
6 | ;; Author: David Gillespie <daveg@synaptics.com> | |
e8fff8ed | 7 | ;; Maintainer: Jay Belanger <jay.p.belanger@gmail.com> |
136211a9 EZ |
8 | |
9 | ;; This file is part of GNU Emacs. | |
10 | ||
7c671b23 GM |
11 | ;; GNU Emacs is free software; you can redistribute it and/or modify |
12 | ;; it under the terms of the GNU General Public License as published by | |
075969b4 | 13 | ;; the Free Software Foundation; either version 3, or (at your option) |
7c671b23 GM |
14 | ;; any later version. |
15 | ||
136211a9 | 16 | ;; GNU Emacs is distributed in the hope that it will be useful, |
7c671b23 GM |
17 | ;; but WITHOUT ANY WARRANTY; without even the implied warranty of |
18 | ;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
19 | ;; GNU General Public License for more details. | |
20 | ||
21 | ;; You should have received a copy of the GNU General Public License | |
22 | ;; along with GNU Emacs; see the file COPYING. If not, write to the | |
23 | ;; Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, | |
24 | ;; Boston, MA 02110-1301, USA. | |
136211a9 | 25 | |
3132f345 | 26 | ;;; Commentary: |
136211a9 | 27 | |
3132f345 | 28 | ;;; Code: |
136211a9 EZ |
29 | |
30 | ;; This file is autoloaded from calc-ext.el. | |
136211a9 | 31 | |
c728e633 | 32 | (require 'calc-ext) |
136211a9 EZ |
33 | (require 'calc-macs) |
34 | ||
05fed923 JB |
35 | ;; Declare functions which are defined elsewhere. |
36 | (declare-function calc-fit-s-shaped-logistic-curve "calc-nlfit" (arg)) | |
37 | (declare-function calc-fit-bell-shaped-logistic-curve "calc-nlfit" (arg)) | |
38 | (declare-function calc-fit-hubbert-linear-curve "calc-nlfit" (&optional sdv)) | |
39 | (declare-function calc-graph-add-curve "calc-graph" (xdata ydata &optional zdata)) | |
40 | (declare-function calc-graph-lookup "calc-graph" (thing)) | |
41 | (declare-function calc-graph-set-styles "calc-graph" (lines points &optional yerr)) | |
42 | (declare-function math-min-list "calc-arith" (a b)) | |
43 | (declare-function math-max-list "calc-arith" (a b)) | |
44 | ||
45 | ||
e5a5704e JB |
46 | (defun math-map-binop (binop args1 args2) |
47 | "Apply BINOP to the elements of the lists ARGS1 and ARGS2" | |
48 | (if args1 | |
49 | (cons | |
50 | (funcall binop (car args1) (car args2)) | |
51 | (funcall 'math-map-binop binop (cdr args1) (cdr args2))))) | |
52 | ||
136211a9 EZ |
53 | (defun calc-find-root (var) |
54 | (interactive "sVariable(s) to solve for: ") | |
55 | (calc-slow-wrapper | |
56 | (let ((func (if (calc-is-hyperbolic) 'calcFunc-wroot 'calcFunc-root))) | |
57 | (if (or (equal var "") (equal var "$")) | |
58 | (calc-enter-result 2 "root" (list func | |
59 | (calc-top-n 3) | |
60 | (calc-top-n 1) | |
61 | (calc-top-n 2))) | |
62 | (let ((var (if (and (string-match ",\\|[^ ] +[^ ]" var) | |
63 | (not (string-match "\\[" var))) | |
64 | (math-read-expr (concat "[" var "]")) | |
65 | (math-read-expr var)))) | |
66 | (if (eq (car-safe var) 'error) | |
67 | (error "Bad format in expression: %s" (nth 1 var))) | |
68 | (calc-enter-result 1 "root" (list func | |
69 | (calc-top-n 2) | |
70 | var | |
bf77c646 | 71 | (calc-top-n 1)))))))) |
136211a9 EZ |
72 | |
73 | (defun calc-find-minimum (var) | |
74 | (interactive "sVariable(s) to minimize over: ") | |
75 | (calc-slow-wrapper | |
76 | (let ((func (if (calc-is-inverse) | |
77 | (if (calc-is-hyperbolic) | |
78 | 'calcFunc-wmaximize 'calcFunc-maximize) | |
79 | (if (calc-is-hyperbolic) | |
80 | 'calcFunc-wminimize 'calcFunc-minimize))) | |
81 | (tag (if (calc-is-inverse) "max" "min"))) | |
82 | (if (or (equal var "") (equal var "$")) | |
83 | (calc-enter-result 2 tag (list func | |
84 | (calc-top-n 3) | |
85 | (calc-top-n 1) | |
86 | (calc-top-n 2))) | |
87 | (let ((var (if (and (string-match ",\\|[^ ] +[^ ]" var) | |
88 | (not (string-match "\\[" var))) | |
89 | (math-read-expr (concat "[" var "]")) | |
90 | (math-read-expr var)))) | |
91 | (if (eq (car-safe var) 'error) | |
92 | (error "Bad format in expression: %s" (nth 1 var))) | |
93 | (calc-enter-result 1 tag (list func | |
94 | (calc-top-n 2) | |
95 | var | |
bf77c646 | 96 | (calc-top-n 1)))))))) |
136211a9 EZ |
97 | |
98 | (defun calc-find-maximum (var) | |
99 | (interactive "sVariable to maximize over: ") | |
100 | (calc-invert-func) | |
bf77c646 | 101 | (calc-find-minimum var)) |
136211a9 EZ |
102 | |
103 | ||
104 | (defun calc-poly-interp (arg) | |
105 | (interactive "P") | |
106 | (calc-slow-wrapper | |
107 | (let ((data (calc-top 2))) | |
108 | (if (or (consp arg) (eq arg 0) (eq arg 2)) | |
109 | (setq data (cons 'vec (calc-top-list 2 2))) | |
110 | (or (null arg) | |
111 | (error "Bad prefix argument"))) | |
112 | (if (calc-is-hyperbolic) | |
113 | (calc-enter-result 1 "rati" (list 'calcFunc-ratint data (calc-top 1))) | |
114 | (calc-enter-result 1 "poli" (list 'calcFunc-polint data | |
bf77c646 | 115 | (calc-top 1))))))) |
136211a9 | 116 | |
03cc1aba JB |
117 | ;; The variables calc-curve-nvars, calc-curve-varnames, calc-curve-model and calc-curve-coefnames are local to calc-curve-fit, but are |
118 | ;; used by calc-get-fit-variables which is called by calc-curve-fit. | |
119 | (defvar calc-curve-nvars) | |
120 | (defvar calc-curve-varnames) | |
121 | (defvar calc-curve-model) | |
122 | (defvar calc-curve-coefnames) | |
136211a9 | 123 | |
c0233753 JB |
124 | (defvar calc-curve-fit-history nil |
125 | "History for calc-curve-fit.") | |
126 | ||
03cc1aba JB |
127 | (defun calc-curve-fit (arg &optional calc-curve-model |
128 | calc-curve-coefnames calc-curve-varnames) | |
136211a9 EZ |
129 | (interactive "P") |
130 | (calc-slow-wrapper | |
131 | (setq calc-aborted-prefix nil) | |
132 | (let ((func (if (calc-is-inverse) 'calcFunc-xfit | |
133 | (if (calc-is-hyperbolic) 'calcFunc-efit | |
134 | 'calcFunc-fit))) | |
135 | key (which 0) | |
b07251cc JB |
136 | (nonlinear nil) |
137 | (plot nil) | |
03cc1aba | 138 | n calc-curve-nvars temp data |
136211a9 EZ |
139 | (homog nil) |
140 | (msgs '( "(Press ? for help)" | |
141 | "1 = linear or multilinear" | |
142 | "2-9 = polynomial fits; i = interpolating polynomial" | |
143 | "p = a x^b, ^ = a b^x" | |
144 | "e = a exp(b x), x = exp(a + b x), l = a + b ln(x)" | |
145 | "E = a 10^(b x), X = 10^(a + b x), L = a + b log10(x)" | |
146 | "q = a + b (x-c)^2" | |
147 | "g = (a/b sqrt(2 pi)) exp(-0.5*((x-c)/b)^2)" | |
b07251cc JB |
148 | "s = a/(1 + exp(b (x - c)))" |
149 | "b = a exp(b (x - c))/(1 + exp(b (x - c)))^2" | |
150 | "o = (y/x) = a (1 - x/b)" | |
136211a9 | 151 | "h prefix = homogeneous model (no constant term)" |
b07251cc | 152 | "P prefix = plot result" |
136211a9 | 153 | "' = alg entry, $ = stack, u = Model1, U = Model2"))) |
03cc1aba | 154 | (while (not calc-curve-model) |
def4f741 | 155 | (message |
48b097e0 | 156 | "Fit to model: %s:%s%s" |
def4f741 | 157 | (nth which msgs) |
2230383b | 158 | (if plot "P" " ") |
48b097e0 | 159 | (if homog "h" "")) |
136211a9 EZ |
160 | (setq key (read-char)) |
161 | (cond ((= key ?\C-g) | |
162 | (keyboard-quit)) | |
163 | ((= key ??) | |
164 | (setq which (% (1+ which) (length msgs)))) | |
165 | ((memq key '(?h ?H)) | |
166 | (setq homog (not homog))) | |
b07251cc | 167 | ((= key ?P) |
def4f741 JB |
168 | (if plot |
169 | (setq plot nil) | |
170 | (let ((data (calc-top 1))) | |
171 | (if (or | |
172 | (calc-is-hyperbolic) | |
173 | (calc-is-inverse) | |
174 | (not (= (length data) 3))) | |
175 | (setq plot "Can't plot") | |
176 | (setq plot data))))) | |
136211a9 EZ |
177 | ((progn |
178 | (if (eq key ?\$) | |
179 | (setq n 1) | |
180 | (setq n 0)) | |
181 | (cond ((null arg) | |
182 | (setq n (1+ n) | |
183 | data (calc-top n))) | |
184 | ((or (consp arg) (eq arg 0)) | |
185 | (setq n (+ n 2) | |
186 | data (calc-top n) | |
187 | data (if (math-matrixp data) | |
188 | (append data (list (calc-top (1- n)))) | |
189 | (list 'vec data (calc-top (1- n)))))) | |
190 | ((> (setq arg (prefix-numeric-value arg)) 0) | |
191 | (setq data (cons 'vec (calc-top-list arg (1+ n))) | |
192 | n (+ n arg))) | |
193 | (t (error "Bad prefix argument"))) | |
194 | (or (math-matrixp data) (not (cdr (cdr data))) | |
195 | (error "Data matrix is not a matrix!")) | |
03cc1aba JB |
196 | (setq calc-curve-nvars (- (length data) 2) |
197 | calc-curve-coefnames nil | |
198 | calc-curve-varnames nil) | |
136211a9 EZ |
199 | nil)) |
200 | ((= key ?1) ; linear or multilinear | |
03cc1aba JB |
201 | (calc-get-fit-variables calc-curve-nvars |
202 | (1+ calc-curve-nvars) (and homog 0)) | |
b07251cc JB |
203 | (setq calc-curve-model |
204 | (math-mul calc-curve-coefnames | |
205 | (cons 'vec (cons 1 (cdr calc-curve-varnames)))))) | |
136211a9 EZ |
206 | ((and (>= key ?2) (<= key ?9)) ; polynomial |
207 | (calc-get-fit-variables 1 (- key ?0 -1) (and homog 0)) | |
03cc1aba JB |
208 | (setq calc-curve-model |
209 | (math-build-polynomial-expr (cdr calc-curve-coefnames) | |
210 | (nth 1 calc-curve-varnames)))) | |
136211a9 EZ |
211 | ((= key ?i) ; exact polynomial |
212 | (calc-get-fit-variables 1 (1- (length (nth 1 data))) | |
213 | (and homog 0)) | |
03cc1aba JB |
214 | (setq calc-curve-model |
215 | (math-build-polynomial-expr (cdr calc-curve-coefnames) | |
216 | (nth 1 calc-curve-varnames)))) | |
136211a9 | 217 | ((= key ?p) ; power law |
03cc1aba JB |
218 | (calc-get-fit-variables calc-curve-nvars |
219 | (1+ calc-curve-nvars) (and homog 1)) | |
b07251cc JB |
220 | (setq calc-curve-model |
221 | (math-mul | |
222 | (nth 1 calc-curve-coefnames) | |
223 | (calcFunc-reduce | |
224 | '(var mul var-mul) | |
225 | (calcFunc-map | |
226 | '(var pow var-pow) | |
227 | calc-curve-varnames | |
228 | (cons 'vec (cdr (cdr calc-curve-coefnames)))))))) | |
136211a9 | 229 | ((= key ?^) ; exponential law |
03cc1aba JB |
230 | (calc-get-fit-variables calc-curve-nvars |
231 | (1+ calc-curve-nvars) (and homog 1)) | |
b07251cc JB |
232 | (setq calc-curve-model |
233 | (math-mul (nth 1 calc-curve-coefnames) | |
234 | (calcFunc-reduce | |
235 | '(var mul var-mul) | |
236 | (calcFunc-map | |
237 | '(var pow var-pow) | |
238 | (cons 'vec (cdr (cdr calc-curve-coefnames))) | |
239 | calc-curve-varnames))))) | |
240 | ((= key ?s) | |
241 | (setq nonlinear t) | |
242 | (setq calc-curve-model t) | |
243 | (require 'calc-nlfit) | |
244 | (calc-fit-s-shaped-logistic-curve func)) | |
245 | ((= key ?b) | |
246 | (setq nonlinear t) | |
247 | (setq calc-curve-model t) | |
248 | (require 'calc-nlfit) | |
249 | (calc-fit-bell-shaped-logistic-curve func)) | |
250 | ((= key ?o) | |
251 | (setq nonlinear t) | |
252 | (setq calc-curve-model t) | |
253 | (require 'calc-nlfit) | |
254 | (if (and plot (not (stringp plot))) | |
255 | (setq plot | |
256 | (list 'vec | |
257 | (nth 1 plot) | |
258 | (cons | |
259 | 'vec | |
e5a5704e JB |
260 | (math-map-binop 'calcFunc-div |
261 | (cdr (nth 2 plot)) | |
262 | (cdr (nth 1 plot))))))) | |
b07251cc | 263 | (calc-fit-hubbert-linear-curve func)) |
136211a9 | 264 | ((memq key '(?e ?E)) |
03cc1aba JB |
265 | (calc-get-fit-variables calc-curve-nvars |
266 | (1+ calc-curve-nvars) (and homog 1)) | |
b07251cc JB |
267 | (setq calc-curve-model |
268 | (math-mul (nth 1 calc-curve-coefnames) | |
269 | (calcFunc-reduce | |
270 | '(var mul var-mul) | |
271 | (calcFunc-map | |
272 | (if (eq key ?e) | |
273 | '(var exp var-exp) | |
274 | '(calcFunc-lambda | |
275 | (var a var-a) | |
276 | (^ 10 (var a var-a)))) | |
277 | (calcFunc-map | |
278 | '(var mul var-mul) | |
279 | (cons 'vec (cdr (cdr calc-curve-coefnames))) | |
280 | calc-curve-varnames)))))) | |
136211a9 | 281 | ((memq key '(?x ?X)) |
03cc1aba JB |
282 | (calc-get-fit-variables calc-curve-nvars |
283 | (1+ calc-curve-nvars) (and homog 0)) | |
b07251cc JB |
284 | (setq calc-curve-model |
285 | (math-mul calc-curve-coefnames | |
286 | (cons 'vec (cons 1 (cdr calc-curve-varnames))))) | |
03cc1aba JB |
287 | (setq calc-curve-model (if (eq key ?x) |
288 | (list 'calcFunc-exp calc-curve-model) | |
289 | (list '^ 10 calc-curve-model)))) | |
136211a9 | 290 | ((memq key '(?l ?L)) |
03cc1aba JB |
291 | (calc-get-fit-variables calc-curve-nvars |
292 | (1+ calc-curve-nvars) (and homog 0)) | |
b07251cc JB |
293 | (setq calc-curve-model |
294 | (math-mul calc-curve-coefnames | |
295 | (cons 'vec | |
296 | (cons 1 (cdr (calcFunc-map | |
297 | (if (eq key ?l) | |
298 | '(var ln var-ln) | |
299 | '(var log10 | |
300 | var-log10)) | |
301 | calc-curve-varnames))))))) | |
136211a9 | 302 | ((= key ?q) |
03cc1aba JB |
303 | (calc-get-fit-variables calc-curve-nvars |
304 | (1+ (* 2 calc-curve-nvars)) (and homog 0)) | |
305 | (let ((c calc-curve-coefnames) | |
306 | (v calc-curve-varnames)) | |
307 | (setq calc-curve-model (nth 1 c)) | |
136211a9 | 308 | (while (setq v (cdr v) c (cdr (cdr c))) |
03cc1aba JB |
309 | (setq calc-curve-model (math-add |
310 | calc-curve-model | |
136211a9 EZ |
311 | (list '* |
312 | (car c) | |
313 | (list '^ | |
314 | (list '- (car v) (nth 1 c)) | |
315 | 2))))))) | |
316 | ((= key ?g) | |
b07251cc JB |
317 | (setq |
318 | calc-curve-model | |
319 | (math-read-expr | |
320 | "(AFit / BFit sqrt(2 pi)) exp(-0.5 * ((XFit - CFit) / BFit)^2)") | |
321 | calc-curve-varnames '(vec (var XFit var-XFit)) | |
322 | calc-curve-coefnames '(vec (var AFit var-AFit) | |
323 | (var BFit var-BFit) | |
324 | (var CFit var-CFit))) | |
03cc1aba JB |
325 | (calc-get-fit-variables 1 (1- (length calc-curve-coefnames)) |
326 | (and homog 1))) | |
136211a9 EZ |
327 | ((memq key '(?\$ ?\' ?u ?U)) |
328 | (let* ((defvars nil) | |
329 | (record-entry nil)) | |
330 | (if (eq key ?\') | |
331 | (let* ((calc-dollar-values calc-arg-values) | |
332 | (calc-dollar-used 0) | |
333 | (calc-hashes-used 0)) | |
b07251cc JB |
334 | (setq calc-curve-model |
335 | (calc-do-alg-entry "" "Model formula: " | |
336 | nil 'calc-curve-fit-history)) | |
03cc1aba | 337 | (if (/= (length calc-curve-model) 1) |
136211a9 | 338 | (error "Bad format")) |
03cc1aba | 339 | (setq calc-curve-model (car calc-curve-model) |
136211a9 EZ |
340 | record-entry t) |
341 | (if (> calc-dollar-used 0) | |
03cc1aba | 342 | (setq calc-curve-coefnames |
136211a9 EZ |
343 | (cons 'vec |
344 | (nthcdr (- (length calc-arg-values) | |
345 | calc-dollar-used) | |
346 | (reverse calc-arg-values)))) | |
347 | (if (> calc-hashes-used 0) | |
03cc1aba | 348 | (setq calc-curve-coefnames |
136211a9 EZ |
349 | (cons 'vec (calc-invent-args |
350 | calc-hashes-used)))))) | |
351 | (progn | |
03cc1aba | 352 | (setq calc-curve-model (cond ((eq key ?u) |
136211a9 EZ |
353 | (calc-var-value 'var-Model1)) |
354 | ((eq key ?U) | |
355 | (calc-var-value 'var-Model2)) | |
356 | (t (calc-top 1)))) | |
03cc1aba JB |
357 | (or calc-curve-model (error "User model not yet defined")) |
358 | (if (math-vectorp calc-curve-model) | |
359 | (if (and (memq (length calc-curve-model) '(3 4)) | |
360 | (not (math-objvecp (nth 1 calc-curve-model))) | |
361 | (math-vectorp (nth 2 calc-curve-model)) | |
362 | (or (null (nth 3 calc-curve-model)) | |
363 | (math-vectorp (nth 3 calc-curve-model)))) | |
364 | (setq calc-curve-varnames (nth 2 calc-curve-model) | |
365 | calc-curve-coefnames | |
366 | (or (nth 3 calc-curve-model) | |
367 | (cons 'vec | |
368 | (math-all-vars-but | |
b07251cc JB |
369 | calc-curve-model |
370 | calc-curve-varnames))) | |
03cc1aba | 371 | calc-curve-model (nth 1 calc-curve-model)) |
136211a9 | 372 | (error "Incorrect model specifier"))))) |
03cc1aba | 373 | (or calc-curve-varnames |
b07251cc JB |
374 | (let ((with-y |
375 | (eq (car-safe calc-curve-model) 'calcFunc-eq))) | |
03cc1aba JB |
376 | (if calc-curve-coefnames |
377 | (calc-get-fit-variables | |
378 | (if with-y (1+ calc-curve-nvars) calc-curve-nvars) | |
379 | (1- (length calc-curve-coefnames)) | |
380 | (math-all-vars-but | |
381 | calc-curve-model calc-curve-coefnames) | |
382 | nil with-y) | |
383 | (let* ((coefs (math-all-vars-but calc-curve-model nil)) | |
136211a9 | 384 | (vars nil) |
b07251cc JB |
385 | (n (- |
386 | (length coefs) | |
387 | calc-curve-nvars | |
388 | (if with-y 2 1))) | |
136211a9 EZ |
389 | p) |
390 | (if (< n 0) | |
391 | (error "Not enough variables in model")) | |
392 | (setq p (nthcdr n coefs)) | |
393 | (setq vars (cdr p)) | |
394 | (setcdr p nil) | |
03cc1aba JB |
395 | (calc-get-fit-variables |
396 | (if with-y (1+ calc-curve-nvars) calc-curve-nvars) | |
397 | (length coefs) | |
398 | vars coefs with-y))))) | |
136211a9 | 399 | (if record-entry |
03cc1aba JB |
400 | (calc-record (list 'vec calc-curve-model |
401 | calc-curve-varnames calc-curve-coefnames) | |
136211a9 EZ |
402 | "modl")))) |
403 | (t (beep)))) | |
b07251cc JB |
404 | (unless nonlinear |
405 | (let ((calc-fit-to-trail t)) | |
406 | (calc-enter-result n (substring (symbol-name func) 9) | |
407 | (list func calc-curve-model | |
408 | (if (= (length calc-curve-varnames) 2) | |
409 | (nth 1 calc-curve-varnames) | |
410 | calc-curve-varnames) | |
411 | (if (= (length calc-curve-coefnames) 2) | |
412 | (nth 1 calc-curve-coefnames) | |
413 | calc-curve-coefnames) | |
414 | data)) | |
415 | (if (consp calc-fit-to-trail) | |
416 | (calc-record (calc-normalize calc-fit-to-trail) "parm")))) | |
417 | (when plot | |
418 | (if (stringp plot) | |
274f1353 | 419 | (message "%s" plot) |
b07251cc JB |
420 | (let ((calc-graph-no-auto-view t)) |
421 | (calc-graph-delete t) | |
422 | (calc-graph-add-curve | |
423 | (calc-graph-lookup (nth 1 plot)) | |
424 | (calc-graph-lookup (nth 2 plot))) | |
425 | (unless (math-contains-sdev-p (nth 2 data)) | |
426 | (calc-graph-set-styles nil nil) | |
427 | (calc-graph-point-style nil)) | |
428 | (setq plot (cdr (nth 1 plot))) | |
429 | (setq plot | |
430 | (list 'intv | |
431 | 3 | |
432 | (math-sub | |
433 | (math-min-list (car plot) (cdr plot)) | |
434 | '(float 5 -1)) | |
435 | (math-add | |
436 | '(float 5 -1) | |
437 | (math-max-list (car plot) (cdr plot))))) | |
438 | (calc-graph-add-curve (calc-graph-lookup plot) | |
439 | (calc-graph-lookup (calc-top-n 1))) | |
440 | (calc-graph-plot nil))))))) | |
136211a9 EZ |
441 | |
442 | (defun calc-invent-independent-variables (n &optional but) | |
bf77c646 | 443 | (calc-invent-variables n but '(x y z t) "x")) |
136211a9 EZ |
444 | |
445 | (defun calc-invent-parameter-variables (n &optional but) | |
bf77c646 | 446 | (calc-invent-variables n but '(a b c d) "a")) |
136211a9 EZ |
447 | |
448 | (defun calc-invent-variables (num but names base) | |
449 | (let ((vars nil) | |
450 | (n num) (nn 0) | |
451 | var) | |
452 | (while (and (> n 0) names) | |
453 | (setq var (math-build-var-name (if (consp names) | |
454 | (car names) | |
67dbc846 CW |
455 | (concat base (int-to-string |
456 | (setq nn (1+ nn))))))) | |
136211a9 EZ |
457 | (or (math-expr-contains (cons 'vec but) var) |
458 | (setq vars (cons var vars) | |
459 | n (1- n))) | |
460 | (or (symbolp names) (setq names (cdr names)))) | |
461 | (if (= n 0) | |
462 | (nreverse vars) | |
bf77c646 | 463 | (calc-invent-variables num but t base)))) |
136211a9 EZ |
464 | |
465 | (defun calc-get-fit-variables (nv nc &optional defv defc with-y homog) | |
03cc1aba | 466 | (or (= nv (if with-y (1+ calc-curve-nvars) calc-curve-nvars)) |
136211a9 EZ |
467 | (error "Wrong number of data vectors for this type of model")) |
468 | (if (integerp defv) | |
469 | (setq homog defv | |
470 | defv nil)) | |
471 | (if homog | |
472 | (setq nc (1- nc))) | |
473 | (or defv | |
474 | (setq defv (calc-invent-independent-variables nv))) | |
475 | (or defc | |
476 | (setq defc (calc-invent-parameter-variables nc defv))) | |
5b76833f | 477 | (let ((vars (read-string (format "Fitting variables (default %s; %s): " |
136211a9 EZ |
478 | (mapconcat 'symbol-name |
479 | (mapcar (function (lambda (v) | |
480 | (nth 1 v))) | |
481 | defv) | |
482 | ",") | |
483 | (mapconcat 'symbol-name | |
484 | (mapcar (function (lambda (v) | |
485 | (nth 1 v))) | |
486 | defc) | |
487 | ",")))) | |
488 | (coefs nil)) | |
489 | (setq vars (if (string-match "\\[" vars) | |
490 | (math-read-expr vars) | |
491 | (math-read-expr (concat "[" vars "]")))) | |
492 | (if (eq (car-safe vars) 'error) | |
493 | (error "Bad format in expression: %s" (nth 2 vars))) | |
494 | (or (math-vectorp vars) | |
495 | (error "Expected a variable or vector of variables")) | |
496 | (if (equal vars '(vec)) | |
497 | (setq vars (cons 'vec defv) | |
498 | coefs (cons 'vec defc)) | |
499 | (if (math-vectorp (nth 1 vars)) | |
500 | (if (and (= (length vars) 3) | |
501 | (math-vectorp (nth 2 vars))) | |
502 | (setq coefs (nth 2 vars) | |
503 | vars (nth 1 vars)) | |
504 | (error | |
505 | "Expected independent variables vector, then parameters vector")) | |
506 | (setq coefs (cons 'vec defc)))) | |
507 | (or (= nv (1- (length vars))) | |
508 | (and (not with-y) (= (1+ nv) (1- (length vars)))) | |
509 | (error "Expected %d independent variable%s" nv (if (= nv 1) "" "s"))) | |
510 | (or (= nc (1- (length coefs))) | |
511 | (error "Expected %d parameter variable%s" nc (if (= nc 1) "" "s"))) | |
512 | (if homog | |
513 | (setq coefs (cons 'vec (cons homog (cdr coefs))))) | |
03cc1aba JB |
514 | (if calc-curve-varnames |
515 | (setq calc-curve-model (math-multi-subst calc-curve-model (cdr calc-curve-varnames) (cdr vars)))) | |
516 | (if calc-curve-coefnames | |
517 | (setq calc-curve-model (math-multi-subst calc-curve-model (cdr calc-curve-coefnames) (cdr coefs)))) | |
518 | (setq calc-curve-varnames vars | |
519 | calc-curve-coefnames coefs))) | |
136211a9 EZ |
520 | |
521 | ||
522 | ||
523 | ||
524 | ;;; The following algorithms are from Numerical Recipes chapter 9. | |
525 | ||
526 | ;;; "rtnewt" with safety kludges | |
03cc1aba JB |
527 | |
528 | (defvar var-DUMMY) | |
529 | ||
136211a9 EZ |
530 | (defun math-newton-root (expr deriv guess orig-guess limit) |
531 | (math-working "newton" guess) | |
532 | (let* ((var-DUMMY guess) | |
533 | next dval) | |
534 | (setq next (math-evaluate-expr expr) | |
535 | dval (math-evaluate-expr deriv)) | |
536 | (if (and (Math-numberp next) | |
537 | (Math-numberp dval) | |
538 | (not (Math-zerop dval))) | |
539 | (progn | |
540 | (setq next (math-sub guess (math-div next dval))) | |
541 | (if (math-nearly-equal guess (setq next (math-float next))) | |
542 | (progn | |
543 | (setq var-DUMMY next) | |
544 | (list 'vec next (math-evaluate-expr expr))) | |
545 | (if (Math-lessp (math-abs-approx (math-sub next orig-guess)) | |
546 | limit) | |
547 | (math-newton-root expr deriv next orig-guess limit) | |
548 | (math-reject-arg next "*Newton's method failed to converge")))) | |
bf77c646 | 549 | (math-reject-arg next "*Newton's method encountered a singularity")))) |
136211a9 EZ |
550 | |
551 | ;;; Inspired by "rtsafe" | |
552 | (defun math-newton-search-root (expr deriv guess vguess ostep oostep | |
553 | low vlow high vhigh) | |
554 | (let ((var-DUMMY guess) | |
555 | (better t) | |
556 | pos step next vnext) | |
557 | (if guess | |
558 | (math-working "newton" (list 'intv 0 low high)) | |
559 | (math-working "bisect" (list 'intv 0 low high)) | |
560 | (setq ostep (math-mul-float (math-sub-float high low) | |
561 | '(float 5 -1)) | |
562 | guess (math-add-float low ostep) | |
563 | var-DUMMY guess | |
564 | vguess (math-evaluate-expr expr)) | |
565 | (or (Math-realp vguess) | |
566 | (progn | |
567 | (setq ostep (math-mul-float ostep '(float 6 -1)) | |
568 | guess (math-add-float low ostep) | |
569 | var-DUMMY guess | |
570 | vguess (math-evaluate-expr expr)) | |
571 | (or (math-realp vguess) | |
572 | (progn | |
573 | (setq ostep (math-mul-float ostep '(float 123456 -5)) | |
574 | guess (math-add-float low ostep) | |
575 | var-DUMMY guess | |
576 | vguess nil)))))) | |
577 | (or vguess | |
578 | (setq vguess (math-evaluate-expr expr))) | |
579 | (or (Math-realp vguess) | |
580 | (math-reject-arg guess "*Newton's method encountered a singularity")) | |
581 | (setq vguess (math-float vguess)) | |
582 | (if (eq (Math-negp vlow) (setq pos (Math-posp vguess))) | |
583 | (setq high guess | |
584 | vhigh vguess) | |
585 | (if (eq (Math-negp vhigh) pos) | |
586 | (setq low guess | |
587 | vlow vguess) | |
588 | (setq better nil))) | |
589 | (if (or (Math-zerop vguess) | |
590 | (math-nearly-equal low high)) | |
591 | (list 'vec guess vguess) | |
592 | (setq step (math-evaluate-expr deriv)) | |
593 | (if (and (Math-realp step) | |
594 | (not (Math-zerop step)) | |
595 | (setq step (math-div-float vguess (math-float step)) | |
596 | next (math-sub-float guess step)) | |
597 | (not (math-lessp-float high next)) | |
598 | (not (math-lessp-float next low))) | |
599 | (progn | |
600 | (setq var-DUMMY next | |
601 | vnext (math-evaluate-expr expr)) | |
602 | (if (or (Math-zerop vnext) | |
603 | (math-nearly-equal next guess)) | |
604 | (list 'vec next vnext) | |
605 | (if (and better | |
606 | (math-lessp-float (math-abs (or oostep | |
607 | (math-sub-float | |
608 | high low))) | |
609 | (math-abs | |
610 | (math-mul-float '(float 2 0) | |
611 | step)))) | |
612 | (math-newton-search-root expr deriv nil nil nil ostep | |
613 | low vlow high vhigh) | |
614 | (math-newton-search-root expr deriv next vnext step ostep | |
615 | low vlow high vhigh)))) | |
616 | (if (or (and (Math-posp vlow) (Math-posp vhigh)) | |
617 | (and (Math-negp vlow) (Math-negp vhigh))) | |
618 | (math-search-root expr deriv low vlow high vhigh) | |
619 | (math-newton-search-root expr deriv nil nil nil ostep | |
bf77c646 | 620 | low vlow high vhigh)))))) |
136211a9 EZ |
621 | |
622 | ;;; Search for a root in an interval with no overt zero crossing. | |
03cc1aba JB |
623 | |
624 | ;; The variable math-root-widen is local to math-find-root, but | |
625 | ;; is used by math-search-root, which is called (directly and | |
626 | ;; indirectly) by math-find-root. | |
627 | (defvar math-root-widen) | |
628 | ||
136211a9 EZ |
629 | (defun math-search-root (expr deriv low vlow high vhigh) |
630 | (let (found) | |
03cc1aba | 631 | (if math-root-widen |
136211a9 | 632 | (let ((iters 0) |
03cc1aba | 633 | (iterlim (if (eq math-root-widen 'point) |
136211a9 EZ |
634 | (+ calc-internal-prec 10) |
635 | 20)) | |
03cc1aba | 636 | (factor (if (eq math-root-widen 'point) |
136211a9 EZ |
637 | '(float 9 0) |
638 | '(float 16 -1))) | |
639 | (prev nil) vprev waslow | |
640 | diff) | |
641 | (while (or (and (math-posp vlow) (math-posp vhigh)) | |
642 | (and (math-negp vlow) (math-negp vhigh))) | |
643 | (math-working "widen" (list 'intv 0 low high)) | |
644 | (if (> (setq iters (1+ iters)) iterlim) | |
645 | (math-reject-arg (list 'intv 0 low high) | |
646 | "*Unable to bracket root")) | |
647 | (if (= iters calc-internal-prec) | |
648 | (setq factor '(float 16 -1))) | |
649 | (setq diff (math-mul-float (math-sub-float high low) factor)) | |
650 | (if (Math-zerop diff) | |
651 | (setq high (calcFunc-incr high 10)) | |
652 | (if (math-lessp-float (math-abs vlow) (math-abs vhigh)) | |
653 | (setq waslow t | |
654 | prev low | |
655 | low (math-sub low diff) | |
656 | var-DUMMY low | |
657 | vprev vlow | |
658 | vlow (math-evaluate-expr expr)) | |
659 | (setq waslow nil | |
660 | prev high | |
661 | high (math-add high diff) | |
662 | var-DUMMY high | |
663 | vprev vhigh | |
664 | vhigh (math-evaluate-expr expr))))) | |
665 | (if prev | |
666 | (if waslow | |
667 | (setq high prev vhigh vprev) | |
668 | (setq low prev vlow vprev))) | |
669 | (setq found t)) | |
670 | (or (Math-realp vlow) | |
671 | (math-reject-arg vlow 'realp)) | |
672 | (or (Math-realp vhigh) | |
673 | (math-reject-arg vhigh 'realp)) | |
674 | (let ((xvals (list low high)) | |
675 | (yvals (list vlow vhigh)) | |
676 | (pos (Math-posp vlow)) | |
677 | (levels 0) | |
678 | (step (math-sub-float high low)) | |
679 | xp yp var-DUMMY) | |
680 | (while (and (<= (setq levels (1+ levels)) 5) | |
681 | (not found)) | |
682 | (setq xp xvals | |
683 | yp yvals | |
684 | step (math-mul-float step '(float 497 -3))) | |
685 | (while (and (cdr xp) (not found)) | |
686 | (if (Math-realp (car yp)) | |
687 | (setq low (car xp) | |
688 | vlow (car yp))) | |
689 | (setq high (math-add-float (car xp) step) | |
690 | var-DUMMY high | |
691 | vhigh (math-evaluate-expr expr)) | |
692 | (math-working "search" high) | |
693 | (if (and (Math-realp vhigh) | |
694 | (eq (math-negp vhigh) pos)) | |
695 | (setq found t) | |
696 | (setcdr xp (cons high (cdr xp))) | |
697 | (setcdr yp (cons vhigh (cdr yp))) | |
698 | (setq xp (cdr (cdr xp)) | |
699 | yp (cdr (cdr yp)))))))) | |
700 | (if found | |
701 | (if (Math-zerop vhigh) | |
702 | (list 'vec high vhigh) | |
703 | (if (Math-zerop vlow) | |
704 | (list 'vec low vlow) | |
705 | (if deriv | |
706 | (math-newton-search-root expr deriv nil nil nil nil | |
707 | low vlow high vhigh) | |
708 | (math-bisect-root expr low vlow high vhigh)))) | |
709 | (math-reject-arg (list 'intv 3 low high) | |
bf77c646 | 710 | "*Unable to find a sign change in this interval")))) |
136211a9 EZ |
711 | |
712 | ;;; "rtbis" (but we should be using Brent's method) | |
713 | (defun math-bisect-root (expr low vlow high vhigh) | |
714 | (let ((step (math-sub-float high low)) | |
715 | (pos (Math-posp vhigh)) | |
716 | var-DUMMY | |
717 | mid vmid) | |
718 | (while (not (or (math-nearly-equal low | |
719 | (setq step (math-mul-float | |
720 | step '(float 5 -1)) | |
721 | mid (math-add-float low step))) | |
722 | (progn | |
723 | (setq var-DUMMY mid | |
724 | vmid (math-evaluate-expr expr)) | |
725 | (Math-zerop vmid)))) | |
726 | (math-working "bisect" mid) | |
727 | (if (eq (Math-posp vmid) pos) | |
728 | (setq high mid | |
729 | vhigh vmid) | |
730 | (setq low mid | |
731 | vlow vmid))) | |
bf77c646 | 732 | (list 'vec mid vmid))) |
136211a9 EZ |
733 | |
734 | ;;; "mnewt" | |
03cc1aba JB |
735 | |
736 | (defvar math-root-vars [(var DUMMY var-DUMMY)]) | |
737 | ||
136211a9 EZ |
738 | (defun math-newton-multi (expr jacob n guess orig-guess limit) |
739 | (let ((m -1) | |
740 | (p guess) | |
741 | p2 expr-val jacob-val next) | |
742 | (while (< (setq p (cdr p) m (1+ m)) n) | |
743 | (set (nth 2 (aref math-root-vars m)) (car p))) | |
744 | (setq expr-val (math-evaluate-expr expr) | |
745 | jacob-val (math-evaluate-expr jacob)) | |
3132f345 CW |
746 | (unless (and (math-constp expr-val) |
747 | (math-constp jacob-val)) | |
748 | (math-reject-arg guess "*Newton's method encountered a singularity")) | |
136211a9 EZ |
749 | (setq next (math-add guess (math-div (math-float (math-neg expr-val)) |
750 | (math-float jacob-val))) | |
751 | p guess p2 next) | |
752 | (math-working "newton" next) | |
753 | (while (and (setq p (cdr p) p2 (cdr p2)) | |
754 | (math-nearly-equal (car p) (car p2)))) | |
755 | (if p | |
756 | (if (Math-lessp (math-abs-approx (math-sub next orig-guess)) | |
757 | limit) | |
758 | (math-newton-multi expr jacob n next orig-guess limit) | |
759 | (math-reject-arg nil "*Newton's method failed to converge")) | |
bf77c646 | 760 | (list 'vec next expr-val)))) |
136211a9 | 761 | |
136211a9 | 762 | |
03cc1aba | 763 | (defun math-find-root (expr var guess math-root-widen) |
136211a9 EZ |
764 | (if (eq (car-safe expr) 'vec) |
765 | (let ((n (1- (length expr))) | |
766 | (calc-symbolic-mode nil) | |
767 | (var-DUMMY nil) | |
768 | (jacob (list 'vec)) | |
769 | p p2 m row) | |
3132f345 CW |
770 | (unless (eq (car-safe var) 'vec) |
771 | (math-reject-arg var 'vectorp)) | |
772 | (unless (= (length var) (1+ n)) | |
773 | (math-dimension-error)) | |
136211a9 EZ |
774 | (setq expr (copy-sequence expr)) |
775 | (while (>= n (length math-root-vars)) | |
776 | (let ((symb (intern (concat "math-root-v" | |
777 | (int-to-string | |
778 | (length math-root-vars)))))) | |
779 | (setq math-root-vars (vconcat math-root-vars | |
780 | (vector (list 'var symb symb)))))) | |
781 | (setq m -1) | |
782 | (while (< (setq m (1+ m)) n) | |
783 | (set (nth 2 (aref math-root-vars m)) nil)) | |
784 | (setq m -1 p var) | |
785 | (while (setq m (1+ m) p (cdr p)) | |
786 | (or (eq (car-safe (car p)) 'var) | |
787 | (math-reject-arg var "*Expected a variable")) | |
788 | (setq p2 expr) | |
789 | (while (setq p2 (cdr p2)) | |
790 | (setcar p2 (math-expr-subst (car p2) (car p) | |
791 | (aref math-root-vars m))))) | |
3132f345 CW |
792 | (unless (eq (car-safe guess) 'vec) |
793 | (math-reject-arg guess 'vectorp)) | |
794 | (unless (= (length guess) (1+ n)) | |
795 | (math-dimension-error)) | |
136211a9 EZ |
796 | (setq guess (copy-sequence guess) |
797 | p guess) | |
798 | (while (setq p (cdr p)) | |
799 | (or (Math-numberp (car guess)) | |
800 | (math-reject-arg guess 'numberp)) | |
801 | (setcar p (math-float (car p)))) | |
802 | (setq p expr) | |
803 | (while (setq p (cdr p)) | |
804 | (if (assq (car-safe (car p)) calc-tweak-eqn-table) | |
805 | (setcar p (math-sub (nth 1 (car p)) (nth 2 (car p))))) | |
806 | (setcar p (math-evaluate-expr (car p))) | |
807 | (setq row (list 'vec) | |
808 | m -1) | |
809 | (while (< (setq m (1+ m)) n) | |
810 | (nconc row (list (math-evaluate-expr | |
811 | (or (calcFunc-deriv (car p) | |
812 | (aref math-root-vars m) | |
813 | nil t) | |
814 | (math-reject-arg | |
815 | expr | |
816 | "*Formulas must be differentiable")))))) | |
817 | (nconc jacob (list row))) | |
818 | (setq m (math-abs-approx guess)) | |
819 | (math-newton-multi expr jacob n guess guess | |
820 | (if (math-zerop m) '(float 1 3) (math-mul m 10)))) | |
3132f345 CW |
821 | (unless (eq (car-safe var) 'var) |
822 | (math-reject-arg var "*Expected a variable")) | |
823 | (unless (math-expr-contains expr var) | |
824 | (math-reject-arg expr "*Formula does not contain specified variable")) | |
136211a9 EZ |
825 | (if (assq (car expr) calc-tweak-eqn-table) |
826 | (setq expr (math-sub (nth 1 expr) (nth 2 expr)))) | |
827 | (math-with-extra-prec 2 | |
828 | (setq expr (math-expr-subst expr var '(var DUMMY var-DUMMY))) | |
829 | (let* ((calc-symbolic-mode nil) | |
830 | (var-DUMMY nil) | |
831 | (expr (math-evaluate-expr expr)) | |
832 | (deriv (calcFunc-deriv expr '(var DUMMY var-DUMMY) nil t)) | |
833 | low high vlow vhigh) | |
834 | (and deriv (setq deriv (math-evaluate-expr deriv))) | |
835 | (setq guess (math-float guess)) | |
836 | (if (and (math-numberp guess) | |
837 | deriv) | |
838 | (math-newton-root expr deriv guess guess | |
839 | (if (math-zerop guess) '(float 1 6) | |
840 | (math-mul (math-abs-approx guess) 100))) | |
841 | (if (Math-realp guess) | |
842 | (setq low guess | |
843 | high guess | |
844 | var-DUMMY guess | |
845 | vlow (math-evaluate-expr expr) | |
846 | vhigh vlow | |
03cc1aba | 847 | math-root-widen 'point) |
136211a9 EZ |
848 | (if (eq (car guess) 'intv) |
849 | (progn | |
850 | (or (math-constp guess) (math-reject-arg guess 'constp)) | |
851 | (setq low (nth 2 guess) | |
852 | high (nth 3 guess)) | |
853 | (if (memq (nth 1 guess) '(0 1)) | |
854 | (setq low (calcFunc-incr low 1 high))) | |
855 | (if (memq (nth 1 guess) '(0 2)) | |
856 | (setq high (calcFunc-incr high -1 low))) | |
857 | (setq var-DUMMY low | |
858 | vlow (math-evaluate-expr expr) | |
859 | var-DUMMY high | |
860 | vhigh (math-evaluate-expr expr))) | |
861 | (if (math-complexp guess) | |
862 | (math-reject-arg "*Complex root finder must have derivative") | |
863 | (math-reject-arg guess 'realp)))) | |
864 | (if (Math-zerop vlow) | |
865 | (list 'vec low vlow) | |
866 | (if (Math-zerop vhigh) | |
867 | (list 'vec high vhigh) | |
868 | (if (and deriv (Math-numberp vlow) (Math-numberp vhigh)) | |
869 | (math-newton-search-root expr deriv nil nil nil nil | |
870 | low vlow high vhigh) | |
871 | (if (or (and (Math-posp vlow) (Math-posp vhigh)) | |
872 | (and (Math-negp vlow) (Math-negp vhigh)) | |
873 | (not (Math-numberp vlow)) | |
874 | (not (Math-numberp vhigh))) | |
875 | (math-search-root expr deriv low vlow high vhigh) | |
bf77c646 | 876 | (math-bisect-root expr low vlow high vhigh)))))))))) |
136211a9 EZ |
877 | |
878 | (defun calcFunc-root (expr var guess) | |
bf77c646 | 879 | (math-find-root expr var guess nil)) |
136211a9 EZ |
880 | |
881 | (defun calcFunc-wroot (expr var guess) | |
bf77c646 | 882 | (math-find-root expr var guess t)) |
136211a9 EZ |
883 | |
884 | ||
885 | ||
886 | ||
887 | ;;; The following algorithms come from Numerical Recipes, chapter 10. | |
888 | ||
03cc1aba JB |
889 | (defvar math-min-vars [(var DUMMY var-DUMMY)]) |
890 | ||
136211a9 EZ |
891 | (defun math-min-eval (expr a) |
892 | (if (Math-vectorp a) | |
893 | (let ((m -1)) | |
894 | (while (setq m (1+ m) a (cdr a)) | |
895 | (set (nth 2 (aref math-min-vars m)) (car a)))) | |
896 | (setq var-DUMMY a)) | |
897 | (setq a (math-evaluate-expr expr)) | |
898 | (if (Math-ratp a) | |
899 | (math-float a) | |
900 | (if (eq (car a) 'float) | |
901 | a | |
bf77c646 | 902 | (math-reject-arg a 'realp)))) |
136211a9 | 903 | |
3132f345 | 904 | (defvar math-min-or-max "minimum") |
136211a9 EZ |
905 | |
906 | ;;; A bracket for a minimum is a < b < c where f(b) < f(a) and f(b) < f(c). | |
907 | ||
908 | ;;; "mnbrak" | |
909 | (defun math-widen-min (expr a b) | |
910 | (let ((done nil) | |
911 | (iters 30) | |
912 | incr c va vb vc u vu r q ulim bc ba qr) | |
913 | (or b (setq b (math-mul a '(float 101 -2)))) | |
914 | (setq va (math-min-eval expr a) | |
915 | vb (math-min-eval expr b)) | |
916 | (if (math-lessp-float va vb) | |
917 | (setq u a a b b u | |
918 | vu va va vb vb vu)) | |
919 | (setq c (math-add-float b (math-mul-float '(float 161803 -5) | |
920 | (math-sub-float b a))) | |
921 | vc (math-min-eval expr c)) | |
922 | (while (and (not done) (math-lessp-float vc vb)) | |
923 | (math-working "widen" (list 'intv 0 a c)) | |
924 | (if (= (setq iters (1- iters)) 0) | |
925 | (math-reject-arg nil (format "*Unable to find a %s near the interval" | |
926 | math-min-or-max))) | |
927 | (setq bc (math-sub-float b c) | |
928 | ba (math-sub-float b a) | |
929 | r (math-mul-float ba (math-sub-float vb vc)) | |
930 | q (math-mul-float bc (math-sub-float vb va)) | |
931 | qr (math-sub-float q r)) | |
932 | (if (math-lessp-float (math-abs qr) '(float 1 -20)) | |
933 | (setq qr (if (math-negp qr) '(float -1 -20) '(float 1 -20)))) | |
934 | (setq u (math-sub-float | |
935 | b | |
936 | (math-div-float (math-sub-float (math-mul-float bc q) | |
937 | (math-mul-float ba r)) | |
938 | (math-mul-float '(float 2 0) qr))) | |
939 | ulim (math-add-float b (math-mul-float '(float -1 2) bc)) | |
940 | incr (math-negp bc)) | |
941 | (if (if incr (math-lessp-float b u) (math-lessp-float u b)) | |
942 | (if (if incr (math-lessp-float u c) (math-lessp-float c u)) | |
943 | (if (math-lessp-float (setq vu (math-min-eval expr u)) vc) | |
944 | (setq a b va vb | |
945 | b u vb vu | |
946 | done t) | |
947 | (if (math-lessp-float vb vu) | |
948 | (setq c u vc vu | |
949 | done t) | |
950 | (setq u (math-add-float c (math-mul-float '(float -161803 -5) | |
951 | bc)) | |
952 | vu (math-min-eval expr u)))) | |
953 | (if (if incr (math-lessp-float u ulim) (math-lessp-float ulim u)) | |
954 | (if (math-lessp-float (setq vu (math-min-eval expr u)) vc) | |
955 | (setq b c vb vc | |
956 | c u vc vu | |
957 | u (math-add-float c (math-mul-float | |
958 | '(float -161803 -5) | |
959 | (math-sub-float b c))) | |
960 | vu (math-min-eval expr u))) | |
961 | (setq u ulim | |
962 | vu (math-min-eval expr u)))) | |
963 | (setq u (math-add-float c (math-mul-float '(float -161803 -5) | |
964 | bc)) | |
965 | vu (math-min-eval expr u))) | |
966 | (setq a b va vb | |
967 | b c vb vc | |
968 | c u vc vu)) | |
969 | (if (math-lessp-float a c) | |
970 | (list a va b vb c vc) | |
bf77c646 | 971 | (list c vc b vb a va)))) |
136211a9 EZ |
972 | |
973 | (defun math-narrow-min (expr a c intv) | |
974 | (let ((xvals (list a c)) | |
975 | (yvals (list (math-min-eval expr a) | |
976 | (math-min-eval expr c))) | |
977 | (levels 0) | |
978 | (step (math-sub-float c a)) | |
979 | (found nil) | |
980 | xp yp b) | |
981 | (while (and (<= (setq levels (1+ levels)) 5) | |
982 | (not found)) | |
983 | (setq xp xvals | |
984 | yp yvals | |
985 | step (math-mul-float step '(float 497 -3))) | |
986 | (while (and (cdr xp) (not found)) | |
987 | (setq b (math-add-float (car xp) step)) | |
988 | (math-working "search" b) | |
989 | (setcdr xp (cons b (cdr xp))) | |
990 | (setcdr yp (cons (math-min-eval expr b) (cdr yp))) | |
991 | (if (and (math-lessp-float (nth 1 yp) (car yp)) | |
992 | (math-lessp-float (nth 1 yp) (nth 2 yp))) | |
993 | (setq found t) | |
994 | (setq xp (cdr xp) | |
995 | yp (cdr yp)) | |
996 | (if (and (cdr (cdr yp)) | |
997 | (math-lessp-float (nth 1 yp) (car yp)) | |
998 | (math-lessp-float (nth 1 yp) (nth 2 yp))) | |
999 | (setq found t) | |
1000 | (setq xp (cdr xp) | |
1001 | yp (cdr yp)))))) | |
1002 | (if found | |
1003 | (list (car xp) (car yp) | |
1004 | (nth 1 xp) (nth 1 yp) | |
1005 | (nth 2 xp) (nth 2 yp)) | |
1006 | (or (if (math-lessp-float (car yvals) (nth 1 yvals)) | |
1007 | (and (memq (nth 1 intv) '(2 3)) | |
1008 | (let ((min (car yvals))) | |
1009 | (while (and (setq yvals (cdr yvals)) | |
1010 | (math-lessp-float min (car yvals)))) | |
1011 | (and (not yvals) | |
1012 | (list (nth 2 intv) min)))) | |
1013 | (and (memq (nth 1 intv) '(1 3)) | |
1014 | (setq yvals (nreverse yvals)) | |
1015 | (let ((min (car yvals))) | |
1016 | (while (and (setq yvals (cdr yvals)) | |
1017 | (math-lessp-float min (car yvals)))) | |
1018 | (and (not yvals) | |
1019 | (list (nth 3 intv) min))))) | |
1020 | (math-reject-arg nil (format "*Unable to find a %s in the interval" | |
bf77c646 | 1021 | math-min-or-max)))))) |
136211a9 EZ |
1022 | |
1023 | ;;; "brent" | |
1024 | (defun math-brent-min (expr prec a va x vx b vb) | |
1025 | (let ((iters (+ 20 (* 5 prec))) | |
1026 | (w x) | |
1027 | (vw vx) | |
1028 | (v x) | |
1029 | (vv vx) | |
1030 | (tol (list 'float 1 (- -1 prec))) | |
1031 | (zeps (list 'float 1 (- -5 prec))) | |
1032 | (e '(float 0 0)) | |
03cc1aba | 1033 | d u vu xm tol1 tol2 etemp p q r xv xw) |
136211a9 EZ |
1034 | (while (progn |
1035 | (setq xm (math-mul-float '(float 5 -1) | |
1036 | (math-add-float a b)) | |
1037 | tol1 (math-add-float | |
1038 | zeps | |
1039 | (math-mul-float tol (math-abs x))) | |
1040 | tol2 (math-mul-float tol1 '(float 2 0))) | |
1041 | (math-lessp-float (math-sub-float tol2 | |
1042 | (math-mul-float | |
1043 | '(float 5 -1) | |
1044 | (math-sub-float b a))) | |
1045 | (math-abs (math-sub-float x xm)))) | |
1046 | (if (= (setq iters (1- iters)) 0) | |
1047 | (math-reject-arg nil (format "*Unable to converge on a %s" | |
1048 | math-min-or-max))) | |
1049 | (math-working "brent" x) | |
1050 | (if (math-lessp-float (math-abs e) tol1) | |
1051 | (setq e (if (math-lessp-float x xm) | |
1052 | (math-sub-float b x) | |
1053 | (math-sub-float a x)) | |
1054 | d (math-mul-float '(float 381966 -6) e)) | |
1055 | (setq xw (math-sub-float x w) | |
1056 | r (math-mul-float xw (math-sub-float vx vv)) | |
1057 | xv (math-sub-float x v) | |
1058 | q (math-mul-float xv (math-sub-float vx vw)) | |
1059 | p (math-sub-float (math-mul-float xv q) | |
1060 | (math-mul-float xw r)) | |
1061 | q (math-mul-float '(float 2 0) (math-sub-float q r))) | |
1062 | (if (math-posp q) | |
1063 | (setq p (math-neg-float p)) | |
1064 | (setq q (math-neg-float q))) | |
1065 | (setq etemp e | |
1066 | e d) | |
1067 | (if (and (math-lessp-float (math-abs p) | |
1068 | (math-abs (math-mul-float | |
1069 | '(float 5 -1) | |
1070 | (math-mul-float q etemp)))) | |
1071 | (math-lessp-float (math-mul-float | |
1072 | q (math-sub-float a x)) p) | |
1073 | (math-lessp-float p (math-mul-float | |
1074 | q (math-sub-float b x)))) | |
1075 | (progn | |
1076 | (setq d (math-div-float p q) | |
1077 | u (math-add-float x d)) | |
1078 | (if (or (math-lessp-float (math-sub-float u a) tol2) | |
1079 | (math-lessp-float (math-sub-float b u) tol2)) | |
1080 | (setq d (if (math-lessp-float xm x) | |
1081 | (math-neg-float tol1) | |
1082 | tol1)))) | |
1083 | (setq e (if (math-lessp-float x xm) | |
1084 | (math-sub-float b x) | |
1085 | (math-sub-float a x)) | |
1086 | d (math-mul-float '(float 381966 -6) e)))) | |
1087 | (setq u (math-add-float x | |
1088 | (if (math-lessp-float (math-abs d) tol1) | |
1089 | (if (math-negp d) | |
1090 | (math-neg-float tol1) | |
1091 | tol1) | |
1092 | d)) | |
1093 | vu (math-min-eval expr u)) | |
1094 | (if (math-lessp-float vx vu) | |
1095 | (progn | |
1096 | (if (math-lessp-float u x) | |
1097 | (setq a u) | |
1098 | (setq b u)) | |
1099 | (if (or (equal w x) | |
1100 | (not (math-lessp-float vw vu))) | |
1101 | (setq v w vv vw | |
1102 | w u vw vu) | |
1103 | (if (or (equal v x) | |
1104 | (equal v w) | |
1105 | (not (math-lessp-float vv vu))) | |
1106 | (setq v u vv vu)))) | |
1107 | (if (math-lessp-float u x) | |
1108 | (setq b x) | |
1109 | (setq a x)) | |
1110 | (setq v w vv vw | |
1111 | w x vw vx | |
1112 | x u vx vu))) | |
bf77c646 | 1113 | (list 'vec x vx))) |
136211a9 EZ |
1114 | |
1115 | ;;; "powell" | |
1116 | (defun math-powell-min (expr n guesses prec) | |
1117 | (let* ((f1dim (math-line-min-func expr n)) | |
1118 | (xi (calcFunc-idn 1 n)) | |
1119 | (p (cons 'vec (mapcar 'car guesses))) | |
1120 | (pt p) | |
1121 | (ftol (list 'float 1 (- prec))) | |
1122 | (fret (math-min-eval expr p)) | |
1123 | fp ptt fptt xit i ibig del diff res) | |
1124 | (while (progn | |
1125 | (setq fp fret | |
1126 | ibig 0 | |
1127 | del '(float 0 0) | |
1128 | i 0) | |
1129 | (while (<= (setq i (1+ i)) n) | |
1130 | (setq fptt fret | |
1131 | res (math-line-min f1dim p | |
1132 | (math-mat-col xi i) | |
1133 | n prec) | |
1134 | p (let ((calc-internal-prec prec)) | |
1135 | (math-normalize (car res))) | |
1136 | fret (nth 2 res) | |
1137 | diff (math-abs (math-sub-float fptt fret))) | |
1138 | (if (math-lessp-float del diff) | |
1139 | (setq del diff | |
1140 | ibig i))) | |
1141 | (math-lessp-float | |
1142 | (math-mul-float ftol | |
1143 | (math-add-float (math-abs fp) | |
1144 | (math-abs fret))) | |
1145 | (math-mul-float '(float 2 0) | |
1146 | (math-abs (math-sub-float fp | |
1147 | fret))))) | |
1148 | (setq ptt (math-sub (math-mul '(float 2 0) p) pt) | |
1149 | xit (math-sub p pt) | |
1150 | pt p | |
1151 | fptt (math-min-eval expr ptt)) | |
1152 | (if (and (math-lessp-float fptt fp) | |
1153 | (math-lessp-float | |
1154 | (math-mul-float | |
1155 | (math-mul-float '(float 2 0) | |
1156 | (math-add-float | |
1157 | (math-sub-float fp | |
1158 | (math-mul-float '(float 2 0) | |
1159 | fret)) | |
1160 | fptt)) | |
1161 | (math-sqr-float (math-sub-float | |
1162 | (math-sub-float fp fret) del))) | |
1163 | (math-mul-float del | |
1164 | (math-sqr-float (math-sub-float fp fptt))))) | |
1165 | (progn | |
1166 | (setq res (math-line-min f1dim p xit n prec) | |
1167 | p (car res) | |
1168 | fret (nth 2 res) | |
1169 | i 0) | |
1170 | (while (<= (setq i (1+ i)) n) | |
1171 | (setcar (nthcdr ibig (nth i xi)) | |
1172 | (nth i (nth 1 res))))))) | |
bf77c646 | 1173 | (list 'vec p fret))) |
136211a9 EZ |
1174 | |
1175 | (defun math-line-min-func (expr n) | |
1176 | (let ((m -1)) | |
1177 | (while (< (setq m (1+ m)) n) | |
1178 | (set (nth 2 (aref math-min-vars m)) | |
1179 | (list '+ | |
1180 | (list '* | |
1181 | '(var DUMMY var-DUMMY) | |
1182 | (list 'calcFunc-mrow '(var line-xi line-xi) (1+ m))) | |
1183 | (list 'calcFunc-mrow '(var line-p line-p) (1+ m))))) | |
bf77c646 | 1184 | (math-evaluate-expr expr))) |
136211a9 EZ |
1185 | |
1186 | (defun math-line-min (f1dim line-p line-xi n prec) | |
1187 | (let* ((var-DUMMY nil) | |
1188 | (expr (math-evaluate-expr f1dim)) | |
1189 | (params (math-widen-min expr '(float 0 0) '(float 1 0))) | |
1190 | (res (apply 'math-brent-min expr prec params)) | |
1191 | (xi (math-mul (nth 1 res) line-xi))) | |
bf77c646 | 1192 | (list (math-add line-p xi) xi (nth 2 res)))) |
136211a9 EZ |
1193 | |
1194 | ||
136211a9 EZ |
1195 | (defun math-find-minimum (expr var guess min-widen) |
1196 | (let* ((calc-symbolic-mode nil) | |
1197 | (n 0) | |
1198 | (var-DUMMY nil) | |
1199 | (isvec (math-vectorp var)) | |
1200 | g guesses) | |
1201 | (or (math-vectorp var) | |
1202 | (setq var (list 'vec var))) | |
1203 | (or (math-vectorp guess) | |
1204 | (setq guess (list 'vec guess))) | |
1205 | (or (= (length var) (length guess)) | |
1206 | (math-dimension-error)) | |
1207 | (while (setq var (cdr var) guess (cdr guess)) | |
1208 | (or (eq (car-safe (car var)) 'var) | |
03cc1aba | 1209 | (math-reject-arg (car var) "*Expected a variable")) |
136211a9 EZ |
1210 | (or (math-expr-contains expr (car var)) |
1211 | (math-reject-arg (car var) | |
1212 | "*Formula does not contain specified variable")) | |
1213 | (while (>= (1+ n) (length math-min-vars)) | |
1214 | (let ((symb (intern (concat "math-min-v" | |
1215 | (int-to-string | |
1216 | (length math-min-vars)))))) | |
1217 | (setq math-min-vars (vconcat math-min-vars | |
1218 | (vector (list 'var symb symb)))))) | |
1219 | (set (nth 2 (aref math-min-vars n)) nil) | |
1220 | (set (nth 2 (aref math-min-vars (1+ n))) nil) | |
1221 | (if (math-complexp (car guess)) | |
1222 | (setq expr (math-expr-subst expr | |
1223 | (car var) | |
1224 | (list '+ (aref math-min-vars n) | |
1225 | (list '* | |
1226 | (aref math-min-vars (1+ n)) | |
1227 | '(cplx 0 1)))) | |
1228 | guesses (let ((g (math-float (math-complex (car guess))))) | |
1229 | (cons (list (nth 2 g) nil nil) | |
1230 | (cons (list (nth 1 g) nil nil t) | |
1231 | guesses))) | |
1232 | n (+ n 2)) | |
1233 | (setq expr (math-expr-subst expr | |
1234 | (car var) | |
1235 | (aref math-min-vars n)) | |
1236 | guesses (cons (if (math-realp (car guess)) | |
1237 | (list (math-float (car guess)) nil nil) | |
1238 | (if (and (eq (car-safe (car guess)) 'intv) | |
1239 | (math-constp (car guess))) | |
1240 | (list (math-mul | |
1241 | (math-add (nth 2 (car guess)) | |
1242 | (nth 3 (car guess))) | |
1243 | '(float 5 -1)) | |
1244 | (math-float (nth 2 (car guess))) | |
1245 | (math-float (nth 3 (car guess))) | |
1246 | (car guess)) | |
1247 | (math-reject-arg (car guess) 'realp))) | |
1248 | guesses) | |
1249 | n (1+ n)))) | |
1250 | (setq guesses (nreverse guesses) | |
1251 | expr (math-evaluate-expr expr)) | |
1252 | (if (= n 1) | |
1253 | (let* ((params (if (nth 1 (car guesses)) | |
1254 | (if min-widen | |
1255 | (math-widen-min expr | |
1256 | (nth 1 (car guesses)) | |
1257 | (nth 2 (car guesses))) | |
1258 | (math-narrow-min expr | |
1259 | (nth 1 (car guesses)) | |
1260 | (nth 2 (car guesses)) | |
1261 | (nth 3 (car guesses)))) | |
1262 | (math-widen-min expr | |
1263 | (car (car guesses)) | |
1264 | nil))) | |
1265 | (prec calc-internal-prec) | |
1266 | (res (if (cdr (cdr params)) | |
1267 | (math-with-extra-prec (+ calc-internal-prec 2) | |
1268 | (apply 'math-brent-min expr prec params)) | |
1269 | (cons 'vec params)))) | |
1270 | (if isvec | |
1271 | (list 'vec (list 'vec (nth 1 res)) (nth 2 res)) | |
1272 | res)) | |
1273 | (let* ((prec calc-internal-prec) | |
1274 | (res (math-with-extra-prec (+ calc-internal-prec 2) | |
1275 | (math-powell-min expr n guesses prec))) | |
1276 | (p (nth 1 res)) | |
1277 | (vec (list 'vec))) | |
1278 | (while (setq p (cdr p)) | |
1279 | (if (nth 3 (car guesses)) | |
1280 | (progn | |
1281 | (nconc vec (list (math-normalize | |
1282 | (list 'cplx (car p) (nth 1 p))))) | |
1283 | (setq p (cdr p) | |
1284 | guesses (cdr guesses))) | |
1285 | (nconc vec (list (car p)))) | |
1286 | (setq guesses (cdr guesses))) | |
1287 | (if isvec | |
1288 | (list 'vec vec (nth 2 res)) | |
bf77c646 | 1289 | (list 'vec (nth 1 vec) (nth 2 res))))))) |
136211a9 EZ |
1290 | |
1291 | (defun calcFunc-minimize (expr var guess) | |
1292 | (let ((calc-internal-prec (max (/ calc-internal-prec 2) 3)) | |
1293 | (math-min-or-max "minimum")) | |
1294 | (math-find-minimum (math-normalize expr) | |
1295 | (math-normalize var) | |
bf77c646 | 1296 | (math-normalize guess) nil))) |
136211a9 EZ |
1297 | |
1298 | (defun calcFunc-wminimize (expr var guess) | |
1299 | (let ((calc-internal-prec (max (/ calc-internal-prec 2) 3)) | |
1300 | (math-min-or-max "minimum")) | |
1301 | (math-find-minimum (math-normalize expr) | |
1302 | (math-normalize var) | |
bf77c646 | 1303 | (math-normalize guess) t))) |
136211a9 EZ |
1304 | |
1305 | (defun calcFunc-maximize (expr var guess) | |
1306 | (let* ((calc-internal-prec (max (/ calc-internal-prec 2) 3)) | |
1307 | (math-min-or-max "maximum") | |
1308 | (res (math-find-minimum (math-normalize (math-neg expr)) | |
1309 | (math-normalize var) | |
1310 | (math-normalize guess) nil))) | |
bf77c646 | 1311 | (list 'vec (nth 1 res) (math-neg (nth 2 res))))) |
136211a9 EZ |
1312 | |
1313 | (defun calcFunc-wmaximize (expr var guess) | |
1314 | (let* ((calc-internal-prec (max (/ calc-internal-prec 2) 3)) | |
1315 | (math-min-or-max "maximum") | |
1316 | (res (math-find-minimum (math-normalize (math-neg expr)) | |
1317 | (math-normalize var) | |
1318 | (math-normalize guess) t))) | |
bf77c646 | 1319 | (list 'vec (nth 1 res) (math-neg (nth 2 res))))) |
136211a9 EZ |
1320 | |
1321 | ||
1322 | ||
1323 | ||
1324 | ;;; The following algorithms come from Numerical Recipes, chapter 3. | |
1325 | ||
1326 | (defun calcFunc-polint (data x) | |
1327 | (or (math-matrixp data) (math-reject-arg data 'matrixp)) | |
1328 | (or (= (length data) 3) | |
1329 | (math-reject-arg data "*Wrong number of data rows")) | |
1330 | (or (> (length (nth 1 data)) 2) | |
1331 | (math-reject-arg data "*Too few data points")) | |
1332 | (if (and (math-vectorp x) (or (math-constp x) math-expand-formulas)) | |
1333 | (cons 'vec (mapcar (function (lambda (x) (calcFunc-polint data x))) | |
1334 | (cdr x))) | |
1335 | (or (math-objectp x) math-expand-formulas (math-reject-arg x 'objectp)) | |
1336 | (math-with-extra-prec 2 | |
1337 | (cons 'vec (math-poly-interp (cdr (nth 1 data)) (cdr (nth 2 data)) x | |
bf77c646 | 1338 | nil))))) |
136211a9 EZ |
1339 | (put 'calcFunc-polint 'math-expandable t) |
1340 | ||
1341 | ||
1342 | (defun calcFunc-ratint (data x) | |
1343 | (or (math-matrixp data) (math-reject-arg data 'matrixp)) | |
1344 | (or (= (length data) 3) | |
1345 | (math-reject-arg data "*Wrong number of data rows")) | |
1346 | (or (> (length (nth 1 data)) 2) | |
1347 | (math-reject-arg data "*Too few data points")) | |
1348 | (if (and (math-vectorp x) (or (math-constp x) math-expand-formulas)) | |
1349 | (cons 'vec (mapcar (function (lambda (x) (calcFunc-ratint data x))) | |
1350 | (cdr x))) | |
1351 | (or (math-objectp x) math-expand-formulas (math-reject-arg x 'objectp)) | |
1352 | (math-with-extra-prec 2 | |
1353 | (cons 'vec (math-poly-interp (cdr (nth 1 data)) (cdr (nth 2 data)) x | |
bf77c646 | 1354 | (cdr (cdr (cdr (nth 1 data))))))))) |
136211a9 EZ |
1355 | (put 'calcFunc-ratint 'math-expandable t) |
1356 | ||
1357 | ||
1358 | (defun math-poly-interp (xa ya x ratp) | |
1359 | (let ((n (length xa)) | |
1360 | (dif nil) | |
1361 | (ns nil) | |
1362 | (xax nil) | |
1363 | (c (copy-sequence ya)) | |
1364 | (d (copy-sequence ya)) | |
1365 | (i 0) | |
1366 | (m 0) | |
1367 | y dy (xp xa) xpm cp dp temp) | |
1368 | (while (<= (setq i (1+ i)) n) | |
1369 | (setq xax (cons (math-sub (car xp) x) xax) | |
1370 | xp (cdr xp) | |
1371 | temp (math-abs (car xax))) | |
1372 | (if (or (null dif) (math-lessp temp dif)) | |
1373 | (setq dif temp | |
1374 | ns i))) | |
1375 | (setq xax (nreverse xax) | |
1376 | ns (1- ns) | |
1377 | y (nth ns ya)) | |
1378 | (if (math-zerop dif) | |
1379 | (list y 0) | |
1380 | (while (< (setq m (1+ m)) n) | |
1381 | (setq i 0 | |
1382 | xp xax | |
1383 | xpm (nthcdr m xax) | |
1384 | cp c | |
1385 | dp d) | |
1386 | (while (<= (setq i (1+ i)) (- n m)) | |
1387 | (if ratp | |
1388 | (let ((t2 (math-div (math-mul (car xp) (car dp)) (car xpm)))) | |
1389 | (setq temp (math-div (math-sub (nth 1 cp) (car dp)) | |
1390 | (math-sub t2 (nth 1 cp)))) | |
1391 | (setcar dp (math-mul (nth 1 cp) temp)) | |
1392 | (setcar cp (math-mul t2 temp))) | |
1393 | (if (math-equal (car xp) (car xpm)) | |
1394 | (math-reject-arg (cons 'vec xa) "*Duplicate X values")) | |
1395 | (setq temp (math-div (math-sub (nth 1 cp) (car dp)) | |
1396 | (math-sub (car xp) (car xpm)))) | |
1397 | (setcar dp (math-mul (car xpm) temp)) | |
1398 | (setcar cp (math-mul (car xp) temp))) | |
1399 | (setq cp (cdr cp) | |
1400 | dp (cdr dp) | |
1401 | xp (cdr xp) | |
1402 | xpm (cdr xpm))) | |
1403 | (if (< (+ ns ns) (- n m)) | |
1404 | (setq dy (nth ns c)) | |
1405 | (setq ns (1- ns) | |
1406 | dy (nth ns d))) | |
1407 | (setq y (math-add y dy))) | |
bf77c646 | 1408 | (list y dy)))) |
136211a9 EZ |
1409 | |
1410 | ||
1411 | ||
1412 | ;;; The following algorithms come from Numerical Recipes, chapter 4. | |
1413 | ||
1414 | (defun calcFunc-ninteg (expr var lo hi) | |
1415 | (setq lo (math-evaluate-expr lo) | |
1416 | hi (math-evaluate-expr hi)) | |
1417 | (or (math-numberp lo) (math-infinitep lo) (math-reject-arg lo 'numberp)) | |
1418 | (or (math-numberp hi) (math-infinitep hi) (math-reject-arg hi 'numberp)) | |
1419 | (if (math-lessp hi lo) | |
1420 | (math-neg (calcFunc-ninteg expr var hi lo)) | |
1421 | (setq expr (math-expr-subst expr var '(var DUMMY var-DUMMY))) | |
1422 | (let ((var-DUMMY nil) | |
1423 | (calc-symbolic-mode nil) | |
1424 | (calc-prefer-frac nil) | |
1425 | (sum 0)) | |
1426 | (setq expr (math-evaluate-expr expr)) | |
1427 | (if (equal lo '(neg (var inf var-inf))) | |
1428 | (let ((thi (if (math-lessp hi '(float -2 0)) | |
1429 | hi '(float -2 0)))) | |
1430 | (setq sum (math-ninteg-romberg | |
1431 | 'math-ninteg-midpoint expr | |
1432 | (math-float lo) (math-float thi) 'inf) | |
1433 | lo thi))) | |
1434 | (if (equal hi '(var inf var-inf)) | |
1435 | (let ((tlo (if (math-lessp '(float 2 0) lo) | |
1436 | lo '(float 2 0)))) | |
1437 | (setq sum (math-add sum | |
1438 | (math-ninteg-romberg | |
1439 | 'math-ninteg-midpoint expr | |
1440 | (math-float tlo) (math-float hi) 'inf)) | |
1441 | hi tlo))) | |
1442 | (or (math-equal lo hi) | |
1443 | (setq sum (math-add sum | |
1444 | (math-ninteg-romberg | |
1445 | 'math-ninteg-midpoint expr | |
1446 | (math-float lo) (math-float hi) nil)))) | |
bf77c646 | 1447 | sum))) |
136211a9 EZ |
1448 | |
1449 | ||
1450 | ;;; Open Romberg method; "qromo" in section 4.4. | |
03cc1aba JB |
1451 | |
1452 | ;; The variable math-ninteg-temp is local to math-ninteg-romberg, | |
1453 | ;; but is used by math-ninteg-midpoint, which is used by | |
1454 | ;; math-ninteg-romberg. | |
1455 | (defvar math-ninteg-temp) | |
1456 | ||
a1506d29 | 1457 | (defun math-ninteg-romberg (func expr lo hi mode) |
136211a9 EZ |
1458 | (let ((curh '(float 1 0)) |
1459 | (h nil) | |
1460 | (s nil) | |
1461 | (j 0) | |
1462 | (ss nil) | |
1463 | (prec calc-internal-prec) | |
03cc1aba | 1464 | (math-ninteg-temp nil)) |
136211a9 EZ |
1465 | (math-with-extra-prec 2 |
1466 | ;; Limit on "j" loop must be 14 or less to keep "it" from overflowing. | |
1467 | (or (while (and (null ss) (<= (setq j (1+ j)) 8)) | |
1468 | (setq s (nconc s (list (funcall func expr lo hi mode))) | |
1469 | h (nconc h (list curh))) | |
1470 | (if (>= j 3) | |
1471 | (let ((res (math-poly-interp h s '(float 0 0) nil))) | |
1472 | (if (math-lessp (math-abs (nth 1 res)) | |
1473 | (calcFunc-scf (math-abs (car res)) | |
1474 | (- prec))) | |
03cc1aba | 1475 | (setq ss (car res))))) |
136211a9 EZ |
1476 | (if (>= j 5) |
1477 | (setq s (cdr s) | |
1478 | h (cdr h))) | |
1479 | (setq curh (math-div-float curh '(float 9 0)))) | |
1480 | ss | |
bf77c646 | 1481 | (math-reject-arg nil (format "*Integral failed to converge")))))) |
136211a9 EZ |
1482 | |
1483 | ||
1484 | (defun math-ninteg-evaluate (expr x mode) | |
1485 | (if (eq mode 'inf) | |
1486 | (setq x (math-div '(float 1 0) x))) | |
1487 | (let* ((var-DUMMY x) | |
1488 | (res (math-evaluate-expr expr))) | |
1489 | (or (Math-numberp res) | |
1490 | (math-reject-arg res "*Integrand does not evaluate to a number")) | |
1491 | (if (eq mode 'inf) | |
1492 | (setq res (math-mul res (math-sqr x)))) | |
bf77c646 | 1493 | res)) |
136211a9 EZ |
1494 | |
1495 | ||
03cc1aba | 1496 | (defun math-ninteg-midpoint (expr lo hi mode) ; uses "math-ninteg-temp" |
136211a9 EZ |
1497 | (if (eq mode 'inf) |
1498 | (let ((math-infinite-mode t) temp) | |
1499 | (setq temp (math-div 1 lo) | |
1500 | lo (math-div 1 hi) | |
1501 | hi temp))) | |
03cc1aba JB |
1502 | (if math-ninteg-temp |
1503 | (let* ((it3 (* 3 (car math-ninteg-temp))) | |
1504 | (math-working-step-2 (* 2 (car math-ninteg-temp))) | |
136211a9 EZ |
1505 | (math-working-step 0) |
1506 | (range (math-sub hi lo)) | |
1507 | (del (math-div range (math-float it3))) | |
1508 | (del2 (math-add del del)) | |
1509 | (del3 (math-add del del2)) | |
1510 | (x (math-add lo (math-mul '(float 5 -1) del))) | |
1511 | (sum '(float 0 0)) | |
1512 | (j 0) temp) | |
03cc1aba | 1513 | (while (<= (setq j (1+ j)) (car math-ninteg-temp)) |
136211a9 EZ |
1514 | (setq math-working-step (1+ math-working-step) |
1515 | temp (math-ninteg-evaluate expr x mode) | |
1516 | math-working-step (1+ math-working-step) | |
1517 | sum (math-add sum (math-add temp (math-ninteg-evaluate | |
1518 | expr (math-add x del2) | |
1519 | mode))) | |
1520 | x (math-add x del3))) | |
03cc1aba JB |
1521 | (setq math-ninteg-temp (list it3 |
1522 | (math-add (math-div (nth 1 math-ninteg-temp) | |
1523 | '(float 3 0)) | |
1524 | (math-mul sum del))))) | |
1525 | (setq math-ninteg-temp (list 1 (math-mul | |
1526 | (math-sub hi lo) | |
1527 | (math-ninteg-evaluate | |
1528 | expr | |
1529 | (math-mul (math-add lo hi) '(float 5 -1)) | |
1530 | mode))))) | |
1531 | (nth 1 math-ninteg-temp)) | |
136211a9 EZ |
1532 | |
1533 | ||
1534 | ||
1535 | ||
1536 | ||
1537 | ;;; The following algorithms come from Numerical Recipes, chapter 14. | |
1538 | ||
3132f345 CW |
1539 | (defvar math-dummy-vars [(var DUMMY var-DUMMY)]) |
1540 | (defvar math-dummy-counter 0) | |
136211a9 EZ |
1541 | (defun math-dummy-variable () |
1542 | (if (= math-dummy-counter (length math-dummy-vars)) | |
1543 | (let ((symb (intern (format "math-dummy-%d" math-dummy-counter)))) | |
1544 | (setq math-dummy-vars (vconcat math-dummy-vars | |
1545 | (vector (list 'var symb symb)))))) | |
1546 | (set (nth 2 (aref math-dummy-vars math-dummy-counter)) nil) | |
1547 | (prog1 | |
1548 | (aref math-dummy-vars math-dummy-counter) | |
bf77c646 | 1549 | (setq math-dummy-counter (1+ math-dummy-counter)))) |
136211a9 | 1550 | |
3132f345 CW |
1551 | (defvar math-in-fit 0) |
1552 | (defvar calc-fit-to-trail nil) | |
136211a9 EZ |
1553 | |
1554 | (defun calcFunc-fit (expr vars &optional coefs data) | |
1555 | (let ((math-in-fit 10)) | |
1556 | (math-with-extra-prec 2 | |
bf77c646 | 1557 | (math-general-fit expr vars coefs data nil)))) |
136211a9 EZ |
1558 | |
1559 | (defun calcFunc-efit (expr vars &optional coefs data) | |
1560 | (let ((math-in-fit 10)) | |
1561 | (math-with-extra-prec 2 | |
bf77c646 | 1562 | (math-general-fit expr vars coefs data 'sdev)))) |
136211a9 EZ |
1563 | |
1564 | (defun calcFunc-xfit (expr vars &optional coefs data) | |
1565 | (let ((math-in-fit 10)) | |
1566 | (math-with-extra-prec 2 | |
bf77c646 | 1567 | (math-general-fit expr vars coefs data 'full)))) |
136211a9 | 1568 | |
03cc1aba JB |
1569 | ;; The variables math-fit-first-var, math-fit-first-coef and |
1570 | ;; math-fit-new-coefs are local to math-general-fit, but are used by | |
1571 | ;; calcFunc-fitvar, calcFunc-fitparam and calcFunc-fitdummy | |
1572 | ;; (respectively), which are used by math-general-fit. | |
1573 | (defvar math-fit-first-var) | |
1574 | (defvar math-fit-first-coef) | |
1575 | (defvar math-fit-new-coefs) | |
1576 | ||
136211a9 EZ |
1577 | (defun math-general-fit (expr vars coefs data mode) |
1578 | (let ((calc-simplify-mode nil) | |
1579 | (math-dummy-counter math-dummy-counter) | |
1580 | (math-in-fit 1) | |
1581 | (extended (eq mode 'full)) | |
03cc1aba JB |
1582 | (math-fit-first-coef math-dummy-counter) |
1583 | math-fit-first-var | |
136211a9 EZ |
1584 | (plain-expr expr) |
1585 | orig-expr | |
1586 | have-sdevs need-chisq chisq | |
1587 | (x-funcs nil) | |
1588 | (y-filter nil) | |
1589 | y-dummy | |
1590 | (coef-filters nil) | |
03cc1aba | 1591 | math-fit-new-coefs |
136211a9 EZ |
1592 | (xy-values nil) |
1593 | (weights nil) | |
1594 | (var-YVAL nil) (var-YVALX nil) | |
1595 | covar beta | |
1596 | n nn m mm v dummy p) | |
1597 | ||
1598 | ;; Validate and parse arguments. | |
1599 | (or data | |
1600 | (if coefs | |
1601 | (setq data coefs | |
1602 | coefs nil) | |
1603 | (if (math-vectorp expr) | |
1604 | (if (memq (length expr) '(3 4)) | |
1605 | (setq data vars | |
1606 | vars (nth 2 expr) | |
1607 | coefs (nth 3 expr) | |
1608 | expr (nth 1 expr)) | |
1609 | (math-dimension-error)) | |
1610 | (setq data vars | |
1611 | vars nil | |
1612 | coefs nil)))) | |
1613 | (or (math-matrixp data) (math-reject-arg data 'matrixp)) | |
1614 | (setq v (1- (length data)) | |
1615 | n (1- (length (nth 1 data)))) | |
1616 | (or (math-vectorp vars) (null vars) | |
1617 | (setq vars (list 'vec vars))) | |
1618 | (or (math-vectorp coefs) (null coefs) | |
1619 | (setq coefs (list 'vec coefs))) | |
1620 | (or coefs | |
1621 | (setq coefs (cons 'vec (math-all-vars-but expr vars)))) | |
1622 | (or vars | |
1623 | (if (<= (1- (length coefs)) v) | |
1624 | (math-reject-arg coefs "*Not enough variables in model") | |
1625 | (setq coefs (copy-sequence coefs)) | |
1626 | (let ((p (nthcdr (- (length coefs) v | |
1627 | (if (eq (car-safe expr) 'calcFunc-eq) 1 0)) | |
1628 | coefs))) | |
1629 | (setq vars (cons 'vec (cdr p))) | |
1630 | (setcdr p nil)))) | |
1631 | (or (= (1- (length vars)) v) | |
1632 | (= (length vars) v) | |
1633 | (math-reject-arg vars "*Number of variables does not match data")) | |
1634 | (setq m (1- (length coefs))) | |
1635 | (if (< m 1) | |
1636 | (math-reject-arg coefs "*Need at least one parameter")) | |
1637 | ||
1638 | ;; Rewrite expr in terms of fitparam and fitvar, make into an equation. | |
1639 | (setq p coefs) | |
1640 | (while (setq p (cdr p)) | |
1641 | (or (eq (car-safe (car p)) 'var) | |
1642 | (math-reject-arg (car p) "*Expected a variable")) | |
1643 | (setq dummy (math-dummy-variable) | |
1644 | expr (math-expr-subst expr (car p) | |
1645 | (list 'calcFunc-fitparam | |
03cc1aba JB |
1646 | (- math-dummy-counter math-fit-first-coef))))) |
1647 | (setq math-fit-first-var math-dummy-counter | |
136211a9 EZ |
1648 | p vars) |
1649 | (while (setq p (cdr p)) | |
1650 | (or (eq (car-safe (car p)) 'var) | |
1651 | (math-reject-arg (car p) "*Expected a variable")) | |
1652 | (setq dummy (math-dummy-variable) | |
1653 | expr (math-expr-subst expr (car p) | |
1654 | (list 'calcFunc-fitvar | |
03cc1aba JB |
1655 | (- math-dummy-counter math-fit-first-var))))) |
1656 | (if (< math-dummy-counter (+ math-fit-first-var v)) | |
136211a9 EZ |
1657 | (setq dummy (math-dummy-variable))) ; dependent variable may be unnamed |
1658 | (setq y-dummy dummy | |
1659 | orig-expr expr) | |
1660 | (or (eq (car-safe expr) 'calcFunc-eq) | |
1661 | (setq expr (list 'calcFunc-eq (list 'calcFunc-fitvar v) expr))) | |
1662 | ||
1663 | (let ((calc-symbolic-mode nil)) | |
1664 | ||
1665 | ;; Apply rewrites to put expr into a linear-like form. | |
1666 | (setq expr (math-evaluate-expr expr) | |
1667 | expr (math-rewrite (list 'calcFunc-fitmodel expr) | |
1668 | '(var FitRules var-FitRules)) | |
1669 | math-in-fit 2 | |
1670 | expr (math-evaluate-expr expr)) | |
1671 | (or (and (eq (car-safe expr) 'calcFunc-fitsystem) | |
1672 | (= (length expr) 4) | |
1673 | (math-vectorp (nth 2 expr)) | |
1674 | (math-vectorp (nth 3 expr)) | |
1675 | (> (length (nth 2 expr)) 1) | |
1676 | (= (length (nth 3 expr)) (1+ m))) | |
1677 | (math-reject-arg plain-expr "*Model expression is too complex")) | |
1678 | (setq y-filter (nth 1 expr) | |
1679 | x-funcs (vconcat (cdr (nth 2 expr))) | |
1680 | coef-filters (nth 3 expr) | |
1681 | mm (length x-funcs)) | |
1682 | (if (equal y-filter y-dummy) | |
1683 | (setq y-filter nil)) | |
1684 | ||
1685 | ;; Build the (square) system of linear equations to be solved. | |
1686 | (setq beta (cons 'vec (make-list mm 0)) | |
1687 | covar (cons 'vec (mapcar 'copy-sequence (make-list mm beta)))) | |
1688 | (let* ((ptrs (vconcat (cdr data))) | |
1689 | (isigsq 1) | |
1690 | (xvals (make-vector mm 0)) | |
1691 | (i 0) | |
1692 | j k xval yval sigmasqr wt covj covjk covk betaj lud) | |
1693 | (while (<= (setq i (1+ i)) n) | |
1694 | ||
1695 | ;; Assign various independent variables for this data point. | |
1696 | (setq j 0 | |
1697 | sigmasqr nil) | |
1698 | (while (< j v) | |
1699 | (aset ptrs j (cdr (aref ptrs j))) | |
1700 | (setq xval (car (aref ptrs j))) | |
1701 | (if (= j (1- v)) | |
1702 | (if sigmasqr | |
1703 | (progn | |
1704 | (if (eq (car-safe xval) 'sdev) | |
1705 | (setq sigmasqr (math-add (math-sqr (nth 2 xval)) | |
1706 | sigmasqr) | |
1707 | xval (nth 1 xval))) | |
1708 | (if y-filter | |
1709 | (setq xval (math-make-sdev xval | |
1710 | (math-sqrt sigmasqr)))))) | |
1711 | (if (eq (car-safe xval) 'sdev) | |
1712 | (setq sigmasqr (math-add (math-sqr (nth 2 xval)) | |
1713 | (or sigmasqr 0)) | |
1714 | xval (nth 1 xval)))) | |
03cc1aba | 1715 | (set (nth 2 (aref math-dummy-vars (+ math-fit-first-var j))) xval) |
136211a9 EZ |
1716 | (setq j (1+ j))) |
1717 | ||
1718 | ;; Compute Y value for this data point. | |
1719 | (if y-filter | |
1720 | (setq yval (math-evaluate-expr y-filter)) | |
1721 | (setq yval (symbol-value (nth 2 y-dummy)))) | |
1722 | (if (eq (car-safe yval) 'sdev) | |
1723 | (setq sigmasqr (math-sqr (nth 2 yval)) | |
1724 | yval (nth 1 yval))) | |
1725 | (if (= i 1) | |
1726 | (setq have-sdevs sigmasqr | |
1727 | need-chisq (or extended | |
1728 | (and (eq mode 'sdev) (not have-sdevs))))) | |
1729 | (if have-sdevs | |
1730 | (if sigmasqr | |
1731 | (progn | |
1732 | (setq isigsq (math-div 1 sigmasqr)) | |
1733 | (if need-chisq | |
1734 | (setq weights (cons isigsq weights)))) | |
1735 | (math-reject-arg yval "*Mixed error forms and plain numbers")) | |
1736 | (if sigmasqr | |
1737 | (math-reject-arg yval "*Mixed error forms and plain numbers"))) | |
1738 | ||
1739 | ;; Compute X values for this data point and update covar and beta. | |
1740 | (if (eq (car-safe xval) 'sdev) | |
1741 | (set (nth 2 y-dummy) (nth 1 xval))) | |
1742 | (setq j 0 | |
1743 | covj covar | |
1744 | betaj beta) | |
1745 | (while (< j mm) | |
1746 | (setq wt (math-evaluate-expr (aref x-funcs j))) | |
1747 | (aset xvals j wt) | |
1748 | (setq wt (math-mul wt isigsq) | |
1749 | betaj (cdr betaj) | |
1750 | covjk (car (setq covj (cdr covj))) | |
1751 | k 0) | |
1752 | (while (<= k j) | |
1753 | (setq covjk (cdr covjk)) | |
1754 | (setcar covjk (math-add (car covjk) | |
1755 | (math-mul wt (aref xvals k)))) | |
1756 | (setq k (1+ k))) | |
1757 | (setcar betaj (math-add (car betaj) (math-mul wt yval))) | |
1758 | (setq j (1+ j))) | |
1759 | (if need-chisq | |
1760 | (setq xy-values (cons (append xvals (list yval)) xy-values)))) | |
1761 | ||
1762 | ;; Fill in symmetric half of covar matrix. | |
1763 | (setq j 0 | |
1764 | covj covar) | |
1765 | (while (< j (1- mm)) | |
1766 | (setq k j | |
1767 | j (1+ j) | |
1768 | covjk (nthcdr j (car (setq covj (cdr covj)))) | |
1769 | covk (nthcdr j covar)) | |
1770 | (while (< (setq k (1+ k)) mm) | |
1771 | (setq covjk (cdr covjk) | |
1772 | covk (cdr covk)) | |
1773 | (setcar covjk (nth j (car covk)))))) | |
1774 | ||
1775 | ;; Solve the linear system. | |
1776 | (if mode | |
1777 | (progn | |
1778 | (setq covar (math-matrix-inv-raw covar)) | |
1779 | (if covar | |
1780 | (setq beta (math-mul covar beta)) | |
1781 | (if (math-zerop (math-abs beta)) | |
1782 | (setq covar (calcFunc-diag 0 (1- (length beta)))) | |
1783 | (math-reject-arg orig-expr "*Singular matrix"))) | |
1784 | (or (math-vectorp covar) | |
1785 | (setq covar (list 'vec (list 'vec covar))))) | |
1786 | (setq beta (math-div beta covar))) | |
1787 | ||
1788 | ;; Compute chi-square statistic if necessary. | |
1789 | (if need-chisq | |
1790 | (let (bp xp sum) | |
1791 | (setq chisq 0) | |
1792 | (while xy-values | |
1793 | (setq bp beta | |
1794 | xp (car xy-values) | |
1795 | sum 0) | |
1796 | (while (setq bp (cdr bp)) | |
1797 | (setq sum (math-add sum (math-mul (car bp) (car xp))) | |
1798 | xp (cdr xp))) | |
1799 | (setq sum (math-sqr (math-sub (car xp) sum))) | |
1800 | (if weights (setq sum (math-mul sum (car weights)))) | |
1801 | (setq chisq (math-add chisq sum) | |
1802 | weights (cdr weights) | |
1803 | xy-values (cdr xy-values))))) | |
1804 | ||
1805 | ;; Convert coefficients back into original terms. | |
03cc1aba JB |
1806 | (setq math-fit-new-coefs (copy-sequence beta)) |
1807 | (let* ((bp math-fit-new-coefs) | |
136211a9 EZ |
1808 | (cp covar) |
1809 | (sigdat 1) | |
1810 | (math-in-fit 3) | |
1811 | (j 0)) | |
1812 | (and mode (not have-sdevs) | |
1813 | (setq sigdat (if (<= n mm) | |
1814 | 0 | |
1815 | (math-div chisq (- n mm))))) | |
1816 | (if mode | |
1817 | (while (setq bp (cdr bp)) | |
1818 | (setcar bp (math-make-sdev | |
1819 | (car bp) | |
1820 | (math-sqrt (math-mul (nth (setq j (1+ j)) | |
1821 | (car (setq cp (cdr cp)))) | |
1822 | sigdat)))))) | |
03cc1aba | 1823 | (setq math-fit-new-coefs (math-evaluate-expr coef-filters)) |
136211a9 | 1824 | (if calc-fit-to-trail |
03cc1aba | 1825 | (let ((bp math-fit-new-coefs) |
136211a9 EZ |
1826 | (cp coefs) |
1827 | (vec nil)) | |
1828 | (while (setq bp (cdr bp) cp (cdr cp)) | |
1829 | (setq vec (cons (list 'calcFunc-eq (car cp) (car bp)) vec))) | |
1830 | (setq calc-fit-to-trail (cons 'vec (nreverse vec))))))) | |
1831 | ||
1832 | ;; Substitute best-fit coefficients back into original formula. | |
1833 | (setq expr (math-multi-subst | |
1834 | orig-expr | |
1835 | (let ((n v) | |
1836 | (vec nil)) | |
1837 | (while (>= n 1) | |
1838 | (setq vec (cons (list 'calcFunc-fitvar n) vec) | |
1839 | n (1- n))) | |
1840 | (setq n m) | |
1841 | (while (>= n 1) | |
1842 | (setq vec (cons (list 'calcFunc-fitparam n) vec) | |
1843 | n (1- n))) | |
1844 | vec) | |
03cc1aba | 1845 | (append (cdr math-fit-new-coefs) (cdr vars)))) |
136211a9 EZ |
1846 | |
1847 | ;; Package the result. | |
1848 | (math-normalize | |
1849 | (if extended | |
1850 | (list 'vec expr beta covar | |
1851 | (let ((p coef-filters) | |
1852 | (n 0)) | |
1853 | (while (and (setq n (1+ n) p (cdr p)) | |
1854 | (eq (car-safe (car p)) 'calcFunc-fitdummy) | |
1855 | (eq (nth 1 (car p)) n))) | |
1856 | (if p | |
1857 | coef-filters | |
1858 | (list 'vec))) | |
1859 | chisq | |
1860 | (if (and have-sdevs (> n mm)) | |
1861 | (list 'calcFunc-utpc chisq (- n mm)) | |
1862 | '(var nan var-nan))) | |
bf77c646 | 1863 | expr)))) |
136211a9 | 1864 | |
136211a9 EZ |
1865 | |
1866 | (defun calcFunc-fitvar (x) | |
1867 | (if (>= math-in-fit 2) | |
1868 | (progn | |
03cc1aba | 1869 | (setq x (aref math-dummy-vars (+ math-fit-first-var x -1))) |
136211a9 | 1870 | (or (calc-var-value (nth 2 x)) x)) |
bf77c646 | 1871 | (math-reject-arg x))) |
136211a9 EZ |
1872 | |
1873 | (defun calcFunc-fitparam (x) | |
1874 | (if (>= math-in-fit 2) | |
1875 | (progn | |
03cc1aba | 1876 | (setq x (aref math-dummy-vars (+ math-fit-first-coef x -1))) |
136211a9 | 1877 | (or (calc-var-value (nth 2 x)) x)) |
bf77c646 | 1878 | (math-reject-arg x))) |
136211a9 EZ |
1879 | |
1880 | (defun calcFunc-fitdummy (x) | |
1881 | (if (= math-in-fit 3) | |
03cc1aba | 1882 | (nth x math-fit-new-coefs) |
bf77c646 | 1883 | (math-reject-arg x))) |
136211a9 EZ |
1884 | |
1885 | (defun calcFunc-hasfitvars (expr) | |
1886 | (if (Math-primp expr) | |
1887 | 0 | |
1888 | (if (eq (car expr) 'calcFunc-fitvar) | |
1889 | (nth 1 expr) | |
bf77c646 | 1890 | (apply 'max (mapcar 'calcFunc-hasfitvars (cdr expr)))))) |
136211a9 EZ |
1891 | |
1892 | (defun calcFunc-hasfitparams (expr) | |
1893 | (if (Math-primp expr) | |
1894 | 0 | |
1895 | (if (eq (car expr) 'calcFunc-fitparam) | |
1896 | (nth 1 expr) | |
bf77c646 | 1897 | (apply 'max (mapcar 'calcFunc-hasfitparams (cdr expr)))))) |
136211a9 EZ |
1898 | |
1899 | ||
1900 | (defun math-all-vars-but (expr but) | |
1901 | (let* ((vars (math-all-vars-in expr)) | |
1902 | (p but)) | |
1903 | (while p | |
1904 | (setq vars (delq (assoc (car-safe p) vars) vars) | |
1905 | p (cdr p))) | |
1906 | (sort (mapcar 'car vars) | |
bf77c646 | 1907 | (function (lambda (x y) (string< (nth 1 x) (nth 1 y))))))) |
136211a9 | 1908 | |
03cc1aba JB |
1909 | ;; The variables math-all-vars-vars (the vars for math-all-vars) and |
1910 | ;; math-all-vars-found are local to math-all-vars-in, but are used by | |
1911 | ;; math-all-vars-rec which is called by math-all-vars-in. | |
1912 | (defvar math-all-vars-vars) | |
1913 | (defvar math-all-vars-found) | |
1914 | ||
136211a9 | 1915 | (defun math-all-vars-in (expr) |
03cc1aba JB |
1916 | (let ((math-all-vars-vars nil) |
1917 | math-all-vars-found) | |
136211a9 | 1918 | (math-all-vars-rec expr) |
03cc1aba | 1919 | math-all-vars-vars)) |
136211a9 EZ |
1920 | |
1921 | (defun math-all-vars-rec (expr) | |
1922 | (if (Math-primp expr) | |
1923 | (if (eq (car-safe expr) 'var) | |
1924 | (or (math-const-var expr) | |
03cc1aba JB |
1925 | (if (setq math-all-vars-found (assoc expr math-all-vars-vars)) |
1926 | (setcdr math-all-vars-found (1+ (cdr math-all-vars-found))) | |
1927 | (setq math-all-vars-vars (cons (cons expr 1) math-all-vars-vars))))) | |
136211a9 | 1928 | (while (setq expr (cdr expr)) |
bf77c646 | 1929 | (math-all-vars-rec (car expr))))) |
136211a9 | 1930 | |
c728e633 JB |
1931 | (provide 'calcalg3) |
1932 | ||
cbee283d | 1933 | ;; arch-tag: ff9f2920-8111-48b5-b3fa-b0682c3e44a6 |
bf77c646 | 1934 | ;;; calcalg3.el ends here |