1;;; calc-map.el --- higher-order functions for Calc
2
3;; Copyright (C) 1990, 1991, 1992, 1993, 2001, 2002, 2003, 2004,
4;;   2005, 2006, 2007 Free Software Foundation, Inc.
5
6;; Author: David Gillespie <daveg@synaptics.com>
7;; Maintainer: Jay Belanger <jay.p.belanger@gmail.com>
8
9;; This file is part of GNU Emacs.
10
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
13;; the Free Software Foundation; either version 2, or (at your option)
14;; any later version.
15
16;; GNU Emacs is distributed in the hope that it will be useful,
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.
25
26;;; Commentary:
27
28;;; Code:
29
30;; This file is autoloaded from calc-ext.el.
31
32(require 'calc-ext)
33(require 'calc-macs)
34
35(defun calc-apply (&optional oper)
36  (interactive)
37  (calc-wrapper
38   (let* ((sel-mode nil)
39	  (calc-dollar-values (mapcar 'calc-get-stack-element
40				      (nthcdr calc-stack-top calc-stack)))
41	  (calc-dollar-used 0)
42	  (oper (or oper (calc-get-operator "Apply"
43					    (if (math-vectorp (calc-top 1))
44						(1- (length (calc-top 1)))
45					      -1))))
46	  (expr (calc-top-n (1+ calc-dollar-used))))
47     (message "Working...")
48     (calc-set-command-flag 'clear-message)
49     (calc-enter-result (1+ calc-dollar-used)
50			(concat (substring "apl" 0 (- 4 (length (nth 2 oper))))
51				(nth 2 oper))
52			(list 'calcFunc-apply
53			      (math-calcFunc-to-var (nth 1 oper))
54			      expr)))))
55
56(defun calc-reduce (&optional oper accum)
57  (interactive)
58  (calc-wrapper
59   (let* ((sel-mode nil)
60	  (nest (calc-is-hyperbolic))
61	  (rev (calc-is-inverse))
62	  (nargs (if (and nest (not rev)) 2 1))
63	  (calc-dollar-values (mapcar 'calc-get-stack-element
64				      (nthcdr calc-stack-top calc-stack)))
65	  (calc-dollar-used 0)
66	  (calc-mapping-dir (and (not accum) (not nest) ""))
67	  (oper (or oper (calc-get-operator
68			  (if nest
69			      (concat (if accum "Accumulate " "")
70				      (if rev "Fixed Point" "Nest"))
71			    (concat (if rev "Inv " "")
72				    (if accum "Accumulate" "Reduce")))
73			  (if nest 1 2)))))
74     (message "Working...")
75     (calc-set-command-flag 'clear-message)
76     (calc-enter-result (+ calc-dollar-used nargs)
77			(concat (substring (if nest
78					       (if rev "fxp" "nst")
79					     (if accum "acc" "red"))
80					   0 (- 4 (length (nth 2 oper))))
81				(nth 2 oper))
82			(if nest
83			    (cons (if rev
84				      (if accum 'calcFunc-afixp 'calcFunc-fixp)
85				    (if accum 'calcFunc-anest 'calcFunc-nest))
86				  (cons (math-calcFunc-to-var (nth 1 oper))
87					(calc-top-list-n
88					 nargs (1+ calc-dollar-used))))
89			  (list (if accum
90				    (if rev 'calcFunc-raccum 'calcFunc-accum)
91				  (intern (concat "calcFunc-"
92						  (if rev "r" "")
93						  "reduce"
94						  calc-mapping-dir)))
95				(math-calcFunc-to-var (nth 1 oper))
96				(calc-top-n (1+ calc-dollar-used))))))))
97
98(defun calc-accumulate (&optional oper)
99  (interactive)
100  (calc-reduce oper t))
101
102(defun calc-map (&optional oper)
103  (interactive)
104  (calc-wrapper
105   (let* ((sel-mode nil)
106	  (calc-dollar-values (mapcar 'calc-get-stack-element
107				      (nthcdr calc-stack-top calc-stack)))
108	  (calc-dollar-used 0)
109	  (calc-mapping-dir "")
110	  (oper (or oper (calc-get-operator "Map")))
111	  (nargs (car oper)))
112     (message "Working...")
113     (calc-set-command-flag 'clear-message)
114     (calc-enter-result (+ nargs calc-dollar-used)
115			(concat (substring "map" 0 (- 4 (length (nth 2 oper))))
116				(nth 2 oper))
117			(cons (intern (concat "calcFunc-map" calc-mapping-dir))
118			      (cons (math-calcFunc-to-var (nth 1 oper))
119				    (calc-top-list-n
120				     nargs
121				     (1+ calc-dollar-used))))))))
122
123(defun calc-map-equation (&optional oper)
124  (interactive)
125  (calc-wrapper
126   (let* ((sel-mode nil)
127	  (calc-dollar-values (mapcar 'calc-get-stack-element
128				      (nthcdr calc-stack-top calc-stack)))
129	  (calc-dollar-used 0)
130	  (oper (or oper (calc-get-operator "Map-equation")))
131	  (nargs (car oper)))
132     (message "Working...")
133     (calc-set-command-flag 'clear-message)
134     (calc-enter-result (+ nargs calc-dollar-used)
135			(concat (substring "map" 0 (- 4 (length (nth 2 oper))))
136				(nth 2 oper))
137			(cons (if (calc-is-inverse)
138				  'calcFunc-mapeqr
139				(if (calc-is-hyperbolic)
140				    'calcFunc-mapeqp 'calcFunc-mapeq))
141			      (cons (math-calcFunc-to-var (nth 1 oper))
142				    (calc-top-list-n
143				     nargs
144				     (1+ calc-dollar-used))))))))
145
146(defvar calc-verify-arglist t)
147(defvar calc-mapping-dir nil)
148(defun calc-map-stack ()
149  "This is meant to be called by calc-keypad mode."
150  (interactive)
151  (let ((calc-verify-arglist nil))
152    (calc-unread-command ?\$)
153    (calc-map)))
154
155(defun calc-outer-product (&optional oper)
156  (interactive)
157  (calc-wrapper
158   (let* ((sel-mode nil)
159	  (calc-dollar-values (mapcar 'calc-get-stack-element
160				      (nthcdr calc-stack-top calc-stack)))
161	  (calc-dollar-used 0)
162	  (oper (or oper (calc-get-operator "Outer" 2))))
163     (message "Working...")
164     (calc-set-command-flag 'clear-message)
165     (calc-enter-result (+ 2 calc-dollar-used)
166			(concat (substring "out" 0 (- 4 (length (nth 2 oper))))
167				(nth 2 oper))
168			(cons 'calcFunc-outer
169			      (cons (math-calcFunc-to-var (nth 1 oper))
170				    (calc-top-list-n
171				     2 (1+ calc-dollar-used))))))))
172
173(defun calc-inner-product (&optional mul-oper add-oper)
174  (interactive)
175  (calc-wrapper
176   (let* ((sel-mode nil)
177	  (calc-dollar-values (mapcar 'calc-get-stack-element
178				      (nthcdr calc-stack-top calc-stack)))
179	  (calc-dollar-used 0)
180	  (mul-oper (or mul-oper (calc-get-operator "Inner (Mult)" 2)))
181	  (mul-used calc-dollar-used)
182	  (calc-dollar-values (if (> mul-used 0)
183				  (cdr calc-dollar-values)
184				calc-dollar-values))
185	  (calc-dollar-used 0)
186	  (add-oper (or add-oper (calc-get-operator "Inner (Add)" 2))))
187     (message "Working...")
188     (calc-set-command-flag 'clear-message)
189     (calc-enter-result (+ 2 mul-used calc-dollar-used)
190			(concat "in"
191				(substring (nth 2 mul-oper) 0 1)
192				(substring (nth 2 add-oper) 0 1))
193			(nconc (list 'calcFunc-inner
194				     (math-calcFunc-to-var (nth 1 mul-oper))
195				     (math-calcFunc-to-var (nth 1 add-oper)))
196			       (calc-top-list-n
197				2 (+ 1 mul-used calc-dollar-used)))))))
198
199(defconst calc-oper-keys '( ( ( ?+ 2 calcFunc-add )
200			      ( ?- 2 calcFunc-sub )
201			      ( ?* 2 calcFunc-mul )
202			      ( ?/ 2 calcFunc-div )
203			      ( ?^ 2 calcFunc-pow )
204			      ( ?| 2 calcFunc-vconcat )
205			      ( ?% 2 calcFunc-mod )
206			      ( ?\\ 2 calcFunc-idiv )
207			      ( ?! 1 calcFunc-fact )
208			      ( ?& 1 calcFunc-inv )
209			      ( ?n 1 calcFunc-neg )
210			      ( ?x user )
211			      ( ?z user )
212			      ( ?A 1 calcFunc-abs )
213			      ( ?J 1 calcFunc-conj )
214			      ( ?G 1 calcFunc-arg )
215			      ( ?Q 1 calcFunc-sqrt )
216			      ( ?N 2 calcFunc-min )
217			      ( ?X 2 calcFunc-max )
218			      ( ?F 1 calcFunc-floor )
219			      ( ?R 1 calcFunc-round )
220			      ( ?S 1 calcFunc-sin )
221			      ( ?C 1 calcFunc-cos )
222			      ( ?T 1 calcFunc-tan )
223			      ( ?L 1 calcFunc-ln )
224			      ( ?E 1 calcFunc-exp )
225			      ( ?B 2 calcFunc-log ) )
226			    ( ( ?F 1 calcFunc-ceil )     ; inverse
227			      ( ?R 1 calcFunc-trunc )
228			      ( ?Q 1 calcFunc-sqr )
229			      ( ?S 1 calcFunc-arcsin )
230			      ( ?C 1 calcFunc-arccos )
231			      ( ?T 1 calcFunc-arctan )
232			      ( ?L 1 calcFunc-exp )
233			      ( ?E 1 calcFunc-ln )
234			      ( ?B 2 calcFunc-alog )
235			      ( ?^ 2 calcFunc-nroot )
236			      ( ?| 2 calcFunc-vconcatrev ) )
237			    ( ( ?F 1 calcFunc-ffloor )   ; hyperbolic
238			      ( ?R 1 calcFunc-fround )
239			      ( ?S 1 calcFunc-sinh )
240			      ( ?C 1 calcFunc-cosh )
241			      ( ?T 1 calcFunc-tanh )
242			      ( ?L 1 calcFunc-log10 )
243			      ( ?E 1 calcFunc-exp10 )
244			      ( ?| 2 calcFunc-append ) )
245			    ( ( ?F 1 calcFunc-fceil )    ; inverse-hyperbolic
246			      ( ?R 1 calcFunc-ftrunc )
247			      ( ?S 1 calcFunc-arcsinh )
248			      ( ?C 1 calcFunc-arccosh )
249			      ( ?T 1 calcFunc-arctanh )
250			      ( ?L 1 calcFunc-exp10 )
251			      ( ?E 1 calcFunc-log10 )
252			      ( ?| 2 calcFunc-appendrev ) )))
253
254(defconst calc-a-oper-keys '( ( ( ?a 3 calcFunc-apart )
255				( ?b 3 calcFunc-subst )
256				( ?c 2 calcFunc-collect )
257				( ?d 2 calcFunc-deriv )
258				( ?e 1 calcFunc-esimplify )
259				( ?f 2 calcFunc-factor )
260				( ?g 2 calcFunc-pgcd )
261				( ?i 2 calcFunc-integ )
262				( ?m 2 calcFunc-match )
263				( ?n 1 calcFunc-nrat )
264				( ?r 2 calcFunc-rewrite )
265				( ?s 1 calcFunc-simplify )
266				( ?t 3 calcFunc-taylor )
267				( ?x 1 calcFunc-expand )
268				( ?M 2 calcFunc-mapeq )
269				( ?N 3 calcFunc-minimize )
270				( ?P 2 calcFunc-roots )
271				( ?R 3 calcFunc-root )
272				( ?S 2 calcFunc-solve )
273				( ?T 4 calcFunc-table )
274				( ?X 3 calcFunc-maximize )
275				( ?= 2 calcFunc-eq )
276				( ?\# 2 calcFunc-neq )
277				( ?< 2 calcFunc-lt )
278				( ?> 2 calcFunc-gt )
279				( ?\[ 2 calcFunc-leq )
280				( ?\] 2 calcFunc-geq )
281				( ?{ 2 calcFunc-in )
282				( ?! 1 calcFunc-lnot )
283				( ?& 2 calcFunc-land )
284				( ?\| 2 calcFunc-lor )
285				( ?: 3 calcFunc-if )
286				( ?. 2 calcFunc-rmeq )
287				( ?+ 4 calcFunc-sum )
288				( ?- 4 calcFunc-asum )
289				( ?* 4 calcFunc-prod )
290				( ?_ 2 calcFunc-subscr )
291				( ?\\ 2 calcFunc-pdiv )
292				( ?% 2 calcFunc-prem )
293				( ?/ 2 calcFunc-pdivrem ) )
294			      ( ( ?m 2 calcFunc-matchnot )
295				( ?M 2 calcFunc-mapeqr )
296				( ?S 2 calcFunc-finv ) )
297			      ( ( ?d 2 calcFunc-tderiv )
298				( ?f 2 calcFunc-factors )
299				( ?M 2 calcFunc-mapeqp )
300				( ?N 3 calcFunc-wminimize )
301				( ?R 3 calcFunc-wroot )
302				( ?S 2 calcFunc-fsolve )
303				( ?X 3 calcFunc-wmaximize )
304				( ?/ 2 calcFunc-pdivide ) )
305			      ( ( ?S 2 calcFunc-ffinv ) )))
306
307(defconst calc-b-oper-keys '( ( ( ?a 2 calcFunc-and )
308				( ?o 2 calcFunc-or )
309				( ?x 2 calcFunc-xor )
310				( ?d 2 calcFunc-diff )
311				( ?n 1 calcFunc-not )
312				( ?c 1 calcFunc-clip )
313				( ?l 2 calcFunc-lsh )
314				( ?r 2 calcFunc-rsh )
315				( ?L 2 calcFunc-ash )
316				( ?R 2 calcFunc-rash )
317				( ?t 2 calcFunc-rot )
318				( ?p 1 calcFunc-vpack )
319				( ?u 1 calcFunc-vunpack )
320				( ?D 4 calcFunc-ddb )
321				( ?F 3 calcFunc-fv )
322				( ?I 1 calcFunc-irr )
323				( ?M 3 calcFunc-pmt )
324				( ?N 2 calcFunc-npv )
325				( ?P 3 calcFunc-pv )
326				( ?S 3 calcFunc-sln )
327				( ?T 3 calcFunc-rate )
328				( ?Y 4 calcFunc-syd )
329				( ?\# 3 calcFunc-nper )
330				( ?\% 2 calcFunc-relch ) )
331			      ( ( ?F 3 calcFunc-fvb )
332				( ?I 1 calcFunc-irrb )
333				( ?M 3 calcFunc-pmtb )
334				( ?N 2 calcFunc-npvb )
335				( ?P 3 calcFunc-pvb )
336				( ?T 3 calcFunc-rateb )
337				( ?\# 3 calcFunc-nperb ) )
338			      ( ( ?F 3 calcFunc-fvl )
339				( ?M 3 calcFunc-pmtl )
340				( ?P 3 calcFunc-pvl )
341				( ?T 3 calcFunc-ratel )
342				( ?\# 3 calcFunc-nperl ) )))
343
344(defconst calc-c-oper-keys '( ( ( ?d 1 calcFunc-deg )
345				( ?r 1 calcFunc-rad )
346				( ?h 1 calcFunc-hms )
347				( ?f 1 calcFunc-float )
348				( ?F 1 calcFunc-frac ) )))
349
350(defconst calc-f-oper-keys '( ( ( ?b 2 calcFunc-beta )
351				( ?e 1 calcFunc-erf )
352				( ?g 1 calcFunc-gamma )
353				( ?h 2 calcFunc-hypot )
354				( ?i 1 calcFunc-im )
355				( ?j 2 calcFunc-besJ )
356				( ?n 2 calcFunc-min )
357				( ?r 1 calcFunc-re )
358				( ?s 1 calcFunc-sign )
359				( ?x 2 calcFunc-max )
360				( ?y 2 calcFunc-besY )
361				( ?A 1 calcFunc-abssqr )
362				( ?B 3 calcFunc-betaI )
363				( ?E 1 calcFunc-expm1 )
364				( ?G 2 calcFunc-gammaP )
365				( ?I 2 calcFunc-ilog )
366				( ?L 1 calcFunc-lnp1 )
367				( ?M 1 calcFunc-mant )
368				( ?Q 1 calcFunc-isqrt )
369				( ?S 1 calcFunc-scf )
370				( ?T 2 calcFunc-arctan2 )
371				( ?X 1 calcFunc-xpon )
372				( ?\[ 2 calcFunc-decr )
373				( ?\] 2 calcFunc-incr ) )
374			      ( ( ?e 1 calcFunc-erfc )
375				( ?E 1 calcFunc-lnp1 )
376				( ?G 2 calcFunc-gammaQ )
377				( ?L 1 calcFunc-expm1 ) )
378			      ( ( ?B 3 calcFunc-betaB )
379				( ?G 2 calcFunc-gammag) )
380			      ( ( ?G 2 calcFunc-gammaG ) )))
381
382(defconst calc-k-oper-keys '( ( ( ?b 1 calcFunc-bern )
383				( ?c 2 calcFunc-choose )
384				( ?d 1 calcFunc-dfact )
385				( ?e 1 calcFunc-euler )
386				( ?f 1 calcFunc-prfac )
387				( ?g 2 calcFunc-gcd )
388				( ?h 2 calcFunc-shuffle )
389				( ?l 2 calcFunc-lcm )
390				( ?m 1 calcFunc-moebius )
391				( ?n 1 calcFunc-nextprime )
392				( ?r 1 calcFunc-random )
393				( ?s 2 calcFunc-stir1 )
394				( ?t 1 calcFunc-totient )
395				( ?B 3 calcFunc-utpb )
396				( ?C 2 calcFunc-utpc )
397				( ?F 3 calcFunc-utpf )
398				( ?N 3 calcFunc-utpn )
399				( ?P 2 calcFunc-utpp )
400				( ?T 2 calcFunc-utpt ) )
401			      ( ( ?n 1 calcFunc-prevprime )
402				( ?B 3 calcFunc-ltpb )
403				( ?C 2 calcFunc-ltpc )
404				( ?F 3 calcFunc-ltpf )
405				( ?N 3 calcFunc-ltpn )
406				( ?P 2 calcFunc-ltpp )
407				( ?T 2 calcFunc-ltpt ) )
408			      ( ( ?b 2 calcFunc-bern )
409				( ?c 2 calcFunc-perm )
410				( ?e 2 calcFunc-euler )
411				( ?s 2 calcFunc-stir2 ) )))
412
413(defconst calc-s-oper-keys '( ( ( ?: 2 calcFunc-assign )
414				( ?= 1 calcFunc-evalto ) )))
415
416(defconst calc-t-oper-keys '( ( ( ?C 3 calcFunc-tzconv )
417				( ?D 1 calcFunc-date )
418				( ?I 2 calcFunc-incmonth )
419				( ?J 1 calcFunc-julian )
420				( ?M 1 calcFunc-newmonth )
421				( ?W 1 calcFunc-newweek )
422				( ?U 1 calcFunc-unixtime )
423				( ?Y 1 calcFunc-newyear ) )))
424
425(defconst calc-u-oper-keys '( ( ( ?C 2 calcFunc-vcov )
426				( ?G 1 calcFunc-vgmean )
427				( ?M 1 calcFunc-vmean )
428				( ?N 1 calcFunc-vmin )
429				( ?S 1 calcFunc-vsdev )
430				( ?X 1 calcFunc-vmax ) )
431			      ( ( ?C 2 calcFunc-vpcov )
432				( ?M 1 calcFunc-vmeane )
433				( ?S 1 calcFunc-vpsdev ) )
434			      ( ( ?C 2 calcFunc-vcorr )
435				( ?G 1 calcFunc-agmean )
436				( ?M 1 calcFunc-vmedian )
437				( ?S 1 calcFunc-vvar ) )
438			      ( ( ?M 1 calcFunc-vhmean )
439				( ?S 1 calcFunc-vpvar ) )))
440
441(defconst calc-v-oper-keys '( ( ( ?a 2 calcFunc-arrange )
442				( ?b 2 calcFunc-cvec )
443				( ?c 2 calcFunc-mcol )
444				( ?d 2 calcFunc-diag )
445				( ?e 2 calcFunc-vexp )
446				( ?f 2 calcFunc-find )
447				( ?h 1 calcFunc-head )
448				( ?k 2 calcFunc-cons )
449				( ?l 1 calcFunc-vlen )
450				( ?m 2 calcFunc-vmask )
451				( ?n 1 calcFunc-rnorm )
452				( ?p 2 calcFunc-pack )
453				( ?r 2 calcFunc-mrow )
454				( ?s 3 calcFunc-subvec )
455				( ?t 1 calcFunc-trn )
456				( ?u 1 calcFunc-unpack )
457				( ?v 1 calcFunc-rev )
458				( ?x 1 calcFunc-index )
459				( ?A 1 calcFunc-apply )
460				( ?C 1 calcFunc-cross )
461				( ?D 1 calcFunc-det )
462				( ?E 1 calcFunc-venum )
463				( ?F 1 calcFunc-vfloor )
464				( ?G 1 calcFunc-grade )
465				( ?H 2 calcFunc-histogram )
466				( ?I 2 calcFunc-inner )
467				( ?L 1 calcFunc-lud )
468				( ?M 0 calcFunc-map )
469				( ?N 1 calcFunc-cnorm )
470				( ?O 2 calcFunc-outer )
471				( ?R 1 calcFunc-reduce )
472				( ?S 1 calcFunc-sort )
473				( ?T 1 calcFunc-tr )
474				( ?U 1 calcFunc-accum )
475				( ?V 2 calcFunc-vunion )
476				( ?X 2 calcFunc-vxor )
477				( ?- 2 calcFunc-vdiff )
478				( ?^ 2 calcFunc-vint )
479				( ?~ 1 calcFunc-vcompl )
480				( ?# 1 calcFunc-vcard )
481				( ?: 1 calcFunc-vspan )
482				( ?+ 1 calcFunc-rdup ) )
483			      ( ( ?h 1 calcFunc-tail )
484				( ?s 3 calcFunc-rsubvec )
485				( ?G 1 calcFunc-rgrade )
486				( ?R 1 calcFunc-rreduce )
487				( ?S 1 calcFunc-rsort )
488				( ?U 1 calcFunc-raccum ) )
489			      ( ( ?e 3 calcFunc-vexp )
490				( ?h 1 calcFunc-rhead )
491				( ?k 2 calcFunc-rcons )
492				( ?H 3 calcFunc-histogram )
493				( ?R 2 calcFunc-nest )
494				( ?U 2 calcFunc-anest ) )
495			      ( ( ?h 1 calcFunc-rtail )
496				( ?R 1 calcFunc-fixp )
497				( ?U 1 calcFunc-afixp ) )))
498
499
500;;; Return a list of the form (nargs func name)
501(defvar calc-get-operator-history nil
502  "History for calc-get-operator.")
503
504(defun calc-get-operator (msg &optional nargs)
505  (setq calc-aborted-prefix nil)
506  (let ((inv nil) (hyp nil) (prefix nil) (forcenargs nil)
507	done key oper (which 0)
508	(msgs '( "(Press ? for help)"
509		 "+, -, *, /, ^, %, \\, :, &, !, |, Neg"
510		 "SHIFT + Abs, conJ, arG; maX, miN; Floor, Round; sQrt"
511		 "SHIFT + Inv, Hyp; Sin, Cos, Tan; Exp, Ln, logB"
512		 "Algebra + Simp, Esimp, Deriv, Integ, !, =, etc."
513		 "Binary + And, Or, Xor, Diff; l/r/t/L/R shifts; Not, Clip"
514		 "Conversions + Deg, Rad, HMS; Float; SHIFT + Fraction"
515		 "Functions + Re, Im; Hypot; Mant, Expon, Scale; etc."
516		 "Kombinatorics + Dfact, Lcm, Gcd, Choose; Random; etc."
517		 "Time/date + newYear, Incmonth, etc."
518		 "Vectors + Length, Row, Col, Diag, Mask, etc."
519		 "_ = mapr/reducea, : = mapc/reduced, = = reducer"
520		 "X or Z = any function by name; ' = alg entry; $ = stack")))
521    (while (not done)
522      (message "%s%s: %s: %s%s%s"
523	       msg
524	       (cond ((equal calc-mapping-dir "r") " rows")
525		     ((equal calc-mapping-dir "c") " columns")
526		     ((equal calc-mapping-dir "a") " across")
527		     ((equal calc-mapping-dir "d") " down")
528		     (t ""))
529	       (if forcenargs
530		   (format "(%d arg%s)"
531			   forcenargs (if (= forcenargs 1) "" "s"))
532		 (nth which msgs))
533	       (if inv "Inv " "") (if hyp "Hyp " "")
534	       (if prefix (concat (char-to-string prefix) "-") ""))
535      (setq key (read-char))
536      (if (>= key 128) (setq key (- key 128)))
537      (cond ((memq key '(?\C-g ?q))
538	     (keyboard-quit))
539	    ((memq key '(?\C-u ?\e)))
540	    ((= key ??)
541	     (setq which (% (1+ which) (length msgs))))
542	    ((and (= key ?I) (null prefix))
543	     (setq inv (not inv)))
544	    ((and (= key ?H) (null prefix))
545	     (setq hyp (not hyp)))
546	    ((and (eq key prefix) (not (eq key ?v)))
547	     (setq prefix nil))
548	    ((and (memq key '(?a ?b ?c ?f ?k ?s ?t ?u ?v ?V))
549		  (null prefix))
550	     (setq prefix (downcase key)))
551	    ((and (eq key ?\=) (null prefix))
552	     (if calc-mapping-dir
553		 (setq calc-mapping-dir (if (equal calc-mapping-dir "r")
554					    "" "r"))
555	       (beep)))
556	    ((and (eq key ?\_) (null prefix))
557	     (if calc-mapping-dir
558		 (if (string-match "map$" msg)
559		     (setq calc-mapping-dir (if (equal calc-mapping-dir "r")
560						"" "r"))
561		   (setq calc-mapping-dir (if (equal calc-mapping-dir "a")
562					      "" "a")))
563	       (beep)))
564	    ((and (eq key ?\:) (null prefix))
565	     (if calc-mapping-dir
566		 (if (string-match "map$" msg)
567		     (setq calc-mapping-dir (if (equal calc-mapping-dir "c")
568						"" "c"))
569		   (setq calc-mapping-dir (if (equal calc-mapping-dir "d")
570					      "" "d")))
571	       (beep)))
572	    ((and (>= key ?0) (<= key ?9) (null prefix))
573	     (setq forcenargs (if (eq forcenargs (- key ?0)) nil (- key ?0)))
574	     (and nargs forcenargs (/= nargs forcenargs) (>= nargs 0)
575		  (error "Must be a %d-argument operator" nargs)))
576	    ((memq key '(?\$ ?\'))
577	     (let* ((arglist nil)
578		    (has-args nil)
579		    (record-entry nil)
580		    (expr (if (eq key ?\$)
581			      (progn
582				(setq calc-dollar-used 1)
583				(if calc-dollar-values
584				    (car calc-dollar-values)
585				  (error "Stack underflow")))
586			    (let* ((calc-dollar-values calc-arg-values)
587				   (calc-dollar-used 0)
588				   (calc-hashes-used 0)
589				   (func (calc-do-alg-entry "" "Function: " nil
590                                                      'calc-get-operator-history)))
591			      (setq record-entry t)
592			      (or (= (length func) 1)
593				  (error "Bad format"))
594			      (if (> calc-dollar-used 0)
595				  (progn
596				    (setq has-args calc-dollar-used
597					  arglist (calc-invent-args has-args))
598				    (math-multi-subst (car func)
599						      (reverse arglist)
600						      arglist))
601				(if (> calc-hashes-used 0)
602				    (setq has-args calc-hashes-used
603					  arglist (calc-invent-args has-args)))
604				(car func))))))
605	       (if (eq (car-safe expr) 'calcFunc-lambda)
606		   (setq oper (list "$" (- (length expr) 2) expr)
607			 done t)
608		 (or has-args
609		     (progn
610		       (calc-default-formula-arglist expr)
611		       (setq record-entry t
612			     arglist (sort arglist 'string-lessp))
613		       (if calc-verify-arglist
614			   (setq arglist (read-from-minibuffer
615					  "Function argument list: "
616					  (if arglist
617					      (prin1-to-string arglist)
618					    "()")
619					  minibuffer-local-map
620					  t)))
621		       (setq arglist (mapcar (function
622					      (lambda (x)
623						(list 'var
624						      x
625						      (intern
626						       (concat
627							"var-"
628							(symbol-name x))))))
629					     arglist))))
630		 (setq oper (list "$"
631				  (length arglist)
632				  (append '(calcFunc-lambda) arglist
633					  (list expr)))
634		       done t))
635	       (if record-entry
636		   (calc-record (nth 2 oper) "oper"))))
637	    ((setq oper (assq key (nth (if inv (if hyp 3 1) (if hyp 2 0))
638				       (if prefix
639					   (symbol-value
640					    (intern (format "calc-%c-oper-keys"
641							    prefix)))
642					 calc-oper-keys))))
643	     (if (eq (nth 1 oper) 'user)
644		 (let ((func (intern
645			      (completing-read "Function name: "
646					       obarray 'fboundp
647					       nil "calcFunc-"))))
648		   (if (or forcenargs nargs)
649		       (setq oper (list "z" (or forcenargs nargs) func)
650			     done t)
651		     (if (fboundp func)
652			 (let* ((defn (symbol-function func)))
653			   (and (symbolp defn)
654				(setq defn (symbol-function defn)))
655			   (if (eq (car-safe defn) 'lambda)
656			       (let ((args (nth 1 defn))
657				     (nargs 0))
658				 (while (not (memq (car args) '(&optional
659								&rest nil)))
660				   (setq nargs (1+ nargs)
661					 args (cdr args)))
662				 (setq oper (list "z" nargs func)
663				       done t))
664			     (error
665			      "Function is not suitable for this operation")))
666		       (message "Number of arguments: ")
667		       (let ((nargs (read-char)))
668			 (if (and (>= nargs ?0) (<= nargs ?9))
669			     (setq oper (list "z" (- nargs ?0) func)
670				   done t)
671			   (beep))))))
672	       (if (or (and (eq prefix ?v) (memq key '(?A ?I ?M ?O ?R ?U)))
673		       (and (eq prefix ?a) (eq key ?M)))
674		   (let* ((dir (cond ((and (equal calc-mapping-dir "")
675					   (string-match "map$" msg))
676				      (setq calc-mapping-dir "r")
677				      " rows")
678				     ((equal calc-mapping-dir "r") " rows")
679				     ((equal calc-mapping-dir "c") " columns")
680				     ((equal calc-mapping-dir "a") " across")
681				     ((equal calc-mapping-dir "d") " down")
682				     (t "")))
683			  (calc-mapping-dir (and (memq (nth 2 oper)
684						       '(calcFunc-map
685							 calcFunc-reduce
686							 calcFunc-rreduce))
687						 ""))
688			  (oper2 (calc-get-operator
689				  (format "%s%s, %s%s" msg dir
690					  (substring (symbol-name (nth 2 oper))
691						     9)
692					  (if (eq key ?I) " (mult)" ""))
693				  (cdr (assq (nth 2 oper)
694					     '((calcFunc-reduce  . 2)
695					       (calcFunc-rreduce . 2)
696					       (calcFunc-accum   . 2)
697					       (calcFunc-raccum  . 2)
698					       (calcFunc-nest    . 2)
699					       (calcFunc-anest   . 2)
700					       (calcFunc-fixp    . 2)
701					       (calcFunc-afixp   . 2))))))
702			  (oper3 (if (eq (nth 2 oper) 'calcFunc-inner)
703				     (calc-get-operator
704				      (format "%s%s, inner (add)" msg dir))
705				   '(0 0 0)))
706			  (args nil)
707			  (nargs (if (> (nth 1 oper) 0)
708				     (nth 1 oper)
709				   (car oper2)))
710			  (n nargs)
711			  (p calc-arg-values))
712		     (while (and p (> n 0))
713		       (or (math-expr-contains (nth 1 oper2) (car p))
714			   (math-expr-contains (nth 1 oper3) (car p))
715			   (setq args (nconc args (list (car p)))
716				 n (1- n)))
717		       (setq p (cdr p)))
718		     (setq oper (list "" nargs
719				      (append
720				       '(calcFunc-lambda)
721				       args
722				       (list (math-build-call
723					      (intern
724					       (concat
725						(symbol-name (nth 2 oper))
726						calc-mapping-dir))
727					      (cons (math-calcFunc-to-var
728						     (nth 1 oper2))
729						    (if (eq key ?I)
730							(cons
731							 (math-calcFunc-to-var
732							  (nth 1 oper3))
733							 args)
734						      args))))))
735			   done t))
736		 (setq done t))))
737	    (t (beep))))
738    (and nargs (>= nargs 0)
739	 (/= nargs (nth 1 oper))
740	 (error "Must be a %d-argument operator" nargs))
741    (append (if forcenargs
742		(cons forcenargs (cdr (cdr oper)))
743	      (cdr oper))
744	    (list
745	     (let ((name (concat (if inv "I" "") (if hyp "H" "")
746				 (if prefix (char-to-string prefix) "")
747				 (char-to-string key))))
748	       (if (> (length name) 3)
749		   (substring name 0 3)
750		 name))))))
751
752
753;;; Convert a variable name (as a formula) into a like-looking function name.
754(defun math-var-to-calcFunc (f)
755  (if (eq (car-safe f) 'var)
756      (if (fboundp (nth 2 f))
757	  (nth 2 f)
758	(intern (concat "calcFunc-" (symbol-name (nth 1 f)))))
759    (if (memq (car-safe f) '(lambda calcFunc-lambda))
760	f
761      (math-reject-arg f "*Expected a function name"))))
762
763;;; Convert a function name into a like-looking variable name formula.
764(defun math-calcFunc-to-var (f)
765  (if (symbolp f)
766      (let* ((func (or (cdr (assq f '( ( + . calcFunc-add )
767				       ( - . calcFunc-sub )
768				       ( * . calcFunc-mul )
769				       ( / . calcFunc-div )
770				       ( ^ . calcFunc-pow )
771				       ( % . calcFunc-mod )
772				       ( neg . calcFunc-neg )
773				       ( | . calcFunc-vconcat ) )))
774		       f))
775	     (base (if (string-match "\\`calcFunc-\\(.+\\)\\'"
776				     (symbol-name func))
777		       (math-match-substring (symbol-name func) 1)
778		     (symbol-name func))))
779	(list 'var
780	      (intern base)
781	      (intern (concat "var-" base))))
782    f))
783
784;;; Expand a function call using "lambda" notation.
785(defun math-build-call (f args)
786  (if (eq (car-safe f) 'calcFunc-lambda)
787      (if (= (length args) (- (length f) 2))
788	  (math-multi-subst (nth (1- (length f)) f) (cdr f) args)
789	(calc-record-why "*Wrong number of arguments" f)
790	(cons 'calcFunc-call (cons (math-calcFunc-to-var f) args)))
791    (if (and (eq f 'calcFunc-neg)
792	     (= (length args) 1))
793	(list 'neg (car args))
794      (let ((func (assq f '( ( calcFunc-add . + )
795			     ( calcFunc-sub . - )
796			     ( calcFunc-mul . * )
797			     ( calcFunc-div . / )
798			     ( calcFunc-pow . ^ )
799			     ( calcFunc-mod . % )
800			     ( calcFunc-vconcat . | ) ))))
801	(if (and func (= (length args) 2))
802	    (cons (cdr func) args)
803	  (cons f args))))))
804
805;;; Do substitutions in parallel to avoid crosstalk.
806
807;; The variables math-ms-temp and math-ms-args are local to
808;; math-multi-subst, but are used by math-multi-subst-rec, which
809;; is called by math-multi-subst.
810(defvar math-ms-temp)
811(defvar math-ms-args)
812
813(defun math-multi-subst (expr olds news)
814  (let ((math-ms-args nil)
815	math-ms-temp)
816    (while (and olds news)
817      (setq math-ms-args (cons (cons (car olds) (car news)) math-ms-args)
818	    olds (cdr olds)
819	    news (cdr news)))
820    (math-multi-subst-rec expr)))
821
822(defun math-multi-subst-rec (expr)
823  (cond ((setq math-ms-temp (assoc expr math-ms-args))
824         (cdr math-ms-temp))
825	((Math-primp expr) expr)
826	((and (eq (car expr) 'calcFunc-lambda) (> (length expr) 2))
827	 (let ((new (list (car expr)))
828	       (math-ms-args math-ms-args))
829	   (while (cdr (setq expr (cdr expr)))
830	     (setq new (cons (car expr) new))
831	     (if (assoc (car expr) math-ms-args)
832		 (setq math-ms-args (cons (cons (car expr) (car expr))
833                                          math-ms-args))))
834	   (nreverse (cons (math-multi-subst-rec (car expr)) new))))
835	(t
836	 (cons (car expr)
837	       (mapcar 'math-multi-subst-rec (cdr expr))))))
838
839(defun calcFunc-call (f &rest args)
840  (setq args (math-build-call (math-var-to-calcFunc f) args))
841  (if (eq (car-safe args) 'calcFunc-call)
842      args
843    (math-normalize args)))
844
845(defun calcFunc-apply (f args)
846  (or (Math-vectorp args)
847      (math-reject-arg args 'vectorp))
848  (apply 'calcFunc-call (cons f (cdr args))))
849
850
851
852
853;;; Map a function over a vector symbolically. [Public]
854(defun math-symb-map (f mode args)
855  (let* ((func (math-var-to-calcFunc f))
856	 (nargs (length args))
857	 (ptrs (vconcat args))
858	 (vflags (make-vector nargs nil))
859	 (heads '(vec))
860	 (head nil)
861	 (vec nil)
862	 (i -1)
863	 (math-working-step 0)
864	 (math-working-step-2 nil)
865	 len cols obj expr)
866    (if (eq mode 'eqn)
867	(setq mode 'elems
868	      heads '(calcFunc-eq calcFunc-neq calcFunc-lt calcFunc-gt
869				  calcFunc-leq calcFunc-geq))
870      (while (and (< (setq i (1+ i)) nargs)
871		  (not (math-matrixp (aref ptrs i)))))
872      (if (< i nargs)
873	  (if (eq mode 'elems)
874	      (setq func (list 'lambda '(&rest x)
875			       (list 'math-symb-map
876				     (list 'quote f) '(quote elems) 'x))
877		    mode 'rows)
878	    (if (eq mode 'cols)
879		(while (< i nargs)
880		  (if (math-matrixp (aref ptrs i))
881		      (aset ptrs i (math-transpose (aref ptrs i))))
882		  (setq i (1+ i)))))
883	(setq mode 'elems))
884      (setq i -1))
885    (while (< (setq i (1+ i)) nargs)
886      (setq obj (aref ptrs i))
887      (if (and (memq (car-safe obj) heads)
888	       (or (eq mode 'elems)
889		   (math-matrixp obj)))
890	  (progn
891	    (aset vflags i t)
892	    (if head
893		(if (cdr heads)
894		    (setq head (nth
895				(aref (aref [ [0 1 2 3 4 5]
896					      [1 1 2 3 2 3]
897					      [2 2 2 1 2 1]
898					      [3 3 1 3 1 3]
899					      [4 2 2 1 4 1]
900					      [5 3 1 3 1 5] ]
901					    (- 6 (length (memq head heads))))
902				      (- 6 (length (memq (car obj) heads))))
903				heads)))
904	      (setq head (car obj)))
905	    (if len
906		(or (= (length obj) len)
907		    (math-dimension-error))
908	      (setq len (length obj))))))
909    (or len
910	(if (= nargs 1)
911	    (math-reject-arg (aref ptrs 0) 'vectorp)
912	  (math-reject-arg nil "At least one argument must be a vector")))
913    (setq math-working-step-2 (1- len))
914    (while (> (setq len (1- len)) 0)
915      (setq expr nil
916	    i -1)
917      (while (< (setq i (1+ i)) nargs)
918	(if (aref vflags i)
919	    (progn
920	      (aset ptrs i (cdr (aref ptrs i)))
921	      (setq expr (nconc expr (list (car (aref ptrs i))))))
922	  (setq expr (nconc expr (list (aref ptrs i))))))
923      (setq math-working-step (1+ math-working-step)
924	    vec (cons (math-normalize (math-build-call func expr)) vec)))
925    (setq vec (cons head (nreverse vec)))
926    (if (and (eq mode 'cols) (math-matrixp vec))
927	(math-transpose vec)
928      vec)))
929
930(defun calcFunc-map (func &rest args)
931  (math-symb-map func 'elems args))
932
933(defun calcFunc-mapr (func &rest args)
934  (math-symb-map func 'rows args))
935
936(defun calcFunc-mapc (func &rest args)
937  (math-symb-map func 'cols args))
938
939(defun calcFunc-mapa (func arg)
940  (if (math-matrixp arg)
941      (math-symb-map func 'elems (cdr (math-transpose arg)))
942    (math-symb-map func 'elems arg)))
943
944(defun calcFunc-mapd (func arg)
945  (if (math-matrixp arg)
946      (math-symb-map func 'elems (cdr arg))
947    (math-symb-map func 'elems arg)))
948
949(defun calcFunc-mapeq (func &rest args)
950  (if (and (or (equal func '(var mul var-mul))
951	       (equal func '(var div var-div)))
952	   (= (length args) 2))
953      (if (math-negp (car args))
954	  (let ((func (nth 1 (assq (car-safe (nth 1 args))
955				   calc-tweak-eqn-table))))
956	    (and func (setq args (list (car args)
957				       (cons func (cdr (nth 1 args)))))))
958	(if (math-negp (nth 1 args))
959	    (let ((func (nth 1 (assq (car-safe (car args))
960				     calc-tweak-eqn-table))))
961	      (and func (setq args (list (cons func (cdr (car args)))
962					 (nth 1 args))))))))
963  (if (or (and (equal func '(var div var-div))
964	       (assq (car-safe (nth 1 args)) calc-tweak-eqn-table))
965	  (equal func '(var neg var-neg))
966	  (equal func '(var inv var-inv)))
967      (apply 'calcFunc-mapeqr func args)
968    (apply 'calcFunc-mapeqp func args)))
969
970(defun calcFunc-mapeqr (func &rest args)
971  (setq args (mapcar (function (lambda (x)
972				 (let ((func (assq (car-safe x)
973						   calc-tweak-eqn-table)))
974				   (if func
975				       (cons (nth 1 func) (cdr x))
976				     x))))
977		     args))
978  (apply 'calcFunc-mapeqp func args))
979
980(defun calcFunc-mapeqp (func &rest args)
981  (if (or (and (memq (car-safe (car args)) '(calcFunc-lt calcFunc-leq))
982	       (memq (car-safe (nth 1 args)) '(calcFunc-gt calcFunc-geq)))
983	  (and (memq (car-safe (car args)) '(calcFunc-gt calcFunc-geq))
984	       (memq (car-safe (nth 1 args)) '(calcFunc-lt calcFunc-leq))))
985      (setq args (cons (car args)
986		       (cons (list (nth 1 (assq (car (nth 1 args))
987						calc-tweak-eqn-table))
988				   (nth 2 (nth 1 args))
989				   (nth 1 (nth 1 args)))
990			     (cdr (cdr args))))))
991  (math-symb-map func 'eqn args))
992
993
994
995;;; Reduce a function over a vector symbolically. [Public]
996(defun calcFunc-reduce (func vec)
997  (if (math-matrixp vec)
998      (let (expr row)
999	(setq func (math-var-to-calcFunc func))
1000	(while (setq vec (cdr vec))
1001	  (setq row (car vec))
1002	  (while (setq row (cdr row))
1003	    (setq expr (if expr
1004			   (if (Math-numberp expr)
1005			       (math-normalize
1006				(math-build-call func (list expr (car row))))
1007			     (math-build-call func (list expr (car row))))
1008			 (car row)))))
1009	(math-normalize expr))
1010    (calcFunc-reducer func vec)))
1011
1012(defun calcFunc-rreduce (func vec)
1013  (if (math-matrixp vec)
1014      (let (expr row)
1015	(setq func (math-var-to-calcFunc func)
1016	      vec (reverse (cdr vec)))
1017	(while vec
1018	  (setq row (reverse (cdr (car vec))))
1019	  (while row
1020	    (setq expr (if expr
1021			   (math-build-call func (list (car row) expr))
1022			 (car row))
1023		  row (cdr row)))
1024	  (setq vec (cdr vec)))
1025	(math-normalize expr))
1026    (calcFunc-rreducer func vec)))
1027
1028(defun calcFunc-reducer (func vec)
1029  (setq func (math-var-to-calcFunc func))
1030  (or (math-vectorp vec)
1031      (math-reject-arg vec 'vectorp))
1032  (let ((expr (car (setq vec (cdr vec)))))
1033    (if expr
1034	(progn
1035	  (condition-case err
1036	      (and (symbolp func)
1037		   (let ((lfunc (or (cdr (assq func
1038					       '( (calcFunc-add . math-add)
1039						  (calcFunc-sub . math-sub)
1040						  (calcFunc-mul . math-mul)
1041						  (calcFunc-div . math-div)
1042						  (calcFunc-pow . math-pow)
1043						  (calcFunc-mod . math-mod)
1044						  (calcFunc-vconcat .
1045						   math-concat) )))
1046				    func)))
1047		     (while (cdr vec)
1048		       (setq expr (funcall lfunc expr (nth 1 vec))
1049			     vec (cdr vec)))))
1050	    (error nil))
1051	  (while (setq vec (cdr vec))
1052	    (setq expr (math-build-call func (list expr (car vec)))))
1053	  (math-normalize expr))
1054      (or (math-identity-value func)
1055	  (math-reject-arg vec "*Vector is empty")))))
1056
1057(defun math-identity-value (func)
1058  (cdr (assq func '( (calcFunc-add . 0) (calcFunc-sub . 0)
1059		     (calcFunc-mul . 1) (calcFunc-div . 1)
1060		     (calcFunc-idiv . 1) (calcFunc-fdiv . 1)
1061		     (calcFunc-min . (var inf var-inf))
1062		     (calcFunc-max . (neg (var inf var-inf)))
1063		     (calcFunc-vconcat . (vec))
1064		     (calcFunc-append . (vec)) ))))
1065
1066(defun calcFunc-rreducer (func vec)
1067  (setq func (math-var-to-calcFunc func))
1068  (or (math-vectorp vec)
1069      (math-reject-arg vec 'vectorp))
1070  (if (eq func 'calcFunc-sub)   ; do this in a way that looks nicer
1071      (let ((expr (car (setq vec (cdr vec)))))
1072	(if expr
1073	    (progn
1074	      (while (setq vec (cdr vec))
1075		(setq expr (math-build-call func (list expr (car vec)))
1076		      func (if (eq func 'calcFunc-sub)
1077			       'calcFunc-add 'calcFunc-sub)))
1078	      (math-normalize expr))
1079	  0))
1080    (let ((expr (car (setq vec (reverse (cdr vec))))))
1081      (if expr
1082	  (progn
1083	    (while (setq vec (cdr vec))
1084	      (setq expr (math-build-call func (list (car vec) expr))))
1085	    (math-normalize expr))
1086	(or (math-identity-value func)
1087	    (math-reject-arg vec "*Vector is empty"))))))
1088
1089(defun calcFunc-reducec (func vec)
1090  (if (math-matrixp vec)
1091      (calcFunc-reducer func (math-transpose vec))
1092    (calcFunc-reducer func vec)))
1093
1094(defun calcFunc-rreducec (func vec)
1095  (if (math-matrixp vec)
1096      (calcFunc-rreducer func (math-transpose vec))
1097    (calcFunc-rreducer func vec)))
1098
1099(defun calcFunc-reducea (func vec)
1100  (if (math-matrixp vec)
1101      (cons 'vec
1102	    (mapcar (function (lambda (x) (calcFunc-reducer func x)))
1103		    (cdr vec)))
1104    (calcFunc-reducer func vec)))
1105
1106(defun calcFunc-rreducea (func vec)
1107  (if (math-matrixp vec)
1108      (cons 'vec
1109	    (mapcar (function (lambda (x) (calcFunc-rreducer func x)))
1110		    (cdr vec)))
1111    (calcFunc-rreducer func vec)))
1112
1113(defun calcFunc-reduced (func vec)
1114  (if (math-matrixp vec)
1115      (cons 'vec
1116	    (mapcar (function (lambda (x) (calcFunc-reducer func x)))
1117		    (cdr (math-transpose vec))))
1118    (calcFunc-reducer func vec)))
1119
1120(defun calcFunc-rreduced (func vec)
1121  (if (math-matrixp vec)
1122      (cons 'vec
1123	    (mapcar (function (lambda (x) (calcFunc-rreducer func x)))
1124		    (cdr (math-transpose vec))))
1125    (calcFunc-rreducer func vec)))
1126
1127(defun calcFunc-accum (func vec)
1128  (setq func (math-var-to-calcFunc func))
1129  (or (math-vectorp vec)
1130      (math-reject-arg vec 'vectorp))
1131  (let* ((expr (car (setq vec (cdr vec))))
1132	 (res (list 'vec expr)))
1133    (or expr
1134	(math-reject-arg vec "*Vector is empty"))
1135    (while (setq vec (cdr vec))
1136      (setq expr (math-build-call func (list expr (car vec)))
1137	    res (nconc res (list expr))))
1138    (math-normalize res)))
1139
1140(defun calcFunc-raccum (func vec)
1141  (setq func (math-var-to-calcFunc func))
1142  (or (math-vectorp vec)
1143      (math-reject-arg vec 'vectorp))
1144  (let* ((expr (car (setq vec (reverse (cdr vec)))))
1145	 (res (list expr)))
1146    (or expr
1147	(math-reject-arg vec "*Vector is empty"))
1148    (while (setq vec (cdr vec))
1149      (setq expr (math-build-call func (list (car vec) expr))
1150	    res (cons (list expr) res)))
1151    (math-normalize (cons 'vec res))))
1152
1153
1154(defun math-nest-calls (func base iters accum tol)
1155  (or (symbolp tol)
1156      (if (math-realp tol)
1157	  (or (math-numberp base) (math-reject-arg base 'numberp))
1158	(math-reject-arg tol 'realp)))
1159  (setq func (math-var-to-calcFunc func))
1160  (or (null iters)
1161      (if (equal iters '(var inf var-inf))
1162	  (setq iters nil)
1163	(progn
1164	  (if (math-messy-integerp iters)
1165	      (setq iters (math-trunc iters)))
1166	  (or (integerp iters) (math-reject-arg iters 'fixnump))
1167	  (or (not tol) (natnump iters) (math-reject-arg iters 'fixnatnump))
1168	  (if (< iters 0)
1169	      (let* ((dummy '(var DummyArg var-DummyArg))
1170		     (dummy2 '(var DummyArg2 var-DummyArg2))
1171		     (finv (math-solve-for (math-build-call func (list dummy2))
1172					   dummy dummy2 nil)))
1173		(or finv (math-reject-arg nil "*Unable to find an inverse"))
1174		(if (and (= (length finv) 2)
1175			 (equal (nth 1 finv) dummy))
1176		    (setq func (car finv))
1177		  (setq func (list 'calcFunc-lambda dummy finv)))
1178		(setq iters (- iters)))))))
1179  (math-with-extra-prec 1
1180    (let ((value base)
1181	  (ovalue nil)
1182	  (avalues (list base))
1183	  (math-working-step 0)
1184	  (math-working-step-2 iters))
1185      (while (and (or (null iters)
1186		      (>= (setq iters (1- iters)) 0))
1187		  (or (null tol)
1188		      (null ovalue)
1189		      (if (eq tol t)
1190			  (not (if (and (Math-numberp value)
1191					(Math-numberp ovalue))
1192				   (math-nearly-equal value ovalue)
1193				 (Math-equal value ovalue)))
1194			(if (math-numberp value)
1195			    (Math-lessp tol (math-abs (math-sub value ovalue)))
1196			  (math-reject-arg value 'numberp)))))
1197	(setq ovalue value
1198	      math-working-step (1+ math-working-step)
1199	      value (math-normalize (math-build-call func (list value))))
1200	(if accum
1201	    (setq avalues (cons value avalues))))
1202      (if accum
1203	  (cons 'vec (nreverse avalues))
1204	value))))
1205
1206(defun calcFunc-nest (func base iters)
1207  (math-nest-calls func base iters nil nil))
1208
1209(defun calcFunc-anest (func base iters)
1210  (math-nest-calls func base iters t nil))
1211
1212(defun calcFunc-fixp (func base &optional iters tol)
1213  (math-nest-calls func base iters nil (or tol t)))
1214
1215(defun calcFunc-afixp (func base &optional iters tol)
1216  (math-nest-calls func base iters t (or tol t)))
1217
1218
1219(defun calcFunc-outer (func a b)
1220  (or (math-vectorp a) (math-reject-arg a 'vectorp))
1221  (or (math-vectorp b) (math-reject-arg b 'vectorp))
1222  (setq func (math-var-to-calcFunc func))
1223  (let ((mat nil))
1224    (while (setq a (cdr a))
1225      (setq mat (cons (cons 'vec
1226			    (mapcar (function (lambda (x)
1227						(math-build-call func
1228								 (list (car a)
1229								       x))))
1230				    (cdr b)))
1231		      mat)))
1232    (math-normalize (cons 'vec (nreverse mat)))))
1233
1234
1235;; The variables math-inner-mul-func and math-inner-add-func are
1236;; local to calcFunc-inner, but are used by math-inner-mats,
1237;; which is called by math-inner-mats.
1238(defvar math-inner-mul-func)
1239(defvar math-inner-add-func)
1240
1241(defun calcFunc-inner (math-inner-mul-func math-inner-add-func a b)
1242  (or (math-vectorp a) (math-reject-arg a 'vectorp))
1243  (or (math-vectorp b) (math-reject-arg b 'vectorp))
1244  (if (math-matrixp a)
1245      (if (math-matrixp b)
1246	  (if (= (length (nth 1 a)) (length b))
1247	      (math-inner-mats a b)
1248	    (math-dimension-error))
1249	(if (= (length (nth 1 a)) 2)
1250	    (if (= (length a) (length b))
1251		(math-inner-mats a (list 'vec b))
1252	      (math-dimension-error))
1253	  (if (= (length (nth 1 a)) (length b))
1254	      (math-mat-col (math-inner-mats a (math-col-matrix b))
1255			    1)
1256	    (math-dimension-error))))
1257    (if (math-matrixp b)
1258	(nth 1 (math-inner-mats (list 'vec a) b))
1259      (calcFunc-reduce math-inner-add-func (calcFunc-map math-inner-mul-func a b)))))
1260
1261(defun math-inner-mats (a b)
1262  (let ((mat nil)
1263	(cols (length (nth 1 b)))
1264	row col ap bp accum)
1265    (while (setq a (cdr a))
1266      (setq col cols
1267	    row nil)
1268      (while (> (setq col (1- col)) 0)
1269	(setq row (cons (calcFunc-reduce math-inner-add-func
1270					 (calcFunc-map math-inner-mul-func
1271						       (car a)
1272						       (math-mat-col b col)))
1273			row)))
1274      (setq mat (cons (cons 'vec row) mat)))
1275    (cons 'vec (nreverse mat))))
1276
1277(provide 'calc-map)
1278
1279;;; arch-tag: 980eac49-00e0-4870-b72a-e726b74c7990
1280;;; calc-map.el ends here
1281