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3132f345 CW |
1 | ;;; calc-vec.el --- vector functions for Calc |
2 | ||
bf77c646 | 3 | ;; Copyright (C) 1990, 1991, 1992, 1993, 2001 Free Software Foundation, Inc. |
3132f345 CW |
4 | |
5 | ;; Author: David Gillespie <daveg@synaptics.com> | |
a1506d29 | 6 | ;; Maintainers: D. Goel <deego@gnufans.org> |
6e1c888a | 7 | ;; Colin Walters <walters@debian.org> |
136211a9 EZ |
8 | |
9 | ;; This file is part of GNU Emacs. | |
10 | ||
11 | ;; GNU Emacs is distributed in the hope that it will be useful, | |
12 | ;; but WITHOUT ANY WARRANTY. No author or distributor | |
13 | ;; accepts responsibility to anyone for the consequences of using it | |
14 | ;; or for whether it serves any particular purpose or works at all, | |
15 | ;; unless he says so in writing. Refer to the GNU Emacs General Public | |
16 | ;; License for full details. | |
17 | ||
18 | ;; Everyone is granted permission to copy, modify and redistribute | |
19 | ;; GNU Emacs, but only under the conditions described in the | |
20 | ;; GNU Emacs General Public License. A copy of this license is | |
21 | ;; supposed to have been given to you along with GNU Emacs so you | |
22 | ;; can know your rights and responsibilities. It should be in a | |
23 | ;; file named COPYING. Among other things, the copyright notice | |
24 | ;; and this notice must be preserved on all copies. | |
25 | ||
3132f345 | 26 | ;;; Commentary: |
136211a9 | 27 | |
3132f345 | 28 | ;;; Code: |
136211a9 EZ |
29 | |
30 | ;; This file is autoloaded from calc-ext.el. | |
31 | (require 'calc-ext) | |
32 | ||
33 | (require 'calc-macs) | |
34 | ||
35 | (defun calc-Need-calc-vec () nil) | |
36 | ||
37 | ||
38 | (defun calc-display-strings (n) | |
39 | (interactive "P") | |
40 | (calc-wrapper | |
41 | (message (if (calc-change-mode 'calc-display-strings n t t) | |
3132f345 CW |
42 | "Displaying vectors of integers as quoted strings" |
43 | "Displaying vectors of integers normally")))) | |
136211a9 EZ |
44 | |
45 | ||
46 | (defun calc-pack (n) | |
47 | (interactive "P") | |
48 | (calc-wrapper | |
49 | (let* ((nn (if n 1 2)) | |
50 | (mode (if n (prefix-numeric-value n) (calc-top-n 1))) | |
51 | (mode (if (and (Math-vectorp mode) (cdr mode)) (cdr mode) | |
52 | (if (integerp mode) mode | |
53 | (error "Packing mode must be an integer or vector of integers")))) | |
54 | (num (calc-pack-size mode)) | |
55 | (items (calc-top-list num nn))) | |
bf77c646 | 56 | (calc-enter-result (+ nn num -1) "pack" (calc-pack-items mode items))))) |
136211a9 EZ |
57 | |
58 | (defun calc-pack-size (mode) | |
59 | (cond ((consp mode) | |
60 | (let ((size 1)) | |
61 | (while mode | |
62 | (or (integerp (car mode)) (error "Vector of integers expected")) | |
63 | (setq size (* size (calc-pack-size (car mode))) | |
64 | mode (cdr mode))) | |
65 | (if (= size 0) | |
66 | (error "Zero dimensions not allowed") | |
67 | size))) | |
68 | ((>= mode 0) mode) | |
69 | (t (or (cdr (assq mode '((-3 . 3) (-13 . 1) (-14 . 3) (-15 . 6)))) | |
bf77c646 | 70 | 2)))) |
136211a9 EZ |
71 | |
72 | (defun calc-pack-items (mode items) | |
73 | (cond ((consp mode) | |
74 | (if (cdr mode) | |
75 | (let* ((size (calc-pack-size (cdr mode))) | |
76 | (len (length items)) | |
77 | (new nil) | |
78 | p row) | |
79 | (while (> len 0) | |
80 | (setq p (nthcdr (1- size) items) | |
81 | row items | |
82 | items (cdr p) | |
83 | len (- len size)) | |
84 | (setcdr p nil) | |
85 | (setq new (cons (calc-pack-items (cdr mode) row) new))) | |
86 | (calc-pack-items (car mode) (nreverse new))) | |
87 | (calc-pack-items (car mode) items))) | |
88 | ((>= mode 0) | |
89 | (cons 'vec items)) | |
90 | ((= mode -3) | |
91 | (if (and (math-objvecp (car items)) | |
92 | (math-objvecp (nth 1 items)) | |
93 | (math-objvecp (nth 2 items))) | |
94 | (if (and (math-num-integerp (car items)) | |
95 | (math-num-integerp (nth 1 items))) | |
96 | (if (math-realp (nth 2 items)) | |
97 | (cons 'hms items) | |
98 | (error "Seconds must be real")) | |
99 | (error "Hours and minutes must be integers")) | |
100 | (math-normalize (list '+ | |
101 | (list '+ | |
102 | (if (eq calc-angle-mode 'rad) | |
103 | (list '* (car items) | |
104 | '(hms 1 0 0)) | |
105 | (car items)) | |
106 | (list '* (nth 1 items) '(hms 0 1 0))) | |
107 | (list '* (nth 2 items) '(hms 0 0 1)))))) | |
108 | ((= mode -13) | |
109 | (if (math-realp (car items)) | |
110 | (cons 'date items) | |
111 | (if (eq (car-safe (car items)) 'date) | |
112 | (car items) | |
113 | (if (math-objvecp (car items)) | |
114 | (error "Date value must be real") | |
115 | (cons 'calcFunc-date items))))) | |
116 | ((memq mode '(-14 -15)) | |
117 | (let ((p items)) | |
118 | (while (and p (math-objvecp (car p))) | |
119 | (or (math-integerp (car p)) | |
120 | (error "Components must be integers")) | |
121 | (setq p (cdr p))) | |
122 | (if p | |
123 | (cons 'calcFunc-date items) | |
124 | (list 'date (math-dt-to-date items))))) | |
125 | ((or (eq (car-safe (car items)) 'vec) | |
126 | (eq (car-safe (nth 1 items)) 'vec)) | |
127 | (let* ((x (car items)) | |
128 | (vx (eq (car-safe x) 'vec)) | |
129 | (y (nth 1 items)) | |
130 | (vy (eq (car-safe y) 'vec)) | |
131 | (z nil) | |
132 | (n (1- (length (if vx x y))))) | |
133 | (and vx vy | |
134 | (/= n (1- (length y))) | |
135 | (error "Vectors must be the same length")) | |
136 | (while (>= (setq n (1- n)) 0) | |
137 | (setq z (cons (calc-pack-items | |
138 | mode | |
139 | (list (if vx (car (setq x (cdr x))) x) | |
140 | (if vy (car (setq y (cdr y))) y))) | |
141 | z))) | |
142 | (cons 'vec (nreverse z)))) | |
143 | ((= mode -1) | |
144 | (if (and (math-realp (car items)) (math-realp (nth 1 items))) | |
145 | (cons 'cplx items) | |
146 | (if (and (math-objectp (car items)) (math-objectp (nth 1 items))) | |
147 | (error "Components must be real")) | |
148 | (math-normalize (list '+ (car items) | |
149 | (list '* (nth 1 items) '(cplx 0 1)))))) | |
150 | ((= mode -2) | |
151 | (if (and (math-realp (car items)) (math-anglep (nth 1 items))) | |
152 | (cons 'polar items) | |
153 | (if (and (math-objectp (car items)) (math-objectp (nth 1 items))) | |
154 | (error "Components must be real")) | |
155 | (math-normalize (list '* (car items) | |
156 | (if (math-anglep (nth 1 items)) | |
157 | (list 'polar 1 (nth 1 items)) | |
158 | (list 'calcFunc-exp | |
159 | (list '* | |
160 | (math-to-radians-2 | |
161 | (nth 1 items)) | |
162 | (list 'polar | |
163 | 1 | |
164 | (math-quarter-circle | |
165 | nil))))))))) | |
166 | ((= mode -4) | |
167 | (let ((x (car items)) | |
168 | (sigma (nth 1 items))) | |
169 | (if (or (math-scalarp x) (not (math-objvecp x))) | |
170 | (if (or (math-anglep sigma) (not (math-objvecp sigma))) | |
171 | (math-make-sdev x sigma) | |
172 | (error "Error component must be real")) | |
173 | (error "Mean component must be real or complex")))) | |
174 | ((= mode -5) | |
175 | (let ((a (car items)) | |
176 | (m (nth 1 items))) | |
177 | (if (and (math-anglep a) (math-anglep m)) | |
178 | (if (math-posp m) | |
179 | (math-make-mod a m) | |
180 | (error "Modulus must be positive")) | |
181 | (if (and (math-objectp a) (math-objectp m)) | |
182 | (error "Components must be real")) | |
183 | (list 'calcFunc-makemod a m)))) | |
184 | ((memq mode '(-6 -7 -8 -9)) | |
185 | (let ((lo (car items)) | |
186 | (hi (nth 1 items))) | |
187 | (if (and (or (math-anglep lo) (eq (car lo) 'date) | |
188 | (not (math-objvecp lo))) | |
189 | (or (math-anglep hi) (eq (car hi) 'date) | |
190 | (not (math-objvecp hi)))) | |
191 | (math-make-intv (+ mode 9) lo hi) | |
192 | (error "Components must be real")))) | |
193 | ((eq mode -10) | |
194 | (if (math-zerop (nth 1 items)) | |
195 | (error "Denominator must not be zero") | |
196 | (if (and (math-integerp (car items)) (math-integerp (nth 1 items))) | |
197 | (math-normalize (cons 'frac items)) | |
198 | (if (and (math-objectp (car items)) (math-objectp (nth 1 items))) | |
199 | (error "Components must be integers")) | |
200 | (cons 'calcFunc-fdiv items)))) | |
201 | ((memq mode '(-11 -12)) | |
202 | (if (and (math-realp (car items)) (math-integerp (nth 1 items))) | |
203 | (calcFunc-scf (math-float (car items)) (nth 1 items)) | |
204 | (if (and (math-objectp (car items)) (math-objectp (nth 1 items))) | |
205 | (error "Components must be integers")) | |
206 | (math-normalize | |
207 | (list 'calcFunc-scf | |
208 | (list 'calcFunc-float (car items)) | |
209 | (nth 1 items))))) | |
210 | (t | |
bf77c646 | 211 | (error "Invalid packing mode: %d" mode)))) |
136211a9 | 212 | |
3132f345 | 213 | (defvar calc-unpack-with-type nil) |
136211a9 EZ |
214 | (defun calc-unpack (mode) |
215 | (interactive "P") | |
216 | (calc-wrapper | |
217 | (let ((calc-unpack-with-type t)) | |
218 | (calc-pop-push-record-list 1 "unpk" (calc-unpack-item | |
219 | (and mode | |
220 | (prefix-numeric-value mode)) | |
bf77c646 | 221 | (calc-top)))))) |
136211a9 EZ |
222 | |
223 | (defun calc-unpack-type (item) | |
224 | (cond ((eq (car-safe item) 'vec) | |
225 | (1- (length item))) | |
226 | ((eq (car-safe item) 'intv) | |
227 | (- (nth 1 item) 9)) | |
228 | (t | |
229 | (or (cdr (assq (car-safe item) '( (cplx . -1) (polar . -2) | |
230 | (hms . -3) (sdev . -4) (mod . -5) | |
231 | (frac . -10) (float . -11) | |
232 | (date . -13) ))) | |
bf77c646 | 233 | (error "Argument must be a composite object"))))) |
136211a9 EZ |
234 | |
235 | (defun calc-unpack-item (mode item) | |
236 | (cond ((not mode) | |
237 | (if (or (and (not (memq (car-safe item) '(frac float cplx polar vec | |
238 | hms date sdev mod | |
239 | intv))) | |
240 | (math-objvecp item)) | |
241 | (eq (car-safe item) 'var)) | |
242 | (error "Argument must be a composite object or function call")) | |
243 | (if (eq (car item) 'intv) | |
244 | (cdr (cdr item)) | |
245 | (cdr item))) | |
246 | ((> mode 0) | |
247 | (let ((dims nil) | |
248 | type new row) | |
249 | (setq item (list item)) | |
250 | (while (> mode 0) | |
251 | (setq type (calc-unpack-type (car item)) | |
252 | dims (cons type dims) | |
253 | new (calc-unpack-item nil (car item))) | |
254 | (while (setq item (cdr item)) | |
255 | (or (= (calc-unpack-type (car item)) type) | |
256 | (error "Inconsistent types or dimensions in vector elements")) | |
257 | (setq new (append new (calc-unpack-item nil (car item))))) | |
258 | (setq item new | |
259 | mode (1- mode))) | |
260 | (if (cdr dims) (setq dims (list (cons 'vec (nreverse dims))))) | |
261 | (cond ((eq calc-unpack-with-type 'pair) | |
262 | (list (car dims) (cons 'vec item))) | |
263 | (calc-unpack-with-type | |
264 | (append item dims)) | |
265 | (t item)))) | |
266 | ((eq calc-unpack-with-type 'pair) | |
267 | (let ((calc-unpack-with-type nil)) | |
268 | (list mode (cons 'vec (calc-unpack-item mode item))))) | |
269 | ((= mode -3) | |
270 | (if (eq (car-safe item) 'hms) | |
271 | (cdr item) | |
272 | (error "Argument must be an HMS form"))) | |
273 | ((= mode -13) | |
274 | (if (eq (car-safe item) 'date) | |
275 | (cdr item) | |
276 | (error "Argument must be a date form"))) | |
277 | ((= mode -14) | |
278 | (if (eq (car-safe item) 'date) | |
279 | (math-date-to-dt (math-floor (nth 1 item))) | |
280 | (error "Argument must be a date form"))) | |
281 | ((= mode -15) | |
282 | (if (eq (car-safe item) 'date) | |
283 | (append (math-date-to-dt (nth 1 item)) | |
284 | (and (not (math-integerp (nth 1 item))) | |
285 | (list 0 0 0))) | |
286 | (error "Argument must be a date form"))) | |
287 | ((eq (car-safe item) 'vec) | |
288 | (let ((x nil) | |
289 | (y nil) | |
290 | res) | |
291 | (while (setq item (cdr item)) | |
292 | (setq res (calc-unpack-item mode (car item)) | |
293 | x (cons (car res) x) | |
294 | y (cons (nth 1 res) y))) | |
295 | (list (cons 'vec (nreverse x)) | |
296 | (cons 'vec (nreverse y))))) | |
297 | ((= mode -1) | |
298 | (if (eq (car-safe item) 'cplx) | |
299 | (cdr item) | |
300 | (if (eq (car-safe item) 'polar) | |
301 | (cdr (math-complex item)) | |
302 | (if (Math-realp item) | |
303 | (list item 0) | |
304 | (error "Argument must be a complex number"))))) | |
305 | ((= mode -2) | |
306 | (if (or (memq (car-safe item) '(cplx polar)) | |
307 | (Math-realp item)) | |
308 | (cdr (math-polar item)) | |
309 | (error "Argument must be a complex number"))) | |
310 | ((= mode -4) | |
311 | (if (eq (car-safe item) 'sdev) | |
312 | (cdr item) | |
313 | (list item 0))) | |
314 | ((= mode -5) | |
315 | (if (eq (car-safe item) 'mod) | |
316 | (cdr item) | |
317 | (error "Argument must be a modulo form"))) | |
318 | ((memq mode '(-6 -7 -8 -9)) | |
319 | (if (eq (car-safe item) 'intv) | |
320 | (cdr (cdr item)) | |
321 | (list item item))) | |
322 | ((= mode -10) | |
323 | (if (eq (car-safe item) 'frac) | |
324 | (cdr item) | |
325 | (if (Math-integerp item) | |
326 | (list item 1) | |
327 | (error "Argument must be a rational number")))) | |
328 | ((= mode -11) | |
329 | (if (eq (car-safe item) 'float) | |
330 | (list (nth 1 item) (math-normalize (nth 2 item))) | |
331 | (error "Expected a floating-point number"))) | |
332 | ((= mode -12) | |
333 | (if (eq (car-safe item) 'float) | |
334 | (list (calcFunc-mant item) (calcFunc-xpon item)) | |
335 | (error "Expected a floating-point number"))) | |
336 | (t | |
bf77c646 | 337 | (error "Invalid unpacking mode: %d" mode)))) |
136211a9 EZ |
338 | |
339 | (defun calc-diag (n) | |
340 | (interactive "P") | |
341 | (calc-wrapper | |
342 | (calc-enter-result 1 "diag" (if n | |
343 | (list 'calcFunc-diag (calc-top-n 1) | |
344 | (prefix-numeric-value n)) | |
bf77c646 | 345 | (list 'calcFunc-diag (calc-top-n 1)))))) |
136211a9 EZ |
346 | |
347 | (defun calc-ident (n) | |
348 | (interactive "NDimension of identity matrix = ") | |
349 | (calc-wrapper | |
350 | (calc-enter-result 0 "idn" (if (eq n 0) | |
351 | '(calcFunc-idn 1) | |
352 | (list 'calcFunc-idn 1 | |
bf77c646 | 353 | (prefix-numeric-value n)))))) |
136211a9 EZ |
354 | |
355 | (defun calc-index (n &optional stack) | |
356 | (interactive "NSize of vector = \nP") | |
357 | (calc-wrapper | |
358 | (if (consp stack) | |
359 | (calc-enter-result 3 "indx" (cons 'calcFunc-index (calc-top-list-n 3))) | |
360 | (calc-enter-result 0 "indx" (list 'calcFunc-index | |
bf77c646 | 361 | (prefix-numeric-value n)))))) |
136211a9 EZ |
362 | |
363 | (defun calc-build-vector (n) | |
364 | (interactive "NSize of vector = ") | |
365 | (calc-wrapper | |
366 | (calc-enter-result 1 "bldv" (list 'calcFunc-cvec | |
367 | (calc-top-n 1) | |
bf77c646 | 368 | (prefix-numeric-value n))))) |
136211a9 EZ |
369 | |
370 | (defun calc-cons (arg) | |
371 | (interactive "P") | |
372 | (calc-wrapper | |
373 | (if (calc-is-hyperbolic) | |
374 | (calc-binary-op "rcns" 'calcFunc-rcons arg) | |
bf77c646 | 375 | (calc-binary-op "cons" 'calcFunc-cons arg)))) |
136211a9 EZ |
376 | |
377 | ||
378 | (defun calc-head (arg) | |
379 | (interactive "P") | |
380 | (calc-wrapper | |
381 | (if (calc-is-inverse) | |
382 | (if (calc-is-hyperbolic) | |
383 | (calc-unary-op "rtai" 'calcFunc-rtail arg) | |
384 | (calc-unary-op "tail" 'calcFunc-tail arg)) | |
385 | (if (calc-is-hyperbolic) | |
386 | (calc-unary-op "rhed" 'calcFunc-rhead arg) | |
bf77c646 | 387 | (calc-unary-op "head" 'calcFunc-head arg))))) |
136211a9 EZ |
388 | |
389 | (defun calc-tail (arg) | |
390 | (interactive "P") | |
391 | (calc-invert-func) | |
bf77c646 | 392 | (calc-head arg)) |
136211a9 EZ |
393 | |
394 | (defun calc-vlength (arg) | |
395 | (interactive "P") | |
396 | (calc-wrapper | |
397 | (if (calc-is-hyperbolic) | |
398 | (calc-unary-op "dims" 'calcFunc-mdims arg) | |
bf77c646 | 399 | (calc-unary-op "len" 'calcFunc-vlen arg)))) |
136211a9 EZ |
400 | |
401 | (defun calc-arrange-vector (n) | |
402 | (interactive "NNumber of columns = ") | |
403 | (calc-wrapper | |
404 | (calc-enter-result 1 "arng" (list 'calcFunc-arrange (calc-top-n 1) | |
bf77c646 | 405 | (prefix-numeric-value n))))) |
136211a9 EZ |
406 | |
407 | (defun calc-vector-find (arg) | |
408 | (interactive "P") | |
409 | (calc-wrapper | |
410 | (let ((func (cons 'calcFunc-find (calc-top-list-n 2)))) | |
411 | (calc-enter-result | |
412 | 2 "find" | |
bf77c646 | 413 | (if arg (append func (list (prefix-numeric-value arg))) func))))) |
136211a9 EZ |
414 | |
415 | (defun calc-subvector () | |
416 | (interactive) | |
417 | (calc-wrapper | |
418 | (if (calc-is-inverse) | |
419 | (calc-enter-result 3 "rsvc" (cons 'calcFunc-rsubvec | |
420 | (calc-top-list-n 3))) | |
bf77c646 | 421 | (calc-enter-result 3 "svec" (cons 'calcFunc-subvec (calc-top-list-n 3)))))) |
136211a9 EZ |
422 | |
423 | (defun calc-reverse-vector (arg) | |
424 | (interactive "P") | |
425 | (calc-wrapper | |
bf77c646 | 426 | (calc-unary-op "rev" 'calcFunc-rev arg))) |
136211a9 EZ |
427 | |
428 | (defun calc-mask-vector (arg) | |
429 | (interactive "P") | |
430 | (calc-wrapper | |
bf77c646 | 431 | (calc-binary-op "vmsk" 'calcFunc-vmask arg))) |
136211a9 EZ |
432 | |
433 | (defun calc-expand-vector (arg) | |
434 | (interactive "P") | |
435 | (calc-wrapper | |
436 | (if (calc-is-hyperbolic) | |
437 | (calc-enter-result 3 "vexp" (cons 'calcFunc-vexp (calc-top-list-n 3))) | |
bf77c646 | 438 | (calc-binary-op "vexp" 'calcFunc-vexp arg)))) |
136211a9 EZ |
439 | |
440 | (defun calc-sort () | |
441 | (interactive) | |
442 | (calc-slow-wrapper | |
443 | (if (calc-is-inverse) | |
444 | (calc-enter-result 1 "rsrt" (list 'calcFunc-rsort (calc-top-n 1))) | |
bf77c646 | 445 | (calc-enter-result 1 "sort" (list 'calcFunc-sort (calc-top-n 1)))))) |
136211a9 EZ |
446 | |
447 | (defun calc-grade () | |
448 | (interactive) | |
449 | (calc-slow-wrapper | |
450 | (if (calc-is-inverse) | |
451 | (calc-enter-result 1 "rgrd" (list 'calcFunc-rgrade (calc-top-n 1))) | |
bf77c646 | 452 | (calc-enter-result 1 "grad" (list 'calcFunc-grade (calc-top-n 1)))))) |
136211a9 EZ |
453 | |
454 | (defun calc-histogram (n) | |
455 | (interactive "NNumber of bins: ") | |
456 | (calc-slow-wrapper | |
457 | (if calc-hyperbolic-flag | |
458 | (calc-enter-result 2 "hist" (list 'calcFunc-histogram | |
459 | (calc-top-n 2) | |
460 | (calc-top-n 1) | |
461 | (prefix-numeric-value n))) | |
462 | (calc-enter-result 1 "hist" (list 'calcFunc-histogram | |
463 | (calc-top-n 1) | |
bf77c646 | 464 | (prefix-numeric-value n)))))) |
136211a9 EZ |
465 | |
466 | (defun calc-transpose (arg) | |
467 | (interactive "P") | |
468 | (calc-wrapper | |
bf77c646 | 469 | (calc-unary-op "trn" 'calcFunc-trn arg))) |
136211a9 EZ |
470 | |
471 | (defun calc-conj-transpose (arg) | |
472 | (interactive "P") | |
473 | (calc-wrapper | |
bf77c646 | 474 | (calc-unary-op "ctrn" 'calcFunc-ctrn arg))) |
136211a9 EZ |
475 | |
476 | (defun calc-cross (arg) | |
477 | (interactive "P") | |
478 | (calc-wrapper | |
bf77c646 | 479 | (calc-binary-op "cros" 'calcFunc-cross arg))) |
136211a9 EZ |
480 | |
481 | (defun calc-remove-duplicates (arg) | |
482 | (interactive "P") | |
483 | (calc-wrapper | |
bf77c646 | 484 | (calc-unary-op "rdup" 'calcFunc-rdup arg))) |
136211a9 EZ |
485 | |
486 | (defun calc-set-union (arg) | |
487 | (interactive "P") | |
488 | (calc-wrapper | |
bf77c646 | 489 | (calc-binary-op "unio" 'calcFunc-vunion arg '(vec) 'calcFunc-rdup))) |
136211a9 EZ |
490 | |
491 | (defun calc-set-intersect (arg) | |
492 | (interactive "P") | |
493 | (calc-wrapper | |
bf77c646 | 494 | (calc-binary-op "intr" 'calcFunc-vint arg '(vec) 'calcFunc-rdup))) |
136211a9 EZ |
495 | |
496 | (defun calc-set-difference (arg) | |
497 | (interactive "P") | |
498 | (calc-wrapper | |
bf77c646 | 499 | (calc-binary-op "diff" 'calcFunc-vdiff arg '(vec) 'calcFunc-rdup))) |
136211a9 EZ |
500 | |
501 | (defun calc-set-xor (arg) | |
502 | (interactive "P") | |
503 | (calc-wrapper | |
bf77c646 | 504 | (calc-binary-op "xor" 'calcFunc-vxor arg '(vec) 'calcFunc-rdup))) |
136211a9 EZ |
505 | |
506 | (defun calc-set-complement (arg) | |
507 | (interactive "P") | |
508 | (calc-wrapper | |
bf77c646 | 509 | (calc-unary-op "cmpl" 'calcFunc-vcompl arg))) |
136211a9 EZ |
510 | |
511 | (defun calc-set-floor (arg) | |
512 | (interactive "P") | |
513 | (calc-wrapper | |
bf77c646 | 514 | (calc-unary-op "vflr" 'calcFunc-vfloor arg))) |
136211a9 EZ |
515 | |
516 | (defun calc-set-enumerate (arg) | |
517 | (interactive "P") | |
518 | (calc-wrapper | |
bf77c646 | 519 | (calc-unary-op "enum" 'calcFunc-venum arg))) |
136211a9 EZ |
520 | |
521 | (defun calc-set-span (arg) | |
522 | (interactive "P") | |
523 | (calc-wrapper | |
bf77c646 | 524 | (calc-unary-op "span" 'calcFunc-vspan arg))) |
136211a9 EZ |
525 | |
526 | (defun calc-set-cardinality (arg) | |
527 | (interactive "P") | |
528 | (calc-wrapper | |
bf77c646 | 529 | (calc-unary-op "card" 'calcFunc-vcard arg))) |
136211a9 EZ |
530 | |
531 | (defun calc-unpack-bits (arg) | |
532 | (interactive "P") | |
533 | (calc-wrapper | |
534 | (if (calc-is-inverse) | |
535 | (calc-unary-op "bpck" 'calcFunc-vpack arg) | |
bf77c646 | 536 | (calc-unary-op "bupk" 'calcFunc-vunpack arg)))) |
136211a9 EZ |
537 | |
538 | (defun calc-pack-bits (arg) | |
539 | (interactive "P") | |
540 | (calc-invert-func) | |
bf77c646 | 541 | (calc-unpack-bits arg)) |
136211a9 EZ |
542 | |
543 | ||
544 | (defun calc-rnorm (arg) | |
545 | (interactive "P") | |
546 | (calc-wrapper | |
bf77c646 | 547 | (calc-unary-op "rnrm" 'calcFunc-rnorm arg))) |
136211a9 EZ |
548 | |
549 | (defun calc-cnorm (arg) | |
550 | (interactive "P") | |
551 | (calc-wrapper | |
bf77c646 | 552 | (calc-unary-op "cnrm" 'calcFunc-cnorm arg))) |
136211a9 EZ |
553 | |
554 | (defun calc-mrow (n &optional nn) | |
555 | (interactive "NRow number: \nP") | |
556 | (calc-wrapper | |
557 | (if (consp nn) | |
558 | (calc-enter-result 2 "mrow" (cons 'calcFunc-mrow (calc-top-list-n 2))) | |
559 | (setq n (prefix-numeric-value n)) | |
560 | (if (= n 0) | |
561 | (calc-enter-result 1 "getd" (list 'calcFunc-getdiag (calc-top-n 1))) | |
562 | (if (< n 0) | |
563 | (calc-enter-result 1 "rrow" (list 'calcFunc-mrrow | |
564 | (calc-top-n 1) (- n))) | |
565 | (calc-enter-result 1 "mrow" (list 'calcFunc-mrow | |
bf77c646 | 566 | (calc-top-n 1) n))))))) |
136211a9 EZ |
567 | |
568 | (defun calc-mcol (n &optional nn) | |
569 | (interactive "NColumn number: \nP") | |
570 | (calc-wrapper | |
571 | (if (consp nn) | |
572 | (calc-enter-result 2 "mcol" (cons 'calcFunc-mcol (calc-top-list-n 2))) | |
573 | (setq n (prefix-numeric-value n)) | |
574 | (if (= n 0) | |
575 | (calc-enter-result 1 "getd" (list 'calcFunc-getdiag (calc-top-n 1))) | |
576 | (if (< n 0) | |
577 | (calc-enter-result 1 "rcol" (list 'calcFunc-mrcol | |
578 | (calc-top-n 1) (- n))) | |
579 | (calc-enter-result 1 "mcol" (list 'calcFunc-mcol | |
bf77c646 | 580 | (calc-top-n 1) n))))))) |
136211a9 EZ |
581 | |
582 | ||
583 | ;;;; Vectors. | |
584 | ||
585 | (defun calcFunc-mdims (m) | |
586 | (or (math-vectorp m) | |
587 | (math-reject-arg m 'vectorp)) | |
bf77c646 | 588 | (cons 'vec (math-mat-dimens m))) |
136211a9 EZ |
589 | |
590 | ||
591 | ;;; Apply a function elementwise to vector A. [V X V; N X N] [Public] | |
592 | (defun math-map-vec (f a) | |
593 | (if (math-vectorp a) | |
594 | (cons 'vec (mapcar f (cdr a))) | |
bf77c646 | 595 | (funcall f a))) |
136211a9 EZ |
596 | |
597 | (defun math-dimension-error () | |
598 | (calc-record-why "*Dimension error") | |
bf77c646 | 599 | (signal 'wrong-type-argument nil)) |
136211a9 EZ |
600 | |
601 | ||
602 | ;;; Build a vector out of a list of objects. [Public] | |
603 | (defun calcFunc-vec (&rest objs) | |
bf77c646 | 604 | (cons 'vec objs)) |
136211a9 EZ |
605 | |
606 | ||
607 | ;;; Build a constant vector or matrix. [Public] | |
608 | (defun calcFunc-cvec (obj &rest dims) | |
bf77c646 | 609 | (math-make-vec-dimen obj dims)) |
136211a9 EZ |
610 | |
611 | (defun math-make-vec-dimen (obj dims) | |
612 | (if dims | |
613 | (if (natnump (car dims)) | |
614 | (if (or (cdr dims) | |
615 | (not (math-numberp obj))) | |
616 | (cons 'vec (copy-sequence | |
617 | (make-list (car dims) | |
618 | (math-make-vec-dimen obj (cdr dims))))) | |
619 | (cons 'vec (make-list (car dims) obj))) | |
620 | (math-reject-arg (car dims) 'fixnatnump)) | |
bf77c646 | 621 | obj)) |
136211a9 EZ |
622 | |
623 | (defun calcFunc-head (vec) | |
624 | (if (and (Math-vectorp vec) | |
625 | (cdr vec)) | |
626 | (nth 1 vec) | |
627 | (calc-record-why 'vectorp vec) | |
bf77c646 | 628 | (list 'calcFunc-head vec))) |
136211a9 EZ |
629 | |
630 | (defun calcFunc-tail (vec) | |
631 | (if (and (Math-vectorp vec) | |
632 | (cdr vec)) | |
633 | (cons 'vec (cdr (cdr vec))) | |
634 | (calc-record-why 'vectorp vec) | |
bf77c646 | 635 | (list 'calcFunc-tail vec))) |
136211a9 EZ |
636 | |
637 | (defun calcFunc-cons (head tail) | |
638 | (if (Math-vectorp tail) | |
639 | (cons 'vec (cons head (cdr tail))) | |
640 | (calc-record-why 'vectorp tail) | |
bf77c646 | 641 | (list 'calcFunc-cons head tail))) |
136211a9 EZ |
642 | |
643 | (defun calcFunc-rhead (vec) | |
644 | (if (and (Math-vectorp vec) | |
645 | (cdr vec)) | |
646 | (let ((vec (copy-sequence vec))) | |
647 | (setcdr (nthcdr (- (length vec) 2) vec) nil) | |
648 | vec) | |
649 | (calc-record-why 'vectorp vec) | |
bf77c646 | 650 | (list 'calcFunc-rhead vec))) |
136211a9 EZ |
651 | |
652 | (defun calcFunc-rtail (vec) | |
653 | (if (and (Math-vectorp vec) | |
654 | (cdr vec)) | |
655 | (nth (1- (length vec)) vec) | |
656 | (calc-record-why 'vectorp vec) | |
bf77c646 | 657 | (list 'calcFunc-rtail vec))) |
136211a9 EZ |
658 | |
659 | (defun calcFunc-rcons (head tail) | |
660 | (if (Math-vectorp head) | |
661 | (append head (list tail)) | |
662 | (calc-record-why 'vectorp head) | |
bf77c646 | 663 | (list 'calcFunc-rcons head tail))) |
136211a9 EZ |
664 | |
665 | ||
666 | ||
667 | ;;; Apply a function elementwise to vectors A and B. [O X O O] [Public] | |
668 | (defun math-map-vec-2 (f a b) | |
669 | (if (math-vectorp a) | |
670 | (if (math-vectorp b) | |
671 | (let ((v nil)) | |
672 | (while (setq a (cdr a)) | |
673 | (or (setq b (cdr b)) | |
674 | (math-dimension-error)) | |
675 | (setq v (cons (funcall f (car a) (car b)) v))) | |
676 | (if a (math-dimension-error)) | |
677 | (cons 'vec (nreverse v))) | |
678 | (let ((v nil)) | |
679 | (while (setq a (cdr a)) | |
680 | (setq v (cons (funcall f (car a) b) v))) | |
681 | (cons 'vec (nreverse v)))) | |
682 | (if (math-vectorp b) | |
683 | (let ((v nil)) | |
684 | (while (setq b (cdr b)) | |
685 | (setq v (cons (funcall f a (car b)) v))) | |
686 | (cons 'vec (nreverse v))) | |
bf77c646 | 687 | (funcall f a b)))) |
136211a9 EZ |
688 | |
689 | ||
690 | ||
691 | ;;; "Reduce" a function over a vector (left-associatively). [O X V] [Public] | |
692 | (defun math-reduce-vec (f a) | |
693 | (if (math-vectorp a) | |
694 | (if (cdr a) | |
695 | (let ((accum (car (setq a (cdr a))))) | |
696 | (while (setq a (cdr a)) | |
697 | (setq accum (funcall f accum (car a)))) | |
698 | accum) | |
699 | 0) | |
bf77c646 | 700 | a)) |
136211a9 EZ |
701 | |
702 | ;;; Reduce a function over the columns of matrix A. [V X V] [Public] | |
703 | (defun math-reduce-cols (f a) | |
704 | (if (math-matrixp a) | |
705 | (cons 'vec (math-reduce-cols-col-step f (cdr a) 1 (length (nth 1 a)))) | |
bf77c646 | 706 | a)) |
136211a9 EZ |
707 | |
708 | (defun math-reduce-cols-col-step (f a col cols) | |
709 | (and (< col cols) | |
710 | (cons (math-reduce-cols-row-step f (nth col (car a)) col (cdr a)) | |
bf77c646 | 711 | (math-reduce-cols-col-step f a (1+ col) cols)))) |
136211a9 EZ |
712 | |
713 | (defun math-reduce-cols-row-step (f tot col a) | |
714 | (if a | |
715 | (math-reduce-cols-row-step f | |
716 | (funcall f tot (nth col (car a))) | |
717 | col | |
718 | (cdr a)) | |
bf77c646 | 719 | tot)) |
136211a9 EZ |
720 | |
721 | ||
722 | ||
723 | (defun math-dot-product (a b) | |
724 | (if (setq a (cdr a) b (cdr b)) | |
725 | (let ((accum (math-mul (car a) (car b)))) | |
726 | (while (setq a (cdr a) b (cdr b)) | |
727 | (setq accum (math-add accum (math-mul (car a) (car b))))) | |
728 | accum) | |
bf77c646 | 729 | 0)) |
136211a9 EZ |
730 | |
731 | ||
732 | ;;; Return the number of elements in vector V. [Public] | |
733 | (defun calcFunc-vlen (v) | |
734 | (if (math-vectorp v) | |
735 | (1- (length v)) | |
736 | (if (math-objectp v) | |
737 | 0 | |
bf77c646 | 738 | (list 'calcFunc-vlen v)))) |
136211a9 EZ |
739 | |
740 | ;;; Get the Nth row of a matrix. | |
741 | (defun calcFunc-mrow (mat n) ; [Public] | |
742 | (if (Math-vectorp n) | |
743 | (math-map-vec (function (lambda (x) (calcFunc-mrow mat x))) n) | |
744 | (if (and (eq (car-safe n) 'intv) (math-constp n)) | |
745 | (calcFunc-subvec mat | |
746 | (math-add (nth 2 n) (if (memq (nth 1 n) '(2 3)) 0 1)) | |
747 | (math-add (nth 3 n) (if (memq (nth 1 n) '(1 3)) 1 0))) | |
748 | (or (and (integerp (setq n (math-check-integer n))) | |
749 | (> n 0)) | |
750 | (math-reject-arg n 'fixposintp)) | |
751 | (or (Math-vectorp mat) | |
752 | (math-reject-arg mat 'vectorp)) | |
753 | (or (nth n mat) | |
bf77c646 | 754 | (math-reject-arg n "*Index out of range"))))) |
136211a9 EZ |
755 | |
756 | (defun calcFunc-subscr (mat n &optional m) | |
757 | (setq mat (calcFunc-mrow mat n)) | |
758 | (if m | |
759 | (if (math-num-integerp n) | |
760 | (calcFunc-mrow mat m) | |
761 | (calcFunc-mcol mat m)) | |
bf77c646 | 762 | mat)) |
136211a9 EZ |
763 | |
764 | ;;; Get the Nth column of a matrix. | |
765 | (defun math-mat-col (mat n) | |
bf77c646 | 766 | (cons 'vec (mapcar (function (lambda (x) (elt x n))) (cdr mat)))) |
136211a9 EZ |
767 | |
768 | (defun calcFunc-mcol (mat n) ; [Public] | |
769 | (if (Math-vectorp n) | |
770 | (calcFunc-trn | |
771 | (math-map-vec (function (lambda (x) (calcFunc-mcol mat x))) n)) | |
772 | (if (and (eq (car-safe n) 'intv) (math-constp n)) | |
773 | (if (math-matrixp mat) | |
774 | (math-map-vec (function (lambda (x) (calcFunc-mrow x n))) mat) | |
775 | (calcFunc-mrow mat n)) | |
776 | (or (and (integerp (setq n (math-check-integer n))) | |
777 | (> n 0)) | |
778 | (math-reject-arg n 'fixposintp)) | |
779 | (or (Math-vectorp mat) | |
780 | (math-reject-arg mat 'vectorp)) | |
781 | (or (if (math-matrixp mat) | |
782 | (and (< n (length (nth 1 mat))) | |
783 | (math-mat-col mat n)) | |
784 | (nth n mat)) | |
bf77c646 | 785 | (math-reject-arg n "*Index out of range"))))) |
136211a9 EZ |
786 | |
787 | ;;; Remove the Nth row from a matrix. | |
788 | (defun math-mat-less-row (mat n) | |
789 | (if (<= n 0) | |
790 | (cdr mat) | |
791 | (cons (car mat) | |
bf77c646 | 792 | (math-mat-less-row (cdr mat) (1- n))))) |
136211a9 EZ |
793 | |
794 | (defun calcFunc-mrrow (mat n) ; [Public] | |
795 | (and (integerp (setq n (math-check-integer n))) | |
796 | (> n 0) | |
797 | (< n (length mat)) | |
bf77c646 | 798 | (math-mat-less-row mat n))) |
136211a9 EZ |
799 | |
800 | ;;; Remove the Nth column from a matrix. | |
801 | (defun math-mat-less-col (mat n) | |
802 | (cons 'vec (mapcar (function (lambda (x) (math-mat-less-row x n))) | |
bf77c646 | 803 | (cdr mat)))) |
136211a9 EZ |
804 | |
805 | (defun calcFunc-mrcol (mat n) ; [Public] | |
806 | (and (integerp (setq n (math-check-integer n))) | |
807 | (> n 0) | |
808 | (if (math-matrixp mat) | |
809 | (and (< n (length (nth 1 mat))) | |
810 | (math-mat-less-col mat n)) | |
bf77c646 | 811 | (math-mat-less-row mat n)))) |
136211a9 EZ |
812 | |
813 | (defun calcFunc-getdiag (mat) ; [Public] | |
814 | (if (math-square-matrixp mat) | |
815 | (cons 'vec (math-get-diag-step (cdr mat) 1)) | |
816 | (calc-record-why 'square-matrixp mat) | |
bf77c646 | 817 | (list 'calcFunc-getdiag mat))) |
136211a9 EZ |
818 | |
819 | (defun math-get-diag-step (row n) | |
820 | (and row | |
821 | (cons (nth n (car row)) | |
bf77c646 | 822 | (math-get-diag-step (cdr row) (1+ n))))) |
136211a9 EZ |
823 | |
824 | (defun math-transpose (mat) ; [Public] | |
825 | (let ((m nil) | |
826 | (col (length (nth 1 mat)))) | |
827 | (while (> (setq col (1- col)) 0) | |
828 | (setq m (cons (math-mat-col mat col) m))) | |
bf77c646 | 829 | (cons 'vec m))) |
136211a9 EZ |
830 | |
831 | (defun calcFunc-trn (mat) | |
832 | (if (math-vectorp mat) | |
833 | (if (math-matrixp mat) | |
834 | (math-transpose mat) | |
835 | (math-col-matrix mat)) | |
836 | (if (math-numberp mat) | |
837 | mat | |
bf77c646 | 838 | (math-reject-arg mat 'matrixp)))) |
136211a9 EZ |
839 | |
840 | (defun calcFunc-ctrn (mat) | |
bf77c646 | 841 | (calcFunc-conj (calcFunc-trn mat))) |
136211a9 EZ |
842 | |
843 | (defun calcFunc-pack (mode els) | |
844 | (or (Math-vectorp els) (math-reject-arg els 'vectorp)) | |
845 | (if (and (Math-vectorp mode) (cdr mode)) | |
846 | (setq mode (cdr mode)) | |
847 | (or (integerp mode) (math-reject-arg mode 'fixnump))) | |
848 | (condition-case err | |
849 | (if (= (calc-pack-size mode) (1- (length els))) | |
850 | (calc-pack-items mode (cdr els)) | |
851 | (math-reject-arg els "*Wrong number of elements")) | |
bf77c646 | 852 | (error (math-reject-arg els (nth 1 err))))) |
136211a9 EZ |
853 | |
854 | (defun calcFunc-unpack (mode thing) | |
855 | (or (integerp mode) (math-reject-arg mode 'fixnump)) | |
856 | (condition-case err | |
857 | (cons 'vec (calc-unpack-item mode thing)) | |
bf77c646 | 858 | (error (math-reject-arg thing (nth 1 err))))) |
136211a9 EZ |
859 | |
860 | (defun calcFunc-unpackt (mode thing) | |
861 | (let ((calc-unpack-with-type 'pair)) | |
bf77c646 | 862 | (calcFunc-unpack mode thing))) |
136211a9 EZ |
863 | |
864 | (defun calcFunc-arrange (vec cols) ; [Public] | |
865 | (setq cols (math-check-fixnum cols t)) | |
866 | (if (math-vectorp vec) | |
867 | (let* ((flat (math-flatten-vector vec)) | |
868 | (mat (list 'vec)) | |
869 | next) | |
870 | (if (<= cols 0) | |
871 | (nconc mat flat) | |
872 | (while (>= (length flat) cols) | |
873 | (setq next (nthcdr cols flat)) | |
874 | (setcdr (nthcdr (1- cols) flat) nil) | |
875 | (setq mat (nconc mat (list (cons 'vec flat))) | |
876 | flat next)) | |
877 | (if flat | |
878 | (setq mat (nconc mat (list (cons 'vec flat))))) | |
bf77c646 | 879 | mat)))) |
136211a9 EZ |
880 | |
881 | (defun math-flatten-vector (vec) ; [L V] | |
882 | (if (math-vectorp vec) | |
883 | (apply 'append (mapcar 'math-flatten-vector (cdr vec))) | |
bf77c646 | 884 | (list vec))) |
136211a9 EZ |
885 | |
886 | (defun calcFunc-vconcat (a b) | |
bf77c646 | 887 | (math-normalize (list '| a b))) |
136211a9 EZ |
888 | |
889 | (defun calcFunc-vconcatrev (a b) | |
bf77c646 | 890 | (math-normalize (list '| b a))) |
136211a9 EZ |
891 | |
892 | (defun calcFunc-append (v1 v2) | |
893 | (if (and (math-vectorp v1) (math-vectorp v2)) | |
894 | (append v1 (cdr v2)) | |
bf77c646 | 895 | (list 'calcFunc-append v1 v2))) |
136211a9 EZ |
896 | |
897 | (defun calcFunc-appendrev (v1 v2) | |
bf77c646 | 898 | (calcFunc-append v2 v1)) |
136211a9 EZ |
899 | |
900 | ||
901 | ;;; Copy a matrix. [Public] | |
902 | (defun math-copy-matrix (m) | |
903 | (if (math-vectorp (nth 1 m)) | |
904 | (cons 'vec (mapcar 'copy-sequence (cdr m))) | |
bf77c646 | 905 | (copy-sequence m))) |
136211a9 EZ |
906 | |
907 | ;;; Convert a scalar or vector into an NxN diagonal matrix. [Public] | |
908 | (defun calcFunc-diag (a &optional n) | |
909 | (and n (not (integerp n)) | |
910 | (setq n (math-check-fixnum n))) | |
911 | (if (math-vectorp a) | |
912 | (if (and n (/= (length a) (1+ n))) | |
913 | (list 'calcFunc-diag a n) | |
914 | (if (math-matrixp a) | |
915 | (if (and n (/= (length (elt a 1)) (1+ n))) | |
916 | (list 'calcFunc-diag a n) | |
917 | a) | |
918 | (cons 'vec (math-diag-step (cdr a) 0 (1- (length a)))))) | |
919 | (if n | |
920 | (cons 'vec (math-diag-step (make-list n a) 0 n)) | |
bf77c646 | 921 | (list 'calcFunc-diag a)))) |
136211a9 EZ |
922 | |
923 | (defun calcFunc-idn (a &optional n) | |
924 | (if n | |
925 | (if (math-vectorp a) | |
926 | (math-reject-arg a 'numberp) | |
927 | (calcFunc-diag a n)) | |
928 | (if (integerp calc-matrix-mode) | |
929 | (calcFunc-idn a calc-matrix-mode) | |
bf77c646 | 930 | (list 'calcFunc-idn a)))) |
136211a9 EZ |
931 | |
932 | (defun math-mimic-ident (a m) | |
933 | (if (math-square-matrixp m) | |
934 | (calcFunc-idn a (1- (length m))) | |
935 | (if (math-vectorp m) | |
936 | (if (math-zerop a) | |
937 | (cons 'vec (mapcar (function (lambda (x) | |
938 | (if (math-vectorp x) | |
939 | (math-mimic-ident a x) | |
940 | a))) | |
941 | (cdr m))) | |
942 | (math-dimension-error)) | |
bf77c646 | 943 | (calcFunc-idn a)))) |
136211a9 EZ |
944 | |
945 | (defun math-diag-step (a n m) | |
946 | (if (< n m) | |
947 | (cons (cons 'vec | |
948 | (nconc (make-list n 0) | |
949 | (cons (car a) | |
950 | (make-list (1- (- m n)) 0)))) | |
951 | (math-diag-step (cdr a) (1+ n) m)) | |
bf77c646 | 952 | nil)) |
136211a9 EZ |
953 | |
954 | ;;; Create a vector of consecutive integers. [Public] | |
955 | (defun calcFunc-index (n &optional start incr) | |
956 | (if (math-messy-integerp n) | |
957 | (math-float (calcFunc-index (math-trunc n) start incr)) | |
958 | (and (not (integerp n)) | |
959 | (setq n (math-check-fixnum n))) | |
960 | (let ((vec nil)) | |
961 | (if start | |
962 | (progn | |
963 | (if (>= n 0) | |
964 | (while (>= (setq n (1- n)) 0) | |
965 | (setq vec (cons start vec) | |
966 | start (math-add start (or incr 1)))) | |
967 | (while (<= (setq n (1+ n)) 0) | |
968 | (setq vec (cons start vec) | |
969 | start (math-mul start (or incr 2))))) | |
970 | (setq vec (nreverse vec))) | |
971 | (if (>= n 0) | |
972 | (while (> n 0) | |
973 | (setq vec (cons n vec) | |
974 | n (1- n))) | |
975 | (let ((i -1)) | |
976 | (while (>= i n) | |
977 | (setq vec (cons i vec) | |
978 | i (1- i)))))) | |
bf77c646 | 979 | (cons 'vec vec)))) |
136211a9 EZ |
980 | |
981 | ;;; Find an element in a vector. | |
982 | (defun calcFunc-find (vec x &optional start) | |
983 | (setq start (if start (math-check-fixnum start t) 1)) | |
984 | (if (< start 1) (math-reject-arg start 'posp)) | |
985 | (setq vec (nthcdr start vec)) | |
986 | (let ((n start)) | |
987 | (while (and vec (not (Math-equal x (car vec)))) | |
988 | (setq n (1+ n) | |
989 | vec (cdr vec))) | |
bf77c646 | 990 | (if vec n 0))) |
136211a9 EZ |
991 | |
992 | ;;; Return a subvector of a vector. | |
993 | (defun calcFunc-subvec (vec start &optional end) | |
994 | (setq start (math-check-fixnum start t) | |
995 | end (math-check-fixnum (or end 0) t)) | |
996 | (or (math-vectorp vec) (math-reject-arg vec 'vectorp)) | |
997 | (let ((len (1- (length vec)))) | |
998 | (if (<= start 0) | |
999 | (setq start (+ len start 1))) | |
1000 | (if (<= end 0) | |
1001 | (setq end (+ len end 1))) | |
1002 | (if (or (> start len) | |
1003 | (<= end start)) | |
1004 | '(vec) | |
1005 | (setq vec (nthcdr start vec)) | |
1006 | (if (<= end len) | |
1007 | (let ((chop (nthcdr (- end start 1) (setq vec (copy-sequence vec))))) | |
1008 | (setcdr chop nil))) | |
bf77c646 | 1009 | (cons 'vec vec)))) |
136211a9 EZ |
1010 | |
1011 | ;;; Remove a subvector from a vector. | |
1012 | (defun calcFunc-rsubvec (vec start &optional end) | |
1013 | (setq start (math-check-fixnum start t) | |
1014 | end (math-check-fixnum (or end 0) t)) | |
1015 | (or (math-vectorp vec) (math-reject-arg vec 'vectorp)) | |
1016 | (let ((len (1- (length vec)))) | |
1017 | (if (<= start 0) | |
1018 | (setq start (+ len start 1))) | |
1019 | (if (<= end 0) | |
1020 | (setq end (+ len end 1))) | |
1021 | (if (or (> start len) | |
1022 | (<= end start)) | |
1023 | vec | |
1024 | (let ((tail (nthcdr end vec)) | |
1025 | (chop (nthcdr (1- start) (setq vec (copy-sequence vec))))) | |
1026 | (setcdr chop nil) | |
bf77c646 | 1027 | (append vec tail))))) |
136211a9 EZ |
1028 | |
1029 | ;;; Reverse the order of the elements of a vector. | |
1030 | (defun calcFunc-rev (vec) | |
1031 | (if (math-vectorp vec) | |
1032 | (cons 'vec (reverse (cdr vec))) | |
bf77c646 | 1033 | (math-reject-arg vec 'vectorp))) |
136211a9 EZ |
1034 | |
1035 | ;;; Compress a vector according to a mask vector. | |
1036 | (defun calcFunc-vmask (mask vec) | |
1037 | (if (math-numberp mask) | |
1038 | (if (math-zerop mask) | |
1039 | '(vec) | |
1040 | vec) | |
1041 | (or (math-vectorp mask) (math-reject-arg mask 'vectorp)) | |
1042 | (or (math-constp mask) (math-reject-arg mask 'constp)) | |
1043 | (or (math-vectorp vec) (math-reject-arg vec 'vectorp)) | |
1044 | (or (= (length mask) (length vec)) (math-dimension-error)) | |
1045 | (let ((new nil)) | |
1046 | (while (setq mask (cdr mask) vec (cdr vec)) | |
1047 | (or (math-zerop (car mask)) | |
1048 | (setq new (cons (car vec) new)))) | |
bf77c646 | 1049 | (cons 'vec (nreverse new))))) |
136211a9 EZ |
1050 | |
1051 | ;;; Expand a vector according to a mask vector. | |
1052 | (defun calcFunc-vexp (mask vec &optional filler) | |
1053 | (or (math-vectorp mask) (math-reject-arg mask 'vectorp)) | |
1054 | (or (math-constp mask) (math-reject-arg mask 'constp)) | |
1055 | (or (math-vectorp vec) (math-reject-arg vec 'vectorp)) | |
1056 | (let ((new nil) | |
1057 | (fvec (and filler (math-vectorp filler)))) | |
1058 | (while (setq mask (cdr mask)) | |
1059 | (if (math-zerop (car mask)) | |
1060 | (setq new (cons (or (if fvec | |
1061 | (car (setq filler (cdr filler))) | |
1062 | filler) | |
1063 | (car mask)) new)) | |
1064 | (setq vec (cdr vec) | |
1065 | new (cons (or (car vec) (car mask)) new)))) | |
bf77c646 | 1066 | (cons 'vec (nreverse new)))) |
136211a9 EZ |
1067 | |
1068 | ||
1069 | ;;; Compute the row and column norms of a vector or matrix. [Public] | |
1070 | (defun calcFunc-rnorm (a) | |
1071 | (if (and (Math-vectorp a) | |
1072 | (math-constp a)) | |
1073 | (if (math-matrixp a) | |
1074 | (math-reduce-vec 'math-max (math-map-vec 'calcFunc-cnorm a)) | |
1075 | (math-reduce-vec 'math-max (math-map-vec 'math-abs a))) | |
1076 | (calc-record-why 'vectorp a) | |
bf77c646 | 1077 | (list 'calcFunc-rnorm a))) |
136211a9 EZ |
1078 | |
1079 | (defun calcFunc-cnorm (a) | |
1080 | (if (and (Math-vectorp a) | |
1081 | (math-constp a)) | |
1082 | (if (math-matrixp a) | |
1083 | (math-reduce-vec 'math-max | |
1084 | (math-reduce-cols 'math-add-abs a)) | |
1085 | (math-reduce-vec 'math-add-abs a)) | |
1086 | (calc-record-why 'vectorp a) | |
bf77c646 | 1087 | (list 'calcFunc-cnorm a))) |
136211a9 EZ |
1088 | |
1089 | (defun math-add-abs (a b) | |
bf77c646 | 1090 | (math-add (math-abs a) (math-abs b))) |
136211a9 EZ |
1091 | |
1092 | ||
1093 | ;;; Sort the elements of a vector into increasing order. | |
1094 | (defun calcFunc-sort (vec) ; [Public] | |
1095 | (if (math-vectorp vec) | |
1096 | (cons 'vec (sort (copy-sequence (cdr vec)) 'math-beforep)) | |
bf77c646 | 1097 | (math-reject-arg vec 'vectorp))) |
136211a9 EZ |
1098 | |
1099 | (defun calcFunc-rsort (vec) ; [Public] | |
1100 | (if (math-vectorp vec) | |
1101 | (cons 'vec (nreverse (sort (copy-sequence (cdr vec)) 'math-beforep))) | |
bf77c646 | 1102 | (math-reject-arg vec 'vectorp))) |
136211a9 EZ |
1103 | |
1104 | (defun calcFunc-grade (grade-vec) | |
1105 | (if (math-vectorp grade-vec) | |
1106 | (let* ((len (1- (length grade-vec)))) | |
1107 | (cons 'vec (sort (cdr (calcFunc-index len)) 'math-grade-beforep))) | |
bf77c646 | 1108 | (math-reject-arg grade-vec 'vectorp))) |
136211a9 EZ |
1109 | |
1110 | (defun calcFunc-rgrade (grade-vec) | |
1111 | (if (math-vectorp grade-vec) | |
1112 | (let* ((len (1- (length grade-vec)))) | |
1113 | (cons 'vec (nreverse (sort (cdr (calcFunc-index len)) | |
1114 | 'math-grade-beforep)))) | |
bf77c646 | 1115 | (math-reject-arg grade-vec 'vectorp))) |
136211a9 EZ |
1116 | |
1117 | (defun math-grade-beforep (i j) | |
bf77c646 | 1118 | (math-beforep (nth i grade-vec) (nth j grade-vec))) |
136211a9 EZ |
1119 | |
1120 | ||
1121 | ;;; Compile a histogram of data from a vector. | |
1122 | (defun calcFunc-histogram (vec wts &optional n) | |
1123 | (or n (setq n wts wts 1)) | |
1124 | (or (Math-vectorp vec) | |
1125 | (math-reject-arg vec 'vectorp)) | |
1126 | (if (Math-vectorp wts) | |
1127 | (or (= (length vec) (length wts)) | |
1128 | (math-dimension-error))) | |
1129 | (or (natnump n) | |
1130 | (math-reject-arg n 'fixnatnump)) | |
1131 | (let ((res (make-vector n 0)) | |
1132 | (vp vec) | |
1133 | (wvec (Math-vectorp wts)) | |
1134 | (wp wts) | |
1135 | bin) | |
1136 | (while (setq vp (cdr vp)) | |
1137 | (setq bin (car vp)) | |
1138 | (or (natnump bin) | |
1139 | (setq bin (math-floor bin))) | |
1140 | (and (natnump bin) | |
1141 | (< bin n) | |
1142 | (aset res bin (math-add (aref res bin) | |
1143 | (if wvec (car (setq wp (cdr wp))) wts))))) | |
bf77c646 | 1144 | (cons 'vec (append res nil)))) |
136211a9 EZ |
1145 | |
1146 | ||
1147 | ;;; Set operations. | |
1148 | ||
1149 | (defun calcFunc-vunion (a b) | |
1150 | (if (Math-objectp a) | |
1151 | (setq a (list 'vec a)) | |
1152 | (or (math-vectorp a) (math-reject-arg a 'vectorp))) | |
1153 | (if (Math-objectp b) | |
1154 | (setq b (list b)) | |
1155 | (or (math-vectorp b) (math-reject-arg b 'vectorp)) | |
1156 | (setq b (cdr b))) | |
bf77c646 | 1157 | (calcFunc-rdup (append a b))) |
136211a9 EZ |
1158 | |
1159 | (defun calcFunc-vint (a b) | |
1160 | (if (and (math-simple-set a) (math-simple-set b)) | |
1161 | (progn | |
1162 | (setq a (cdr (calcFunc-rdup a))) | |
1163 | (setq b (cdr (calcFunc-rdup b))) | |
1164 | (let ((vec (list 'vec))) | |
1165 | (while (and a b) | |
1166 | (if (math-beforep (car a) (car b)) | |
1167 | (setq a (cdr a)) | |
1168 | (if (Math-equal (car a) (car b)) | |
1169 | (setq vec (cons (car a) vec) | |
1170 | a (cdr a))) | |
1171 | (setq b (cdr b)))) | |
1172 | (nreverse vec))) | |
1173 | (calcFunc-vcompl (calcFunc-vunion (calcFunc-vcompl a) | |
bf77c646 | 1174 | (calcFunc-vcompl b))))) |
136211a9 EZ |
1175 | |
1176 | (defun calcFunc-vdiff (a b) | |
1177 | (if (and (math-simple-set a) (math-simple-set b)) | |
1178 | (progn | |
1179 | (setq a (cdr (calcFunc-rdup a))) | |
1180 | (setq b (cdr (calcFunc-rdup b))) | |
1181 | (let ((vec (list 'vec))) | |
1182 | (while a | |
1183 | (while (and b (math-beforep (car b) (car a))) | |
1184 | (setq b (cdr b))) | |
1185 | (if (and b (Math-equal (car a) (car b))) | |
1186 | (setq a (cdr a) | |
1187 | b (cdr b)) | |
1188 | (setq vec (cons (car a) vec) | |
1189 | a (cdr a)))) | |
1190 | (nreverse vec))) | |
bf77c646 | 1191 | (calcFunc-vcompl (calcFunc-vunion (calcFunc-vcompl a) b)))) |
136211a9 EZ |
1192 | |
1193 | (defun calcFunc-vxor (a b) | |
1194 | (if (and (math-simple-set a) (math-simple-set b)) | |
1195 | (progn | |
1196 | (setq a (cdr (calcFunc-rdup a))) | |
1197 | (setq b (cdr (calcFunc-rdup b))) | |
1198 | (let ((vec (list 'vec))) | |
1199 | (while (or a b) | |
1200 | (if (and a | |
1201 | (or (not b) | |
1202 | (math-beforep (car a) (car b)))) | |
1203 | (setq vec (cons (car a) vec) | |
1204 | a (cdr a)) | |
1205 | (if (and a (Math-equal (car a) (car b))) | |
1206 | (setq a (cdr a)) | |
1207 | (setq vec (cons (car b) vec))) | |
1208 | (setq b (cdr b)))) | |
1209 | (nreverse vec))) | |
1210 | (let ((ca (calcFunc-vcompl a)) | |
1211 | (cb (calcFunc-vcompl b))) | |
1212 | (calcFunc-vunion (calcFunc-vcompl (calcFunc-vunion ca b)) | |
bf77c646 | 1213 | (calcFunc-vcompl (calcFunc-vunion a cb)))))) |
136211a9 EZ |
1214 | |
1215 | (defun calcFunc-vcompl (a) | |
1216 | (setq a (math-prepare-set a)) | |
1217 | (let ((vec (list 'vec)) | |
1218 | (prev '(neg (var inf var-inf))) | |
1219 | (closed 2)) | |
1220 | (while (setq a (cdr a)) | |
1221 | (or (and (equal (nth 2 (car a)) '(neg (var inf var-inf))) | |
1222 | (memq (nth 1 (car a)) '(2 3))) | |
1223 | (setq vec (cons (list 'intv | |
1224 | (+ closed | |
1225 | (if (memq (nth 1 (car a)) '(0 1)) 1 0)) | |
1226 | prev | |
1227 | (nth 2 (car a))) | |
1228 | vec))) | |
1229 | (setq prev (nth 3 (car a)) | |
1230 | closed (if (memq (nth 1 (car a)) '(0 2)) 2 0))) | |
1231 | (or (and (equal prev '(var inf var-inf)) | |
1232 | (= closed 0)) | |
1233 | (setq vec (cons (list 'intv (+ closed 1) | |
1234 | prev '(var inf var-inf)) | |
1235 | vec))) | |
bf77c646 | 1236 | (math-clean-set (nreverse vec)))) |
136211a9 EZ |
1237 | |
1238 | (defun calcFunc-vspan (a) | |
1239 | (setq a (math-prepare-set a)) | |
1240 | (if (cdr a) | |
1241 | (let ((last (nth (1- (length a)) a))) | |
1242 | (math-make-intv (+ (logand (nth 1 (nth 1 a)) 2) | |
1243 | (logand (nth 1 last) 1)) | |
1244 | (nth 2 (nth 1 a)) | |
1245 | (nth 3 last))) | |
bf77c646 | 1246 | '(intv 2 0 0))) |
136211a9 EZ |
1247 | |
1248 | (defun calcFunc-vfloor (a &optional always-vec) | |
1249 | (setq a (math-prepare-set a)) | |
1250 | (let ((vec (list 'vec)) (p a) (prev nil) b mask) | |
1251 | (while (setq p (cdr p)) | |
1252 | (setq mask (nth 1 (car p)) | |
1253 | a (nth 2 (car p)) | |
1254 | b (nth 3 (car p))) | |
1255 | (and (memq mask '(0 1)) | |
1256 | (not (math-infinitep a)) | |
1257 | (setq mask (logior mask 2)) | |
1258 | (math-num-integerp a) | |
1259 | (setq a (math-add a 1))) | |
1260 | (setq a (math-ceiling a)) | |
1261 | (and (memq mask '(0 2)) | |
1262 | (not (math-infinitep b)) | |
1263 | (setq mask (logior mask 1)) | |
1264 | (math-num-integerp b) | |
1265 | (setq b (math-sub b 1))) | |
1266 | (setq b (math-floor b)) | |
1267 | (if (and prev (Math-equal (math-sub a 1) (nth 3 prev))) | |
1268 | (setcar (nthcdr 3 prev) b) | |
1269 | (or (Math-lessp b a) | |
1270 | (setq vec (cons (setq prev (list 'intv mask a b)) vec))))) | |
1271 | (setq vec (nreverse vec)) | |
bf77c646 | 1272 | (math-clean-set vec always-vec))) |
136211a9 EZ |
1273 | |
1274 | (defun calcFunc-vcard (a) | |
1275 | (setq a (calcFunc-vfloor a t)) | |
1276 | (or (math-constp a) (math-reject-arg a "*Set must be finite")) | |
1277 | (let ((count 0)) | |
1278 | (while (setq a (cdr a)) | |
1279 | (if (eq (car-safe (car a)) 'intv) | |
1280 | (setq count (math-add count (math-sub (nth 3 (car a)) | |
1281 | (nth 2 (car a)))))) | |
1282 | (setq count (math-add count 1))) | |
bf77c646 | 1283 | count)) |
136211a9 EZ |
1284 | |
1285 | (defun calcFunc-venum (a) | |
1286 | (setq a (calcFunc-vfloor a t)) | |
1287 | (or (math-constp a) (math-reject-arg a "*Set must be finite")) | |
1288 | (let ((p a) next) | |
1289 | (while (cdr p) | |
1290 | (setq next (cdr p)) | |
1291 | (if (eq (car-safe (nth 1 p)) 'intv) | |
1292 | (setcdr p (nconc (cdr (calcFunc-index (math-add | |
1293 | (math-sub (nth 3 (nth 1 p)) | |
1294 | (nth 2 (nth 1 p))) | |
1295 | 1) | |
1296 | (nth 2 (nth 1 p)))) | |
1297 | (cdr (cdr p))))) | |
1298 | (setq p next)) | |
bf77c646 | 1299 | a)) |
136211a9 EZ |
1300 | |
1301 | (defun calcFunc-vpack (a) | |
1302 | (setq a (calcFunc-vfloor a t)) | |
1303 | (if (and (cdr a) | |
1304 | (math-negp (if (eq (car-safe (nth 1 a)) 'intv) | |
1305 | (nth 2 (nth 1 a)) | |
1306 | (nth 1 a)))) | |
1307 | (math-reject-arg (nth 1 a) 'posp)) | |
1308 | (let ((accum 0)) | |
1309 | (while (setq a (cdr a)) | |
1310 | (if (eq (car-safe (car a)) 'intv) | |
1311 | (if (equal (nth 3 (car a)) '(var inf var-inf)) | |
1312 | (setq accum (math-sub accum | |
1313 | (math-power-of-2 (nth 2 (car a))))) | |
1314 | (setq accum (math-add accum | |
1315 | (math-sub | |
1316 | (math-power-of-2 (1+ (nth 3 (car a)))) | |
1317 | (math-power-of-2 (nth 2 (car a))))))) | |
1318 | (setq accum (math-add accum (math-power-of-2 (car a)))))) | |
bf77c646 | 1319 | accum)) |
136211a9 EZ |
1320 | |
1321 | (defun calcFunc-vunpack (a &optional w) | |
1322 | (or (math-num-integerp a) (math-reject-arg a 'integerp)) | |
1323 | (if w (setq a (math-clip a w))) | |
1324 | (if (math-messy-integerp a) (setq a (math-trunc a))) | |
1325 | (let* ((calc-number-radix 2) | |
1326 | (neg (math-negp a)) | |
1327 | (aa (if neg (math-sub -1 a) a)) | |
1328 | (str (if (eq aa 0) | |
1329 | "" | |
1330 | (if (consp aa) | |
1331 | (math-format-bignum-binary (cdr aa)) | |
1332 | (math-format-binary aa)))) | |
1333 | (zero (if neg ?1 ?0)) | |
1334 | (one (if neg ?0 ?1)) | |
1335 | (len (length str)) | |
1336 | (vec (list 'vec)) | |
1337 | (pos (1- len)) pos2) | |
1338 | (while (>= pos 0) | |
1339 | (if (eq (aref str pos) zero) | |
1340 | (setq pos (1- pos)) | |
1341 | (setq pos2 pos) | |
1342 | (while (and (>= pos 0) (eq (aref str pos) one)) | |
1343 | (setq pos (1- pos))) | |
1344 | (setq vec (cons (if (= pos (1- pos2)) | |
1345 | (- len pos2 1) | |
1346 | (list 'intv 3 (- len pos2 1) (- len pos 2))) | |
1347 | vec)))) | |
1348 | (if neg | |
1349 | (setq vec (cons (list 'intv 2 len '(var inf var-inf)) vec))) | |
bf77c646 | 1350 | (math-clean-set (nreverse vec)))) |
136211a9 EZ |
1351 | |
1352 | (defun calcFunc-rdup (a) | |
1353 | (if (math-simple-set a) | |
1354 | (progn | |
1355 | (and (Math-objectp a) (setq a (list 'vec a))) | |
1356 | (or (math-vectorp a) (math-reject-arg a 'vectorp)) | |
1357 | (setq a (sort (copy-sequence (cdr a)) 'math-beforep)) | |
1358 | (let ((p a)) | |
1359 | (while (cdr p) | |
1360 | (if (Math-equal (car p) (nth 1 p)) | |
1361 | (setcdr p (cdr (cdr p))) | |
1362 | (setq p (cdr p))))) | |
1363 | (cons 'vec a)) | |
bf77c646 | 1364 | (math-clean-set (math-prepare-set a)))) |
136211a9 EZ |
1365 | |
1366 | (defun math-prepare-set (a) | |
1367 | (if (Math-objectp a) | |
1368 | (setq a (list 'vec a)) | |
1369 | (or (math-vectorp a) (math-reject-arg a 'vectorp)) | |
1370 | (setq a (cons 'vec (sort (copy-sequence (cdr a)) 'math-beforep)))) | |
1371 | (let ((p a) res) | |
1372 | ||
1373 | ;; Convert all elements to non-empty intervals. | |
1374 | (while (cdr p) | |
1375 | (if (eq (car-safe (nth 1 p)) 'intv) | |
1376 | (if (math-intv-constp (nth 1 p)) | |
1377 | (if (and (memq (nth 1 (nth 1 p)) '(0 1 2)) | |
1378 | (Math-equal (nth 2 (nth 1 p)) (nth 3 (nth 1 p)))) | |
1379 | (setcdr p (cdr (cdr p))) | |
1380 | (setq p (cdr p))) | |
1381 | (math-reject-arg (nth 1 p) 'constp)) | |
1382 | (or (Math-anglep (nth 1 p)) | |
1383 | (eq (car (nth 1 p)) 'date) | |
1384 | (equal (nth 1 p) '(var inf var-inf)) | |
1385 | (equal (nth 1 p) '(neg (var inf var-inf))) | |
1386 | (math-reject-arg (nth 1 p) 'realp)) | |
1387 | (setcar (cdr p) (list 'intv 3 (nth 1 p) (nth 1 p))) | |
1388 | (setq p (cdr p)))) | |
1389 | ||
1390 | ;; Combine redundant intervals. | |
1391 | (setq p a) | |
1392 | (while (cdr (cdr p)) | |
1393 | (if (or (memq (setq res (math-compare (nth 3 (nth 1 p)) | |
1394 | (nth 2 (nth 2 p)))) | |
1395 | '(-1 2)) | |
1396 | (and (eq res 0) | |
1397 | (memq (nth 1 (nth 1 p)) '(0 2)) | |
1398 | (memq (nth 1 (nth 2 p)) '(0 1)))) | |
1399 | (setq p (cdr p)) | |
1400 | (setq res (math-compare (nth 3 (nth 1 p)) (nth 3 (nth 2 p)))) | |
1401 | (setcdr p (cons (list 'intv | |
1402 | (+ (logand (logior (nth 1 (nth 1 p)) | |
1403 | (if (Math-equal | |
1404 | (nth 2 (nth 1 p)) | |
1405 | (nth 2 (nth 2 p))) | |
1406 | (nth 1 (nth 2 p)) | |
1407 | 0)) | |
1408 | 2) | |
1409 | (logand (logior (if (memq res '(1 0 2)) | |
1410 | (nth 1 (nth 1 p)) 0) | |
1411 | (if (memq res '(-1 0 2)) | |
1412 | (nth 1 (nth 2 p)) 0)) | |
1413 | 1)) | |
1414 | (nth 2 (nth 1 p)) | |
1415 | (if (eq res 1) | |
1416 | (nth 3 (nth 1 p)) | |
1417 | (nth 3 (nth 2 p)))) | |
1418 | (cdr (cdr (cdr p)))))))) | |
bf77c646 | 1419 | a) |
136211a9 EZ |
1420 | |
1421 | (defun math-clean-set (a &optional always-vec) | |
1422 | (let ((p a) res) | |
1423 | (while (cdr p) | |
1424 | (if (and (eq (car-safe (nth 1 p)) 'intv) | |
1425 | (Math-equal (nth 2 (nth 1 p)) (nth 3 (nth 1 p)))) | |
1426 | (setcar (cdr p) (nth 2 (nth 1 p)))) | |
1427 | (setq p (cdr p))) | |
1428 | (if (and (not (cdr (cdr a))) | |
1429 | (eq (car-safe (nth 1 a)) 'intv) | |
1430 | (not always-vec)) | |
1431 | (nth 1 a) | |
bf77c646 | 1432 | a))) |
136211a9 EZ |
1433 | |
1434 | (defun math-simple-set (a) | |
1435 | (or (and (Math-objectp a) | |
1436 | (not (eq (car-safe a) 'intv))) | |
1437 | (and (Math-vectorp a) | |
1438 | (progn | |
1439 | (while (and (setq a (cdr a)) | |
1440 | (not (eq (car-safe (car a)) 'intv)))) | |
bf77c646 | 1441 | (null a))))) |
136211a9 EZ |
1442 | |
1443 | ||
1444 | ||
1445 | ||
1446 | ;;; Compute a right-handed vector cross product. [O O O] [Public] | |
1447 | (defun calcFunc-cross (a b) | |
1448 | (if (and (eq (car-safe a) 'vec) | |
1449 | (= (length a) 4)) | |
1450 | (if (and (eq (car-safe b) 'vec) | |
1451 | (= (length b) 4)) | |
1452 | (list 'vec | |
1453 | (math-sub (math-mul (nth 2 a) (nth 3 b)) | |
1454 | (math-mul (nth 3 a) (nth 2 b))) | |
1455 | (math-sub (math-mul (nth 3 a) (nth 1 b)) | |
1456 | (math-mul (nth 1 a) (nth 3 b))) | |
1457 | (math-sub (math-mul (nth 1 a) (nth 2 b)) | |
1458 | (math-mul (nth 2 a) (nth 1 b)))) | |
1459 | (math-reject-arg b "*Three-vector expected")) | |
bf77c646 | 1460 | (math-reject-arg a "*Three-vector expected"))) |
136211a9 EZ |
1461 | |
1462 | ||
1463 | ||
1464 | ||
1465 | ||
1466 | (defun math-read-brackets (space-sep close) | |
1467 | (and space-sep (setq space-sep (not (math-check-for-commas)))) | |
1468 | (math-read-token) | |
1469 | (while (eq exp-token 'space) | |
1470 | (math-read-token)) | |
1471 | (if (or (equal exp-data close) | |
1472 | (eq exp-token 'end)) | |
1473 | (progn | |
1474 | (math-read-token) | |
1475 | '(vec)) | |
1476 | (let ((save-exp-pos exp-pos) | |
1477 | (save-exp-old-pos exp-old-pos) | |
1478 | (save-exp-token exp-token) | |
1479 | (save-exp-data exp-data) | |
1480 | (vals (let ((exp-keep-spaces space-sep)) | |
1481 | (if (or (equal exp-data "\\dots") | |
1482 | (equal exp-data "\\ldots")) | |
1483 | '(vec (neg (var inf var-inf))) | |
1484 | (catch 'syntax (math-read-vector)))))) | |
1485 | (if (stringp vals) | |
1486 | (if space-sep | |
1487 | (let ((error-exp-pos exp-pos) | |
1488 | (error-exp-old-pos exp-old-pos) | |
1489 | vals2) | |
1490 | (setq exp-pos save-exp-pos | |
1491 | exp-old-pos save-exp-old-pos | |
1492 | exp-token save-exp-token | |
1493 | exp-data save-exp-data) | |
1494 | (let ((exp-keep-spaces nil)) | |
1495 | (setq vals2 (catch 'syntax (math-read-vector)))) | |
1496 | (if (and (not (stringp vals2)) | |
1497 | (or (assoc exp-data '(("\\ldots") ("\\dots") (";"))) | |
1498 | (equal exp-data close) | |
1499 | (eq exp-token 'end))) | |
1500 | (setq space-sep nil | |
1501 | vals vals2) | |
1502 | (setq exp-pos error-exp-pos | |
1503 | exp-old-pos error-exp-old-pos) | |
1504 | (throw 'syntax vals))) | |
1505 | (throw 'syntax vals))) | |
1506 | (if (or (equal exp-data "\\dots") | |
1507 | (equal exp-data "\\ldots")) | |
1508 | (progn | |
1509 | (math-read-token) | |
1510 | (setq vals (if (> (length vals) 2) | |
1511 | (cons 'calcFunc-mul (cdr vals)) (nth 1 vals))) | |
1512 | (let ((exp2 (if (or (equal exp-data close) | |
1513 | (equal exp-data ")") | |
1514 | (eq exp-token 'end)) | |
1515 | '(var inf var-inf) | |
1516 | (math-read-expr-level 0)))) | |
1517 | (setq vals | |
1518 | (list 'intv | |
1519 | (if (equal exp-data ")") 2 3) | |
1520 | vals | |
1521 | exp2))) | |
1522 | (if (not (or (equal exp-data close) | |
1523 | (equal exp-data ")") | |
1524 | (eq exp-token 'end))) | |
1525 | (throw 'syntax "Expected `]'"))) | |
1526 | (if (equal exp-data ";") | |
1527 | (let ((exp-keep-spaces space-sep)) | |
1528 | (setq vals (cons 'vec (math-read-matrix (list vals)))))) | |
1529 | (if (not (or (equal exp-data close) | |
1530 | (eq exp-token 'end))) | |
1531 | (throw 'syntax "Expected `]'"))) | |
1532 | (or (eq exp-token 'end) | |
1533 | (math-read-token)) | |
bf77c646 | 1534 | vals))) |
136211a9 EZ |
1535 | |
1536 | (defun math-check-for-commas (&optional balancing) | |
1537 | (let ((count 0) | |
1538 | (pos (1- exp-pos))) | |
1539 | (while (and (>= count 0) | |
1540 | (setq pos (string-match | |
1541 | (if balancing "[],[{}()<>]" "[],[{}()]") | |
1542 | exp-str (1+ pos))) | |
1543 | (or (/= (aref exp-str pos) ?,) (> count 0) balancing)) | |
1544 | (cond ((memq (aref exp-str pos) '(?\[ ?\{ ?\( ?\<)) | |
1545 | (setq count (1+ count))) | |
1546 | ((memq (aref exp-str pos) '(?\] ?\} ?\) ?\>)) | |
1547 | (setq count (1- count))))) | |
1548 | (if balancing | |
1549 | pos | |
bf77c646 | 1550 | (and pos (= (aref exp-str pos) ?,))))) |
136211a9 EZ |
1551 | |
1552 | (defun math-read-vector () | |
1553 | (let* ((val (list (math-read-expr-level 0))) | |
1554 | (last val)) | |
1555 | (while (progn | |
1556 | (while (eq exp-token 'space) | |
1557 | (math-read-token)) | |
1558 | (and (not (eq exp-token 'end)) | |
1559 | (not (equal exp-data ";")) | |
1560 | (not (equal exp-data close)) | |
1561 | (not (equal exp-data "\\dots")) | |
1562 | (not (equal exp-data "\\ldots")))) | |
1563 | (if (equal exp-data ",") | |
1564 | (math-read-token)) | |
1565 | (while (eq exp-token 'space) | |
1566 | (math-read-token)) | |
1567 | (let ((rest (list (math-read-expr-level 0)))) | |
1568 | (setcdr last rest) | |
1569 | (setq last rest))) | |
bf77c646 | 1570 | (cons 'vec val))) |
136211a9 EZ |
1571 | |
1572 | (defun math-read-matrix (mat) | |
1573 | (while (equal exp-data ";") | |
1574 | (math-read-token) | |
1575 | (while (eq exp-token 'space) | |
1576 | (math-read-token)) | |
1577 | (setq mat (nconc mat (list (math-read-vector))))) | |
bf77c646 | 1578 | mat) |
136211a9 | 1579 | |
ab5796a9 | 1580 | ;;; arch-tag: 7902a7af-ec69-440a-8635-ebb4db263402 |
bf77c646 | 1581 | ;;; calc-vec.el ends here |