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3132f345 CW |
1 | ;;; calc-vec.el --- vector functions for Calc |
2 | ||
ab422c4d | 3 | ;; Copyright (C) 1990-1993, 2001-2013 Free Software Foundation, Inc. |
3132f345 CW |
4 | |
5 | ;; Author: David Gillespie <daveg@synaptics.com> | |
e8fff8ed | 6 | ;; Maintainer: Jay Belanger <jay.p.belanger@gmail.com> |
136211a9 EZ |
7 | |
8 | ;; This file is part of GNU Emacs. | |
9 | ||
662c9c64 | 10 | ;; GNU Emacs is free software: you can redistribute it and/or modify |
7c671b23 | 11 | ;; it under the terms of the GNU General Public License as published by |
662c9c64 GM |
12 | ;; the Free Software Foundation, either version 3 of the License, or |
13 | ;; (at your option) any later version. | |
7c671b23 | 14 | |
136211a9 | 15 | ;; GNU Emacs is distributed in the hope that it will be useful, |
7c671b23 GM |
16 | ;; but WITHOUT ANY WARRANTY; without even the implied warranty of |
17 | ;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
18 | ;; GNU General Public License for more details. | |
19 | ||
20 | ;; You should have received a copy of the GNU General Public License | |
662c9c64 | 21 | ;; along with GNU Emacs. If not, see <http://www.gnu.org/licenses/>. |
136211a9 | 22 | |
3132f345 | 23 | ;;; Commentary: |
136211a9 | 24 | |
3132f345 | 25 | ;;; Code: |
136211a9 EZ |
26 | |
27 | ;; This file is autoloaded from calc-ext.el. | |
136211a9 | 28 | |
429dae43 | 29 | (require 'calc-ext) |
136211a9 EZ |
30 | (require 'calc-macs) |
31 | ||
c4efb858 JB |
32 | ;; Declare functions which are defined elsewhere. |
33 | (declare-function math-read-expr-level "calc-aent" (exp-prec &optional exp-term)) | |
34 | ||
35 | ||
136211a9 EZ |
36 | (defun calc-display-strings (n) |
37 | (interactive "P") | |
38 | (calc-wrapper | |
39 | (message (if (calc-change-mode 'calc-display-strings n t t) | |
3132f345 CW |
40 | "Displaying vectors of integers as quoted strings" |
41 | "Displaying vectors of integers normally")))) | |
136211a9 EZ |
42 | |
43 | ||
44 | (defun calc-pack (n) | |
45 | (interactive "P") | |
46 | (calc-wrapper | |
47 | (let* ((nn (if n 1 2)) | |
48 | (mode (if n (prefix-numeric-value n) (calc-top-n 1))) | |
49 | (mode (if (and (Math-vectorp mode) (cdr mode)) (cdr mode) | |
50 | (if (integerp mode) mode | |
51 | (error "Packing mode must be an integer or vector of integers")))) | |
52 | (num (calc-pack-size mode)) | |
53 | (items (calc-top-list num nn))) | |
bf77c646 | 54 | (calc-enter-result (+ nn num -1) "pack" (calc-pack-items mode items))))) |
136211a9 EZ |
55 | |
56 | (defun calc-pack-size (mode) | |
57 | (cond ((consp mode) | |
58 | (let ((size 1)) | |
59 | (while mode | |
60 | (or (integerp (car mode)) (error "Vector of integers expected")) | |
61 | (setq size (* size (calc-pack-size (car mode))) | |
62 | mode (cdr mode))) | |
63 | (if (= size 0) | |
64 | (error "Zero dimensions not allowed") | |
65 | size))) | |
66 | ((>= mode 0) mode) | |
67 | (t (or (cdr (assq mode '((-3 . 3) (-13 . 1) (-14 . 3) (-15 . 6)))) | |
bf77c646 | 68 | 2)))) |
136211a9 EZ |
69 | |
70 | (defun calc-pack-items (mode items) | |
71 | (cond ((consp mode) | |
72 | (if (cdr mode) | |
73 | (let* ((size (calc-pack-size (cdr mode))) | |
74 | (len (length items)) | |
75 | (new nil) | |
76 | p row) | |
77 | (while (> len 0) | |
78 | (setq p (nthcdr (1- size) items) | |
79 | row items | |
80 | items (cdr p) | |
81 | len (- len size)) | |
82 | (setcdr p nil) | |
83 | (setq new (cons (calc-pack-items (cdr mode) row) new))) | |
84 | (calc-pack-items (car mode) (nreverse new))) | |
85 | (calc-pack-items (car mode) items))) | |
86 | ((>= mode 0) | |
87 | (cons 'vec items)) | |
88 | ((= mode -3) | |
89 | (if (and (math-objvecp (car items)) | |
90 | (math-objvecp (nth 1 items)) | |
91 | (math-objvecp (nth 2 items))) | |
92 | (if (and (math-num-integerp (car items)) | |
93 | (math-num-integerp (nth 1 items))) | |
94 | (if (math-realp (nth 2 items)) | |
95 | (cons 'hms items) | |
96 | (error "Seconds must be real")) | |
97 | (error "Hours and minutes must be integers")) | |
98 | (math-normalize (list '+ | |
99 | (list '+ | |
100 | (if (eq calc-angle-mode 'rad) | |
101 | (list '* (car items) | |
102 | '(hms 1 0 0)) | |
103 | (car items)) | |
104 | (list '* (nth 1 items) '(hms 0 1 0))) | |
105 | (list '* (nth 2 items) '(hms 0 0 1)))))) | |
106 | ((= mode -13) | |
107 | (if (math-realp (car items)) | |
108 | (cons 'date items) | |
109 | (if (eq (car-safe (car items)) 'date) | |
110 | (car items) | |
111 | (if (math-objvecp (car items)) | |
112 | (error "Date value must be real") | |
113 | (cons 'calcFunc-date items))))) | |
114 | ((memq mode '(-14 -15)) | |
115 | (let ((p items)) | |
116 | (while (and p (math-objvecp (car p))) | |
117 | (or (math-integerp (car p)) | |
118 | (error "Components must be integers")) | |
119 | (setq p (cdr p))) | |
120 | (if p | |
121 | (cons 'calcFunc-date items) | |
122 | (list 'date (math-dt-to-date items))))) | |
123 | ((or (eq (car-safe (car items)) 'vec) | |
124 | (eq (car-safe (nth 1 items)) 'vec)) | |
125 | (let* ((x (car items)) | |
126 | (vx (eq (car-safe x) 'vec)) | |
127 | (y (nth 1 items)) | |
128 | (vy (eq (car-safe y) 'vec)) | |
129 | (z nil) | |
130 | (n (1- (length (if vx x y))))) | |
131 | (and vx vy | |
132 | (/= n (1- (length y))) | |
133 | (error "Vectors must be the same length")) | |
134 | (while (>= (setq n (1- n)) 0) | |
135 | (setq z (cons (calc-pack-items | |
136 | mode | |
137 | (list (if vx (car (setq x (cdr x))) x) | |
138 | (if vy (car (setq y (cdr y))) y))) | |
139 | z))) | |
140 | (cons 'vec (nreverse z)))) | |
141 | ((= mode -1) | |
142 | (if (and (math-realp (car items)) (math-realp (nth 1 items))) | |
143 | (cons 'cplx items) | |
144 | (if (and (math-objectp (car items)) (math-objectp (nth 1 items))) | |
145 | (error "Components must be real")) | |
146 | (math-normalize (list '+ (car items) | |
147 | (list '* (nth 1 items) '(cplx 0 1)))))) | |
148 | ((= mode -2) | |
149 | (if (and (math-realp (car items)) (math-anglep (nth 1 items))) | |
150 | (cons 'polar items) | |
151 | (if (and (math-objectp (car items)) (math-objectp (nth 1 items))) | |
152 | (error "Components must be real")) | |
153 | (math-normalize (list '* (car items) | |
154 | (if (math-anglep (nth 1 items)) | |
155 | (list 'polar 1 (nth 1 items)) | |
156 | (list 'calcFunc-exp | |
157 | (list '* | |
158 | (math-to-radians-2 | |
159 | (nth 1 items)) | |
160 | (list 'polar | |
161 | 1 | |
162 | (math-quarter-circle | |
163 | nil))))))))) | |
164 | ((= mode -4) | |
165 | (let ((x (car items)) | |
166 | (sigma (nth 1 items))) | |
167 | (if (or (math-scalarp x) (not (math-objvecp x))) | |
168 | (if (or (math-anglep sigma) (not (math-objvecp sigma))) | |
169 | (math-make-sdev x sigma) | |
170 | (error "Error component must be real")) | |
171 | (error "Mean component must be real or complex")))) | |
172 | ((= mode -5) | |
173 | (let ((a (car items)) | |
174 | (m (nth 1 items))) | |
175 | (if (and (math-anglep a) (math-anglep m)) | |
176 | (if (math-posp m) | |
177 | (math-make-mod a m) | |
178 | (error "Modulus must be positive")) | |
179 | (if (and (math-objectp a) (math-objectp m)) | |
180 | (error "Components must be real")) | |
181 | (list 'calcFunc-makemod a m)))) | |
182 | ((memq mode '(-6 -7 -8 -9)) | |
183 | (let ((lo (car items)) | |
184 | (hi (nth 1 items))) | |
185 | (if (and (or (math-anglep lo) (eq (car lo) 'date) | |
186 | (not (math-objvecp lo))) | |
187 | (or (math-anglep hi) (eq (car hi) 'date) | |
188 | (not (math-objvecp hi)))) | |
189 | (math-make-intv (+ mode 9) lo hi) | |
190 | (error "Components must be real")))) | |
191 | ((eq mode -10) | |
192 | (if (math-zerop (nth 1 items)) | |
193 | (error "Denominator must not be zero") | |
194 | (if (and (math-integerp (car items)) (math-integerp (nth 1 items))) | |
195 | (math-normalize (cons 'frac items)) | |
196 | (if (and (math-objectp (car items)) (math-objectp (nth 1 items))) | |
197 | (error "Components must be integers")) | |
198 | (cons 'calcFunc-fdiv items)))) | |
199 | ((memq mode '(-11 -12)) | |
200 | (if (and (math-realp (car items)) (math-integerp (nth 1 items))) | |
201 | (calcFunc-scf (math-float (car items)) (nth 1 items)) | |
202 | (if (and (math-objectp (car items)) (math-objectp (nth 1 items))) | |
203 | (error "Components must be integers")) | |
204 | (math-normalize | |
205 | (list 'calcFunc-scf | |
206 | (list 'calcFunc-float (car items)) | |
207 | (nth 1 items))))) | |
208 | (t | |
bf77c646 | 209 | (error "Invalid packing mode: %d" mode)))) |
136211a9 | 210 | |
3132f345 | 211 | (defvar calc-unpack-with-type nil) |
136211a9 EZ |
212 | (defun calc-unpack (mode) |
213 | (interactive "P") | |
214 | (calc-wrapper | |
215 | (let ((calc-unpack-with-type t)) | |
216 | (calc-pop-push-record-list 1 "unpk" (calc-unpack-item | |
217 | (and mode | |
218 | (prefix-numeric-value mode)) | |
bf77c646 | 219 | (calc-top)))))) |
136211a9 EZ |
220 | |
221 | (defun calc-unpack-type (item) | |
222 | (cond ((eq (car-safe item) 'vec) | |
223 | (1- (length item))) | |
224 | ((eq (car-safe item) 'intv) | |
225 | (- (nth 1 item) 9)) | |
226 | (t | |
227 | (or (cdr (assq (car-safe item) '( (cplx . -1) (polar . -2) | |
228 | (hms . -3) (sdev . -4) (mod . -5) | |
229 | (frac . -10) (float . -11) | |
230 | (date . -13) ))) | |
bf77c646 | 231 | (error "Argument must be a composite object"))))) |
136211a9 EZ |
232 | |
233 | (defun calc-unpack-item (mode item) | |
234 | (cond ((not mode) | |
235 | (if (or (and (not (memq (car-safe item) '(frac float cplx polar vec | |
236 | hms date sdev mod | |
237 | intv))) | |
238 | (math-objvecp item)) | |
239 | (eq (car-safe item) 'var)) | |
240 | (error "Argument must be a composite object or function call")) | |
241 | (if (eq (car item) 'intv) | |
242 | (cdr (cdr item)) | |
243 | (cdr item))) | |
244 | ((> mode 0) | |
245 | (let ((dims nil) | |
246 | type new row) | |
247 | (setq item (list item)) | |
248 | (while (> mode 0) | |
249 | (setq type (calc-unpack-type (car item)) | |
250 | dims (cons type dims) | |
251 | new (calc-unpack-item nil (car item))) | |
252 | (while (setq item (cdr item)) | |
253 | (or (= (calc-unpack-type (car item)) type) | |
254 | (error "Inconsistent types or dimensions in vector elements")) | |
255 | (setq new (append new (calc-unpack-item nil (car item))))) | |
256 | (setq item new | |
257 | mode (1- mode))) | |
258 | (if (cdr dims) (setq dims (list (cons 'vec (nreverse dims))))) | |
259 | (cond ((eq calc-unpack-with-type 'pair) | |
260 | (list (car dims) (cons 'vec item))) | |
261 | (calc-unpack-with-type | |
262 | (append item dims)) | |
263 | (t item)))) | |
264 | ((eq calc-unpack-with-type 'pair) | |
265 | (let ((calc-unpack-with-type nil)) | |
266 | (list mode (cons 'vec (calc-unpack-item mode item))))) | |
267 | ((= mode -3) | |
268 | (if (eq (car-safe item) 'hms) | |
269 | (cdr item) | |
270 | (error "Argument must be an HMS form"))) | |
271 | ((= mode -13) | |
272 | (if (eq (car-safe item) 'date) | |
273 | (cdr item) | |
274 | (error "Argument must be a date form"))) | |
275 | ((= mode -14) | |
276 | (if (eq (car-safe item) 'date) | |
277 | (math-date-to-dt (math-floor (nth 1 item))) | |
278 | (error "Argument must be a date form"))) | |
279 | ((= mode -15) | |
280 | (if (eq (car-safe item) 'date) | |
281 | (append (math-date-to-dt (nth 1 item)) | |
282 | (and (not (math-integerp (nth 1 item))) | |
283 | (list 0 0 0))) | |
284 | (error "Argument must be a date form"))) | |
285 | ((eq (car-safe item) 'vec) | |
286 | (let ((x nil) | |
287 | (y nil) | |
288 | res) | |
289 | (while (setq item (cdr item)) | |
290 | (setq res (calc-unpack-item mode (car item)) | |
291 | x (cons (car res) x) | |
292 | y (cons (nth 1 res) y))) | |
293 | (list (cons 'vec (nreverse x)) | |
294 | (cons 'vec (nreverse y))))) | |
295 | ((= mode -1) | |
296 | (if (eq (car-safe item) 'cplx) | |
297 | (cdr item) | |
298 | (if (eq (car-safe item) 'polar) | |
299 | (cdr (math-complex item)) | |
300 | (if (Math-realp item) | |
301 | (list item 0) | |
302 | (error "Argument must be a complex number"))))) | |
303 | ((= mode -2) | |
304 | (if (or (memq (car-safe item) '(cplx polar)) | |
305 | (Math-realp item)) | |
306 | (cdr (math-polar item)) | |
307 | (error "Argument must be a complex number"))) | |
308 | ((= mode -4) | |
309 | (if (eq (car-safe item) 'sdev) | |
310 | (cdr item) | |
311 | (list item 0))) | |
312 | ((= mode -5) | |
313 | (if (eq (car-safe item) 'mod) | |
314 | (cdr item) | |
315 | (error "Argument must be a modulo form"))) | |
316 | ((memq mode '(-6 -7 -8 -9)) | |
317 | (if (eq (car-safe item) 'intv) | |
318 | (cdr (cdr item)) | |
319 | (list item item))) | |
320 | ((= mode -10) | |
321 | (if (eq (car-safe item) 'frac) | |
322 | (cdr item) | |
323 | (if (Math-integerp item) | |
324 | (list item 1) | |
325 | (error "Argument must be a rational number")))) | |
326 | ((= mode -11) | |
327 | (if (eq (car-safe item) 'float) | |
328 | (list (nth 1 item) (math-normalize (nth 2 item))) | |
329 | (error "Expected a floating-point number"))) | |
330 | ((= mode -12) | |
331 | (if (eq (car-safe item) 'float) | |
332 | (list (calcFunc-mant item) (calcFunc-xpon item)) | |
333 | (error "Expected a floating-point number"))) | |
334 | (t | |
bf77c646 | 335 | (error "Invalid unpacking mode: %d" mode)))) |
136211a9 EZ |
336 | |
337 | (defun calc-diag (n) | |
338 | (interactive "P") | |
339 | (calc-wrapper | |
340 | (calc-enter-result 1 "diag" (if n | |
341 | (list 'calcFunc-diag (calc-top-n 1) | |
342 | (prefix-numeric-value n)) | |
bf77c646 | 343 | (list 'calcFunc-diag (calc-top-n 1)))))) |
136211a9 EZ |
344 | |
345 | (defun calc-ident (n) | |
346 | (interactive "NDimension of identity matrix = ") | |
347 | (calc-wrapper | |
348 | (calc-enter-result 0 "idn" (if (eq n 0) | |
349 | '(calcFunc-idn 1) | |
350 | (list 'calcFunc-idn 1 | |
bf77c646 | 351 | (prefix-numeric-value n)))))) |
136211a9 EZ |
352 | |
353 | (defun calc-index (n &optional stack) | |
354 | (interactive "NSize of vector = \nP") | |
355 | (calc-wrapper | |
356 | (if (consp stack) | |
357 | (calc-enter-result 3 "indx" (cons 'calcFunc-index (calc-top-list-n 3))) | |
358 | (calc-enter-result 0 "indx" (list 'calcFunc-index | |
bf77c646 | 359 | (prefix-numeric-value n)))))) |
136211a9 EZ |
360 | |
361 | (defun calc-build-vector (n) | |
362 | (interactive "NSize of vector = ") | |
363 | (calc-wrapper | |
364 | (calc-enter-result 1 "bldv" (list 'calcFunc-cvec | |
365 | (calc-top-n 1) | |
bf77c646 | 366 | (prefix-numeric-value n))))) |
136211a9 EZ |
367 | |
368 | (defun calc-cons (arg) | |
369 | (interactive "P") | |
370 | (calc-wrapper | |
371 | (if (calc-is-hyperbolic) | |
372 | (calc-binary-op "rcns" 'calcFunc-rcons arg) | |
bf77c646 | 373 | (calc-binary-op "cons" 'calcFunc-cons arg)))) |
136211a9 EZ |
374 | |
375 | ||
376 | (defun calc-head (arg) | |
377 | (interactive "P") | |
378 | (calc-wrapper | |
379 | (if (calc-is-inverse) | |
380 | (if (calc-is-hyperbolic) | |
381 | (calc-unary-op "rtai" 'calcFunc-rtail arg) | |
382 | (calc-unary-op "tail" 'calcFunc-tail arg)) | |
383 | (if (calc-is-hyperbolic) | |
384 | (calc-unary-op "rhed" 'calcFunc-rhead arg) | |
bf77c646 | 385 | (calc-unary-op "head" 'calcFunc-head arg))))) |
136211a9 EZ |
386 | |
387 | (defun calc-tail (arg) | |
388 | (interactive "P") | |
389 | (calc-invert-func) | |
bf77c646 | 390 | (calc-head arg)) |
136211a9 EZ |
391 | |
392 | (defun calc-vlength (arg) | |
393 | (interactive "P") | |
394 | (calc-wrapper | |
395 | (if (calc-is-hyperbolic) | |
396 | (calc-unary-op "dims" 'calcFunc-mdims arg) | |
bf77c646 | 397 | (calc-unary-op "len" 'calcFunc-vlen arg)))) |
136211a9 EZ |
398 | |
399 | (defun calc-arrange-vector (n) | |
400 | (interactive "NNumber of columns = ") | |
401 | (calc-wrapper | |
402 | (calc-enter-result 1 "arng" (list 'calcFunc-arrange (calc-top-n 1) | |
bf77c646 | 403 | (prefix-numeric-value n))))) |
136211a9 EZ |
404 | |
405 | (defun calc-vector-find (arg) | |
406 | (interactive "P") | |
407 | (calc-wrapper | |
408 | (let ((func (cons 'calcFunc-find (calc-top-list-n 2)))) | |
409 | (calc-enter-result | |
410 | 2 "find" | |
bf77c646 | 411 | (if arg (append func (list (prefix-numeric-value arg))) func))))) |
136211a9 EZ |
412 | |
413 | (defun calc-subvector () | |
414 | (interactive) | |
415 | (calc-wrapper | |
416 | (if (calc-is-inverse) | |
417 | (calc-enter-result 3 "rsvc" (cons 'calcFunc-rsubvec | |
418 | (calc-top-list-n 3))) | |
bf77c646 | 419 | (calc-enter-result 3 "svec" (cons 'calcFunc-subvec (calc-top-list-n 3)))))) |
136211a9 EZ |
420 | |
421 | (defun calc-reverse-vector (arg) | |
422 | (interactive "P") | |
423 | (calc-wrapper | |
bf77c646 | 424 | (calc-unary-op "rev" 'calcFunc-rev arg))) |
136211a9 EZ |
425 | |
426 | (defun calc-mask-vector (arg) | |
427 | (interactive "P") | |
428 | (calc-wrapper | |
bf77c646 | 429 | (calc-binary-op "vmsk" 'calcFunc-vmask arg))) |
136211a9 EZ |
430 | |
431 | (defun calc-expand-vector (arg) | |
432 | (interactive "P") | |
433 | (calc-wrapper | |
434 | (if (calc-is-hyperbolic) | |
435 | (calc-enter-result 3 "vexp" (cons 'calcFunc-vexp (calc-top-list-n 3))) | |
bf77c646 | 436 | (calc-binary-op "vexp" 'calcFunc-vexp arg)))) |
136211a9 EZ |
437 | |
438 | (defun calc-sort () | |
439 | (interactive) | |
440 | (calc-slow-wrapper | |
441 | (if (calc-is-inverse) | |
442 | (calc-enter-result 1 "rsrt" (list 'calcFunc-rsort (calc-top-n 1))) | |
bf77c646 | 443 | (calc-enter-result 1 "sort" (list 'calcFunc-sort (calc-top-n 1)))))) |
136211a9 EZ |
444 | |
445 | (defun calc-grade () | |
446 | (interactive) | |
447 | (calc-slow-wrapper | |
448 | (if (calc-is-inverse) | |
449 | (calc-enter-result 1 "rgrd" (list 'calcFunc-rgrade (calc-top-n 1))) | |
bf77c646 | 450 | (calc-enter-result 1 "grad" (list 'calcFunc-grade (calc-top-n 1)))))) |
136211a9 EZ |
451 | |
452 | (defun calc-histogram (n) | |
597517ef JB |
453 | (interactive "P") |
454 | (unless (natnump n) | |
455 | (setq n (math-read-expr (read-string "Centers of bins: ")))) | |
136211a9 EZ |
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) | |
597517ef | 461 | n)) |
136211a9 EZ |
462 | (calc-enter-result 1 "hist" (list 'calcFunc-histogram |
463 | (calc-top-n 1) | |
597517ef | 464 | 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 | 480 | |
1aa484e3 JB |
481 | (defun calc-kron (arg) |
482 | (interactive "P") | |
483 | (calc-wrapper | |
484 | (calc-binary-op "kron" 'calcFunc-kron arg))) | |
485 | ||
136211a9 EZ |
486 | (defun calc-remove-duplicates (arg) |
487 | (interactive "P") | |
488 | (calc-wrapper | |
bf77c646 | 489 | (calc-unary-op "rdup" 'calcFunc-rdup arg))) |
136211a9 EZ |
490 | |
491 | (defun calc-set-union (arg) | |
492 | (interactive "P") | |
493 | (calc-wrapper | |
bf77c646 | 494 | (calc-binary-op "unio" 'calcFunc-vunion arg '(vec) 'calcFunc-rdup))) |
136211a9 EZ |
495 | |
496 | (defun calc-set-intersect (arg) | |
497 | (interactive "P") | |
498 | (calc-wrapper | |
bf77c646 | 499 | (calc-binary-op "intr" 'calcFunc-vint arg '(vec) 'calcFunc-rdup))) |
136211a9 EZ |
500 | |
501 | (defun calc-set-difference (arg) | |
502 | (interactive "P") | |
503 | (calc-wrapper | |
bf77c646 | 504 | (calc-binary-op "diff" 'calcFunc-vdiff arg '(vec) 'calcFunc-rdup))) |
136211a9 EZ |
505 | |
506 | (defun calc-set-xor (arg) | |
507 | (interactive "P") | |
508 | (calc-wrapper | |
bf77c646 | 509 | (calc-binary-op "xor" 'calcFunc-vxor arg '(vec) 'calcFunc-rdup))) |
136211a9 EZ |
510 | |
511 | (defun calc-set-complement (arg) | |
512 | (interactive "P") | |
513 | (calc-wrapper | |
bf77c646 | 514 | (calc-unary-op "cmpl" 'calcFunc-vcompl arg))) |
136211a9 EZ |
515 | |
516 | (defun calc-set-floor (arg) | |
517 | (interactive "P") | |
518 | (calc-wrapper | |
bf77c646 | 519 | (calc-unary-op "vflr" 'calcFunc-vfloor arg))) |
136211a9 EZ |
520 | |
521 | (defun calc-set-enumerate (arg) | |
522 | (interactive "P") | |
523 | (calc-wrapper | |
bf77c646 | 524 | (calc-unary-op "enum" 'calcFunc-venum arg))) |
136211a9 EZ |
525 | |
526 | (defun calc-set-span (arg) | |
527 | (interactive "P") | |
528 | (calc-wrapper | |
bf77c646 | 529 | (calc-unary-op "span" 'calcFunc-vspan arg))) |
136211a9 EZ |
530 | |
531 | (defun calc-set-cardinality (arg) | |
532 | (interactive "P") | |
533 | (calc-wrapper | |
bf77c646 | 534 | (calc-unary-op "card" 'calcFunc-vcard arg))) |
136211a9 EZ |
535 | |
536 | (defun calc-unpack-bits (arg) | |
537 | (interactive "P") | |
538 | (calc-wrapper | |
539 | (if (calc-is-inverse) | |
540 | (calc-unary-op "bpck" 'calcFunc-vpack arg) | |
bf77c646 | 541 | (calc-unary-op "bupk" 'calcFunc-vunpack arg)))) |
136211a9 EZ |
542 | |
543 | (defun calc-pack-bits (arg) | |
544 | (interactive "P") | |
545 | (calc-invert-func) | |
bf77c646 | 546 | (calc-unpack-bits arg)) |
136211a9 EZ |
547 | |
548 | ||
549 | (defun calc-rnorm (arg) | |
550 | (interactive "P") | |
551 | (calc-wrapper | |
bf77c646 | 552 | (calc-unary-op "rnrm" 'calcFunc-rnorm arg))) |
136211a9 EZ |
553 | |
554 | (defun calc-cnorm (arg) | |
555 | (interactive "P") | |
556 | (calc-wrapper | |
bf77c646 | 557 | (calc-unary-op "cnrm" 'calcFunc-cnorm arg))) |
136211a9 EZ |
558 | |
559 | (defun calc-mrow (n &optional nn) | |
560 | (interactive "NRow number: \nP") | |
561 | (calc-wrapper | |
562 | (if (consp nn) | |
563 | (calc-enter-result 2 "mrow" (cons 'calcFunc-mrow (calc-top-list-n 2))) | |
564 | (setq n (prefix-numeric-value n)) | |
565 | (if (= n 0) | |
566 | (calc-enter-result 1 "getd" (list 'calcFunc-getdiag (calc-top-n 1))) | |
567 | (if (< n 0) | |
568 | (calc-enter-result 1 "rrow" (list 'calcFunc-mrrow | |
569 | (calc-top-n 1) (- n))) | |
570 | (calc-enter-result 1 "mrow" (list 'calcFunc-mrow | |
bf77c646 | 571 | (calc-top-n 1) n))))))) |
136211a9 EZ |
572 | |
573 | (defun calc-mcol (n &optional nn) | |
574 | (interactive "NColumn number: \nP") | |
575 | (calc-wrapper | |
576 | (if (consp nn) | |
577 | (calc-enter-result 2 "mcol" (cons 'calcFunc-mcol (calc-top-list-n 2))) | |
578 | (setq n (prefix-numeric-value n)) | |
579 | (if (= n 0) | |
580 | (calc-enter-result 1 "getd" (list 'calcFunc-getdiag (calc-top-n 1))) | |
581 | (if (< n 0) | |
582 | (calc-enter-result 1 "rcol" (list 'calcFunc-mrcol | |
583 | (calc-top-n 1) (- n))) | |
584 | (calc-enter-result 1 "mcol" (list 'calcFunc-mcol | |
bf77c646 | 585 | (calc-top-n 1) n))))))) |
136211a9 EZ |
586 | |
587 | ||
588 | ;;;; Vectors. | |
589 | ||
590 | (defun calcFunc-mdims (m) | |
591 | (or (math-vectorp m) | |
592 | (math-reject-arg m 'vectorp)) | |
bf77c646 | 593 | (cons 'vec (math-mat-dimens m))) |
136211a9 EZ |
594 | |
595 | ||
596 | ;;; Apply a function elementwise to vector A. [V X V; N X N] [Public] | |
597 | (defun math-map-vec (f a) | |
598 | (if (math-vectorp a) | |
599 | (cons 'vec (mapcar f (cdr a))) | |
bf77c646 | 600 | (funcall f a))) |
136211a9 EZ |
601 | |
602 | (defun math-dimension-error () | |
603 | (calc-record-why "*Dimension error") | |
bf77c646 | 604 | (signal 'wrong-type-argument nil)) |
136211a9 EZ |
605 | |
606 | ||
607 | ;;; Build a vector out of a list of objects. [Public] | |
608 | (defun calcFunc-vec (&rest objs) | |
bf77c646 | 609 | (cons 'vec objs)) |
136211a9 EZ |
610 | |
611 | ||
612 | ;;; Build a constant vector or matrix. [Public] | |
613 | (defun calcFunc-cvec (obj &rest dims) | |
bf77c646 | 614 | (math-make-vec-dimen obj dims)) |
136211a9 EZ |
615 | |
616 | (defun math-make-vec-dimen (obj dims) | |
617 | (if dims | |
618 | (if (natnump (car dims)) | |
619 | (if (or (cdr dims) | |
620 | (not (math-numberp obj))) | |
621 | (cons 'vec (copy-sequence | |
622 | (make-list (car dims) | |
623 | (math-make-vec-dimen obj (cdr dims))))) | |
624 | (cons 'vec (make-list (car dims) obj))) | |
625 | (math-reject-arg (car dims) 'fixnatnump)) | |
bf77c646 | 626 | obj)) |
136211a9 EZ |
627 | |
628 | (defun calcFunc-head (vec) | |
629 | (if (and (Math-vectorp vec) | |
630 | (cdr vec)) | |
631 | (nth 1 vec) | |
632 | (calc-record-why 'vectorp vec) | |
bf77c646 | 633 | (list 'calcFunc-head vec))) |
136211a9 EZ |
634 | |
635 | (defun calcFunc-tail (vec) | |
636 | (if (and (Math-vectorp vec) | |
637 | (cdr vec)) | |
638 | (cons 'vec (cdr (cdr vec))) | |
639 | (calc-record-why 'vectorp vec) | |
bf77c646 | 640 | (list 'calcFunc-tail vec))) |
136211a9 EZ |
641 | |
642 | (defun calcFunc-cons (head tail) | |
643 | (if (Math-vectorp tail) | |
644 | (cons 'vec (cons head (cdr tail))) | |
645 | (calc-record-why 'vectorp tail) | |
bf77c646 | 646 | (list 'calcFunc-cons head tail))) |
136211a9 EZ |
647 | |
648 | (defun calcFunc-rhead (vec) | |
649 | (if (and (Math-vectorp vec) | |
650 | (cdr vec)) | |
651 | (let ((vec (copy-sequence vec))) | |
652 | (setcdr (nthcdr (- (length vec) 2) vec) nil) | |
653 | vec) | |
654 | (calc-record-why 'vectorp vec) | |
bf77c646 | 655 | (list 'calcFunc-rhead vec))) |
136211a9 EZ |
656 | |
657 | (defun calcFunc-rtail (vec) | |
658 | (if (and (Math-vectorp vec) | |
659 | (cdr vec)) | |
660 | (nth (1- (length vec)) vec) | |
661 | (calc-record-why 'vectorp vec) | |
bf77c646 | 662 | (list 'calcFunc-rtail vec))) |
136211a9 EZ |
663 | |
664 | (defun calcFunc-rcons (head tail) | |
665 | (if (Math-vectorp head) | |
666 | (append head (list tail)) | |
667 | (calc-record-why 'vectorp head) | |
bf77c646 | 668 | (list 'calcFunc-rcons head tail))) |
136211a9 EZ |
669 | |
670 | ||
671 | ||
672 | ;;; Apply a function elementwise to vectors A and B. [O X O O] [Public] | |
673 | (defun math-map-vec-2 (f a b) | |
674 | (if (math-vectorp a) | |
675 | (if (math-vectorp b) | |
676 | (let ((v nil)) | |
677 | (while (setq a (cdr a)) | |
678 | (or (setq b (cdr b)) | |
679 | (math-dimension-error)) | |
680 | (setq v (cons (funcall f (car a) (car b)) v))) | |
681 | (if a (math-dimension-error)) | |
682 | (cons 'vec (nreverse v))) | |
683 | (let ((v nil)) | |
684 | (while (setq a (cdr a)) | |
685 | (setq v (cons (funcall f (car a) b) v))) | |
686 | (cons 'vec (nreverse v)))) | |
687 | (if (math-vectorp b) | |
688 | (let ((v nil)) | |
689 | (while (setq b (cdr b)) | |
690 | (setq v (cons (funcall f a (car b)) v))) | |
691 | (cons 'vec (nreverse v))) | |
bf77c646 | 692 | (funcall f a b)))) |
136211a9 EZ |
693 | |
694 | ||
695 | ||
696 | ;;; "Reduce" a function over a vector (left-associatively). [O X V] [Public] | |
697 | (defun math-reduce-vec (f a) | |
698 | (if (math-vectorp a) | |
699 | (if (cdr a) | |
700 | (let ((accum (car (setq a (cdr a))))) | |
701 | (while (setq a (cdr a)) | |
702 | (setq accum (funcall f accum (car a)))) | |
703 | accum) | |
704 | 0) | |
bf77c646 | 705 | a)) |
136211a9 EZ |
706 | |
707 | ;;; Reduce a function over the columns of matrix A. [V X V] [Public] | |
708 | (defun math-reduce-cols (f a) | |
709 | (if (math-matrixp a) | |
710 | (cons 'vec (math-reduce-cols-col-step f (cdr a) 1 (length (nth 1 a)))) | |
bf77c646 | 711 | a)) |
136211a9 EZ |
712 | |
713 | (defun math-reduce-cols-col-step (f a col cols) | |
714 | (and (< col cols) | |
715 | (cons (math-reduce-cols-row-step f (nth col (car a)) col (cdr a)) | |
bf77c646 | 716 | (math-reduce-cols-col-step f a (1+ col) cols)))) |
136211a9 EZ |
717 | |
718 | (defun math-reduce-cols-row-step (f tot col a) | |
719 | (if a | |
720 | (math-reduce-cols-row-step f | |
721 | (funcall f tot (nth col (car a))) | |
722 | col | |
723 | (cdr a)) | |
bf77c646 | 724 | tot)) |
136211a9 EZ |
725 | |
726 | ||
727 | ||
728 | (defun math-dot-product (a b) | |
729 | (if (setq a (cdr a) b (cdr b)) | |
730 | (let ((accum (math-mul (car a) (car b)))) | |
731 | (while (setq a (cdr a) b (cdr b)) | |
732 | (setq accum (math-add accum (math-mul (car a) (car b))))) | |
733 | accum) | |
bf77c646 | 734 | 0)) |
136211a9 EZ |
735 | |
736 | ||
737 | ;;; Return the number of elements in vector V. [Public] | |
738 | (defun calcFunc-vlen (v) | |
739 | (if (math-vectorp v) | |
740 | (1- (length v)) | |
741 | (if (math-objectp v) | |
742 | 0 | |
bf77c646 | 743 | (list 'calcFunc-vlen v)))) |
136211a9 EZ |
744 | |
745 | ;;; Get the Nth row of a matrix. | |
746 | (defun calcFunc-mrow (mat n) ; [Public] | |
747 | (if (Math-vectorp n) | |
748 | (math-map-vec (function (lambda (x) (calcFunc-mrow mat x))) n) | |
749 | (if (and (eq (car-safe n) 'intv) (math-constp n)) | |
750 | (calcFunc-subvec mat | |
751 | (math-add (nth 2 n) (if (memq (nth 1 n) '(2 3)) 0 1)) | |
752 | (math-add (nth 3 n) (if (memq (nth 1 n) '(1 3)) 1 0))) | |
753 | (or (and (integerp (setq n (math-check-integer n))) | |
754 | (> n 0)) | |
755 | (math-reject-arg n 'fixposintp)) | |
756 | (or (Math-vectorp mat) | |
757 | (math-reject-arg mat 'vectorp)) | |
758 | (or (nth n mat) | |
bf77c646 | 759 | (math-reject-arg n "*Index out of range"))))) |
136211a9 EZ |
760 | |
761 | (defun calcFunc-subscr (mat n &optional m) | |
53f963cf JB |
762 | (if (eq (car-safe mat) 'var) nil |
763 | (setq mat (calcFunc-mrow mat n)) | |
764 | (if m | |
765 | (if (math-num-integerp n) | |
766 | (calcFunc-mrow mat m) | |
767 | (calcFunc-mcol mat m)) | |
768 | mat))) | |
136211a9 EZ |
769 | |
770 | ;;; Get the Nth column of a matrix. | |
771 | (defun math-mat-col (mat n) | |
bf77c646 | 772 | (cons 'vec (mapcar (function (lambda (x) (elt x n))) (cdr mat)))) |
136211a9 EZ |
773 | |
774 | (defun calcFunc-mcol (mat n) ; [Public] | |
775 | (if (Math-vectorp n) | |
776 | (calcFunc-trn | |
777 | (math-map-vec (function (lambda (x) (calcFunc-mcol mat x))) n)) | |
778 | (if (and (eq (car-safe n) 'intv) (math-constp n)) | |
779 | (if (math-matrixp mat) | |
780 | (math-map-vec (function (lambda (x) (calcFunc-mrow x n))) mat) | |
781 | (calcFunc-mrow mat n)) | |
782 | (or (and (integerp (setq n (math-check-integer n))) | |
783 | (> n 0)) | |
784 | (math-reject-arg n 'fixposintp)) | |
785 | (or (Math-vectorp mat) | |
786 | (math-reject-arg mat 'vectorp)) | |
787 | (or (if (math-matrixp mat) | |
788 | (and (< n (length (nth 1 mat))) | |
789 | (math-mat-col mat n)) | |
790 | (nth n mat)) | |
bf77c646 | 791 | (math-reject-arg n "*Index out of range"))))) |
136211a9 EZ |
792 | |
793 | ;;; Remove the Nth row from a matrix. | |
794 | (defun math-mat-less-row (mat n) | |
795 | (if (<= n 0) | |
796 | (cdr mat) | |
797 | (cons (car mat) | |
bf77c646 | 798 | (math-mat-less-row (cdr mat) (1- n))))) |
136211a9 EZ |
799 | |
800 | (defun calcFunc-mrrow (mat n) ; [Public] | |
801 | (and (integerp (setq n (math-check-integer n))) | |
802 | (> n 0) | |
803 | (< n (length mat)) | |
bf77c646 | 804 | (math-mat-less-row mat n))) |
136211a9 EZ |
805 | |
806 | ;;; Remove the Nth column from a matrix. | |
807 | (defun math-mat-less-col (mat n) | |
808 | (cons 'vec (mapcar (function (lambda (x) (math-mat-less-row x n))) | |
bf77c646 | 809 | (cdr mat)))) |
136211a9 EZ |
810 | |
811 | (defun calcFunc-mrcol (mat n) ; [Public] | |
812 | (and (integerp (setq n (math-check-integer n))) | |
813 | (> n 0) | |
814 | (if (math-matrixp mat) | |
815 | (and (< n (length (nth 1 mat))) | |
816 | (math-mat-less-col mat n)) | |
bf77c646 | 817 | (math-mat-less-row mat n)))) |
136211a9 EZ |
818 | |
819 | (defun calcFunc-getdiag (mat) ; [Public] | |
820 | (if (math-square-matrixp mat) | |
821 | (cons 'vec (math-get-diag-step (cdr mat) 1)) | |
822 | (calc-record-why 'square-matrixp mat) | |
bf77c646 | 823 | (list 'calcFunc-getdiag mat))) |
136211a9 EZ |
824 | |
825 | (defun math-get-diag-step (row n) | |
826 | (and row | |
827 | (cons (nth n (car row)) | |
bf77c646 | 828 | (math-get-diag-step (cdr row) (1+ n))))) |
136211a9 EZ |
829 | |
830 | (defun math-transpose (mat) ; [Public] | |
831 | (let ((m nil) | |
832 | (col (length (nth 1 mat)))) | |
833 | (while (> (setq col (1- col)) 0) | |
834 | (setq m (cons (math-mat-col mat col) m))) | |
bf77c646 | 835 | (cons 'vec m))) |
136211a9 EZ |
836 | |
837 | (defun calcFunc-trn (mat) | |
838 | (if (math-vectorp mat) | |
839 | (if (math-matrixp mat) | |
840 | (math-transpose mat) | |
841 | (math-col-matrix mat)) | |
842 | (if (math-numberp mat) | |
843 | mat | |
bf77c646 | 844 | (math-reject-arg mat 'matrixp)))) |
136211a9 EZ |
845 | |
846 | (defun calcFunc-ctrn (mat) | |
bf77c646 | 847 | (calcFunc-conj (calcFunc-trn mat))) |
136211a9 EZ |
848 | |
849 | (defun calcFunc-pack (mode els) | |
850 | (or (Math-vectorp els) (math-reject-arg els 'vectorp)) | |
851 | (if (and (Math-vectorp mode) (cdr mode)) | |
852 | (setq mode (cdr mode)) | |
853 | (or (integerp mode) (math-reject-arg mode 'fixnump))) | |
854 | (condition-case err | |
855 | (if (= (calc-pack-size mode) (1- (length els))) | |
856 | (calc-pack-items mode (cdr els)) | |
857 | (math-reject-arg els "*Wrong number of elements")) | |
bf77c646 | 858 | (error (math-reject-arg els (nth 1 err))))) |
136211a9 EZ |
859 | |
860 | (defun calcFunc-unpack (mode thing) | |
861 | (or (integerp mode) (math-reject-arg mode 'fixnump)) | |
862 | (condition-case err | |
863 | (cons 'vec (calc-unpack-item mode thing)) | |
bf77c646 | 864 | (error (math-reject-arg thing (nth 1 err))))) |
136211a9 EZ |
865 | |
866 | (defun calcFunc-unpackt (mode thing) | |
867 | (let ((calc-unpack-with-type 'pair)) | |
bf77c646 | 868 | (calcFunc-unpack mode thing))) |
136211a9 EZ |
869 | |
870 | (defun calcFunc-arrange (vec cols) ; [Public] | |
871 | (setq cols (math-check-fixnum cols t)) | |
872 | (if (math-vectorp vec) | |
873 | (let* ((flat (math-flatten-vector vec)) | |
874 | (mat (list 'vec)) | |
875 | next) | |
876 | (if (<= cols 0) | |
877 | (nconc mat flat) | |
878 | (while (>= (length flat) cols) | |
879 | (setq next (nthcdr cols flat)) | |
880 | (setcdr (nthcdr (1- cols) flat) nil) | |
881 | (setq mat (nconc mat (list (cons 'vec flat))) | |
882 | flat next)) | |
883 | (if flat | |
884 | (setq mat (nconc mat (list (cons 'vec flat))))) | |
bf77c646 | 885 | mat)))) |
136211a9 EZ |
886 | |
887 | (defun math-flatten-vector (vec) ; [L V] | |
888 | (if (math-vectorp vec) | |
889 | (apply 'append (mapcar 'math-flatten-vector (cdr vec))) | |
bf77c646 | 890 | (list vec))) |
136211a9 EZ |
891 | |
892 | (defun calcFunc-vconcat (a b) | |
bf77c646 | 893 | (math-normalize (list '| a b))) |
136211a9 EZ |
894 | |
895 | (defun calcFunc-vconcatrev (a b) | |
bf77c646 | 896 | (math-normalize (list '| b a))) |
136211a9 EZ |
897 | |
898 | (defun calcFunc-append (v1 v2) | |
899 | (if (and (math-vectorp v1) (math-vectorp v2)) | |
900 | (append v1 (cdr v2)) | |
bf77c646 | 901 | (list 'calcFunc-append v1 v2))) |
136211a9 EZ |
902 | |
903 | (defun calcFunc-appendrev (v1 v2) | |
bf77c646 | 904 | (calcFunc-append v2 v1)) |
136211a9 EZ |
905 | |
906 | ||
907 | ;;; Copy a matrix. [Public] | |
908 | (defun math-copy-matrix (m) | |
909 | (if (math-vectorp (nth 1 m)) | |
910 | (cons 'vec (mapcar 'copy-sequence (cdr m))) | |
bf77c646 | 911 | (copy-sequence m))) |
136211a9 EZ |
912 | |
913 | ;;; Convert a scalar or vector into an NxN diagonal matrix. [Public] | |
914 | (defun calcFunc-diag (a &optional n) | |
915 | (and n (not (integerp n)) | |
916 | (setq n (math-check-fixnum n))) | |
917 | (if (math-vectorp a) | |
918 | (if (and n (/= (length a) (1+ n))) | |
919 | (list 'calcFunc-diag a n) | |
920 | (if (math-matrixp a) | |
921 | (if (and n (/= (length (elt a 1)) (1+ n))) | |
922 | (list 'calcFunc-diag a n) | |
923 | a) | |
924 | (cons 'vec (math-diag-step (cdr a) 0 (1- (length a)))))) | |
925 | (if n | |
926 | (cons 'vec (math-diag-step (make-list n a) 0 n)) | |
bf77c646 | 927 | (list 'calcFunc-diag a)))) |
136211a9 EZ |
928 | |
929 | (defun calcFunc-idn (a &optional n) | |
930 | (if n | |
931 | (if (math-vectorp a) | |
932 | (math-reject-arg a 'numberp) | |
933 | (calcFunc-diag a n)) | |
934 | (if (integerp calc-matrix-mode) | |
935 | (calcFunc-idn a calc-matrix-mode) | |
bf77c646 | 936 | (list 'calcFunc-idn a)))) |
136211a9 EZ |
937 | |
938 | (defun math-mimic-ident (a m) | |
939 | (if (math-square-matrixp m) | |
940 | (calcFunc-idn a (1- (length m))) | |
941 | (if (math-vectorp m) | |
942 | (if (math-zerop a) | |
943 | (cons 'vec (mapcar (function (lambda (x) | |
944 | (if (math-vectorp x) | |
945 | (math-mimic-ident a x) | |
946 | a))) | |
947 | (cdr m))) | |
948 | (math-dimension-error)) | |
bf77c646 | 949 | (calcFunc-idn a)))) |
136211a9 EZ |
950 | |
951 | (defun math-diag-step (a n m) | |
952 | (if (< n m) | |
953 | (cons (cons 'vec | |
954 | (nconc (make-list n 0) | |
955 | (cons (car a) | |
956 | (make-list (1- (- m n)) 0)))) | |
957 | (math-diag-step (cdr a) (1+ n) m)) | |
bf77c646 | 958 | nil)) |
136211a9 EZ |
959 | |
960 | ;;; Create a vector of consecutive integers. [Public] | |
961 | (defun calcFunc-index (n &optional start incr) | |
962 | (if (math-messy-integerp n) | |
963 | (math-float (calcFunc-index (math-trunc n) start incr)) | |
964 | (and (not (integerp n)) | |
965 | (setq n (math-check-fixnum n))) | |
966 | (let ((vec nil)) | |
967 | (if start | |
968 | (progn | |
969 | (if (>= n 0) | |
970 | (while (>= (setq n (1- n)) 0) | |
971 | (setq vec (cons start vec) | |
972 | start (math-add start (or incr 1)))) | |
973 | (while (<= (setq n (1+ n)) 0) | |
974 | (setq vec (cons start vec) | |
975 | start (math-mul start (or incr 2))))) | |
976 | (setq vec (nreverse vec))) | |
977 | (if (>= n 0) | |
978 | (while (> n 0) | |
979 | (setq vec (cons n vec) | |
980 | n (1- n))) | |
981 | (let ((i -1)) | |
982 | (while (>= i n) | |
983 | (setq vec (cons i vec) | |
984 | i (1- i)))))) | |
bf77c646 | 985 | (cons 'vec vec)))) |
136211a9 EZ |
986 | |
987 | ;;; Find an element in a vector. | |
988 | (defun calcFunc-find (vec x &optional start) | |
989 | (setq start (if start (math-check-fixnum start t) 1)) | |
990 | (if (< start 1) (math-reject-arg start 'posp)) | |
991 | (setq vec (nthcdr start vec)) | |
992 | (let ((n start)) | |
993 | (while (and vec (not (Math-equal x (car vec)))) | |
994 | (setq n (1+ n) | |
995 | vec (cdr vec))) | |
bf77c646 | 996 | (if vec n 0))) |
136211a9 EZ |
997 | |
998 | ;;; Return a subvector of a vector. | |
999 | (defun calcFunc-subvec (vec start &optional end) | |
1000 | (setq start (math-check-fixnum start t) | |
1001 | end (math-check-fixnum (or end 0) t)) | |
1002 | (or (math-vectorp vec) (math-reject-arg vec 'vectorp)) | |
1003 | (let ((len (1- (length vec)))) | |
1004 | (if (<= start 0) | |
1005 | (setq start (+ len start 1))) | |
1006 | (if (<= end 0) | |
1007 | (setq end (+ len end 1))) | |
1008 | (if (or (> start len) | |
1009 | (<= end start)) | |
1010 | '(vec) | |
1011 | (setq vec (nthcdr start vec)) | |
1012 | (if (<= end len) | |
1013 | (let ((chop (nthcdr (- end start 1) (setq vec (copy-sequence vec))))) | |
1014 | (setcdr chop nil))) | |
bf77c646 | 1015 | (cons 'vec vec)))) |
136211a9 EZ |
1016 | |
1017 | ;;; Remove a subvector from a vector. | |
1018 | (defun calcFunc-rsubvec (vec start &optional end) | |
1019 | (setq start (math-check-fixnum start t) | |
1020 | end (math-check-fixnum (or end 0) t)) | |
1021 | (or (math-vectorp vec) (math-reject-arg vec 'vectorp)) | |
1022 | (let ((len (1- (length vec)))) | |
1023 | (if (<= start 0) | |
1024 | (setq start (+ len start 1))) | |
1025 | (if (<= end 0) | |
1026 | (setq end (+ len end 1))) | |
1027 | (if (or (> start len) | |
1028 | (<= end start)) | |
1029 | vec | |
1030 | (let ((tail (nthcdr end vec)) | |
1031 | (chop (nthcdr (1- start) (setq vec (copy-sequence vec))))) | |
1032 | (setcdr chop nil) | |
bf77c646 | 1033 | (append vec tail))))) |
136211a9 EZ |
1034 | |
1035 | ;;; Reverse the order of the elements of a vector. | |
1036 | (defun calcFunc-rev (vec) | |
1037 | (if (math-vectorp vec) | |
1038 | (cons 'vec (reverse (cdr vec))) | |
bf77c646 | 1039 | (math-reject-arg vec 'vectorp))) |
136211a9 EZ |
1040 | |
1041 | ;;; Compress a vector according to a mask vector. | |
1042 | (defun calcFunc-vmask (mask vec) | |
1043 | (if (math-numberp mask) | |
1044 | (if (math-zerop mask) | |
1045 | '(vec) | |
1046 | vec) | |
1047 | (or (math-vectorp mask) (math-reject-arg mask 'vectorp)) | |
1048 | (or (math-constp mask) (math-reject-arg mask 'constp)) | |
1049 | (or (math-vectorp vec) (math-reject-arg vec 'vectorp)) | |
1050 | (or (= (length mask) (length vec)) (math-dimension-error)) | |
1051 | (let ((new nil)) | |
1052 | (while (setq mask (cdr mask) vec (cdr vec)) | |
1053 | (or (math-zerop (car mask)) | |
1054 | (setq new (cons (car vec) new)))) | |
bf77c646 | 1055 | (cons 'vec (nreverse new))))) |
136211a9 EZ |
1056 | |
1057 | ;;; Expand a vector according to a mask vector. | |
1058 | (defun calcFunc-vexp (mask vec &optional filler) | |
1059 | (or (math-vectorp mask) (math-reject-arg mask 'vectorp)) | |
1060 | (or (math-constp mask) (math-reject-arg mask 'constp)) | |
1061 | (or (math-vectorp vec) (math-reject-arg vec 'vectorp)) | |
1062 | (let ((new nil) | |
1063 | (fvec (and filler (math-vectorp filler)))) | |
1064 | (while (setq mask (cdr mask)) | |
1065 | (if (math-zerop (car mask)) | |
1066 | (setq new (cons (or (if fvec | |
1067 | (car (setq filler (cdr filler))) | |
1068 | filler) | |
1069 | (car mask)) new)) | |
1070 | (setq vec (cdr vec) | |
1071 | new (cons (or (car vec) (car mask)) new)))) | |
bf77c646 | 1072 | (cons 'vec (nreverse new)))) |
136211a9 EZ |
1073 | |
1074 | ||
1075 | ;;; Compute the row and column norms of a vector or matrix. [Public] | |
1076 | (defun calcFunc-rnorm (a) | |
1077 | (if (and (Math-vectorp a) | |
1078 | (math-constp a)) | |
1079 | (if (math-matrixp a) | |
1080 | (math-reduce-vec 'math-max (math-map-vec 'calcFunc-cnorm a)) | |
1081 | (math-reduce-vec 'math-max (math-map-vec 'math-abs a))) | |
1082 | (calc-record-why 'vectorp a) | |
bf77c646 | 1083 | (list 'calcFunc-rnorm a))) |
136211a9 EZ |
1084 | |
1085 | (defun calcFunc-cnorm (a) | |
1086 | (if (and (Math-vectorp a) | |
1087 | (math-constp a)) | |
1088 | (if (math-matrixp a) | |
1089 | (math-reduce-vec 'math-max | |
1090 | (math-reduce-cols 'math-add-abs a)) | |
1091 | (math-reduce-vec 'math-add-abs a)) | |
1092 | (calc-record-why 'vectorp a) | |
bf77c646 | 1093 | (list 'calcFunc-cnorm a))) |
136211a9 EZ |
1094 | |
1095 | (defun math-add-abs (a b) | |
bf77c646 | 1096 | (math-add (math-abs a) (math-abs b))) |
136211a9 EZ |
1097 | |
1098 | ||
1099 | ;;; Sort the elements of a vector into increasing order. | |
1100 | (defun calcFunc-sort (vec) ; [Public] | |
1101 | (if (math-vectorp vec) | |
1102 | (cons 'vec (sort (copy-sequence (cdr vec)) 'math-beforep)) | |
bf77c646 | 1103 | (math-reject-arg vec 'vectorp))) |
136211a9 EZ |
1104 | |
1105 | (defun calcFunc-rsort (vec) ; [Public] | |
1106 | (if (math-vectorp vec) | |
1107 | (cons 'vec (nreverse (sort (copy-sequence (cdr vec)) 'math-beforep))) | |
bf77c646 | 1108 | (math-reject-arg vec 'vectorp))) |
136211a9 | 1109 | |
866ebaa9 JB |
1110 | ;; The variable math-grade-vec is local to calcFunc-grade and |
1111 | ;; calcFunc-rgrade, but is used by math-grade-beforep, which is called | |
1112 | ;; by calcFunc-grade and calcFunc-rgrade. | |
1113 | (defvar math-grade-vec) | |
1114 | ||
1115 | (defun calcFunc-grade (math-grade-vec) | |
1116 | (if (math-vectorp math-grade-vec) | |
1117 | (let* ((len (1- (length math-grade-vec)))) | |
136211a9 | 1118 | (cons 'vec (sort (cdr (calcFunc-index len)) 'math-grade-beforep))) |
866ebaa9 | 1119 | (math-reject-arg math-grade-vec 'vectorp))) |
136211a9 | 1120 | |
866ebaa9 JB |
1121 | (defun calcFunc-rgrade (math-grade-vec) |
1122 | (if (math-vectorp math-grade-vec) | |
1123 | (let* ((len (1- (length math-grade-vec)))) | |
136211a9 EZ |
1124 | (cons 'vec (nreverse (sort (cdr (calcFunc-index len)) |
1125 | 'math-grade-beforep)))) | |
866ebaa9 | 1126 | (math-reject-arg math-grade-vec 'vectorp))) |
136211a9 EZ |
1127 | |
1128 | (defun math-grade-beforep (i j) | |
866ebaa9 | 1129 | (math-beforep (nth i math-grade-vec) (nth j math-grade-vec))) |
136211a9 EZ |
1130 | |
1131 | ||
1132 | ;;; Compile a histogram of data from a vector. | |
1133 | (defun calcFunc-histogram (vec wts &optional n) | |
1134 | (or n (setq n wts wts 1)) | |
1135 | (or (Math-vectorp vec) | |
1136 | (math-reject-arg vec 'vectorp)) | |
1137 | (if (Math-vectorp wts) | |
1138 | (or (= (length vec) (length wts)) | |
1139 | (math-dimension-error))) | |
597517ef JB |
1140 | (cond ((natnump n) |
1141 | (let ((res (make-vector n 0)) | |
1142 | (vp vec) | |
1143 | (wvec (Math-vectorp wts)) | |
1144 | (wp wts) | |
1145 | bin) | |
1146 | (while (setq vp (cdr vp)) | |
1147 | (setq bin (car vp)) | |
1148 | (or (natnump bin) | |
1149 | (setq bin (math-floor bin))) | |
1150 | (and (natnump bin) | |
1151 | (< bin n) | |
1152 | (aset res bin | |
1153 | (math-add (aref res bin) | |
1154 | (if wvec (car (setq wp (cdr wp))) wts))))) | |
1155 | (cons 'vec (append res nil)))) | |
1156 | ((Math-vectorp n) ;; n is a vector of midpoints | |
1157 | (let* ((bds (math-vector-avg n)) | |
1158 | (res (make-vector (1- (length n)) 0)) | |
1159 | (vp (cdr vec)) | |
1160 | (wvec (Math-vectorp wts)) | |
1161 | (wp wts) | |
1162 | num) | |
1163 | (while vp | |
1164 | (setq num (car vp)) | |
1165 | (let ((tbds (cdr bds)) | |
1166 | (i 0)) | |
1167 | (while (and tbds (Math-lessp (car tbds) num)) | |
1168 | (setq i (1+ i)) | |
1169 | (setq tbds (cdr tbds))) | |
1170 | (aset res i | |
1171 | (math-add (aref res i) | |
1172 | (if wvec (car (setq wp (cdr wp))) wts)))) | |
1173 | (setq vp (cdr vp))) | |
1174 | (cons 'vec (append res nil)))) | |
1175 | (t | |
1176 | (math-reject-arg n "*Expecting an integer or vector")))) | |
1177 | ||
1178 | ;;; Replace a vector [a b c ...] with a vector of averages | |
1179 | ;;; [(a+b)/2 (b+c)/2 ...] | |
1180 | (defun math-vector-avg (vec) | |
00681a3c | 1181 | (let ((vp (sort (copy-sequence (cdr vec)) 'math-beforep)) |
597517ef JB |
1182 | (res nil)) |
1183 | (while (and vp (cdr vp)) | |
1184 | (setq res (cons (math-div (math-add (car vp) (cadr vp)) 2) res) | |
1185 | vp (cdr vp))) | |
1186 | (cons 'vec (reverse res)))) | |
136211a9 EZ |
1187 | |
1188 | ||
1189 | ;;; Set operations. | |
1190 | ||
1191 | (defun calcFunc-vunion (a b) | |
1192 | (if (Math-objectp a) | |
1193 | (setq a (list 'vec a)) | |
1194 | (or (math-vectorp a) (math-reject-arg a 'vectorp))) | |
1195 | (if (Math-objectp b) | |
1196 | (setq b (list b)) | |
1197 | (or (math-vectorp b) (math-reject-arg b 'vectorp)) | |
1198 | (setq b (cdr b))) | |
bf77c646 | 1199 | (calcFunc-rdup (append a b))) |
136211a9 EZ |
1200 | |
1201 | (defun calcFunc-vint (a b) | |
1202 | (if (and (math-simple-set a) (math-simple-set b)) | |
1203 | (progn | |
1204 | (setq a (cdr (calcFunc-rdup a))) | |
1205 | (setq b (cdr (calcFunc-rdup b))) | |
1206 | (let ((vec (list 'vec))) | |
1207 | (while (and a b) | |
1208 | (if (math-beforep (car a) (car b)) | |
1209 | (setq a (cdr a)) | |
1210 | (if (Math-equal (car a) (car b)) | |
1211 | (setq vec (cons (car a) vec) | |
1212 | a (cdr a))) | |
1213 | (setq b (cdr b)))) | |
1214 | (nreverse vec))) | |
1215 | (calcFunc-vcompl (calcFunc-vunion (calcFunc-vcompl a) | |
bf77c646 | 1216 | (calcFunc-vcompl b))))) |
136211a9 EZ |
1217 | |
1218 | (defun calcFunc-vdiff (a b) | |
1219 | (if (and (math-simple-set a) (math-simple-set b)) | |
1220 | (progn | |
1221 | (setq a (cdr (calcFunc-rdup a))) | |
1222 | (setq b (cdr (calcFunc-rdup b))) | |
1223 | (let ((vec (list 'vec))) | |
1224 | (while a | |
1225 | (while (and b (math-beforep (car b) (car a))) | |
1226 | (setq b (cdr b))) | |
1227 | (if (and b (Math-equal (car a) (car b))) | |
1228 | (setq a (cdr a) | |
1229 | b (cdr b)) | |
1230 | (setq vec (cons (car a) vec) | |
1231 | a (cdr a)))) | |
1232 | (nreverse vec))) | |
bf77c646 | 1233 | (calcFunc-vcompl (calcFunc-vunion (calcFunc-vcompl a) b)))) |
136211a9 EZ |
1234 | |
1235 | (defun calcFunc-vxor (a b) | |
1236 | (if (and (math-simple-set a) (math-simple-set b)) | |
1237 | (progn | |
1238 | (setq a (cdr (calcFunc-rdup a))) | |
1239 | (setq b (cdr (calcFunc-rdup b))) | |
1240 | (let ((vec (list 'vec))) | |
1241 | (while (or a b) | |
1242 | (if (and a | |
1243 | (or (not b) | |
1244 | (math-beforep (car a) (car b)))) | |
1245 | (setq vec (cons (car a) vec) | |
1246 | a (cdr a)) | |
1247 | (if (and a (Math-equal (car a) (car b))) | |
1248 | (setq a (cdr a)) | |
1249 | (setq vec (cons (car b) vec))) | |
1250 | (setq b (cdr b)))) | |
1251 | (nreverse vec))) | |
1252 | (let ((ca (calcFunc-vcompl a)) | |
1253 | (cb (calcFunc-vcompl b))) | |
1254 | (calcFunc-vunion (calcFunc-vcompl (calcFunc-vunion ca b)) | |
bf77c646 | 1255 | (calcFunc-vcompl (calcFunc-vunion a cb)))))) |
136211a9 EZ |
1256 | |
1257 | (defun calcFunc-vcompl (a) | |
1258 | (setq a (math-prepare-set a)) | |
1259 | (let ((vec (list 'vec)) | |
1260 | (prev '(neg (var inf var-inf))) | |
1261 | (closed 2)) | |
1262 | (while (setq a (cdr a)) | |
1263 | (or (and (equal (nth 2 (car a)) '(neg (var inf var-inf))) | |
1264 | (memq (nth 1 (car a)) '(2 3))) | |
1265 | (setq vec (cons (list 'intv | |
1266 | (+ closed | |
1267 | (if (memq (nth 1 (car a)) '(0 1)) 1 0)) | |
1268 | prev | |
1269 | (nth 2 (car a))) | |
1270 | vec))) | |
1271 | (setq prev (nth 3 (car a)) | |
1272 | closed (if (memq (nth 1 (car a)) '(0 2)) 2 0))) | |
1273 | (or (and (equal prev '(var inf var-inf)) | |
1274 | (= closed 0)) | |
1275 | (setq vec (cons (list 'intv (+ closed 1) | |
1276 | prev '(var inf var-inf)) | |
1277 | vec))) | |
bf77c646 | 1278 | (math-clean-set (nreverse vec)))) |
136211a9 EZ |
1279 | |
1280 | (defun calcFunc-vspan (a) | |
1281 | (setq a (math-prepare-set a)) | |
1282 | (if (cdr a) | |
1283 | (let ((last (nth (1- (length a)) a))) | |
1284 | (math-make-intv (+ (logand (nth 1 (nth 1 a)) 2) | |
1285 | (logand (nth 1 last) 1)) | |
1286 | (nth 2 (nth 1 a)) | |
1287 | (nth 3 last))) | |
bf77c646 | 1288 | '(intv 2 0 0))) |
136211a9 EZ |
1289 | |
1290 | (defun calcFunc-vfloor (a &optional always-vec) | |
1291 | (setq a (math-prepare-set a)) | |
1292 | (let ((vec (list 'vec)) (p a) (prev nil) b mask) | |
1293 | (while (setq p (cdr p)) | |
1294 | (setq mask (nth 1 (car p)) | |
1295 | a (nth 2 (car p)) | |
1296 | b (nth 3 (car p))) | |
1297 | (and (memq mask '(0 1)) | |
1298 | (not (math-infinitep a)) | |
1299 | (setq mask (logior mask 2)) | |
1300 | (math-num-integerp a) | |
1301 | (setq a (math-add a 1))) | |
1302 | (setq a (math-ceiling a)) | |
1303 | (and (memq mask '(0 2)) | |
1304 | (not (math-infinitep b)) | |
1305 | (setq mask (logior mask 1)) | |
1306 | (math-num-integerp b) | |
1307 | (setq b (math-sub b 1))) | |
1308 | (setq b (math-floor b)) | |
1309 | (if (and prev (Math-equal (math-sub a 1) (nth 3 prev))) | |
1310 | (setcar (nthcdr 3 prev) b) | |
1311 | (or (Math-lessp b a) | |
1312 | (setq vec (cons (setq prev (list 'intv mask a b)) vec))))) | |
1313 | (setq vec (nreverse vec)) | |
bf77c646 | 1314 | (math-clean-set vec always-vec))) |
136211a9 EZ |
1315 | |
1316 | (defun calcFunc-vcard (a) | |
1317 | (setq a (calcFunc-vfloor a t)) | |
1318 | (or (math-constp a) (math-reject-arg a "*Set must be finite")) | |
1319 | (let ((count 0)) | |
1320 | (while (setq a (cdr a)) | |
1321 | (if (eq (car-safe (car a)) 'intv) | |
1322 | (setq count (math-add count (math-sub (nth 3 (car a)) | |
1323 | (nth 2 (car a)))))) | |
1324 | (setq count (math-add count 1))) | |
bf77c646 | 1325 | count)) |
136211a9 EZ |
1326 | |
1327 | (defun calcFunc-venum (a) | |
1328 | (setq a (calcFunc-vfloor a t)) | |
1329 | (or (math-constp a) (math-reject-arg a "*Set must be finite")) | |
11041c99 JB |
1330 | (let* ((prev a) (this (cdr prev)) this-val next this-last) |
1331 | (while this | |
1332 | (setq next (cdr this) | |
1333 | this-val (car this)) | |
1334 | (if (eq (car-safe this-val) 'intv) | |
1335 | (progn | |
1336 | (setq this (cdr (calcFunc-index (math-add | |
1337 | (math-sub (nth 3 this-val) | |
1338 | (nth 2 this-val)) | |
1339 | 1) | |
1340 | (nth 2 this-val)))) | |
1341 | (setq this-last (last this)) | |
1342 | (setcdr this-last next) | |
1343 | (setcdr prev this) | |
1344 | (setq prev this-last)) | |
1345 | (setq prev this)) | |
1346 | (setq this next))) | |
1347 | a) | |
136211a9 EZ |
1348 | |
1349 | (defun calcFunc-vpack (a) | |
1350 | (setq a (calcFunc-vfloor a t)) | |
1351 | (if (and (cdr a) | |
1352 | (math-negp (if (eq (car-safe (nth 1 a)) 'intv) | |
1353 | (nth 2 (nth 1 a)) | |
1354 | (nth 1 a)))) | |
1355 | (math-reject-arg (nth 1 a) 'posp)) | |
1356 | (let ((accum 0)) | |
1357 | (while (setq a (cdr a)) | |
1358 | (if (eq (car-safe (car a)) 'intv) | |
1359 | (if (equal (nth 3 (car a)) '(var inf var-inf)) | |
1360 | (setq accum (math-sub accum | |
1361 | (math-power-of-2 (nth 2 (car a))))) | |
1362 | (setq accum (math-add accum | |
1363 | (math-sub | |
1364 | (math-power-of-2 (1+ (nth 3 (car a)))) | |
1365 | (math-power-of-2 (nth 2 (car a))))))) | |
1366 | (setq accum (math-add accum (math-power-of-2 (car a)))))) | |
bf77c646 | 1367 | accum)) |
136211a9 EZ |
1368 | |
1369 | (defun calcFunc-vunpack (a &optional w) | |
1370 | (or (math-num-integerp a) (math-reject-arg a 'integerp)) | |
1371 | (if w (setq a (math-clip a w))) | |
1372 | (if (math-messy-integerp a) (setq a (math-trunc a))) | |
1373 | (let* ((calc-number-radix 2) | |
e6e9cfbd | 1374 | (calc-twos-complement-mode nil) |
136211a9 EZ |
1375 | (neg (math-negp a)) |
1376 | (aa (if neg (math-sub -1 a) a)) | |
1377 | (str (if (eq aa 0) | |
1378 | "" | |
1379 | (if (consp aa) | |
1380 | (math-format-bignum-binary (cdr aa)) | |
1381 | (math-format-binary aa)))) | |
1382 | (zero (if neg ?1 ?0)) | |
1383 | (one (if neg ?0 ?1)) | |
1384 | (len (length str)) | |
1385 | (vec (list 'vec)) | |
1386 | (pos (1- len)) pos2) | |
1387 | (while (>= pos 0) | |
1388 | (if (eq (aref str pos) zero) | |
1389 | (setq pos (1- pos)) | |
1390 | (setq pos2 pos) | |
1391 | (while (and (>= pos 0) (eq (aref str pos) one)) | |
1392 | (setq pos (1- pos))) | |
1393 | (setq vec (cons (if (= pos (1- pos2)) | |
1394 | (- len pos2 1) | |
1395 | (list 'intv 3 (- len pos2 1) (- len pos 2))) | |
1396 | vec)))) | |
1397 | (if neg | |
1398 | (setq vec (cons (list 'intv 2 len '(var inf var-inf)) vec))) | |
bf77c646 | 1399 | (math-clean-set (nreverse vec)))) |
136211a9 EZ |
1400 | |
1401 | (defun calcFunc-rdup (a) | |
1402 | (if (math-simple-set a) | |
1403 | (progn | |
1404 | (and (Math-objectp a) (setq a (list 'vec a))) | |
1405 | (or (math-vectorp a) (math-reject-arg a 'vectorp)) | |
1406 | (setq a (sort (copy-sequence (cdr a)) 'math-beforep)) | |
1407 | (let ((p a)) | |
1408 | (while (cdr p) | |
1409 | (if (Math-equal (car p) (nth 1 p)) | |
1410 | (setcdr p (cdr (cdr p))) | |
1411 | (setq p (cdr p))))) | |
1412 | (cons 'vec a)) | |
bf77c646 | 1413 | (math-clean-set (math-prepare-set a)))) |
136211a9 EZ |
1414 | |
1415 | (defun math-prepare-set (a) | |
1416 | (if (Math-objectp a) | |
1417 | (setq a (list 'vec a)) | |
1418 | (or (math-vectorp a) (math-reject-arg a 'vectorp)) | |
1419 | (setq a (cons 'vec (sort (copy-sequence (cdr a)) 'math-beforep)))) | |
1420 | (let ((p a) res) | |
1421 | ||
1422 | ;; Convert all elements to non-empty intervals. | |
1423 | (while (cdr p) | |
1424 | (if (eq (car-safe (nth 1 p)) 'intv) | |
1425 | (if (math-intv-constp (nth 1 p)) | |
1426 | (if (and (memq (nth 1 (nth 1 p)) '(0 1 2)) | |
1427 | (Math-equal (nth 2 (nth 1 p)) (nth 3 (nth 1 p)))) | |
1428 | (setcdr p (cdr (cdr p))) | |
1429 | (setq p (cdr p))) | |
1430 | (math-reject-arg (nth 1 p) 'constp)) | |
1431 | (or (Math-anglep (nth 1 p)) | |
1432 | (eq (car (nth 1 p)) 'date) | |
1433 | (equal (nth 1 p) '(var inf var-inf)) | |
1434 | (equal (nth 1 p) '(neg (var inf var-inf))) | |
1435 | (math-reject-arg (nth 1 p) 'realp)) | |
1436 | (setcar (cdr p) (list 'intv 3 (nth 1 p) (nth 1 p))) | |
1437 | (setq p (cdr p)))) | |
1438 | ||
1439 | ;; Combine redundant intervals. | |
1440 | (setq p a) | |
1441 | (while (cdr (cdr p)) | |
1442 | (if (or (memq (setq res (math-compare (nth 3 (nth 1 p)) | |
1443 | (nth 2 (nth 2 p)))) | |
1444 | '(-1 2)) | |
1445 | (and (eq res 0) | |
1446 | (memq (nth 1 (nth 1 p)) '(0 2)) | |
1447 | (memq (nth 1 (nth 2 p)) '(0 1)))) | |
1448 | (setq p (cdr p)) | |
1449 | (setq res (math-compare (nth 3 (nth 1 p)) (nth 3 (nth 2 p)))) | |
1450 | (setcdr p (cons (list 'intv | |
1451 | (+ (logand (logior (nth 1 (nth 1 p)) | |
1452 | (if (Math-equal | |
1453 | (nth 2 (nth 1 p)) | |
1454 | (nth 2 (nth 2 p))) | |
1455 | (nth 1 (nth 2 p)) | |
1456 | 0)) | |
1457 | 2) | |
1458 | (logand (logior (if (memq res '(1 0 2)) | |
1459 | (nth 1 (nth 1 p)) 0) | |
1460 | (if (memq res '(-1 0 2)) | |
1461 | (nth 1 (nth 2 p)) 0)) | |
1462 | 1)) | |
1463 | (nth 2 (nth 1 p)) | |
1464 | (if (eq res 1) | |
1465 | (nth 3 (nth 1 p)) | |
1466 | (nth 3 (nth 2 p)))) | |
1467 | (cdr (cdr (cdr p)))))))) | |
bf77c646 | 1468 | a) |
136211a9 EZ |
1469 | |
1470 | (defun math-clean-set (a &optional always-vec) | |
1471 | (let ((p a) res) | |
1472 | (while (cdr p) | |
1473 | (if (and (eq (car-safe (nth 1 p)) 'intv) | |
1474 | (Math-equal (nth 2 (nth 1 p)) (nth 3 (nth 1 p)))) | |
1475 | (setcar (cdr p) (nth 2 (nth 1 p)))) | |
1476 | (setq p (cdr p))) | |
1477 | (if (and (not (cdr (cdr a))) | |
1478 | (eq (car-safe (nth 1 a)) 'intv) | |
1479 | (not always-vec)) | |
1480 | (nth 1 a) | |
bf77c646 | 1481 | a))) |
136211a9 EZ |
1482 | |
1483 | (defun math-simple-set (a) | |
1484 | (or (and (Math-objectp a) | |
1485 | (not (eq (car-safe a) 'intv))) | |
1486 | (and (Math-vectorp a) | |
1487 | (progn | |
1488 | (while (and (setq a (cdr a)) | |
1489 | (not (eq (car-safe (car a)) 'intv)))) | |
bf77c646 | 1490 | (null a))))) |
136211a9 EZ |
1491 | |
1492 | ||
1493 | ||
1494 | ||
1495 | ;;; Compute a right-handed vector cross product. [O O O] [Public] | |
1496 | (defun calcFunc-cross (a b) | |
1497 | (if (and (eq (car-safe a) 'vec) | |
1498 | (= (length a) 4)) | |
1499 | (if (and (eq (car-safe b) 'vec) | |
1500 | (= (length b) 4)) | |
1501 | (list 'vec | |
1502 | (math-sub (math-mul (nth 2 a) (nth 3 b)) | |
1503 | (math-mul (nth 3 a) (nth 2 b))) | |
1504 | (math-sub (math-mul (nth 3 a) (nth 1 b)) | |
1505 | (math-mul (nth 1 a) (nth 3 b))) | |
1506 | (math-sub (math-mul (nth 1 a) (nth 2 b)) | |
1507 | (math-mul (nth 2 a) (nth 1 b)))) | |
1508 | (math-reject-arg b "*Three-vector expected")) | |
bf77c646 | 1509 | (math-reject-arg a "*Three-vector expected"))) |
136211a9 EZ |
1510 | |
1511 | ||
1aa484e3 JB |
1512 | ;;; Compute a Kronecker product |
1513 | (defun calcFunc-kron (x y &optional nocheck) | |
1514 | "The Kronecker product of objects X and Y. | |
1515 | The objects X and Y may be scalars, vectors or matrices. | |
1516 | The type of the result depends on the types of the operands; | |
1517 | the product of two scalars is a scalar, | |
1518 | of one scalar and a vector is a vector, | |
1519 | of two vectors is a vector. | |
1520 | of one vector and a matrix is a matrix, | |
1521 | of two matrices is a matrix." | |
1522 | (unless nocheck | |
1523 | (cond ((or (math-matrixp x) | |
1524 | (math-matrixp y)) | |
1525 | (unless (math-matrixp x) | |
1526 | (setq x (if (math-vectorp x) | |
1527 | (list 'vec x) | |
1528 | (list 'vec (list 'vec x))))) | |
1529 | (unless (math-matrixp y) | |
1530 | (setq y (if (math-vectorp y) | |
1531 | (list 'vec y) | |
1532 | (list 'vec (list 'vec y)))))) | |
1533 | ((or (math-vectorp x) | |
1534 | (math-vectorp y)) | |
1535 | (unless (math-vectorp x) | |
1536 | (setq x (list 'vec x))) | |
1537 | (unless (math-vectorp y) | |
1538 | (setq y (list 'vec y)))))) | |
1539 | (if (math-vectorp x) | |
1540 | (let (ret) | |
1541 | (dolist (v (cdr x)) | |
1542 | (dolist (w (cdr y)) | |
1543 | (setq ret (cons (calcFunc-kron v w t) ret)))) | |
1544 | (cons 'vec (nreverse ret))) | |
1545 | (math-mul x y))) | |
1546 | ||
136211a9 | 1547 | |
866ebaa9 JB |
1548 | ;; The variable math-rb-close is local to math-read-brackets, but |
1549 | ;; is used by math-read-vector, which is called (directly and | |
1550 | ;; indirectly) by math-read-brackets. | |
1551 | (defvar math-rb-close) | |
136211a9 | 1552 | |
388df0be JB |
1553 | ;; The next few variables are local to math-read-exprs in calc-aent.el |
1554 | ;; and math-read-expr in calc-ext.el, but are set in functions they call. | |
1555 | (defvar math-exp-pos) | |
1556 | (defvar math-exp-str) | |
1557 | (defvar math-exp-old-pos) | |
1558 | (defvar math-exp-token) | |
1559 | (defvar math-exp-keep-spaces) | |
1560 | (defvar math-expr-data) | |
1561 | ||
866ebaa9 | 1562 | (defun math-read-brackets (space-sep math-rb-close) |
136211a9 EZ |
1563 | (and space-sep (setq space-sep (not (math-check-for-commas)))) |
1564 | (math-read-token) | |
411b1407 | 1565 | (while (eq math-exp-token 'space) |
136211a9 | 1566 | (math-read-token)) |
866ebaa9 | 1567 | (if (or (equal math-expr-data math-rb-close) |
411b1407 | 1568 | (eq math-exp-token 'end)) |
136211a9 EZ |
1569 | (progn |
1570 | (math-read-token) | |
1571 | '(vec)) | |
411b1407 JB |
1572 | (let ((save-exp-pos math-exp-pos) |
1573 | (save-exp-old-pos math-exp-old-pos) | |
1574 | (save-exp-token math-exp-token) | |
5c8a5f96 | 1575 | (save-exp-data math-expr-data) |
411b1407 | 1576 | (vals (let ((math-exp-keep-spaces space-sep)) |
5c8a5f96 JB |
1577 | (if (or (equal math-expr-data "\\dots") |
1578 | (equal math-expr-data "\\ldots")) | |
136211a9 EZ |
1579 | '(vec (neg (var inf var-inf))) |
1580 | (catch 'syntax (math-read-vector)))))) | |
1581 | (if (stringp vals) | |
1582 | (if space-sep | |
411b1407 JB |
1583 | (let ((error-exp-pos math-exp-pos) |
1584 | (error-exp-old-pos math-exp-old-pos) | |
136211a9 | 1585 | vals2) |
411b1407 JB |
1586 | (setq math-exp-pos save-exp-pos |
1587 | math-exp-old-pos save-exp-old-pos | |
1588 | math-exp-token save-exp-token | |
5c8a5f96 | 1589 | math-expr-data save-exp-data) |
411b1407 | 1590 | (let ((math-exp-keep-spaces nil)) |
136211a9 EZ |
1591 | (setq vals2 (catch 'syntax (math-read-vector)))) |
1592 | (if (and (not (stringp vals2)) | |
5c8a5f96 | 1593 | (or (assoc math-expr-data '(("\\ldots") ("\\dots") (";"))) |
866ebaa9 | 1594 | (equal math-expr-data math-rb-close) |
411b1407 | 1595 | (eq math-exp-token 'end))) |
136211a9 EZ |
1596 | (setq space-sep nil |
1597 | vals vals2) | |
411b1407 JB |
1598 | (setq math-exp-pos error-exp-pos |
1599 | math-exp-old-pos error-exp-old-pos) | |
136211a9 EZ |
1600 | (throw 'syntax vals))) |
1601 | (throw 'syntax vals))) | |
5c8a5f96 JB |
1602 | (if (or (equal math-expr-data "\\dots") |
1603 | (equal math-expr-data "\\ldots")) | |
136211a9 EZ |
1604 | (progn |
1605 | (math-read-token) | |
1606 | (setq vals (if (> (length vals) 2) | |
1607 | (cons 'calcFunc-mul (cdr vals)) (nth 1 vals))) | |
866ebaa9 | 1608 | (let ((exp2 (if (or (equal math-expr-data math-rb-close) |
5c8a5f96 | 1609 | (equal math-expr-data ")") |
411b1407 | 1610 | (eq math-exp-token 'end)) |
136211a9 EZ |
1611 | '(var inf var-inf) |
1612 | (math-read-expr-level 0)))) | |
1613 | (setq vals | |
1614 | (list 'intv | |
5c8a5f96 | 1615 | (if (equal math-expr-data ")") 2 3) |
136211a9 EZ |
1616 | vals |
1617 | exp2))) | |
866ebaa9 | 1618 | (if (not (or (equal math-expr-data math-rb-close) |
5c8a5f96 | 1619 | (equal math-expr-data ")") |
411b1407 | 1620 | (eq math-exp-token 'end))) |
136211a9 | 1621 | (throw 'syntax "Expected `]'"))) |
5c8a5f96 | 1622 | (if (equal math-expr-data ";") |
411b1407 | 1623 | (let ((math-exp-keep-spaces space-sep)) |
136211a9 | 1624 | (setq vals (cons 'vec (math-read-matrix (list vals)))))) |
866ebaa9 | 1625 | (if (not (or (equal math-expr-data math-rb-close) |
411b1407 | 1626 | (eq math-exp-token 'end))) |
136211a9 | 1627 | (throw 'syntax "Expected `]'"))) |
411b1407 | 1628 | (or (eq math-exp-token 'end) |
136211a9 | 1629 | (math-read-token)) |
bf77c646 | 1630 | vals))) |
136211a9 EZ |
1631 | |
1632 | (defun math-check-for-commas (&optional balancing) | |
1633 | (let ((count 0) | |
411b1407 | 1634 | (pos (1- math-exp-pos))) |
136211a9 EZ |
1635 | (while (and (>= count 0) |
1636 | (setq pos (string-match | |
1637 | (if balancing "[],[{}()<>]" "[],[{}()]") | |
411b1407 JB |
1638 | math-exp-str (1+ pos))) |
1639 | (or (/= (aref math-exp-str pos) ?,) (> count 0) balancing)) | |
1640 | (cond ((memq (aref math-exp-str pos) '(?\[ ?\{ ?\( ?\<)) | |
136211a9 | 1641 | (setq count (1+ count))) |
411b1407 | 1642 | ((memq (aref math-exp-str pos) '(?\] ?\} ?\) ?\>)) |
136211a9 EZ |
1643 | (setq count (1- count))))) |
1644 | (if balancing | |
1645 | pos | |
411b1407 | 1646 | (and pos (= (aref math-exp-str pos) ?,))))) |
136211a9 EZ |
1647 | |
1648 | (defun math-read-vector () | |
1649 | (let* ((val (list (math-read-expr-level 0))) | |
1650 | (last val)) | |
1651 | (while (progn | |
411b1407 | 1652 | (while (eq math-exp-token 'space) |
136211a9 | 1653 | (math-read-token)) |
411b1407 | 1654 | (and (not (eq math-exp-token 'end)) |
5c8a5f96 | 1655 | (not (equal math-expr-data ";")) |
866ebaa9 | 1656 | (not (equal math-expr-data math-rb-close)) |
5c8a5f96 JB |
1657 | (not (equal math-expr-data "\\dots")) |
1658 | (not (equal math-expr-data "\\ldots")))) | |
1659 | (if (equal math-expr-data ",") | |
136211a9 | 1660 | (math-read-token)) |
411b1407 | 1661 | (while (eq math-exp-token 'space) |
136211a9 EZ |
1662 | (math-read-token)) |
1663 | (let ((rest (list (math-read-expr-level 0)))) | |
1664 | (setcdr last rest) | |
1665 | (setq last rest))) | |
bf77c646 | 1666 | (cons 'vec val))) |
136211a9 EZ |
1667 | |
1668 | (defun math-read-matrix (mat) | |
5c8a5f96 | 1669 | (while (equal math-expr-data ";") |
136211a9 | 1670 | (math-read-token) |
411b1407 | 1671 | (while (eq math-exp-token 'space) |
136211a9 EZ |
1672 | (math-read-token)) |
1673 | (setq mat (nconc mat (list (math-read-vector))))) | |
bf77c646 | 1674 | mat) |
136211a9 | 1675 | |
429dae43 JB |
1676 | (provide 'calc-vec) |
1677 | ||
bf77c646 | 1678 | ;;; calc-vec.el ends here |