Remove unnecessary stack overflow dependency
[emacs.git] / lisp / calc / calc-vec.el
blobc1ef8954c3c87b6c6457f17374af244dd04a6715
1 ;;; calc-vec.el --- vector functions for Calc
3 ;; Copyright (C) 1990-1993, 2001-2015 Free Software Foundation, Inc.
5 ;; Author: David Gillespie <daveg@synaptics.com>
6 ;; Maintainer: Jay Belanger <jay.p.belanger@gmail.com>
8 ;; This file is part of GNU Emacs.
10 ;; GNU Emacs is free software: you can redistribute it and/or modify
11 ;; it under the terms of the GNU General Public License as published by
12 ;; the Free Software Foundation, either version 3 of the License, or
13 ;; (at your option) any later version.
15 ;; GNU Emacs is distributed in the hope that it will be useful,
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.
20 ;; You should have received a copy of the GNU General Public License
21 ;; along with GNU Emacs. If not, see <http://www.gnu.org/licenses/>.
23 ;;; Commentary:
25 ;;; Code:
27 ;; This file is autoloaded from calc-ext.el.
29 (require 'calc-ext)
30 (require 'calc-macs)
32 ;; Declare functions which are defined elsewhere.
33 (declare-function math-read-expr-level "calc-aent" (exp-prec &optional exp-term))
36 (defun calc-display-strings (n)
37 (interactive "P")
38 (calc-wrapper
39 (message (if (calc-change-mode 'calc-display-strings n t t)
40 "Displaying vectors of integers as quoted strings"
41 "Displaying vectors of integers normally"))))
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)))
54 (calc-enter-result (+ nn num -1) "pack" (calc-pack-items mode items)))))
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))))
68 2))))
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
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)))))
209 (error "Invalid packing mode: %d" mode))))
211 (defvar calc-unpack-with-type nil)
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))
219 (calc-top))))))
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))
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) )))
231 (error "Argument must be a composite object")))))
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")))
335 (error "Invalid unpacking mode: %d" mode))))
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))
343 (list 'calcFunc-diag (calc-top-n 1))))))
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
351 (prefix-numeric-value n))))))
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
359 (prefix-numeric-value n))))))
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)
366 (prefix-numeric-value n)))))
368 (defun calc-cons (arg)
369 (interactive "P")
370 (calc-wrapper
371 (if (calc-is-hyperbolic)
372 (calc-binary-op "rcns" 'calcFunc-rcons arg)
373 (calc-binary-op "cons" 'calcFunc-cons arg))))
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)
385 (calc-unary-op "head" 'calcFunc-head arg)))))
387 (defun calc-tail (arg)
388 (interactive "P")
389 (calc-invert-func)
390 (calc-head arg))
392 (defun calc-vlength (arg)
393 (interactive "P")
394 (calc-wrapper
395 (if (calc-is-hyperbolic)
396 (calc-unary-op "dims" 'calcFunc-mdims arg)
397 (calc-unary-op "len" 'calcFunc-vlen arg))))
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)
403 (prefix-numeric-value n)))))
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"
411 (if arg (append func (list (prefix-numeric-value arg))) func)))))
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)))
419 (calc-enter-result 3 "svec" (cons 'calcFunc-subvec (calc-top-list-n 3))))))
421 (defun calc-reverse-vector (arg)
422 (interactive "P")
423 (calc-wrapper
424 (calc-unary-op "rev" 'calcFunc-rev arg)))
426 (defun calc-mask-vector (arg)
427 (interactive "P")
428 (calc-wrapper
429 (calc-binary-op "vmsk" 'calcFunc-vmask arg)))
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)))
436 (calc-binary-op "vexp" 'calcFunc-vexp arg))))
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)))
443 (calc-enter-result 1 "sort" (list 'calcFunc-sort (calc-top-n 1))))))
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)))
450 (calc-enter-result 1 "grad" (list 'calcFunc-grade (calc-top-n 1))))))
452 (defun calc-histogram (n)
453 (interactive "P")
454 (unless (natnump n)
455 (setq n (math-read-expr (read-string "Centers 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)
462 (calc-enter-result 1 "hist" (list 'calcFunc-histogram
463 (calc-top-n 1)
464 n)))))
466 (defun calc-transpose (arg)
467 (interactive "P")
468 (calc-wrapper
469 (calc-unary-op "trn" 'calcFunc-trn arg)))
471 (defun calc-conj-transpose (arg)
472 (interactive "P")
473 (calc-wrapper
474 (calc-unary-op "ctrn" 'calcFunc-ctrn arg)))
476 (defun calc-cross (arg)
477 (interactive "P")
478 (calc-wrapper
479 (calc-binary-op "cros" 'calcFunc-cross arg)))
481 (defun calc-kron (arg)
482 (interactive "P")
483 (calc-wrapper
484 (calc-binary-op "kron" 'calcFunc-kron arg)))
486 (defun calc-remove-duplicates (arg)
487 (interactive "P")
488 (calc-wrapper
489 (calc-unary-op "rdup" 'calcFunc-rdup arg)))
491 (defun calc-set-union (arg)
492 (interactive "P")
493 (calc-wrapper
494 (calc-binary-op "unio" 'calcFunc-vunion arg '(vec) 'calcFunc-rdup)))
496 (defun calc-set-intersect (arg)
497 (interactive "P")
498 (calc-wrapper
499 (calc-binary-op "intr" 'calcFunc-vint arg '(vec) 'calcFunc-rdup)))
501 (defun calc-set-difference (arg)
502 (interactive "P")
503 (calc-wrapper
504 (calc-binary-op "diff" 'calcFunc-vdiff arg '(vec) 'calcFunc-rdup)))
506 (defun calc-set-xor (arg)
507 (interactive "P")
508 (calc-wrapper
509 (calc-binary-op "xor" 'calcFunc-vxor arg '(vec) 'calcFunc-rdup)))
511 (defun calc-set-complement (arg)
512 (interactive "P")
513 (calc-wrapper
514 (calc-unary-op "cmpl" 'calcFunc-vcompl arg)))
516 (defun calc-set-floor (arg)
517 (interactive "P")
518 (calc-wrapper
519 (calc-unary-op "vflr" 'calcFunc-vfloor arg)))
521 (defun calc-set-enumerate (arg)
522 (interactive "P")
523 (calc-wrapper
524 (calc-unary-op "enum" 'calcFunc-venum arg)))
526 (defun calc-set-span (arg)
527 (interactive "P")
528 (calc-wrapper
529 (calc-unary-op "span" 'calcFunc-vspan arg)))
531 (defun calc-set-cardinality (arg)
532 (interactive "P")
533 (calc-wrapper
534 (calc-unary-op "card" 'calcFunc-vcard arg)))
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)
541 (calc-unary-op "bupk" 'calcFunc-vunpack arg))))
543 (defun calc-pack-bits (arg)
544 (interactive "P")
545 (calc-invert-func)
546 (calc-unpack-bits arg))
549 (defun calc-rnorm (arg)
550 (interactive "P")
551 (calc-wrapper
552 (calc-unary-op "rnrm" 'calcFunc-rnorm arg)))
554 (defun calc-cnorm (arg)
555 (interactive "P")
556 (calc-wrapper
557 (calc-unary-op "cnrm" 'calcFunc-cnorm arg)))
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
571 (calc-top-n 1) n)))))))
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
585 (calc-top-n 1) n)))))))
588 ;;;; Vectors.
590 (defun calcFunc-mdims (m)
591 (or (math-vectorp m)
592 (math-reject-arg m 'vectorp))
593 (cons 'vec (math-mat-dimens m)))
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)))
600 (funcall f a)))
602 (defun math-dimension-error ()
603 (calc-record-why "*Dimension error")
604 (signal 'wrong-type-argument nil))
607 ;;; Build a vector out of a list of objects. [Public]
608 (defun calcFunc-vec (&rest objs)
609 (cons 'vec objs))
612 ;;; Build a constant vector or matrix. [Public]
613 (defun calcFunc-cvec (obj &rest dims)
614 (math-make-vec-dimen obj dims))
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))
626 obj))
628 (defun calcFunc-head (vec)
629 (if (and (Math-vectorp vec)
630 (cdr vec))
631 (nth 1 vec)
632 (calc-record-why 'vectorp vec)
633 (list 'calcFunc-head vec)))
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)
640 (list 'calcFunc-tail vec)))
642 (defun calcFunc-cons (head tail)
643 (if (Math-vectorp tail)
644 (cons 'vec (cons head (cdr tail)))
645 (calc-record-why 'vectorp tail)
646 (list 'calcFunc-cons head tail)))
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)
655 (list 'calcFunc-rhead vec)))
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)
662 (list 'calcFunc-rtail vec)))
664 (defun calcFunc-rcons (head tail)
665 (if (Math-vectorp head)
666 (append head (list tail))
667 (calc-record-why 'vectorp head)
668 (list 'calcFunc-rcons head tail)))
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)))
692 (funcall f a b))))
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)
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))))
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))
716 (math-reduce-cols-col-step f a (1+ col) cols))))
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)))
723 (cdr a))
724 tot))
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)
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)
743 (list 'calcFunc-vlen v))))
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)
759 (math-reject-arg n "*Index out of range")))))
761 (defun calcFunc-subscr (mat n &optional m)
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)))
770 ;;; Get the Nth column of a matrix.
771 (defun math-mat-col (mat n)
772 (cons 'vec (mapcar (function (lambda (x) (elt x n))) (cdr mat))))
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))
791 (math-reject-arg n "*Index out of range")))))
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)
798 (math-mat-less-row (cdr mat) (1- n)))))
800 (defun calcFunc-mrrow (mat n) ; [Public]
801 (and (integerp (setq n (math-check-integer n)))
802 (> n 0)
803 (< n (length mat))
804 (math-mat-less-row mat n)))
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)))
809 (cdr mat))))
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))
817 (math-mat-less-row mat n))))
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)
823 (list 'calcFunc-getdiag mat)))
825 (defun math-get-diag-step (row n)
826 (and row
827 (cons (nth n (car row))
828 (math-get-diag-step (cdr row) (1+ n)))))
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)))
835 (cons 'vec m)))
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)
844 (math-reject-arg mat 'matrixp))))
846 (defun calcFunc-ctrn (mat)
847 (calcFunc-conj (calcFunc-trn mat)))
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"))
858 (error (math-reject-arg els (nth 1 err)))))
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))
864 (error (math-reject-arg thing (nth 1 err)))))
866 (defun calcFunc-unpackt (mode thing)
867 (let ((calc-unpack-with-type 'pair))
868 (calcFunc-unpack mode thing)))
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)))))
885 mat))))
887 (defun math-flatten-vector (vec) ; [L V]
888 (if (math-vectorp vec)
889 (apply 'append (mapcar 'math-flatten-vector (cdr vec)))
890 (list vec)))
892 (defun calcFunc-vconcat (a b)
893 (math-normalize (list '| a b)))
895 (defun calcFunc-vconcatrev (a b)
896 (math-normalize (list '| b a)))
898 (defun calcFunc-append (v1 v2)
899 (if (and (math-vectorp v1) (math-vectorp v2))
900 (append v1 (cdr v2))
901 (list 'calcFunc-append v1 v2)))
903 (defun calcFunc-appendrev (v1 v2)
904 (calcFunc-append v2 v1))
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)))
911 (copy-sequence m)))
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)
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))
927 (list 'calcFunc-diag a))))
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)
936 (list 'calcFunc-idn a))))
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))
949 (calcFunc-idn a))))
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))
958 nil))
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))))))
985 (cons 'vec vec))))
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)))
996 (if vec n 0)))
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)))
1015 (cons 'vec vec))))
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))
1030 (let ((tail (nthcdr end vec))
1031 (chop (nthcdr (1- start) (setq vec (copy-sequence vec)))))
1032 (setcdr chop nil)
1033 (append vec tail)))))
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)))
1039 (math-reject-arg vec 'vectorp)))
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))))
1055 (cons 'vec (nreverse new)))))
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))))
1072 (cons 'vec (nreverse new))))
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)
1083 (list 'calcFunc-rnorm a)))
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)
1093 (list 'calcFunc-cnorm a)))
1095 (defun math-add-abs (a b)
1096 (math-add (math-abs a) (math-abs b)))
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))
1103 (math-reject-arg vec 'vectorp)))
1105 (defun calcFunc-rsort (vec) ; [Public]
1106 (if (math-vectorp vec)
1107 (cons 'vec (nreverse (sort (copy-sequence (cdr vec)) 'math-beforep)))
1108 (math-reject-arg vec 'vectorp)))
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)
1115 (defun calcFunc-grade (math-grade-vec)
1116 (if (math-vectorp math-grade-vec)
1117 (let* ((len (1- (length math-grade-vec))))
1118 (cons 'vec (sort (cdr (calcFunc-index len)) 'math-grade-beforep)))
1119 (math-reject-arg math-grade-vec 'vectorp)))
1121 (defun calcFunc-rgrade (math-grade-vec)
1122 (if (math-vectorp math-grade-vec)
1123 (let* ((len (1- (length math-grade-vec))))
1124 (cons 'vec (nreverse (sort (cdr (calcFunc-index len))
1125 'math-grade-beforep))))
1126 (math-reject-arg math-grade-vec 'vectorp)))
1128 (defun math-grade-beforep (i j)
1129 (math-beforep (nth i math-grade-vec) (nth j math-grade-vec)))
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)))
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))))
1176 (math-reject-arg n "*Expecting an integer or vector"))))
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)
1181 (let ((vp (sort (copy-sequence (cdr vec)) 'math-beforep))
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))))
1189 ;;; Set operations.
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)))
1199 (calcFunc-rdup (append a b)))
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)
1216 (calcFunc-vcompl b)))))
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)))
1233 (calcFunc-vcompl (calcFunc-vunion (calcFunc-vcompl a) b))))
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))
1255 (calcFunc-vcompl (calcFunc-vunion a cb))))))
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)))
1278 (math-clean-set (nreverse vec))))
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)))
1288 '(intv 2 0 0)))
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))
1314 (math-clean-set vec always-vec)))
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)))
1325 count))
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"))
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))
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)))
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))))))
1367 accum))
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)
1374 (calc-twos-complement-mode nil)
1375 (neg (math-negp a))
1376 (aa (if neg (math-sub -1 a) a))
1377 (str (if (eq aa 0)
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)))
1399 (math-clean-set (nreverse vec))))
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))
1413 (math-clean-set (math-prepare-set a))))
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)
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))))
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))
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))
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))))))))
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)
1481 a)))
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))))
1490 (null a)))))
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"))
1509 (math-reject-arg a "*Three-vector expected")))
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)))
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)
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)
1562 (defun math-read-brackets (space-sep math-rb-close)
1563 (and space-sep (setq space-sep (not (math-check-for-commas))))
1564 (math-read-token)
1565 (while (eq math-exp-token 'space)
1566 (math-read-token))
1567 (if (or (equal math-expr-data math-rb-close)
1568 (eq math-exp-token 'end))
1569 (progn
1570 (math-read-token)
1571 '(vec))
1572 (let ((save-exp-pos math-exp-pos)
1573 (save-exp-old-pos math-exp-old-pos)
1574 (save-exp-token math-exp-token)
1575 (save-exp-data math-expr-data)
1576 (vals (let ((math-exp-keep-spaces space-sep))
1577 (if (or (equal math-expr-data "\\dots")
1578 (equal math-expr-data "\\ldots"))
1579 '(vec (neg (var inf var-inf)))
1580 (catch 'syntax (math-read-vector))))))
1581 (if (stringp vals)
1582 (if space-sep
1583 (let ((error-exp-pos math-exp-pos)
1584 (error-exp-old-pos math-exp-old-pos)
1585 vals2)
1586 (setq math-exp-pos save-exp-pos
1587 math-exp-old-pos save-exp-old-pos
1588 math-exp-token save-exp-token
1589 math-expr-data save-exp-data)
1590 (let ((math-exp-keep-spaces nil))
1591 (setq vals2 (catch 'syntax (math-read-vector))))
1592 (if (and (not (stringp vals2))
1593 (or (assoc math-expr-data '(("\\ldots") ("\\dots") (";")))
1594 (equal math-expr-data math-rb-close)
1595 (eq math-exp-token 'end)))
1596 (setq space-sep nil
1597 vals vals2)
1598 (setq math-exp-pos error-exp-pos
1599 math-exp-old-pos error-exp-old-pos)
1600 (throw 'syntax vals)))
1601 (throw 'syntax vals)))
1602 (if (or (equal math-expr-data "\\dots")
1603 (equal math-expr-data "\\ldots"))
1604 (progn
1605 (math-read-token)
1606 (setq vals (if (> (length vals) 2)
1607 (cons 'calcFunc-mul (cdr vals)) (nth 1 vals)))
1608 (let ((exp2 (if (or (equal math-expr-data math-rb-close)
1609 (equal math-expr-data ")")
1610 (eq math-exp-token 'end))
1611 '(var inf var-inf)
1612 (math-read-expr-level 0))))
1613 (setq vals
1614 (list 'intv
1615 (if (equal math-expr-data ")") 2 3)
1616 vals
1617 exp2)))
1618 (if (not (or (equal math-expr-data math-rb-close)
1619 (equal math-expr-data ")")
1620 (eq math-exp-token 'end)))
1621 (throw 'syntax "Expected `]'")))
1622 (if (equal math-expr-data ";")
1623 (let ((math-exp-keep-spaces space-sep))
1624 (setq vals (cons 'vec (math-read-matrix (list vals))))))
1625 (if (not (or (equal math-expr-data math-rb-close)
1626 (eq math-exp-token 'end)))
1627 (throw 'syntax "Expected `]'")))
1628 (or (eq math-exp-token 'end)
1629 (math-read-token))
1630 vals)))
1632 (defun math-check-for-commas (&optional balancing)
1633 (let ((count 0)
1634 (pos (1- math-exp-pos)))
1635 (while (and (>= count 0)
1636 (setq pos (string-match
1637 (if balancing "[],[{}()<>]" "[],[{}()]")
1638 math-exp-str (1+ pos)))
1639 (or (/= (aref math-exp-str pos) ?,) (> count 0) balancing))
1640 (cond ((memq (aref math-exp-str pos) '(?\[ ?\{ ?\( ?\<))
1641 (setq count (1+ count)))
1642 ((memq (aref math-exp-str pos) '(?\] ?\} ?\) ?\>))
1643 (setq count (1- count)))))
1644 (if balancing
1646 (and pos (= (aref math-exp-str pos) ?,)))))
1648 (defun math-read-vector ()
1649 (let* ((val (list (math-read-expr-level 0)))
1650 (last val))
1651 (while (progn
1652 (while (eq math-exp-token 'space)
1653 (math-read-token))
1654 (and (not (eq math-exp-token 'end))
1655 (not (equal math-expr-data ";"))
1656 (not (equal math-expr-data math-rb-close))
1657 (not (equal math-expr-data "\\dots"))
1658 (not (equal math-expr-data "\\ldots"))))
1659 (if (equal math-expr-data ",")
1660 (math-read-token))
1661 (while (eq math-exp-token 'space)
1662 (math-read-token))
1663 (let ((rest (list (math-read-expr-level 0))))
1664 (setcdr last rest)
1665 (setq last rest)))
1666 (cons 'vec val)))
1668 (defun math-read-matrix (mat)
1669 (while (equal math-expr-data ";")
1670 (math-read-token)
1671 (while (eq math-exp-token 'space)
1672 (math-read-token))
1673 (setq mat (nconc mat (list (math-read-vector)))))
1674 mat)
1676 (provide 'calc-vec)
1678 ;;; calc-vec.el ends here