1 ;;; calc-mtx.el --- matrix functions for Calc
3 ;; Copyright (C) 1990, 1991, 1992, 1993, 2001 Free Software Foundation, Inc.
5 ;; Author: David Gillespie <daveg@synaptics.com>
6 ;; Maintainers: D. Goel <deego@gnufans.org>
7 ;; Colin Walters <walters@debian.org>
9 ;; This file is part of GNU Emacs.
11 ;; GNU Emacs is distributed in the hope that it will be useful,
12 ;; but WITHOUT ANY WARRANTY. No author or distributor
13 ;; accepts responsibility to anyone for the consequences of using it
14 ;; or for whether it serves any particular purpose or works at all,
15 ;; unless he says so in writing. Refer to the GNU Emacs General Public
16 ;; License for full details.
18 ;; Everyone is granted permission to copy, modify and redistribute
19 ;; GNU Emacs, but only under the conditions described in the
20 ;; GNU Emacs General Public License. A copy of this license is
21 ;; supposed to have been given to you along with GNU Emacs so you
22 ;; can know your rights and responsibilities. It should be in a
23 ;; file named COPYING. Among other things, the copyright notice
24 ;; and this notice must be preserved on all copies.
31 ;; This file is autoloaded from calc-ext.el.
36 (defun calc-Need-calc-mat () nil
)
39 (defun calc-mdet (arg)
42 (calc-unary-op "mdet" 'calcFunc-det arg
)))
44 (defun calc-mtrace (arg)
47 (calc-unary-op "mtr" 'calcFunc-tr arg
)))
49 (defun calc-mlud (arg)
52 (calc-unary-op "mlud" 'calcFunc-lud arg
)))
55 ;;; Coerce row vector A to be a matrix. [V V]
56 (defun math-row-matrix (a)
57 (if (and (Math-vectorp a
)
58 (not (math-matrixp a
)))
62 ;;; Coerce column vector A to be a matrix. [V V]
63 (defun math-col-matrix (a)
64 (if (and (Math-vectorp a
)
65 (not (math-matrixp a
)))
66 (cons 'vec
(mapcar (function (lambda (x) (list 'vec x
))) (cdr a
)))
71 ;;; Multiply matrices A and B. [V V V]
72 (defun math-mul-mats (a b
)
74 (cols (length (nth 1 b
)))
76 (while (setq a
(cdr a
))
79 (while (> (setq col
(1- col
)) 0)
80 (setq ap
(cdr (car a
))
82 accum
(math-mul (car ap
) (nth col
(car bp
))))
83 (while (setq ap
(cdr ap
) bp
(cdr bp
))
84 (setq accum
(math-add accum
(math-mul (car ap
) (nth col
(car bp
))))))
85 (setq row
(cons accum row
)))
86 (setq mat
(cons (cons 'vec row
) mat
)))
87 (cons 'vec
(nreverse mat
))))
89 (defun math-mul-mat-vec (a b
)
90 (cons 'vec
(mapcar (function (lambda (row)
91 (math-dot-product row b
)))
96 (defun calcFunc-tr (mat) ; [Public]
97 (if (math-square-matrixp mat
)
98 (math-matrix-trace-step 2 (1- (length mat
)) mat
(nth 1 (nth 1 mat
)))
99 (math-reject-arg mat
'square-matrixp
)))
101 (defun math-matrix-trace-step (n size mat sum
)
103 (math-matrix-trace-step (1+ n
) size mat
104 (math-add sum
(nth n
(nth n mat
))))
108 ;;; Matrix inverse and determinant.
109 (defun math-matrix-inv-raw (m)
110 (let ((n (1- (length m
))))
112 (let ((det (math-det-raw m
)))
113 (and (not (math-zerop det
))
120 (math-neg (nth 2 (nth 1 m
))))
122 (math-neg (nth 1 (nth 2 m
)))
127 (math-sub (math-mul (nth 3 (nth 3 m
))
129 (math-mul (nth 3 (nth 2 m
))
131 (math-sub (math-mul (nth 3 (nth 1 m
))
133 (math-mul (nth 3 (nth 3 m
))
135 (math-sub (math-mul (nth 3 (nth 2 m
))
137 (math-mul (nth 3 (nth 1 m
))
140 (math-sub (math-mul (nth 3 (nth 2 m
))
142 (math-mul (nth 3 (nth 3 m
))
144 (math-sub (math-mul (nth 3 (nth 3 m
))
146 (math-mul (nth 3 (nth 1 m
))
148 (math-sub (math-mul (nth 3 (nth 1 m
))
150 (math-mul (nth 3 (nth 2 m
))
153 (math-sub (math-mul (nth 2 (nth 3 m
))
155 (math-mul (nth 2 (nth 2 m
))
157 (math-sub (math-mul (nth 2 (nth 1 m
))
159 (math-mul (nth 2 (nth 3 m
))
161 (math-sub (math-mul (nth 2 (nth 2 m
))
163 (math-mul (nth 2 (nth 1 m
))
164 (nth 1 (nth 2 m
))))))))
166 (let ((lud (math-matrix-lud m
)))
168 (math-lud-solve lud
(calcFunc-idn 1 n
)))))))
170 (defun calcFunc-det (m)
171 (if (math-square-matrixp m
)
172 (math-with-extra-prec 2 (math-det-raw m
))
173 (if (and (eq (car-safe m
) 'calcFunc-idn
)
174 (or (math-zerop (nth 1 m
))
175 (math-equal-int (nth 1 m
) 1)))
177 (math-reject-arg m
'square-matrixp
))))
179 (defun math-det-raw (m)
180 (let ((n (1- (length m
))))
184 (math-sub (math-mul (nth 1 (nth 1 m
))
186 (math-mul (nth 2 (nth 1 m
))
194 (math-mul (nth 1 (nth 1 m
))
195 (math-mul (nth 2 (nth 2 m
))
197 (math-mul (nth 2 (nth 1 m
))
198 (math-mul (nth 3 (nth 2 m
))
200 (math-mul (nth 3 (nth 1 m
))
201 (math-mul (nth 1 (nth 2 m
))
203 (math-mul (nth 3 (nth 1 m
))
204 (math-mul (nth 2 (nth 2 m
))
206 (math-mul (nth 1 (nth 1 m
))
207 (math-mul (nth 3 (nth 2 m
))
209 (math-mul (nth 2 (nth 1 m
))
210 (math-mul (nth 1 (nth 2 m
))
211 (nth 3 (nth 3 m
))))))
212 (t (let ((lud (math-matrix-lud m
)))
214 (let ((lu (car lud
)))
215 (math-det-step n
(nth 2 lud
)))
218 (defun math-det-step (n prod
)
220 (math-det-step (1- n
) (math-mul prod
(nth n
(nth n lu
))))
223 ;;; This returns a list (LU index d), or nil if not possible.
224 ;;; Argument M must be a square matrix.
225 (defvar math-lud-cache nil
)
226 (defun math-matrix-lud (m)
227 (let ((old (assoc m math-lud-cache
))
228 (context (list calc-internal-prec calc-prefer-frac
)))
229 (if (and old
(equal (nth 1 old
) context
))
231 (let* ((lud (catch 'singular
(math-do-matrix-lud m
)))
232 (entry (cons context lud
)))
235 (setq math-lud-cache
(cons (cons m entry
) math-lud-cache
)))
238 ;;; Numerical Recipes section 2.3; implicit pivoting omitted.
239 (defun math-do-matrix-lud (m)
240 (let* ((lu (math-copy-matrix m
))
242 i
(j 1) k imax sum big
249 (math-working "LUD step" (format "%d/%d" j i
))
250 (setq sum
(nth j
(nth i lu
))
253 (setq sum
(math-sub sum
(math-mul (nth k
(nth i lu
))
256 (setcar (nthcdr j
(nth i lu
)) sum
)
259 (math-working "LUD step" (format "%d/%d" j i
))
260 (setq sum
(nth j
(nth i lu
))
263 (setq sum
(math-sub sum
(math-mul (nth k
(nth i lu
))
266 (setcar (nthcdr j
(nth i lu
)) sum
)
267 (let ((dum (math-abs-approx sum
)))
268 (if (Math-lessp big dum
)
273 (setq lu
(math-swap-rows lu j imax
)
275 (setq index
(cons imax index
))
276 (let ((pivot (nth j
(nth j lu
))))
277 (if (math-zerop pivot
)
278 (throw 'singular nil
)
280 (while (<= (setq i
(1+ i
)) n
)
281 (setcar (nthcdr j
(nth i lu
))
282 (math-div (nth j
(nth i lu
)) pivot
)))))
284 (list lu
(nreverse index
) d
)))
286 (defun math-swap-rows (m r1 r2
)
288 (let* ((r1prev (nthcdr (1- r1
) m
))
290 (r2prev (nthcdr (1- r2
) m
))
295 (setcdr row2
(cdr row1
))
296 (setcdr row1 r2next
)))
300 (defun math-lud-solve (lud b
&optional need
)
302 (let* ((x (math-copy-matrix b
))
304 (m (1- (length (nth 1 x
))))
309 (math-working "LUD solver step" col
)
316 sum
(nth col
(nth ip x
)))
317 (setcar (nthcdr col
(nth ip x
)) (nth col
(nth i x
)))
323 (setq sum
(math-sub sum
(math-mul (nth j
(nth i lu
))
324 (nth col
(nth j x
))))
326 (setcar (nthcdr col
(nth i x
)) sum
)
328 (while (>= (setq i
(1- i
)) 1)
329 (setq sum
(nth col
(nth i x
))
331 (while (<= (setq j
(1+ j
)) n
)
332 (setq sum
(math-sub sum
(math-mul (nth j
(nth i lu
))
333 (nth col
(nth j x
))))))
334 (setcar (nthcdr col
(nth i x
))
335 (math-div sum
(nth i
(nth i lu
)))))
339 (math-reject-arg need
"*Singular matrix"))))
341 (defun calcFunc-lud (m)
342 (if (math-square-matrixp m
)
343 (or (math-with-extra-prec 2
344 (let ((lud (math-matrix-lud m
)))
346 (let* ((lmat (math-copy-matrix (car lud
)))
347 (umat (math-copy-matrix (car lud
)))
348 (n (1- (length (car lud
))))
349 (perm (calcFunc-idn 1 n
))
354 (setcar (nthcdr j
(nth i lmat
)) 0)
356 (setcar (nthcdr j
(nth j lmat
)) 1)
357 (while (<= (setq i
(1+ i
)) n
)
358 (setcar (nthcdr j
(nth i umat
)) 0))
360 (while (>= (setq j
(1- j
)) 1)
361 (let ((pos (nth (1- j
) (nth 1 lud
))))
363 (setq perm
(math-swap-rows perm j pos
)))))
364 (list 'vec perm lmat umat
)))))
365 (math-reject-arg m
"*Singular matrix"))
366 (math-reject-arg m
'square-matrixp
)))
368 ;;; arch-tag: fc0947b1-90e1-4a23-8950-d8ead9c3a306
369 ;;; calc-mtx.el ends here