| 1 | ;;; calc-map.el --- higher-order functions for Calc |
| 2 | |
| 3 | ;; Copyright (C) 1990-1993, 2001-2014 Free Software Foundation, Inc. |
| 4 | |
| 5 | ;; Author: David Gillespie <daveg@synaptics.com> |
| 6 | ;; Maintainer: Jay Belanger <jay.p.belanger@gmail.com> |
| 7 | |
| 8 | ;; This file is part of GNU Emacs. |
| 9 | |
| 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. |
| 14 | |
| 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. |
| 19 | |
| 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/>. |
| 22 | |
| 23 | ;;; Commentary: |
| 24 | |
| 25 | ;;; Code: |
| 26 | |
| 27 | ;; This file is autoloaded from calc-ext.el. |
| 28 | |
| 29 | (require 'calc-ext) |
| 30 | (require 'calc-macs) |
| 31 | |
| 32 | (defun calc-apply (&optional oper) |
| 33 | (interactive) |
| 34 | (calc-wrapper |
| 35 | (let* ((calc-dollar-values (mapcar #'calc-get-stack-element |
| 36 | (nthcdr calc-stack-top calc-stack))) |
| 37 | (calc-dollar-used 0) |
| 38 | (oper (or oper (calc-get-operator "Apply" |
| 39 | (if (math-vectorp (calc-top 1)) |
| 40 | (1- (length (calc-top 1))) |
| 41 | -1)))) |
| 42 | (expr (calc-top-n (1+ calc-dollar-used)))) |
| 43 | (message "Working...") |
| 44 | (calc-set-command-flag 'clear-message) |
| 45 | (calc-enter-result (1+ calc-dollar-used) |
| 46 | (concat (substring "apl" 0 (- 4 (length (nth 2 oper)))) |
| 47 | (nth 2 oper)) |
| 48 | (list 'calcFunc-apply |
| 49 | (math-calcFunc-to-var (nth 1 oper)) |
| 50 | expr))))) |
| 51 | |
| 52 | (defun calc-reduce (&optional oper accum) |
| 53 | (interactive) |
| 54 | (calc-wrapper |
| 55 | (let* ((nest (calc-is-hyperbolic)) |
| 56 | (rev (calc-is-inverse)) |
| 57 | (nargs (if (and nest (not rev)) 2 1)) |
| 58 | (calc-dollar-values (mapcar #'calc-get-stack-element |
| 59 | (nthcdr calc-stack-top calc-stack))) |
| 60 | (calc-dollar-used 0) |
| 61 | (calc-mapping-dir (and (not accum) (not nest) "")) |
| 62 | (oper (or oper (calc-get-operator |
| 63 | (if nest |
| 64 | (concat (if accum "Accumulate " "") |
| 65 | (if rev "Fixed Point" "Nest")) |
| 66 | (concat (if rev "Inv " "") |
| 67 | (if accum "Accumulate" "Reduce"))) |
| 68 | (if nest 1 2))))) |
| 69 | (message "Working...") |
| 70 | (calc-set-command-flag 'clear-message) |
| 71 | (calc-enter-result (+ calc-dollar-used nargs) |
| 72 | (concat (substring (if nest |
| 73 | (if rev "fxp" "nst") |
| 74 | (if accum "acc" "red")) |
| 75 | 0 (- 4 (length (nth 2 oper)))) |
| 76 | (nth 2 oper)) |
| 77 | (if nest |
| 78 | (cons (if rev |
| 79 | (if accum 'calcFunc-afixp 'calcFunc-fixp) |
| 80 | (if accum 'calcFunc-anest 'calcFunc-nest)) |
| 81 | (cons (math-calcFunc-to-var (nth 1 oper)) |
| 82 | (calc-top-list-n |
| 83 | nargs (1+ calc-dollar-used)))) |
| 84 | (list (if accum |
| 85 | (if rev 'calcFunc-raccum 'calcFunc-accum) |
| 86 | (intern (concat "calcFunc-" |
| 87 | (if rev "r" "") |
| 88 | "reduce" |
| 89 | calc-mapping-dir))) |
| 90 | (math-calcFunc-to-var (nth 1 oper)) |
| 91 | (calc-top-n (1+ calc-dollar-used)))))))) |
| 92 | |
| 93 | (defun calc-accumulate (&optional oper) |
| 94 | (interactive) |
| 95 | (calc-reduce oper t)) |
| 96 | |
| 97 | (defun calc-map (&optional oper) |
| 98 | (interactive) |
| 99 | (calc-wrapper |
| 100 | (let* ((calc-dollar-values (mapcar #'calc-get-stack-element |
| 101 | (nthcdr calc-stack-top calc-stack))) |
| 102 | (calc-dollar-used 0) |
| 103 | (calc-mapping-dir "") |
| 104 | (oper (or oper (calc-get-operator "Map"))) |
| 105 | (nargs (car oper))) |
| 106 | (message "Working...") |
| 107 | (calc-set-command-flag 'clear-message) |
| 108 | (calc-enter-result (+ nargs calc-dollar-used) |
| 109 | (concat (substring "map" 0 (- 4 (length (nth 2 oper)))) |
| 110 | (nth 2 oper)) |
| 111 | (cons (intern (concat "calcFunc-map" calc-mapping-dir)) |
| 112 | (cons (math-calcFunc-to-var (nth 1 oper)) |
| 113 | (calc-top-list-n |
| 114 | nargs |
| 115 | (1+ calc-dollar-used)))))))) |
| 116 | |
| 117 | (defun calc-map-equation (&optional oper) |
| 118 | (interactive) |
| 119 | (calc-wrapper |
| 120 | (let* ((calc-dollar-values (mapcar #'calc-get-stack-element |
| 121 | (nthcdr calc-stack-top calc-stack))) |
| 122 | (calc-dollar-used 0) |
| 123 | (oper (or oper (calc-get-operator "Map-equation"))) |
| 124 | (nargs (car oper))) |
| 125 | (message "Working...") |
| 126 | (calc-set-command-flag 'clear-message) |
| 127 | (calc-enter-result (+ nargs calc-dollar-used) |
| 128 | (concat (substring "map" 0 (- 4 (length (nth 2 oper)))) |
| 129 | (nth 2 oper)) |
| 130 | (cons (if (calc-is-inverse) |
| 131 | 'calcFunc-mapeqr |
| 132 | (if (calc-is-hyperbolic) |
| 133 | 'calcFunc-mapeqp 'calcFunc-mapeq)) |
| 134 | (cons (math-calcFunc-to-var (nth 1 oper)) |
| 135 | (calc-top-list-n |
| 136 | nargs |
| 137 | (1+ calc-dollar-used)))))))) |
| 138 | |
| 139 | (defvar calc-verify-arglist t) |
| 140 | (defvar calc-mapping-dir nil) |
| 141 | (defun calc-map-stack () |
| 142 | "This is meant to be called by calc-keypad mode." |
| 143 | (interactive) |
| 144 | (let ((calc-verify-arglist nil)) |
| 145 | (calc-unread-command ?\$) |
| 146 | (calc-map))) |
| 147 | |
| 148 | (defun calc-outer-product (&optional oper) |
| 149 | (interactive) |
| 150 | (calc-wrapper |
| 151 | (let* ((calc-dollar-values (mapcar #'calc-get-stack-element |
| 152 | (nthcdr calc-stack-top calc-stack))) |
| 153 | (calc-dollar-used 0) |
| 154 | (oper (or oper (calc-get-operator "Outer" 2)))) |
| 155 | (message "Working...") |
| 156 | (calc-set-command-flag 'clear-message) |
| 157 | (calc-enter-result (+ 2 calc-dollar-used) |
| 158 | (concat (substring "out" 0 (- 4 (length (nth 2 oper)))) |
| 159 | (nth 2 oper)) |
| 160 | (cons 'calcFunc-outer |
| 161 | (cons (math-calcFunc-to-var (nth 1 oper)) |
| 162 | (calc-top-list-n |
| 163 | 2 (1+ calc-dollar-used)))))))) |
| 164 | |
| 165 | (defun calc-inner-product (&optional mul-oper add-oper) |
| 166 | (interactive) |
| 167 | (calc-wrapper |
| 168 | (let* ((calc-dollar-values (mapcar #'calc-get-stack-element |
| 169 | (nthcdr calc-stack-top calc-stack))) |
| 170 | (calc-dollar-used 0) |
| 171 | (mul-oper (or mul-oper (calc-get-operator "Inner (Mult)" 2))) |
| 172 | (mul-used calc-dollar-used) |
| 173 | (calc-dollar-values (if (> mul-used 0) |
| 174 | (cdr calc-dollar-values) |
| 175 | calc-dollar-values)) |
| 176 | (calc-dollar-used 0) |
| 177 | (add-oper (or add-oper (calc-get-operator "Inner (Add)" 2)))) |
| 178 | (message "Working...") |
| 179 | (calc-set-command-flag 'clear-message) |
| 180 | (calc-enter-result (+ 2 mul-used calc-dollar-used) |
| 181 | (concat "in" |
| 182 | (substring (nth 2 mul-oper) 0 1) |
| 183 | (substring (nth 2 add-oper) 0 1)) |
| 184 | (nconc (list 'calcFunc-inner |
| 185 | (math-calcFunc-to-var (nth 1 mul-oper)) |
| 186 | (math-calcFunc-to-var (nth 1 add-oper))) |
| 187 | (calc-top-list-n |
| 188 | 2 (+ 1 mul-used calc-dollar-used))))))) |
| 189 | |
| 190 | (defconst calc-oper-keys '( ( ( ?+ 2 calcFunc-add ) |
| 191 | ( ?- 2 calcFunc-sub ) |
| 192 | ( ?* 2 calcFunc-mul ) |
| 193 | ( ?/ 2 calcFunc-div ) |
| 194 | ( ?^ 2 calcFunc-pow ) |
| 195 | ( ?| 2 calcFunc-vconcat ) |
| 196 | ( ?% 2 calcFunc-mod ) |
| 197 | ( ?\\ 2 calcFunc-idiv ) |
| 198 | ( ?! 1 calcFunc-fact ) |
| 199 | ( ?& 1 calcFunc-inv ) |
| 200 | ( ?n 1 calcFunc-neg ) |
| 201 | ( ?x user ) |
| 202 | ( ?z user ) |
| 203 | ( ?A 1 calcFunc-abs ) |
| 204 | ( ?J 1 calcFunc-conj ) |
| 205 | ( ?G 1 calcFunc-arg ) |
| 206 | ( ?Q 1 calcFunc-sqrt ) |
| 207 | ( ?N 2 calcFunc-min ) |
| 208 | ( ?X 2 calcFunc-max ) |
| 209 | ( ?F 1 calcFunc-floor ) |
| 210 | ( ?R 1 calcFunc-round ) |
| 211 | ( ?S 1 calcFunc-sin ) |
| 212 | ( ?C 1 calcFunc-cos ) |
| 213 | ( ?T 1 calcFunc-tan ) |
| 214 | ( ?L 1 calcFunc-ln ) |
| 215 | ( ?E 1 calcFunc-exp ) |
| 216 | ( ?B 2 calcFunc-log ) ) |
| 217 | ( ( ?F 1 calcFunc-ceil ) ; inverse |
| 218 | ( ?R 1 calcFunc-trunc ) |
| 219 | ( ?Q 1 calcFunc-sqr ) |
| 220 | ( ?S 1 calcFunc-arcsin ) |
| 221 | ( ?C 1 calcFunc-arccos ) |
| 222 | ( ?T 1 calcFunc-arctan ) |
| 223 | ( ?L 1 calcFunc-exp ) |
| 224 | ( ?E 1 calcFunc-ln ) |
| 225 | ( ?B 2 calcFunc-alog ) |
| 226 | ( ?^ 2 calcFunc-nroot ) |
| 227 | ( ?| 2 calcFunc-vconcatrev ) ) |
| 228 | ( ( ?F 1 calcFunc-ffloor ) ; hyperbolic |
| 229 | ( ?R 1 calcFunc-fround ) |
| 230 | ( ?S 1 calcFunc-sinh ) |
| 231 | ( ?C 1 calcFunc-cosh ) |
| 232 | ( ?T 1 calcFunc-tanh ) |
| 233 | ( ?L 1 calcFunc-log10 ) |
| 234 | ( ?E 1 calcFunc-exp10 ) |
| 235 | ( ?| 2 calcFunc-append ) ) |
| 236 | ( ( ?F 1 calcFunc-fceil ) ; inverse-hyperbolic |
| 237 | ( ?R 1 calcFunc-ftrunc ) |
| 238 | ( ?S 1 calcFunc-arcsinh ) |
| 239 | ( ?C 1 calcFunc-arccosh ) |
| 240 | ( ?T 1 calcFunc-arctanh ) |
| 241 | ( ?L 1 calcFunc-exp10 ) |
| 242 | ( ?E 1 calcFunc-log10 ) |
| 243 | ( ?| 2 calcFunc-appendrev ) ))) |
| 244 | |
| 245 | (defconst calc-a-oper-keys '( ( ( ?a 3 calcFunc-apart ) |
| 246 | ( ?b 3 calcFunc-subst ) |
| 247 | ( ?c 2 calcFunc-collect ) |
| 248 | ( ?d 2 calcFunc-deriv ) |
| 249 | ( ?e 1 calcFunc-esimplify ) |
| 250 | ( ?f 2 calcFunc-factor ) |
| 251 | ( ?g 2 calcFunc-pgcd ) |
| 252 | ( ?i 2 calcFunc-integ ) |
| 253 | ( ?m 2 calcFunc-match ) |
| 254 | ( ?n 1 calcFunc-nrat ) |
| 255 | ( ?r 2 calcFunc-rewrite ) |
| 256 | ( ?s 1 calcFunc-simplify ) |
| 257 | ( ?t 3 calcFunc-taylor ) |
| 258 | ( ?x 1 calcFunc-expand ) |
| 259 | ( ?M 2 calcFunc-mapeq ) |
| 260 | ( ?N 3 calcFunc-minimize ) |
| 261 | ( ?P 2 calcFunc-roots ) |
| 262 | ( ?R 3 calcFunc-root ) |
| 263 | ( ?S 2 calcFunc-solve ) |
| 264 | ( ?T 4 calcFunc-table ) |
| 265 | ( ?X 3 calcFunc-maximize ) |
| 266 | ( ?= 2 calcFunc-eq ) |
| 267 | ( ?\# 2 calcFunc-neq ) |
| 268 | ( ?< 2 calcFunc-lt ) |
| 269 | ( ?> 2 calcFunc-gt ) |
| 270 | ( ?\[ 2 calcFunc-leq ) |
| 271 | ( ?\] 2 calcFunc-geq ) |
| 272 | ( ?{ 2 calcFunc-in ) |
| 273 | ( ?! 1 calcFunc-lnot ) |
| 274 | ( ?& 2 calcFunc-land ) |
| 275 | ( ?\| 2 calcFunc-lor ) |
| 276 | ( ?: 3 calcFunc-if ) |
| 277 | ( ?. 2 calcFunc-rmeq ) |
| 278 | ( ?+ 4 calcFunc-sum ) |
| 279 | ( ?- 4 calcFunc-asum ) |
| 280 | ( ?* 4 calcFunc-prod ) |
| 281 | ( ?_ 2 calcFunc-subscr ) |
| 282 | ( ?\\ 2 calcFunc-pdiv ) |
| 283 | ( ?% 2 calcFunc-prem ) |
| 284 | ( ?/ 2 calcFunc-pdivrem ) ) |
| 285 | ( ( ?m 2 calcFunc-matchnot ) |
| 286 | ( ?M 2 calcFunc-mapeqr ) |
| 287 | ( ?S 2 calcFunc-finv ) ) |
| 288 | ( ( ?d 2 calcFunc-tderiv ) |
| 289 | ( ?f 2 calcFunc-factors ) |
| 290 | ( ?M 2 calcFunc-mapeqp ) |
| 291 | ( ?N 3 calcFunc-wminimize ) |
| 292 | ( ?R 3 calcFunc-wroot ) |
| 293 | ( ?S 2 calcFunc-fsolve ) |
| 294 | ( ?X 3 calcFunc-wmaximize ) |
| 295 | ( ?/ 2 calcFunc-pdivide ) ) |
| 296 | ( ( ?S 2 calcFunc-ffinv ) ))) |
| 297 | |
| 298 | (defconst calc-b-oper-keys '( ( ( ?a 2 calcFunc-and ) |
| 299 | ( ?o 2 calcFunc-or ) |
| 300 | ( ?x 2 calcFunc-xor ) |
| 301 | ( ?d 2 calcFunc-diff ) |
| 302 | ( ?n 1 calcFunc-not ) |
| 303 | ( ?c 1 calcFunc-clip ) |
| 304 | ( ?l 2 calcFunc-lsh ) |
| 305 | ( ?r 2 calcFunc-rsh ) |
| 306 | ( ?L 2 calcFunc-ash ) |
| 307 | ( ?R 2 calcFunc-rash ) |
| 308 | ( ?t 2 calcFunc-rot ) |
| 309 | ( ?p 1 calcFunc-vpack ) |
| 310 | ( ?u 1 calcFunc-vunpack ) |
| 311 | ( ?D 4 calcFunc-ddb ) |
| 312 | ( ?F 3 calcFunc-fv ) |
| 313 | ( ?I 1 calcFunc-irr ) |
| 314 | ( ?M 3 calcFunc-pmt ) |
| 315 | ( ?N 2 calcFunc-npv ) |
| 316 | ( ?P 3 calcFunc-pv ) |
| 317 | ( ?S 3 calcFunc-sln ) |
| 318 | ( ?T 3 calcFunc-rate ) |
| 319 | ( ?Y 4 calcFunc-syd ) |
| 320 | ( ?\# 3 calcFunc-nper ) |
| 321 | ( ?\% 2 calcFunc-relch ) ) |
| 322 | ( ( ?F 3 calcFunc-fvb ) |
| 323 | ( ?I 1 calcFunc-irrb ) |
| 324 | ( ?M 3 calcFunc-pmtb ) |
| 325 | ( ?N 2 calcFunc-npvb ) |
| 326 | ( ?P 3 calcFunc-pvb ) |
| 327 | ( ?T 3 calcFunc-rateb ) |
| 328 | ( ?\# 3 calcFunc-nperb ) ) |
| 329 | ( ( ?F 3 calcFunc-fvl ) |
| 330 | ( ?M 3 calcFunc-pmtl ) |
| 331 | ( ?P 3 calcFunc-pvl ) |
| 332 | ( ?T 3 calcFunc-ratel ) |
| 333 | ( ?\# 3 calcFunc-nperl ) ))) |
| 334 | |
| 335 | (defconst calc-c-oper-keys '( ( ( ?d 1 calcFunc-deg ) |
| 336 | ( ?r 1 calcFunc-rad ) |
| 337 | ( ?h 1 calcFunc-hms ) |
| 338 | ( ?f 1 calcFunc-float ) |
| 339 | ( ?F 1 calcFunc-frac ) ))) |
| 340 | |
| 341 | (defconst calc-f-oper-keys '( ( ( ?b 2 calcFunc-beta ) |
| 342 | ( ?e 1 calcFunc-erf ) |
| 343 | ( ?g 1 calcFunc-gamma ) |
| 344 | ( ?h 2 calcFunc-hypot ) |
| 345 | ( ?i 1 calcFunc-im ) |
| 346 | ( ?j 2 calcFunc-besJ ) |
| 347 | ( ?n 2 calcFunc-min ) |
| 348 | ( ?r 1 calcFunc-re ) |
| 349 | ( ?s 1 calcFunc-sign ) |
| 350 | ( ?x 2 calcFunc-max ) |
| 351 | ( ?y 2 calcFunc-besY ) |
| 352 | ( ?A 1 calcFunc-abssqr ) |
| 353 | ( ?B 3 calcFunc-betaI ) |
| 354 | ( ?E 1 calcFunc-expm1 ) |
| 355 | ( ?G 2 calcFunc-gammaP ) |
| 356 | ( ?I 2 calcFunc-ilog ) |
| 357 | ( ?L 1 calcFunc-lnp1 ) |
| 358 | ( ?M 1 calcFunc-mant ) |
| 359 | ( ?Q 1 calcFunc-isqrt ) |
| 360 | ( ?S 1 calcFunc-scf ) |
| 361 | ( ?T 2 calcFunc-arctan2 ) |
| 362 | ( ?X 1 calcFunc-xpon ) |
| 363 | ( ?\[ 2 calcFunc-decr ) |
| 364 | ( ?\] 2 calcFunc-incr ) ) |
| 365 | ( ( ?e 1 calcFunc-erfc ) |
| 366 | ( ?E 1 calcFunc-lnp1 ) |
| 367 | ( ?G 2 calcFunc-gammaQ ) |
| 368 | ( ?L 1 calcFunc-expm1 ) ) |
| 369 | ( ( ?B 3 calcFunc-betaB ) |
| 370 | ( ?G 2 calcFunc-gammag) ) |
| 371 | ( ( ?G 2 calcFunc-gammaG ) ))) |
| 372 | |
| 373 | (defconst calc-k-oper-keys '( ( ( ?b 1 calcFunc-bern ) |
| 374 | ( ?c 2 calcFunc-choose ) |
| 375 | ( ?d 1 calcFunc-dfact ) |
| 376 | ( ?e 1 calcFunc-euler ) |
| 377 | ( ?f 1 calcFunc-prfac ) |
| 378 | ( ?g 2 calcFunc-gcd ) |
| 379 | ( ?h 2 calcFunc-shuffle ) |
| 380 | ( ?l 2 calcFunc-lcm ) |
| 381 | ( ?m 1 calcFunc-moebius ) |
| 382 | ( ?n 1 calcFunc-nextprime ) |
| 383 | ( ?r 1 calcFunc-random ) |
| 384 | ( ?s 2 calcFunc-stir1 ) |
| 385 | ( ?t 1 calcFunc-totient ) |
| 386 | ( ?B 3 calcFunc-utpb ) |
| 387 | ( ?C 2 calcFunc-utpc ) |
| 388 | ( ?F 3 calcFunc-utpf ) |
| 389 | ( ?N 3 calcFunc-utpn ) |
| 390 | ( ?P 2 calcFunc-utpp ) |
| 391 | ( ?T 2 calcFunc-utpt ) ) |
| 392 | ( ( ?n 1 calcFunc-prevprime ) |
| 393 | ( ?B 3 calcFunc-ltpb ) |
| 394 | ( ?C 2 calcFunc-ltpc ) |
| 395 | ( ?F 3 calcFunc-ltpf ) |
| 396 | ( ?N 3 calcFunc-ltpn ) |
| 397 | ( ?P 2 calcFunc-ltpp ) |
| 398 | ( ?T 2 calcFunc-ltpt ) ) |
| 399 | ( ( ?b 2 calcFunc-bern ) |
| 400 | ( ?c 2 calcFunc-perm ) |
| 401 | ( ?e 2 calcFunc-euler ) |
| 402 | ( ?s 2 calcFunc-stir2 ) ))) |
| 403 | |
| 404 | (defconst calc-s-oper-keys '( ( ( ?: 2 calcFunc-assign ) |
| 405 | ( ?= 1 calcFunc-evalto ) ))) |
| 406 | |
| 407 | (defconst calc-t-oper-keys '( ( ( ?C 3 calcFunc-tzconv ) |
| 408 | ( ?D 1 calcFunc-date ) |
| 409 | ( ?I 2 calcFunc-incmonth ) |
| 410 | ( ?J 1 calcFunc-julian ) |
| 411 | ( ?M 1 calcFunc-newmonth ) |
| 412 | ( ?W 1 calcFunc-newweek ) |
| 413 | ( ?U 1 calcFunc-unixtime ) |
| 414 | ( ?Y 1 calcFunc-newyear ) ))) |
| 415 | |
| 416 | (defconst calc-u-oper-keys '( ( ( ?C 2 calcFunc-vcov ) |
| 417 | ( ?G 1 calcFunc-vgmean ) |
| 418 | ( ?M 1 calcFunc-vmean ) |
| 419 | ( ?N 1 calcFunc-vmin ) |
| 420 | ( ?S 1 calcFunc-vsdev ) |
| 421 | ( ?X 1 calcFunc-vmax ) ) |
| 422 | ( ( ?C 2 calcFunc-vpcov ) |
| 423 | ( ?M 1 calcFunc-vmeane ) |
| 424 | ( ?S 1 calcFunc-vpsdev ) ) |
| 425 | ( ( ?C 2 calcFunc-vcorr ) |
| 426 | ( ?G 1 calcFunc-agmean ) |
| 427 | ( ?M 1 calcFunc-vmedian ) |
| 428 | ( ?S 1 calcFunc-vvar ) ) |
| 429 | ( ( ?M 1 calcFunc-vhmean ) |
| 430 | ( ?S 1 calcFunc-vpvar ) ))) |
| 431 | |
| 432 | (defconst calc-v-oper-keys '( ( ( ?a 2 calcFunc-arrange ) |
| 433 | ( ?b 2 calcFunc-cvec ) |
| 434 | ( ?c 2 calcFunc-mcol ) |
| 435 | ( ?d 2 calcFunc-diag ) |
| 436 | ( ?e 2 calcFunc-vexp ) |
| 437 | ( ?f 2 calcFunc-find ) |
| 438 | ( ?h 1 calcFunc-head ) |
| 439 | ( ?k 2 calcFunc-cons ) |
| 440 | ( ?l 1 calcFunc-vlen ) |
| 441 | ( ?m 2 calcFunc-vmask ) |
| 442 | ( ?n 1 calcFunc-rnorm ) |
| 443 | ( ?p 2 calcFunc-pack ) |
| 444 | ( ?r 2 calcFunc-mrow ) |
| 445 | ( ?s 3 calcFunc-subvec ) |
| 446 | ( ?t 1 calcFunc-trn ) |
| 447 | ( ?u 1 calcFunc-unpack ) |
| 448 | ( ?v 1 calcFunc-rev ) |
| 449 | ( ?x 1 calcFunc-index ) |
| 450 | ( ?A 1 calcFunc-apply ) |
| 451 | ( ?C 1 calcFunc-cross ) |
| 452 | ( ?D 1 calcFunc-det ) |
| 453 | ( ?E 1 calcFunc-venum ) |
| 454 | ( ?F 1 calcFunc-vfloor ) |
| 455 | ( ?G 1 calcFunc-grade ) |
| 456 | ( ?H 2 calcFunc-histogram ) |
| 457 | ( ?I 2 calcFunc-inner ) |
| 458 | ( ?L 1 calcFunc-lud ) |
| 459 | ( ?M 0 calcFunc-map ) |
| 460 | ( ?N 1 calcFunc-cnorm ) |
| 461 | ( ?O 2 calcFunc-outer ) |
| 462 | ( ?R 1 calcFunc-reduce ) |
| 463 | ( ?S 1 calcFunc-sort ) |
| 464 | ( ?T 1 calcFunc-tr ) |
| 465 | ( ?U 1 calcFunc-accum ) |
| 466 | ( ?V 2 calcFunc-vunion ) |
| 467 | ( ?X 2 calcFunc-vxor ) |
| 468 | ( ?- 2 calcFunc-vdiff ) |
| 469 | ( ?^ 2 calcFunc-vint ) |
| 470 | ( ?~ 1 calcFunc-vcompl ) |
| 471 | ( ?# 1 calcFunc-vcard ) |
| 472 | ( ?: 1 calcFunc-vspan ) |
| 473 | ( ?+ 1 calcFunc-rdup ) ) |
| 474 | ( ( ?h 1 calcFunc-tail ) |
| 475 | ( ?s 3 calcFunc-rsubvec ) |
| 476 | ( ?G 1 calcFunc-rgrade ) |
| 477 | ( ?R 1 calcFunc-rreduce ) |
| 478 | ( ?S 1 calcFunc-rsort ) |
| 479 | ( ?U 1 calcFunc-raccum ) ) |
| 480 | ( ( ?e 3 calcFunc-vexp ) |
| 481 | ( ?h 1 calcFunc-rhead ) |
| 482 | ( ?k 2 calcFunc-rcons ) |
| 483 | ( ?H 3 calcFunc-histogram ) |
| 484 | ( ?R 2 calcFunc-nest ) |
| 485 | ( ?U 2 calcFunc-anest ) ) |
| 486 | ( ( ?h 1 calcFunc-rtail ) |
| 487 | ( ?R 1 calcFunc-fixp ) |
| 488 | ( ?U 1 calcFunc-afixp ) ))) |
| 489 | |
| 490 | |
| 491 | ;;; Return a list of the form (nargs func name) |
| 492 | (defvar calc-get-operator-history nil |
| 493 | "History for calc-get-operator.") |
| 494 | |
| 495 | (defun calc-get-operator (msg &optional nargs) |
| 496 | (setq calc-aborted-prefix nil) |
| 497 | (let ((inv nil) (hyp nil) (prefix nil) (forcenargs nil) |
| 498 | done key oper (which 0) |
| 499 | (msgs '( "(Press ? for help)" |
| 500 | "+, -, *, /, ^, %, \\, :, &, !, |, Neg" |
| 501 | "SHIFT + Abs, conJ, arG; maX, miN; Floor, Round; sQrt" |
| 502 | "SHIFT + Inv, Hyp; Sin, Cos, Tan; Exp, Ln, logB" |
| 503 | "Algebra + Simp, Esimp, Deriv, Integ, !, =, etc." |
| 504 | "Binary + And, Or, Xor, Diff; l/r/t/L/R shifts; Not, Clip" |
| 505 | "Conversions + Deg, Rad, HMS; Float; SHIFT + Fraction" |
| 506 | "Functions + Re, Im; Hypot; Mant, Expon, Scale; etc." |
| 507 | "Kombinatorics + Dfact, Lcm, Gcd, Choose; Random; etc." |
| 508 | "Time/date + newYear, Incmonth, etc." |
| 509 | "Vectors + Length, Row, Col, Diag, Mask, etc." |
| 510 | "_ = mapr/reducea, : = mapc/reduced, = = reducer" |
| 511 | "X or Z = any function by name; ' = alg entry; $ = stack"))) |
| 512 | (while (not done) |
| 513 | (message "%s%s: %s: %s%s%s" |
| 514 | msg |
| 515 | (cond ((equal calc-mapping-dir "r") " rows") |
| 516 | ((equal calc-mapping-dir "c") " columns") |
| 517 | ((equal calc-mapping-dir "a") " across") |
| 518 | ((equal calc-mapping-dir "d") " down") |
| 519 | (t "")) |
| 520 | (if forcenargs |
| 521 | (format "(%d arg%s)" |
| 522 | forcenargs (if (= forcenargs 1) "" "s")) |
| 523 | (nth which msgs)) |
| 524 | (if inv "Inv " "") (if hyp "Hyp " "") |
| 525 | (if prefix (concat (char-to-string prefix) "-") "")) |
| 526 | (setq key (read-char)) |
| 527 | (if (>= key 128) (setq key (- key 128))) |
| 528 | (cond ((memq key '(?\C-g ?q)) |
| 529 | (keyboard-quit)) |
| 530 | ((memq key '(?\C-u ?\e))) |
| 531 | ((= key ??) |
| 532 | (setq which (% (1+ which) (length msgs)))) |
| 533 | ((and (= key ?I) (null prefix)) |
| 534 | (setq inv (not inv))) |
| 535 | ((and (= key ?H) (null prefix)) |
| 536 | (setq hyp (not hyp))) |
| 537 | ((and (eq key prefix) (not (eq key ?v))) |
| 538 | (setq prefix nil)) |
| 539 | ((and (memq key '(?a ?b ?c ?f ?k ?s ?t ?u ?v ?V)) |
| 540 | (null prefix)) |
| 541 | (setq prefix (downcase key))) |
| 542 | ((and (eq key ?\=) (null prefix)) |
| 543 | (if calc-mapping-dir |
| 544 | (setq calc-mapping-dir (if (equal calc-mapping-dir "r") |
| 545 | "" "r")) |
| 546 | (beep))) |
| 547 | ((and (eq key ?\_) (null prefix)) |
| 548 | (if calc-mapping-dir |
| 549 | (if (string-match "map$" msg) |
| 550 | (setq calc-mapping-dir (if (equal calc-mapping-dir "r") |
| 551 | "" "r")) |
| 552 | (setq calc-mapping-dir (if (equal calc-mapping-dir "a") |
| 553 | "" "a"))) |
| 554 | (beep))) |
| 555 | ((and (eq key ?\:) (null prefix)) |
| 556 | (if calc-mapping-dir |
| 557 | (if (string-match "map$" msg) |
| 558 | (setq calc-mapping-dir (if (equal calc-mapping-dir "c") |
| 559 | "" "c")) |
| 560 | (setq calc-mapping-dir (if (equal calc-mapping-dir "d") |
| 561 | "" "d"))) |
| 562 | (beep))) |
| 563 | ((and (>= key ?0) (<= key ?9) (null prefix)) |
| 564 | (setq forcenargs (if (eq forcenargs (- key ?0)) nil (- key ?0))) |
| 565 | (and nargs forcenargs (/= nargs forcenargs) (>= nargs 0) |
| 566 | (error "Must be a %d-argument operator" nargs))) |
| 567 | ((memq key '(?\$ ?\')) |
| 568 | (let* ((math-arglist nil) |
| 569 | (has-args nil) |
| 570 | (record-entry nil) |
| 571 | (expr (if (eq key ?\$) |
| 572 | (progn |
| 573 | (setq calc-dollar-used 1) |
| 574 | (if calc-dollar-values |
| 575 | (car calc-dollar-values) |
| 576 | (error "Stack underflow"))) |
| 577 | (let* ((calc-dollar-values calc-arg-values) |
| 578 | (calc-dollar-used 0) |
| 579 | (calc-hashes-used 0) |
| 580 | (func (calc-do-alg-entry "" "Function: " nil |
| 581 | 'calc-get-operator-history))) |
| 582 | (setq record-entry t) |
| 583 | (or (= (length func) 1) |
| 584 | (error "Bad format")) |
| 585 | (if (> calc-dollar-used 0) |
| 586 | (progn |
| 587 | (setq has-args calc-dollar-used |
| 588 | math-arglist (calc-invent-args has-args)) |
| 589 | (math-multi-subst (car func) |
| 590 | (reverse math-arglist) |
| 591 | math-arglist)) |
| 592 | (if (> calc-hashes-used 0) |
| 593 | (setq has-args calc-hashes-used |
| 594 | math-arglist (calc-invent-args has-args))) |
| 595 | (car func)))))) |
| 596 | (if (eq (car-safe expr) 'calcFunc-lambda) |
| 597 | (setq oper (list "$" (- (length expr) 2) expr) |
| 598 | done t) |
| 599 | (or has-args |
| 600 | (progn |
| 601 | (calc-default-formula-arglist expr) |
| 602 | (setq record-entry t |
| 603 | math-arglist (sort math-arglist 'string-lessp)) |
| 604 | (if calc-verify-arglist |
| 605 | (setq math-arglist (read-from-minibuffer |
| 606 | "Function argument list: " |
| 607 | (if math-arglist |
| 608 | (prin1-to-string math-arglist) |
| 609 | "()") |
| 610 | minibuffer-local-map |
| 611 | t))) |
| 612 | (setq math-arglist (mapcar (function |
| 613 | (lambda (x) |
| 614 | (list 'var |
| 615 | x |
| 616 | (intern |
| 617 | (concat |
| 618 | "var-" |
| 619 | (symbol-name x)))))) |
| 620 | math-arglist)))) |
| 621 | (setq oper (list "$" |
| 622 | (length math-arglist) |
| 623 | (append '(calcFunc-lambda) math-arglist |
| 624 | (list expr))) |
| 625 | done t)) |
| 626 | (if record-entry |
| 627 | (calc-record (nth 2 oper) "oper")))) |
| 628 | ((setq oper (assq key (nth (if inv (if hyp 3 1) (if hyp 2 0)) |
| 629 | (if prefix |
| 630 | (symbol-value |
| 631 | (intern (format "calc-%c-oper-keys" |
| 632 | prefix))) |
| 633 | calc-oper-keys)))) |
| 634 | (if (eq (nth 1 oper) 'user) |
| 635 | (let ((func (intern |
| 636 | (completing-read "Function name: " |
| 637 | obarray 'fboundp |
| 638 | nil "calcFunc-")))) |
| 639 | (if (or forcenargs nargs) |
| 640 | (setq oper (list "z" (or forcenargs nargs) func) |
| 641 | done t) |
| 642 | (if (fboundp func) |
| 643 | (let* ((defn (symbol-function func))) |
| 644 | (and (symbolp defn) |
| 645 | (setq defn (symbol-function defn))) |
| 646 | (if (eq (car-safe defn) 'lambda) |
| 647 | (let ((args (nth 1 defn)) |
| 648 | (nargs 0)) |
| 649 | (while (not (memq (car args) '(&optional |
| 650 | &rest nil))) |
| 651 | (setq nargs (1+ nargs) |
| 652 | args (cdr args))) |
| 653 | (setq oper (list "z" nargs func) |
| 654 | done t)) |
| 655 | (error |
| 656 | "Function is not suitable for this operation"))) |
| 657 | (message "Number of arguments: ") |
| 658 | (let ((nargs (read-char))) |
| 659 | (if (and (>= nargs ?0) (<= nargs ?9)) |
| 660 | (setq oper (list "z" (- nargs ?0) func) |
| 661 | done t) |
| 662 | (beep)))))) |
| 663 | (if (or (and (eq prefix ?v) (memq key '(?A ?I ?M ?O ?R ?U))) |
| 664 | (and (eq prefix ?a) (eq key ?M))) |
| 665 | (let* ((dir (cond ((and (equal calc-mapping-dir "") |
| 666 | (string-match "map$" msg)) |
| 667 | (setq calc-mapping-dir "r") |
| 668 | " rows") |
| 669 | ((equal calc-mapping-dir "r") " rows") |
| 670 | ((equal calc-mapping-dir "c") " columns") |
| 671 | ((equal calc-mapping-dir "a") " across") |
| 672 | ((equal calc-mapping-dir "d") " down") |
| 673 | (t ""))) |
| 674 | (calc-mapping-dir (and (memq (nth 2 oper) |
| 675 | '(calcFunc-map |
| 676 | calcFunc-reduce |
| 677 | calcFunc-rreduce)) |
| 678 | "")) |
| 679 | (oper2 (calc-get-operator |
| 680 | (format "%s%s, %s%s" msg dir |
| 681 | (substring (symbol-name (nth 2 oper)) |
| 682 | 9) |
| 683 | (if (eq key ?I) " (mult)" "")) |
| 684 | (cdr (assq (nth 2 oper) |
| 685 | '((calcFunc-reduce . 2) |
| 686 | (calcFunc-rreduce . 2) |
| 687 | (calcFunc-accum . 2) |
| 688 | (calcFunc-raccum . 2) |
| 689 | (calcFunc-nest . 2) |
| 690 | (calcFunc-anest . 2) |
| 691 | (calcFunc-fixp . 2) |
| 692 | (calcFunc-afixp . 2)))))) |
| 693 | (oper3 (if (eq (nth 2 oper) 'calcFunc-inner) |
| 694 | (calc-get-operator |
| 695 | (format "%s%s, inner (add)" msg dir)) |
| 696 | '(0 0 0))) |
| 697 | (args nil) |
| 698 | (nargs (if (> (nth 1 oper) 0) |
| 699 | (nth 1 oper) |
| 700 | (car oper2))) |
| 701 | (n nargs) |
| 702 | (p calc-arg-values)) |
| 703 | (while (and p (> n 0)) |
| 704 | (or (math-expr-contains (nth 1 oper2) (car p)) |
| 705 | (math-expr-contains (nth 1 oper3) (car p)) |
| 706 | (setq args (nconc args (list (car p))) |
| 707 | n (1- n))) |
| 708 | (setq p (cdr p))) |
| 709 | (setq oper (list "" nargs |
| 710 | (append |
| 711 | '(calcFunc-lambda) |
| 712 | args |
| 713 | (list (math-build-call |
| 714 | (intern |
| 715 | (concat |
| 716 | (symbol-name (nth 2 oper)) |
| 717 | calc-mapping-dir)) |
| 718 | (cons (math-calcFunc-to-var |
| 719 | (nth 1 oper2)) |
| 720 | (if (eq key ?I) |
| 721 | (cons |
| 722 | (math-calcFunc-to-var |
| 723 | (nth 1 oper3)) |
| 724 | args) |
| 725 | args)))))) |
| 726 | done t)) |
| 727 | (setq done t)))) |
| 728 | (t (beep)))) |
| 729 | (and nargs (>= nargs 0) |
| 730 | (/= nargs (nth 1 oper)) |
| 731 | (error "Must be a %d-argument operator" nargs)) |
| 732 | (append (if forcenargs |
| 733 | (cons forcenargs (cdr (cdr oper))) |
| 734 | (cdr oper)) |
| 735 | (list |
| 736 | (let ((name (concat (if inv "I" "") (if hyp "H" "") |
| 737 | (if prefix (char-to-string prefix) "") |
| 738 | (char-to-string key)))) |
| 739 | (if (> (length name) 3) |
| 740 | (substring name 0 3) |
| 741 | name)))))) |
| 742 | |
| 743 | |
| 744 | ;;; Convert a variable name (as a formula) into a like-looking function name. |
| 745 | (defun math-var-to-calcFunc (f) |
| 746 | (if (eq (car-safe f) 'var) |
| 747 | (if (fboundp (nth 2 f)) |
| 748 | (nth 2 f) |
| 749 | (intern (concat "calcFunc-" (symbol-name (nth 1 f))))) |
| 750 | (if (memq (car-safe f) '(lambda calcFunc-lambda)) |
| 751 | f |
| 752 | (math-reject-arg f "*Expected a function name")))) |
| 753 | |
| 754 | ;;; Convert a function name into a like-looking variable name formula. |
| 755 | (defun math-calcFunc-to-var (f) |
| 756 | (if (symbolp f) |
| 757 | (let* ((func (or (cdr (assq f '( ( + . calcFunc-add ) |
| 758 | ( - . calcFunc-sub ) |
| 759 | ( * . calcFunc-mul ) |
| 760 | ( / . calcFunc-div ) |
| 761 | ( ^ . calcFunc-pow ) |
| 762 | ( % . calcFunc-mod ) |
| 763 | ( neg . calcFunc-neg ) |
| 764 | ( | . calcFunc-vconcat ) ))) |
| 765 | f)) |
| 766 | (base (if (string-match "\\`calcFunc-\\(.+\\)\\'" |
| 767 | (symbol-name func)) |
| 768 | (math-match-substring (symbol-name func) 1) |
| 769 | (symbol-name func)))) |
| 770 | (list 'var |
| 771 | (intern base) |
| 772 | (intern (concat "var-" base)))) |
| 773 | f)) |
| 774 | |
| 775 | ;;; Expand a function call using "lambda" notation. |
| 776 | (defun math-build-call (f args) |
| 777 | (if (eq (car-safe f) 'calcFunc-lambda) |
| 778 | (if (= (length args) (- (length f) 2)) |
| 779 | (math-multi-subst (nth (1- (length f)) f) (cdr f) args) |
| 780 | (calc-record-why "*Wrong number of arguments" f) |
| 781 | (cons 'calcFunc-call (cons (math-calcFunc-to-var f) args))) |
| 782 | (if (and (eq f 'calcFunc-neg) |
| 783 | (= (length args) 1)) |
| 784 | (list 'neg (car args)) |
| 785 | (let ((func (assq f '( ( calcFunc-add . + ) |
| 786 | ( calcFunc-sub . - ) |
| 787 | ( calcFunc-mul . * ) |
| 788 | ( calcFunc-div . / ) |
| 789 | ( calcFunc-pow . ^ ) |
| 790 | ( calcFunc-mod . % ) |
| 791 | ( calcFunc-vconcat . | ) )))) |
| 792 | (if (and func (= (length args) 2)) |
| 793 | (cons (cdr func) args) |
| 794 | (cons f args)))))) |
| 795 | |
| 796 | ;;; Do substitutions in parallel to avoid crosstalk. |
| 797 | |
| 798 | ;; The variables math-ms-temp and math-ms-args are local to |
| 799 | ;; math-multi-subst, but are used by math-multi-subst-rec, which |
| 800 | ;; is called by math-multi-subst. |
| 801 | (defvar math-ms-temp) |
| 802 | (defvar math-ms-args) |
| 803 | |
| 804 | (defun math-multi-subst (expr olds news) |
| 805 | (let ((math-ms-args nil) |
| 806 | math-ms-temp) |
| 807 | (while (and olds news) |
| 808 | (setq math-ms-args (cons (cons (car olds) (car news)) math-ms-args) |
| 809 | olds (cdr olds) |
| 810 | news (cdr news))) |
| 811 | (math-multi-subst-rec expr))) |
| 812 | |
| 813 | (defun math-multi-subst-rec (expr) |
| 814 | (cond ((setq math-ms-temp (assoc expr math-ms-args)) |
| 815 | (cdr math-ms-temp)) |
| 816 | ((Math-primp expr) expr) |
| 817 | ((and (eq (car expr) 'calcFunc-lambda) (> (length expr) 2)) |
| 818 | (let ((new (list (car expr))) |
| 819 | (math-ms-args math-ms-args)) |
| 820 | (while (cdr (setq expr (cdr expr))) |
| 821 | (setq new (cons (car expr) new)) |
| 822 | (if (assoc (car expr) math-ms-args) |
| 823 | (setq math-ms-args (cons (cons (car expr) (car expr)) |
| 824 | math-ms-args)))) |
| 825 | (nreverse (cons (math-multi-subst-rec (car expr)) new)))) |
| 826 | (t |
| 827 | (cons (car expr) |
| 828 | (mapcar 'math-multi-subst-rec (cdr expr)))))) |
| 829 | |
| 830 | (defun calcFunc-call (f &rest args) |
| 831 | (setq args (math-build-call (math-var-to-calcFunc f) args)) |
| 832 | (if (eq (car-safe args) 'calcFunc-call) |
| 833 | args |
| 834 | (math-normalize args))) |
| 835 | |
| 836 | (defun calcFunc-apply (f args) |
| 837 | (or (Math-vectorp args) |
| 838 | (math-reject-arg args 'vectorp)) |
| 839 | (apply 'calcFunc-call (cons f (cdr args)))) |
| 840 | |
| 841 | |
| 842 | |
| 843 | |
| 844 | ;;; Map a function over a vector symbolically. [Public] |
| 845 | (defun math-symb-map (f mode args) |
| 846 | (let* ((func (math-var-to-calcFunc f)) |
| 847 | (nargs (length args)) |
| 848 | (ptrs (vconcat args)) |
| 849 | (vflags (make-vector nargs nil)) |
| 850 | (heads '(vec)) |
| 851 | (head nil) |
| 852 | (vec nil) |
| 853 | (i -1) |
| 854 | (math-working-step 0) |
| 855 | (math-working-step-2 nil) |
| 856 | len cols obj expr) |
| 857 | (if (eq mode 'eqn) |
| 858 | (setq mode 'elems |
| 859 | heads '(calcFunc-eq calcFunc-neq calcFunc-lt calcFunc-gt |
| 860 | calcFunc-leq calcFunc-geq)) |
| 861 | (while (and (< (setq i (1+ i)) nargs) |
| 862 | (not (math-matrixp (aref ptrs i))))) |
| 863 | (if (< i nargs) |
| 864 | (if (eq mode 'elems) |
| 865 | (setq func (list 'lambda '(&rest x) |
| 866 | (list 'math-symb-map |
| 867 | (list 'quote f) '(quote elems) 'x)) |
| 868 | mode 'rows) |
| 869 | (if (eq mode 'cols) |
| 870 | (while (< i nargs) |
| 871 | (if (math-matrixp (aref ptrs i)) |
| 872 | (aset ptrs i (math-transpose (aref ptrs i)))) |
| 873 | (setq i (1+ i))))) |
| 874 | (setq mode 'elems)) |
| 875 | (setq i -1)) |
| 876 | (while (< (setq i (1+ i)) nargs) |
| 877 | (setq obj (aref ptrs i)) |
| 878 | (if (and (memq (car-safe obj) heads) |
| 879 | (or (eq mode 'elems) |
| 880 | (math-matrixp obj))) |
| 881 | (progn |
| 882 | (aset vflags i t) |
| 883 | (if head |
| 884 | (if (cdr heads) |
| 885 | (setq head (nth |
| 886 | (aref (aref [ [0 1 2 3 4 5] |
| 887 | [1 1 2 3 2 3] |
| 888 | [2 2 2 1 2 1] |
| 889 | [3 3 1 3 1 3] |
| 890 | [4 2 2 1 4 1] |
| 891 | [5 3 1 3 1 5] ] |
| 892 | (- 6 (length (memq head heads)))) |
| 893 | (- 6 (length (memq (car obj) heads)))) |
| 894 | heads))) |
| 895 | (setq head (car obj))) |
| 896 | (if len |
| 897 | (or (= (length obj) len) |
| 898 | (math-dimension-error)) |
| 899 | (setq len (length obj)))))) |
| 900 | (or len |
| 901 | (if (= nargs 1) |
| 902 | (math-reject-arg (aref ptrs 0) 'vectorp) |
| 903 | (math-reject-arg nil "At least one argument must be a vector"))) |
| 904 | (setq math-working-step-2 (1- len)) |
| 905 | (while (> (setq len (1- len)) 0) |
| 906 | (setq expr nil |
| 907 | i -1) |
| 908 | (while (< (setq i (1+ i)) nargs) |
| 909 | (if (aref vflags i) |
| 910 | (progn |
| 911 | (aset ptrs i (cdr (aref ptrs i))) |
| 912 | (setq expr (nconc expr (list (car (aref ptrs i)))))) |
| 913 | (setq expr (nconc expr (list (aref ptrs i)))))) |
| 914 | (setq math-working-step (1+ math-working-step) |
| 915 | vec (cons (math-normalize (math-build-call func expr)) vec))) |
| 916 | (setq vec (cons head (nreverse vec))) |
| 917 | (if (and (eq mode 'cols) (math-matrixp vec)) |
| 918 | (math-transpose vec) |
| 919 | vec))) |
| 920 | |
| 921 | (defun calcFunc-map (func &rest args) |
| 922 | (math-symb-map func 'elems args)) |
| 923 | |
| 924 | (defun calcFunc-mapr (func &rest args) |
| 925 | (math-symb-map func 'rows args)) |
| 926 | |
| 927 | (defun calcFunc-mapc (func &rest args) |
| 928 | (math-symb-map func 'cols args)) |
| 929 | |
| 930 | (defun calcFunc-mapa (func arg) |
| 931 | (if (math-matrixp arg) |
| 932 | (math-symb-map func 'elems (cdr (math-transpose arg))) |
| 933 | (math-symb-map func 'elems arg))) |
| 934 | |
| 935 | (defun calcFunc-mapd (func arg) |
| 936 | (if (math-matrixp arg) |
| 937 | (math-symb-map func 'elems (cdr arg)) |
| 938 | (math-symb-map func 'elems arg))) |
| 939 | |
| 940 | (defun calcFunc-mapeq (func &rest args) |
| 941 | (if (and (or (equal func '(var mul var-mul)) |
| 942 | (equal func '(var div var-div))) |
| 943 | (= (length args) 2)) |
| 944 | (if (math-negp (car args)) |
| 945 | (let ((func (nth 1 (assq (car-safe (nth 1 args)) |
| 946 | calc-tweak-eqn-table)))) |
| 947 | (and func (setq args (list (car args) |
| 948 | (cons func (cdr (nth 1 args))))))) |
| 949 | (if (math-negp (nth 1 args)) |
| 950 | (let ((func (nth 1 (assq (car-safe (car args)) |
| 951 | calc-tweak-eqn-table)))) |
| 952 | (and func (setq args (list (cons func (cdr (car args))) |
| 953 | (nth 1 args)))))))) |
| 954 | (if (or (and (equal func '(var div var-div)) |
| 955 | (assq (car-safe (nth 1 args)) calc-tweak-eqn-table)) |
| 956 | (equal func '(var neg var-neg)) |
| 957 | (equal func '(var inv var-inv))) |
| 958 | (apply 'calcFunc-mapeqr func args) |
| 959 | (apply 'calcFunc-mapeqp func args))) |
| 960 | |
| 961 | (defun calcFunc-mapeqr (func &rest args) |
| 962 | (setq args (mapcar (function (lambda (x) |
| 963 | (let ((func (assq (car-safe x) |
| 964 | calc-tweak-eqn-table))) |
| 965 | (if func |
| 966 | (cons (nth 1 func) (cdr x)) |
| 967 | x)))) |
| 968 | args)) |
| 969 | (apply 'calcFunc-mapeqp func args)) |
| 970 | |
| 971 | (defun calcFunc-mapeqp (func &rest args) |
| 972 | (if (or (and (memq (car-safe (car args)) '(calcFunc-lt calcFunc-leq)) |
| 973 | (memq (car-safe (nth 1 args)) '(calcFunc-gt calcFunc-geq))) |
| 974 | (and (memq (car-safe (car args)) '(calcFunc-gt calcFunc-geq)) |
| 975 | (memq (car-safe (nth 1 args)) '(calcFunc-lt calcFunc-leq)))) |
| 976 | (setq args (cons (car args) |
| 977 | (cons (list (nth 1 (assq (car (nth 1 args)) |
| 978 | calc-tweak-eqn-table)) |
| 979 | (nth 2 (nth 1 args)) |
| 980 | (nth 1 (nth 1 args))) |
| 981 | (cdr (cdr args)))))) |
| 982 | (math-symb-map func 'eqn args)) |
| 983 | |
| 984 | |
| 985 | |
| 986 | ;;; Reduce a function over a vector symbolically. [Public] |
| 987 | (defun calcFunc-reduce (func vec) |
| 988 | (if (math-matrixp vec) |
| 989 | (let (expr row) |
| 990 | (setq func (math-var-to-calcFunc func)) |
| 991 | (while (setq vec (cdr vec)) |
| 992 | (setq row (car vec)) |
| 993 | (while (setq row (cdr row)) |
| 994 | (setq expr (if expr |
| 995 | (if (Math-numberp expr) |
| 996 | (math-normalize |
| 997 | (math-build-call func (list expr (car row)))) |
| 998 | (math-build-call func (list expr (car row)))) |
| 999 | (car row))))) |
| 1000 | (math-normalize expr)) |
| 1001 | (calcFunc-reducer func vec))) |
| 1002 | |
| 1003 | (defun calcFunc-rreduce (func vec) |
| 1004 | (if (math-matrixp vec) |
| 1005 | (let (expr row) |
| 1006 | (setq func (math-var-to-calcFunc func) |
| 1007 | vec (reverse (cdr vec))) |
| 1008 | (while vec |
| 1009 | (setq row (reverse (cdr (car vec)))) |
| 1010 | (while row |
| 1011 | (setq expr (if expr |
| 1012 | (math-build-call func (list (car row) expr)) |
| 1013 | (car row)) |
| 1014 | row (cdr row))) |
| 1015 | (setq vec (cdr vec))) |
| 1016 | (math-normalize expr)) |
| 1017 | (calcFunc-rreducer func vec))) |
| 1018 | |
| 1019 | (defun calcFunc-reducer (func vec) |
| 1020 | (setq func (math-var-to-calcFunc func)) |
| 1021 | (or (math-vectorp vec) |
| 1022 | (math-reject-arg vec 'vectorp)) |
| 1023 | (let ((expr (car (setq vec (cdr vec))))) |
| 1024 | (if expr |
| 1025 | (progn |
| 1026 | (condition-case err |
| 1027 | (and (symbolp func) |
| 1028 | (let ((lfunc (or (cdr (assq func |
| 1029 | '( (calcFunc-add . math-add) |
| 1030 | (calcFunc-sub . math-sub) |
| 1031 | (calcFunc-mul . math-mul) |
| 1032 | (calcFunc-div . math-div) |
| 1033 | (calcFunc-pow . math-pow) |
| 1034 | (calcFunc-mod . math-mod) |
| 1035 | (calcFunc-vconcat . |
| 1036 | math-concat) ))) |
| 1037 | func))) |
| 1038 | (while (cdr vec) |
| 1039 | (setq expr (funcall lfunc expr (nth 1 vec)) |
| 1040 | vec (cdr vec))))) |
| 1041 | (error nil)) |
| 1042 | (while (setq vec (cdr vec)) |
| 1043 | (setq expr (math-build-call func (list expr (car vec))))) |
| 1044 | (math-normalize expr)) |
| 1045 | (or (math-identity-value func) |
| 1046 | (math-reject-arg vec "*Vector is empty"))))) |
| 1047 | |
| 1048 | (defun math-identity-value (func) |
| 1049 | (cdr (assq func '( (calcFunc-add . 0) (calcFunc-sub . 0) |
| 1050 | (calcFunc-mul . 1) (calcFunc-div . 1) |
| 1051 | (calcFunc-idiv . 1) (calcFunc-fdiv . 1) |
| 1052 | (calcFunc-min . (var inf var-inf)) |
| 1053 | (calcFunc-max . (neg (var inf var-inf))) |
| 1054 | (calcFunc-vconcat . (vec)) |
| 1055 | (calcFunc-append . (vec)) )))) |
| 1056 | |
| 1057 | (defun calcFunc-rreducer (func vec) |
| 1058 | (setq func (math-var-to-calcFunc func)) |
| 1059 | (or (math-vectorp vec) |
| 1060 | (math-reject-arg vec 'vectorp)) |
| 1061 | (if (eq func 'calcFunc-sub) ; do this in a way that looks nicer |
| 1062 | (let ((expr (car (setq vec (cdr vec))))) |
| 1063 | (if expr |
| 1064 | (progn |
| 1065 | (while (setq vec (cdr vec)) |
| 1066 | (setq expr (math-build-call func (list expr (car vec))) |
| 1067 | func (if (eq func 'calcFunc-sub) |
| 1068 | 'calcFunc-add 'calcFunc-sub))) |
| 1069 | (math-normalize expr)) |
| 1070 | 0)) |
| 1071 | (let ((expr (car (setq vec (reverse (cdr vec)))))) |
| 1072 | (if expr |
| 1073 | (progn |
| 1074 | (while (setq vec (cdr vec)) |
| 1075 | (setq expr (math-build-call func (list (car vec) expr)))) |
| 1076 | (math-normalize expr)) |
| 1077 | (or (math-identity-value func) |
| 1078 | (math-reject-arg vec "*Vector is empty")))))) |
| 1079 | |
| 1080 | (defun calcFunc-reducec (func vec) |
| 1081 | (if (math-matrixp vec) |
| 1082 | (calcFunc-reducer func (math-transpose vec)) |
| 1083 | (calcFunc-reducer func vec))) |
| 1084 | |
| 1085 | (defun calcFunc-rreducec (func vec) |
| 1086 | (if (math-matrixp vec) |
| 1087 | (calcFunc-rreducer func (math-transpose vec)) |
| 1088 | (calcFunc-rreducer func vec))) |
| 1089 | |
| 1090 | (defun calcFunc-reducea (func vec) |
| 1091 | (if (math-matrixp vec) |
| 1092 | (cons 'vec |
| 1093 | (mapcar (function (lambda (x) (calcFunc-reducer func x))) |
| 1094 | (cdr vec))) |
| 1095 | (calcFunc-reducer func vec))) |
| 1096 | |
| 1097 | (defun calcFunc-rreducea (func vec) |
| 1098 | (if (math-matrixp vec) |
| 1099 | (cons 'vec |
| 1100 | (mapcar (function (lambda (x) (calcFunc-rreducer func x))) |
| 1101 | (cdr vec))) |
| 1102 | (calcFunc-rreducer func vec))) |
| 1103 | |
| 1104 | (defun calcFunc-reduced (func vec) |
| 1105 | (if (math-matrixp vec) |
| 1106 | (cons 'vec |
| 1107 | (mapcar (function (lambda (x) (calcFunc-reducer func x))) |
| 1108 | (cdr (math-transpose vec)))) |
| 1109 | (calcFunc-reducer func vec))) |
| 1110 | |
| 1111 | (defun calcFunc-rreduced (func vec) |
| 1112 | (if (math-matrixp vec) |
| 1113 | (cons 'vec |
| 1114 | (mapcar (function (lambda (x) (calcFunc-rreducer func x))) |
| 1115 | (cdr (math-transpose vec)))) |
| 1116 | (calcFunc-rreducer func vec))) |
| 1117 | |
| 1118 | (defun calcFunc-accum (func vec) |
| 1119 | (setq func (math-var-to-calcFunc func)) |
| 1120 | (or (math-vectorp vec) |
| 1121 | (math-reject-arg vec 'vectorp)) |
| 1122 | (let* ((expr (car (setq vec (cdr vec)))) |
| 1123 | (res (list 'vec expr))) |
| 1124 | (or expr |
| 1125 | (math-reject-arg vec "*Vector is empty")) |
| 1126 | (while (setq vec (cdr vec)) |
| 1127 | (setq expr (math-build-call func (list expr (car vec))) |
| 1128 | res (nconc res (list expr)))) |
| 1129 | (math-normalize res))) |
| 1130 | |
| 1131 | (defun calcFunc-raccum (func vec) |
| 1132 | (setq func (math-var-to-calcFunc func)) |
| 1133 | (or (math-vectorp vec) |
| 1134 | (math-reject-arg vec 'vectorp)) |
| 1135 | (let* ((expr (car (setq vec (reverse (cdr vec))))) |
| 1136 | (res (list expr))) |
| 1137 | (or expr |
| 1138 | (math-reject-arg vec "*Vector is empty")) |
| 1139 | (while (setq vec (cdr vec)) |
| 1140 | (setq expr (math-build-call func (list (car vec) expr)) |
| 1141 | res (cons (list expr) res))) |
| 1142 | (math-normalize (cons 'vec res)))) |
| 1143 | |
| 1144 | |
| 1145 | (defun math-nest-calls (func base iters accum tol) |
| 1146 | (or (symbolp tol) |
| 1147 | (if (math-realp tol) |
| 1148 | (or (math-numberp base) (math-reject-arg base 'numberp)) |
| 1149 | (math-reject-arg tol 'realp))) |
| 1150 | (setq func (math-var-to-calcFunc func)) |
| 1151 | (or (null iters) |
| 1152 | (if (equal iters '(var inf var-inf)) |
| 1153 | (setq iters nil) |
| 1154 | (progn |
| 1155 | (if (math-messy-integerp iters) |
| 1156 | (setq iters (math-trunc iters))) |
| 1157 | (or (integerp iters) (math-reject-arg iters 'fixnump)) |
| 1158 | (or (not tol) (natnump iters) (math-reject-arg iters 'fixnatnump)) |
| 1159 | (if (< iters 0) |
| 1160 | (let* ((dummy '(var DummyArg var-DummyArg)) |
| 1161 | (dummy2 '(var DummyArg2 var-DummyArg2)) |
| 1162 | (finv (math-solve-for (math-build-call func (list dummy2)) |
| 1163 | dummy dummy2 nil))) |
| 1164 | (or finv (math-reject-arg nil "*Unable to find an inverse")) |
| 1165 | (if (and (= (length finv) 2) |
| 1166 | (equal (nth 1 finv) dummy)) |
| 1167 | (setq func (car finv)) |
| 1168 | (setq func (list 'calcFunc-lambda dummy finv))) |
| 1169 | (setq iters (- iters))))))) |
| 1170 | (math-with-extra-prec 1 |
| 1171 | (let ((value base) |
| 1172 | (ovalue nil) |
| 1173 | (avalues (list base)) |
| 1174 | (math-working-step 0) |
| 1175 | (math-working-step-2 iters)) |
| 1176 | (while (and (or (null iters) |
| 1177 | (>= (setq iters (1- iters)) 0)) |
| 1178 | (or (null tol) |
| 1179 | (null ovalue) |
| 1180 | (if (eq tol t) |
| 1181 | (not (if (and (Math-numberp value) |
| 1182 | (Math-numberp ovalue)) |
| 1183 | (math-nearly-equal value ovalue) |
| 1184 | (Math-equal value ovalue))) |
| 1185 | (if (math-numberp value) |
| 1186 | (Math-lessp tol (math-abs (math-sub value ovalue))) |
| 1187 | (math-reject-arg value 'numberp))))) |
| 1188 | (setq ovalue value |
| 1189 | math-working-step (1+ math-working-step) |
| 1190 | value (math-normalize (math-build-call func (list value)))) |
| 1191 | (if accum |
| 1192 | (setq avalues (cons value avalues)))) |
| 1193 | (if accum |
| 1194 | (cons 'vec (nreverse avalues)) |
| 1195 | value)))) |
| 1196 | |
| 1197 | (defun calcFunc-nest (func base iters) |
| 1198 | (math-nest-calls func base iters nil nil)) |
| 1199 | |
| 1200 | (defun calcFunc-anest (func base iters) |
| 1201 | (math-nest-calls func base iters t nil)) |
| 1202 | |
| 1203 | (defun calcFunc-fixp (func base &optional iters tol) |
| 1204 | (math-nest-calls func base iters nil (or tol t))) |
| 1205 | |
| 1206 | (defun calcFunc-afixp (func base &optional iters tol) |
| 1207 | (math-nest-calls func base iters t (or tol t))) |
| 1208 | |
| 1209 | |
| 1210 | (defun calcFunc-outer (func a b) |
| 1211 | (or (math-vectorp a) (math-reject-arg a 'vectorp)) |
| 1212 | (or (math-vectorp b) (math-reject-arg b 'vectorp)) |
| 1213 | (setq func (math-var-to-calcFunc func)) |
| 1214 | (let ((mat nil)) |
| 1215 | (while (setq a (cdr a)) |
| 1216 | (setq mat (cons (cons 'vec |
| 1217 | (mapcar (function (lambda (x) |
| 1218 | (math-build-call func |
| 1219 | (list (car a) |
| 1220 | x)))) |
| 1221 | (cdr b))) |
| 1222 | mat))) |
| 1223 | (math-normalize (cons 'vec (nreverse mat))))) |
| 1224 | |
| 1225 | |
| 1226 | ;; The variables math-inner-mul-func and math-inner-add-func are |
| 1227 | ;; local to calcFunc-inner, but are used by math-inner-mats, |
| 1228 | ;; which is called by math-inner-mats. |
| 1229 | (defvar math-inner-mul-func) |
| 1230 | (defvar math-inner-add-func) |
| 1231 | |
| 1232 | (defun calcFunc-inner (math-inner-mul-func math-inner-add-func a b) |
| 1233 | (or (math-vectorp a) (math-reject-arg a 'vectorp)) |
| 1234 | (or (math-vectorp b) (math-reject-arg b 'vectorp)) |
| 1235 | (if (math-matrixp a) |
| 1236 | (if (math-matrixp b) |
| 1237 | (if (= (length (nth 1 a)) (length b)) |
| 1238 | (math-inner-mats a b) |
| 1239 | (math-dimension-error)) |
| 1240 | (if (= (length (nth 1 a)) 2) |
| 1241 | (if (= (length a) (length b)) |
| 1242 | (math-inner-mats a (list 'vec b)) |
| 1243 | (math-dimension-error)) |
| 1244 | (if (= (length (nth 1 a)) (length b)) |
| 1245 | (math-mat-col (math-inner-mats a (math-col-matrix b)) |
| 1246 | 1) |
| 1247 | (math-dimension-error)))) |
| 1248 | (if (math-matrixp b) |
| 1249 | (nth 1 (math-inner-mats (list 'vec a) b)) |
| 1250 | (calcFunc-reduce math-inner-add-func (calcFunc-map math-inner-mul-func a b))))) |
| 1251 | |
| 1252 | (defun math-inner-mats (a b) |
| 1253 | (let ((mat nil) |
| 1254 | (cols (length (nth 1 b))) |
| 1255 | row col ap bp accum) |
| 1256 | (while (setq a (cdr a)) |
| 1257 | (setq col cols |
| 1258 | row nil) |
| 1259 | (while (> (setq col (1- col)) 0) |
| 1260 | (setq row (cons (calcFunc-reduce math-inner-add-func |
| 1261 | (calcFunc-map math-inner-mul-func |
| 1262 | (car a) |
| 1263 | (math-mat-col b col))) |
| 1264 | row))) |
| 1265 | (setq mat (cons (cons 'vec row) mat))) |
| 1266 | (cons 'vec (nreverse mat)))) |
| 1267 | |
| 1268 | (provide 'calc-map) |
| 1269 | |
| 1270 | ;;; calc-map.el ends here |