| 1 | ;;; calc-vec.el --- vector functions for Calc |
| 2 | |
| 3 | ;; Copyright (C) 1990, 1991, 1992, 1993, 2001, 2002, 2003, 2004, |
| 4 | ;; 2005, 2006, 2007, 2008, 2009, 2010 Free Software Foundation, Inc. |
| 5 | |
| 6 | ;; Author: David Gillespie <daveg@synaptics.com> |
| 7 | ;; Maintainer: Jay Belanger <jay.p.belanger@gmail.com> |
| 8 | |
| 9 | ;; This file is part of GNU Emacs. |
| 10 | |
| 11 | ;; GNU Emacs is free software: you can redistribute it and/or modify |
| 12 | ;; it under the terms of the GNU General Public License as published by |
| 13 | ;; the Free Software Foundation, either version 3 of the License, or |
| 14 | ;; (at your option) any later version. |
| 15 | |
| 16 | ;; GNU Emacs is distributed in the hope that it will be useful, |
| 17 | ;; but WITHOUT ANY WARRANTY; without even the implied warranty of |
| 18 | ;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
| 19 | ;; GNU General Public License for more details. |
| 20 | |
| 21 | ;; You should have received a copy of the GNU General Public License |
| 22 | ;; along with GNU Emacs. If not, see <http://www.gnu.org/licenses/>. |
| 23 | |
| 24 | ;;; Commentary: |
| 25 | |
| 26 | ;;; Code: |
| 27 | |
| 28 | ;; This file is autoloaded from calc-ext.el. |
| 29 | |
| 30 | (require 'calc-ext) |
| 31 | (require 'calc-macs) |
| 32 | |
| 33 | ;; Declare functions which are defined elsewhere. |
| 34 | (declare-function math-read-expr-level "calc-aent" (exp-prec &optional exp-term)) |
| 35 | |
| 36 | |
| 37 | (defun calc-display-strings (n) |
| 38 | (interactive "P") |
| 39 | (calc-wrapper |
| 40 | (message (if (calc-change-mode 'calc-display-strings n t t) |
| 41 | "Displaying vectors of integers as quoted strings" |
| 42 | "Displaying vectors of integers normally")))) |
| 43 | |
| 44 | |
| 45 | (defun calc-pack (n) |
| 46 | (interactive "P") |
| 47 | (calc-wrapper |
| 48 | (let* ((nn (if n 1 2)) |
| 49 | (mode (if n (prefix-numeric-value n) (calc-top-n 1))) |
| 50 | (mode (if (and (Math-vectorp mode) (cdr mode)) (cdr mode) |
| 51 | (if (integerp mode) mode |
| 52 | (error "Packing mode must be an integer or vector of integers")))) |
| 53 | (num (calc-pack-size mode)) |
| 54 | (items (calc-top-list num nn))) |
| 55 | (calc-enter-result (+ nn num -1) "pack" (calc-pack-items mode items))))) |
| 56 | |
| 57 | (defun calc-pack-size (mode) |
| 58 | (cond ((consp mode) |
| 59 | (let ((size 1)) |
| 60 | (while mode |
| 61 | (or (integerp (car mode)) (error "Vector of integers expected")) |
| 62 | (setq size (* size (calc-pack-size (car mode))) |
| 63 | mode (cdr mode))) |
| 64 | (if (= size 0) |
| 65 | (error "Zero dimensions not allowed") |
| 66 | size))) |
| 67 | ((>= mode 0) mode) |
| 68 | (t (or (cdr (assq mode '((-3 . 3) (-13 . 1) (-14 . 3) (-15 . 6)))) |
| 69 | 2)))) |
| 70 | |
| 71 | (defun calc-pack-items (mode items) |
| 72 | (cond ((consp mode) |
| 73 | (if (cdr mode) |
| 74 | (let* ((size (calc-pack-size (cdr mode))) |
| 75 | (len (length items)) |
| 76 | (new nil) |
| 77 | p row) |
| 78 | (while (> len 0) |
| 79 | (setq p (nthcdr (1- size) items) |
| 80 | row items |
| 81 | items (cdr p) |
| 82 | len (- len size)) |
| 83 | (setcdr p nil) |
| 84 | (setq new (cons (calc-pack-items (cdr mode) row) new))) |
| 85 | (calc-pack-items (car mode) (nreverse new))) |
| 86 | (calc-pack-items (car mode) items))) |
| 87 | ((>= mode 0) |
| 88 | (cons 'vec items)) |
| 89 | ((= mode -3) |
| 90 | (if (and (math-objvecp (car items)) |
| 91 | (math-objvecp (nth 1 items)) |
| 92 | (math-objvecp (nth 2 items))) |
| 93 | (if (and (math-num-integerp (car items)) |
| 94 | (math-num-integerp (nth 1 items))) |
| 95 | (if (math-realp (nth 2 items)) |
| 96 | (cons 'hms items) |
| 97 | (error "Seconds must be real")) |
| 98 | (error "Hours and minutes must be integers")) |
| 99 | (math-normalize (list '+ |
| 100 | (list '+ |
| 101 | (if (eq calc-angle-mode 'rad) |
| 102 | (list '* (car items) |
| 103 | '(hms 1 0 0)) |
| 104 | (car items)) |
| 105 | (list '* (nth 1 items) '(hms 0 1 0))) |
| 106 | (list '* (nth 2 items) '(hms 0 0 1)))))) |
| 107 | ((= mode -13) |
| 108 | (if (math-realp (car items)) |
| 109 | (cons 'date items) |
| 110 | (if (eq (car-safe (car items)) 'date) |
| 111 | (car items) |
| 112 | (if (math-objvecp (car items)) |
| 113 | (error "Date value must be real") |
| 114 | (cons 'calcFunc-date items))))) |
| 115 | ((memq mode '(-14 -15)) |
| 116 | (let ((p items)) |
| 117 | (while (and p (math-objvecp (car p))) |
| 118 | (or (math-integerp (car p)) |
| 119 | (error "Components must be integers")) |
| 120 | (setq p (cdr p))) |
| 121 | (if p |
| 122 | (cons 'calcFunc-date items) |
| 123 | (list 'date (math-dt-to-date items))))) |
| 124 | ((or (eq (car-safe (car items)) 'vec) |
| 125 | (eq (car-safe (nth 1 items)) 'vec)) |
| 126 | (let* ((x (car items)) |
| 127 | (vx (eq (car-safe x) 'vec)) |
| 128 | (y (nth 1 items)) |
| 129 | (vy (eq (car-safe y) 'vec)) |
| 130 | (z nil) |
| 131 | (n (1- (length (if vx x y))))) |
| 132 | (and vx vy |
| 133 | (/= n (1- (length y))) |
| 134 | (error "Vectors must be the same length")) |
| 135 | (while (>= (setq n (1- n)) 0) |
| 136 | (setq z (cons (calc-pack-items |
| 137 | mode |
| 138 | (list (if vx (car (setq x (cdr x))) x) |
| 139 | (if vy (car (setq y (cdr y))) y))) |
| 140 | z))) |
| 141 | (cons 'vec (nreverse z)))) |
| 142 | ((= mode -1) |
| 143 | (if (and (math-realp (car items)) (math-realp (nth 1 items))) |
| 144 | (cons 'cplx items) |
| 145 | (if (and (math-objectp (car items)) (math-objectp (nth 1 items))) |
| 146 | (error "Components must be real")) |
| 147 | (math-normalize (list '+ (car items) |
| 148 | (list '* (nth 1 items) '(cplx 0 1)))))) |
| 149 | ((= mode -2) |
| 150 | (if (and (math-realp (car items)) (math-anglep (nth 1 items))) |
| 151 | (cons 'polar items) |
| 152 | (if (and (math-objectp (car items)) (math-objectp (nth 1 items))) |
| 153 | (error "Components must be real")) |
| 154 | (math-normalize (list '* (car items) |
| 155 | (if (math-anglep (nth 1 items)) |
| 156 | (list 'polar 1 (nth 1 items)) |
| 157 | (list 'calcFunc-exp |
| 158 | (list '* |
| 159 | (math-to-radians-2 |
| 160 | (nth 1 items)) |
| 161 | (list 'polar |
| 162 | 1 |
| 163 | (math-quarter-circle |
| 164 | nil))))))))) |
| 165 | ((= mode -4) |
| 166 | (let ((x (car items)) |
| 167 | (sigma (nth 1 items))) |
| 168 | (if (or (math-scalarp x) (not (math-objvecp x))) |
| 169 | (if (or (math-anglep sigma) (not (math-objvecp sigma))) |
| 170 | (math-make-sdev x sigma) |
| 171 | (error "Error component must be real")) |
| 172 | (error "Mean component must be real or complex")))) |
| 173 | ((= mode -5) |
| 174 | (let ((a (car items)) |
| 175 | (m (nth 1 items))) |
| 176 | (if (and (math-anglep a) (math-anglep m)) |
| 177 | (if (math-posp m) |
| 178 | (math-make-mod a m) |
| 179 | (error "Modulus must be positive")) |
| 180 | (if (and (math-objectp a) (math-objectp m)) |
| 181 | (error "Components must be real")) |
| 182 | (list 'calcFunc-makemod a m)))) |
| 183 | ((memq mode '(-6 -7 -8 -9)) |
| 184 | (let ((lo (car items)) |
| 185 | (hi (nth 1 items))) |
| 186 | (if (and (or (math-anglep lo) (eq (car lo) 'date) |
| 187 | (not (math-objvecp lo))) |
| 188 | (or (math-anglep hi) (eq (car hi) 'date) |
| 189 | (not (math-objvecp hi)))) |
| 190 | (math-make-intv (+ mode 9) lo hi) |
| 191 | (error "Components must be real")))) |
| 192 | ((eq mode -10) |
| 193 | (if (math-zerop (nth 1 items)) |
| 194 | (error "Denominator must not be zero") |
| 195 | (if (and (math-integerp (car items)) (math-integerp (nth 1 items))) |
| 196 | (math-normalize (cons 'frac items)) |
| 197 | (if (and (math-objectp (car items)) (math-objectp (nth 1 items))) |
| 198 | (error "Components must be integers")) |
| 199 | (cons 'calcFunc-fdiv items)))) |
| 200 | ((memq mode '(-11 -12)) |
| 201 | (if (and (math-realp (car items)) (math-integerp (nth 1 items))) |
| 202 | (calcFunc-scf (math-float (car items)) (nth 1 items)) |
| 203 | (if (and (math-objectp (car items)) (math-objectp (nth 1 items))) |
| 204 | (error "Components must be integers")) |
| 205 | (math-normalize |
| 206 | (list 'calcFunc-scf |
| 207 | (list 'calcFunc-float (car items)) |
| 208 | (nth 1 items))))) |
| 209 | (t |
| 210 | (error "Invalid packing mode: %d" mode)))) |
| 211 | |
| 212 | (defvar calc-unpack-with-type nil) |
| 213 | (defun calc-unpack (mode) |
| 214 | (interactive "P") |
| 215 | (calc-wrapper |
| 216 | (let ((calc-unpack-with-type t)) |
| 217 | (calc-pop-push-record-list 1 "unpk" (calc-unpack-item |
| 218 | (and mode |
| 219 | (prefix-numeric-value mode)) |
| 220 | (calc-top)))))) |
| 221 | |
| 222 | (defun calc-unpack-type (item) |
| 223 | (cond ((eq (car-safe item) 'vec) |
| 224 | (1- (length item))) |
| 225 | ((eq (car-safe item) 'intv) |
| 226 | (- (nth 1 item) 9)) |
| 227 | (t |
| 228 | (or (cdr (assq (car-safe item) '( (cplx . -1) (polar . -2) |
| 229 | (hms . -3) (sdev . -4) (mod . -5) |
| 230 | (frac . -10) (float . -11) |
| 231 | (date . -13) ))) |
| 232 | (error "Argument must be a composite object"))))) |
| 233 | |
| 234 | (defun calc-unpack-item (mode item) |
| 235 | (cond ((not mode) |
| 236 | (if (or (and (not (memq (car-safe item) '(frac float cplx polar vec |
| 237 | hms date sdev mod |
| 238 | intv))) |
| 239 | (math-objvecp item)) |
| 240 | (eq (car-safe item) 'var)) |
| 241 | (error "Argument must be a composite object or function call")) |
| 242 | (if (eq (car item) 'intv) |
| 243 | (cdr (cdr item)) |
| 244 | (cdr item))) |
| 245 | ((> mode 0) |
| 246 | (let ((dims nil) |
| 247 | type new row) |
| 248 | (setq item (list item)) |
| 249 | (while (> mode 0) |
| 250 | (setq type (calc-unpack-type (car item)) |
| 251 | dims (cons type dims) |
| 252 | new (calc-unpack-item nil (car item))) |
| 253 | (while (setq item (cdr item)) |
| 254 | (or (= (calc-unpack-type (car item)) type) |
| 255 | (error "Inconsistent types or dimensions in vector elements")) |
| 256 | (setq new (append new (calc-unpack-item nil (car item))))) |
| 257 | (setq item new |
| 258 | mode (1- mode))) |
| 259 | (if (cdr dims) (setq dims (list (cons 'vec (nreverse dims))))) |
| 260 | (cond ((eq calc-unpack-with-type 'pair) |
| 261 | (list (car dims) (cons 'vec item))) |
| 262 | (calc-unpack-with-type |
| 263 | (append item dims)) |
| 264 | (t item)))) |
| 265 | ((eq calc-unpack-with-type 'pair) |
| 266 | (let ((calc-unpack-with-type nil)) |
| 267 | (list mode (cons 'vec (calc-unpack-item mode item))))) |
| 268 | ((= mode -3) |
| 269 | (if (eq (car-safe item) 'hms) |
| 270 | (cdr item) |
| 271 | (error "Argument must be an HMS form"))) |
| 272 | ((= mode -13) |
| 273 | (if (eq (car-safe item) 'date) |
| 274 | (cdr item) |
| 275 | (error "Argument must be a date form"))) |
| 276 | ((= mode -14) |
| 277 | (if (eq (car-safe item) 'date) |
| 278 | (math-date-to-dt (math-floor (nth 1 item))) |
| 279 | (error "Argument must be a date form"))) |
| 280 | ((= mode -15) |
| 281 | (if (eq (car-safe item) 'date) |
| 282 | (append (math-date-to-dt (nth 1 item)) |
| 283 | (and (not (math-integerp (nth 1 item))) |
| 284 | (list 0 0 0))) |
| 285 | (error "Argument must be a date form"))) |
| 286 | ((eq (car-safe item) 'vec) |
| 287 | (let ((x nil) |
| 288 | (y nil) |
| 289 | res) |
| 290 | (while (setq item (cdr item)) |
| 291 | (setq res (calc-unpack-item mode (car item)) |
| 292 | x (cons (car res) x) |
| 293 | y (cons (nth 1 res) y))) |
| 294 | (list (cons 'vec (nreverse x)) |
| 295 | (cons 'vec (nreverse y))))) |
| 296 | ((= mode -1) |
| 297 | (if (eq (car-safe item) 'cplx) |
| 298 | (cdr item) |
| 299 | (if (eq (car-safe item) 'polar) |
| 300 | (cdr (math-complex item)) |
| 301 | (if (Math-realp item) |
| 302 | (list item 0) |
| 303 | (error "Argument must be a complex number"))))) |
| 304 | ((= mode -2) |
| 305 | (if (or (memq (car-safe item) '(cplx polar)) |
| 306 | (Math-realp item)) |
| 307 | (cdr (math-polar item)) |
| 308 | (error "Argument must be a complex number"))) |
| 309 | ((= mode -4) |
| 310 | (if (eq (car-safe item) 'sdev) |
| 311 | (cdr item) |
| 312 | (list item 0))) |
| 313 | ((= mode -5) |
| 314 | (if (eq (car-safe item) 'mod) |
| 315 | (cdr item) |
| 316 | (error "Argument must be a modulo form"))) |
| 317 | ((memq mode '(-6 -7 -8 -9)) |
| 318 | (if (eq (car-safe item) 'intv) |
| 319 | (cdr (cdr item)) |
| 320 | (list item item))) |
| 321 | ((= mode -10) |
| 322 | (if (eq (car-safe item) 'frac) |
| 323 | (cdr item) |
| 324 | (if (Math-integerp item) |
| 325 | (list item 1) |
| 326 | (error "Argument must be a rational number")))) |
| 327 | ((= mode -11) |
| 328 | (if (eq (car-safe item) 'float) |
| 329 | (list (nth 1 item) (math-normalize (nth 2 item))) |
| 330 | (error "Expected a floating-point number"))) |
| 331 | ((= mode -12) |
| 332 | (if (eq (car-safe item) 'float) |
| 333 | (list (calcFunc-mant item) (calcFunc-xpon item)) |
| 334 | (error "Expected a floating-point number"))) |
| 335 | (t |
| 336 | (error "Invalid unpacking mode: %d" mode)))) |
| 337 | |
| 338 | (defun calc-diag (n) |
| 339 | (interactive "P") |
| 340 | (calc-wrapper |
| 341 | (calc-enter-result 1 "diag" (if n |
| 342 | (list 'calcFunc-diag (calc-top-n 1) |
| 343 | (prefix-numeric-value n)) |
| 344 | (list 'calcFunc-diag (calc-top-n 1)))))) |
| 345 | |
| 346 | (defun calc-ident (n) |
| 347 | (interactive "NDimension of identity matrix = ") |
| 348 | (calc-wrapper |
| 349 | (calc-enter-result 0 "idn" (if (eq n 0) |
| 350 | '(calcFunc-idn 1) |
| 351 | (list 'calcFunc-idn 1 |
| 352 | (prefix-numeric-value n)))))) |
| 353 | |
| 354 | (defun calc-index (n &optional stack) |
| 355 | (interactive "NSize of vector = \nP") |
| 356 | (calc-wrapper |
| 357 | (if (consp stack) |
| 358 | (calc-enter-result 3 "indx" (cons 'calcFunc-index (calc-top-list-n 3))) |
| 359 | (calc-enter-result 0 "indx" (list 'calcFunc-index |
| 360 | (prefix-numeric-value n)))))) |
| 361 | |
| 362 | (defun calc-build-vector (n) |
| 363 | (interactive "NSize of vector = ") |
| 364 | (calc-wrapper |
| 365 | (calc-enter-result 1 "bldv" (list 'calcFunc-cvec |
| 366 | (calc-top-n 1) |
| 367 | (prefix-numeric-value n))))) |
| 368 | |
| 369 | (defun calc-cons (arg) |
| 370 | (interactive "P") |
| 371 | (calc-wrapper |
| 372 | (if (calc-is-hyperbolic) |
| 373 | (calc-binary-op "rcns" 'calcFunc-rcons arg) |
| 374 | (calc-binary-op "cons" 'calcFunc-cons arg)))) |
| 375 | |
| 376 | |
| 377 | (defun calc-head (arg) |
| 378 | (interactive "P") |
| 379 | (calc-wrapper |
| 380 | (if (calc-is-inverse) |
| 381 | (if (calc-is-hyperbolic) |
| 382 | (calc-unary-op "rtai" 'calcFunc-rtail arg) |
| 383 | (calc-unary-op "tail" 'calcFunc-tail arg)) |
| 384 | (if (calc-is-hyperbolic) |
| 385 | (calc-unary-op "rhed" 'calcFunc-rhead arg) |
| 386 | (calc-unary-op "head" 'calcFunc-head arg))))) |
| 387 | |
| 388 | (defun calc-tail (arg) |
| 389 | (interactive "P") |
| 390 | (calc-invert-func) |
| 391 | (calc-head arg)) |
| 392 | |
| 393 | (defun calc-vlength (arg) |
| 394 | (interactive "P") |
| 395 | (calc-wrapper |
| 396 | (if (calc-is-hyperbolic) |
| 397 | (calc-unary-op "dims" 'calcFunc-mdims arg) |
| 398 | (calc-unary-op "len" 'calcFunc-vlen arg)))) |
| 399 | |
| 400 | (defun calc-arrange-vector (n) |
| 401 | (interactive "NNumber of columns = ") |
| 402 | (calc-wrapper |
| 403 | (calc-enter-result 1 "arng" (list 'calcFunc-arrange (calc-top-n 1) |
| 404 | (prefix-numeric-value n))))) |
| 405 | |
| 406 | (defun calc-vector-find (arg) |
| 407 | (interactive "P") |
| 408 | (calc-wrapper |
| 409 | (let ((func (cons 'calcFunc-find (calc-top-list-n 2)))) |
| 410 | (calc-enter-result |
| 411 | 2 "find" |
| 412 | (if arg (append func (list (prefix-numeric-value arg))) func))))) |
| 413 | |
| 414 | (defun calc-subvector () |
| 415 | (interactive) |
| 416 | (calc-wrapper |
| 417 | (if (calc-is-inverse) |
| 418 | (calc-enter-result 3 "rsvc" (cons 'calcFunc-rsubvec |
| 419 | (calc-top-list-n 3))) |
| 420 | (calc-enter-result 3 "svec" (cons 'calcFunc-subvec (calc-top-list-n 3)))))) |
| 421 | |
| 422 | (defun calc-reverse-vector (arg) |
| 423 | (interactive "P") |
| 424 | (calc-wrapper |
| 425 | (calc-unary-op "rev" 'calcFunc-rev arg))) |
| 426 | |
| 427 | (defun calc-mask-vector (arg) |
| 428 | (interactive "P") |
| 429 | (calc-wrapper |
| 430 | (calc-binary-op "vmsk" 'calcFunc-vmask arg))) |
| 431 | |
| 432 | (defun calc-expand-vector (arg) |
| 433 | (interactive "P") |
| 434 | (calc-wrapper |
| 435 | (if (calc-is-hyperbolic) |
| 436 | (calc-enter-result 3 "vexp" (cons 'calcFunc-vexp (calc-top-list-n 3))) |
| 437 | (calc-binary-op "vexp" 'calcFunc-vexp arg)))) |
| 438 | |
| 439 | (defun calc-sort () |
| 440 | (interactive) |
| 441 | (calc-slow-wrapper |
| 442 | (if (calc-is-inverse) |
| 443 | (calc-enter-result 1 "rsrt" (list 'calcFunc-rsort (calc-top-n 1))) |
| 444 | (calc-enter-result 1 "sort" (list 'calcFunc-sort (calc-top-n 1)))))) |
| 445 | |
| 446 | (defun calc-grade () |
| 447 | (interactive) |
| 448 | (calc-slow-wrapper |
| 449 | (if (calc-is-inverse) |
| 450 | (calc-enter-result 1 "rgrd" (list 'calcFunc-rgrade (calc-top-n 1))) |
| 451 | (calc-enter-result 1 "grad" (list 'calcFunc-grade (calc-top-n 1)))))) |
| 452 | |
| 453 | (defun calc-histogram (n) |
| 454 | (interactive "P") |
| 455 | (unless (natnump n) |
| 456 | (setq n (math-read-expr (read-string "Centers of bins: ")))) |
| 457 | (calc-slow-wrapper |
| 458 | (if calc-hyperbolic-flag |
| 459 | (calc-enter-result 2 "hist" (list 'calcFunc-histogram |
| 460 | (calc-top-n 2) |
| 461 | (calc-top-n 1) |
| 462 | n)) |
| 463 | (calc-enter-result 1 "hist" (list 'calcFunc-histogram |
| 464 | (calc-top-n 1) |
| 465 | n))))) |
| 466 | |
| 467 | (defun calc-transpose (arg) |
| 468 | (interactive "P") |
| 469 | (calc-wrapper |
| 470 | (calc-unary-op "trn" 'calcFunc-trn arg))) |
| 471 | |
| 472 | (defun calc-conj-transpose (arg) |
| 473 | (interactive "P") |
| 474 | (calc-wrapper |
| 475 | (calc-unary-op "ctrn" 'calcFunc-ctrn arg))) |
| 476 | |
| 477 | (defun calc-cross (arg) |
| 478 | (interactive "P") |
| 479 | (calc-wrapper |
| 480 | (calc-binary-op "cros" 'calcFunc-cross arg))) |
| 481 | |
| 482 | (defun calc-kron (arg) |
| 483 | (interactive "P") |
| 484 | (calc-wrapper |
| 485 | (calc-binary-op "kron" 'calcFunc-kron arg))) |
| 486 | |
| 487 | (defun calc-remove-duplicates (arg) |
| 488 | (interactive "P") |
| 489 | (calc-wrapper |
| 490 | (calc-unary-op "rdup" 'calcFunc-rdup arg))) |
| 491 | |
| 492 | (defun calc-set-union (arg) |
| 493 | (interactive "P") |
| 494 | (calc-wrapper |
| 495 | (calc-binary-op "unio" 'calcFunc-vunion arg '(vec) 'calcFunc-rdup))) |
| 496 | |
| 497 | (defun calc-set-intersect (arg) |
| 498 | (interactive "P") |
| 499 | (calc-wrapper |
| 500 | (calc-binary-op "intr" 'calcFunc-vint arg '(vec) 'calcFunc-rdup))) |
| 501 | |
| 502 | (defun calc-set-difference (arg) |
| 503 | (interactive "P") |
| 504 | (calc-wrapper |
| 505 | (calc-binary-op "diff" 'calcFunc-vdiff arg '(vec) 'calcFunc-rdup))) |
| 506 | |
| 507 | (defun calc-set-xor (arg) |
| 508 | (interactive "P") |
| 509 | (calc-wrapper |
| 510 | (calc-binary-op "xor" 'calcFunc-vxor arg '(vec) 'calcFunc-rdup))) |
| 511 | |
| 512 | (defun calc-set-complement (arg) |
| 513 | (interactive "P") |
| 514 | (calc-wrapper |
| 515 | (calc-unary-op "cmpl" 'calcFunc-vcompl arg))) |
| 516 | |
| 517 | (defun calc-set-floor (arg) |
| 518 | (interactive "P") |
| 519 | (calc-wrapper |
| 520 | (calc-unary-op "vflr" 'calcFunc-vfloor arg))) |
| 521 | |
| 522 | (defun calc-set-enumerate (arg) |
| 523 | (interactive "P") |
| 524 | (calc-wrapper |
| 525 | (calc-unary-op "enum" 'calcFunc-venum arg))) |
| 526 | |
| 527 | (defun calc-set-span (arg) |
| 528 | (interactive "P") |
| 529 | (calc-wrapper |
| 530 | (calc-unary-op "span" 'calcFunc-vspan arg))) |
| 531 | |
| 532 | (defun calc-set-cardinality (arg) |
| 533 | (interactive "P") |
| 534 | (calc-wrapper |
| 535 | (calc-unary-op "card" 'calcFunc-vcard arg))) |
| 536 | |
| 537 | (defun calc-unpack-bits (arg) |
| 538 | (interactive "P") |
| 539 | (calc-wrapper |
| 540 | (if (calc-is-inverse) |
| 541 | (calc-unary-op "bpck" 'calcFunc-vpack arg) |
| 542 | (calc-unary-op "bupk" 'calcFunc-vunpack arg)))) |
| 543 | |
| 544 | (defun calc-pack-bits (arg) |
| 545 | (interactive "P") |
| 546 | (calc-invert-func) |
| 547 | (calc-unpack-bits arg)) |
| 548 | |
| 549 | |
| 550 | (defun calc-rnorm (arg) |
| 551 | (interactive "P") |
| 552 | (calc-wrapper |
| 553 | (calc-unary-op "rnrm" 'calcFunc-rnorm arg))) |
| 554 | |
| 555 | (defun calc-cnorm (arg) |
| 556 | (interactive "P") |
| 557 | (calc-wrapper |
| 558 | (calc-unary-op "cnrm" 'calcFunc-cnorm arg))) |
| 559 | |
| 560 | (defun calc-mrow (n &optional nn) |
| 561 | (interactive "NRow number: \nP") |
| 562 | (calc-wrapper |
| 563 | (if (consp nn) |
| 564 | (calc-enter-result 2 "mrow" (cons 'calcFunc-mrow (calc-top-list-n 2))) |
| 565 | (setq n (prefix-numeric-value n)) |
| 566 | (if (= n 0) |
| 567 | (calc-enter-result 1 "getd" (list 'calcFunc-getdiag (calc-top-n 1))) |
| 568 | (if (< n 0) |
| 569 | (calc-enter-result 1 "rrow" (list 'calcFunc-mrrow |
| 570 | (calc-top-n 1) (- n))) |
| 571 | (calc-enter-result 1 "mrow" (list 'calcFunc-mrow |
| 572 | (calc-top-n 1) n))))))) |
| 573 | |
| 574 | (defun calc-mcol (n &optional nn) |
| 575 | (interactive "NColumn number: \nP") |
| 576 | (calc-wrapper |
| 577 | (if (consp nn) |
| 578 | (calc-enter-result 2 "mcol" (cons 'calcFunc-mcol (calc-top-list-n 2))) |
| 579 | (setq n (prefix-numeric-value n)) |
| 580 | (if (= n 0) |
| 581 | (calc-enter-result 1 "getd" (list 'calcFunc-getdiag (calc-top-n 1))) |
| 582 | (if (< n 0) |
| 583 | (calc-enter-result 1 "rcol" (list 'calcFunc-mrcol |
| 584 | (calc-top-n 1) (- n))) |
| 585 | (calc-enter-result 1 "mcol" (list 'calcFunc-mcol |
| 586 | (calc-top-n 1) n))))))) |
| 587 | |
| 588 | |
| 589 | ;;;; Vectors. |
| 590 | |
| 591 | (defun calcFunc-mdims (m) |
| 592 | (or (math-vectorp m) |
| 593 | (math-reject-arg m 'vectorp)) |
| 594 | (cons 'vec (math-mat-dimens m))) |
| 595 | |
| 596 | |
| 597 | ;;; Apply a function elementwise to vector A. [V X V; N X N] [Public] |
| 598 | (defun math-map-vec (f a) |
| 599 | (if (math-vectorp a) |
| 600 | (cons 'vec (mapcar f (cdr a))) |
| 601 | (funcall f a))) |
| 602 | |
| 603 | (defun math-dimension-error () |
| 604 | (calc-record-why "*Dimension error") |
| 605 | (signal 'wrong-type-argument nil)) |
| 606 | |
| 607 | |
| 608 | ;;; Build a vector out of a list of objects. [Public] |
| 609 | (defun calcFunc-vec (&rest objs) |
| 610 | (cons 'vec objs)) |
| 611 | |
| 612 | |
| 613 | ;;; Build a constant vector or matrix. [Public] |
| 614 | (defun calcFunc-cvec (obj &rest dims) |
| 615 | (math-make-vec-dimen obj dims)) |
| 616 | |
| 617 | (defun math-make-vec-dimen (obj dims) |
| 618 | (if dims |
| 619 | (if (natnump (car dims)) |
| 620 | (if (or (cdr dims) |
| 621 | (not (math-numberp obj))) |
| 622 | (cons 'vec (copy-sequence |
| 623 | (make-list (car dims) |
| 624 | (math-make-vec-dimen obj (cdr dims))))) |
| 625 | (cons 'vec (make-list (car dims) obj))) |
| 626 | (math-reject-arg (car dims) 'fixnatnump)) |
| 627 | obj)) |
| 628 | |
| 629 | (defun calcFunc-head (vec) |
| 630 | (if (and (Math-vectorp vec) |
| 631 | (cdr vec)) |
| 632 | (nth 1 vec) |
| 633 | (calc-record-why 'vectorp vec) |
| 634 | (list 'calcFunc-head vec))) |
| 635 | |
| 636 | (defun calcFunc-tail (vec) |
| 637 | (if (and (Math-vectorp vec) |
| 638 | (cdr vec)) |
| 639 | (cons 'vec (cdr (cdr vec))) |
| 640 | (calc-record-why 'vectorp vec) |
| 641 | (list 'calcFunc-tail vec))) |
| 642 | |
| 643 | (defun calcFunc-cons (head tail) |
| 644 | (if (Math-vectorp tail) |
| 645 | (cons 'vec (cons head (cdr tail))) |
| 646 | (calc-record-why 'vectorp tail) |
| 647 | (list 'calcFunc-cons head tail))) |
| 648 | |
| 649 | (defun calcFunc-rhead (vec) |
| 650 | (if (and (Math-vectorp vec) |
| 651 | (cdr vec)) |
| 652 | (let ((vec (copy-sequence vec))) |
| 653 | (setcdr (nthcdr (- (length vec) 2) vec) nil) |
| 654 | vec) |
| 655 | (calc-record-why 'vectorp vec) |
| 656 | (list 'calcFunc-rhead vec))) |
| 657 | |
| 658 | (defun calcFunc-rtail (vec) |
| 659 | (if (and (Math-vectorp vec) |
| 660 | (cdr vec)) |
| 661 | (nth (1- (length vec)) vec) |
| 662 | (calc-record-why 'vectorp vec) |
| 663 | (list 'calcFunc-rtail vec))) |
| 664 | |
| 665 | (defun calcFunc-rcons (head tail) |
| 666 | (if (Math-vectorp head) |
| 667 | (append head (list tail)) |
| 668 | (calc-record-why 'vectorp head) |
| 669 | (list 'calcFunc-rcons head tail))) |
| 670 | |
| 671 | |
| 672 | |
| 673 | ;;; Apply a function elementwise to vectors A and B. [O X O O] [Public] |
| 674 | (defun math-map-vec-2 (f a b) |
| 675 | (if (math-vectorp a) |
| 676 | (if (math-vectorp b) |
| 677 | (let ((v nil)) |
| 678 | (while (setq a (cdr a)) |
| 679 | (or (setq b (cdr b)) |
| 680 | (math-dimension-error)) |
| 681 | (setq v (cons (funcall f (car a) (car b)) v))) |
| 682 | (if a (math-dimension-error)) |
| 683 | (cons 'vec (nreverse v))) |
| 684 | (let ((v nil)) |
| 685 | (while (setq a (cdr a)) |
| 686 | (setq v (cons (funcall f (car a) b) v))) |
| 687 | (cons 'vec (nreverse v)))) |
| 688 | (if (math-vectorp b) |
| 689 | (let ((v nil)) |
| 690 | (while (setq b (cdr b)) |
| 691 | (setq v (cons (funcall f a (car b)) v))) |
| 692 | (cons 'vec (nreverse v))) |
| 693 | (funcall f a b)))) |
| 694 | |
| 695 | |
| 696 | |
| 697 | ;;; "Reduce" a function over a vector (left-associatively). [O X V] [Public] |
| 698 | (defun math-reduce-vec (f a) |
| 699 | (if (math-vectorp a) |
| 700 | (if (cdr a) |
| 701 | (let ((accum (car (setq a (cdr a))))) |
| 702 | (while (setq a (cdr a)) |
| 703 | (setq accum (funcall f accum (car a)))) |
| 704 | accum) |
| 705 | 0) |
| 706 | a)) |
| 707 | |
| 708 | ;;; Reduce a function over the columns of matrix A. [V X V] [Public] |
| 709 | (defun math-reduce-cols (f a) |
| 710 | (if (math-matrixp a) |
| 711 | (cons 'vec (math-reduce-cols-col-step f (cdr a) 1 (length (nth 1 a)))) |
| 712 | a)) |
| 713 | |
| 714 | (defun math-reduce-cols-col-step (f a col cols) |
| 715 | (and (< col cols) |
| 716 | (cons (math-reduce-cols-row-step f (nth col (car a)) col (cdr a)) |
| 717 | (math-reduce-cols-col-step f a (1+ col) cols)))) |
| 718 | |
| 719 | (defun math-reduce-cols-row-step (f tot col a) |
| 720 | (if a |
| 721 | (math-reduce-cols-row-step f |
| 722 | (funcall f tot (nth col (car a))) |
| 723 | col |
| 724 | (cdr a)) |
| 725 | tot)) |
| 726 | |
| 727 | |
| 728 | |
| 729 | (defun math-dot-product (a b) |
| 730 | (if (setq a (cdr a) b (cdr b)) |
| 731 | (let ((accum (math-mul (car a) (car b)))) |
| 732 | (while (setq a (cdr a) b (cdr b)) |
| 733 | (setq accum (math-add accum (math-mul (car a) (car b))))) |
| 734 | accum) |
| 735 | 0)) |
| 736 | |
| 737 | |
| 738 | ;;; Return the number of elements in vector V. [Public] |
| 739 | (defun calcFunc-vlen (v) |
| 740 | (if (math-vectorp v) |
| 741 | (1- (length v)) |
| 742 | (if (math-objectp v) |
| 743 | 0 |
| 744 | (list 'calcFunc-vlen v)))) |
| 745 | |
| 746 | ;;; Get the Nth row of a matrix. |
| 747 | (defun calcFunc-mrow (mat n) ; [Public] |
| 748 | (if (Math-vectorp n) |
| 749 | (math-map-vec (function (lambda (x) (calcFunc-mrow mat x))) n) |
| 750 | (if (and (eq (car-safe n) 'intv) (math-constp n)) |
| 751 | (calcFunc-subvec mat |
| 752 | (math-add (nth 2 n) (if (memq (nth 1 n) '(2 3)) 0 1)) |
| 753 | (math-add (nth 3 n) (if (memq (nth 1 n) '(1 3)) 1 0))) |
| 754 | (or (and (integerp (setq n (math-check-integer n))) |
| 755 | (> n 0)) |
| 756 | (math-reject-arg n 'fixposintp)) |
| 757 | (or (Math-vectorp mat) |
| 758 | (math-reject-arg mat 'vectorp)) |
| 759 | (or (nth n mat) |
| 760 | (math-reject-arg n "*Index out of range"))))) |
| 761 | |
| 762 | (defun calcFunc-subscr (mat n &optional m) |
| 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)) |
| 769 | |
| 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)))) |
| 773 | |
| 774 | (defun calcFunc-mcol (mat n) ; [Public] |
| 775 | (if (Math-vectorp n) |
| 776 | (calcFunc-trn |
| 777 | (math-map-vec (function (lambda (x) (calcFunc-mcol mat x))) n)) |
| 778 | (if (and (eq (car-safe n) 'intv) (math-constp n)) |
| 779 | (if (math-matrixp mat) |
| 780 | (math-map-vec (function (lambda (x) (calcFunc-mrow x n))) mat) |
| 781 | (calcFunc-mrow mat n)) |
| 782 | (or (and (integerp (setq n (math-check-integer n))) |
| 783 | (> n 0)) |
| 784 | (math-reject-arg n 'fixposintp)) |
| 785 | (or (Math-vectorp mat) |
| 786 | (math-reject-arg mat 'vectorp)) |
| 787 | (or (if (math-matrixp mat) |
| 788 | (and (< n (length (nth 1 mat))) |
| 789 | (math-mat-col mat n)) |
| 790 | (nth n mat)) |
| 791 | (math-reject-arg n "*Index out of range"))))) |
| 792 | |
| 793 | ;;; Remove the Nth row from a matrix. |
| 794 | (defun math-mat-less-row (mat n) |
| 795 | (if (<= n 0) |
| 796 | (cdr mat) |
| 797 | (cons (car mat) |
| 798 | (math-mat-less-row (cdr mat) (1- n))))) |
| 799 | |
| 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))) |
| 805 | |
| 806 | ;;; Remove the Nth column from a matrix. |
| 807 | (defun math-mat-less-col (mat n) |
| 808 | (cons 'vec (mapcar (function (lambda (x) (math-mat-less-row x n))) |
| 809 | (cdr mat)))) |
| 810 | |
| 811 | (defun calcFunc-mrcol (mat n) ; [Public] |
| 812 | (and (integerp (setq n (math-check-integer n))) |
| 813 | (> n 0) |
| 814 | (if (math-matrixp mat) |
| 815 | (and (< n (length (nth 1 mat))) |
| 816 | (math-mat-less-col mat n)) |
| 817 | (math-mat-less-row mat n)))) |
| 818 | |
| 819 | (defun calcFunc-getdiag (mat) ; [Public] |
| 820 | (if (math-square-matrixp mat) |
| 821 | (cons 'vec (math-get-diag-step (cdr mat) 1)) |
| 822 | (calc-record-why 'square-matrixp mat) |
| 823 | (list 'calcFunc-getdiag mat))) |
| 824 | |
| 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))))) |
| 829 | |
| 830 | (defun math-transpose (mat) ; [Public] |
| 831 | (let ((m nil) |
| 832 | (col (length (nth 1 mat)))) |
| 833 | (while (> (setq col (1- col)) 0) |
| 834 | (setq m (cons (math-mat-col mat col) m))) |
| 835 | (cons 'vec m))) |
| 836 | |
| 837 | (defun calcFunc-trn (mat) |
| 838 | (if (math-vectorp mat) |
| 839 | (if (math-matrixp mat) |
| 840 | (math-transpose mat) |
| 841 | (math-col-matrix mat)) |
| 842 | (if (math-numberp mat) |
| 843 | mat |
| 844 | (math-reject-arg mat 'matrixp)))) |
| 845 | |
| 846 | (defun calcFunc-ctrn (mat) |
| 847 | (calcFunc-conj (calcFunc-trn mat))) |
| 848 | |
| 849 | (defun calcFunc-pack (mode els) |
| 850 | (or (Math-vectorp els) (math-reject-arg els 'vectorp)) |
| 851 | (if (and (Math-vectorp mode) (cdr mode)) |
| 852 | (setq mode (cdr mode)) |
| 853 | (or (integerp mode) (math-reject-arg mode 'fixnump))) |
| 854 | (condition-case err |
| 855 | (if (= (calc-pack-size mode) (1- (length els))) |
| 856 | (calc-pack-items mode (cdr els)) |
| 857 | (math-reject-arg els "*Wrong number of elements")) |
| 858 | (error (math-reject-arg els (nth 1 err))))) |
| 859 | |
| 860 | (defun calcFunc-unpack (mode thing) |
| 861 | (or (integerp mode) (math-reject-arg mode 'fixnump)) |
| 862 | (condition-case err |
| 863 | (cons 'vec (calc-unpack-item mode thing)) |
| 864 | (error (math-reject-arg thing (nth 1 err))))) |
| 865 | |
| 866 | (defun calcFunc-unpackt (mode thing) |
| 867 | (let ((calc-unpack-with-type 'pair)) |
| 868 | (calcFunc-unpack mode thing))) |
| 869 | |
| 870 | (defun calcFunc-arrange (vec cols) ; [Public] |
| 871 | (setq cols (math-check-fixnum cols t)) |
| 872 | (if (math-vectorp vec) |
| 873 | (let* ((flat (math-flatten-vector vec)) |
| 874 | (mat (list 'vec)) |
| 875 | next) |
| 876 | (if (<= cols 0) |
| 877 | (nconc mat flat) |
| 878 | (while (>= (length flat) cols) |
| 879 | (setq next (nthcdr cols flat)) |
| 880 | (setcdr (nthcdr (1- cols) flat) nil) |
| 881 | (setq mat (nconc mat (list (cons 'vec flat))) |
| 882 | flat next)) |
| 883 | (if flat |
| 884 | (setq mat (nconc mat (list (cons 'vec flat))))) |
| 885 | mat)))) |
| 886 | |
| 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))) |
| 891 | |
| 892 | (defun calcFunc-vconcat (a b) |
| 893 | (math-normalize (list '| a b))) |
| 894 | |
| 895 | (defun calcFunc-vconcatrev (a b) |
| 896 | (math-normalize (list '| b a))) |
| 897 | |
| 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))) |
| 902 | |
| 903 | (defun calcFunc-appendrev (v1 v2) |
| 904 | (calcFunc-append v2 v1)) |
| 905 | |
| 906 | |
| 907 | ;;; Copy a matrix. [Public] |
| 908 | (defun math-copy-matrix (m) |
| 909 | (if (math-vectorp (nth 1 m)) |
| 910 | (cons 'vec (mapcar 'copy-sequence (cdr m))) |
| 911 | (copy-sequence m))) |
| 912 | |
| 913 | ;;; Convert a scalar or vector into an NxN diagonal matrix. [Public] |
| 914 | (defun calcFunc-diag (a &optional n) |
| 915 | (and n (not (integerp n)) |
| 916 | (setq n (math-check-fixnum n))) |
| 917 | (if (math-vectorp a) |
| 918 | (if (and n (/= (length a) (1+ n))) |
| 919 | (list 'calcFunc-diag a n) |
| 920 | (if (math-matrixp a) |
| 921 | (if (and n (/= (length (elt a 1)) (1+ n))) |
| 922 | (list 'calcFunc-diag a n) |
| 923 | a) |
| 924 | (cons 'vec (math-diag-step (cdr a) 0 (1- (length a)))))) |
| 925 | (if n |
| 926 | (cons 'vec (math-diag-step (make-list n a) 0 n)) |
| 927 | (list 'calcFunc-diag a)))) |
| 928 | |
| 929 | (defun calcFunc-idn (a &optional n) |
| 930 | (if n |
| 931 | (if (math-vectorp a) |
| 932 | (math-reject-arg a 'numberp) |
| 933 | (calcFunc-diag a n)) |
| 934 | (if (integerp calc-matrix-mode) |
| 935 | (calcFunc-idn a calc-matrix-mode) |
| 936 | (list 'calcFunc-idn a)))) |
| 937 | |
| 938 | (defun math-mimic-ident (a m) |
| 939 | (if (math-square-matrixp m) |
| 940 | (calcFunc-idn a (1- (length m))) |
| 941 | (if (math-vectorp m) |
| 942 | (if (math-zerop a) |
| 943 | (cons 'vec (mapcar (function (lambda (x) |
| 944 | (if (math-vectorp x) |
| 945 | (math-mimic-ident a x) |
| 946 | a))) |
| 947 | (cdr m))) |
| 948 | (math-dimension-error)) |
| 949 | (calcFunc-idn a)))) |
| 950 | |
| 951 | (defun math-diag-step (a n m) |
| 952 | (if (< n m) |
| 953 | (cons (cons 'vec |
| 954 | (nconc (make-list n 0) |
| 955 | (cons (car a) |
| 956 | (make-list (1- (- m n)) 0)))) |
| 957 | (math-diag-step (cdr a) (1+ n) m)) |
| 958 | nil)) |
| 959 | |
| 960 | ;;; Create a vector of consecutive integers. [Public] |
| 961 | (defun calcFunc-index (n &optional start incr) |
| 962 | (if (math-messy-integerp n) |
| 963 | (math-float (calcFunc-index (math-trunc n) start incr)) |
| 964 | (and (not (integerp n)) |
| 965 | (setq n (math-check-fixnum n))) |
| 966 | (let ((vec nil)) |
| 967 | (if start |
| 968 | (progn |
| 969 | (if (>= n 0) |
| 970 | (while (>= (setq n (1- n)) 0) |
| 971 | (setq vec (cons start vec) |
| 972 | start (math-add start (or incr 1)))) |
| 973 | (while (<= (setq n (1+ n)) 0) |
| 974 | (setq vec (cons start vec) |
| 975 | start (math-mul start (or incr 2))))) |
| 976 | (setq vec (nreverse vec))) |
| 977 | (if (>= n 0) |
| 978 | (while (> n 0) |
| 979 | (setq vec (cons n vec) |
| 980 | n (1- n))) |
| 981 | (let ((i -1)) |
| 982 | (while (>= i n) |
| 983 | (setq vec (cons i vec) |
| 984 | i (1- i)))))) |
| 985 | (cons 'vec vec)))) |
| 986 | |
| 987 | ;;; Find an element in a vector. |
| 988 | (defun calcFunc-find (vec x &optional start) |
| 989 | (setq start (if start (math-check-fixnum start t) 1)) |
| 990 | (if (< start 1) (math-reject-arg start 'posp)) |
| 991 | (setq vec (nthcdr start vec)) |
| 992 | (let ((n start)) |
| 993 | (while (and vec (not (Math-equal x (car vec)))) |
| 994 | (setq n (1+ n) |
| 995 | vec (cdr vec))) |
| 996 | (if vec n 0))) |
| 997 | |
| 998 | ;;; Return a subvector of a vector. |
| 999 | (defun calcFunc-subvec (vec start &optional end) |
| 1000 | (setq start (math-check-fixnum start t) |
| 1001 | end (math-check-fixnum (or end 0) t)) |
| 1002 | (or (math-vectorp vec) (math-reject-arg vec 'vectorp)) |
| 1003 | (let ((len (1- (length vec)))) |
| 1004 | (if (<= start 0) |
| 1005 | (setq start (+ len start 1))) |
| 1006 | (if (<= end 0) |
| 1007 | (setq end (+ len end 1))) |
| 1008 | (if (or (> start len) |
| 1009 | (<= end start)) |
| 1010 | '(vec) |
| 1011 | (setq vec (nthcdr start vec)) |
| 1012 | (if (<= end len) |
| 1013 | (let ((chop (nthcdr (- end start 1) (setq vec (copy-sequence vec))))) |
| 1014 | (setcdr chop nil))) |
| 1015 | (cons 'vec vec)))) |
| 1016 | |
| 1017 | ;;; Remove a subvector from a vector. |
| 1018 | (defun calcFunc-rsubvec (vec start &optional end) |
| 1019 | (setq start (math-check-fixnum start t) |
| 1020 | end (math-check-fixnum (or end 0) t)) |
| 1021 | (or (math-vectorp vec) (math-reject-arg vec 'vectorp)) |
| 1022 | (let ((len (1- (length vec)))) |
| 1023 | (if (<= start 0) |
| 1024 | (setq start (+ len start 1))) |
| 1025 | (if (<= end 0) |
| 1026 | (setq end (+ len end 1))) |
| 1027 | (if (or (> start len) |
| 1028 | (<= end start)) |
| 1029 | vec |
| 1030 | (let ((tail (nthcdr end vec)) |
| 1031 | (chop (nthcdr (1- start) (setq vec (copy-sequence vec))))) |
| 1032 | (setcdr chop nil) |
| 1033 | (append vec tail))))) |
| 1034 | |
| 1035 | ;;; Reverse the order of the elements of a vector. |
| 1036 | (defun calcFunc-rev (vec) |
| 1037 | (if (math-vectorp vec) |
| 1038 | (cons 'vec (reverse (cdr vec))) |
| 1039 | (math-reject-arg vec 'vectorp))) |
| 1040 | |
| 1041 | ;;; Compress a vector according to a mask vector. |
| 1042 | (defun calcFunc-vmask (mask vec) |
| 1043 | (if (math-numberp mask) |
| 1044 | (if (math-zerop mask) |
| 1045 | '(vec) |
| 1046 | vec) |
| 1047 | (or (math-vectorp mask) (math-reject-arg mask 'vectorp)) |
| 1048 | (or (math-constp mask) (math-reject-arg mask 'constp)) |
| 1049 | (or (math-vectorp vec) (math-reject-arg vec 'vectorp)) |
| 1050 | (or (= (length mask) (length vec)) (math-dimension-error)) |
| 1051 | (let ((new nil)) |
| 1052 | (while (setq mask (cdr mask) vec (cdr vec)) |
| 1053 | (or (math-zerop (car mask)) |
| 1054 | (setq new (cons (car vec) new)))) |
| 1055 | (cons 'vec (nreverse new))))) |
| 1056 | |
| 1057 | ;;; Expand a vector according to a mask vector. |
| 1058 | (defun calcFunc-vexp (mask vec &optional filler) |
| 1059 | (or (math-vectorp mask) (math-reject-arg mask 'vectorp)) |
| 1060 | (or (math-constp mask) (math-reject-arg mask 'constp)) |
| 1061 | (or (math-vectorp vec) (math-reject-arg vec 'vectorp)) |
| 1062 | (let ((new nil) |
| 1063 | (fvec (and filler (math-vectorp filler)))) |
| 1064 | (while (setq mask (cdr mask)) |
| 1065 | (if (math-zerop (car mask)) |
| 1066 | (setq new (cons (or (if fvec |
| 1067 | (car (setq filler (cdr filler))) |
| 1068 | filler) |
| 1069 | (car mask)) new)) |
| 1070 | (setq vec (cdr vec) |
| 1071 | new (cons (or (car vec) (car mask)) new)))) |
| 1072 | (cons 'vec (nreverse new)))) |
| 1073 | |
| 1074 | |
| 1075 | ;;; Compute the row and column norms of a vector or matrix. [Public] |
| 1076 | (defun calcFunc-rnorm (a) |
| 1077 | (if (and (Math-vectorp a) |
| 1078 | (math-constp a)) |
| 1079 | (if (math-matrixp a) |
| 1080 | (math-reduce-vec 'math-max (math-map-vec 'calcFunc-cnorm a)) |
| 1081 | (math-reduce-vec 'math-max (math-map-vec 'math-abs a))) |
| 1082 | (calc-record-why 'vectorp a) |
| 1083 | (list 'calcFunc-rnorm a))) |
| 1084 | |
| 1085 | (defun calcFunc-cnorm (a) |
| 1086 | (if (and (Math-vectorp a) |
| 1087 | (math-constp a)) |
| 1088 | (if (math-matrixp a) |
| 1089 | (math-reduce-vec 'math-max |
| 1090 | (math-reduce-cols 'math-add-abs a)) |
| 1091 | (math-reduce-vec 'math-add-abs a)) |
| 1092 | (calc-record-why 'vectorp a) |
| 1093 | (list 'calcFunc-cnorm a))) |
| 1094 | |
| 1095 | (defun math-add-abs (a b) |
| 1096 | (math-add (math-abs a) (math-abs b))) |
| 1097 | |
| 1098 | |
| 1099 | ;;; Sort the elements of a vector into increasing order. |
| 1100 | (defun calcFunc-sort (vec) ; [Public] |
| 1101 | (if (math-vectorp vec) |
| 1102 | (cons 'vec (sort (copy-sequence (cdr vec)) 'math-beforep)) |
| 1103 | (math-reject-arg vec 'vectorp))) |
| 1104 | |
| 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))) |
| 1109 | |
| 1110 | ;; The variable math-grade-vec is local to calcFunc-grade and |
| 1111 | ;; calcFunc-rgrade, but is used by math-grade-beforep, which is called |
| 1112 | ;; by calcFunc-grade and calcFunc-rgrade. |
| 1113 | (defvar math-grade-vec) |
| 1114 | |
| 1115 | (defun calcFunc-grade (math-grade-vec) |
| 1116 | (if (math-vectorp math-grade-vec) |
| 1117 | (let* ((len (1- (length math-grade-vec)))) |
| 1118 | (cons 'vec (sort (cdr (calcFunc-index len)) 'math-grade-beforep))) |
| 1119 | (math-reject-arg math-grade-vec 'vectorp))) |
| 1120 | |
| 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))) |
| 1127 | |
| 1128 | (defun math-grade-beforep (i j) |
| 1129 | (math-beforep (nth i math-grade-vec) (nth j math-grade-vec))) |
| 1130 | |
| 1131 | |
| 1132 | ;;; Compile a histogram of data from a vector. |
| 1133 | (defun calcFunc-histogram (vec wts &optional n) |
| 1134 | (or n (setq n wts wts 1)) |
| 1135 | (or (Math-vectorp vec) |
| 1136 | (math-reject-arg vec 'vectorp)) |
| 1137 | (if (Math-vectorp wts) |
| 1138 | (or (= (length vec) (length wts)) |
| 1139 | (math-dimension-error))) |
| 1140 | (cond ((natnump n) |
| 1141 | (let ((res (make-vector n 0)) |
| 1142 | (vp vec) |
| 1143 | (wvec (Math-vectorp wts)) |
| 1144 | (wp wts) |
| 1145 | bin) |
| 1146 | (while (setq vp (cdr vp)) |
| 1147 | (setq bin (car vp)) |
| 1148 | (or (natnump bin) |
| 1149 | (setq bin (math-floor bin))) |
| 1150 | (and (natnump bin) |
| 1151 | (< bin n) |
| 1152 | (aset res bin |
| 1153 | (math-add (aref res bin) |
| 1154 | (if wvec (car (setq wp (cdr wp))) wts))))) |
| 1155 | (cons 'vec (append res nil)))) |
| 1156 | ((Math-vectorp n) ;; n is a vector of midpoints |
| 1157 | (let* ((bds (math-vector-avg n)) |
| 1158 | (res (make-vector (1- (length n)) 0)) |
| 1159 | (vp (cdr vec)) |
| 1160 | (wvec (Math-vectorp wts)) |
| 1161 | (wp wts) |
| 1162 | num) |
| 1163 | (while vp |
| 1164 | (setq num (car vp)) |
| 1165 | (let ((tbds (cdr bds)) |
| 1166 | (i 0)) |
| 1167 | (while (and tbds (Math-lessp (car tbds) num)) |
| 1168 | (setq i (1+ i)) |
| 1169 | (setq tbds (cdr tbds))) |
| 1170 | (aset res i |
| 1171 | (math-add (aref res i) |
| 1172 | (if wvec (car (setq wp (cdr wp))) wts)))) |
| 1173 | (setq vp (cdr vp))) |
| 1174 | (cons 'vec (append res nil)))) |
| 1175 | (t |
| 1176 | (math-reject-arg n "*Expecting an integer or vector")))) |
| 1177 | |
| 1178 | ;;; Replace a vector [a b c ...] with a vector of averages |
| 1179 | ;;; [(a+b)/2 (b+c)/2 ...] |
| 1180 | (defun math-vector-avg (vec) |
| 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)))) |
| 1187 | |
| 1188 | |
| 1189 | ;;; Set operations. |
| 1190 | |
| 1191 | (defun calcFunc-vunion (a b) |
| 1192 | (if (Math-objectp a) |
| 1193 | (setq a (list 'vec a)) |
| 1194 | (or (math-vectorp a) (math-reject-arg a 'vectorp))) |
| 1195 | (if (Math-objectp b) |
| 1196 | (setq b (list b)) |
| 1197 | (or (math-vectorp b) (math-reject-arg b 'vectorp)) |
| 1198 | (setq b (cdr b))) |
| 1199 | (calcFunc-rdup (append a b))) |
| 1200 | |
| 1201 | (defun calcFunc-vint (a b) |
| 1202 | (if (and (math-simple-set a) (math-simple-set b)) |
| 1203 | (progn |
| 1204 | (setq a (cdr (calcFunc-rdup a))) |
| 1205 | (setq b (cdr (calcFunc-rdup b))) |
| 1206 | (let ((vec (list 'vec))) |
| 1207 | (while (and a b) |
| 1208 | (if (math-beforep (car a) (car b)) |
| 1209 | (setq a (cdr a)) |
| 1210 | (if (Math-equal (car a) (car b)) |
| 1211 | (setq vec (cons (car a) vec) |
| 1212 | a (cdr a))) |
| 1213 | (setq b (cdr b)))) |
| 1214 | (nreverse vec))) |
| 1215 | (calcFunc-vcompl (calcFunc-vunion (calcFunc-vcompl a) |
| 1216 | (calcFunc-vcompl b))))) |
| 1217 | |
| 1218 | (defun calcFunc-vdiff (a b) |
| 1219 | (if (and (math-simple-set a) (math-simple-set b)) |
| 1220 | (progn |
| 1221 | (setq a (cdr (calcFunc-rdup a))) |
| 1222 | (setq b (cdr (calcFunc-rdup b))) |
| 1223 | (let ((vec (list 'vec))) |
| 1224 | (while a |
| 1225 | (while (and b (math-beforep (car b) (car a))) |
| 1226 | (setq b (cdr b))) |
| 1227 | (if (and b (Math-equal (car a) (car b))) |
| 1228 | (setq a (cdr a) |
| 1229 | b (cdr b)) |
| 1230 | (setq vec (cons (car a) vec) |
| 1231 | a (cdr a)))) |
| 1232 | (nreverse vec))) |
| 1233 | (calcFunc-vcompl (calcFunc-vunion (calcFunc-vcompl a) b)))) |
| 1234 | |
| 1235 | (defun calcFunc-vxor (a b) |
| 1236 | (if (and (math-simple-set a) (math-simple-set b)) |
| 1237 | (progn |
| 1238 | (setq a (cdr (calcFunc-rdup a))) |
| 1239 | (setq b (cdr (calcFunc-rdup b))) |
| 1240 | (let ((vec (list 'vec))) |
| 1241 | (while (or a b) |
| 1242 | (if (and a |
| 1243 | (or (not b) |
| 1244 | (math-beforep (car a) (car b)))) |
| 1245 | (setq vec (cons (car a) vec) |
| 1246 | a (cdr a)) |
| 1247 | (if (and a (Math-equal (car a) (car b))) |
| 1248 | (setq a (cdr a)) |
| 1249 | (setq vec (cons (car b) vec))) |
| 1250 | (setq b (cdr b)))) |
| 1251 | (nreverse vec))) |
| 1252 | (let ((ca (calcFunc-vcompl a)) |
| 1253 | (cb (calcFunc-vcompl b))) |
| 1254 | (calcFunc-vunion (calcFunc-vcompl (calcFunc-vunion ca b)) |
| 1255 | (calcFunc-vcompl (calcFunc-vunion a cb)))))) |
| 1256 | |
| 1257 | (defun calcFunc-vcompl (a) |
| 1258 | (setq a (math-prepare-set a)) |
| 1259 | (let ((vec (list 'vec)) |
| 1260 | (prev '(neg (var inf var-inf))) |
| 1261 | (closed 2)) |
| 1262 | (while (setq a (cdr a)) |
| 1263 | (or (and (equal (nth 2 (car a)) '(neg (var inf var-inf))) |
| 1264 | (memq (nth 1 (car a)) '(2 3))) |
| 1265 | (setq vec (cons (list 'intv |
| 1266 | (+ closed |
| 1267 | (if (memq (nth 1 (car a)) '(0 1)) 1 0)) |
| 1268 | prev |
| 1269 | (nth 2 (car a))) |
| 1270 | vec))) |
| 1271 | (setq prev (nth 3 (car a)) |
| 1272 | closed (if (memq (nth 1 (car a)) '(0 2)) 2 0))) |
| 1273 | (or (and (equal prev '(var inf var-inf)) |
| 1274 | (= closed 0)) |
| 1275 | (setq vec (cons (list 'intv (+ closed 1) |
| 1276 | prev '(var inf var-inf)) |
| 1277 | vec))) |
| 1278 | (math-clean-set (nreverse vec)))) |
| 1279 | |
| 1280 | (defun calcFunc-vspan (a) |
| 1281 | (setq a (math-prepare-set a)) |
| 1282 | (if (cdr a) |
| 1283 | (let ((last (nth (1- (length a)) a))) |
| 1284 | (math-make-intv (+ (logand (nth 1 (nth 1 a)) 2) |
| 1285 | (logand (nth 1 last) 1)) |
| 1286 | (nth 2 (nth 1 a)) |
| 1287 | (nth 3 last))) |
| 1288 | '(intv 2 0 0))) |
| 1289 | |
| 1290 | (defun calcFunc-vfloor (a &optional always-vec) |
| 1291 | (setq a (math-prepare-set a)) |
| 1292 | (let ((vec (list 'vec)) (p a) (prev nil) b mask) |
| 1293 | (while (setq p (cdr p)) |
| 1294 | (setq mask (nth 1 (car p)) |
| 1295 | a (nth 2 (car p)) |
| 1296 | b (nth 3 (car p))) |
| 1297 | (and (memq mask '(0 1)) |
| 1298 | (not (math-infinitep a)) |
| 1299 | (setq mask (logior mask 2)) |
| 1300 | (math-num-integerp a) |
| 1301 | (setq a (math-add a 1))) |
| 1302 | (setq a (math-ceiling a)) |
| 1303 | (and (memq mask '(0 2)) |
| 1304 | (not (math-infinitep b)) |
| 1305 | (setq mask (logior mask 1)) |
| 1306 | (math-num-integerp b) |
| 1307 | (setq b (math-sub b 1))) |
| 1308 | (setq b (math-floor b)) |
| 1309 | (if (and prev (Math-equal (math-sub a 1) (nth 3 prev))) |
| 1310 | (setcar (nthcdr 3 prev) b) |
| 1311 | (or (Math-lessp b a) |
| 1312 | (setq vec (cons (setq prev (list 'intv mask a b)) vec))))) |
| 1313 | (setq vec (nreverse vec)) |
| 1314 | (math-clean-set vec always-vec))) |
| 1315 | |
| 1316 | (defun calcFunc-vcard (a) |
| 1317 | (setq a (calcFunc-vfloor a t)) |
| 1318 | (or (math-constp a) (math-reject-arg a "*Set must be finite")) |
| 1319 | (let ((count 0)) |
| 1320 | (while (setq a (cdr a)) |
| 1321 | (if (eq (car-safe (car a)) 'intv) |
| 1322 | (setq count (math-add count (math-sub (nth 3 (car a)) |
| 1323 | (nth 2 (car a)))))) |
| 1324 | (setq count (math-add count 1))) |
| 1325 | count)) |
| 1326 | |
| 1327 | (defun calcFunc-venum (a) |
| 1328 | (setq a (calcFunc-vfloor a t)) |
| 1329 | (or (math-constp a) (math-reject-arg a "*Set must be finite")) |
| 1330 | (let* ((prev a) (this (cdr prev)) this-val next this-last) |
| 1331 | (while this |
| 1332 | (setq next (cdr this) |
| 1333 | this-val (car this)) |
| 1334 | (if (eq (car-safe this-val) 'intv) |
| 1335 | (progn |
| 1336 | (setq this (cdr (calcFunc-index (math-add |
| 1337 | (math-sub (nth 3 this-val) |
| 1338 | (nth 2 this-val)) |
| 1339 | 1) |
| 1340 | (nth 2 this-val)))) |
| 1341 | (setq this-last (last this)) |
| 1342 | (setcdr this-last next) |
| 1343 | (setcdr prev this) |
| 1344 | (setq prev this-last)) |
| 1345 | (setq prev this)) |
| 1346 | (setq this next))) |
| 1347 | a) |
| 1348 | |
| 1349 | (defun calcFunc-vpack (a) |
| 1350 | (setq a (calcFunc-vfloor a t)) |
| 1351 | (if (and (cdr a) |
| 1352 | (math-negp (if (eq (car-safe (nth 1 a)) 'intv) |
| 1353 | (nth 2 (nth 1 a)) |
| 1354 | (nth 1 a)))) |
| 1355 | (math-reject-arg (nth 1 a) 'posp)) |
| 1356 | (let ((accum 0)) |
| 1357 | (while (setq a (cdr a)) |
| 1358 | (if (eq (car-safe (car a)) 'intv) |
| 1359 | (if (equal (nth 3 (car a)) '(var inf var-inf)) |
| 1360 | (setq accum (math-sub accum |
| 1361 | (math-power-of-2 (nth 2 (car a))))) |
| 1362 | (setq accum (math-add accum |
| 1363 | (math-sub |
| 1364 | (math-power-of-2 (1+ (nth 3 (car a)))) |
| 1365 | (math-power-of-2 (nth 2 (car a))))))) |
| 1366 | (setq accum (math-add accum (math-power-of-2 (car a)))))) |
| 1367 | accum)) |
| 1368 | |
| 1369 | (defun calcFunc-vunpack (a &optional w) |
| 1370 | (or (math-num-integerp a) (math-reject-arg a 'integerp)) |
| 1371 | (if w (setq a (math-clip a w))) |
| 1372 | (if (math-messy-integerp a) (setq a (math-trunc a))) |
| 1373 | (let* ((calc-number-radix 2) |
| 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) |
| 1378 | "" |
| 1379 | (if (consp aa) |
| 1380 | (math-format-bignum-binary (cdr aa)) |
| 1381 | (math-format-binary aa)))) |
| 1382 | (zero (if neg ?1 ?0)) |
| 1383 | (one (if neg ?0 ?1)) |
| 1384 | (len (length str)) |
| 1385 | (vec (list 'vec)) |
| 1386 | (pos (1- len)) pos2) |
| 1387 | (while (>= pos 0) |
| 1388 | (if (eq (aref str pos) zero) |
| 1389 | (setq pos (1- pos)) |
| 1390 | (setq pos2 pos) |
| 1391 | (while (and (>= pos 0) (eq (aref str pos) one)) |
| 1392 | (setq pos (1- pos))) |
| 1393 | (setq vec (cons (if (= pos (1- pos2)) |
| 1394 | (- len pos2 1) |
| 1395 | (list 'intv 3 (- len pos2 1) (- len pos 2))) |
| 1396 | vec)))) |
| 1397 | (if neg |
| 1398 | (setq vec (cons (list 'intv 2 len '(var inf var-inf)) vec))) |
| 1399 | (math-clean-set (nreverse vec)))) |
| 1400 | |
| 1401 | (defun calcFunc-rdup (a) |
| 1402 | (if (math-simple-set a) |
| 1403 | (progn |
| 1404 | (and (Math-objectp a) (setq a (list 'vec a))) |
| 1405 | (or (math-vectorp a) (math-reject-arg a 'vectorp)) |
| 1406 | (setq a (sort (copy-sequence (cdr a)) 'math-beforep)) |
| 1407 | (let ((p a)) |
| 1408 | (while (cdr p) |
| 1409 | (if (Math-equal (car p) (nth 1 p)) |
| 1410 | (setcdr p (cdr (cdr p))) |
| 1411 | (setq p (cdr p))))) |
| 1412 | (cons 'vec a)) |
| 1413 | (math-clean-set (math-prepare-set a)))) |
| 1414 | |
| 1415 | (defun math-prepare-set (a) |
| 1416 | (if (Math-objectp a) |
| 1417 | (setq a (list 'vec a)) |
| 1418 | (or (math-vectorp a) (math-reject-arg a 'vectorp)) |
| 1419 | (setq a (cons 'vec (sort (copy-sequence (cdr a)) 'math-beforep)))) |
| 1420 | (let ((p a) res) |
| 1421 | |
| 1422 | ;; Convert all elements to non-empty intervals. |
| 1423 | (while (cdr p) |
| 1424 | (if (eq (car-safe (nth 1 p)) 'intv) |
| 1425 | (if (math-intv-constp (nth 1 p)) |
| 1426 | (if (and (memq (nth 1 (nth 1 p)) '(0 1 2)) |
| 1427 | (Math-equal (nth 2 (nth 1 p)) (nth 3 (nth 1 p)))) |
| 1428 | (setcdr p (cdr (cdr p))) |
| 1429 | (setq p (cdr p))) |
| 1430 | (math-reject-arg (nth 1 p) 'constp)) |
| 1431 | (or (Math-anglep (nth 1 p)) |
| 1432 | (eq (car (nth 1 p)) 'date) |
| 1433 | (equal (nth 1 p) '(var inf var-inf)) |
| 1434 | (equal (nth 1 p) '(neg (var inf var-inf))) |
| 1435 | (math-reject-arg (nth 1 p) 'realp)) |
| 1436 | (setcar (cdr p) (list 'intv 3 (nth 1 p) (nth 1 p))) |
| 1437 | (setq p (cdr p)))) |
| 1438 | |
| 1439 | ;; Combine redundant intervals. |
| 1440 | (setq p a) |
| 1441 | (while (cdr (cdr p)) |
| 1442 | (if (or (memq (setq res (math-compare (nth 3 (nth 1 p)) |
| 1443 | (nth 2 (nth 2 p)))) |
| 1444 | '(-1 2)) |
| 1445 | (and (eq res 0) |
| 1446 | (memq (nth 1 (nth 1 p)) '(0 2)) |
| 1447 | (memq (nth 1 (nth 2 p)) '(0 1)))) |
| 1448 | (setq p (cdr p)) |
| 1449 | (setq res (math-compare (nth 3 (nth 1 p)) (nth 3 (nth 2 p)))) |
| 1450 | (setcdr p (cons (list 'intv |
| 1451 | (+ (logand (logior (nth 1 (nth 1 p)) |
| 1452 | (if (Math-equal |
| 1453 | (nth 2 (nth 1 p)) |
| 1454 | (nth 2 (nth 2 p))) |
| 1455 | (nth 1 (nth 2 p)) |
| 1456 | 0)) |
| 1457 | 2) |
| 1458 | (logand (logior (if (memq res '(1 0 2)) |
| 1459 | (nth 1 (nth 1 p)) 0) |
| 1460 | (if (memq res '(-1 0 2)) |
| 1461 | (nth 1 (nth 2 p)) 0)) |
| 1462 | 1)) |
| 1463 | (nth 2 (nth 1 p)) |
| 1464 | (if (eq res 1) |
| 1465 | (nth 3 (nth 1 p)) |
| 1466 | (nth 3 (nth 2 p)))) |
| 1467 | (cdr (cdr (cdr p)))))))) |
| 1468 | a) |
| 1469 | |
| 1470 | (defun math-clean-set (a &optional always-vec) |
| 1471 | (let ((p a) res) |
| 1472 | (while (cdr p) |
| 1473 | (if (and (eq (car-safe (nth 1 p)) 'intv) |
| 1474 | (Math-equal (nth 2 (nth 1 p)) (nth 3 (nth 1 p)))) |
| 1475 | (setcar (cdr p) (nth 2 (nth 1 p)))) |
| 1476 | (setq p (cdr p))) |
| 1477 | (if (and (not (cdr (cdr a))) |
| 1478 | (eq (car-safe (nth 1 a)) 'intv) |
| 1479 | (not always-vec)) |
| 1480 | (nth 1 a) |
| 1481 | a))) |
| 1482 | |
| 1483 | (defun math-simple-set (a) |
| 1484 | (or (and (Math-objectp a) |
| 1485 | (not (eq (car-safe a) 'intv))) |
| 1486 | (and (Math-vectorp a) |
| 1487 | (progn |
| 1488 | (while (and (setq a (cdr a)) |
| 1489 | (not (eq (car-safe (car a)) 'intv)))) |
| 1490 | (null a))))) |
| 1491 | |
| 1492 | |
| 1493 | |
| 1494 | |
| 1495 | ;;; Compute a right-handed vector cross product. [O O O] [Public] |
| 1496 | (defun calcFunc-cross (a b) |
| 1497 | (if (and (eq (car-safe a) 'vec) |
| 1498 | (= (length a) 4)) |
| 1499 | (if (and (eq (car-safe b) 'vec) |
| 1500 | (= (length b) 4)) |
| 1501 | (list 'vec |
| 1502 | (math-sub (math-mul (nth 2 a) (nth 3 b)) |
| 1503 | (math-mul (nth 3 a) (nth 2 b))) |
| 1504 | (math-sub (math-mul (nth 3 a) (nth 1 b)) |
| 1505 | (math-mul (nth 1 a) (nth 3 b))) |
| 1506 | (math-sub (math-mul (nth 1 a) (nth 2 b)) |
| 1507 | (math-mul (nth 2 a) (nth 1 b)))) |
| 1508 | (math-reject-arg b "*Three-vector expected")) |
| 1509 | (math-reject-arg a "*Three-vector expected"))) |
| 1510 | |
| 1511 | |
| 1512 | ;;; Compute a Kronecker product |
| 1513 | (defun calcFunc-kron (x y &optional nocheck) |
| 1514 | "The Kronecker product of objects X and Y. |
| 1515 | The objects X and Y may be scalars, vectors or matrices. |
| 1516 | The type of the result depends on the types of the operands; |
| 1517 | the product of two scalars is a scalar, |
| 1518 | of one scalar and a vector is a vector, |
| 1519 | of two vectors is a vector. |
| 1520 | of one vector and a matrix is a matrix, |
| 1521 | of two matrices is a matrix." |
| 1522 | (unless nocheck |
| 1523 | (cond ((or (math-matrixp x) |
| 1524 | (math-matrixp y)) |
| 1525 | (unless (math-matrixp x) |
| 1526 | (setq x (if (math-vectorp x) |
| 1527 | (list 'vec x) |
| 1528 | (list 'vec (list 'vec x))))) |
| 1529 | (unless (math-matrixp y) |
| 1530 | (setq y (if (math-vectorp y) |
| 1531 | (list 'vec y) |
| 1532 | (list 'vec (list 'vec y)))))) |
| 1533 | ((or (math-vectorp x) |
| 1534 | (math-vectorp y)) |
| 1535 | (unless (math-vectorp x) |
| 1536 | (setq x (list 'vec x))) |
| 1537 | (unless (math-vectorp y) |
| 1538 | (setq y (list 'vec y)))))) |
| 1539 | (if (math-vectorp x) |
| 1540 | (let (ret) |
| 1541 | (dolist (v (cdr x)) |
| 1542 | (dolist (w (cdr y)) |
| 1543 | (setq ret (cons (calcFunc-kron v w t) ret)))) |
| 1544 | (cons 'vec (nreverse ret))) |
| 1545 | (math-mul x y))) |
| 1546 | |
| 1547 | |
| 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) |
| 1552 | |
| 1553 | ;; The next few variables are local to math-read-exprs in calc-aent.el |
| 1554 | ;; and math-read-expr in calc-ext.el, but are set in functions they call. |
| 1555 | (defvar math-exp-pos) |
| 1556 | (defvar math-exp-str) |
| 1557 | (defvar math-exp-old-pos) |
| 1558 | (defvar math-exp-token) |
| 1559 | (defvar math-exp-keep-spaces) |
| 1560 | (defvar math-expr-data) |
| 1561 | |
| 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))) |
| 1631 | |
| 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 |
| 1645 | pos |
| 1646 | (and pos (= (aref math-exp-str pos) ?,))))) |
| 1647 | |
| 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))) |
| 1667 | |
| 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) |
| 1675 | |
| 1676 | (provide 'calc-vec) |
| 1677 | |
| 1678 | ;; arch-tag: 7902a7af-ec69-440a-8635-ebb4db263402 |
| 1679 | ;;; calc-vec.el ends here |