| 1 | ;;; calc-stat.el --- statistical 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 | ;;; Statistical operations on vectors. |
| 33 | |
| 34 | (defun calc-vector-count (arg) |
| 35 | (interactive "P") |
| 36 | (calc-slow-wrapper |
| 37 | (calc-vector-op "coun" 'calcFunc-vcount arg))) |
| 38 | |
| 39 | (defun calc-vector-sum (arg) |
| 40 | (interactive "P") |
| 41 | (calc-slow-wrapper |
| 42 | (if (calc-is-hyperbolic) |
| 43 | (calc-vector-op "vprd" 'calcFunc-vprod arg) |
| 44 | (calc-vector-op "vsum" 'calcFunc-vsum arg)))) |
| 45 | |
| 46 | (defun calc-vector-product (arg) |
| 47 | (interactive "P") |
| 48 | (calc-hyperbolic-func) |
| 49 | (calc-vector-sum arg)) |
| 50 | |
| 51 | (defun calc-vector-max (arg) |
| 52 | (interactive "P") |
| 53 | (calc-slow-wrapper |
| 54 | (if (calc-is-inverse) |
| 55 | (calc-vector-op "vmin" 'calcFunc-vmin arg) |
| 56 | (calc-vector-op "vmax" 'calcFunc-vmax arg)))) |
| 57 | |
| 58 | (defun calc-vector-min (arg) |
| 59 | (interactive "P") |
| 60 | (calc-invert-func) |
| 61 | (calc-vector-max arg)) |
| 62 | |
| 63 | (defun calc-vector-mean (arg) |
| 64 | (interactive "P") |
| 65 | (calc-slow-wrapper |
| 66 | (if (calc-is-hyperbolic) |
| 67 | (if (calc-is-inverse) |
| 68 | (calc-vector-op "harm" 'calcFunc-vhmean arg) |
| 69 | (calc-vector-op "medn" 'calcFunc-vmedian arg)) |
| 70 | (if (calc-is-inverse) |
| 71 | (calc-vector-op "meae" 'calcFunc-vmeane arg) |
| 72 | (calc-vector-op "mean" 'calcFunc-vmean arg))))) |
| 73 | |
| 74 | (defun calc-vector-mean-error (arg) |
| 75 | (interactive "P") |
| 76 | (calc-invert-func) |
| 77 | (calc-vector-mean arg)) |
| 78 | |
| 79 | (defun calc-vector-median (arg) |
| 80 | (interactive "P") |
| 81 | (calc-hyperbolic-func) |
| 82 | (calc-vector-mean arg)) |
| 83 | |
| 84 | (defun calc-vector-harmonic-mean (arg) |
| 85 | (interactive "P") |
| 86 | (calc-invert-func) |
| 87 | (calc-hyperbolic-func) |
| 88 | (calc-vector-mean arg)) |
| 89 | |
| 90 | (defun calc-vector-geometric-mean (arg) |
| 91 | (interactive "P") |
| 92 | (calc-slow-wrapper |
| 93 | (if (calc-is-hyperbolic) |
| 94 | (calc-binary-op "geom" 'calcFunc-agmean arg) |
| 95 | (calc-vector-op "geom" 'calcFunc-vgmean arg)))) |
| 96 | |
| 97 | (defun calc-vector-sdev (arg) |
| 98 | (interactive "P") |
| 99 | (calc-slow-wrapper |
| 100 | (if (calc-is-hyperbolic) |
| 101 | (if (calc-is-inverse) |
| 102 | (calc-vector-op "pvar" 'calcFunc-vpvar arg) |
| 103 | (calc-vector-op "var" 'calcFunc-vvar arg)) |
| 104 | (if (calc-is-inverse) |
| 105 | (calc-vector-op "psdv" 'calcFunc-vpsdev arg) |
| 106 | (calc-vector-op "sdev" 'calcFunc-vsdev arg))))) |
| 107 | |
| 108 | (defun calc-vector-pop-sdev (arg) |
| 109 | (interactive "P") |
| 110 | (calc-invert-func) |
| 111 | (calc-vector-sdev arg)) |
| 112 | |
| 113 | (defun calc-vector-variance (arg) |
| 114 | (interactive "P") |
| 115 | (calc-hyperbolic-func) |
| 116 | (calc-vector-sdev arg)) |
| 117 | |
| 118 | (defun calc-vector-pop-variance (arg) |
| 119 | (interactive "P") |
| 120 | (calc-invert-func) |
| 121 | (calc-hyperbolic-func) |
| 122 | (calc-vector-sdev arg)) |
| 123 | |
| 124 | (defun calc-vector-covariance (arg) |
| 125 | (interactive "P") |
| 126 | (calc-slow-wrapper |
| 127 | (let ((n (if (eq arg 1) 1 2))) |
| 128 | (if (calc-is-hyperbolic) |
| 129 | (calc-enter-result n "corr" (cons 'calcFunc-vcorr |
| 130 | (calc-top-list-n n))) |
| 131 | (if (calc-is-inverse) |
| 132 | (calc-enter-result n "pcov" (cons 'calcFunc-vpcov |
| 133 | (calc-top-list-n n))) |
| 134 | (calc-enter-result n "cov" (cons 'calcFunc-vcov |
| 135 | (calc-top-list-n n)))))))) |
| 136 | |
| 137 | (defun calc-vector-pop-covariance (arg) |
| 138 | (interactive "P") |
| 139 | (calc-invert-func) |
| 140 | (calc-vector-covariance arg)) |
| 141 | |
| 142 | (defun calc-vector-correlation (arg) |
| 143 | (interactive "P") |
| 144 | (calc-hyperbolic-func) |
| 145 | (calc-vector-covariance arg)) |
| 146 | |
| 147 | (defun calc-vector-op (name func arg) |
| 148 | (setq calc-aborted-prefix name |
| 149 | arg (prefix-numeric-value arg)) |
| 150 | (if (< arg 0) |
| 151 | (error "Negative arguments not allowed")) |
| 152 | (calc-enter-result arg name (cons func (calc-top-list-n arg)))) |
| 153 | |
| 154 | |
| 155 | |
| 156 | |
| 157 | ;;; Useful statistical functions |
| 158 | |
| 159 | ;;; Sum, product, etc., of one or more values or vectors. |
| 160 | ;;; Each argument must be either a number or a vector. Vectors |
| 161 | ;;; are flattened, but variables inside are assumed to represent |
| 162 | ;;; non-vectors. |
| 163 | |
| 164 | (defun calcFunc-vsum (&rest vecs) |
| 165 | (math-reduce-many-vecs 'calcFunc-add 'calcFunc-vsum vecs 0)) |
| 166 | |
| 167 | (defun calcFunc-vprod (&rest vecs) |
| 168 | (math-reduce-many-vecs 'calcFunc-mul 'calcFunc-vprod vecs 1)) |
| 169 | |
| 170 | (defun calcFunc-vmax (&rest vecs) |
| 171 | (if (eq (car-safe (car vecs)) 'sdev) |
| 172 | '(var inf var-inf) |
| 173 | (if (eq (car-safe (car vecs)) 'intv) |
| 174 | (nth 3 (math-fix-int-intv (car vecs))) |
| 175 | (math-reduce-many-vecs 'calcFunc-max 'calcFunc-vmax vecs |
| 176 | '(neg (var inf var-inf)))))) |
| 177 | |
| 178 | (defun calcFunc-vmin (&rest vecs) |
| 179 | (if (eq (car-safe (car vecs)) 'sdev) |
| 180 | '(neg (var inf var-inf)) |
| 181 | (if (eq (car-safe (car vecs)) 'intv) |
| 182 | (nth 2 (math-fix-int-intv (car vecs))) |
| 183 | (math-reduce-many-vecs 'calcFunc-min 'calcFunc-vmin vecs |
| 184 | '(var inf var-inf))))) |
| 185 | |
| 186 | (defun math-reduce-many-vecs (func whole-func vecs ident) |
| 187 | (let ((const-part nil) |
| 188 | (symb-part nil) |
| 189 | val vec) |
| 190 | (let ((calc-internal-prec (+ calc-internal-prec 2))) |
| 191 | (while vecs |
| 192 | (setq val (car vecs)) |
| 193 | (and (eq (car-safe val) 'var) |
| 194 | (eq (car-safe (calc-var-value (nth 2 val))) 'vec) |
| 195 | (setq val (symbol-value (nth 2 val)))) |
| 196 | (cond ((Math-vectorp val) |
| 197 | (setq vec (append (and const-part (list const-part)) |
| 198 | (math-flatten-vector val))) |
| 199 | (setq const-part (if vec |
| 200 | (calcFunc-reducer |
| 201 | (math-calcFunc-to-var func) |
| 202 | (cons 'vec vec)) |
| 203 | ident))) |
| 204 | ((or (Math-objectp val) (math-infinitep val)) |
| 205 | (setq const-part (if const-part |
| 206 | (funcall func const-part val) |
| 207 | val))) |
| 208 | (t |
| 209 | (setq symb-part (nconc symb-part (list val))))) |
| 210 | (setq vecs (cdr vecs)))) |
| 211 | (if const-part |
| 212 | (progn |
| 213 | (setq const-part (math-normalize const-part)) |
| 214 | (if symb-part |
| 215 | (funcall func const-part (cons whole-func symb-part)) |
| 216 | const-part)) |
| 217 | (if symb-part (cons whole-func symb-part) ident)))) |
| 218 | |
| 219 | |
| 220 | ;;; Return the number of data elements among the arguments. |
| 221 | (defun calcFunc-vcount (&rest vecs) |
| 222 | (let ((count 0)) |
| 223 | (while vecs |
| 224 | (setq count (if (Math-vectorp (car vecs)) |
| 225 | (+ count (math-count-elements (car vecs))) |
| 226 | (if (Math-objectp (car vecs)) |
| 227 | (1+ count) |
| 228 | (if (and (eq (car-safe (car vecs)) 'var) |
| 229 | (eq (car-safe (calc-var-value |
| 230 | (nth 2 (car vecs)))) |
| 231 | 'vec)) |
| 232 | (+ count (math-count-elements |
| 233 | (symbol-value (nth 2 (car vecs))))) |
| 234 | (math-reject-arg (car vecs) 'numvecp)))) |
| 235 | vecs (cdr vecs))) |
| 236 | count)) |
| 237 | |
| 238 | (defun math-count-elements (vec) |
| 239 | (let ((count 0)) |
| 240 | (while (setq vec (cdr vec)) |
| 241 | (setq count (if (Math-vectorp (car vec)) |
| 242 | (+ count (math-count-elements (car vec))) |
| 243 | (1+ count)))) |
| 244 | count)) |
| 245 | |
| 246 | |
| 247 | (defun math-flatten-many-vecs (vecs) |
| 248 | (let ((p vecs) |
| 249 | (vec (list 'vec))) |
| 250 | (while p |
| 251 | (setq vec (nconc vec |
| 252 | (if (Math-vectorp (car p)) |
| 253 | (math-flatten-vector (car p)) |
| 254 | (if (Math-objectp (car p)) |
| 255 | (list (car p)) |
| 256 | (if (and (eq (car-safe (car p)) 'var) |
| 257 | (eq (car-safe (calc-var-value |
| 258 | (nth 2 (car p)))) 'vec)) |
| 259 | (math-flatten-vector (symbol-value |
| 260 | (nth 2 (car p)))) |
| 261 | (math-reject-arg (car p) 'numvecp))))) |
| 262 | p (cdr p))) |
| 263 | vec)) |
| 264 | |
| 265 | (defun calcFunc-vflat (&rest vecs) |
| 266 | (math-flatten-many-vecs vecs)) |
| 267 | |
| 268 | (defun math-split-sdev-vec (vec zero-ok) |
| 269 | (let ((means (list 'vec)) |
| 270 | (wts (list 'vec)) |
| 271 | (exact nil) |
| 272 | (p vec)) |
| 273 | (while (and (setq p (cdr p)) |
| 274 | (not (and (consp (car p)) |
| 275 | (eq (car (car p)) 'sdev))))) |
| 276 | (if (null p) |
| 277 | (list vec nil) |
| 278 | (while (setq vec (cdr vec)) |
| 279 | (if (and (consp (setq p (car vec))) |
| 280 | (eq (car p) 'sdev)) |
| 281 | (or exact |
| 282 | (setq means (cons (nth 1 p) means) |
| 283 | wts (cons (nth 2 p) wts))) |
| 284 | (if zero-ok |
| 285 | (setq means (cons (nth 1 p) means) |
| 286 | wts (cons 0 wts)) |
| 287 | (or exact |
| 288 | (setq means (list 'vec) |
| 289 | wts nil |
| 290 | exact t)) |
| 291 | (setq means (cons p means))))) |
| 292 | (list (nreverse means) |
| 293 | (and wts (nreverse wts)))))) |
| 294 | |
| 295 | |
| 296 | ;;; Return the arithmetic mean of the argument numbers or vectors. |
| 297 | ;;; (If numbers are error forms, computes the weighted mean.) |
| 298 | (defun calcFunc-vmean (&rest vecs) |
| 299 | (let* ((split (math-split-sdev-vec (math-flatten-many-vecs vecs) nil)) |
| 300 | (means (car split)) |
| 301 | (wts (nth 1 split)) |
| 302 | (len (1- (length means)))) |
| 303 | (if (= len 0) |
| 304 | (math-reject-arg nil "*Must be at least 1 argument") |
| 305 | (if (and (= len 1) (eq (car-safe (nth 1 means)) 'intv)) |
| 306 | (let ((x (math-fix-int-intv (nth 1 means)))) |
| 307 | (calcFunc-vmean (nth 2 x) (nth 3 x))) |
| 308 | (math-with-extra-prec 2 |
| 309 | (if (and wts (> len 1)) |
| 310 | (let* ((sqrwts (calcFunc-map '(var mul var-mul) wts wts)) |
| 311 | (suminvsqrwts (calcFunc-reduce |
| 312 | '(var add var-add) |
| 313 | (calcFunc-map '(var div var-div) |
| 314 | 1 sqrwts)))) |
| 315 | (math-div (calcFunc-reduce '(var add var-add) |
| 316 | (calcFunc-map '(var div var-div) |
| 317 | means sqrwts)) |
| 318 | suminvsqrwts)) |
| 319 | (math-div (calcFunc-reduce '(var add var-add) means) len))))))) |
| 320 | |
| 321 | (defun math-fix-int-intv (x) |
| 322 | (if (math-floatp x) |
| 323 | x |
| 324 | (list 'intv 3 |
| 325 | (if (memq (nth 1 x) '(2 3)) (nth 2 x) (math-add (nth 2 x) 1)) |
| 326 | (if (memq (nth 1 x) '(1 3)) (nth 3 x) (math-sub (nth 3 x) 1))))) |
| 327 | |
| 328 | ;;; Compute the mean with an error estimate. |
| 329 | (defun calcFunc-vmeane (&rest vecs) |
| 330 | (let* ((split (math-split-sdev-vec (math-flatten-many-vecs vecs) nil)) |
| 331 | (means (car split)) |
| 332 | (wts (nth 1 split)) |
| 333 | (len (1- (length means)))) |
| 334 | (if (= len 0) |
| 335 | (math-reject-arg nil "*Must be at least 1 argument") |
| 336 | (math-with-extra-prec 2 |
| 337 | (if wts |
| 338 | (let* ((sqrwts (calcFunc-map '(var mul var-mul) wts wts)) |
| 339 | (suminvsqrwts (calcFunc-reduce |
| 340 | '(var add var-add) |
| 341 | (calcFunc-map '(var div var-div) |
| 342 | 1 sqrwts)))) |
| 343 | (math-make-sdev |
| 344 | (math-div (calcFunc-reduce '(var add var-add) |
| 345 | (calcFunc-map '(var div var-div) |
| 346 | means sqrwts)) |
| 347 | suminvsqrwts) |
| 348 | (list 'calcFunc-sqrt (math-div 1 suminvsqrwts)))) |
| 349 | (let ((mean (math-div (calcFunc-reduce '(var add var-add) means) |
| 350 | len))) |
| 351 | (math-make-sdev |
| 352 | mean |
| 353 | (list 'calcFunc-sqrt |
| 354 | (math-div (calcFunc-reducer |
| 355 | '(var add var-add) |
| 356 | (calcFunc-map '(var pow var-pow) |
| 357 | (calcFunc-map '(var abs var-abs) |
| 358 | (calcFunc-map |
| 359 | '(var add var-add) |
| 360 | means |
| 361 | (math-neg mean))) |
| 362 | 2)) |
| 363 | (math-mul len (1- len))))))))))) |
| 364 | |
| 365 | |
| 366 | ;;; Compute the median of a list of values. |
| 367 | (defun calcFunc-vmedian (&rest vecs) |
| 368 | (let* ((flat (copy-sequence (cdr (math-flatten-many-vecs vecs)))) |
| 369 | (p flat) |
| 370 | (len (length flat)) |
| 371 | (hlen (/ len 2))) |
| 372 | (if (= len 0) |
| 373 | (math-reject-arg nil "*Must be at least 1 argument") |
| 374 | (if (and (= len 1) (memq (car-safe (car flat)) '(sdev intv))) |
| 375 | (calcFunc-vmean (car flat)) |
| 376 | (while p |
| 377 | (if (eq (car-safe (car p)) 'sdev) |
| 378 | (setcar p (nth 1 (car p)))) |
| 379 | (or (Math-anglep (car p)) |
| 380 | (math-reject-arg (car p) 'anglep)) |
| 381 | (setq p (cdr p))) |
| 382 | (setq flat (sort flat 'math-lessp)) |
| 383 | (if (= (% len 2) 0) |
| 384 | (math-div (math-add (nth (1- hlen) flat) (nth hlen flat)) 2) |
| 385 | (nth hlen flat)))))) |
| 386 | |
| 387 | |
| 388 | (defun calcFunc-vgmean (&rest vecs) |
| 389 | (let* ((flat (math-flatten-many-vecs vecs)) |
| 390 | (len (1- (length flat)))) |
| 391 | (if (= len 0) |
| 392 | (math-reject-arg nil "*Must be at least 1 argument") |
| 393 | (math-with-extra-prec 2 |
| 394 | (let ((x (calcFunc-reduce '(var mul math-mul) flat))) |
| 395 | (if (= len 2) |
| 396 | (math-sqrt x) |
| 397 | (math-pow x (list 'frac 1 len)))))))) |
| 398 | |
| 399 | |
| 400 | (defun calcFunc-agmean (a b) |
| 401 | (cond ((Math-equal a b) a) |
| 402 | ((math-zerop a) a) |
| 403 | ((math-zerop b) b) |
| 404 | (calc-symbolic-mode (math-inexact-result)) |
| 405 | ((not (Math-realp a)) (math-reject-arg a 'realp)) |
| 406 | ((not (Math-realp b)) (math-reject-arg b 'realp)) |
| 407 | (t |
| 408 | (math-with-extra-prec 2 |
| 409 | (setq a (math-float (math-abs a)) |
| 410 | b (math-float (math-abs b))) |
| 411 | (let (mean) |
| 412 | (while (not (math-nearly-equal-float a b)) |
| 413 | (setq mean (math-mul-float (math-add-float a b) '(float 5 -1)) |
| 414 | b (math-sqrt-float (math-mul-float a b)) |
| 415 | a mean)) |
| 416 | a))))) |
| 417 | |
| 418 | |
| 419 | (defun calcFunc-vhmean (&rest vecs) |
| 420 | (let* ((flat (math-flatten-many-vecs vecs)) |
| 421 | (len (1- (length flat)))) |
| 422 | (if (= len 0) |
| 423 | (math-reject-arg nil "*Must be at least 1 argument") |
| 424 | (math-with-extra-prec 2 |
| 425 | (math-div len |
| 426 | (calcFunc-reduce '(var add math-add) |
| 427 | (calcFunc-map '(var inv var-inv) flat))))))) |
| 428 | |
| 429 | |
| 430 | |
| 431 | ;;; Compute the sample variance or standard deviation of numbers or vectors. |
| 432 | ;;; (If the numbers are error forms, only the mean part of them is used.) |
| 433 | (defun calcFunc-vvar (&rest vecs) |
| 434 | (if (and (= (length vecs) 1) |
| 435 | (memq (car-safe (car vecs)) '(sdev intv))) |
| 436 | (if (eq (car-safe (car vecs)) 'intv) |
| 437 | (math-intv-variance (car vecs) nil) |
| 438 | (math-sqr (nth 2 (car vecs)))) |
| 439 | (math-covariance vecs nil nil 0))) |
| 440 | |
| 441 | (defun calcFunc-vsdev (&rest vecs) |
| 442 | (if (and (= (length vecs) 1) |
| 443 | (memq (car-safe (car vecs)) '(sdev intv))) |
| 444 | (if (eq (car-safe (car vecs)) 'intv) |
| 445 | (if (math-floatp (car vecs)) |
| 446 | (math-div (math-sub (nth 3 (car vecs)) (nth 2 (car vecs))) |
| 447 | (math-sqrt-12)) |
| 448 | (math-sqrt (calcFunc-vvar (car vecs)))) |
| 449 | (nth 2 (car vecs))) |
| 450 | (math-sqrt (math-covariance vecs nil nil 0)))) |
| 451 | |
| 452 | ;;; Compute the population variance or std deviation of numbers or vectors. |
| 453 | (defun calcFunc-vpvar (&rest vecs) |
| 454 | (if (and (= (length vecs) 1) |
| 455 | (memq (car-safe (car vecs)) '(sdev intv))) |
| 456 | (if (eq (car-safe (car vecs)) 'intv) |
| 457 | (math-intv-variance (car vecs) t) |
| 458 | (math-sqr (nth 2 (car vecs)))) |
| 459 | (math-covariance vecs nil t 0))) |
| 460 | |
| 461 | (defun calcFunc-vpsdev (&rest vecs) |
| 462 | (if (and (= (length vecs) 1) |
| 463 | (memq (car-safe (car vecs)) '(sdev intv))) |
| 464 | (if (eq (car-safe (car vecs)) 'intv) |
| 465 | (if (math-floatp (car vecs)) |
| 466 | (math-div (math-sub (nth 3 (car vecs)) (nth 2 (car vecs))) |
| 467 | (math-sqrt-12)) |
| 468 | (math-sqrt (calcFunc-vpvar (car vecs)))) |
| 469 | (nth 2 (car vecs))) |
| 470 | (math-sqrt (math-covariance vecs nil t 0)))) |
| 471 | |
| 472 | (defun math-intv-variance (x pop) |
| 473 | (or (math-constp x) (math-reject-arg x 'constp)) |
| 474 | (if (math-floatp x) |
| 475 | (math-div (math-sqr (math-sub (nth 3 x) (nth 2 x))) 12) |
| 476 | (let* ((x (math-fix-int-intv x)) |
| 477 | (len (math-sub (nth 3 x) (nth 2 x))) |
| 478 | (hlen (math-quotient len 2))) |
| 479 | (math-div (if (math-evenp len) |
| 480 | (calcFunc-sum '(^ (var X var-X) 2) '(var X var-X) |
| 481 | (math-neg hlen) hlen) |
| 482 | (calcFunc-sum '(^ (- (var X var-X) (/ 1 2)) 2) |
| 483 | '(var X var-X) |
| 484 | (math-neg hlen) (math-add hlen 1))) |
| 485 | (if pop (math-add len 1) len))))) |
| 486 | |
| 487 | ;;; Compute the covariance and linear correlation coefficient. |
| 488 | (defun calcFunc-vcov (vec1 &optional vec2) |
| 489 | (math-covariance (list vec1) (list vec2) nil 1)) |
| 490 | |
| 491 | (defun calcFunc-vpcov (vec1 &optional vec2) |
| 492 | (math-covariance (list vec1) (list vec2) t 1)) |
| 493 | |
| 494 | (defun calcFunc-vcorr (vec1 &optional vec2) |
| 495 | (math-covariance (list vec1) (list vec2) nil 2)) |
| 496 | |
| 497 | |
| 498 | (defun math-covariance (vec1 vec2 pop mode) |
| 499 | (or (car vec2) (= mode 0) |
| 500 | (progn |
| 501 | (if (and (eq (car-safe (car vec1)) 'var) |
| 502 | (eq (car-safe (calc-var-value (nth 2 (car vec1)))) 'vec)) |
| 503 | (setq vec1 (symbol-value (nth 2 (car vec1)))) |
| 504 | (setq vec1 (car vec1))) |
| 505 | (or (math-matrixp vec1) (math-dimension-error)) |
| 506 | (or (= (length (nth 1 vec1)) 3) (math-dimension-error)) |
| 507 | (setq vec2 (list (math-mat-col vec1 2)) |
| 508 | vec1 (list (math-mat-col vec1 1))))) |
| 509 | (math-with-extra-prec 2 |
| 510 | (let* ((split1 (math-split-sdev-vec (math-flatten-many-vecs vec1) nil)) |
| 511 | (means1 (car split1)) |
| 512 | (wts1 (nth 1 split1)) |
| 513 | split2 means2 (wts2 nil) |
| 514 | (sqrwts nil) |
| 515 | suminvsqrwts |
| 516 | (len (1- (length means1)))) |
| 517 | (if (< len (if pop 1 2)) |
| 518 | (math-reject-arg nil (if pop |
| 519 | "*Must be at least 1 argument" |
| 520 | "*Must be at least 2 arguments"))) |
| 521 | (if (or wts1 wts2) |
| 522 | (setq sqrwts (math-add |
| 523 | (if wts1 |
| 524 | (calcFunc-map '(var mul var-mul) wts1 wts1) |
| 525 | 0) |
| 526 | (if wts2 |
| 527 | (calcFunc-map '(var mul var-mul) wts2 wts2) |
| 528 | 0)) |
| 529 | suminvsqrwts (calcFunc-reduce |
| 530 | '(var add var-add) |
| 531 | (calcFunc-map '(var div var-div) 1 sqrwts)))) |
| 532 | (or (= mode 0) |
| 533 | (progn |
| 534 | (setq split2 (math-split-sdev-vec (math-flatten-many-vecs vec2) |
| 535 | nil) |
| 536 | means2 (car split2) |
| 537 | wts2 (nth 2 split1)) |
| 538 | (or (= len (1- (length means2))) (math-dimension-error)))) |
| 539 | (let* ((diff1 (calcFunc-map |
| 540 | '(var add var-add) |
| 541 | means1 |
| 542 | (if sqrwts |
| 543 | (math-div (calcFunc-reduce |
| 544 | '(var add var-add) |
| 545 | (calcFunc-map '(var div var-div) |
| 546 | means1 sqrwts)) |
| 547 | (math-neg suminvsqrwts)) |
| 548 | (math-div (calcFunc-reducer '(var add var-add) means1) |
| 549 | (- len))))) |
| 550 | (diff2 (if (= mode 0) |
| 551 | diff1 |
| 552 | (calcFunc-map |
| 553 | '(var add var-add) |
| 554 | means2 |
| 555 | (if sqrwts |
| 556 | (math-div (calcFunc-reduce |
| 557 | '(var add var-add) |
| 558 | (calcFunc-map '(var div var-div) |
| 559 | means2 sqrwts)) |
| 560 | (math-neg suminvsqrwts)) |
| 561 | (math-div (calcFunc-reducer '(var add var-add) means2) |
| 562 | (- len)))))) |
| 563 | (covar (calcFunc-map '(var mul var-mul) diff1 diff2))) |
| 564 | (if sqrwts |
| 565 | (setq covar (calcFunc-map '(var div var-div) covar sqrwts))) |
| 566 | (math-div |
| 567 | (calcFunc-reducer '(var add var-add) covar) |
| 568 | (if (= mode 2) |
| 569 | (let ((var1 (calcFunc-map '(var mul var-mul) diff1 diff1)) |
| 570 | (var2 (calcFunc-map '(var mul var-mul) diff2 diff2))) |
| 571 | (if sqrwts |
| 572 | (setq var1 (calcFunc-map '(var div var-div) var1 sqrwts) |
| 573 | var2 (calcFunc-map '(var div var-div) var2 sqrwts))) |
| 574 | (math-sqrt |
| 575 | (math-mul (calcFunc-reducer '(var add var-add) var1) |
| 576 | (calcFunc-reducer '(var add var-add) var2)))) |
| 577 | (if sqrwts |
| 578 | (if pop |
| 579 | suminvsqrwts |
| 580 | (math-div (math-mul suminvsqrwts (1- len)) len)) |
| 581 | (if pop len (1- len))))))))) |
| 582 | |
| 583 | (provide 'calc-stat) |
| 584 | |
| 585 | ;;; calc-stat.el ends here |