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3132f345 CW |
1 | ;;; calc-stat.el --- statistical functions for Calc |
2 | ||
bf77c646 | 3 | ;; Copyright (C) 1990, 1991, 1992, 1993, 2001 Free Software Foundation, Inc. |
3132f345 CW |
4 | |
5 | ;; Author: David Gillespie <daveg@synaptics.com> | |
a1506d29 | 6 | ;; Maintainers: D. Goel <deego@gnufans.org> |
6e1c888a | 7 | ;; Colin Walters <walters@debian.org> |
136211a9 EZ |
8 | |
9 | ;; This file is part of GNU Emacs. | |
10 | ||
11 | ;; GNU Emacs is distributed in the hope that it will be useful, | |
12 | ;; but WITHOUT ANY WARRANTY. No author or distributor | |
13 | ;; accepts responsibility to anyone for the consequences of using it | |
14 | ;; or for whether it serves any particular purpose or works at all, | |
15 | ;; unless he says so in writing. Refer to the GNU Emacs General Public | |
16 | ;; License for full details. | |
17 | ||
18 | ;; Everyone is granted permission to copy, modify and redistribute | |
19 | ;; GNU Emacs, but only under the conditions described in the | |
20 | ;; GNU Emacs General Public License. A copy of this license is | |
21 | ;; supposed to have been given to you along with GNU Emacs so you | |
22 | ;; can know your rights and responsibilities. It should be in a | |
23 | ;; file named COPYING. Among other things, the copyright notice | |
24 | ;; and this notice must be preserved on all copies. | |
25 | ||
3132f345 | 26 | ;;; Commentary: |
136211a9 | 27 | |
3132f345 | 28 | ;;; Code: |
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29 | |
30 | ;; This file is autoloaded from calc-ext.el. | |
31 | (require 'calc-ext) | |
32 | ||
33 | (require 'calc-macs) | |
34 | ||
35 | (defun calc-Need-calc-stat () nil) | |
36 | ||
37 | ||
38 | ;;; Statistical operations on vectors. | |
39 | ||
40 | (defun calc-vector-count (arg) | |
41 | (interactive "P") | |
42 | (calc-slow-wrapper | |
bf77c646 | 43 | (calc-vector-op "coun" 'calcFunc-vcount arg))) |
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44 | |
45 | (defun calc-vector-sum (arg) | |
46 | (interactive "P") | |
47 | (calc-slow-wrapper | |
48 | (if (calc-is-hyperbolic) | |
49 | (calc-vector-op "vprd" 'calcFunc-vprod arg) | |
bf77c646 | 50 | (calc-vector-op "vsum" 'calcFunc-vsum arg)))) |
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51 | |
52 | (defun calc-vector-product (arg) | |
53 | (interactive "P") | |
54 | (calc-hyperbolic-func) | |
bf77c646 | 55 | (calc-vector-sum arg)) |
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56 | |
57 | (defun calc-vector-max (arg) | |
58 | (interactive "P") | |
59 | (calc-slow-wrapper | |
60 | (if (calc-is-inverse) | |
61 | (calc-vector-op "vmin" 'calcFunc-vmin arg) | |
bf77c646 | 62 | (calc-vector-op "vmax" 'calcFunc-vmax arg)))) |
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63 | |
64 | (defun calc-vector-min (arg) | |
65 | (interactive "P") | |
66 | (calc-invert-func) | |
bf77c646 | 67 | (calc-vector-max arg)) |
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68 | |
69 | (defun calc-vector-mean (arg) | |
70 | (interactive "P") | |
71 | (calc-slow-wrapper | |
72 | (if (calc-is-hyperbolic) | |
73 | (if (calc-is-inverse) | |
74 | (calc-vector-op "harm" 'calcFunc-vhmean arg) | |
75 | (calc-vector-op "medn" 'calcFunc-vmedian arg)) | |
76 | (if (calc-is-inverse) | |
77 | (calc-vector-op "meae" 'calcFunc-vmeane arg) | |
bf77c646 | 78 | (calc-vector-op "mean" 'calcFunc-vmean arg))))) |
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79 | |
80 | (defun calc-vector-mean-error (arg) | |
81 | (interactive "P") | |
82 | (calc-invert-func) | |
bf77c646 | 83 | (calc-vector-mean arg)) |
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84 | |
85 | (defun calc-vector-median (arg) | |
86 | (interactive "P") | |
87 | (calc-hyperbolic-func) | |
bf77c646 | 88 | (calc-vector-mean arg)) |
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89 | |
90 | (defun calc-vector-harmonic-mean (arg) | |
91 | (interactive "P") | |
92 | (calc-invert-func) | |
93 | (calc-hyperbolic-func) | |
bf77c646 | 94 | (calc-vector-mean arg)) |
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95 | |
96 | (defun calc-vector-geometric-mean (arg) | |
97 | (interactive "P") | |
98 | (calc-slow-wrapper | |
99 | (if (calc-is-hyperbolic) | |
100 | (calc-binary-op "geom" 'calcFunc-agmean arg) | |
bf77c646 | 101 | (calc-vector-op "geom" 'calcFunc-vgmean arg)))) |
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102 | |
103 | (defun calc-vector-sdev (arg) | |
104 | (interactive "P") | |
105 | (calc-slow-wrapper | |
106 | (if (calc-is-hyperbolic) | |
107 | (if (calc-is-inverse) | |
108 | (calc-vector-op "pvar" 'calcFunc-vpvar arg) | |
109 | (calc-vector-op "var" 'calcFunc-vvar arg)) | |
110 | (if (calc-is-inverse) | |
111 | (calc-vector-op "psdv" 'calcFunc-vpsdev arg) | |
bf77c646 | 112 | (calc-vector-op "sdev" 'calcFunc-vsdev arg))))) |
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113 | |
114 | (defun calc-vector-pop-sdev (arg) | |
115 | (interactive "P") | |
116 | (calc-invert-func) | |
bf77c646 | 117 | (calc-vector-sdev arg)) |
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118 | |
119 | (defun calc-vector-variance (arg) | |
120 | (interactive "P") | |
121 | (calc-hyperbolic-func) | |
bf77c646 | 122 | (calc-vector-sdev arg)) |
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123 | |
124 | (defun calc-vector-pop-variance (arg) | |
125 | (interactive "P") | |
126 | (calc-invert-func) | |
127 | (calc-hyperbolic-func) | |
bf77c646 | 128 | (calc-vector-sdev arg)) |
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129 | |
130 | (defun calc-vector-covariance (arg) | |
131 | (interactive "P") | |
132 | (calc-slow-wrapper | |
133 | (let ((n (if (eq arg 1) 1 2))) | |
134 | (if (calc-is-hyperbolic) | |
135 | (calc-enter-result n "corr" (cons 'calcFunc-vcorr | |
136 | (calc-top-list-n n))) | |
137 | (if (calc-is-inverse) | |
138 | (calc-enter-result n "pcov" (cons 'calcFunc-vpcov | |
139 | (calc-top-list-n n))) | |
140 | (calc-enter-result n "cov" (cons 'calcFunc-vcov | |
bf77c646 | 141 | (calc-top-list-n n)))))))) |
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142 | |
143 | (defun calc-vector-pop-covariance (arg) | |
144 | (interactive "P") | |
145 | (calc-invert-func) | |
bf77c646 | 146 | (calc-vector-covariance arg)) |
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147 | |
148 | (defun calc-vector-correlation (arg) | |
149 | (interactive "P") | |
150 | (calc-hyperbolic-func) | |
bf77c646 | 151 | (calc-vector-covariance arg)) |
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152 | |
153 | (defun calc-vector-op (name func arg) | |
154 | (setq calc-aborted-prefix name | |
155 | arg (prefix-numeric-value arg)) | |
156 | (if (< arg 0) | |
157 | (error "Negative arguments not allowed")) | |
bf77c646 | 158 | (calc-enter-result arg name (cons func (calc-top-list-n arg)))) |
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159 | |
160 | ||
161 | ||
162 | ||
163 | ;;; Useful statistical functions | |
164 | ||
165 | ;;; Sum, product, etc., of one or more values or vectors. | |
166 | ;;; Each argument must be either a number or a vector. Vectors | |
167 | ;;; are flattened, but variables inside are assumed to represent | |
168 | ;;; non-vectors. | |
169 | ||
170 | (defun calcFunc-vsum (&rest vecs) | |
bf77c646 | 171 | (math-reduce-many-vecs 'calcFunc-add 'calcFunc-vsum vecs 0)) |
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172 | |
173 | (defun calcFunc-vprod (&rest vecs) | |
bf77c646 | 174 | (math-reduce-many-vecs 'calcFunc-mul 'calcFunc-vprod vecs 1)) |
136211a9 EZ |
175 | |
176 | (defun calcFunc-vmax (&rest vecs) | |
177 | (if (eq (car-safe (car vecs)) 'sdev) | |
178 | '(var inf var-inf) | |
179 | (if (eq (car-safe (car vecs)) 'intv) | |
180 | (nth 3 (math-fix-int-intv (car vecs))) | |
181 | (math-reduce-many-vecs 'calcFunc-max 'calcFunc-vmax vecs | |
bf77c646 | 182 | '(neg (var inf var-inf)))))) |
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183 | |
184 | (defun calcFunc-vmin (&rest vecs) | |
185 | (if (eq (car-safe (car vecs)) 'sdev) | |
186 | '(neg (var inf var-inf)) | |
187 | (if (eq (car-safe (car vecs)) 'intv) | |
188 | (nth 2 (math-fix-int-intv (car vecs))) | |
189 | (math-reduce-many-vecs 'calcFunc-min 'calcFunc-vmin vecs | |
bf77c646 | 190 | '(var inf var-inf))))) |
136211a9 EZ |
191 | |
192 | (defun math-reduce-many-vecs (func whole-func vecs ident) | |
193 | (let ((const-part nil) | |
194 | (symb-part nil) | |
195 | val vec) | |
196 | (let ((calc-internal-prec (+ calc-internal-prec 2))) | |
197 | (while vecs | |
198 | (setq val (car vecs)) | |
199 | (and (eq (car-safe val) 'var) | |
200 | (eq (car-safe (calc-var-value (nth 2 val))) 'vec) | |
201 | (setq val (symbol-value (nth 2 val)))) | |
202 | (cond ((Math-vectorp val) | |
203 | (setq vec (append (and const-part (list const-part)) | |
204 | (math-flatten-vector val))) | |
205 | (setq const-part (if vec | |
206 | (calcFunc-reducer | |
207 | (math-calcFunc-to-var func) | |
208 | (cons 'vec vec)) | |
209 | ident))) | |
210 | ((or (Math-objectp val) (math-infinitep val)) | |
211 | (setq const-part (if const-part | |
212 | (funcall func const-part val) | |
213 | val))) | |
214 | (t | |
215 | (setq symb-part (nconc symb-part (list val))))) | |
216 | (setq vecs (cdr vecs)))) | |
217 | (if const-part | |
218 | (progn | |
219 | (setq const-part (math-normalize const-part)) | |
220 | (if symb-part | |
221 | (funcall func const-part (cons whole-func symb-part)) | |
222 | const-part)) | |
bf77c646 | 223 | (if symb-part (cons whole-func symb-part) ident)))) |
136211a9 EZ |
224 | |
225 | ||
226 | ;;; Return the number of data elements among the arguments. | |
227 | (defun calcFunc-vcount (&rest vecs) | |
228 | (let ((count 0)) | |
229 | (while vecs | |
230 | (setq count (if (Math-vectorp (car vecs)) | |
231 | (+ count (math-count-elements (car vecs))) | |
232 | (if (Math-objectp (car vecs)) | |
233 | (1+ count) | |
234 | (if (and (eq (car-safe (car vecs)) 'var) | |
235 | (eq (car-safe (calc-var-value | |
236 | (nth 2 (car vecs)))) | |
237 | 'vec)) | |
238 | (+ count (math-count-elements | |
239 | (symbol-value (nth 2 (car vecs))))) | |
240 | (math-reject-arg (car vecs) 'numvecp)))) | |
241 | vecs (cdr vecs))) | |
bf77c646 | 242 | count)) |
136211a9 EZ |
243 | |
244 | (defun math-count-elements (vec) | |
245 | (let ((count 0)) | |
246 | (while (setq vec (cdr vec)) | |
247 | (setq count (if (Math-vectorp (car vec)) | |
248 | (+ count (math-count-elements (car vec))) | |
249 | (1+ count)))) | |
bf77c646 | 250 | count)) |
136211a9 EZ |
251 | |
252 | ||
253 | (defun math-flatten-many-vecs (vecs) | |
254 | (let ((p vecs) | |
255 | (vec (list 'vec))) | |
256 | (while p | |
257 | (setq vec (nconc vec | |
258 | (if (Math-vectorp (car p)) | |
259 | (math-flatten-vector (car p)) | |
260 | (if (Math-objectp (car p)) | |
261 | (list (car p)) | |
262 | (if (and (eq (car-safe (car p)) 'var) | |
263 | (eq (car-safe (calc-var-value | |
264 | (nth 2 (car p)))) 'vec)) | |
265 | (math-flatten-vector (symbol-value | |
266 | (nth 2 (car p)))) | |
267 | (math-reject-arg (car p) 'numvecp))))) | |
268 | p (cdr p))) | |
bf77c646 | 269 | vec)) |
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270 | |
271 | (defun calcFunc-vflat (&rest vecs) | |
bf77c646 | 272 | (math-flatten-many-vecs vecs)) |
136211a9 EZ |
273 | |
274 | (defun math-split-sdev-vec (vec zero-ok) | |
275 | (let ((means (list 'vec)) | |
276 | (wts (list 'vec)) | |
277 | (exact nil) | |
278 | (p vec)) | |
279 | (while (and (setq p (cdr p)) | |
280 | (not (and (consp (car p)) | |
281 | (eq (car (car p)) 'sdev))))) | |
282 | (if (null p) | |
283 | (list vec nil) | |
284 | (while (setq vec (cdr vec)) | |
285 | (if (and (consp (setq p (car vec))) | |
286 | (eq (car p) 'sdev)) | |
287 | (or exact | |
288 | (setq means (cons (nth 1 p) means) | |
289 | wts (cons (nth 2 p) wts))) | |
290 | (if zero-ok | |
291 | (setq means (cons (nth 1 p) means) | |
292 | wts (cons 0 wts)) | |
293 | (or exact | |
294 | (setq means (list 'vec) | |
295 | wts nil | |
296 | exact t)) | |
297 | (setq means (cons p means))))) | |
298 | (list (nreverse means) | |
bf77c646 | 299 | (and wts (nreverse wts)))))) |
136211a9 EZ |
300 | |
301 | ||
302 | ;;; Return the arithmetic mean of the argument numbers or vectors. | |
303 | ;;; (If numbers are error forms, computes the weighted mean.) | |
304 | (defun calcFunc-vmean (&rest vecs) | |
305 | (let* ((split (math-split-sdev-vec (math-flatten-many-vecs vecs) nil)) | |
306 | (means (car split)) | |
307 | (wts (nth 1 split)) | |
308 | (len (1- (length means)))) | |
309 | (if (= len 0) | |
310 | (math-reject-arg nil "*Must be at least 1 argument") | |
311 | (if (and (= len 1) (eq (car-safe (nth 1 means)) 'intv)) | |
312 | (let ((x (math-fix-int-intv (nth 1 means)))) | |
313 | (calcFunc-vmean (nth 2 x) (nth 3 x))) | |
314 | (math-with-extra-prec 2 | |
315 | (if (and wts (> len 1)) | |
316 | (let* ((sqrwts (calcFunc-map '(var mul var-mul) wts wts)) | |
317 | (suminvsqrwts (calcFunc-reduce | |
318 | '(var add var-add) | |
319 | (calcFunc-map '(var div var-div) | |
320 | 1 sqrwts)))) | |
321 | (math-div (calcFunc-reduce '(var add var-add) | |
322 | (calcFunc-map '(var div var-div) | |
323 | means sqrwts)) | |
324 | suminvsqrwts)) | |
bf77c646 | 325 | (math-div (calcFunc-reduce '(var add var-add) means) len))))))) |
136211a9 EZ |
326 | |
327 | (defun math-fix-int-intv (x) | |
328 | (if (math-floatp x) | |
329 | x | |
330 | (list 'intv 3 | |
331 | (if (memq (nth 1 x) '(2 3)) (nth 2 x) (math-add (nth 2 x) 1)) | |
bf77c646 | 332 | (if (memq (nth 1 x) '(1 3)) (nth 3 x) (math-sub (nth 3 x) 1))))) |
136211a9 EZ |
333 | |
334 | ;;; Compute the mean with an error estimate. | |
335 | (defun calcFunc-vmeane (&rest vecs) | |
336 | (let* ((split (math-split-sdev-vec (math-flatten-many-vecs vecs) nil)) | |
337 | (means (car split)) | |
338 | (wts (nth 1 split)) | |
339 | (len (1- (length means)))) | |
340 | (if (= len 0) | |
341 | (math-reject-arg nil "*Must be at least 1 argument") | |
342 | (math-with-extra-prec 2 | |
343 | (if wts | |
344 | (let* ((sqrwts (calcFunc-map '(var mul var-mul) wts wts)) | |
345 | (suminvsqrwts (calcFunc-reduce | |
346 | '(var add var-add) | |
347 | (calcFunc-map '(var div var-div) | |
348 | 1 sqrwts)))) | |
349 | (math-make-sdev | |
350 | (math-div (calcFunc-reduce '(var add var-add) | |
351 | (calcFunc-map '(var div var-div) | |
352 | means sqrwts)) | |
353 | suminvsqrwts) | |
354 | (list 'calcFunc-sqrt (math-div 1 suminvsqrwts)))) | |
355 | (let ((mean (math-div (calcFunc-reduce '(var add var-add) means) | |
356 | len))) | |
357 | (math-make-sdev | |
358 | mean | |
359 | (list 'calcFunc-sqrt | |
360 | (math-div (calcFunc-reducer | |
361 | '(var add var-add) | |
362 | (calcFunc-map '(var pow var-pow) | |
363 | (calcFunc-map '(var abs var-abs) | |
364 | (calcFunc-map | |
365 | '(var add var-add) | |
366 | means | |
367 | (math-neg mean))) | |
368 | 2)) | |
bf77c646 | 369 | (math-mul len (1- len))))))))))) |
136211a9 EZ |
370 | |
371 | ||
372 | ;;; Compute the median of a list of values. | |
373 | (defun calcFunc-vmedian (&rest vecs) | |
374 | (let* ((flat (copy-sequence (cdr (math-flatten-many-vecs vecs)))) | |
375 | (p flat) | |
376 | (len (length flat)) | |
377 | (hlen (/ len 2))) | |
378 | (if (= len 0) | |
379 | (math-reject-arg nil "*Must be at least 1 argument") | |
380 | (if (and (= len 1) (memq (car-safe (car flat)) '(sdev intv))) | |
381 | (calcFunc-vmean (car flat)) | |
382 | (while p | |
383 | (if (eq (car-safe (car p)) 'sdev) | |
384 | (setcar p (nth 1 (car p)))) | |
385 | (or (Math-anglep (car p)) | |
386 | (math-reject-arg (car p) 'anglep)) | |
387 | (setq p (cdr p))) | |
388 | (setq flat (sort flat 'math-lessp)) | |
389 | (if (= (% len 2) 0) | |
390 | (math-div (math-add (nth (1- hlen) flat) (nth hlen flat)) 2) | |
bf77c646 | 391 | (nth hlen flat)))))) |
136211a9 EZ |
392 | |
393 | ||
394 | (defun calcFunc-vgmean (&rest vecs) | |
395 | (let* ((flat (math-flatten-many-vecs vecs)) | |
396 | (len (1- (length flat)))) | |
397 | (if (= len 0) | |
398 | (math-reject-arg nil "*Must be at least 1 argument") | |
399 | (math-with-extra-prec 2 | |
400 | (let ((x (calcFunc-reduce '(var mul math-mul) flat))) | |
401 | (if (= len 2) | |
402 | (math-sqrt x) | |
bf77c646 | 403 | (math-pow x (list 'frac 1 len)))))))) |
136211a9 EZ |
404 | |
405 | ||
406 | (defun calcFunc-agmean (a b) | |
407 | (cond ((Math-equal a b) a) | |
408 | ((math-zerop a) a) | |
409 | ((math-zerop b) b) | |
410 | (calc-symbolic-mode (math-inexact-result)) | |
411 | ((not (Math-realp a)) (math-reject-arg a 'realp)) | |
412 | ((not (Math-realp b)) (math-reject-arg b 'realp)) | |
413 | (t | |
414 | (math-with-extra-prec 2 | |
415 | (setq a (math-float (math-abs a)) | |
416 | b (math-float (math-abs b))) | |
417 | (let (mean) | |
418 | (while (not (math-nearly-equal-float a b)) | |
419 | (setq mean (math-mul-float (math-add-float a b) '(float 5 -1)) | |
420 | b (math-sqrt-float (math-mul-float a b)) | |
421 | a mean)) | |
bf77c646 | 422 | a))))) |
136211a9 EZ |
423 | |
424 | ||
425 | (defun calcFunc-vhmean (&rest vecs) | |
426 | (let* ((flat (math-flatten-many-vecs vecs)) | |
427 | (len (1- (length flat)))) | |
428 | (if (= len 0) | |
429 | (math-reject-arg nil "*Must be at least 1 argument") | |
430 | (math-with-extra-prec 2 | |
431 | (math-div len | |
432 | (calcFunc-reduce '(var add math-add) | |
bf77c646 | 433 | (calcFunc-map '(var inv var-inv) flat))))))) |
136211a9 EZ |
434 | |
435 | ||
436 | ||
437 | ;;; Compute the sample variance or standard deviation of numbers or vectors. | |
438 | ;;; (If the numbers are error forms, only the mean part of them is used.) | |
439 | (defun calcFunc-vvar (&rest vecs) | |
440 | (if (and (= (length vecs) 1) | |
441 | (memq (car-safe (car vecs)) '(sdev intv))) | |
442 | (if (eq (car-safe (car vecs)) 'intv) | |
443 | (math-intv-variance (car vecs) nil) | |
444 | (math-sqr (nth 2 (car vecs)))) | |
bf77c646 | 445 | (math-covariance vecs nil nil 0))) |
136211a9 EZ |
446 | |
447 | (defun calcFunc-vsdev (&rest vecs) | |
448 | (if (and (= (length vecs) 1) | |
449 | (memq (car-safe (car vecs)) '(sdev intv))) | |
450 | (if (eq (car-safe (car vecs)) 'intv) | |
451 | (if (math-floatp (car vecs)) | |
452 | (math-div (math-sub (nth 3 (car vecs)) (nth 2 (car vecs))) | |
453 | (math-sqrt-12)) | |
454 | (math-sqrt (calcFunc-vvar (car vecs)))) | |
455 | (nth 2 (car vecs))) | |
bf77c646 | 456 | (math-sqrt (math-covariance vecs nil nil 0)))) |
136211a9 EZ |
457 | |
458 | ;;; Compute the population variance or std deviation of numbers or vectors. | |
459 | (defun calcFunc-vpvar (&rest vecs) | |
460 | (if (and (= (length vecs) 1) | |
461 | (memq (car-safe (car vecs)) '(sdev intv))) | |
462 | (if (eq (car-safe (car vecs)) 'intv) | |
463 | (math-intv-variance (car vecs) t) | |
464 | (math-sqr (nth 2 (car vecs)))) | |
bf77c646 | 465 | (math-covariance vecs nil t 0))) |
136211a9 EZ |
466 | |
467 | (defun calcFunc-vpsdev (&rest vecs) | |
468 | (if (and (= (length vecs) 1) | |
469 | (memq (car-safe (car vecs)) '(sdev intv))) | |
470 | (if (eq (car-safe (car vecs)) 'intv) | |
471 | (if (math-floatp (car vecs)) | |
472 | (math-div (math-sub (nth 3 (car vecs)) (nth 2 (car vecs))) | |
473 | (math-sqrt-12)) | |
474 | (math-sqrt (calcFunc-vpvar (car vecs)))) | |
475 | (nth 2 (car vecs))) | |
bf77c646 | 476 | (math-sqrt (math-covariance vecs nil t 0)))) |
136211a9 EZ |
477 | |
478 | (defun math-intv-variance (x pop) | |
479 | (or (math-constp x) (math-reject-arg x 'constp)) | |
480 | (if (math-floatp x) | |
481 | (math-div (math-sqr (math-sub (nth 3 x) (nth 2 x))) 12) | |
482 | (let* ((x (math-fix-int-intv x)) | |
483 | (len (math-sub (nth 3 x) (nth 2 x))) | |
484 | (hlen (math-quotient len 2))) | |
485 | (math-div (if (math-evenp len) | |
486 | (calcFunc-sum '(^ (var X var-X) 2) '(var X var-X) | |
487 | (math-neg hlen) hlen) | |
488 | (calcFunc-sum '(^ (- (var X var-X) (/ 1 2)) 2) | |
489 | '(var X var-X) | |
490 | (math-neg hlen) (math-add hlen 1))) | |
bf77c646 | 491 | (if pop (math-add len 1) len))))) |
136211a9 EZ |
492 | |
493 | ;;; Compute the covariance and linear correlation coefficient. | |
494 | (defun calcFunc-vcov (vec1 &optional vec2) | |
bf77c646 | 495 | (math-covariance (list vec1) (list vec2) nil 1)) |
136211a9 EZ |
496 | |
497 | (defun calcFunc-vpcov (vec1 &optional vec2) | |
bf77c646 | 498 | (math-covariance (list vec1) (list vec2) t 1)) |
136211a9 EZ |
499 | |
500 | (defun calcFunc-vcorr (vec1 &optional vec2) | |
bf77c646 | 501 | (math-covariance (list vec1) (list vec2) nil 2)) |
136211a9 EZ |
502 | |
503 | ||
504 | (defun math-covariance (vec1 vec2 pop mode) | |
505 | (or (car vec2) (= mode 0) | |
506 | (progn | |
507 | (if (and (eq (car-safe (car vec1)) 'var) | |
508 | (eq (car-safe (calc-var-value (nth 2 (car vec1)))) 'vec)) | |
509 | (setq vec1 (symbol-value (nth 2 (car vec1)))) | |
510 | (setq vec1 (car vec1))) | |
511 | (or (math-matrixp vec1) (math-dimension-error)) | |
512 | (or (= (length (nth 1 vec1)) 3) (math-dimension-error)) | |
513 | (setq vec2 (list (math-mat-col vec1 2)) | |
514 | vec1 (list (math-mat-col vec1 1))))) | |
515 | (math-with-extra-prec 2 | |
516 | (let* ((split1 (math-split-sdev-vec (math-flatten-many-vecs vec1) nil)) | |
517 | (means1 (car split1)) | |
518 | (wts1 (nth 1 split1)) | |
519 | split2 means2 (wts2 nil) | |
520 | (sqrwts nil) | |
521 | suminvsqrwts | |
522 | (len (1- (length means1)))) | |
523 | (if (< len (if pop 1 2)) | |
524 | (math-reject-arg nil (if pop | |
525 | "*Must be at least 1 argument" | |
526 | "*Must be at least 2 arguments"))) | |
527 | (if (or wts1 wts2) | |
528 | (setq sqrwts (math-add | |
529 | (if wts1 | |
530 | (calcFunc-map '(var mul var-mul) wts1 wts1) | |
531 | 0) | |
532 | (if wts2 | |
533 | (calcFunc-map '(var mul var-mul) wts2 wts2) | |
534 | 0)) | |
535 | suminvsqrwts (calcFunc-reduce | |
536 | '(var add var-add) | |
537 | (calcFunc-map '(var div var-div) 1 sqrwts)))) | |
538 | (or (= mode 0) | |
539 | (progn | |
540 | (setq split2 (math-split-sdev-vec (math-flatten-many-vecs vec2) | |
541 | nil) | |
542 | means2 (car split2) | |
543 | wts2 (nth 2 split1)) | |
544 | (or (= len (1- (length means2))) (math-dimension-error)))) | |
545 | (let* ((diff1 (calcFunc-map | |
546 | '(var add var-add) | |
547 | means1 | |
548 | (if sqrwts | |
549 | (math-div (calcFunc-reduce | |
550 | '(var add var-add) | |
551 | (calcFunc-map '(var div var-div) | |
552 | means1 sqrwts)) | |
553 | (math-neg suminvsqrwts)) | |
554 | (math-div (calcFunc-reducer '(var add var-add) means1) | |
555 | (- len))))) | |
556 | (diff2 (if (= mode 0) | |
557 | diff1 | |
558 | (calcFunc-map | |
559 | '(var add var-add) | |
560 | means2 | |
561 | (if sqrwts | |
562 | (math-div (calcFunc-reduce | |
563 | '(var add var-add) | |
564 | (calcFunc-map '(var div var-div) | |
565 | means2 sqrwts)) | |
566 | (math-neg suminvsqrwts)) | |
567 | (math-div (calcFunc-reducer '(var add var-add) means2) | |
568 | (- len)))))) | |
569 | (covar (calcFunc-map '(var mul var-mul) diff1 diff2))) | |
570 | (if sqrwts | |
571 | (setq covar (calcFunc-map '(var div var-div) covar sqrwts))) | |
572 | (math-div | |
573 | (calcFunc-reducer '(var add var-add) covar) | |
574 | (if (= mode 2) | |
575 | (let ((var1 (calcFunc-map '(var mul var-mul) diff1 diff1)) | |
576 | (var2 (calcFunc-map '(var mul var-mul) diff2 diff2))) | |
577 | (if sqrwts | |
578 | (setq var1 (calcFunc-map '(var div var-div) var1 sqrwts) | |
579 | var2 (calcFunc-map '(var div var-div) var2 sqrwts))) | |
580 | (math-sqrt | |
581 | (math-mul (calcFunc-reducer '(var add var-add) var1) | |
582 | (calcFunc-reducer '(var add var-add) var2)))) | |
583 | (if sqrwts | |
584 | (if pop | |
585 | suminvsqrwts | |
586 | (math-div (math-mul suminvsqrwts (1- len)) len)) | |
bf77c646 | 587 | (if pop len (1- len))))))))) |
136211a9 | 588 | |
6b61353c | 589 | ;;; arch-tag: 423858e9-8513-489c-9f35-710cd9d9c307 |
bf77c646 | 590 | ;;; calc-stat.el ends here |