1 ;;; calc-stat.el --- statistical functions for Calc
3 ;; Copyright (C) 1990, 1991, 1992, 1993, 2001, 2002, 2003, 2004,
4 ;; 2005, 2006, 2007, 2008, 2009 Free Software Foundation, Inc.
6 ;; Author: David Gillespie <daveg@synaptics.com>
7 ;; Maintainer: Jay Belanger <jay.p.belanger@gmail.com>
9 ;; This file is part of GNU Emacs.
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.
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.
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/>.
28 ;; This file is autoloaded from calc-ext.el.
33 ;;; Statistical operations on vectors.
35 (defun calc-vector-count (arg)
38 (calc-vector-op "coun" 'calcFunc-vcount arg)))
40 (defun calc-vector-sum (arg)
43 (if (calc-is-hyperbolic)
44 (calc-vector-op "vprd" 'calcFunc-vprod arg)
45 (calc-vector-op "vsum" 'calcFunc-vsum arg))))
47 (defun calc-vector-product (arg)
49 (calc-hyperbolic-func)
50 (calc-vector-sum arg))
52 (defun calc-vector-max (arg)
56 (calc-vector-op "vmin" 'calcFunc-vmin arg)
57 (calc-vector-op "vmax" 'calcFunc-vmax arg))))
59 (defun calc-vector-min (arg)
62 (calc-vector-max arg))
64 (defun calc-vector-mean (arg)
67 (if (calc-is-hyperbolic)
69 (calc-vector-op "harm" 'calcFunc-vhmean arg)
70 (calc-vector-op "medn" 'calcFunc-vmedian arg))
72 (calc-vector-op "meae" 'calcFunc-vmeane arg)
73 (calc-vector-op "mean" 'calcFunc-vmean arg)))))
75 (defun calc-vector-mean-error (arg)
78 (calc-vector-mean arg))
80 (defun calc-vector-median (arg)
82 (calc-hyperbolic-func)
83 (calc-vector-mean arg))
85 (defun calc-vector-harmonic-mean (arg)
88 (calc-hyperbolic-func)
89 (calc-vector-mean arg))
91 (defun calc-vector-geometric-mean (arg)
94 (if (calc-is-hyperbolic)
95 (calc-binary-op "geom" 'calcFunc-agmean arg)
96 (calc-vector-op "geom" 'calcFunc-vgmean arg))))
98 (defun calc-vector-sdev (arg)
101 (if (calc-is-hyperbolic)
102 (if (calc-is-inverse)
103 (calc-vector-op "pvar" 'calcFunc-vpvar arg)
104 (calc-vector-op "var" 'calcFunc-vvar arg))
105 (if (calc-is-inverse)
106 (calc-vector-op "psdv" 'calcFunc-vpsdev arg)
107 (calc-vector-op "sdev" 'calcFunc-vsdev arg)))))
109 (defun calc-vector-pop-sdev (arg)
112 (calc-vector-sdev arg))
114 (defun calc-vector-variance (arg)
116 (calc-hyperbolic-func)
117 (calc-vector-sdev arg))
119 (defun calc-vector-pop-variance (arg)
122 (calc-hyperbolic-func)
123 (calc-vector-sdev arg))
125 (defun calc-vector-covariance (arg)
128 (let ((n (if (eq arg 1) 1 2)))
129 (if (calc-is-hyperbolic)
130 (calc-enter-result n "corr" (cons 'calcFunc-vcorr
131 (calc-top-list-n n)))
132 (if (calc-is-inverse)
133 (calc-enter-result n "pcov" (cons 'calcFunc-vpcov
134 (calc-top-list-n n)))
135 (calc-enter-result n "cov" (cons 'calcFunc-vcov
136 (calc-top-list-n n))))))))
138 (defun calc-vector-pop-covariance (arg)
141 (calc-vector-covariance arg))
143 (defun calc-vector-correlation (arg)
145 (calc-hyperbolic-func)
146 (calc-vector-covariance arg))
148 (defun calc-vector-op (name func arg)
149 (setq calc-aborted-prefix name
150 arg (prefix-numeric-value arg))
152 (error "Negative arguments not allowed"))
153 (calc-enter-result arg name (cons func (calc-top-list-n arg))))
158 ;;; Useful statistical functions
160 ;;; Sum, product, etc., of one or more values or vectors.
161 ;;; Each argument must be either a number or a vector. Vectors
162 ;;; are flattened, but variables inside are assumed to represent
165 (defun calcFunc-vsum (&rest vecs)
166 (math-reduce-many-vecs 'calcFunc-add 'calcFunc-vsum vecs 0))
168 (defun calcFunc-vprod (&rest vecs)
169 (math-reduce-many-vecs 'calcFunc-mul 'calcFunc-vprod vecs 1))
171 (defun calcFunc-vmax (&rest vecs)
172 (if (eq (car-safe (car vecs)) 'sdev)
174 (if (eq (car-safe (car vecs)) 'intv)
175 (nth 3 (math-fix-int-intv (car vecs)))
176 (math-reduce-many-vecs 'calcFunc-max 'calcFunc-vmax vecs
177 '(neg (var inf var-inf))))))
179 (defun calcFunc-vmin (&rest vecs)
180 (if (eq (car-safe (car vecs)) 'sdev)
181 '(neg (var inf var-inf))
182 (if (eq (car-safe (car vecs)) 'intv)
183 (nth 2 (math-fix-int-intv (car vecs)))
184 (math-reduce-many-vecs 'calcFunc-min 'calcFunc-vmin vecs
185 '(var inf var-inf)))))
187 (defun math-reduce-many-vecs (func whole-func vecs ident)
188 (let ((const-part nil)
191 (let ((calc-internal-prec (+ calc-internal-prec 2)))
193 (setq val (car vecs))
194 (and (eq (car-safe val) 'var)
195 (eq (car-safe (calc-var-value (nth 2 val))) 'vec)
196 (setq val (symbol-value (nth 2 val))))
197 (cond ((Math-vectorp val)
198 (setq vec (append (and const-part (list const-part))
199 (math-flatten-vector val)))
200 (setq const-part (if vec
202 (math-calcFunc-to-var func)
205 ((or (Math-objectp val) (math-infinitep val))
206 (setq const-part (if const-part
207 (funcall func const-part val)
210 (setq symb-part (nconc symb-part (list val)))))
211 (setq vecs (cdr vecs))))
214 (setq const-part (math-normalize const-part))
216 (funcall func const-part (cons whole-func symb-part))
218 (if symb-part (cons whole-func symb-part) ident))))
221 ;;; Return the number of data elements among the arguments.
222 (defun calcFunc-vcount (&rest vecs)
225 (setq count (if (Math-vectorp (car vecs))
226 (+ count (math-count-elements (car vecs)))
227 (if (Math-objectp (car vecs))
229 (if (and (eq (car-safe (car vecs)) 'var)
230 (eq (car-safe (calc-var-value
233 (+ count (math-count-elements
234 (symbol-value (nth 2 (car vecs)))))
235 (math-reject-arg (car vecs) 'numvecp))))
239 (defun math-count-elements (vec)
241 (while (setq vec (cdr vec))
242 (setq count (if (Math-vectorp (car vec))
243 (+ count (math-count-elements (car vec)))
248 (defun math-flatten-many-vecs (vecs)
253 (if (Math-vectorp (car p))
254 (math-flatten-vector (car p))
255 (if (Math-objectp (car p))
257 (if (and (eq (car-safe (car p)) 'var)
258 (eq (car-safe (calc-var-value
259 (nth 2 (car p)))) 'vec))
260 (math-flatten-vector (symbol-value
262 (math-reject-arg (car p) 'numvecp)))))
266 (defun calcFunc-vflat (&rest vecs)
267 (math-flatten-many-vecs vecs))
269 (defun math-split-sdev-vec (vec zero-ok)
270 (let ((means (list 'vec))
274 (while (and (setq p (cdr p))
275 (not (and (consp (car p))
276 (eq (car (car p)) 'sdev)))))
279 (while (setq vec (cdr vec))
280 (if (and (consp (setq p (car vec)))
283 (setq means (cons (nth 1 p) means)
284 wts (cons (nth 2 p) wts)))
286 (setq means (cons (nth 1 p) means)
289 (setq means (list 'vec)
292 (setq means (cons p means)))))
293 (list (nreverse means)
294 (and wts (nreverse wts))))))
297 ;;; Return the arithmetic mean of the argument numbers or vectors.
298 ;;; (If numbers are error forms, computes the weighted mean.)
299 (defun calcFunc-vmean (&rest vecs)
300 (let* ((split (math-split-sdev-vec (math-flatten-many-vecs vecs) nil))
303 (len (1- (length means))))
305 (math-reject-arg nil "*Must be at least 1 argument")
306 (if (and (= len 1) (eq (car-safe (nth 1 means)) 'intv))
307 (let ((x (math-fix-int-intv (nth 1 means))))
308 (calcFunc-vmean (nth 2 x) (nth 3 x)))
309 (math-with-extra-prec 2
310 (if (and wts (> len 1))
311 (let* ((sqrwts (calcFunc-map '(var mul var-mul) wts wts))
312 (suminvsqrwts (calcFunc-reduce
314 (calcFunc-map '(var div var-div)
316 (math-div (calcFunc-reduce '(var add var-add)
317 (calcFunc-map '(var div var-div)
320 (math-div (calcFunc-reduce '(var add var-add) means) len)))))))
322 (defun math-fix-int-intv (x)
326 (if (memq (nth 1 x) '(2 3)) (nth 2 x) (math-add (nth 2 x) 1))
327 (if (memq (nth 1 x) '(1 3)) (nth 3 x) (math-sub (nth 3 x) 1)))))
329 ;;; Compute the mean with an error estimate.
330 (defun calcFunc-vmeane (&rest vecs)
331 (let* ((split (math-split-sdev-vec (math-flatten-many-vecs vecs) nil))
334 (len (1- (length means))))
336 (math-reject-arg nil "*Must be at least 1 argument")
337 (math-with-extra-prec 2
339 (let* ((sqrwts (calcFunc-map '(var mul var-mul) wts wts))
340 (suminvsqrwts (calcFunc-reduce
342 (calcFunc-map '(var div var-div)
345 (math-div (calcFunc-reduce '(var add var-add)
346 (calcFunc-map '(var div var-div)
349 (list 'calcFunc-sqrt (math-div 1 suminvsqrwts))))
350 (let ((mean (math-div (calcFunc-reduce '(var add var-add) means)
355 (math-div (calcFunc-reducer
357 (calcFunc-map '(var pow var-pow)
358 (calcFunc-map '(var abs var-abs)
364 (math-mul len (1- len)))))))))))
367 ;;; Compute the median of a list of values.
368 (defun calcFunc-vmedian (&rest vecs)
369 (let* ((flat (copy-sequence (cdr (math-flatten-many-vecs vecs))))
374 (math-reject-arg nil "*Must be at least 1 argument")
375 (if (and (= len 1) (memq (car-safe (car flat)) '(sdev intv)))
376 (calcFunc-vmean (car flat))
378 (if (eq (car-safe (car p)) 'sdev)
379 (setcar p (nth 1 (car p))))
380 (or (Math-anglep (car p))
381 (math-reject-arg (car p) 'anglep))
383 (setq flat (sort flat 'math-lessp))
385 (math-div (math-add (nth (1- hlen) flat) (nth hlen flat)) 2)
389 (defun calcFunc-vgmean (&rest vecs)
390 (let* ((flat (math-flatten-many-vecs vecs))
391 (len (1- (length flat))))
393 (math-reject-arg nil "*Must be at least 1 argument")
394 (math-with-extra-prec 2
395 (let ((x (calcFunc-reduce '(var mul math-mul) flat)))
398 (math-pow x (list 'frac 1 len))))))))
401 (defun calcFunc-agmean (a b)
402 (cond ((Math-equal a b) a)
405 (calc-symbolic-mode (math-inexact-result))
406 ((not (Math-realp a)) (math-reject-arg a 'realp))
407 ((not (Math-realp b)) (math-reject-arg b 'realp))
409 (math-with-extra-prec 2
410 (setq a (math-float (math-abs a))
411 b (math-float (math-abs b)))
413 (while (not (math-nearly-equal-float a b))
414 (setq mean (math-mul-float (math-add-float a b) '(float 5 -1))
415 b (math-sqrt-float (math-mul-float a b))
420 (defun calcFunc-vhmean (&rest vecs)
421 (let* ((flat (math-flatten-many-vecs vecs))
422 (len (1- (length flat))))
424 (math-reject-arg nil "*Must be at least 1 argument")
425 (math-with-extra-prec 2
427 (calcFunc-reduce '(var add math-add)
428 (calcFunc-map '(var inv var-inv) flat)))))))
432 ;;; Compute the sample variance or standard deviation of numbers or vectors.
433 ;;; (If the numbers are error forms, only the mean part of them is used.)
434 (defun calcFunc-vvar (&rest vecs)
435 (if (and (= (length vecs) 1)
436 (memq (car-safe (car vecs)) '(sdev intv)))
437 (if (eq (car-safe (car vecs)) 'intv)
438 (math-intv-variance (car vecs) nil)
439 (math-sqr (nth 2 (car vecs))))
440 (math-covariance vecs nil nil 0)))
442 (defun calcFunc-vsdev (&rest vecs)
443 (if (and (= (length vecs) 1)
444 (memq (car-safe (car vecs)) '(sdev intv)))
445 (if (eq (car-safe (car vecs)) 'intv)
446 (if (math-floatp (car vecs))
447 (math-div (math-sub (nth 3 (car vecs)) (nth 2 (car vecs)))
449 (math-sqrt (calcFunc-vvar (car vecs))))
451 (math-sqrt (math-covariance vecs nil nil 0))))
453 ;;; Compute the population variance or std deviation of numbers or vectors.
454 (defun calcFunc-vpvar (&rest vecs)
455 (if (and (= (length vecs) 1)
456 (memq (car-safe (car vecs)) '(sdev intv)))
457 (if (eq (car-safe (car vecs)) 'intv)
458 (math-intv-variance (car vecs) t)
459 (math-sqr (nth 2 (car vecs))))
460 (math-covariance vecs nil t 0)))
462 (defun calcFunc-vpsdev (&rest vecs)
463 (if (and (= (length vecs) 1)
464 (memq (car-safe (car vecs)) '(sdev intv)))
465 (if (eq (car-safe (car vecs)) 'intv)
466 (if (math-floatp (car vecs))
467 (math-div (math-sub (nth 3 (car vecs)) (nth 2 (car vecs)))
469 (math-sqrt (calcFunc-vpvar (car vecs))))
471 (math-sqrt (math-covariance vecs nil t 0))))
473 (defun math-intv-variance (x pop)
474 (or (math-constp x) (math-reject-arg x 'constp))
476 (math-div (math-sqr (math-sub (nth 3 x) (nth 2 x))) 12)
477 (let* ((x (math-fix-int-intv x))
478 (len (math-sub (nth 3 x) (nth 2 x)))
479 (hlen (math-quotient len 2)))
480 (math-div (if (math-evenp len)
481 (calcFunc-sum '(^ (var X var-X) 2) '(var X var-X)
482 (math-neg hlen) hlen)
483 (calcFunc-sum '(^ (- (var X var-X) (/ 1 2)) 2)
485 (math-neg hlen) (math-add hlen 1)))
486 (if pop (math-add len 1) len)))))
488 ;;; Compute the covariance and linear correlation coefficient.
489 (defun calcFunc-vcov (vec1 &optional vec2)
490 (math-covariance (list vec1) (list vec2) nil 1))
492 (defun calcFunc-vpcov (vec1 &optional vec2)
493 (math-covariance (list vec1) (list vec2) t 1))
495 (defun calcFunc-vcorr (vec1 &optional vec2)
496 (math-covariance (list vec1) (list vec2) nil 2))
499 (defun math-covariance (vec1 vec2 pop mode)
500 (or (car vec2) (= mode 0)
502 (if (and (eq (car-safe (car vec1)) 'var)
503 (eq (car-safe (calc-var-value (nth 2 (car vec1)))) 'vec))
504 (setq vec1 (symbol-value (nth 2 (car vec1))))
505 (setq vec1 (car vec1)))
506 (or (math-matrixp vec1) (math-dimension-error))
507 (or (= (length (nth 1 vec1)) 3) (math-dimension-error))
508 (setq vec2 (list (math-mat-col vec1 2))
509 vec1 (list (math-mat-col vec1 1)))))
510 (math-with-extra-prec 2
511 (let* ((split1 (math-split-sdev-vec (math-flatten-many-vecs vec1) nil))
512 (means1 (car split1))
513 (wts1 (nth 1 split1))
514 split2 means2 (wts2 nil)
517 (len (1- (length means1))))
518 (if (< len (if pop 1 2))
519 (math-reject-arg nil (if pop
520 "*Must be at least 1 argument"
521 "*Must be at least 2 arguments")))
523 (setq sqrwts (math-add
525 (calcFunc-map '(var mul var-mul) wts1 wts1)
528 (calcFunc-map '(var mul var-mul) wts2 wts2)
530 suminvsqrwts (calcFunc-reduce
532 (calcFunc-map '(var div var-div) 1 sqrwts))))
535 (setq split2 (math-split-sdev-vec (math-flatten-many-vecs vec2)
539 (or (= len (1- (length means2))) (math-dimension-error))))
540 (let* ((diff1 (calcFunc-map
544 (math-div (calcFunc-reduce
546 (calcFunc-map '(var div var-div)
548 (math-neg suminvsqrwts))
549 (math-div (calcFunc-reducer '(var add var-add) means1)
551 (diff2 (if (= mode 0)
557 (math-div (calcFunc-reduce
559 (calcFunc-map '(var div var-div)
561 (math-neg suminvsqrwts))
562 (math-div (calcFunc-reducer '(var add var-add) means2)
564 (covar (calcFunc-map '(var mul var-mul) diff1 diff2)))
566 (setq covar (calcFunc-map '(var div var-div) covar sqrwts)))
568 (calcFunc-reducer '(var add var-add) covar)
570 (let ((var1 (calcFunc-map '(var mul var-mul) diff1 diff1))
571 (var2 (calcFunc-map '(var mul var-mul) diff2 diff2)))
573 (setq var1 (calcFunc-map '(var div var-div) var1 sqrwts)
574 var2 (calcFunc-map '(var div var-div) var2 sqrwts)))
576 (math-mul (calcFunc-reducer '(var add var-add) var1)
577 (calcFunc-reducer '(var add var-add) var2))))
581 (math-div (math-mul suminvsqrwts (1- len)) len))
582 (if pop len (1- len)))))))))
586 ;; arch-tag: 423858e9-8513-489c-9f35-710cd9d9c307
587 ;;; calc-stat.el ends here