1 ;;; calc-stat.el --- statistical functions for Calc
3 ;; Copyright (C) 1990-1993, 2001-2015 Free Software Foundation, Inc.
5 ;; Author: David Gillespie <daveg@synaptics.com>
6 ;; Maintainer: Jay Belanger <jay.p.belanger@gmail.com>
8 ;; This file is part of GNU Emacs.
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.
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.
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/>.
27 ;; This file is autoloaded from calc-ext.el.
32 ;;; Statistical operations on vectors.
34 (defun calc-vector-count (arg)
37 (calc-vector-op "coun" 'calcFunc-vcount arg)))
39 (defun calc-vector-sum (arg)
42 (if (calc-is-hyperbolic)
43 (calc-vector-op "vprd" 'calcFunc-vprod arg)
44 (calc-vector-op "vsum" 'calcFunc-vsum arg))))
46 (defun calc-vector-product (arg)
48 (calc-hyperbolic-func)
49 (calc-vector-sum arg))
51 (defun calc-vector-max (arg)
55 (calc-vector-op "vmin" 'calcFunc-vmin arg)
56 (calc-vector-op "vmax" 'calcFunc-vmax arg))))
58 (defun calc-vector-min (arg)
61 (calc-vector-max arg))
63 (defun calc-vector-mean (arg)
66 (if (calc-is-hyperbolic)
68 (calc-vector-op "harm" 'calcFunc-vhmean arg)
69 (calc-vector-op "medn" 'calcFunc-vmedian arg))
71 (calc-vector-op "meae" 'calcFunc-vmeane arg)
72 (calc-vector-op "mean" 'calcFunc-vmean arg)))))
74 (defun calc-vector-mean-error (arg)
77 (calc-vector-mean arg))
79 (defun calc-vector-median (arg)
81 (calc-hyperbolic-func)
82 (calc-vector-mean arg))
84 (defun calc-vector-harmonic-mean (arg)
87 (calc-hyperbolic-func)
88 (calc-vector-mean arg))
90 (defun calc-vector-geometric-mean (arg)
93 (if (calc-is-hyperbolic)
94 (calc-binary-op "geom" 'calcFunc-agmean arg)
95 (calc-vector-op "geom" 'calcFunc-vgmean arg))))
97 (defun calc-vector-sdev (arg)
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)))))
108 (defun calc-vector-pop-sdev (arg)
111 (calc-vector-sdev arg))
113 (defun calc-vector-variance (arg)
115 (calc-hyperbolic-func)
116 (calc-vector-sdev arg))
118 (defun calc-vector-pop-variance (arg)
121 (calc-hyperbolic-func)
122 (calc-vector-sdev arg))
124 (defun calc-vector-covariance (arg)
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))))))))
137 (defun calc-vector-pop-covariance (arg)
140 (calc-vector-covariance arg))
142 (defun calc-vector-correlation (arg)
144 (calc-hyperbolic-func)
145 (calc-vector-covariance arg))
147 (defun calc-vector-op (name func arg)
148 (setq calc-aborted-prefix name
149 arg (prefix-numeric-value arg))
151 (error "Negative arguments not allowed"))
152 (calc-enter-result arg name (cons func (calc-top-list-n arg))))
157 ;;; Useful statistical functions
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
164 (defun calcFunc-vsum (&rest vecs)
165 (math-reduce-many-vecs 'calcFunc-add 'calcFunc-vsum vecs 0))
167 (defun calcFunc-vprod (&rest vecs)
168 (math-reduce-many-vecs 'calcFunc-mul 'calcFunc-vprod vecs 1))
170 (defun calcFunc-vmax (&rest vecs)
171 (if (eq (car-safe (car vecs)) 'sdev)
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))))))
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)))))
186 (defun math-reduce-many-vecs (func whole-func vecs ident)
187 (let ((const-part nil)
190 (let ((calc-internal-prec (+ calc-internal-prec 2)))
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
201 (math-calcFunc-to-var func)
204 ((or (Math-objectp val) (math-infinitep val))
205 (setq const-part (if const-part
206 (funcall func const-part val)
209 (setq symb-part (nconc symb-part (list val)))))
210 (setq vecs (cdr vecs))))
213 (setq const-part (math-normalize const-part))
215 (funcall func const-part (cons whole-func symb-part))
217 (if symb-part (cons whole-func symb-part) ident))))
220 ;;; Return the number of data elements among the arguments.
221 (defun calcFunc-vcount (&rest vecs)
224 (setq count (if (Math-vectorp (car vecs))
225 (+ count (math-count-elements (car vecs)))
226 (if (Math-objectp (car vecs))
228 (if (and (eq (car-safe (car vecs)) 'var)
229 (eq (car-safe (calc-var-value
232 (+ count (math-count-elements
233 (symbol-value (nth 2 (car vecs)))))
234 (math-reject-arg (car vecs) 'numvecp))))
238 (defun math-count-elements (vec)
240 (while (setq vec (cdr vec))
241 (setq count (if (Math-vectorp (car vec))
242 (+ count (math-count-elements (car vec)))
247 (defun math-flatten-many-vecs (vecs)
252 (if (Math-vectorp (car p))
253 (math-flatten-vector (car p))
254 (if (Math-objectp (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
261 (math-reject-arg (car p) 'numvecp)))))
265 (defun calcFunc-vflat (&rest vecs)
266 (math-flatten-many-vecs vecs))
268 (defun math-split-sdev-vec (vec zero-ok)
269 (let ((means (list 'vec))
273 (while (and (setq p (cdr p))
274 (not (and (consp (car p))
275 (eq (car (car p)) 'sdev)))))
278 (while (setq vec (cdr vec))
279 (if (and (consp (setq p (car vec)))
282 (setq means (cons (nth 1 p) means)
283 wts (cons (nth 2 p) wts)))
285 (setq means (cons (nth 1 p) means)
288 (setq means (list 'vec)
291 (setq means (cons p means)))))
292 (list (nreverse means)
293 (and wts (nreverse wts))))))
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))
302 (len (1- (length means))))
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
313 (calcFunc-map '(var div var-div)
315 (math-div (calcFunc-reduce '(var add var-add)
316 (calcFunc-map '(var div var-div)
319 (math-div (calcFunc-reduce '(var add var-add) means) len)))))))
321 (defun math-fix-int-intv (x)
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)))))
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))
333 (len (1- (length means))))
335 (math-reject-arg nil "*Must be at least 1 argument")
336 (math-with-extra-prec 2
338 (let* ((sqrwts (calcFunc-map '(var mul var-mul) wts wts))
339 (suminvsqrwts (calcFunc-reduce
341 (calcFunc-map '(var div var-div)
344 (math-div (calcFunc-reduce '(var add var-add)
345 (calcFunc-map '(var div var-div)
348 (list 'calcFunc-sqrt (math-div 1 suminvsqrwts))))
349 (let ((mean (math-div (calcFunc-reduce '(var add var-add) means)
354 (math-div (calcFunc-reducer
356 (calcFunc-map '(var pow var-pow)
357 (calcFunc-map '(var abs var-abs)
363 (math-mul len (1- len)))))))))))
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))))
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))
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))
382 (setq flat (sort flat 'math-lessp))
384 (math-div (math-add (nth (1- hlen) flat) (nth hlen flat)) 2)
388 (defun calcFunc-vgmean (&rest vecs)
389 (let* ((flat (math-flatten-many-vecs vecs))
390 (len (1- (length flat))))
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)))
397 (math-pow x (list 'frac 1 len))))))))
400 (defun calcFunc-agmean (a b)
401 (cond ((Math-equal a b) a)
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))
408 (math-with-extra-prec 2
409 (setq a (math-float (math-abs a))
410 b (math-float (math-abs b)))
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))
419 (defun calcFunc-vhmean (&rest vecs)
420 (let* ((flat (math-flatten-many-vecs vecs))
421 (len (1- (length flat))))
423 (math-reject-arg nil "*Must be at least 1 argument")
424 (math-with-extra-prec 2
426 (calcFunc-reduce '(var add math-add)
427 (calcFunc-map '(var inv var-inv) flat)))))))
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)))
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)))
448 (math-sqrt (calcFunc-vvar (car vecs))))
450 (math-sqrt (math-covariance vecs nil nil 0))))
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)))
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)))
468 (math-sqrt (calcFunc-vpvar (car vecs))))
470 (math-sqrt (math-covariance vecs nil t 0))))
472 (defun math-intv-variance (x pop)
473 (or (math-constp x) (math-reject-arg x 'constp))
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)
484 (math-neg hlen) (math-add hlen 1)))
485 (if pop (math-add len 1) len)))))
487 ;;; Compute the covariance and linear correlation coefficient.
488 (defun calcFunc-vcov (vec1 &optional vec2)
489 (math-covariance (list vec1) (list vec2) nil 1))
491 (defun calcFunc-vpcov (vec1 &optional vec2)
492 (math-covariance (list vec1) (list vec2) t 1))
494 (defun calcFunc-vcorr (vec1 &optional vec2)
495 (math-covariance (list vec1) (list vec2) nil 2))
498 (defun math-covariance (vec1 vec2 pop mode)
499 (or (car vec2) (= mode 0)
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)
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")))
522 (setq sqrwts (math-add
524 (calcFunc-map '(var mul var-mul) wts1 wts1)
527 (calcFunc-map '(var mul var-mul) wts2 wts2)
529 suminvsqrwts (calcFunc-reduce
531 (calcFunc-map '(var div var-div) 1 sqrwts))))
534 (setq split2 (math-split-sdev-vec (math-flatten-many-vecs vec2)
538 (or (= len (1- (length means2))) (math-dimension-error))))
539 (let* ((diff1 (calcFunc-map
543 (math-div (calcFunc-reduce
545 (calcFunc-map '(var div var-div)
547 (math-neg suminvsqrwts))
548 (math-div (calcFunc-reducer '(var add var-add) means1)
550 (diff2 (if (= mode 0)
556 (math-div (calcFunc-reduce
558 (calcFunc-map '(var div var-div)
560 (math-neg suminvsqrwts))
561 (math-div (calcFunc-reducer '(var add var-add) means2)
563 (covar (calcFunc-map '(var mul var-mul) diff1 diff2)))
565 (setq covar (calcFunc-map '(var div var-div) covar sqrwts)))
567 (calcFunc-reducer '(var add var-add) covar)
569 (let ((var1 (calcFunc-map '(var mul var-mul) diff1 diff1))
570 (var2 (calcFunc-map '(var mul var-mul) diff2 diff2)))
572 (setq var1 (calcFunc-map '(var div var-div) var1 sqrwts)
573 var2 (calcFunc-map '(var div var-div) var2 sqrwts)))
575 (math-mul (calcFunc-reducer '(var add var-add) var1)
576 (calcFunc-reducer '(var add var-add) var2))))
580 (math-div (math-mul suminvsqrwts (1- len)) len))
581 (if pop len (1- len)))))))))
585 ;;; calc-stat.el ends here