1 ;;; calc-stat.el --- statistical functions for Calc
3 ;; Copyright (C) 1990, 1991, 1992, 1993, 2001 Free Software Foundation, Inc.
5 ;; Author: David Gillespie <daveg@synaptics.com>
6 ;; Maintainer: Jay Belanger <belanger@truman.edu>
8 ;; This file is part of GNU Emacs.
10 ;; GNU Emacs is distributed in the hope that it will be useful,
11 ;; but WITHOUT ANY WARRANTY. No author or distributor
12 ;; accepts responsibility to anyone for the consequences of using it
13 ;; or for whether it serves any particular purpose or works at all,
14 ;; unless he says so in writing. Refer to the GNU Emacs General Public
15 ;; License for full details.
17 ;; Everyone is granted permission to copy, modify and redistribute
18 ;; GNU Emacs, but only under the conditions described in the
19 ;; GNU Emacs General Public License. A copy of this license is
20 ;; supposed to have been given to you along with GNU Emacs so you
21 ;; can know your rights and responsibilities. It should be in a
22 ;; file named COPYING. Among other things, the copyright notice
23 ;; and this notice must be preserved on all copies.
29 ;; This file is autoloaded from calc-ext.el.
34 ;;; Statistical operations on vectors.
36 (defun calc-vector-count (arg)
39 (calc-vector-op "coun" 'calcFunc-vcount arg)))
41 (defun calc-vector-sum (arg)
44 (if (calc-is-hyperbolic)
45 (calc-vector-op "vprd" 'calcFunc-vprod arg)
46 (calc-vector-op "vsum" 'calcFunc-vsum arg))))
48 (defun calc-vector-product (arg)
50 (calc-hyperbolic-func)
51 (calc-vector-sum arg))
53 (defun calc-vector-max (arg)
57 (calc-vector-op "vmin" 'calcFunc-vmin arg)
58 (calc-vector-op "vmax" 'calcFunc-vmax arg))))
60 (defun calc-vector-min (arg)
63 (calc-vector-max arg))
65 (defun calc-vector-mean (arg)
68 (if (calc-is-hyperbolic)
70 (calc-vector-op "harm" 'calcFunc-vhmean arg)
71 (calc-vector-op "medn" 'calcFunc-vmedian arg))
73 (calc-vector-op "meae" 'calcFunc-vmeane arg)
74 (calc-vector-op "mean" 'calcFunc-vmean arg)))))
76 (defun calc-vector-mean-error (arg)
79 (calc-vector-mean arg))
81 (defun calc-vector-median (arg)
83 (calc-hyperbolic-func)
84 (calc-vector-mean arg))
86 (defun calc-vector-harmonic-mean (arg)
89 (calc-hyperbolic-func)
90 (calc-vector-mean arg))
92 (defun calc-vector-geometric-mean (arg)
95 (if (calc-is-hyperbolic)
96 (calc-binary-op "geom" 'calcFunc-agmean arg)
97 (calc-vector-op "geom" 'calcFunc-vgmean arg))))
99 (defun calc-vector-sdev (arg)
102 (if (calc-is-hyperbolic)
103 (if (calc-is-inverse)
104 (calc-vector-op "pvar" 'calcFunc-vpvar arg)
105 (calc-vector-op "var" 'calcFunc-vvar arg))
106 (if (calc-is-inverse)
107 (calc-vector-op "psdv" 'calcFunc-vpsdev arg)
108 (calc-vector-op "sdev" 'calcFunc-vsdev arg)))))
110 (defun calc-vector-pop-sdev (arg)
113 (calc-vector-sdev arg))
115 (defun calc-vector-variance (arg)
117 (calc-hyperbolic-func)
118 (calc-vector-sdev arg))
120 (defun calc-vector-pop-variance (arg)
123 (calc-hyperbolic-func)
124 (calc-vector-sdev arg))
126 (defun calc-vector-covariance (arg)
129 (let ((n (if (eq arg 1) 1 2)))
130 (if (calc-is-hyperbolic)
131 (calc-enter-result n "corr" (cons 'calcFunc-vcorr
132 (calc-top-list-n n)))
133 (if (calc-is-inverse)
134 (calc-enter-result n "pcov" (cons 'calcFunc-vpcov
135 (calc-top-list-n n)))
136 (calc-enter-result n "cov" (cons 'calcFunc-vcov
137 (calc-top-list-n n))))))))
139 (defun calc-vector-pop-covariance (arg)
142 (calc-vector-covariance arg))
144 (defun calc-vector-correlation (arg)
146 (calc-hyperbolic-func)
147 (calc-vector-covariance arg))
149 (defun calc-vector-op (name func arg)
150 (setq calc-aborted-prefix name
151 arg (prefix-numeric-value arg))
153 (error "Negative arguments not allowed"))
154 (calc-enter-result arg name (cons func (calc-top-list-n arg))))
159 ;;; Useful statistical functions
161 ;;; Sum, product, etc., of one or more values or vectors.
162 ;;; Each argument must be either a number or a vector. Vectors
163 ;;; are flattened, but variables inside are assumed to represent
166 (defun calcFunc-vsum (&rest vecs)
167 (math-reduce-many-vecs 'calcFunc-add 'calcFunc-vsum vecs 0))
169 (defun calcFunc-vprod (&rest vecs)
170 (math-reduce-many-vecs 'calcFunc-mul 'calcFunc-vprod vecs 1))
172 (defun calcFunc-vmax (&rest vecs)
173 (if (eq (car-safe (car vecs)) 'sdev)
175 (if (eq (car-safe (car vecs)) 'intv)
176 (nth 3 (math-fix-int-intv (car vecs)))
177 (math-reduce-many-vecs 'calcFunc-max 'calcFunc-vmax vecs
178 '(neg (var inf var-inf))))))
180 (defun calcFunc-vmin (&rest vecs)
181 (if (eq (car-safe (car vecs)) 'sdev)
182 '(neg (var inf var-inf))
183 (if (eq (car-safe (car vecs)) 'intv)
184 (nth 2 (math-fix-int-intv (car vecs)))
185 (math-reduce-many-vecs 'calcFunc-min 'calcFunc-vmin vecs
186 '(var inf var-inf)))))
188 (defun math-reduce-many-vecs (func whole-func vecs ident)
189 (let ((const-part nil)
192 (let ((calc-internal-prec (+ calc-internal-prec 2)))
194 (setq val (car vecs))
195 (and (eq (car-safe val) 'var)
196 (eq (car-safe (calc-var-value (nth 2 val))) 'vec)
197 (setq val (symbol-value (nth 2 val))))
198 (cond ((Math-vectorp val)
199 (setq vec (append (and const-part (list const-part))
200 (math-flatten-vector val)))
201 (setq const-part (if vec
203 (math-calcFunc-to-var func)
206 ((or (Math-objectp val) (math-infinitep val))
207 (setq const-part (if const-part
208 (funcall func const-part val)
211 (setq symb-part (nconc symb-part (list val)))))
212 (setq vecs (cdr vecs))))
215 (setq const-part (math-normalize const-part))
217 (funcall func const-part (cons whole-func symb-part))
219 (if symb-part (cons whole-func symb-part) ident))))
222 ;;; Return the number of data elements among the arguments.
223 (defun calcFunc-vcount (&rest vecs)
226 (setq count (if (Math-vectorp (car vecs))
227 (+ count (math-count-elements (car vecs)))
228 (if (Math-objectp (car vecs))
230 (if (and (eq (car-safe (car vecs)) 'var)
231 (eq (car-safe (calc-var-value
234 (+ count (math-count-elements
235 (symbol-value (nth 2 (car vecs)))))
236 (math-reject-arg (car vecs) 'numvecp))))
240 (defun math-count-elements (vec)
242 (while (setq vec (cdr vec))
243 (setq count (if (Math-vectorp (car vec))
244 (+ count (math-count-elements (car vec)))
249 (defun math-flatten-many-vecs (vecs)
254 (if (Math-vectorp (car p))
255 (math-flatten-vector (car p))
256 (if (Math-objectp (car p))
258 (if (and (eq (car-safe (car p)) 'var)
259 (eq (car-safe (calc-var-value
260 (nth 2 (car p)))) 'vec))
261 (math-flatten-vector (symbol-value
263 (math-reject-arg (car p) 'numvecp)))))
267 (defun calcFunc-vflat (&rest vecs)
268 (math-flatten-many-vecs vecs))
270 (defun math-split-sdev-vec (vec zero-ok)
271 (let ((means (list 'vec))
275 (while (and (setq p (cdr p))
276 (not (and (consp (car p))
277 (eq (car (car p)) 'sdev)))))
280 (while (setq vec (cdr vec))
281 (if (and (consp (setq p (car vec)))
284 (setq means (cons (nth 1 p) means)
285 wts (cons (nth 2 p) wts)))
287 (setq means (cons (nth 1 p) means)
290 (setq means (list 'vec)
293 (setq means (cons p means)))))
294 (list (nreverse means)
295 (and wts (nreverse wts))))))
298 ;;; Return the arithmetic mean of the argument numbers or vectors.
299 ;;; (If numbers are error forms, computes the weighted mean.)
300 (defun calcFunc-vmean (&rest vecs)
301 (let* ((split (math-split-sdev-vec (math-flatten-many-vecs vecs) nil))
304 (len (1- (length means))))
306 (math-reject-arg nil "*Must be at least 1 argument")
307 (if (and (= len 1) (eq (car-safe (nth 1 means)) 'intv))
308 (let ((x (math-fix-int-intv (nth 1 means))))
309 (calcFunc-vmean (nth 2 x) (nth 3 x)))
310 (math-with-extra-prec 2
311 (if (and wts (> len 1))
312 (let* ((sqrwts (calcFunc-map '(var mul var-mul) wts wts))
313 (suminvsqrwts (calcFunc-reduce
315 (calcFunc-map '(var div var-div)
317 (math-div (calcFunc-reduce '(var add var-add)
318 (calcFunc-map '(var div var-div)
321 (math-div (calcFunc-reduce '(var add var-add) means) len)))))))
323 (defun math-fix-int-intv (x)
327 (if (memq (nth 1 x) '(2 3)) (nth 2 x) (math-add (nth 2 x) 1))
328 (if (memq (nth 1 x) '(1 3)) (nth 3 x) (math-sub (nth 3 x) 1)))))
330 ;;; Compute the mean with an error estimate.
331 (defun calcFunc-vmeane (&rest vecs)
332 (let* ((split (math-split-sdev-vec (math-flatten-many-vecs vecs) nil))
335 (len (1- (length means))))
337 (math-reject-arg nil "*Must be at least 1 argument")
338 (math-with-extra-prec 2
340 (let* ((sqrwts (calcFunc-map '(var mul var-mul) wts wts))
341 (suminvsqrwts (calcFunc-reduce
343 (calcFunc-map '(var div var-div)
346 (math-div (calcFunc-reduce '(var add var-add)
347 (calcFunc-map '(var div var-div)
350 (list 'calcFunc-sqrt (math-div 1 suminvsqrwts))))
351 (let ((mean (math-div (calcFunc-reduce '(var add var-add) means)
356 (math-div (calcFunc-reducer
358 (calcFunc-map '(var pow var-pow)
359 (calcFunc-map '(var abs var-abs)
365 (math-mul len (1- len)))))))))))
368 ;;; Compute the median of a list of values.
369 (defun calcFunc-vmedian (&rest vecs)
370 (let* ((flat (copy-sequence (cdr (math-flatten-many-vecs vecs))))
375 (math-reject-arg nil "*Must be at least 1 argument")
376 (if (and (= len 1) (memq (car-safe (car flat)) '(sdev intv)))
377 (calcFunc-vmean (car flat))
379 (if (eq (car-safe (car p)) 'sdev)
380 (setcar p (nth 1 (car p))))
381 (or (Math-anglep (car p))
382 (math-reject-arg (car p) 'anglep))
384 (setq flat (sort flat 'math-lessp))
386 (math-div (math-add (nth (1- hlen) flat) (nth hlen flat)) 2)
390 (defun calcFunc-vgmean (&rest vecs)
391 (let* ((flat (math-flatten-many-vecs vecs))
392 (len (1- (length flat))))
394 (math-reject-arg nil "*Must be at least 1 argument")
395 (math-with-extra-prec 2
396 (let ((x (calcFunc-reduce '(var mul math-mul) flat)))
399 (math-pow x (list 'frac 1 len))))))))
402 (defun calcFunc-agmean (a b)
403 (cond ((Math-equal a b) a)
406 (calc-symbolic-mode (math-inexact-result))
407 ((not (Math-realp a)) (math-reject-arg a 'realp))
408 ((not (Math-realp b)) (math-reject-arg b 'realp))
410 (math-with-extra-prec 2
411 (setq a (math-float (math-abs a))
412 b (math-float (math-abs b)))
414 (while (not (math-nearly-equal-float a b))
415 (setq mean (math-mul-float (math-add-float a b) '(float 5 -1))
416 b (math-sqrt-float (math-mul-float a b))
421 (defun calcFunc-vhmean (&rest vecs)
422 (let* ((flat (math-flatten-many-vecs vecs))
423 (len (1- (length flat))))
425 (math-reject-arg nil "*Must be at least 1 argument")
426 (math-with-extra-prec 2
428 (calcFunc-reduce '(var add math-add)
429 (calcFunc-map '(var inv var-inv) flat)))))))
433 ;;; Compute the sample variance or standard deviation of numbers or vectors.
434 ;;; (If the numbers are error forms, only the mean part of them is used.)
435 (defun calcFunc-vvar (&rest vecs)
436 (if (and (= (length vecs) 1)
437 (memq (car-safe (car vecs)) '(sdev intv)))
438 (if (eq (car-safe (car vecs)) 'intv)
439 (math-intv-variance (car vecs) nil)
440 (math-sqr (nth 2 (car vecs))))
441 (math-covariance vecs nil nil 0)))
443 (defun calcFunc-vsdev (&rest vecs)
444 (if (and (= (length vecs) 1)
445 (memq (car-safe (car vecs)) '(sdev intv)))
446 (if (eq (car-safe (car vecs)) 'intv)
447 (if (math-floatp (car vecs))
448 (math-div (math-sub (nth 3 (car vecs)) (nth 2 (car vecs)))
450 (math-sqrt (calcFunc-vvar (car vecs))))
452 (math-sqrt (math-covariance vecs nil nil 0))))
454 ;;; Compute the population variance or std deviation of numbers or vectors.
455 (defun calcFunc-vpvar (&rest vecs)
456 (if (and (= (length vecs) 1)
457 (memq (car-safe (car vecs)) '(sdev intv)))
458 (if (eq (car-safe (car vecs)) 'intv)
459 (math-intv-variance (car vecs) t)
460 (math-sqr (nth 2 (car vecs))))
461 (math-covariance vecs nil t 0)))
463 (defun calcFunc-vpsdev (&rest vecs)
464 (if (and (= (length vecs) 1)
465 (memq (car-safe (car vecs)) '(sdev intv)))
466 (if (eq (car-safe (car vecs)) 'intv)
467 (if (math-floatp (car vecs))
468 (math-div (math-sub (nth 3 (car vecs)) (nth 2 (car vecs)))
470 (math-sqrt (calcFunc-vpvar (car vecs))))
472 (math-sqrt (math-covariance vecs nil t 0))))
474 (defun math-intv-variance (x pop)
475 (or (math-constp x) (math-reject-arg x 'constp))
477 (math-div (math-sqr (math-sub (nth 3 x) (nth 2 x))) 12)
478 (let* ((x (math-fix-int-intv x))
479 (len (math-sub (nth 3 x) (nth 2 x)))
480 (hlen (math-quotient len 2)))
481 (math-div (if (math-evenp len)
482 (calcFunc-sum '(^ (var X var-X) 2) '(var X var-X)
483 (math-neg hlen) hlen)
484 (calcFunc-sum '(^ (- (var X var-X) (/ 1 2)) 2)
486 (math-neg hlen) (math-add hlen 1)))
487 (if pop (math-add len 1) len)))))
489 ;;; Compute the covariance and linear correlation coefficient.
490 (defun calcFunc-vcov (vec1 &optional vec2)
491 (math-covariance (list vec1) (list vec2) nil 1))
493 (defun calcFunc-vpcov (vec1 &optional vec2)
494 (math-covariance (list vec1) (list vec2) t 1))
496 (defun calcFunc-vcorr (vec1 &optional vec2)
497 (math-covariance (list vec1) (list vec2) nil 2))
500 (defun math-covariance (vec1 vec2 pop mode)
501 (or (car vec2) (= mode 0)
503 (if (and (eq (car-safe (car vec1)) 'var)
504 (eq (car-safe (calc-var-value (nth 2 (car vec1)))) 'vec))
505 (setq vec1 (symbol-value (nth 2 (car vec1))))
506 (setq vec1 (car vec1)))
507 (or (math-matrixp vec1) (math-dimension-error))
508 (or (= (length (nth 1 vec1)) 3) (math-dimension-error))
509 (setq vec2 (list (math-mat-col vec1 2))
510 vec1 (list (math-mat-col vec1 1)))))
511 (math-with-extra-prec 2
512 (let* ((split1 (math-split-sdev-vec (math-flatten-many-vecs vec1) nil))
513 (means1 (car split1))
514 (wts1 (nth 1 split1))
515 split2 means2 (wts2 nil)
518 (len (1- (length means1))))
519 (if (< len (if pop 1 2))
520 (math-reject-arg nil (if pop
521 "*Must be at least 1 argument"
522 "*Must be at least 2 arguments")))
524 (setq sqrwts (math-add
526 (calcFunc-map '(var mul var-mul) wts1 wts1)
529 (calcFunc-map '(var mul var-mul) wts2 wts2)
531 suminvsqrwts (calcFunc-reduce
533 (calcFunc-map '(var div var-div) 1 sqrwts))))
536 (setq split2 (math-split-sdev-vec (math-flatten-many-vecs vec2)
540 (or (= len (1- (length means2))) (math-dimension-error))))
541 (let* ((diff1 (calcFunc-map
545 (math-div (calcFunc-reduce
547 (calcFunc-map '(var div var-div)
549 (math-neg suminvsqrwts))
550 (math-div (calcFunc-reducer '(var add var-add) means1)
552 (diff2 (if (= mode 0)
558 (math-div (calcFunc-reduce
560 (calcFunc-map '(var div var-div)
562 (math-neg suminvsqrwts))
563 (math-div (calcFunc-reducer '(var add var-add) means2)
565 (covar (calcFunc-map '(var mul var-mul) diff1 diff2)))
567 (setq covar (calcFunc-map '(var div var-div) covar sqrwts)))
569 (calcFunc-reducer '(var add var-add) covar)
571 (let ((var1 (calcFunc-map '(var mul var-mul) diff1 diff1))
572 (var2 (calcFunc-map '(var mul var-mul) diff2 diff2)))
574 (setq var1 (calcFunc-map '(var div var-div) var1 sqrwts)
575 var2 (calcFunc-map '(var div var-div) var2 sqrwts)))
577 (math-mul (calcFunc-reducer '(var add var-add) var1)
578 (calcFunc-reducer '(var add var-add) var2))))
582 (math-div (math-mul suminvsqrwts (1- len)) len))
583 (if pop len (1- len)))))))))
587 ;;; arch-tag: 423858e9-8513-489c-9f35-710cd9d9c307
588 ;;; calc-stat.el ends here