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 ;; Maintainers: D. Goel <deego@gnufans.org>
7 ;; Colin Walters <walters@debian.org>
9 ;; This file is part of GNU Emacs.
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.
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.
30 ;; This file is autoloaded from calc-ext.el.
35 (defun calc-Need-calc-stat () nil
)
38 ;;; Statistical operations on vectors.
40 (defun calc-vector-count (arg)
43 (calc-vector-op "coun" 'calcFunc-vcount arg
)))
45 (defun calc-vector-sum (arg)
48 (if (calc-is-hyperbolic)
49 (calc-vector-op "vprd" 'calcFunc-vprod arg
)
50 (calc-vector-op "vsum" 'calcFunc-vsum arg
))))
52 (defun calc-vector-product (arg)
54 (calc-hyperbolic-func)
55 (calc-vector-sum arg
))
57 (defun calc-vector-max (arg)
61 (calc-vector-op "vmin" 'calcFunc-vmin arg
)
62 (calc-vector-op "vmax" 'calcFunc-vmax arg
))))
64 (defun calc-vector-min (arg)
67 (calc-vector-max arg
))
69 (defun calc-vector-mean (arg)
72 (if (calc-is-hyperbolic)
74 (calc-vector-op "harm" 'calcFunc-vhmean arg
)
75 (calc-vector-op "medn" 'calcFunc-vmedian arg
))
77 (calc-vector-op "meae" 'calcFunc-vmeane arg
)
78 (calc-vector-op "mean" 'calcFunc-vmean arg
)))))
80 (defun calc-vector-mean-error (arg)
83 (calc-vector-mean arg
))
85 (defun calc-vector-median (arg)
87 (calc-hyperbolic-func)
88 (calc-vector-mean arg
))
90 (defun calc-vector-harmonic-mean (arg)
93 (calc-hyperbolic-func)
94 (calc-vector-mean arg
))
96 (defun calc-vector-geometric-mean (arg)
99 (if (calc-is-hyperbolic)
100 (calc-binary-op "geom" 'calcFunc-agmean arg
)
101 (calc-vector-op "geom" 'calcFunc-vgmean arg
))))
103 (defun calc-vector-sdev (arg)
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
)
112 (calc-vector-op "sdev" 'calcFunc-vsdev arg
)))))
114 (defun calc-vector-pop-sdev (arg)
117 (calc-vector-sdev arg
))
119 (defun calc-vector-variance (arg)
121 (calc-hyperbolic-func)
122 (calc-vector-sdev arg
))
124 (defun calc-vector-pop-variance (arg)
127 (calc-hyperbolic-func)
128 (calc-vector-sdev arg
))
130 (defun calc-vector-covariance (arg)
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
141 (calc-top-list-n n
))))))))
143 (defun calc-vector-pop-covariance (arg)
146 (calc-vector-covariance arg
))
148 (defun calc-vector-correlation (arg)
150 (calc-hyperbolic-func)
151 (calc-vector-covariance arg
))
153 (defun calc-vector-op (name func arg
)
154 (setq calc-aborted-prefix name
155 arg
(prefix-numeric-value arg
))
157 (error "Negative arguments not allowed"))
158 (calc-enter-result arg name
(cons func
(calc-top-list-n arg
))))
163 ;;; Useful statistical functions
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
170 (defun calcFunc-vsum (&rest vecs
)
171 (math-reduce-many-vecs 'calcFunc-add
'calcFunc-vsum vecs
0))
173 (defun calcFunc-vprod (&rest vecs
)
174 (math-reduce-many-vecs 'calcFunc-mul
'calcFunc-vprod vecs
1))
176 (defun calcFunc-vmax (&rest vecs
)
177 (if (eq (car-safe (car vecs
)) 'sdev
)
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
182 '(neg (var inf var-inf
))))))
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
190 '(var inf var-inf
)))))
192 (defun math-reduce-many-vecs (func whole-func vecs ident
)
193 (let ((const-part nil
)
196 (let ((calc-internal-prec (+ calc-internal-prec
2)))
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
207 (math-calcFunc-to-var func
)
210 ((or (Math-objectp val
) (math-infinitep val
))
211 (setq const-part
(if const-part
212 (funcall func const-part val
)
215 (setq symb-part
(nconc symb-part
(list val
)))))
216 (setq vecs
(cdr vecs
))))
219 (setq const-part
(math-normalize const-part
))
221 (funcall func const-part
(cons whole-func symb-part
))
223 (if symb-part
(cons whole-func symb-part
) ident
))))
226 ;;; Return the number of data elements among the arguments.
227 (defun calcFunc-vcount (&rest vecs
)
230 (setq count
(if (Math-vectorp (car vecs
))
231 (+ count
(math-count-elements (car vecs
)))
232 (if (Math-objectp (car vecs
))
234 (if (and (eq (car-safe (car vecs
)) 'var
)
235 (eq (car-safe (calc-var-value
238 (+ count
(math-count-elements
239 (symbol-value (nth 2 (car vecs
)))))
240 (math-reject-arg (car vecs
) 'numvecp
))))
244 (defun math-count-elements (vec)
246 (while (setq vec
(cdr vec
))
247 (setq count
(if (Math-vectorp (car vec
))
248 (+ count
(math-count-elements (car vec
)))
253 (defun math-flatten-many-vecs (vecs)
258 (if (Math-vectorp (car p
))
259 (math-flatten-vector (car p
))
260 (if (Math-objectp (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
267 (math-reject-arg (car p
) 'numvecp
)))))
271 (defun calcFunc-vflat (&rest vecs
)
272 (math-flatten-many-vecs vecs
))
274 (defun math-split-sdev-vec (vec zero-ok
)
275 (let ((means (list 'vec
))
279 (while (and (setq p
(cdr p
))
280 (not (and (consp (car p
))
281 (eq (car (car p
)) 'sdev
)))))
284 (while (setq vec
(cdr vec
))
285 (if (and (consp (setq p
(car vec
)))
288 (setq means
(cons (nth 1 p
) means
)
289 wts
(cons (nth 2 p
) wts
)))
291 (setq means
(cons (nth 1 p
) means
)
294 (setq means
(list 'vec
)
297 (setq means
(cons p means
)))))
298 (list (nreverse means
)
299 (and wts
(nreverse wts
))))))
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
))
308 (len (1- (length means
))))
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
319 (calcFunc-map '(var div var-div
)
321 (math-div (calcFunc-reduce '(var add var-add
)
322 (calcFunc-map '(var div var-div
)
325 (math-div (calcFunc-reduce '(var add var-add
) means
) len
)))))))
327 (defun math-fix-int-intv (x)
331 (if (memq (nth 1 x
) '(2 3)) (nth 2 x
) (math-add (nth 2 x
) 1))
332 (if (memq (nth 1 x
) '(1 3)) (nth 3 x
) (math-sub (nth 3 x
) 1)))))
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
))
339 (len (1- (length means
))))
341 (math-reject-arg nil
"*Must be at least 1 argument")
342 (math-with-extra-prec 2
344 (let* ((sqrwts (calcFunc-map '(var mul var-mul
) wts wts
))
345 (suminvsqrwts (calcFunc-reduce
347 (calcFunc-map '(var div var-div
)
350 (math-div (calcFunc-reduce '(var add var-add
)
351 (calcFunc-map '(var div var-div
)
354 (list 'calcFunc-sqrt
(math-div 1 suminvsqrwts
))))
355 (let ((mean (math-div (calcFunc-reduce '(var add var-add
) means
)
360 (math-div (calcFunc-reducer
362 (calcFunc-map '(var pow var-pow
)
363 (calcFunc-map '(var abs var-abs
)
369 (math-mul len
(1- len
)))))))))))
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
))))
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
))
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
))
388 (setq flat
(sort flat
'math-lessp
))
390 (math-div (math-add (nth (1- hlen
) flat
) (nth hlen flat
)) 2)
394 (defun calcFunc-vgmean (&rest vecs
)
395 (let* ((flat (math-flatten-many-vecs vecs
))
396 (len (1- (length flat
))))
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
)))
403 (math-pow x
(list 'frac
1 len
))))))))
406 (defun calcFunc-agmean (a b
)
407 (cond ((Math-equal a b
) a
)
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
))
414 (math-with-extra-prec 2
415 (setq a
(math-float (math-abs a
))
416 b
(math-float (math-abs b
)))
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
))
425 (defun calcFunc-vhmean (&rest vecs
)
426 (let* ((flat (math-flatten-many-vecs vecs
))
427 (len (1- (length flat
))))
429 (math-reject-arg nil
"*Must be at least 1 argument")
430 (math-with-extra-prec 2
432 (calcFunc-reduce '(var add math-add
)
433 (calcFunc-map '(var inv var-inv
) flat
)))))))
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
))))
445 (math-covariance vecs nil nil
0)))
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
)))
454 (math-sqrt (calcFunc-vvar (car vecs
))))
456 (math-sqrt (math-covariance vecs nil nil
0))))
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
))))
465 (math-covariance vecs nil t
0)))
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
)))
474 (math-sqrt (calcFunc-vpvar (car vecs
))))
476 (math-sqrt (math-covariance vecs nil t
0))))
478 (defun math-intv-variance (x pop
)
479 (or (math-constp x
) (math-reject-arg x
'constp
))
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)
490 (math-neg hlen
) (math-add hlen
1)))
491 (if pop
(math-add len
1) len
)))))
493 ;;; Compute the covariance and linear correlation coefficient.
494 (defun calcFunc-vcov (vec1 &optional vec2
)
495 (math-covariance (list vec1
) (list vec2
) nil
1))
497 (defun calcFunc-vpcov (vec1 &optional vec2
)
498 (math-covariance (list vec1
) (list vec2
) t
1))
500 (defun calcFunc-vcorr (vec1 &optional vec2
)
501 (math-covariance (list vec1
) (list vec2
) nil
2))
504 (defun math-covariance (vec1 vec2 pop mode
)
505 (or (car vec2
) (= mode
0)
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
)
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")))
528 (setq sqrwts
(math-add
530 (calcFunc-map '(var mul var-mul
) wts1 wts1
)
533 (calcFunc-map '(var mul var-mul
) wts2 wts2
)
535 suminvsqrwts
(calcFunc-reduce
537 (calcFunc-map '(var div var-div
) 1 sqrwts
))))
540 (setq split2
(math-split-sdev-vec (math-flatten-many-vecs vec2
)
544 (or (= len
(1- (length means2
))) (math-dimension-error))))
545 (let* ((diff1 (calcFunc-map
549 (math-div (calcFunc-reduce
551 (calcFunc-map '(var div var-div
)
553 (math-neg suminvsqrwts
))
554 (math-div (calcFunc-reducer '(var add var-add
) means1
)
556 (diff2 (if (= mode
0)
562 (math-div (calcFunc-reduce
564 (calcFunc-map '(var div var-div
)
566 (math-neg suminvsqrwts
))
567 (math-div (calcFunc-reducer '(var add var-add
) means2
)
569 (covar (calcFunc-map '(var mul var-mul
) diff1 diff2
)))
571 (setq covar
(calcFunc-map '(var div var-div
) covar sqrwts
)))
573 (calcFunc-reducer '(var add var-add
) covar
)
575 (let ((var1 (calcFunc-map '(var mul var-mul
) diff1 diff1
))
576 (var2 (calcFunc-map '(var mul var-mul
) diff2 diff2
)))
578 (setq var1
(calcFunc-map '(var div var-div
) var1 sqrwts
)
579 var2
(calcFunc-map '(var div var-div
) var2 sqrwts
)))
581 (math-mul (calcFunc-reducer '(var add var-add
) var1
)
582 (calcFunc-reducer '(var add var-add
) var2
))))
586 (math-div (math-mul suminvsqrwts
(1- len
)) len
))
587 (if pop len
(1- len
)))))))))
589 ;;; arch-tag: 423858e9-8513-489c-9f35-710cd9d9c307
590 ;;; calc-stat.el ends here