1 ;;; calc-stat.el --- statistical functions for Calc
3 ;; Copyright (C) 1990, 1991, 1992, 1993, 2001, 2005 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