lisp/calc/calc-stat.el

   1 ;;; calc-stat.el --- statistical functions for Calc
   2
   3 ;; Copyright (C) 1990, 1991, 1992, 1993, 2001, 2002, 2003, 2004,
   4 ;;   2005, 2006, 2007, 2008 Free Software Foundation, Inc.
   5
   6 ;; Author: David Gillespie <daveg@synaptics.com>
   7 ;; Maintainer: Jay Belanger <jay.p.belanger@gmail.com>
   8
   9 ;; This file is part of GNU Emacs.
  10
  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, or (at your option)
  14 ;; any later version.
  15
  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.
  20
  21 ;; You should have received a copy of the GNU General Public License
  22 ;; along with GNU Emacs; see the file COPYING.  If not, write to the
  23 ;; Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
  24 ;; Boston, MA 02110-1301, USA.
  25
  26 ;;; Commentary:
  27
  28 ;;; Code:
  29
  30 ;; This file is autoloaded from calc-ext.el.
  31
  32 (require 'calc-ext)
  33 (require 'calc-macs)
  34
  35 ;;; Statistical operations on vectors.
  36
  37 (defun calc-vector-count (arg)
  38   (interactive "P")
  39   (calc-slow-wrapper
  40    (calc-vector-op "coun" 'calcFunc-vcount arg)))
  41
  42 (defun calc-vector-sum (arg)
  43   (interactive "P")
  44   (calc-slow-wrapper
  45    (if (calc-is-hyperbolic)
  46        (calc-vector-op "vprd" 'calcFunc-vprod arg)
  47      (calc-vector-op "vsum" 'calcFunc-vsum arg))))
  48
  49 (defun calc-vector-product (arg)
  50   (interactive "P")
  51   (calc-hyperbolic-func)
  52   (calc-vector-sum arg))
  53
  54 (defun calc-vector-max (arg)
  55   (interactive "P")
  56   (calc-slow-wrapper
  57    (if (calc-is-inverse)
  58        (calc-vector-op "vmin" 'calcFunc-vmin arg)
  59      (calc-vector-op "vmax" 'calcFunc-vmax arg))))
  60
  61 (defun calc-vector-min (arg)
  62   (interactive "P")
  63   (calc-invert-func)
  64   (calc-vector-max arg))
  65
  66 (defun calc-vector-mean (arg)
  67   (interactive "P")
  68   (calc-slow-wrapper
  69    (if (calc-is-hyperbolic)
  70        (if (calc-is-inverse)
  71            (calc-vector-op "harm" 'calcFunc-vhmean arg)
  72          (calc-vector-op "medn" 'calcFunc-vmedian arg))
  73      (if (calc-is-inverse)
  74          (calc-vector-op "meae" 'calcFunc-vmeane arg)
  75        (calc-vector-op "mean" 'calcFunc-vmean arg)))))
  76
  77 (defun calc-vector-mean-error (arg)
  78   (interactive "P")
  79   (calc-invert-func)
  80   (calc-vector-mean arg))
  81
  82 (defun calc-vector-median (arg)
  83   (interactive "P")
  84   (calc-hyperbolic-func)
  85   (calc-vector-mean arg))
  86
  87 (defun calc-vector-harmonic-mean (arg)
  88   (interactive "P")
  89   (calc-invert-func)
  90   (calc-hyperbolic-func)
  91   (calc-vector-mean arg))
  92
  93 (defun calc-vector-geometric-mean (arg)
  94   (interactive "P")
  95   (calc-slow-wrapper
  96    (if (calc-is-hyperbolic)
  97        (calc-binary-op "geom" 'calcFunc-agmean arg)
  98      (calc-vector-op "geom" 'calcFunc-vgmean arg))))
  99
 100 (defun calc-vector-sdev (arg)
 101   (interactive "P")
 102   (calc-slow-wrapper
 103    (if (calc-is-hyperbolic)
 104        (if (calc-is-inverse)
 105            (calc-vector-op "pvar" 'calcFunc-vpvar arg)
 106          (calc-vector-op "var" 'calcFunc-vvar arg))
 107      (if (calc-is-inverse)
 108          (calc-vector-op "psdv" 'calcFunc-vpsdev arg)
 109        (calc-vector-op "sdev" 'calcFunc-vsdev arg)))))
 110
 111 (defun calc-vector-pop-sdev (arg)
 112   (interactive "P")
 113   (calc-invert-func)
 114   (calc-vector-sdev arg))
 115
 116 (defun calc-vector-variance (arg)
 117   (interactive "P")
 118   (calc-hyperbolic-func)
 119   (calc-vector-sdev arg))
 120
 121 (defun calc-vector-pop-variance (arg)
 122   (interactive "P")
 123   (calc-invert-func)
 124   (calc-hyperbolic-func)
 125   (calc-vector-sdev arg))
 126
 127 (defun calc-vector-covariance (arg)
 128   (interactive "P")
 129   (calc-slow-wrapper
 130    (let ((n (if (eq arg 1) 1 2)))
 131      (if (calc-is-hyperbolic)
 132          (calc-enter-result n "corr" (cons 'calcFunc-vcorr
 133                                            (calc-top-list-n n)))
 134        (if (calc-is-inverse)
 135            (calc-enter-result n "pcov" (cons 'calcFunc-vpcov
 136                                              (calc-top-list-n n)))
 137          (calc-enter-result n "cov" (cons 'calcFunc-vcov
 138                                           (calc-top-list-n n))))))))
 139
 140 (defun calc-vector-pop-covariance (arg)
 141   (interactive "P")
 142   (calc-invert-func)
 143   (calc-vector-covariance arg))
 144
 145 (defun calc-vector-correlation (arg)
 146   (interactive "P")
 147   (calc-hyperbolic-func)
 148   (calc-vector-covariance arg))
 149
 150 (defun calc-vector-op (name func arg)
 151   (setq calc-aborted-prefix name
 152         arg (prefix-numeric-value arg))
 153   (if (< arg 0)
 154       (error "Negative arguments not allowed"))
 155   (calc-enter-result arg name (cons func (calc-top-list-n arg))))
 156
 157
 158
 159
 160 ;;; Useful statistical functions
 161
 162 ;;; Sum, product, etc., of one or more values or vectors.
 163 ;;; Each argument must be either a number or a vector.  Vectors
 164 ;;; are flattened, but variables inside are assumed to represent
 165 ;;; non-vectors.
 166
 167 (defun calcFunc-vsum (&rest vecs)
 168   (math-reduce-many-vecs 'calcFunc-add 'calcFunc-vsum vecs 0))
 169
 170 (defun calcFunc-vprod (&rest vecs)
 171   (math-reduce-many-vecs 'calcFunc-mul 'calcFunc-vprod vecs 1))
 172
 173 (defun calcFunc-vmax (&rest vecs)
 174   (if (eq (car-safe (car vecs)) 'sdev)
 175       '(var inf var-inf)
 176     (if (eq (car-safe (car vecs)) 'intv)
 177         (nth 3 (math-fix-int-intv (car vecs)))
 178       (math-reduce-many-vecs 'calcFunc-max 'calcFunc-vmax vecs
 179                              '(neg (var inf var-inf))))))
 180
 181 (defun calcFunc-vmin (&rest vecs)
 182   (if (eq (car-safe (car vecs)) 'sdev)
 183       '(neg (var inf var-inf))
 184     (if (eq (car-safe (car vecs)) 'intv)
 185         (nth 2 (math-fix-int-intv (car vecs)))
 186       (math-reduce-many-vecs 'calcFunc-min 'calcFunc-vmin vecs
 187                              '(var inf var-inf)))))
 188
 189 (defun math-reduce-many-vecs (func whole-func vecs ident)
 190   (let ((const-part nil)
 191         (symb-part nil)
 192         val vec)
 193     (let ((calc-internal-prec (+ calc-internal-prec 2)))
 194       (while vecs
 195         (setq val (car vecs))
 196         (and (eq (car-safe val) 'var)
 197              (eq (car-safe (calc-var-value (nth 2 val))) 'vec)
 198              (setq val (symbol-value (nth 2 val))))
 199         (cond ((Math-vectorp val)
 200                (setq vec (append (and const-part (list const-part))
 201                                  (math-flatten-vector val)))
 202                (setq const-part (if vec
 203                                     (calcFunc-reducer
 204                                      (math-calcFunc-to-var func)
 205                                      (cons 'vec vec))
 206                                   ident)))
 207               ((or (Math-objectp val) (math-infinitep val))
 208                (setq const-part (if const-part
 209                                     (funcall func const-part val)
 210                                   val)))
 211               (t
 212                (setq symb-part (nconc symb-part (list val)))))
 213         (setq vecs (cdr vecs))))
 214     (if const-part
 215         (progn
 216           (setq const-part (math-normalize const-part))
 217           (if symb-part
 218               (funcall func const-part (cons whole-func symb-part))
 219             const-part))
 220       (if symb-part (cons whole-func symb-part) ident))))
 221
 222
 223 ;;; Return the number of data elements among the arguments.
 224 (defun calcFunc-vcount (&rest vecs)
 225   (let ((count 0))
 226     (while vecs
 227       (setq count (if (Math-vectorp (car vecs))
 228                       (+ count (math-count-elements (car vecs)))
 229                     (if (Math-objectp (car vecs))
 230                         (1+ count)
 231                       (if (and (eq (car-safe (car vecs)) 'var)
 232                                (eq (car-safe (calc-var-value
 233                                               (nth 2 (car vecs))))
 234                                    'vec))
 235                           (+ count (math-count-elements
 236                                     (symbol-value (nth 2 (car vecs)))))
 237                         (math-reject-arg (car vecs) 'numvecp))))
 238             vecs (cdr vecs)))
 239     count))
 240
 241 (defun math-count-elements (vec)
 242   (let ((count 0))
 243     (while (setq vec (cdr vec))
 244       (setq count (if (Math-vectorp (car vec))
 245                       (+ count (math-count-elements (car vec)))
 246                     (1+ count))))
 247     count))
 248
 249
 250 (defun math-flatten-many-vecs (vecs)
 251   (let ((p vecs)
 252         (vec (list 'vec)))
 253     (while p
 254       (setq vec (nconc vec
 255                        (if (Math-vectorp (car p))
 256                            (math-flatten-vector (car p))
 257                          (if (Math-objectp (car p))
 258                              (list (car p))
 259                            (if (and (eq (car-safe (car p)) 'var)
 260                                     (eq (car-safe (calc-var-value
 261                                                    (nth 2 (car p)))) 'vec))
 262                                (math-flatten-vector (symbol-value
 263                                                      (nth 2 (car p))))
 264                              (math-reject-arg (car p) 'numvecp)))))
 265             p (cdr p)))
 266     vec))
 267
 268 (defun calcFunc-vflat (&rest vecs)
 269   (math-flatten-many-vecs vecs))
 270
 271 (defun math-split-sdev-vec (vec zero-ok)
 272   (let ((means (list 'vec))
 273         (wts (list 'vec))
 274         (exact nil)
 275         (p vec))
 276     (while (and (setq p (cdr p))
 277                 (not (and (consp (car p))
 278                           (eq (car (car p)) 'sdev)))))
 279     (if (null p)
 280         (list vec nil)
 281       (while (setq vec (cdr vec))
 282         (if (and (consp (setq p (car vec)))
 283                  (eq (car p) 'sdev))
 284             (or exact
 285                 (setq means (cons (nth 1 p) means)
 286                       wts (cons (nth 2 p) wts)))
 287           (if zero-ok
 288               (setq means (cons (nth 1 p) means)
 289                     wts (cons 0 wts))
 290             (or exact
 291                 (setq means (list 'vec)
 292                       wts nil
 293                       exact t))
 294             (setq means (cons p means)))))
 295       (list (nreverse means)
 296             (and wts (nreverse wts))))))
 297
 298
 299 ;;; Return the arithmetic mean of the argument numbers or vectors.
 300 ;;; (If numbers are error forms, computes the weighted mean.)
 301 (defun calcFunc-vmean (&rest vecs)
 302   (let* ((split (math-split-sdev-vec (math-flatten-many-vecs vecs) nil))
 303          (means (car split))
 304          (wts (nth 1 split))
 305          (len (1- (length means))))
 306     (if (= len 0)
 307         (math-reject-arg nil "*Must be at least 1 argument")
 308       (if (and (= len 1) (eq (car-safe (nth 1 means)) 'intv))
 309           (let ((x (math-fix-int-intv (nth 1 means))))
 310             (calcFunc-vmean (nth 2 x) (nth 3 x)))
 311         (math-with-extra-prec 2
 312           (if (and wts (> len 1))
 313               (let* ((sqrwts (calcFunc-map '(var mul var-mul) wts wts))
 314                      (suminvsqrwts (calcFunc-reduce
 315                                     '(var add var-add)
 316                                     (calcFunc-map '(var div var-div)
 317                                                   1 sqrwts))))
 318                 (math-div (calcFunc-reduce '(var add var-add)
 319                                            (calcFunc-map '(var div var-div)
 320                                                          means sqrwts))
 321                           suminvsqrwts))
 322             (math-div (calcFunc-reduce '(var add var-add) means) len)))))))
 323
 324 (defun math-fix-int-intv (x)
 325   (if (math-floatp x)
 326       x
 327     (list 'intv 3
 328           (if (memq (nth 1 x) '(2 3)) (nth 2 x) (math-add (nth 2 x) 1))
 329           (if (memq (nth 1 x) '(1 3)) (nth 3 x) (math-sub (nth 3 x) 1)))))
 330
 331 ;;; Compute the mean with an error estimate.
 332 (defun calcFunc-vmeane (&rest vecs)
 333   (let* ((split (math-split-sdev-vec (math-flatten-many-vecs vecs) nil))
 334          (means (car split))
 335          (wts (nth 1 split))
 336          (len (1- (length means))))
 337     (if (= len 0)
 338         (math-reject-arg nil "*Must be at least 1 argument")
 339       (math-with-extra-prec 2
 340         (if wts
 341             (let* ((sqrwts (calcFunc-map '(var mul var-mul) wts wts))
 342                    (suminvsqrwts (calcFunc-reduce
 343                                   '(var add var-add)
 344                                   (calcFunc-map '(var div var-div)
 345                                                 1 sqrwts))))
 346               (math-make-sdev
 347                (math-div (calcFunc-reduce '(var add var-add)
 348                                           (calcFunc-map '(var div var-div)
 349                                                         means sqrwts))
 350                          suminvsqrwts)
 351                (list 'calcFunc-sqrt (math-div 1 suminvsqrwts))))
 352           (let ((mean (math-div (calcFunc-reduce '(var add var-add) means)
 353                                 len)))
 354             (math-make-sdev
 355              mean
 356              (list 'calcFunc-sqrt
 357                    (math-div (calcFunc-reducer
 358                               '(var add var-add)
 359                               (calcFunc-map '(var pow var-pow)
 360                                             (calcFunc-map '(var abs var-abs)
 361                                                           (calcFunc-map
 362                                                            '(var add var-add)
 363                                                            means
 364                                                            (math-neg mean)))
 365                                             2))
 366                              (math-mul len (1- len)))))))))))
 367
 368
 369 ;;; Compute the median of a list of values.
 370 (defun calcFunc-vmedian (&rest vecs)
 371   (let* ((flat (copy-sequence (cdr (math-flatten-many-vecs vecs))))
 372          (p flat)
 373          (len (length flat))
 374          (hlen (/ len 2)))
 375     (if (= len 0)
 376         (math-reject-arg nil "*Must be at least 1 argument")
 377       (if (and (= len 1) (memq (car-safe (car flat)) '(sdev intv)))
 378           (calcFunc-vmean (car flat))
 379         (while p
 380           (if (eq (car-safe (car p)) 'sdev)
 381               (setcar p (nth 1 (car p))))
 382           (or (Math-anglep (car p))
 383               (math-reject-arg (car p) 'anglep))
 384           (setq p (cdr p)))
 385         (setq flat (sort flat 'math-lessp))
 386         (if (= (% len 2) 0)
 387             (math-div (math-add (nth (1- hlen) flat) (nth hlen flat)) 2)
 388           (nth hlen flat))))))
 389
 390
 391 (defun calcFunc-vgmean (&rest vecs)
 392   (let* ((flat (math-flatten-many-vecs vecs))
 393          (len (1- (length flat))))
 394     (if (= len 0)
 395         (math-reject-arg nil "*Must be at least 1 argument")
 396       (math-with-extra-prec 2
 397         (let ((x (calcFunc-reduce '(var mul math-mul) flat)))
 398           (if (= len 2)
 399               (math-sqrt x)
 400             (math-pow x (list 'frac 1 len))))))))
 401
 402
 403 (defun calcFunc-agmean (a b)
 404   (cond ((Math-equal a b) a)
 405         ((math-zerop a) a)
 406         ((math-zerop b) b)
 407         (calc-symbolic-mode (math-inexact-result))
 408         ((not (Math-realp a)) (math-reject-arg a 'realp))
 409         ((not (Math-realp b)) (math-reject-arg b 'realp))
 410         (t
 411          (math-with-extra-prec 2
 412            (setq a (math-float (math-abs a))
 413                  b (math-float (math-abs b)))
 414            (let (mean)
 415              (while (not (math-nearly-equal-float a b))
 416                (setq mean (math-mul-float (math-add-float a b) '(float 5 -1))
 417                      b (math-sqrt-float (math-mul-float a b))
 418                      a mean))
 419              a)))))
 420
 421
 422 (defun calcFunc-vhmean (&rest vecs)
 423   (let* ((flat (math-flatten-many-vecs vecs))
 424          (len (1- (length flat))))
 425     (if (= len 0)
 426         (math-reject-arg nil "*Must be at least 1 argument")
 427       (math-with-extra-prec 2
 428         (math-div len
 429                   (calcFunc-reduce '(var add math-add)
 430                                    (calcFunc-map '(var inv var-inv) flat)))))))
 431
 432
 433
 434 ;;; Compute the sample variance or standard deviation of numbers or vectors.
 435 ;;; (If the numbers are error forms, only the mean part of them is used.)
 436 (defun calcFunc-vvar (&rest vecs)
 437   (if (and (= (length vecs) 1)
 438            (memq (car-safe (car vecs)) '(sdev intv)))
 439       (if (eq (car-safe (car vecs)) 'intv)
 440           (math-intv-variance (car vecs) nil)
 441         (math-sqr (nth 2 (car vecs))))
 442     (math-covariance vecs nil nil 0)))
 443
 444 (defun calcFunc-vsdev (&rest vecs)
 445   (if (and (= (length vecs) 1)
 446            (memq (car-safe (car vecs)) '(sdev intv)))
 447       (if (eq (car-safe (car vecs)) 'intv)
 448           (if (math-floatp (car vecs))
 449               (math-div (math-sub (nth 3 (car vecs)) (nth 2 (car vecs)))
 450                         (math-sqrt-12))
 451             (math-sqrt (calcFunc-vvar (car vecs))))
 452         (nth 2 (car vecs)))
 453     (math-sqrt (math-covariance vecs nil nil 0))))
 454
 455 ;;; Compute the population variance or std deviation of numbers or vectors.
 456 (defun calcFunc-vpvar (&rest vecs)
 457   (if (and (= (length vecs) 1)
 458            (memq (car-safe (car vecs)) '(sdev intv)))
 459       (if (eq (car-safe (car vecs)) 'intv)
 460           (math-intv-variance (car vecs) t)
 461         (math-sqr (nth 2 (car vecs))))
 462     (math-covariance vecs nil t 0)))
 463
 464 (defun calcFunc-vpsdev (&rest vecs)
 465   (if (and (= (length vecs) 1)
 466            (memq (car-safe (car vecs)) '(sdev intv)))
 467       (if (eq (car-safe (car vecs)) 'intv)
 468           (if (math-floatp (car vecs))
 469               (math-div (math-sub (nth 3 (car vecs)) (nth 2 (car vecs)))
 470                         (math-sqrt-12))
 471             (math-sqrt (calcFunc-vpvar (car vecs))))
 472         (nth 2 (car vecs)))
 473     (math-sqrt (math-covariance vecs nil t 0))))
 474
 475 (defun math-intv-variance (x pop)
 476   (or (math-constp x) (math-reject-arg x 'constp))
 477   (if (math-floatp x)
 478       (math-div (math-sqr (math-sub (nth 3 x) (nth 2 x))) 12)
 479     (let* ((x (math-fix-int-intv x))
 480            (len (math-sub (nth 3 x) (nth 2 x)))
 481            (hlen (math-quotient len 2)))
 482       (math-div (if (math-evenp len)
 483                     (calcFunc-sum '(^ (var X var-X) 2) '(var X var-X)
 484                                   (math-neg hlen) hlen)
 485                   (calcFunc-sum '(^ (- (var X var-X) (/ 1 2)) 2)
 486                                 '(var X var-X)
 487                                 (math-neg hlen) (math-add hlen 1)))
 488                 (if pop (math-add len 1) len)))))
 489
 490 ;;; Compute the covariance and linear correlation coefficient.
 491 (defun calcFunc-vcov (vec1 &optional vec2)
 492   (math-covariance (list vec1) (list vec2) nil 1))
 493
 494 (defun calcFunc-vpcov (vec1 &optional vec2)
 495   (math-covariance (list vec1) (list vec2) t 1))
 496
 497 (defun calcFunc-vcorr (vec1 &optional vec2)
 498   (math-covariance (list vec1) (list vec2) nil 2))
 499
 500
 501 (defun math-covariance (vec1 vec2 pop mode)
 502   (or (car vec2) (= mode 0)
 503       (progn
 504         (if (and (eq (car-safe (car vec1)) 'var)
 505                  (eq (car-safe (calc-var-value (nth 2 (car vec1)))) 'vec))
 506             (setq vec1 (symbol-value (nth 2 (car vec1))))
 507           (setq vec1 (car vec1)))
 508         (or (math-matrixp vec1) (math-dimension-error))
 509         (or (= (length (nth 1 vec1)) 3) (math-dimension-error))
 510         (setq vec2 (list (math-mat-col vec1 2))
 511               vec1 (list (math-mat-col vec1 1)))))
 512   (math-with-extra-prec 2
 513     (let* ((split1 (math-split-sdev-vec (math-flatten-many-vecs vec1) nil))
 514            (means1 (car split1))
 515            (wts1 (nth 1 split1))
 516            split2 means2 (wts2 nil)
 517            (sqrwts nil)
 518            suminvsqrwts
 519            (len (1- (length means1))))
 520       (if (< len (if pop 1 2))
 521           (math-reject-arg nil (if pop
 522                                    "*Must be at least 1 argument"
 523                                  "*Must be at least 2 arguments")))
 524       (if (or wts1 wts2)
 525           (setq sqrwts (math-add
 526                         (if wts1
 527                             (calcFunc-map '(var mul var-mul) wts1 wts1)
 528                           0)
 529                         (if wts2
 530                             (calcFunc-map '(var mul var-mul) wts2 wts2)
 531                           0))
 532                 suminvsqrwts (calcFunc-reduce
 533                               '(var add var-add)
 534                               (calcFunc-map '(var div var-div) 1 sqrwts))))
 535       (or (= mode 0)
 536           (progn
 537             (setq split2 (math-split-sdev-vec (math-flatten-many-vecs vec2)
 538                                               nil)
 539                   means2 (car split2)
 540                   wts2 (nth 2 split1))
 541             (or (= len (1- (length means2))) (math-dimension-error))))
 542       (let* ((diff1 (calcFunc-map
 543                      '(var add var-add)
 544                      means1
 545                      (if sqrwts
 546                          (math-div (calcFunc-reduce
 547                                     '(var add var-add)
 548                                     (calcFunc-map '(var div var-div)
 549                                                   means1 sqrwts))
 550                                    (math-neg suminvsqrwts))
 551                        (math-div (calcFunc-reducer '(var add var-add) means1)
 552                                  (- len)))))
 553              (diff2 (if (= mode 0)
 554                         diff1
 555                       (calcFunc-map
 556                        '(var add var-add)
 557                        means2
 558                        (if sqrwts
 559                            (math-div (calcFunc-reduce
 560                                       '(var add var-add)
 561                                       (calcFunc-map '(var div var-div)
 562                                                     means2 sqrwts))
 563                                      (math-neg suminvsqrwts))
 564                          (math-div (calcFunc-reducer '(var add var-add) means2)
 565                                    (- len))))))
 566              (covar (calcFunc-map '(var mul var-mul) diff1 diff2)))
 567         (if sqrwts
 568             (setq covar (calcFunc-map '(var div var-div) covar sqrwts)))
 569         (math-div
 570          (calcFunc-reducer '(var add var-add) covar)
 571          (if (= mode 2)
 572              (let ((var1 (calcFunc-map '(var mul var-mul) diff1 diff1))
 573                    (var2 (calcFunc-map '(var mul var-mul) diff2 diff2)))
 574                (if sqrwts
 575                    (setq var1 (calcFunc-map '(var div var-div) var1 sqrwts)
 576                          var2 (calcFunc-map '(var div var-div) var2 sqrwts)))
 577                (math-sqrt
 578                 (math-mul (calcFunc-reducer '(var add var-add) var1)
 579                           (calcFunc-reducer '(var add var-add) var2))))
 580            (if sqrwts
 581                (if pop
 582                    suminvsqrwts
 583                  (math-div (math-mul suminvsqrwts (1- len)) len))
 584              (if pop len (1- len)))))))))
 585
 586 (provide 'calc-stat)
 587
 588 ;;; arch-tag: 423858e9-8513-489c-9f35-710cd9d9c307
 589 ;;; calc-stat.el ends here