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, 2009, 2010, 2011 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 of the License, or
  14 ;; (at your option) 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.  If not, see <http://www.gnu.org/licenses/>.
  23
  24 ;;; Commentary:
  25
  26 ;;; Code:
  27
  28 ;; This file is autoloaded from calc-ext.el.
  29
  30 (require 'calc-ext)
  31 (require 'calc-macs)
  32
  33 ;;; Statistical operations on vectors.
  34
  35 (defun calc-vector-count (arg)
  36   (interactive "P")
  37   (calc-slow-wrapper
  38    (calc-vector-op "coun" 'calcFunc-vcount arg)))
  39
  40 (defun calc-vector-sum (arg)
  41   (interactive "P")
  42   (calc-slow-wrapper
  43    (if (calc-is-hyperbolic)
  44        (calc-vector-op "vprd" 'calcFunc-vprod arg)
  45      (calc-vector-op "vsum" 'calcFunc-vsum arg))))
  46
  47 (defun calc-vector-product (arg)
  48   (interactive "P")
  49   (calc-hyperbolic-func)
  50   (calc-vector-sum arg))
  51
  52 (defun calc-vector-max (arg)
  53   (interactive "P")
  54   (calc-slow-wrapper
  55    (if (calc-is-inverse)
  56        (calc-vector-op "vmin" 'calcFunc-vmin arg)
  57      (calc-vector-op "vmax" 'calcFunc-vmax arg))))
  58
  59 (defun calc-vector-min (arg)
  60   (interactive "P")
  61   (calc-invert-func)
  62   (calc-vector-max arg))
  63
  64 (defun calc-vector-mean (arg)
  65   (interactive "P")
  66   (calc-slow-wrapper
  67    (if (calc-is-hyperbolic)
  68        (if (calc-is-inverse)
  69            (calc-vector-op "harm" 'calcFunc-vhmean arg)
  70          (calc-vector-op "medn" 'calcFunc-vmedian arg))
  71      (if (calc-is-inverse)
  72          (calc-vector-op "meae" 'calcFunc-vmeane arg)
  73        (calc-vector-op "mean" 'calcFunc-vmean arg)))))
  74
  75 (defun calc-vector-mean-error (arg)
  76   (interactive "P")
  77   (calc-invert-func)
  78   (calc-vector-mean arg))
  79
  80 (defun calc-vector-median (arg)
  81   (interactive "P")
  82   (calc-hyperbolic-func)
  83   (calc-vector-mean arg))
  84
  85 (defun calc-vector-harmonic-mean (arg)
  86   (interactive "P")
  87   (calc-invert-func)
  88   (calc-hyperbolic-func)
  89   (calc-vector-mean arg))
  90
  91 (defun calc-vector-geometric-mean (arg)
  92   (interactive "P")
  93   (calc-slow-wrapper
  94    (if (calc-is-hyperbolic)
  95        (calc-binary-op "geom" 'calcFunc-agmean arg)
  96      (calc-vector-op "geom" 'calcFunc-vgmean arg))))
  97
  98 (defun calc-vector-sdev (arg)
  99   (interactive "P")
 100   (calc-slow-wrapper
 101    (if (calc-is-hyperbolic)
 102        (if (calc-is-inverse)
 103            (calc-vector-op "pvar" 'calcFunc-vpvar arg)
 104          (calc-vector-op "var" 'calcFunc-vvar arg))
 105      (if (calc-is-inverse)
 106          (calc-vector-op "psdv" 'calcFunc-vpsdev arg)
 107        (calc-vector-op "sdev" 'calcFunc-vsdev arg)))))
 108
 109 (defun calc-vector-pop-sdev (arg)
 110   (interactive "P")
 111   (calc-invert-func)
 112   (calc-vector-sdev arg))
 113
 114 (defun calc-vector-variance (arg)
 115   (interactive "P")
 116   (calc-hyperbolic-func)
 117   (calc-vector-sdev arg))
 118
 119 (defun calc-vector-pop-variance (arg)
 120   (interactive "P")
 121   (calc-invert-func)
 122   (calc-hyperbolic-func)
 123   (calc-vector-sdev arg))
 124
 125 (defun calc-vector-covariance (arg)
 126   (interactive "P")
 127   (calc-slow-wrapper
 128    (let ((n (if (eq arg 1) 1 2)))
 129      (if (calc-is-hyperbolic)
 130          (calc-enter-result n "corr" (cons 'calcFunc-vcorr
 131                                            (calc-top-list-n n)))
 132        (if (calc-is-inverse)
 133            (calc-enter-result n "pcov" (cons 'calcFunc-vpcov
 134                                              (calc-top-list-n n)))
 135          (calc-enter-result n "cov" (cons 'calcFunc-vcov
 136                                           (calc-top-list-n n))))))))
 137
 138 (defun calc-vector-pop-covariance (arg)
 139   (interactive "P")
 140   (calc-invert-func)
 141   (calc-vector-covariance arg))
 142
 143 (defun calc-vector-correlation (arg)
 144   (interactive "P")
 145   (calc-hyperbolic-func)
 146   (calc-vector-covariance arg))
 147
 148 (defun calc-vector-op (name func arg)
 149   (setq calc-aborted-prefix name
 150         arg (prefix-numeric-value arg))
 151   (if (< arg 0)
 152       (error "Negative arguments not allowed"))
 153   (calc-enter-result arg name (cons func (calc-top-list-n arg))))
 154
 155
 156
 157
 158 ;;; Useful statistical functions
 159
 160 ;;; Sum, product, etc., of one or more values or vectors.
 161 ;;; Each argument must be either a number or a vector.  Vectors
 162 ;;; are flattened, but variables inside are assumed to represent
 163 ;;; non-vectors.
 164
 165 (defun calcFunc-vsum (&rest vecs)
 166   (math-reduce-many-vecs 'calcFunc-add 'calcFunc-vsum vecs 0))
 167
 168 (defun calcFunc-vprod (&rest vecs)
 169   (math-reduce-many-vecs 'calcFunc-mul 'calcFunc-vprod vecs 1))
 170
 171 (defun calcFunc-vmax (&rest vecs)
 172   (if (eq (car-safe (car vecs)) 'sdev)
 173       '(var inf var-inf)
 174     (if (eq (car-safe (car vecs)) 'intv)
 175         (nth 3 (math-fix-int-intv (car vecs)))
 176       (math-reduce-many-vecs 'calcFunc-max 'calcFunc-vmax vecs
 177                              '(neg (var inf var-inf))))))
 178
 179 (defun calcFunc-vmin (&rest vecs)
 180   (if (eq (car-safe (car vecs)) 'sdev)
 181       '(neg (var inf var-inf))
 182     (if (eq (car-safe (car vecs)) 'intv)
 183         (nth 2 (math-fix-int-intv (car vecs)))
 184       (math-reduce-many-vecs 'calcFunc-min 'calcFunc-vmin vecs
 185                              '(var inf var-inf)))))
 186
 187 (defun math-reduce-many-vecs (func whole-func vecs ident)
 188   (let ((const-part nil)
 189         (symb-part nil)
 190         val vec)
 191     (let ((calc-internal-prec (+ calc-internal-prec 2)))
 192       (while vecs
 193         (setq val (car vecs))
 194         (and (eq (car-safe val) 'var)
 195              (eq (car-safe (calc-var-value (nth 2 val))) 'vec)
 196              (setq val (symbol-value (nth 2 val))))
 197         (cond ((Math-vectorp val)
 198                (setq vec (append (and const-part (list const-part))
 199                                  (math-flatten-vector val)))
 200                (setq const-part (if vec
 201                                     (calcFunc-reducer
 202                                      (math-calcFunc-to-var func)
 203                                      (cons 'vec vec))
 204                                   ident)))
 205               ((or (Math-objectp val) (math-infinitep val))
 206                (setq const-part (if const-part
 207                                     (funcall func const-part val)
 208                                   val)))
 209               (t
 210                (setq symb-part (nconc symb-part (list val)))))
 211         (setq vecs (cdr vecs))))
 212     (if const-part
 213         (progn
 214           (setq const-part (math-normalize const-part))
 215           (if symb-part
 216               (funcall func const-part (cons whole-func symb-part))
 217             const-part))
 218       (if symb-part (cons whole-func symb-part) ident))))
 219
 220
 221 ;;; Return the number of data elements among the arguments.
 222 (defun calcFunc-vcount (&rest vecs)
 223   (let ((count 0))
 224     (while vecs
 225       (setq count (if (Math-vectorp (car vecs))
 226                       (+ count (math-count-elements (car vecs)))
 227                     (if (Math-objectp (car vecs))
 228                         (1+ count)
 229                       (if (and (eq (car-safe (car vecs)) 'var)
 230                                (eq (car-safe (calc-var-value
 231                                               (nth 2 (car vecs))))
 232                                    'vec))
 233                           (+ count (math-count-elements
 234                                     (symbol-value (nth 2 (car vecs)))))
 235                         (math-reject-arg (car vecs) 'numvecp))))
 236             vecs (cdr vecs)))
 237     count))
 238
 239 (defun math-count-elements (vec)
 240   (let ((count 0))
 241     (while (setq vec (cdr vec))
 242       (setq count (if (Math-vectorp (car vec))
 243                       (+ count (math-count-elements (car vec)))
 244                     (1+ count))))
 245     count))
 246
 247
 248 (defun math-flatten-many-vecs (vecs)
 249   (let ((p vecs)
 250         (vec (list 'vec)))
 251     (while p
 252       (setq vec (nconc vec
 253                        (if (Math-vectorp (car p))
 254                            (math-flatten-vector (car p))
 255                          (if (Math-objectp (car p))
 256                              (list (car p))
 257                            (if (and (eq (car-safe (car p)) 'var)
 258                                     (eq (car-safe (calc-var-value
 259                                                    (nth 2 (car p)))) 'vec))
 260                                (math-flatten-vector (symbol-value
 261                                                      (nth 2 (car p))))
 262                              (math-reject-arg (car p) 'numvecp)))))
 263             p (cdr p)))
 264     vec))
 265
 266 (defun calcFunc-vflat (&rest vecs)
 267   (math-flatten-many-vecs vecs))
 268
 269 (defun math-split-sdev-vec (vec zero-ok)
 270   (let ((means (list 'vec))
 271         (wts (list 'vec))
 272         (exact nil)
 273         (p vec))
 274     (while (and (setq p (cdr p))
 275                 (not (and (consp (car p))
 276                           (eq (car (car p)) 'sdev)))))
 277     (if (null p)
 278         (list vec nil)
 279       (while (setq vec (cdr vec))
 280         (if (and (consp (setq p (car vec)))
 281                  (eq (car p) 'sdev))
 282             (or exact
 283                 (setq means (cons (nth 1 p) means)
 284                       wts (cons (nth 2 p) wts)))
 285           (if zero-ok
 286               (setq means (cons (nth 1 p) means)
 287                     wts (cons 0 wts))
 288             (or exact
 289                 (setq means (list 'vec)
 290                       wts nil
 291                       exact t))
 292             (setq means (cons p means)))))
 293       (list (nreverse means)
 294             (and wts (nreverse wts))))))
 295
 296
 297 ;;; Return the arithmetic mean of the argument numbers or vectors.
 298 ;;; (If numbers are error forms, computes the weighted mean.)
 299 (defun calcFunc-vmean (&rest vecs)
 300   (let* ((split (math-split-sdev-vec (math-flatten-many-vecs vecs) nil))
 301          (means (car split))
 302          (wts (nth 1 split))
 303          (len (1- (length means))))
 304     (if (= len 0)
 305         (math-reject-arg nil "*Must be at least 1 argument")
 306       (if (and (= len 1) (eq (car-safe (nth 1 means)) 'intv))
 307           (let ((x (math-fix-int-intv (nth 1 means))))
 308             (calcFunc-vmean (nth 2 x) (nth 3 x)))
 309         (math-with-extra-prec 2
 310           (if (and wts (> len 1))
 311               (let* ((sqrwts (calcFunc-map '(var mul var-mul) wts wts))
 312                      (suminvsqrwts (calcFunc-reduce
 313                                     '(var add var-add)
 314                                     (calcFunc-map '(var div var-div)
 315                                                   1 sqrwts))))
 316                 (math-div (calcFunc-reduce '(var add var-add)
 317                                            (calcFunc-map '(var div var-div)
 318                                                          means sqrwts))
 319                           suminvsqrwts))
 320             (math-div (calcFunc-reduce '(var add var-add) means) len)))))))
 321
 322 (defun math-fix-int-intv (x)
 323   (if (math-floatp x)
 324       x
 325     (list 'intv 3
 326           (if (memq (nth 1 x) '(2 3)) (nth 2 x) (math-add (nth 2 x) 1))
 327           (if (memq (nth 1 x) '(1 3)) (nth 3 x) (math-sub (nth 3 x) 1)))))
 328
 329 ;;; Compute the mean with an error estimate.
 330 (defun calcFunc-vmeane (&rest vecs)
 331   (let* ((split (math-split-sdev-vec (math-flatten-many-vecs vecs) nil))
 332          (means (car split))
 333          (wts (nth 1 split))
 334          (len (1- (length means))))
 335     (if (= len 0)
 336         (math-reject-arg nil "*Must be at least 1 argument")
 337       (math-with-extra-prec 2
 338         (if wts
 339             (let* ((sqrwts (calcFunc-map '(var mul var-mul) wts wts))
 340                    (suminvsqrwts (calcFunc-reduce
 341                                   '(var add var-add)
 342                                   (calcFunc-map '(var div var-div)
 343                                                 1 sqrwts))))
 344               (math-make-sdev
 345                (math-div (calcFunc-reduce '(var add var-add)
 346                                           (calcFunc-map '(var div var-div)
 347                                                         means sqrwts))
 348                          suminvsqrwts)
 349                (list 'calcFunc-sqrt (math-div 1 suminvsqrwts))))
 350           (let ((mean (math-div (calcFunc-reduce '(var add var-add) means)
 351                                 len)))
 352             (math-make-sdev
 353              mean
 354              (list 'calcFunc-sqrt
 355                    (math-div (calcFunc-reducer
 356                               '(var add var-add)
 357                               (calcFunc-map '(var pow var-pow)
 358                                             (calcFunc-map '(var abs var-abs)
 359                                                           (calcFunc-map
 360                                                            '(var add var-add)
 361                                                            means
 362                                                            (math-neg mean)))
 363                                             2))
 364                              (math-mul len (1- len)))))))))))
 365
 366
 367 ;;; Compute the median of a list of values.
 368 (defun calcFunc-vmedian (&rest vecs)
 369   (let* ((flat (copy-sequence (cdr (math-flatten-many-vecs vecs))))
 370          (p flat)
 371          (len (length flat))
 372          (hlen (/ len 2)))
 373     (if (= len 0)
 374         (math-reject-arg nil "*Must be at least 1 argument")
 375       (if (and (= len 1) (memq (car-safe (car flat)) '(sdev intv)))
 376           (calcFunc-vmean (car flat))
 377         (while p
 378           (if (eq (car-safe (car p)) 'sdev)
 379               (setcar p (nth 1 (car p))))
 380           (or (Math-anglep (car p))
 381               (math-reject-arg (car p) 'anglep))
 382           (setq p (cdr p)))
 383         (setq flat (sort flat 'math-lessp))
 384         (if (= (% len 2) 0)
 385             (math-div (math-add (nth (1- hlen) flat) (nth hlen flat)) 2)
 386           (nth hlen flat))))))
 387
 388
 389 (defun calcFunc-vgmean (&rest vecs)
 390   (let* ((flat (math-flatten-many-vecs vecs))
 391          (len (1- (length flat))))
 392     (if (= len 0)
 393         (math-reject-arg nil "*Must be at least 1 argument")
 394       (math-with-extra-prec 2
 395         (let ((x (calcFunc-reduce '(var mul math-mul) flat)))
 396           (if (= len 2)
 397               (math-sqrt x)
 398             (math-pow x (list 'frac 1 len))))))))
 399
 400
 401 (defun calcFunc-agmean (a b)
 402   (cond ((Math-equal a b) a)
 403         ((math-zerop a) a)
 404         ((math-zerop b) b)
 405         (calc-symbolic-mode (math-inexact-result))
 406         ((not (Math-realp a)) (math-reject-arg a 'realp))
 407         ((not (Math-realp b)) (math-reject-arg b 'realp))
 408         (t
 409          (math-with-extra-prec 2
 410            (setq a (math-float (math-abs a))
 411                  b (math-float (math-abs b)))
 412            (let (mean)
 413              (while (not (math-nearly-equal-float a b))
 414                (setq mean (math-mul-float (math-add-float a b) '(float 5 -1))
 415                      b (math-sqrt-float (math-mul-float a b))
 416                      a mean))
 417              a)))))
 418
 419
 420 (defun calcFunc-vhmean (&rest vecs)
 421   (let* ((flat (math-flatten-many-vecs vecs))
 422          (len (1- (length flat))))
 423     (if (= len 0)
 424         (math-reject-arg nil "*Must be at least 1 argument")
 425       (math-with-extra-prec 2
 426         (math-div len
 427                   (calcFunc-reduce '(var add math-add)
 428                                    (calcFunc-map '(var inv var-inv) flat)))))))
 429
 430
 431
 432 ;;; Compute the sample variance or standard deviation of numbers or vectors.
 433 ;;; (If the numbers are error forms, only the mean part of them is used.)
 434 (defun calcFunc-vvar (&rest vecs)
 435   (if (and (= (length vecs) 1)
 436            (memq (car-safe (car vecs)) '(sdev intv)))
 437       (if (eq (car-safe (car vecs)) 'intv)
 438           (math-intv-variance (car vecs) nil)
 439         (math-sqr (nth 2 (car vecs))))
 440     (math-covariance vecs nil nil 0)))
 441
 442 (defun calcFunc-vsdev (&rest vecs)
 443   (if (and (= (length vecs) 1)
 444            (memq (car-safe (car vecs)) '(sdev intv)))
 445       (if (eq (car-safe (car vecs)) 'intv)
 446           (if (math-floatp (car vecs))
 447               (math-div (math-sub (nth 3 (car vecs)) (nth 2 (car vecs)))
 448                         (math-sqrt-12))
 449             (math-sqrt (calcFunc-vvar (car vecs))))
 450         (nth 2 (car vecs)))
 451     (math-sqrt (math-covariance vecs nil nil 0))))
 452
 453 ;;; Compute the population variance or std deviation of numbers or vectors.
 454 (defun calcFunc-vpvar (&rest vecs)
 455   (if (and (= (length vecs) 1)
 456            (memq (car-safe (car vecs)) '(sdev intv)))
 457       (if (eq (car-safe (car vecs)) 'intv)
 458           (math-intv-variance (car vecs) t)
 459         (math-sqr (nth 2 (car vecs))))
 460     (math-covariance vecs nil t 0)))
 461
 462 (defun calcFunc-vpsdev (&rest vecs)
 463   (if (and (= (length vecs) 1)
 464            (memq (car-safe (car vecs)) '(sdev intv)))
 465       (if (eq (car-safe (car vecs)) 'intv)
 466           (if (math-floatp (car vecs))
 467               (math-div (math-sub (nth 3 (car vecs)) (nth 2 (car vecs)))
 468                         (math-sqrt-12))
 469             (math-sqrt (calcFunc-vpvar (car vecs))))
 470         (nth 2 (car vecs)))
 471     (math-sqrt (math-covariance vecs nil t 0))))
 472
 473 (defun math-intv-variance (x pop)
 474   (or (math-constp x) (math-reject-arg x 'constp))
 475   (if (math-floatp x)
 476       (math-div (math-sqr (math-sub (nth 3 x) (nth 2 x))) 12)
 477     (let* ((x (math-fix-int-intv x))
 478            (len (math-sub (nth 3 x) (nth 2 x)))
 479            (hlen (math-quotient len 2)))
 480       (math-div (if (math-evenp len)
 481                     (calcFunc-sum '(^ (var X var-X) 2) '(var X var-X)
 482                                   (math-neg hlen) hlen)
 483                   (calcFunc-sum '(^ (- (var X var-X) (/ 1 2)) 2)
 484                                 '(var X var-X)
 485                                 (math-neg hlen) (math-add hlen 1)))
 486                 (if pop (math-add len 1) len)))))
 487
 488 ;;; Compute the covariance and linear correlation coefficient.
 489 (defun calcFunc-vcov (vec1 &optional vec2)
 490   (math-covariance (list vec1) (list vec2) nil 1))
 491
 492 (defun calcFunc-vpcov (vec1 &optional vec2)
 493   (math-covariance (list vec1) (list vec2) t 1))
 494
 495 (defun calcFunc-vcorr (vec1 &optional vec2)
 496   (math-covariance (list vec1) (list vec2) nil 2))
 497
 498
 499 (defun math-covariance (vec1 vec2 pop mode)
 500   (or (car vec2) (= mode 0)
 501       (progn
 502         (if (and (eq (car-safe (car vec1)) 'var)
 503                  (eq (car-safe (calc-var-value (nth 2 (car vec1)))) 'vec))
 504             (setq vec1 (symbol-value (nth 2 (car vec1))))
 505           (setq vec1 (car vec1)))
 506         (or (math-matrixp vec1) (math-dimension-error))
 507         (or (= (length (nth 1 vec1)) 3) (math-dimension-error))
 508         (setq vec2 (list (math-mat-col vec1 2))
 509               vec1 (list (math-mat-col vec1 1)))))
 510   (math-with-extra-prec 2
 511     (let* ((split1 (math-split-sdev-vec (math-flatten-many-vecs vec1) nil))
 512            (means1 (car split1))
 513            (wts1 (nth 1 split1))
 514            split2 means2 (wts2 nil)
 515            (sqrwts nil)
 516            suminvsqrwts
 517            (len (1- (length means1))))
 518       (if (< len (if pop 1 2))
 519           (math-reject-arg nil (if pop
 520                                    "*Must be at least 1 argument"
 521                                  "*Must be at least 2 arguments")))
 522       (if (or wts1 wts2)
 523           (setq sqrwts (math-add
 524                         (if wts1
 525                             (calcFunc-map '(var mul var-mul) wts1 wts1)
 526                           0)
 527                         (if wts2
 528                             (calcFunc-map '(var mul var-mul) wts2 wts2)
 529                           0))
 530                 suminvsqrwts (calcFunc-reduce
 531                               '(var add var-add)
 532                               (calcFunc-map '(var div var-div) 1 sqrwts))))
 533       (or (= mode 0)
 534           (progn
 535             (setq split2 (math-split-sdev-vec (math-flatten-many-vecs vec2)
 536                                               nil)
 537                   means2 (car split2)
 538                   wts2 (nth 2 split1))
 539             (or (= len (1- (length means2))) (math-dimension-error))))
 540       (let* ((diff1 (calcFunc-map
 541                      '(var add var-add)
 542                      means1
 543                      (if sqrwts
 544                          (math-div (calcFunc-reduce
 545                                     '(var add var-add)
 546                                     (calcFunc-map '(var div var-div)
 547                                                   means1 sqrwts))
 548                                    (math-neg suminvsqrwts))
 549                        (math-div (calcFunc-reducer '(var add var-add) means1)
 550                                  (- len)))))
 551              (diff2 (if (= mode 0)
 552                         diff1
 553                       (calcFunc-map
 554                        '(var add var-add)
 555                        means2
 556                        (if sqrwts
 557                            (math-div (calcFunc-reduce
 558                                       '(var add var-add)
 559                                       (calcFunc-map '(var div var-div)
 560                                                     means2 sqrwts))
 561                                      (math-neg suminvsqrwts))
 562                          (math-div (calcFunc-reducer '(var add var-add) means2)
 563                                    (- len))))))
 564              (covar (calcFunc-map '(var mul var-mul) diff1 diff2)))
 565         (if sqrwts
 566             (setq covar (calcFunc-map '(var div var-div) covar sqrwts)))
 567         (math-div
 568          (calcFunc-reducer '(var add var-add) covar)
 569          (if (= mode 2)
 570              (let ((var1 (calcFunc-map '(var mul var-mul) diff1 diff1))
 571                    (var2 (calcFunc-map '(var mul var-mul) diff2 diff2)))
 572                (if sqrwts
 573                    (setq var1 (calcFunc-map '(var div var-div) var1 sqrwts)
 574                          var2 (calcFunc-map '(var div var-div) var2 sqrwts)))
 575                (math-sqrt
 576                 (math-mul (calcFunc-reducer '(var add var-add) var1)
 577                           (calcFunc-reducer '(var add var-add) var2))))
 578            (if sqrwts
 579                (if pop
 580                    suminvsqrwts
 581                  (math-div (math-mul suminvsqrwts (1- len)) len))
 582              (if pop len (1- len)))))))))
 583
 584 (provide 'calc-stat)
 585
 586 ;; arch-tag: 423858e9-8513-489c-9f35-710cd9d9c307
 587 ;;; calc-stat.el ends here