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Most of this change is to boilerplate commentary such as license URLs. This change was prompted by ftp://ftp.gnu.org's going-away party, planned for November. Change these FTP URLs to https://ftp.gnu.org instead. Make similar changes for URLs to other organizations moving away from FTP. Also, change HTTP to HTTPS for URLs to gnu.org and fsf.org when this works, as this will further help defend against man-in-the-middle attacks (for this part I omitted the MS-DOS and MS-Windows sources and the test tarballs to keep the workload down). HTTPS is not fully working to lists.gnu.org so I left those URLs alone for now.
596 lines
18 KiB
EmacsLisp
596 lines
18 KiB
EmacsLisp
;;; calc-stat.el --- statistical functions for Calc
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;; Copyright (C) 1990-1993, 2001-2017 Free Software Foundation, Inc.
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;; Author: David Gillespie <daveg@synaptics.com>
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;; This file is part of GNU Emacs.
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;; GNU Emacs is free software: you can redistribute it and/or modify
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;; it under the terms of the GNU General Public License as published by
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;; the Free Software Foundation, either version 3 of the License, or
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;; (at your option) any later version.
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;; GNU Emacs is distributed in the hope that it will be useful,
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;; but WITHOUT ANY WARRANTY; without even the implied warranty of
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;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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;; GNU General Public License for more details.
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;; You should have received a copy of the GNU General Public License
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;; along with GNU Emacs. If not, see <https://www.gnu.org/licenses/>.
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;;; Commentary:
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;;; Code:
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;; This file is autoloaded from calc-ext.el.
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(require 'calc-ext)
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(require 'calc-macs)
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;;; Statistical operations on vectors.
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(defun calc-vector-count (arg)
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(interactive "P")
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(calc-slow-wrapper
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(calc-vector-op "coun" 'calcFunc-vcount arg)))
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(defun calc-vector-sum (arg)
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(interactive "P")
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(calc-slow-wrapper
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(if (calc-is-hyperbolic)
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(calc-vector-op "vprd" 'calcFunc-vprod arg)
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(calc-vector-op "vsum" 'calcFunc-vsum arg))))
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(defun calc-vector-product (arg)
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(interactive "P")
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(calc-hyperbolic-func)
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(calc-vector-sum arg))
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(defun calc-vector-max (arg)
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(interactive "P")
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(calc-slow-wrapper
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(if (calc-is-inverse)
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(calc-vector-op "vmin" 'calcFunc-vmin arg)
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(calc-vector-op "vmax" 'calcFunc-vmax arg))))
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(defun calc-vector-min (arg)
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(interactive "P")
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(calc-invert-func)
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(calc-vector-max arg))
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(defun calc-vector-mean (arg)
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(interactive "P")
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(calc-slow-wrapper
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(if (calc-is-hyperbolic)
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(if (calc-is-inverse)
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(calc-vector-op "harm" 'calcFunc-vhmean arg)
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(calc-vector-op "medn" 'calcFunc-vmedian arg))
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(if (calc-is-inverse)
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(calc-vector-op "meae" 'calcFunc-vmeane arg)
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(calc-vector-op "mean" 'calcFunc-vmean arg)))))
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(defun calc-vector-rms (arg)
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(interactive "P")
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(calc-slow-wrapper
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(calc-vector-op "rms" 'calcFunc-rms arg)))
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(defun calc-vector-mean-error (arg)
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(interactive "P")
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(calc-invert-func)
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(calc-vector-mean arg))
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(defun calc-vector-median (arg)
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(interactive "P")
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(calc-hyperbolic-func)
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(calc-vector-mean arg))
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(defun calc-vector-harmonic-mean (arg)
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(interactive "P")
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(calc-invert-func)
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(calc-hyperbolic-func)
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(calc-vector-mean arg))
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(defun calc-vector-geometric-mean (arg)
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(interactive "P")
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(calc-slow-wrapper
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(if (calc-is-hyperbolic)
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(calc-binary-op "geom" 'calcFunc-agmean arg)
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(calc-vector-op "geom" 'calcFunc-vgmean arg))))
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(defun calc-vector-sdev (arg)
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(interactive "P")
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(calc-slow-wrapper
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(if (calc-is-hyperbolic)
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(if (calc-is-inverse)
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(calc-vector-op "pvar" 'calcFunc-vpvar arg)
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(calc-vector-op "var" 'calcFunc-vvar arg))
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(if (calc-is-inverse)
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(calc-vector-op "psdv" 'calcFunc-vpsdev arg)
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(calc-vector-op "sdev" 'calcFunc-vsdev arg)))))
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(defun calc-vector-pop-sdev (arg)
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(interactive "P")
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(calc-invert-func)
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(calc-vector-sdev arg))
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(defun calc-vector-variance (arg)
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(interactive "P")
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(calc-hyperbolic-func)
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(calc-vector-sdev arg))
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(defun calc-vector-pop-variance (arg)
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(interactive "P")
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(calc-invert-func)
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(calc-hyperbolic-func)
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(calc-vector-sdev arg))
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(defun calc-vector-covariance (arg)
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(interactive "P")
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(calc-slow-wrapper
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(let ((n (if (eq arg 1) 1 2)))
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(if (calc-is-hyperbolic)
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(calc-enter-result n "corr" (cons 'calcFunc-vcorr
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(calc-top-list-n n)))
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(if (calc-is-inverse)
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(calc-enter-result n "pcov" (cons 'calcFunc-vpcov
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(calc-top-list-n n)))
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(calc-enter-result n "cov" (cons 'calcFunc-vcov
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(calc-top-list-n n))))))))
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(defun calc-vector-pop-covariance (arg)
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(interactive "P")
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(calc-invert-func)
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(calc-vector-covariance arg))
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(defun calc-vector-correlation (arg)
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(interactive "P")
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(calc-hyperbolic-func)
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(calc-vector-covariance arg))
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(defun calc-vector-op (name func arg)
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(setq calc-aborted-prefix name
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arg (prefix-numeric-value arg))
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(if (< arg 0)
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(error "Negative arguments not allowed"))
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(calc-enter-result arg name (cons func (calc-top-list-n arg))))
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;;; Useful statistical functions
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;;; Sum, product, etc., of one or more values or vectors.
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;;; Each argument must be either a number or a vector. Vectors
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;;; are flattened, but variables inside are assumed to represent
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;;; non-vectors.
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(defun calcFunc-vsum (&rest vecs)
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(math-reduce-many-vecs 'calcFunc-add 'calcFunc-vsum vecs 0))
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(defun calcFunc-vprod (&rest vecs)
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(math-reduce-many-vecs 'calcFunc-mul 'calcFunc-vprod vecs 1))
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(defun calcFunc-vmax (&rest vecs)
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(if (eq (car-safe (car vecs)) 'sdev)
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'(var inf var-inf)
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(if (eq (car-safe (car vecs)) 'intv)
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(nth 3 (math-fix-int-intv (car vecs)))
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(math-reduce-many-vecs 'calcFunc-max 'calcFunc-vmax vecs
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'(neg (var inf var-inf))))))
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(defun calcFunc-vmin (&rest vecs)
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(if (eq (car-safe (car vecs)) 'sdev)
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'(neg (var inf var-inf))
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(if (eq (car-safe (car vecs)) 'intv)
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(nth 2 (math-fix-int-intv (car vecs)))
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(math-reduce-many-vecs 'calcFunc-min 'calcFunc-vmin vecs
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'(var inf var-inf)))))
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(defun math-reduce-many-vecs (func whole-func vecs ident)
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(let ((const-part nil)
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(symb-part nil)
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val vec)
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(let ((calc-internal-prec (+ calc-internal-prec 2)))
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(while vecs
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(setq val (car vecs))
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(and (eq (car-safe val) 'var)
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(eq (car-safe (calc-var-value (nth 2 val))) 'vec)
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(setq val (symbol-value (nth 2 val))))
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(cond ((Math-vectorp val)
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(setq vec (append (and const-part (list const-part))
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(math-flatten-vector val)))
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(setq const-part (if vec
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(calcFunc-reducer
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(math-calcFunc-to-var func)
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(cons 'vec vec))
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ident)))
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((or (Math-objectp val) (math-infinitep val))
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(setq const-part (if const-part
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(funcall func const-part val)
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val)))
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(t
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(setq symb-part (nconc symb-part (list val)))))
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(setq vecs (cdr vecs))))
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(if const-part
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(progn
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(setq const-part (math-normalize const-part))
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(if symb-part
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(funcall func const-part (cons whole-func symb-part))
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const-part))
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(if symb-part (cons whole-func symb-part) ident))))
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;;; Return the number of data elements among the arguments.
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(defun calcFunc-vcount (&rest vecs)
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(let ((count 0))
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(while vecs
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(setq count (if (Math-vectorp (car vecs))
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(+ count (math-count-elements (car vecs)))
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(if (Math-objectp (car vecs))
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(1+ count)
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(if (and (eq (car-safe (car vecs)) 'var)
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(eq (car-safe (calc-var-value
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(nth 2 (car vecs))))
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'vec))
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(+ count (math-count-elements
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(symbol-value (nth 2 (car vecs)))))
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(math-reject-arg (car vecs) 'numvecp))))
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vecs (cdr vecs)))
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count))
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(defun math-count-elements (vec)
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(let ((count 0))
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(while (setq vec (cdr vec))
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(setq count (if (Math-vectorp (car vec))
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(+ count (math-count-elements (car vec)))
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(1+ count))))
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count))
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(defun math-flatten-many-vecs (vecs)
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(let ((p vecs)
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(vec (list 'vec)))
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(while p
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(setq vec (nconc vec
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(if (Math-vectorp (car p))
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(math-flatten-vector (car p))
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(if (Math-objectp (car p))
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(list (car p))
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(if (and (eq (car-safe (car p)) 'var)
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(eq (car-safe (calc-var-value
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(nth 2 (car p)))) 'vec))
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(math-flatten-vector (symbol-value
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(nth 2 (car p))))
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(math-reject-arg (car p) 'numvecp)))))
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p (cdr p)))
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vec))
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(defun calcFunc-vflat (&rest vecs)
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(math-flatten-many-vecs vecs))
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(defun math-split-sdev-vec (vec zero-ok)
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(let ((means (list 'vec))
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(wts (list 'vec))
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(exact nil)
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(p vec))
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(while (and (setq p (cdr p))
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(not (and (consp (car p))
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(eq (car (car p)) 'sdev)))))
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(if (null p)
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(list vec nil)
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(while (setq vec (cdr vec))
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(if (and (consp (setq p (car vec)))
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(eq (car p) 'sdev))
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(or exact
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(setq means (cons (nth 1 p) means)
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wts (cons (nth 2 p) wts)))
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(if zero-ok
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(setq means (cons (nth 1 p) means)
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wts (cons 0 wts))
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(or exact
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(setq means (list 'vec)
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wts nil
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exact t))
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(setq means (cons p means)))))
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(list (nreverse means)
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(and wts (nreverse wts))))))
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;;; Return the arithmetic mean of the argument numbers or vectors.
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;;; (If numbers are error forms, computes the weighted mean.)
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(defun calcFunc-vmean (&rest vecs)
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(let* ((split (math-split-sdev-vec (math-flatten-many-vecs vecs) nil))
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(means (car split))
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(wts (nth 1 split))
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(len (1- (length means))))
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(if (= len 0)
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(math-reject-arg nil "*Must be at least 1 argument")
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(if (and (= len 1) (eq (car-safe (nth 1 means)) 'intv))
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(let ((x (math-fix-int-intv (nth 1 means))))
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(calcFunc-vmean (nth 2 x) (nth 3 x)))
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(math-with-extra-prec 2
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(if (and wts (> len 1))
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(let* ((sqrwts (calcFunc-map '(var mul var-mul) wts wts))
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(suminvsqrwts (calcFunc-reduce
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'(var add var-add)
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(calcFunc-map '(var div var-div)
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1 sqrwts))))
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(math-div (calcFunc-reduce '(var add var-add)
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(calcFunc-map '(var div var-div)
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means sqrwts))
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suminvsqrwts))
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(math-div (calcFunc-reduce '(var add var-add) means) len)))))))
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(defun calcFunc-rms (a)
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"Return the root-mean-square of the vector A."
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(math-sqrt
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(calcFunc-vmean
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(calcFunc-map '(var abssqr var-abssqr) a))))
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(defun math-fix-int-intv (x)
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(if (math-floatp x)
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x
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(list 'intv 3
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(if (memq (nth 1 x) '(2 3)) (nth 2 x) (math-add (nth 2 x) 1))
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(if (memq (nth 1 x) '(1 3)) (nth 3 x) (math-sub (nth 3 x) 1)))))
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;;; Compute the mean with an error estimate.
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(defun calcFunc-vmeane (&rest vecs)
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(let* ((split (math-split-sdev-vec (math-flatten-many-vecs vecs) nil))
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(means (car split))
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(wts (nth 1 split))
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(len (1- (length means))))
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(if (= len 0)
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(math-reject-arg nil "*Must be at least 1 argument")
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(math-with-extra-prec 2
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(if wts
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(let* ((sqrwts (calcFunc-map '(var mul var-mul) wts wts))
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(suminvsqrwts (calcFunc-reduce
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'(var add var-add)
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(calcFunc-map '(var div var-div)
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1 sqrwts))))
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(math-make-sdev
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(math-div (calcFunc-reduce '(var add var-add)
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(calcFunc-map '(var div var-div)
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means sqrwts))
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suminvsqrwts)
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(list 'calcFunc-sqrt (math-div 1 suminvsqrwts))))
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(let ((mean (math-div (calcFunc-reduce '(var add var-add) means)
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len)))
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(math-make-sdev
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mean
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(list 'calcFunc-sqrt
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(math-div (calcFunc-reducer
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'(var add var-add)
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(calcFunc-map '(var pow var-pow)
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(calcFunc-map '(var abs var-abs)
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(calcFunc-map
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'(var add var-add)
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means
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(math-neg mean)))
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2))
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(math-mul len (1- len)))))))))))
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;;; Compute the median of a list of values.
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(defun calcFunc-vmedian (&rest vecs)
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(let* ((flat (copy-sequence (cdr (math-flatten-many-vecs vecs))))
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(p flat)
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(len (length flat))
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(hlen (/ len 2)))
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(if (= len 0)
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(math-reject-arg nil "*Must be at least 1 argument")
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(if (and (= len 1) (memq (car-safe (car flat)) '(sdev intv)))
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(calcFunc-vmean (car flat))
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(while p
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(if (eq (car-safe (car p)) 'sdev)
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(setcar p (nth 1 (car p))))
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(or (Math-anglep (car p))
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(math-reject-arg (car p) 'anglep))
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(setq p (cdr p)))
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(setq flat (sort flat 'math-lessp))
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(if (= (% len 2) 0)
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(math-div (math-add (nth (1- hlen) flat) (nth hlen flat)) 2)
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(nth hlen flat))))))
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(defun calcFunc-vgmean (&rest vecs)
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(let* ((flat (math-flatten-many-vecs vecs))
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(len (1- (length flat))))
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(if (= len 0)
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(math-reject-arg nil "*Must be at least 1 argument")
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(math-with-extra-prec 2
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(let ((x (calcFunc-reduce '(var mul math-mul) flat)))
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(if (= len 2)
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(math-sqrt x)
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(math-pow x (list 'frac 1 len))))))))
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(defun calcFunc-agmean (a b)
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(cond ((Math-equal a b) a)
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((math-zerop a) a)
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((math-zerop b) b)
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(calc-symbolic-mode (math-inexact-result))
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((not (Math-realp a)) (math-reject-arg a 'realp))
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((not (Math-realp b)) (math-reject-arg b 'realp))
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(t
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(math-with-extra-prec 2
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(setq a (math-float (math-abs a))
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b (math-float (math-abs b)))
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(let (mean)
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(while (not (math-nearly-equal-float a b))
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(setq mean (math-mul-float (math-add-float a b) '(float 5 -1))
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b (math-sqrt-float (math-mul-float a b))
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a mean))
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a)))))
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(defun calcFunc-vhmean (&rest vecs)
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(let* ((flat (math-flatten-many-vecs vecs))
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(len (1- (length flat))))
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(if (= len 0)
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(math-reject-arg nil "*Must be at least 1 argument")
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(math-with-extra-prec 2
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(math-div len
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(calcFunc-reduce '(var add math-add)
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(calcFunc-map '(var inv var-inv) flat)))))))
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;;; Compute the sample variance or standard deviation of numbers or vectors.
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;;; (If the numbers are error forms, only the mean part of them is used.)
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(defun calcFunc-vvar (&rest vecs)
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(if (and (= (length vecs) 1)
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(memq (car-safe (car vecs)) '(sdev intv)))
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(if (eq (car-safe (car vecs)) 'intv)
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(math-intv-variance (car vecs) nil)
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(math-sqr (nth 2 (car vecs))))
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(math-covariance vecs nil nil 0)))
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(defun calcFunc-vsdev (&rest vecs)
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(if (and (= (length vecs) 1)
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(memq (car-safe (car vecs)) '(sdev intv)))
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(if (eq (car-safe (car vecs)) 'intv)
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(if (math-floatp (car vecs))
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(math-div (math-sub (nth 3 (car vecs)) (nth 2 (car vecs)))
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(math-sqrt-12))
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(math-sqrt (calcFunc-vvar (car vecs))))
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(nth 2 (car vecs)))
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(math-sqrt (math-covariance vecs nil nil 0))))
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;;; Compute the population variance or std deviation of numbers or vectors.
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(defun calcFunc-vpvar (&rest vecs)
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(if (and (= (length vecs) 1)
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(memq (car-safe (car vecs)) '(sdev intv)))
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(if (eq (car-safe (car vecs)) 'intv)
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(math-intv-variance (car vecs) t)
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(math-sqr (nth 2 (car vecs))))
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(math-covariance vecs nil t 0)))
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|
|
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(defun calcFunc-vpsdev (&rest vecs)
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(if (and (= (length vecs) 1)
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(memq (car-safe (car vecs)) '(sdev intv)))
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(if (eq (car-safe (car vecs)) 'intv)
|
|
(if (math-floatp (car vecs))
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|
(math-div (math-sub (nth 3 (car vecs)) (nth 2 (car vecs)))
|
|
(math-sqrt-12))
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|
(math-sqrt (calcFunc-vpvar (car vecs))))
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|
(nth 2 (car vecs)))
|
|
(math-sqrt (math-covariance vecs nil t 0))))
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|
|
|
(defun math-intv-variance (x pop)
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|
(or (math-constp x) (math-reject-arg x 'constp))
|
|
(if (math-floatp x)
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|
(math-div (math-sqr (math-sub (nth 3 x) (nth 2 x))) 12)
|
|
(let* ((x (math-fix-int-intv x))
|
|
(len (math-sub (nth 3 x) (nth 2 x)))
|
|
(hlen (math-quotient len 2)))
|
|
(math-div (if (math-evenp len)
|
|
(calcFunc-sum '(^ (var X var-X) 2) '(var X var-X)
|
|
(math-neg hlen) hlen)
|
|
(calcFunc-sum '(^ (- (var X var-X) (/ 1 2)) 2)
|
|
'(var X var-X)
|
|
(math-neg hlen) (math-add hlen 1)))
|
|
(if pop (math-add len 1) len)))))
|
|
|
|
;;; Compute the covariance and linear correlation coefficient.
|
|
(defun calcFunc-vcov (vec1 &optional vec2)
|
|
(math-covariance (list vec1) (list vec2) nil 1))
|
|
|
|
(defun calcFunc-vpcov (vec1 &optional vec2)
|
|
(math-covariance (list vec1) (list vec2) t 1))
|
|
|
|
(defun calcFunc-vcorr (vec1 &optional vec2)
|
|
(math-covariance (list vec1) (list vec2) nil 2))
|
|
|
|
|
|
(defun math-covariance (vec1 vec2 pop mode)
|
|
(or (car vec2) (= mode 0)
|
|
(progn
|
|
(if (and (eq (car-safe (car vec1)) 'var)
|
|
(eq (car-safe (calc-var-value (nth 2 (car vec1)))) 'vec))
|
|
(setq vec1 (symbol-value (nth 2 (car vec1))))
|
|
(setq vec1 (car vec1)))
|
|
(or (math-matrixp vec1) (math-dimension-error))
|
|
(or (= (length (nth 1 vec1)) 3) (math-dimension-error))
|
|
(setq vec2 (list (math-mat-col vec1 2))
|
|
vec1 (list (math-mat-col vec1 1)))))
|
|
(math-with-extra-prec 2
|
|
(let* ((split1 (math-split-sdev-vec (math-flatten-many-vecs vec1) nil))
|
|
(means1 (car split1))
|
|
(wts1 (nth 1 split1))
|
|
split2 means2 (wts2 nil)
|
|
(sqrwts nil)
|
|
suminvsqrwts
|
|
(len (1- (length means1))))
|
|
(if (< len (if pop 1 2))
|
|
(math-reject-arg nil (if pop
|
|
"*Must be at least 1 argument"
|
|
"*Must be at least 2 arguments")))
|
|
(if (or wts1 wts2)
|
|
(setq sqrwts (math-add
|
|
(if wts1
|
|
(calcFunc-map '(var mul var-mul) wts1 wts1)
|
|
0)
|
|
(if wts2
|
|
(calcFunc-map '(var mul var-mul) wts2 wts2)
|
|
0))
|
|
suminvsqrwts (calcFunc-reduce
|
|
'(var add var-add)
|
|
(calcFunc-map '(var div var-div) 1 sqrwts))))
|
|
(or (= mode 0)
|
|
(progn
|
|
(setq split2 (math-split-sdev-vec (math-flatten-many-vecs vec2)
|
|
nil)
|
|
means2 (car split2)
|
|
wts2 (nth 2 split1))
|
|
(or (= len (1- (length means2))) (math-dimension-error))))
|
|
(let* ((diff1 (calcFunc-map
|
|
'(var add var-add)
|
|
means1
|
|
(if sqrwts
|
|
(math-div (calcFunc-reduce
|
|
'(var add var-add)
|
|
(calcFunc-map '(var div var-div)
|
|
means1 sqrwts))
|
|
(math-neg suminvsqrwts))
|
|
(math-div (calcFunc-reducer '(var add var-add) means1)
|
|
(- len)))))
|
|
(diff2 (if (= mode 0)
|
|
diff1
|
|
(calcFunc-map
|
|
'(var add var-add)
|
|
means2
|
|
(if sqrwts
|
|
(math-div (calcFunc-reduce
|
|
'(var add var-add)
|
|
(calcFunc-map '(var div var-div)
|
|
means2 sqrwts))
|
|
(math-neg suminvsqrwts))
|
|
(math-div (calcFunc-reducer '(var add var-add) means2)
|
|
(- len))))))
|
|
(covar (calcFunc-map '(var mul var-mul) diff1 diff2)))
|
|
(if sqrwts
|
|
(setq covar (calcFunc-map '(var div var-div) covar sqrwts)))
|
|
(math-div
|
|
(calcFunc-reducer '(var add var-add) covar)
|
|
(if (= mode 2)
|
|
(let ((var1 (calcFunc-map '(var mul var-mul) diff1 diff1))
|
|
(var2 (calcFunc-map '(var mul var-mul) diff2 diff2)))
|
|
(if sqrwts
|
|
(setq var1 (calcFunc-map '(var div var-div) var1 sqrwts)
|
|
var2 (calcFunc-map '(var div var-div) var2 sqrwts)))
|
|
(math-sqrt
|
|
(math-mul (calcFunc-reducer '(var add var-add) var1)
|
|
(calcFunc-reducer '(var add var-add) var2))))
|
|
(if sqrwts
|
|
(if pop
|
|
suminvsqrwts
|
|
(math-div (math-mul suminvsqrwts (1- len)) len))
|
|
(if pop len (1- len)))))))))
|
|
|
|
(provide 'calc-stat)
|
|
|
|
;;; calc-stat.el ends here
|