statistics.lsp

   1 ;;; -*- mode: lisp -*-
   2 ;;; Copyright (c) 2005--2007, by A.J. Rossini <blindglobe@gmail.com>
   3 ;;; See COPYRIGHT file for any additional restrictions (BSD license).
   4 ;;; Since 1991, ANSI was finally finished.  Edited for ANSI Common Lisp.
   5
   6 ;;; XLisp-ism's removed to focus on Common Lisp.  Original source from:
   7 ;;;; statistics.lsp XLISP-STAT statistics functions
   8 ;;;; XLISP-STAT 2.1 Copyright (c) 1990, by Luke Tierney
   9 ;;;; Additions to Xlisp 2.1, Copyright (c) 1989 by David Michael Betz
  10 ;;;; You may give out copies of this software; for conditions see the file
  11 ;;;; COPYING included with this distribution.
  12
  13 (in-package :cl-user)
  14
  15 (defpackage :lisp-stat-descriptive-statistics
  16  (:use :common-lisp
  17        :lisp-stat-data
  18        :lisp-stat-math
  19        :lisp-stat-compound-data
  20        :lisp-stat-matrix
  21        :lisp-stat-linalg-data
  22        :lisp-stat-linalg
  23        :lisp-stat-basics)
  24    (:shadowing-import-from :lisp-stat-math
  25       expt + - * / ** mod rem abs 1+ 1- log exp sqrt sin cos tan
  26       asin acos atan sinh cosh tanh asinh acosh atanh float random
  27       truncate floor ceiling round minusp zerop plusp evenp oddp
  28       < <= = /= >= > complex conjugate realpart imagpart phase
  29       min max logand logior logxor lognot ffloor fceiling
  30       ftruncate fround signum cis)
  31    (:export ;; descriptive stats
  32           standard-deviation quantile median interquartile-range
  33           fivnum
  34
  35           sample
  36
  37
  38           ))
  39
  40 (in-package :lisp-stat-descriptive-statistics)
  41
  42 ;;;;
  43 ;;;; Basic Summary Statistics
  44 ;;;;
  45
  46 (defun standard-deviation (x)
  47 "Args: (x)
  48 Returns the standard deviation of the elements x. Vector reducing."
  49   (let ((n (count-elements x))
  50         (r (- x (mean x))))
  51     (sqrt (* (mean (* r r)) (/ n (- n 1))))))
  52
  53
  54 ;; FIXME the following assume that we are using the vector based functions
  55 (defun quantile (x p)
  56 "Args: (x p)
  57 Returns the P-th quantile(s) of sequence X. P can be a number or a sequence."
  58   (let* ((x (sort-data x))
  59          (n (length x))
  60          (np (* p (- n 1)))
  61          (low (floor np))
  62          (high (ceiling np)))
  63     (/ (+ (select x low) (select x high)) 2)))
  64
  65 (defun median (x)
  66 "Args: (x)
  67 Returns the median of the elements of X."
  68   (quantile x 0.5))
  69
  70 (defun interquartile-range (x)
  71 "Args: (number-data)
  72 Returns the interquartile range of the elements of X."
  73   (reduce #'- (quantile x '(0.75 0.25))))
  74
  75 (defun fivnum (x)
  76 "Args: (number-data)
  77 Returns the five number summary (min, 1st quartile, medinan, 3rd quartile,
  78 max) of the elements X."
  79   (quantile x '(0 .25 .5 .75 1)))
  80
  81 (defun covariance-matrix (&rest args)
  82 "Args: (&rest args)
  83 Returns the sample covariance matrix of the data columns in ARGS. ARGS may
  84 consist of lists, vectors or matrices."
  85   (let ((columns (apply #'append
  86                         (mapcar #'(lambda (x)
  87                                     (if (matrixp x) (column-list x) (list x)))
  88                                 args))))
  89     (/ (cross-product (apply #'bind-columns
  90                              (- columns (mapcar #'mean columns))))
  91        (- (length (car columns)) 1))))
  92
  93 ;;;; Sampling / Resampling
  94
  95 (defun sample (x ssize &optional replace)
  96 "Args: (x n &optional (replace nil))
  97 Returns a list of a random sample of size N from sequence X drawn with or
  98 without replacement."
  99   (check-sequence x)
 100   (let ((n (length x))
 101         (x (if (consp x) (coerce x 'vector) (copy-vector x)))
 102         (result nil))
 103     (if (< 0 n)
 104         (dotimes (i ssize result)
 105                  (let ((j (if replace (random n) (+ i (random (- n i))))))
 106                    (setf result (cons (aref x j) result))
 107                    (unless replace     ;; swap elements i and j
 108                            (let ((temp (aref x i)))
 109                              (setf (aref x i) (aref x j))
 110                              (setf (aref x j) temp))))))))
 111
 112
 113
 114 (defun mean (x)
 115 "Args: (x)
 116 Returns the mean of the elements x. Vector reducing."
 117   (let ((mean 0.0)
 118         (count 0.0))
 119     (labels ((add-to-mean (x)
 120               (let ((count+1 (+ count 1.0)))
 121                 (setf mean (+ (* (/ count count+1) mean) (* (/ count+1) x)))
 122                 (setf count count+1)))
 123              (find-mean (x)
 124                (if (numberp x)
 125                  (add-to-mean x)
 126                  (let ((seq (compound-data-seq x)))
 127                    (if (consp seq)
 128                      (dolist (x seq)
 129                        (if (numberp x) (add-to-mean x) (find-mean x)))
 130                      (let ((n (length seq)))
 131                        (dotimes (i n)
 132                          (declare (fixnum i))
 133                          (let ((x (aref seq i)))
 134                            (if (numberp x)
 135                                (add-to-mean x)
 136                                (find-mean x))))))))))
 137       (find-mean x)
 138       mean)))
 139