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 standard-deviation quantile median interquartile-range
  32             fivnum sample))
  33
  34 (in-package :lisp-stat-descriptive-statistics)
  35
  36 ;;;
  37 ;;; Basic Summary Statistics
  38 ;;;
  39
  40 (defun standard-deviation (x)
  41 "Args: (x)
  42 Returns the standard deviation of the elements x. Vector reducing."
  43   (let ((n (count-elements x))
  44         (r (- x (mean x))))
  45     (sqrt (* (mean (* r r)) (/ n (- n 1))))))
  46
  47
  48 ;; FIXME the following assume that we are using the vector based functions
  49 (defun quantile (x p)
  50 "Args: (x p)
  51 Returns the P-th quantile(s) of sequence X. P can be a number or a sequence."
  52   (let* ((x (sort-data x))
  53          (n (length x))
  54          (np (* p (- n 1)))
  55          (low (floor np))
  56          (high (ceiling np)))
  57     (/ (+ (select x low) (select x high)) 2)))
  58
  59 (defun median (x)
  60 "Args: (x)
  61 Returns the median of the elements of X."
  62   (quantile x 0.5))
  63
  64 (defun interquartile-range (x)
  65 "Args: (number-data)
  66 Returns the interquartile range of the elements of X."
  67   (reduce #'- (quantile x '(0.75 0.25))))
  68
  69 (defun fivnum (x)
  70 "Args: (number-data)
  71 Returns the five number summary (min, 1st quartile, medinan, 3rd quartile,
  72 max) of the elements X."
  73   (quantile x '(0 .25 .5 .75 1)))
  74
  75 (defun covariance-matrix (&rest args)
  76 "Args: (&rest args)
  77 Returns the sample covariance matrix of the data columns in ARGS. ARGS may
  78 consist of lists, vectors or matrices."
  79   (let ((columns (apply #'append
  80                         (mapcar #'(lambda (x)
  81                                     (if (matrixp x) (column-list x) (list x)))
  82                                 args))))
  83     (/ (cross-product (apply #'bind-columns
  84                              (- columns (mapcar #'mean columns))))
  85        (- (length (car columns)) 1))))
  86
  87 ;;;; Sampling / Resampling
  88
  89 (defun sample (x ssize &optional replace)
  90 "Args: (x n &optional (replace nil))
  91 Returns a list of a random sample of size N from sequence X drawn with or
  92 without replacement."
  93   (check-sequence x)
  94   (let ((n (length x))
  95         (x (if (consp x) (coerce x 'vector) (copy-vector x)))
  96         (result nil))
  97     (if (< 0 n)
  98         (dotimes (i ssize result)
  99                  (let ((j (if replace (random n) (+ i (random (- n i))))))
 100                    (setf result (cons (aref x j) result))
 101                    (unless replace     ;; swap elements i and j
 102                            (let ((temp (aref x i)))
 103                              (setf (aref x i) (aref x j))
 104                              (setf (aref x j) temp))))))))
 105
 106
 107
 108 (defun mean (x)
 109 "Args: (x)
 110 Returns the mean of the elements x. Vector reducing."
 111   (let ((mean 0.0)
 112         (count 0.0))
 113     (labels ((add-to-mean (x)
 114               (let ((count+1 (+ count 1.0)))
 115                 (setf mean (+ (* (/ count count+1) mean) (* (/ count+1) x)))
 116                 (setf count count+1)))
 117              (find-mean (x)
 118                (if (numberp x)
 119                  (add-to-mean x)
 120                  (let ((seq (compound-data-seq x)))
 121                    (if (consp seq)
 122                      (dolist (x seq)
 123                        (if (numberp x) (add-to-mean x) (find-mean x)))
 124                      (let ((n (length seq)))
 125                        (dotimes (i n)
 126                          (declare (fixnum i))
 127                          (let ((x (aref seq i)))
 128                            (if (numberp x)
 129                                (add-to-mean x)
 130                                (find-mean x))))))))))
 131       (find-mean x)
 132       mean)))
 133