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
  29       conjugate realpart imagpart phase
  30       min max logand logior logxor lognot ffloor fceiling
  31       ftruncate fround signum cis)
  32    (:export standard-deviation quantile median interquartile-range
  33             fivnum sample))
  34
  35 (in-package :lisp-stat-descriptive-statistics)
  36
  37 ;;;
  38 ;;; Basic Summary Statistics
  39 ;;;
  40
  41 (defun standard-deviation (x)
  42 "Args: (x)
  43 Returns the standard deviation of the elements x. Vector reducing."
  44   (let ((n (count-elements x))
  45         (r (- x (mean x))))
  46     (sqrt (* (mean (* r r)) (/ n (- n 1))))))
  47
  48
  49 ;; FIXME the following assume that we are using the vector based functions
  50 (defun quantile (x p)
  51 "Args: (x p)
  52 Returns the P-th quantile(s) of sequence X. P can be a number or a sequence."
  53   (let* ((x (sort-data x))
  54          (n (length x))
  55          (np (* p (- n 1)))
  56          (low (floor np))
  57          (high (ceiling np)))
  58     (/ (+ (select x low) (select x high)) 2)))
  59
  60 (defun median (x)
  61 "Args: (x)
  62 Returns the median of the elements of X."
  63   (quantile x 0.5))
  64
  65 (defun interquartile-range (x)
  66 "Args: (number-data)
  67 Returns the interquartile range of the elements of X."
  68   (reduce #'- (quantile x '(0.75 0.25))))
  69
  70 (defun fivnum (x)
  71 "Args: (number-data)
  72 Returns the five number summary (min, 1st quartile, medinan, 3rd quartile,
  73 max) of the elements X."
  74   (quantile x '(0 .25 .5 .75 1)))
  75
  76 (defun covariance-matrix (&rest args)
  77 "Args: (&rest args)
  78 Returns the sample covariance matrix of the data columns in ARGS. ARGS may
  79 consist of lists, vectors or matrices."
  80   (let ((columns (apply #'append
  81                         (mapcar #'(lambda (x)
  82                                     (if (matrixp x) (column-list x) (list x)))
  83                                 args))))
  84     (/ (cross-product (apply #'bind-columns
  85                              (- columns (mapcar #'mean columns))))
  86        (- (length (car columns)) 1))))
  87
  88 ;;;; Sampling / Resampling
  89
  90 (defun sample (x ssize &optional replace)
  91 "Args: (x n &optional (replace nil))
  92 Returns a list of a random sample of size N from sequence X drawn with or
  93 without replacement."
  94   (check-sequence x)
  95   (let ((n (length x))
  96         (x (if (consp x) (coerce x 'vector) (copy-vector x)))
  97         (result nil))
  98     (if (< 0 n)
  99         (dotimes (i ssize result)
 100                  (let ((j (if replace (random n) (+ i (random (- n i))))))
 101                    (setf result (cons (aref x j) result))
 102                    (unless replace     ;; swap elements i and j
 103                            (let ((temp (aref x i)))
 104                              (setf (aref x i) (aref x j))
 105                              (setf (aref x j) temp))))))))
 106
 107
 108
 109 (defun mean (x)
 110 "Args: (x)
 111 Returns the mean of the elements x. Vector reducing."
 112   (let ((mean 0.0)
 113         (count 0.0))
 114     (labels ((add-to-mean (x)
 115               (let ((count+1 (+ count 1.0)))
 116                 (setf mean (+ (* (/ count count+1) mean) (* (/ count+1) x)))
 117                 (setf count count+1)))
 118              (find-mean (x)
 119                (if (numberp x)
 120                  (add-to-mean x)
 121                  (let ((seq (compound-data-seq x)))
 122                    (if (consp seq)
 123                      (dolist (x seq)
 124                        (if (numberp x) (add-to-mean x) (find-mean x)))
 125                      (let ((n (length seq)))
 126                        (dotimes (i n)
 127                          (declare (fixnum i))
 128                          (let ((x (aref seq i)))
 129                            (if (numberp x)
 130                                (add-to-mean x)
 131                                (find-mean x))))))))))
 132       (find-mean x)
 133       mean)))
 134