matrix-matlisp.lisp

   1 i;;; -*- mode: lisp -*-
   2 ;;;
   3 ;;; Copyright (c) 2008--, by A.J. Rossini <blindglobe@gmail.com>
   4 ;;; See COPYRIGHT file for any additional restrictions (BSD license).
   5 ;;; Since 1991, ANSI was finally finished.  Modified to match ANSI
   6 ;;; Common Lisp.
   7
   8 ;; matrix-matlisp -- extended functions for matrix and linear algebra
   9 ;; using MATLISP.
  10
  11 ;; Package Setup
  12
  13 (in-package :cl-user)
  14
  15 (defpackage :lisp-stat-matrix-matlisp
  16   (:use :common-lisp
  17         :matlisp)
  18   (:export sweep
  19            ))
  20
  21 (in-package :lisp-stat-matrix-matlisp)
  22
  23 ;; Might check with features that we've (pushnew :matlisp *features*)
  24 ;; and then we can do  #+matlisp    as needed.
  25
  26 ;;;
  27 ;;; SWEEP Operator, MATLISP implementation.
  28 ;;;
  29
  30 (defun make-sweep-front (x y w n p mode has_w x_mean result)
  31   "X is:
  32 y is:
  33 w is =:
  34 n is :
  35 p is:
  36 mode is: real, complex
  37 has_w :
  38 x_mean:
  39 result:
  40 ."
  41   (declare (fixnum n p mode has_w))
  42   (let ((x_data nil)
  43         (result_data nil)
  44         (val 0.0)
  45         (dxi 0.0)
  46         (dyi 0.0)
  47         (dv 0.0)
  48         (dw 0.0)
  49         (sum_w 0.0)
  50         (dxik 0.0)
  51         (dxjk 0.0)
  52         (dyj 0.0)
  53         (dx_meani 0.0)
  54         (dx_meanj 0.0)
  55         (dy_mean 0.0)
  56         (has-w (if (/= 0 has_w) t nil))
  57         (RE 1))
  58     (declare (long-float val dxi dyi dv dw sum_w dxik dxjk dyj
  59                     dx_meani dx_meanj dy_mean))
  60
  61     (setf x_data (compound-data-seq x))
  62     (setf result_data (compound-data-seq result))
  63
  64     ;; find the mean of y
  65     (setf val 0.0)
  66     (setf sum_w 0.0)
  67     (dotimes (i n)
  68       (declare (fixnum i))
  69       (setf dyi (makedouble (aref y i)))
  70       (when has-w
  71         (setf dw (makedouble (aref w i)))
  72         (incf sum_w dw)
  73         (setf dyi (* dyi dw)))
  74       (incf val dyi))
  75     (if (not has-w) (setf sum_w (float n 0.0)))
  76     (if (<= sum_w 0.0) (error "non positive sum of weights"))
  77     (setf dy_mean (/ val sum_w))
  78
  79     ;; find the column means
  80     (dotimes (j p)
  81       (declare (fixnum j))
  82       (setf val 0.0)
  83       (dotimes (i n)
  84         (declare (fixnum i))
  85         (setf dxi (makedouble (aref x_data (+ (* p i) j))))
  86         (when has-w
  87           (setf dw (makedouble (aref w i)))
  88           (setf dxi (* dxi dw)))
  89         (incf val dxi))
  90       (setf (aref x_mean j) (/ val sum_w)))
  91
  92     ;; put 1/sum_w in topleft, means on left, minus means on top
  93     (setf (aref result_data 0) (/ 1.0 sum_w))
  94     (dotimes (i p)
  95       (declare (fixnum i))
  96       (setf dxi (makedouble (aref x_mean i)))
  97       (setf (aref result_data (+ i 1)) (- dxi))
  98       (setf (aref result_data (* (+ i 1) (+ p 2))) dxi))
  99     (setf (aref result_data (+ p 1)) (- dy_mean))
 100     (setf (aref result_data (* (+ p 1) (+ p 2))) dy_mean)
 101
 102     ;; put sums of adjusted cross products in body
 103     (dotimes (i p)
 104       (declare (fixnum i))
 105       (dotimes (j p)
 106         (declare (fixnum j))
 107         (setf val 0.0)
 108         (dotimes (k n)
 109           (declare (fixnum k))
 110           (setf dxik (makedouble (aref x_data (+ (* p k) i))))
 111           (setf dxjk (makedouble (aref x_data (+ (* p k) j))))
 112           (setf dx_meani (makedouble (aref x_mean i)))
 113           (setf dx_meanj (makedouble (aref x_mean j)))
 114           (setf dv (* (- dxik dx_meani) (- dxjk dx_meanj)))
 115           (when has-w
 116             (setf dw (makedouble (aref w k)))
 117             (setf dv (* dv dw)))
 118           (incf val dv))
 119         (setf (aref result_data (+ (* (+ i 1) (+ p 2)) (+ j 1))) val)
 120         (setf (aref result_data (+ (* (+ j 1) (+ p 2)) (+ i 1))) val))
 121       (setf val 0.0)
 122       (dotimes (j n)
 123         (declare (fixnum j))
 124         (setf dxik (makedouble (aref x_data (+ (* p j) i))))
 125         (setf dyj (makedouble (aref y j)))
 126         (setf dx_meani (makedouble (aref x_mean i)))
 127         (setf dv (* (- dxik dx_meani) (- dyj dy_mean)))
 128         (when has-w
 129           (setf dw (makedouble (aref w j)))
 130           (setf dv (* dv dw)))
 131         (incf val dv))
 132       (setf (aref result_data (+ (* (+ i 1) (+ p 2)) (+ p 1))) val)
 133       (setf (aref result_data (+ (* (+ p 1) (+ p 2)) (+ i 1))) val))
 134     (setf val 0.0)
 135     (dotimes (j n)
 136       (declare (fixnum j))
 137       (setf dyj (makedouble (aref y j)))
 138       (setf dv (* (- dyj dy_mean) (- dyj dy_mean)))
 139       (when has-w
 140         (setf dw (makedouble (aref w j)))
 141         (setf dv (* dv dw)))
 142       (incf val dv))
 143     (setf (aref result_data (+ (* (+ p 1) (+ p 2)) (+ p 1))) val)))
 144
 145 ;;; FIXME: use matlisp
 146 (defun sweep-in-place-front (a rows cols mode k tol)
 147   "Sweep algorithm for linear regression."
 148   (declare (long-float tol))
 149   (declare (fixnum rows cols mode k))
 150   (let ((data nil)
 151         (pivot 0.0)
 152         (aij 0.0)
 153         (aik 0.0)
 154         (akj 0.0)
 155         (akk 0.0)
 156         (RE 1))
 157     (declare (long-float pivot aij aik akj akk))
 158
 159     (if (> mode RE) (error "not supported for complex data yet"))
 160     (if (or (< k 0) (>= k rows) (>= k cols)) (error "index out of range"))
 161
 162     (setf tol (max tol machine-epsilon))
 163     (setf data (compound-data-seq a))
 164
 165     (setf pivot (makedouble (aref data (+ (* cols k) k))))
 166
 167     (cond
 168      ((or (> pivot tol) (< pivot (- tol)))
 169       (dotimes (i rows)
 170         (declare (fixnum i))
 171         (dotimes (j cols)
 172           (declare (fixnum j))
 173           (when (and (/= i k) (/= j k))
 174             (setf aij (makedouble (aref data (+ (* cols i) j))))
 175             (setf aik (makedouble (aref data (+ (* cols i) k))))
 176             (setf akj (makedouble (aref data (+ (* cols k) j))))
 177             (setf aij (- aij (/ (* aik akj) pivot)))
 178             (setf (aref data (+ (* cols i) j)) aij))))
 179
 180       (dotimes (i rows)
 181         (declare (fixnum i))
 182         (setf aik (makedouble (aref data (+ (* cols i) k))))
 183         (when (/= i k)
 184           (setf aik (/ aik pivot))
 185           (setf (aref data (+ (* cols i) k)) aik)))
 186
 187       (dotimes (j cols)
 188         (declare (fixnum j))
 189         (setf akj (makedouble (aref data (+ (* cols k) j))))
 190         (when (/= j k)
 191           (setf akj (- (/ akj pivot)))
 192           (setf (aref data (+ (* cols k) j)) akj)))
 193
 194       (setf akk (/ 1.0 pivot))
 195       (setf (aref data (+ (* cols k) k)) akk)
 196       1)
 197      (t 0))))
 198
 199 ;; FIXME: use matlisp
 200 (defun make-sweep-matrix (x y &optional w)
 201   "Args: (x y &optional weights)
 202  X is matrix, Y and WEIGHTS are sequences. Returns the sweep matrix of the
 203  (weighted) regression of Y on X"
 204    (check-matrix x)
 205    (check-sequence y)
 206    (if w (check-sequence w))
 207    (let ((n (num-rows x))
 208         (p (num-cols x)))
 209       (if (/= n (length y)) (error "dimensions do not match"))
 210     (if (and w (/= n (length w))) (error "dimensions do not match"))
 211     (let ((mode (max (la-data-mode x)
 212                      (la-data-mode x)
 213                      (if w (la-data-mode w) 0)))
 214           (result (make-array (list (+ p 2) (+ p 2))))
 215           (x-mean (make-array p))
 216           (y (coerce y 'vector))
 217           (w (if w (coerce w 'vector)))
 218           (has-w (if w 1 0)))
 219       (make-sweep-front x y w n p mode has-w x-mean result)
 220       result)))
 221
 222  (defun sweep-in-place (a k tol)
 223   (check-matrix a)
 224   (check-one-fixnum k)
 225   (check-one-real tol)
 226   (let ((rows (num-rows a))
 227         (cols (num-cols a))
 228         (mode (la-data-mode a)))
 229     (let ((swept (sweep-in-place-front a rows cols mode k tol)))
 230       (if (/= 0 swept) t nil))))
 231
 232 (defun sweep-operator (a columns &optional tolerances)
 233   "Args: (a indices &optional tolerances)
 234
 235 A is a matrix, INDICES a sequence of the column indices to be
 236 swept. Returns a list of the swept result and the list of the columns
 237 actually swept. (See MULTREG documentation.) If supplied, TOLERANCES
 238 should be a list of real numbers the same length as INDICES. An index
 239 will only be swept if its pivot element is larger than the
 240 corresponding element of TOLERANCES."
 241
 242   ;; Why we should use generics/methods....
 243   (if (not (typep a 'real-matrix))
 244       (error "a is not a matrix"))
 245   ;; following: we need integer?
 246   (if (and (not (typep columns 'sequence))
 247            (not (typep (setf columns (list columns)) 'sequence)))
 248       (error "columns not coerceable to sequence"))
 249   (if tolerances
 250       (if (and (not (typep tolerances 'sequence))
 251                (not (setf tolerances (list tolerances))))
 252           (error "tolerances not coercable to sequence.")))
 253
 254   ;; (check-real a) done by matlisp.
 255   (check-fixnum columns)
 256   (if tolerances (check-real tolerances))
 257
 258   (do ((tol .0000001)
 259        (result (copy-array a))
 260        (swept-columns nil)
 261        (columns (coerce columns 'list) (cdr columns))
 262        (tolerances (if (consp tolerances) (coerce tolerances 'list))
 263                    (if (consp tolerances) (cdr tolerances))))
 264       ((null columns) (list result swept-columns))
 265     ;; this should be done in the context of matlisp, I think...?
 266     (let ((col (first columns))
 267             (tol (if (consp tolerances) (first tolerances) tol)))
 268         (if (sweep-in-place result col tol)
 269             (setf swept-columns (cons col swept-columns))))))
 270