matrices.lsp

   1 ;;; -*- mode: lisp -*-
   2 ;;;
   3 ;;; Copyright (c) 2005--2007, 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 ;;;; matrices -- Basic matrix operations
   9 ;;;;
  10 ;;;; Copyright (c) 1991, by Luke Tierney. Permission is granted for
  11 ;;;; unrestricted use.
  12
  13
  14 ;;; Need to extend to use CLEM
  15
  16 ;;;
  17 ;;; Package Setup
  18 ;;;
  19
  20 (in-package :cl-user)
  21
  22 (defpackage :lisp-stat-matrix
  23   (:use :common-lisp
  24         :cffi
  25         :lisp-stat-compound-data)
  26   (:export matrixp num-rows num-cols matmult identity-matrix diagonal
  27            row-list column-list inner-product outer-product
  28            cross-product transpose bind-columns bind-rows
  29            array-data-vector vector-to-array
  30
  31            check-matrix check-square-matrix
  32
  33            copy-array copy-vector
  34            ))
  35
  36 (in-package :lisp-stat-matrix)
  37
  38 (deftype matrix () 'array)  ;; temp fix
  39
  40 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
  41 ;;;;
  42 ;;;;          Array to Row-Major Data Vector Conversion Functions
  43 ;;;;
  44 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
  45
  46 (defun array-data-vector (a)
  47 "Args: (a)
  48 Displaces array A to a vector"
  49   (make-array (array-total-size a)
  50               :displaced-to a
  51               :element-type (array-element-type a)))
  52
  53 (defun vector-to-array (v dims)
  54 "Args: (v dims)
  55 Displaces vector V to array with dimensions DIMS"
  56   (make-array dims
  57               :displaced-to v
  58               :element-type (array-element-type v)))
  59
  60 ;;;;
  61
  62 (defun check-matrix (a)
  63   (if (not (and (typep a' array)
  64                 (= (array-rank a) 2)))
  65       (error "not a matrix - ~s" a)
  66       t))
  67
  68 (defun check-square-matrix (a)
  69   (if (and (check-matrix a)
  70            (/= (array-dimension a 0) (array-dimension a 1))
  71            (error "matrix not square - ~s" a))
  72       t))
  73
  74 (defun matrixp (x)
  75 "Args: (x)
  76
  77 Returns:
  78    T if X is a 2-d array (i.e. a matrix),
  79    NIL otherwise."
  80   (and (typep x 'array)
  81        (= (array-rank x) 2)))
  82
  83 (defun num-rows (x)
  84   "Args: (x)
  85
  86 Returns number of rows in X."
  87   (if (matrixp x)
  88       (array-dimension x 0)
  89       (error "only useful for matrices.")))
  90
  91 (defun num-cols (x)
  92   "Args: (x)
  93
  94 Returns number of columns in X."
  95   (if (matrixp x)
  96       (array-dimension x 1)
  97       (error "only useful for matrices.")))
  98
  99
 100 ;;; Look at this!  Prime target for generic function dispatch!
 101 (defun matmult (a b &rest args)
 102   "Args: (a b &rest args)
 103 Returns the matrix product of matrices a, b, etc. If a is a vector it is
 104 treated as a row vector; if b is a vector it is treated as a column vector."
 105   ;; fixme: why does SBCL claim this is unreachable?
 106   (let ((rtype (cond ((and (typep a 'matrix)
 107                            (typep b 'matrix)) 'matrix)
 108                      ((and (typep a 'matrix)
 109                            (typep b 'sequence)) 'vector)
 110                      ((and (typep a 'sequence)
 111                            (typep b 'matrix)) 'vector)
 112                      ((and (typep a 'sequence)
 113                            (typep b 'sequence)) 'number)
 114                      ((typep a 'sequence)
 115                       (if (consp a) 'list 'vector))
 116                      ((typep b 'sequence)
 117                       (if (consp b) 'list 'vector)))))
 118
 119     (if (typep a 'sequence)
 120       (setf a (vector-to-array (coerce a 'vector) (list 1 (length a)))))
 121     (if (typep b 'sequence)
 122       (setf b (vector-to-array (coerce b 'vector) (list (length b) 1))))
 123     (if (not (= (array-dimension a 1) (array-dimension b 0)))
 124       (error "dimensions do not match"))
 125     (if args
 126       (reduce #'matmult args :initial-value (matmult a b))
 127       (let* ((n (array-dimension a 0))
 128              (m (array-dimension b 1))
 129              (p (array-dimension a 1))
 130              (c (make-array (list n m)))
 131              x)
 132         (declare (fixnum n m p))
 133         (dotimes (i n)
 134           (declare (fixnum i))
 135           (dotimes (j m)
 136             (declare (fixnum j))
 137             (setq x 0)
 138             (dotimes (k p)
 139               (declare (fixnum k))
 140               (setq x (+ x
 141                          (* (aref a i k)
 142                             (aref b k j)))))
 143             (setf (aref c i j) x)))
 144         (case rtype
 145           (matrix c)
 146           (number (aref c 0 0))
 147           (t (coerce (compound-data-seq c) rtype)))))))
 148
 149 (defun identity-matrix (n)
 150 "Args: (n)
 151 Returns the identity matrix of rank N."
 152   (let ((result (make-array (list n n) :initial-element 0)))
 153     (dotimes (i n result)
 154              (declare (fixnum i))
 155              (setf (aref result i i) 1))))
 156
 157 ;; this thing is not very efficient at this point - too much coercing
 158 (defun diagonal (x)
 159 "Args: (x)
 160 If X is a matrix, returns the diagonal of X. If X is a sequence, returns a
 161 diagonal matrix of rank (length X) with diagonal elements eq to the elements
 162 of X."
 163   (cond ((typep x 'matrix)
 164          (let* ((n (min (num-rows x) (num-cols x)))
 165                 (result (make-array n)))
 166            (dotimes (i n (coerce result 'list))
 167                     (setf (aref result i) (aref x i i)))))
 168         ((typep x 'sequence)
 169          (let* ((x (coerce x 'vector))
 170                 (n (length x))
 171                 (result (make-array (list n n) :initial-element 0)))
 172            (dotimes (i n result)
 173                     (setf (aref result i i) (aref x i)))))
 174         (t (error "argument must be a matrix or a sequence"))))
 175
 176 (defun row-list (x)
 177   "Args: (m)
 178
 179 Returns a list of the rows of M as vectors"
 180   (check-matrix x)
 181   (let ((m (num-rows x))
 182         (n (num-cols x))
 183         (result nil))
 184     (declare (fixnum m n))
 185     (flet ((get-row (k)
 186              (declare (fixnum k))
 187              (let ((row (make-array n)))
 188                (dotimes (i n row)
 189                  (declare (fixnum i))
 190                  (setf (aref row i) (aref x k i))))))
 191       (dotimes (i m result)
 192         (declare (fixnum i))
 193         (setf result (cons (get-row (- m i 1)) result))))))
 194
 195 (defun column-list (x)
 196   "Args: (m)
 197
 198 Returns a list of the columns of M as vectors"
 199   (check-matrix x)
 200   (let ((m (num-rows x))
 201         (n (num-cols x))
 202         (result nil))
 203     (declare (fixnum m n))
 204     (flet ((get-col (k)
 205              (declare (fixnum k))
 206              (let ((col (make-array m)))
 207                (dotimes (i m col)
 208                  (declare (fixnum i))
 209                  (setf (aref col i) (aref x i k))))))
 210       (dotimes (i n result)
 211         (declare (fixnum i))
 212         (setf result (cons (get-col (- n i 1)) result))))))
 213
 214 (defun inner-product (x y)
 215   "Args: (x y)
 216
 217 Returns inner product of sequences X and Y."
 218   (check-sequence x)
 219   (check-sequence y)
 220   (let ((n (length x))
 221         (cx (make-next-element x))
 222         (cy (make-next-element y))
 223         (result 0))
 224     (declare (fixnum n))
 225     (if (/= n (length y)) (error "sequence lengths do not match"))
 226     (dotimes (i n result)
 227       (declare (fixnum i))
 228       (setf result
 229             (+ result (* (get-next-element cx i)
 230                          (get-next-element cy i)))))))
 231
 232 (defun outer-product (x y &optional (f #'*))
 233   "Args: (x y &optional (fcn #'*))
 234
 235 Returns the generalized outer product of x and y, using fcn. Tat is, the result
 236 is a matrix of dimension ((length x) (length y)) and the (i j) element of the
 237 result is computed as (apply fcn (aref x i) (aref y j))."
 238
 239   (let* ((x (coerce x 'vector))
 240          (y (coerce y 'vector))
 241          (m (length x))
 242          (n (length y))
 243          (a (make-array (list m n))))
 244     (declare (fixnum m n))
 245     (dotimes (i m a)
 246       (declare (fixnum i))
 247       (dotimes (j n)
 248         (declare (fixnum j))
 249         (setf (aref a i j) (funcall f (aref x i) (aref y j)))))))
 250
 251 (defun cross-product (x)
 252   "Args: (x)
 253
 254 If X is a matrix returns (matmult (transpose X) X). If X is a vector returns
 255 (inner-product X X)."
 256
 257   (check-matrix x)
 258   (let* ((n (num-rows x))
 259          (p (num-cols x))
 260          (c (make-array (list p p))))
 261     (declare (fixnum n p))
 262     (dotimes (i p c)
 263       (declare (fixnum i))
 264       (dotimes (j (+ i 1))
 265         (declare (fixnum j))
 266         (let ((val 0))
 267           (dotimes (k n)
 268             (declare (fixnum k))
 269             (incf val (* (aref x k i) (aref x k j))))
 270           (setf (aref c i j) val)
 271           (setf (aref c j i) val))))))
 272
 273 (defun transpose-list (x)
 274   (let ((m (length (first x))))
 275     (dolist (next x)
 276       (if (not (consp next)) (error "not a list - ~a" x))
 277       (if (/= m (length next)) (error "sublists not the same length")))
 278     (do* ((cx (copy-list x))
 279           (result (make-list m))
 280           (next result (cdr next)))
 281          ((null next) result)
 282       (setf (first next) (mapcar #'first cx))
 283       (do ((next cx (cdr next)))
 284           ((null next))
 285         (setf (first next) (rest (first next)))))))
 286
 287 (defun transpose (x)
 288 "Args: (m)
 289 Returns the transpose of the matrix M."
 290   (cond
 291    ((consp x) (transpose-list x))
 292    (t
 293     (check-matrix x)
 294     (let* ((m (num-rows x))
 295            (n (num-cols x))
 296            (tx (make-array (list n m))))
 297       (declare (fixnum m n))
 298       (dotimes (i m tx)
 299         (declare (fixnum i))
 300         (dotimes (j n)
 301           (declare (fixnum j))
 302           (setf (aref tx j i) (aref x i j))))))))
 303
 304 (defun bind-columns (&rest args)
 305   "Args (&rest args)
 306
 307 The ARGS can be matrices, vectors, or lists. Arguments are bound into a matrix
 308 along their columns.  Example:
 309     (bind-columns #2a((1 2)(3 4)) #(5 6)) returns #2a((1 2 5)(3 4 6))"
 310
 311   (flet ((check-arg (x)
 312            (if (not (or (typep x 'sequence) (typep x 'matrix)))
 313                (error "bad argument type")))
 314          (arg-cols (x) (if (typep x 'sequence) 1 (num-cols x)))
 315          (arg-rows (x) (if (typep x 'sequence) (length x) (num-rows x))))
 316     (dolist (x args) (check-arg x)) ;; verify data structure conformance.
 317     (let ((m (arg-rows (first args)))
 318           (n (arg-cols (first args))))
 319       (declare (fixnum m n))
 320       (dolist (x (rest args))
 321         (if (/= m (arg-rows x)) (error "column lengths do not match"))
 322         (incf n (arg-cols x)))
 323       (do* ((result (make-array (list m n)))
 324             (args args (rest args))
 325             (firstcol 0)
 326             (x (first args) (first args)))
 327            ((null args) result)
 328         (cond
 329           ((typep x 'sequence)
 330            (let ((cx (make-next-element x)))
 331             (dotimes (i m)
 332               (setf (aref result i firstcol) (get-next-element cx i)))))
 333           (t
 334            (let ((k (arg-cols x)))
 335              (dotimes (i m)
 336                (dotimes (j k)
 337                  (setf (aref result i (+ firstcol j)) (aref x i j)))))))
 338         (incf firstcol (arg-cols x))))))
 339
 340 (defun bind-rows (&rest args)
 341   "Args (&rest args)
 342
 343 The ARGS can be matrices, vectors, or lists. Arguments are bound into a matrix
 344 along their rows. Example:
 345    (bind-rows #2a((1 2)(3 4)) #(5 6)) returns #2a((1 2)(3 4)(5 6))"
 346
 347   (flet ((check-arg (x)
 348            (if (not (or (typep x 'sequence)
 349                         (typep x 'matrix)))
 350                (error "bad argument type")))
 351          (arg-cols (x) (if (typep x 'sequence) (length x) (num-cols x)))
 352          (arg-rows (x) (if (typep x 'sequence) 1 (num-rows x))))
 353     (dolist (x args) (check-arg x))
 354     (let ((m (arg-rows (first args)))
 355           (n (arg-cols (first args))))
 356       (declare (fixnum m n))
 357       (dolist (x (rest args))
 358         (if (/= n (arg-cols x)) (error "row lengths do not match"))
 359         (incf m (arg-rows x)))
 360       (do* ((result (make-array (list m n)))
 361             (args args (rest args))
 362             (firstrow 0)
 363             (x (first args) (first args)))
 364            ((null args) result)
 365         (cond
 366          ((typep x 'sequence)
 367           (let ((cx (make-next-element x)))
 368             (dotimes (i n)
 369               (setf (aref result firstrow i) (get-next-element cx i)))))
 370          (t
 371           (let ((k (arg-rows x)))
 372             (dotimes (i n)
 373               (dotimes (j k)
 374                 (setf (aref result (+ firstrow j) i) (aref x j i)))))))
 375         (incf firstrow (arg-rows x))))))
 376
 377
 378 ;;;
 379 ;;; Copying Functions
 380 ;;;
 381
 382 (defun copy-vector (x)
 383   "Args: (x)
 384
 385 Returns a copy of the vector X"
 386   (copy-seq x))
 387
 388 (defun copy-array (a)
 389   "Args: (a)
 390
 391 Returns a copy of the array A"
 392   (vector-to-array (copy-seq (array-data-vector a))
 393                    (array-dimensions a)))
 394
 395 (defgeneric copy (x)
 396    (:documentation "methods for copying linaar algebra forms."))
 397
 398 (defmethod copy ((x vector)))
 399
 400 (defmethod copy ((x matrix)))
 401