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;;; -*- mode: lisp -*-
;;;
;;; Copyright (c) 2005--2007, by A.J. Rossini <blindglobe@gmail.com>
;;; See COPYRIGHT file for any additional restrictions (BSD license).
;;; Since 1991, ANSI was finally finished. Modified to match ANSI
;;; Common Lisp.
;;;; matrices -- Basic matrix operations
;;;;
;;;; Copyright (c) 1991, by Luke Tierney. Permission is granted for
;;;; unrestricted use.
;;; Issues:
;;; #1 - Need to extend to use lisp-matrix?
;;; #2 - do as a second alternative?
(in-package :lisp-stat-matrix)
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;;;
;;;; Array to Row-Major Data Vector Conversion Functions
;;;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(defun array-data-vector (a)
"Args: (a)
Displaces array A to a vector"
(make-array (array-total-size a)
:displaced-to a
:element-type (array-element-type a)))
(defun vector-to-array (v dims)
"Args: (v dims)
Displaces vector V to array with dimensions DIMS"
(make-array dims
:displaced-to v
:element-type (array-element-type v)))
(defun check-square-matrix (a)
(if (and (check-matrix a)
(/= (array-dimension a 0) (array-dimension a 1))
(error "matrix not square - ~s" a))
t))
(defun inner-product (x y)
"Args: (x y)
Returns inner product of sequences X and Y."
(check-sequence x)
(check-sequence y)
(let ((n (length x))
(cx (make-next-element x))
(cy (make-next-element y))
(result 0))
(declare (fixnum n))
(if (/= n (length y)) (error "sequence lengths do not match"))
(dotimes (i n result)
(declare (fixnum i))
(setf result
(+ result (* (get-next-element cx i)
(get-next-element cy i)))))))
(defun outer-product (x y &optional (f #'*))
"Args: (x y &optional (fcn #'*))
Returns the generalized outer product of x and y, using fcn. Tat is, the result
is a matrix of dimension ((length x) (length y)) and the (i j) element of the
result is computed as (apply fcn (aref x i) (aref y j))."
(let* ((x (coerce x 'vector))
(y (coerce y 'vector))
(m (length x))
(n (length y))
(a (make-array (list m n))))
(declare (fixnum m n))
(dotimes (i m a)
(declare (fixnum i))
(dotimes (j n)
(declare (fixnum j))
(setf (aref a i j) (funcall f (aref x i) (aref y j)))))))
(defun cross-product (x)
"Args: (x)
If X is a matrix returns (matmult (transpose X) X). If X is a vector returns
(inner-product X X)."
(check-matrix x)
(let* ((n (num-rows x))
(p (num-cols x))
(c (make-array (list p p))))
(declare (fixnum n p))
(dotimes (i p c)
(declare (fixnum i))
(dotimes (j (+ i 1))
(declare (fixnum j))
(let ((val 0))
(dotimes (k n)
(declare (fixnum k))
(incf val (* (aref x k i) (aref x k j))))
(setf (aref c i j) val)
(setf (aref c j i) val))))))
(defun transpose-list (x)
(let ((m (length (first x))))
(dolist (next x)
(if (not (consp next)) (error "not a list - ~a" x))
(if (/= m (length next)) (error "sublists not the same length")))
(do* ((cx (copy-list x))
(result (make-list m))
(next result (cdr next)))
((null next) result)
(setf (first next) (mapcar #'first cx))
(do ((next cx (cdr next)))
((null next))
(setf (first next) (rest (first next)))))))
(defun transpose (x)
"Args: (m)
Returns the transpose of the matrix M."
(cond
((consp x) (transpose-list x))
(t
(check-matrix x)
(let* ((m (num-rows x))
(n (num-cols x))
(tx (make-array (list n m))))
(declare (fixnum m n))
(dotimes (i m tx)
(declare (fixnum i))
(dotimes (j n)
(declare (fixnum j))
(setf (aref tx j i) (aref x i j))))))))
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