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128 lines
4.4 KiB
Scheme
128 lines
4.4 KiB
Scheme
;;; matrix.ss
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;;; Copyright (C) 1996 R. Kent Dybvig
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;;; from "The Scheme Programming Language, 2ed" by R. Kent Dybvig
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;;; Permission is hereby granted, free of charge, to any person obtaining a
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;;; copy of this software and associated documentation files (the "Software"),
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;;; to deal in the Software without restriction, including without limitation
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;;; the rights to use, copy, modify, merge, publish, distribute, sublicense,
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;;; and/or sell copies of the Software, and to permit persons to whom the
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;;; Software is furnished to do so, subject to the following conditions:
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;;;
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;;; The above copyright notice and this permission notice shall be included in
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;;; all copies or substantial portions of the Software.
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;;;
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;;; THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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;;; IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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;;; FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
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;;; THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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;;; LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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;;; FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
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;;; DEALINGS IN THE SOFTWARE.
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;;; make-matrix creates a matrix (a vector of vectors).
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(define make-matrix
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(lambda (rows columns)
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(do ((m (make-vector rows))
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(i 0 (+ i 1)))
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((= i rows) m)
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(vector-set! m i (make-vector columns)))))
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;;; matrix? checks to see if its argument is a matrix.
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;;; It isn't foolproof, but it's generally good enough.
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(define matrix?
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(lambda (x)
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(and (vector? x)
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(> (vector-length x) 0)
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(vector? (vector-ref x 0)))))
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;;; matrix-ref returns the jth element of the ith row.
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(define matrix-ref
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(lambda (m i j)
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(vector-ref (vector-ref m i) j)))
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;;; matrix-set! changes the jth element of the ith row.
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(define matrix-set!
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(lambda (m i j x)
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(vector-set! (vector-ref m i) j x)))
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;;; mul is the generic matrix/scalar multiplication procedure
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(define mul
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(lambda (x y)
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;; type-error is called to complain when mul receives an invalid
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;; type of argument.
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(define type-error
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(lambda (what)
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(error 'mul
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"~s is not a number or matrix"
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what)))
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;; match-error is called to complain when mul receives a pair of
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;; incompatible arguments.
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(define match-error
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(lambda (what1 what2)
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(error 'mul
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"~s and ~s are incompatible operands"
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what1
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what2)))
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;; matrix-rows returns the number of rows in a matrix.
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(define matrix-rows
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(lambda (x)
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(vector-length x)))
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;; matrix-columns returns the number of columns in a matrix.
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(define matrix-columns
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(lambda (x)
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(vector-length (vector-ref x 0))))
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;; mat-sca-mul multiplies a matrix by a scalar.
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(define mat-sca-mul
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(lambda (m x)
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(let* ((nr (matrix-rows m))
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(nc (matrix-columns m))
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(r (make-matrix nr nc)))
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(do ((i 0 (+ i 1)))
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((= i nr) r)
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(do ((j 0 (+ j 1)))
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((= j nc))
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(matrix-set! r i j
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(* x (matrix-ref m i j))))))))
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;; mat-mat-mul multiplies one matrix by another, after verifying
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;; that the first matrix has as many columns as the second
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;; matrix has rows.
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(define mat-mat-mul
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(lambda (m1 m2)
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(let* ((nr1 (matrix-rows m1))
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(nr2 (matrix-rows m2))
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(nc2 (matrix-columns m2))
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(r (make-matrix nr1 nc2)))
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(if (not (= (matrix-columns m1) nr2))
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(match-error m1 m2))
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(do ((i 0 (+ i 1)))
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((= i nr1) r)
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(do ((j 0 (+ j 1)))
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((= j nc2))
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(do ((k 0 (+ k 1))
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(a 0
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(+ a
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(* (matrix-ref m1 i k)
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(matrix-ref m2 k j)))))
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((= k nr2)
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(matrix-set! r i j a))))))))
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;; body of mul; dispatch based on input types
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(cond
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((number? x)
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(cond
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((number? y) (* x y))
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((matrix? y) (mat-sca-mul y x))
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(else (type-error y))))
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((matrix? x)
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(cond
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((number? y) (mat-sca-mul x y))
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((matrix? y) (mat-mat-mul x y))
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(else (type-error y))))
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(else (type-error x)))))
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