1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
|
;;; matrix.ss
;;; Copyright (C) 1996 R. Kent Dybvig
;;; from "The Scheme Programming Language, 2ed" by R. Kent Dybvig
;;; Permission is hereby granted, free of charge, to any person obtaining a
;;; copy of this software and associated documentation files (the "Software"),
;;; to deal in the Software without restriction, including without limitation
;;; the rights to use, copy, modify, merge, publish, distribute, sublicense,
;;; and/or sell copies of the Software, and to permit persons to whom the
;;; Software is furnished to do so, subject to the following conditions:
;;;
;;; The above copyright notice and this permission notice shall be included in
;;; all copies or substantial portions of the Software.
;;;
;;; THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
;;; IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
;;; FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
;;; THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
;;; LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
;;; FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
;;; DEALINGS IN THE SOFTWARE.
;;; make-matrix creates a matrix (a vector of vectors).
(define make-matrix
(lambda (rows columns)
(do ((m (make-vector rows))
(i 0 (+ i 1)))
((= i rows) m)
(vector-set! m i (make-vector columns)))))
;;; matrix? checks to see if its argument is a matrix.
;;; It isn't foolproof, but it's generally good enough.
(define matrix?
(lambda (x)
(and (vector? x)
(> (vector-length x) 0)
(vector? (vector-ref x 0)))))
;;; matrix-ref returns the jth element of the ith row.
(define matrix-ref
(lambda (m i j)
(vector-ref (vector-ref m i) j)))
;;; matrix-set! changes the jth element of the ith row.
(define matrix-set!
(lambda (m i j x)
(vector-set! (vector-ref m i) j x)))
;;; mul is the generic matrix/scalar multiplication procedure
(define mul
(lambda (x y)
;; type-error is called to complain when mul receives an invalid
;; type of argument.
(define type-error
(lambda (what)
(error 'mul
"~s is not a number or matrix"
what)))
;; match-error is called to complain when mul receives a pair of
;; incompatible arguments.
(define match-error
(lambda (what1 what2)
(error 'mul
"~s and ~s are incompatible operands"
what1
what2)))
;; matrix-rows returns the number of rows in a matrix.
(define matrix-rows
(lambda (x)
(vector-length x)))
;; matrix-columns returns the number of columns in a matrix.
(define matrix-columns
(lambda (x)
(vector-length (vector-ref x 0))))
;; mat-sca-mul multiplies a matrix by a scalar.
(define mat-sca-mul
(lambda (m x)
(let* ((nr (matrix-rows m))
(nc (matrix-columns m))
(r (make-matrix nr nc)))
(do ((i 0 (+ i 1)))
((= i nr) r)
(do ((j 0 (+ j 1)))
((= j nc))
(matrix-set! r i j
(* x (matrix-ref m i j))))))))
;; mat-mat-mul multiplies one matrix by another, after verifying
;; that the first matrix has as many columns as the second
;; matrix has rows.
(define mat-mat-mul
(lambda (m1 m2)
(let* ((nr1 (matrix-rows m1))
(nr2 (matrix-rows m2))
(nc2 (matrix-columns m2))
(r (make-matrix nr1 nc2)))
(if (not (= (matrix-columns m1) nr2))
(match-error m1 m2))
(do ((i 0 (+ i 1)))
((= i nr1) r)
(do ((j 0 (+ j 1)))
((= j nc2))
(do ((k 0 (+ k 1))
(a 0
(+ a
(* (matrix-ref m1 i k)
(matrix-ref m2 k j)))))
((= k nr2)
(matrix-set! r i j a))))))))
;; body of mul; dispatch based on input types
(cond
((number? x)
(cond
((number? y) (* x y))
((matrix? y) (mat-sca-mul y x))
(else (type-error y))))
((matrix? x)
(cond
((number? y) (mat-sca-mul x y))
((matrix? y) (mat-mat-mul x y))
(else (type-error y))))
(else (type-error x)))))
|
