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
|
function ex_1
%EX_1: four methods for creating the same matrix.
% (please wait, this can take a while...)
% Example:
% ex_1
% See also: cs_demo
% CXSparse, Copyright (c) 2006-2022, Timothy A. Davis. All Rights Reserved.
% SPDX-License-Identifier: LGPL-2.1+
n = 1000 ;
nz = 1e5 ;
tic
% method 1: A(i,j) = ...
rand ('state', 0) ;
A = sparse (n,n) ;
for k = 1:nz
% compute some arbitrary entry and add it into the matrix
i = 1 + fix (n * rand (1)) ;
j = 1 + fix (n * rand (1)) ;
x = rand (1) ;
A (i,j) = A (i,j) + x ; % VERY slow, esp. if A(i,j) not already nonzero!
end
fprintf ('Method 1: ') ;
toc
A1 = A ;
tic
% method 2: triplet form, one entry at a time
rand ('state', 0) ;
ii = zeros (nz, 1) ; % preallocate ii, jj, and xx
jj = zeros (nz, 1) ;
xx = zeros (nz, 1) ;
for k = 1:nz
% compute some arbitrary entry and add it into the matrix
ii (k) = 1 + fix (n * rand (1)) ;
jj (k) = 1 + fix (n * rand (1)) ;
xx (k) = rand (1) ;
end
A = sparse (ii,jj,xx) ;
fprintf ('Method 2: ') ;
toc
A2 = A ;
disp (A1-A2) ;
tic
% method 3: triplet form, one entry at a time, pretend nz is unknown
rand ('state', 0) ;
len = 16 ;
ii = zeros (len, 1) ;
jj = zeros (len, 1) ;
xx = zeros (len, 1) ;
for k = 1:nz
% compute some arbitrary entry and add it into the matrix
if (k > len)
% double the size of ii,jj,xx
len = 2*len ;
ii (len) = 0 ;
jj (len) = 0 ;
xx (len) = 0 ;
end
ii (k) = 1 + fix (n * rand (1)) ;
jj (k) = 1 + fix (n * rand (1)) ;
xx (k) = rand (1) ;
end
A = sparse (ii (1:k), jj (1:k), xx (1:k)) ;
fprintf ('Method 3: ') ;
toc
A3 = A ;
disp (A1-A3) ;
tic
% method 4: avoid the for loop
rand ('state', 0) ;
e = rand (3, nz) ;
e (1,:) = 1 + fix (n * e (1,:)) ;
e (2,:) = 1 + fix (n * e (2,:)) ;
A = sparse (e (1,:), e (2,:), e (3,:)) ;
fprintf ('Method 4: ') ;
toc
A4 = A ;
disp (A1-A4) ;
|
