forked from johannesgerer/jburkardt-f
-
Notifications
You must be signed in to change notification settings - Fork 1
/
asa006.html
204 lines (172 loc) · 5.22 KB
/
asa006.html
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
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
<html>
<head>
<title>
ASA006 - Cholesky Factor of a Positive Definite Symmetric Matrix
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
ASA006 <br> Cholesky Factor of a Positive Definite Symmetric Matrix
</h1>
<hr>
<p>
<b>ASA006</b>
is a FORTRAN90 library which
computes the Cholesky factor of a positive definite symmetric matrix.
</p>
<p>
<b>ASA006</b> is Applied Statistics Algorithm 6. Source code for many
Applied Statistics Algorithms is available through
<a href = "http://lib.stat.cmu.edu/apstat">STATLIB</a>.
</p>
<p>
If <b>A</b> is a positive definite symmetric matrix, then there is an
upper triangular matrix <b>U</b> with the property that
<blockquote><b>
A = U' * U
</b></blockquote>
The matrix <b>U</b> is known as the <i>Cholesky factor</i> of <b>A</b>,
and can be used to easily solve linear systems involving <b>A</b>
or compute the inverse of <b>A</b>.
</p>
<p>
The algorithm implemented here uses a compressed storage for both the
matrix <b>A</b> and the factor <b>U</b>. This saves some storage, but
can make computations a little awkward.
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>ASA006</b> is available in
<a href = "../../c_src/asa006/asa006.html">a C version</a> and
<a href = "../../cpp_src/asa006/asa006.html">a C++ version</a> and
<a href = "../../f77_src/asa006/asa006.html">a FORTRAN77 version</a> and
<a href = "../../f_src/asa006/asa006.html">a FORTRAN90 version</a> and
<a href = "../../m_src/asa006/asa006.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/asa007/asa007.html">
ASA007</a>,
a FORTRAN90 library which
computes the inverse of a symmetric positive definite matrix,
and uses a version of ASA006 for for Cholesky factorization.
</p>
<p>
<a href = "../../f_src/asa047/asa047.html">
ASA047</a>,
a FORTRAN90 library which
implements the Nelder-Mead minimization algorithm,
and uses a version of ASA006 for Cholesky factorization.
</p>
<p>
<a href = "../../f_src/lapack_examples/lapack_examples.html">
LAPACK_EXAMPLES</a>,
a FORTRAN90 program which
demonstrates the use of the LAPACK linear algebra library.
</p>
<p>
<a href = "../../f_src/linpack/linpack.html">
LINPACK</a>,
a FORTRAN90 library which
includes routines for Cholesky factorization.
</p>
<p>
<a href = "../../f_src/pppack/pppack.html">
PPPACK</a>,
a FORTRAN90 library which
computes piecewise polynomial functions, including cubic splines.
</p>
<p>
<a href = "../../f_src/toeplitz_cholesky/toeplitz_cholesky.html">
TOEPLITZ_CHOLESKY</a>,
a FORTRAN90 library which
computes the Cholesky factorization of a nonnegative definite symmetric
Toeplitz matrix.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
PR Freeman,<br>
Remark AS R44:
A Remark on AS 6 and AS7: Triangular decomposition of a symmetric matrix
and Inversion of a positive semi-definite symmetric matrix,<br>
Applied Statistics,<br>
Volume 31, Number 3, 1982, pages 336-339.
</li>
<li>
Michael Healy,<br>
Algorithm AS 6:
Triangular decomposition of a symmetric matrix,<br>
Applied Statistics,<br>
Volume 17, Number 2, 1968, pages 195-197.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "asa006.f90">asa006.f90</a>, the source code.
</li>
<li>
<a href = "asa006.sh">asa006.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "asa006_prb.f90">asa006_prb.f90</a>,
a sample calling program.
</li>
<li>
<a href = "asa006_prb.sh">asa006_prb.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "asa006_prb_output.txt">asa006_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>CHOLESKY</b> computes the Cholesky factorization of a PDS matrix.
</li>
<li>
<b>SUBCHL</b> computes the Cholesky factorization of a (subset of a ) PDS matrix.
</li>
<li>
<b>TIMESTAMP</b> prints out the current YMDHMS date as a timestamp.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 01 February 2008.
</i>
<!-- John Burkardt -->
</body>
<!-- Initial HTML skeleton created by HTMLINDEX. -->
</html>