forked from johannesgerer/jburkardt-cpp
-
Notifications
You must be signed in to change notification settings - Fork 0
/
eispack.html
306 lines (273 loc) · 8.63 KB
/
eispack.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
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
<html>
<head>
<title>
EISPACK - Eigenvalue Calculations
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
EISPACK <br> Eigenvalue Calculations
</h1>
<hr>
<p>
<b>EISPACK</b>
is a C++ library which
calculates the eigenvalues and eigenvectors of a matrix.
</p>
<p>
Despite the following documentation, please note that only a FEW
of the EISPACK routines have actually been
converted to C++ at this time.
</p>
<p>
A variety of options are available for special matrix formats.
</p>
<p>
Note that EISPACK "simulates" complex arithmetic. That is,
complex data is stored as pairs of real numbers, and complex
arithmetic is done by carefully manipulating the real numbers.
</p>
<p>
EISPACK is old, and its functionality has been replaced by
the more modern and efficient LAPACK. There are some advantages,
not all sentimental, to keeping a copy of EISPACK around. For
one thing, the implementation of the LAPACK routines makes it
a trying task to try to comprehend the algorithm by reading the
source code. A single user level routine may refer indirectly to
thirty or forty others.
</p>
<p>
EISPACK includes a function to compute the singular value decomposition (SVD)
of a rectangular matrix.
</p>
<p>
The pristine correct original source code for <b>EISPACK</b> is available
through
<a href = "http://www.netlib.org/">the NETLIB web site</a>.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>EISPACK</b> is available in
<a href = "../../c_src/eispack/eispack.html">a C version</a> and
<a href = "../../cpp_src/eispack/eispack.html">a C++ version</a> and
<a href = "../../f77_src/eispack/eispack.html">a FORTRAN77 version</a> and
<a href = "../../f_src/eispack/eispack.html">a FORTRAN90 version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/jacobi_eigenvalue/jacobi_eigenvalue.html">
JACOBI_EIGENVALUE</a>,
a C++ library which
implements the Jacobi iteration for the iterative determination
of the eigenvalues and eigenvectors of a real symmetric matrix.
</p>
<p>
<a href = "../../cpp_src/test_eigen/test_eigen.html">
TEST_EIGEN</a>,
a C++ library which
defines various eigenvalue test cases.
</p>
<p>
<a href = "../../cpp_src/test_mat/test_mat.html">
TEST_MAT</a>,
a C++ library which
defines test matrices, some of
which have known eigenvalues and eigenvectors.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Hilary Bowdler, Roger Martin, Christian Reinsch, James Wilkinson,<br>
The QR and QL algorithms for Symmetric Matrices: TQL1 and TQL2,<br>
Numerische Mathematik,<br>
Volume 11, Number 4, May 1968, pages 293-306.
</li>
<li>
Gene Golub, Christian Reinsch,<br>
Singular Value Decomposition and Least Squares Solutions,<br>
Numerische Mathematik,<br>
Volume 14, Number 5, April 1970, pages 403-420.
</li>
<li>
Roger Martin, G Peters, James Wilkinson,<br>
HQR, The QR Algorithm for Real Hessenberg Matrices,<br>
Numerische Mathematik,<br>
Volume 14, Number 3, February 1970, pages 219-231.
</li>
<li>
Roger Martin, Christian Reinsch, James Wilkinson,<br>
Householder's Tridiagonalization of a Symmetric Matrix:
TRED1, TRED2 and TRED3,<br>
Numerische Mathematik,<br>
Volume 11, Number 3, March 1968, pages 181-195.
</li>
<li>
Roger Martin, James Wilkinson,<br>
Similarity Reduction of a General Matrix to Hessenberg Form:
ELMHES,<br>
Numerische Mathematik,<br>
Volume 12, Number 5, December 1968, pages 349-368.
</li>
<li>
Beresford Parlett, Christian Reinsch,<br>
Balancing a Matrix for Calculation of Eigenvalues and
Eigenvectors,<br>
Numerische Mathematik,<br>
Volume 13, Number 4, August 1969, pages 293-304.
</li>
<li>
Christian Reinsch,<br>
Algorithm 464:
Eigenvalues of a real symmetric tridiagonal matrix,<br>
Communications of the ACM,<br>
Volume 16, Number 11, November 1973, page 689.
</li>
<li>
Brian Smith, James Boyle, Jack Dongarra, Burton Garbow,
Yasuhiko Ikebe, Virginia Klema, Cleve Moler,<br>
Matrix Eigensystem Routines, EISPACK Guide,<br>
Lecture Notes in Computer Science, Volume 6,<br>
Springer, 1976,<br>
ISBN13: 978-3540075462,<br>
LC: QA193.M37.
</li>
<li>
James Wilkinson, Christian Reinsch,<br>
Handbook for Automatic Computation,<br>
Volume II, Linear Algebra, Part 2,<br>
Springer, 1971,<br>
ISBN: 0387054146,<br>
LC: QA251.W67.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "eispack.cpp">eispack.cpp</a>, the source code;
</li>
<li>
<a href = "eispack.hpp">eispack.hpp</a>, the include file;
</li>
<li>
<a href = "eispack.sh">eispack.sh</a>,
commands to compile the souce code;
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>EISPACK_PRB1</b> is a test program that demonstrates the use of
a number of EISPACK routines.
<ul>
<li>
<a href = "eispack_prb1.cpp">eispack_prb1.cpp</a>, the calling program;
</li>
<li>
<a href = "eispack_prb1.sh">eispack_prb1.sh</a>,
commands to compile, link and run the calling program;
</li>
<li>
<a href = "eispack_prb1_output.txt">eispack_prb1_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>BAKVEC</b> determines eigenvectors by reversing the FIGI transformation.
</li>
<li>
<b>CBABK2</b> finds eigenvectors by undoing the CBAL transformation.
</li>
<li>
<b>I4_MAX</b> returns the maximum of two I4's.
</li>
<li>
<b>I4_MIN</b> returns the smaller of two I4's.
</li>
<li>
<b>PYTHAG</b> computes SQRT ( A * A + B * B ) carefully.
</li>
<li>
<b>R8_ABS</b> returns the absolute value of an R8.
</li>
<li>
<b>R8_EPSILON</b> returns the R8 round off unit.
</li>
<li>
<b>R8_MAX</b> returns the maximum of two R8's.
</li>
<li>
<b>R8_MIN</b> returns the minimum of two R8's.
</li>
<li>
<b>R8_SIGN</b> returns the sign of an R8.
</li>
<li>
<b>R8MAT_MM_NEW</b> multiplies two matrices.
</li>
<li>
<b>R8MAT_PRINT</b> prints an R8MAT.
</li>
<li>
<b>R8MAT_PRINT_SOME</b> prints some of an R8MAT.
</li>
<li>
<b>R8VEC_PRINT</b> prints an R8VEC.
</li>
<li>
<b>RS</b> computes eigenvalues and eigenvectors of real symmetric matrix.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>TQL2</b> computes all eigenvalues/vectors, real symmetric tridiagonal matrix.
</li>
<li>
<b>TQLRAT</b> computes all eigenvalues of a real symmetric tridiagonal matrix.
</li>
<li>
<b>TRED1</b> transforms a real symmetric matrix to symmetric tridiagonal form.
</li>
<li>
<b>TRED2</b> transforms a real symmetric matrix to symmetric tridiagonal form.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 09 November 2012.
</i>
<!-- John Burkardt -->
</body>
</html>