-
Notifications
You must be signed in to change notification settings - Fork 59
/
test_ls.html
321 lines (286 loc) · 8.96 KB
/
test_ls.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
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
<html>
<head>
<title>
TEST_LS - Linear Least Squares Test Problems
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TEST_LS <br> Linear Least Squares Test Problems
</h1>
<hr>
<p>
<b>TEST_LS</b>
is a FORTRAN90 library which
defines a number of linear least squares problems of the form A*x=b,
where A is an M by N matrix.
</p>
<p>
Some linear least squares problems include constraints on the data,
such as requiring that every entry of X be positive. This library
only contains unconstrained problems. For such problems, the task is
typically to find a vector X which minimizes the Euclidean norm of
the residual r=Ax-b, or, in cases where multiple minimizers exist,
to find the minimizer of minimal Euclidean norm.
</p>
<p>
<b>TEST_LS</b> requires access to a compiled copy of the R8LIB library.
</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>TEST_LS</b> is available in
<a href = "../../c_src/test_ls/test_ls.html">a C version</a> and
<a href = "../../cpp_src/test_ls/test_ls.html">a C++ version</a> and
<a href = "../../f77_src/test_ls/test_ls.html">a FORTRAN77 version</a> and
<a href = "../../f_src/test_ls/test_ls.html">a FORTRAN90 version</a> and
<a href = "../../m_src/test_ls/test_ls.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/bvls/bvls.html">
BVLS</a>,
a FORTRAN90 library which
applies least squares methods to solve a linear system for which
lower and upper constraints may have been placed on every variable,
by Charles Lawson and Richard Hanson.
</p>
<p>
<a href = "../../f_src/dqed/dqed.html">
DQED</a>,
a FORTRAN90 library which
solves constrained least squares problems,
by Richard Hanson and Fred Krogh.
</p>
<p>
<a href = "../../f_src/lawson/lawson.html">
LAWSON</a>,
a FORTRAN90 library which
contains routines for solving least squares problems and singular value
decompositions (SVD),
by Charles Lawson, Richard Hanson.
</p>
<p>
<a href = "../../f_src/llsq/llsq.html">
LLSQ</a>,
a FORTRAN90 library which
solves the simple linear least squares problem of finding the formula
of a straight line y=a*x+b which minimizes the root-mean-square error
to a set of N data points.
</p>
<p>
<a href = "../../f_src/minpack/minpack.html">
MINPACK</a>,
a FORTRAN90 library which
solves systems of nonlinear equations, or the least squares minimization of the
residual of a set of linear or nonlinear equations.
</p>
<p>
<a href = "../../f_src/nms/nms.html">
NMS</a>,
a FORTRAN90 library which
includes a wide variety of numerical software, including
solvers for linear systems of equations, interpolation of data,
numerical quadrature, linear least squares data fitting,
the solution of nonlinear equations, ordinary differential equations,
optimization and nonlinear least squares, simulation and random numbers,
trigonometric approximation and Fast Fourier Transforms (FFT).
</p>
<p>
<a href = "../../f_src/qr_solve/qr_solve.html">
QR_SOLVE</a>,
a FORTRAN90 library which
computes the least squares solution of a linear system A*x=b.
</p>
<p>
<a href = "../../f_src/r8lib/r8lib.html">
R8LIB</a>,
a FORTRAN90 library which
contains many utility routines using double precision real (R8) arithmetic.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Cleve Moler,<br>
Numerical Computing with MATLAB,<br>
SIAM, 2004,<br>
ISBN13: 978-0-898716-60-3,<br>
LC: QA297.M625,<br>
ebook: http://www.mathworks.com/moler/chapters.html
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "test_ls.f90">test_ls.f90</a>, the source code.
</li>
<li>
<a href = "test_ls.sh">test_ls.sh</a>,
BASH commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "test_ls_prb.f90">test_ls_prb.f90</a>,
a sample calling program.
</li>
<li>
<a href = "test_ls_prb.sh">test_ls_prb.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "test_ls_prb_output.txt">test_ls_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>P00_A</b> returns the matrix A for any least squares problem.
</li>
<li>
<b>P00_B</b> returns the right hand side B for any least squares problem.
</li>
<li>
<b>P00_M</b> returns the number of equations M for any least squares problem.
</li>
<li>
<b>P00_N</b> returns the number of variables N for any least squares problem.
</li>
<li>
<b>P00_PROB_NUM</b> returns the number of least squares problems.
</li>
<li>
<b>P00_X</b> returns the least squares solution X for any least squares problem.
</li>
<li>
<b>P01_A</b> returns the matrix A for problem 1.
</li>
<li>
<b>P01_B</b> returns the right hand side B for problem 1.
</li>
<li>
<b>P01_M</b> returns the number of equations M for problem 1.
</li>
<li>
<b>P01_N</b> returns the number of variables N for problem 1.
</li>
<li>
<b>P01_X</b> returns the least squares solution X for problem 1.
</li>
<li>
<b>P02_A</b> returns the matrix A for problem 2.
</li>
<li>
<b>P02_B</b> returns the right hand side B for problem 2.
</li>
<li>
<b>P02_M</b> returns the number of equations M for problem 2.
</li>
<li>
<b>P02_N</b> returns the number of variables N for problem 2.
</li>
<li>
<b>P02_X</b> returns the least squares solution X for problem 2.
</li>
<li>
<b>P03_A</b> returns the matrix A for problem 3.
</li>
<li>
<b>P03_B</b> returns the right hand side B for problem 3.
</li>
<li>
<b>P03_M</b> returns the number of equations M for problem 3.
</li>
<li>
<b>P03_N</b> returns the number of variables N for problem 3.
</li>
<li>
<b>P03_X</b> returns the least squares solution X for problem 3.
</li>
<li>
<b>P04_A</b> returns the matrix A for problem 4.
</li>
<li>
<b>P04_B</b> returns the right hand side B for problem 4.
</li>
<li>
<b>P04_M</b> returns the number of equations M for problem 4.
</li>
<li>
<b>P04_N</b> returns the number of variables N for problem 4.
</li>
<li>
<b>P04_X</b> returns the least squares solution X for problem 4.
</li>
<li>
<b>P05_A</b> returns the matrix A for problem 5.
</li>
<li>
<b>P05_B</b> returns the right hand side B for problem 5.
</li>
<li>
<b>P05_M</b> returns the number of equations M for problem 5.
</li>
<li>
<b>P05_N</b> returns the number of variables N for problem 5.
</li>
<li>
<b>P05_X</b> returns the least squares solution X for problem 5.
</li>
<li>
<b>P06_A</b> returns the matrix A for problem 6.
</li>
<li>
<b>P06_B</b> returns the right hand side B for problem 6.
</li>
<li>
<b>P06_M</b> returns the number of equations M for problem 6.
</li>
<li>
<b>P06_N</b> returns the number of variables N for problem 6.
</li>
<li>
<b>P06_X</b> returns the least squares solution X for problem 6.
</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 04 October 2012.
</i>
<!-- John Burkardt -->
</body>
<!-- Initial HTML skeleton created by HTMLINDEX. -->
</html>