-
Notifications
You must be signed in to change notification settings - Fork 57
/
Copy pathnintlib.html
297 lines (262 loc) · 7.96 KB
/
nintlib.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
<html>
<head>
<title>
NINTLIB - Multi-dimensional quadrature
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
NINTLIB <br> Multi-dimensional quadrature
</h1>
<hr>
<p>
<b>NINTLIB</b>
is a MATLAB library which
estimates integrals over multi-dimensional
regions.
</p>
<p>
Please note that these routines are simple and academic. A good
program for computing an integral in multiple dimensions must
include error estimation and adaptivity. Simple straightforward
approaches to reducing the error will cause a ruinous explosion
in the number of function evaluations required.
</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>NINTLIB</b> is available in
<a href = "../../c_src/nintlib/nintlib.html">a C version</a> and
<a href = "../../cpp_src/nintlib/nintlib.html">a C++ version</a> and
<a href = "../../f77_src/nintlib/nintlib.html">a FORTRAN77 version</a> and
<a href = "../../f_src/nintlib/nintlib.html">a FORTRAN90 version</a> and
<a href = "../../m_src/nintlib/nintlib.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/integral_test/integral_test.html">
INTEGRAL_TEST</a>,
a FORTRAN90 program which
tests the suitability of
a set of N points for use in an equal-weight quadrature rule over
the multi-dimensional unit hypercube.
</p>
<p>
<a href = "../../f_src/intlib/intlib.html">
INTLIB</a>,
a FORTRAN90 library which
estimates
the integral of a function over a one-dimensional interval.
</p>
<p>
<a href = "../../m_src/nint_exactness/nint_exactness.html">
NINT_EXACTNESS</a>,
a MATLAB program which
demonstrates how to measure the
polynomial exactness of a multidimensional quadrature rule.
</p>
<p>
<a href = "../../m_src/product_rule/product_rule.html">
PRODUCT_RULE</a>,
a MATLAB program which
can create a multidimensional quadrature rule as a product of
one dimensional rules.
</p>
<p>
<a href = "../../m_src/quadrature_test/quadrature_test.html">
QUADRATURE_TEST</a>,
a MATLAB program which
reads the definition of a
multidimensional quadrature rule from three files, applies
the rule to a number of test integrals, and prints the
results.
</p>
<p>
<a href = "../../m_src/quadrule/quadrule.html">
QUADRULE</a>,
a MATLAB library which
defines a variety of
(mostly 1-dimensional) quadrature rules.
</p>
<p>
<a href = "../../m_src/quadrule_fast/quadrule_fast.html">
QUADRULE_FAST</a>,
a MATLAB library which
defines efficient versions
of a few 1D quadrature rules.
</p>
<p>
<a href = "../../m_src/stroud/stroud.html">
STROUD</a>,
a MATLAB library which
defines
quadrature rules over various "interesting" geometric shapes.
</p>
<p>
<a href = "../../m_src/test_int_2d/test_int_2d.html">
TEST_INT_2D</a>,
a MATLAB library which
defines test integrands for 2D quadrature rules.
</p>
<p>
<a href = "../../m_src/test_nint/test_nint.html">
TEST_NINT</a>,
a MATLAB library which
tests multi-dimensional quadrature routines.
</p>
<p>
<a href = "../../m_src/testpack/testpack.html">
TESTPACK</a>,
a MATLAB library which
defines a set of integrands used to test multidimensional quadrature.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Philip Davis, Philip Rabinowitz,<br>
Methods of Numerical Integration,<br>
Second Edition,<br>
Dover, 2007,<br>
ISBN: 0486453391,<br>
LC: QA299.3.D28.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "box_nd.m">box_nd.m</a>,
computes the integral of F(X) over a product box.
</li>
<li>
<a href = "i4_huge.m">i4_huge.m</a>,
returns a huge I4.
</li>
<li>
<a href = "monte_carlo_nd.m">monte_carlo_nd.m</a>,
computes a Monte Carlo estimate of an integral in a box.
</li>
<li>
<a href = "p5_nd.m">p5_nd.m</a>,
approximates the integral of F(X) over a product region.
</li>
<li>
<a href = "r8vec_uniform_01.m">r8vec_uniform_01.m</a>,
returns a unit pseudorandom R8VEC.
</li>
<li>
<a href = "romberg_nd.m">romberg_nd.m</a>,
approximates the integral of a F(X) over a product region.
</li>
<li>
<a href = "sample_nd.m">sample_nd.m</a>,
estimates the integral of F(X) over the multi-dimensional unit box.
</li>
<li>
<a href = "sum2_nd.m">sum2_nd.m</a>,
computes the integral of F(X) over a multi-dimensional product region.
</li>
<li>
<a href = "timestamp.m">timestamp.m</a>,
prints the current YMDHMS date as a time stamp.
</li>
<li>
<a href = "tuple_next.m">tuple_next.m</a>,
computes the next element of a tuple space.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "nintlib_test.m">nintlib_test.m</a>, calls all the tests;
</li>
<li>
<a href = "nintlib_test_output.txt">nintlib_test_output.txt</a>,
the output file.
</li>
<li>
<a href = "nintlib_testnd.m">nintlib_testnd.m</a>,
calls all the integrators for one test integrand.
</li>
<li>
<a href = "nintlib_test01.m">nintlib_test01.m</a>,
tests BOX_ND.
</li>
<li>
<a href = "nintlib_test02.m">nintlib_test02.m</a>,
tests P5_ND.
</li>
<li>
<a href = "nintlib_test03.m">nintlib_test03.m</a>,
tests ROMBERG_ND.
</li>
<li>
<a href = "nintlib_test04.m">nintlib_test04.m</a>,
tests SAMPLE_ND;
</li>
<li>
<a href = "nintlib_test05.m">nintlib_test05.m</a>,
demonstrates how to refine multi-dimensional integration results.
</li>
<li>
<a href = "nintlib_test06.m">nintlib_test06.m</a>,
tests MONTE_CARLO_ND.
</li>
<li>
<a href = "f1dn.m">f1dn.m</a>,
evaluates integrand F(X(1:DIM_NUM)) = 1;
</li>
<li>
<a href = "fbdn.m">fbdn.m</a>,
evaluates integrand F(X(1:DIM_NUM)) = 1/(1+(X(1:DIM_NUM)**2));
</li>
<li>
<a href = "fedn.m">fedn.m</a>,
evaluates integrand F(X(1:DIM_NUM)) = exp (sum(X(1:DIM_NUM));
</li>
<li>
<a href = "fxdn.m">fxdn.m</a>,
evaluates integrand F(X(1:DIM_NUM)) = sum ( X(1:DIM_NUM) );
</li>
<li>
<a href = "fx2dn.m">fx2dn.m</a>,
evaluates integrand F(X(1:DIM_NUM)) = sum ( X(1:DIM_NUM)^2 );
</li>
<li>
<a href = "fx3dn.m">fx3dn.m</a>,
evaluates integrand F(X(1:DIM_NUM)) = sum ( X(1:DIM_NUM)^3 );
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 01 March 2007.
</i>
<!-- John Burkardt -->
</body>
</html>