forked from johannesgerer/jburkardt-cpp
-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathpyramid_monte_carlo.html
342 lines (295 loc) · 10.2 KB
/
pyramid_monte_carlo.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
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
<html>
<head>
<title>
PYRAMID_MONTE_CARLO - Monte Carlo Estimate of Integrals in Unit Pyramid
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
PYRAMID_MONTE_CARLO <br> Monte Carlo Estimate of Integrals in Unit Pyramid
</h1>
<hr>
<p>
<b>PYRAMID_MONTE_CARLO</b>
is a C++ library which
estimates the integral of a function F(X,Y,Z)
over the interior of the unit pyramid in 3D.
</p>
<p>
The unit pyramid has a square base of area 4, and a height of 1.
Specifically, the integration region is:
<pre>
- ( 1 - Z ) <= X <= 1 - Z
- ( 1 - Z ) <= Y <= 1 - Z
0 <= Z <= 1.
</pre>
The volume of the unit pyramid is 4/3.
</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>PYRAMID_MONTE_CARLO</b> is available in
<a href = "../../c_src/pyramid_monte_carlo/pyramid_monte_carlo.html">a C version</a> and
<a href = "../../cpp_src/pyramid_monte_carlo/pyramid_monte_carlo.html">a C++ version</a> and
<a href = "../../f77_src/pyramid_monte_carlo/pyramid_monte_carlo.html">a FORTRAN77 version</a> and
<a href = "../../f_src/pyramid_monte_carlo/pyramid_monte_carlo.html">a FORTRAN90 version</a> and
<a href = "../../m_src/pyramid_monte_carlo/pyramid_monte_carlo.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/ball_monte_carlo/ball_monte_carlo.html">
BALL_MONTE_CARLO</a>,
a C++ library which
applies a Monte Carlo method to estimate integrals of a function
over the interior of the unit ball in 3D;
</p>
<p>
<a href = "../../cpp_src/circle_monte_carlo/circle_monte_carlo.html">
CIRCLE_MONTE_CARLO</a>,
a C++ library which
applies a Monte Carlo method to estimate the integral of a function
over the circumference of the unit circle in 2D.
</p>
<p>
<a href = "../../cpp_src/cube_monte_carlo/cube_monte_carlo.html">
CUBE_MONTE_CARLO</a>,
a C++ library which
applies a Monte Carlo method to estimate the integral of a function
over the interior of the unit cube in 3D;
</p>
<p>
<a href = "../../cpp_src/disk_monte_carlo/disk_monte_carlo.html">
DISK_MONTE_CARLO</a>,
a C++ library which
applies a Monte Carlo method to estimate the integral of a function
over the interior of the unit disk in 2D;
</p>
<p>
<a href = "../../cpp_src/ellipse_monte_carlo/ellipse_monte_carlo.html">
ELLIPSE_MONTE_CARLO</a>
a C++ library which
uses the Monte Carlo method to estimate the value of integrals
over the interior of an ellipse in 2D.
</p>
<p>
<a href = "../../cpp_src/ellipsoid_monte_carlo/ellipsoid_monte_carlo.html">
ELLIPSOID_MONTE_CARLO</a>
a C++ library which
uses the Monte Carlo method to estimate the value of integrals
over the interior of an ellipsoid in M dimensions.
</p>
<p>
<a href = "../../cpp_src/hyperball_monte_carlo/hyperball_monte_carlo.html">
HYPERBALL_MONTE_CARLO</a>,
a C++ library which
applies a Monte Carlo method to estimate the integral of a function
over the interior of the unit hyperball in M dimensions;
</p>
<p>
<a href = "../../cpp_src/hyperball_volume_monte_carlo/hyperball_volume_monte_carlo.html">
HYPERBALL_VOLUME_MONTE_CARLO</a>,
a C++ program which
applies a Monte Carlo method to estimate the volume of the unit hyperball
in M dimensions;
</p>
<p>
<a href = "../../c++_src/hypercube_monte_carlo/hypercube_monte_carlo.html">
HYPERCUBE_MONTE_CARLO</a>,
a C++ library which
applies a Monte Carlo method to estimate the integral of a function
over the interior of the unit hypercube in M dimensions;
</p>
<p>
<a href = "../../cpp_src/hypersphere_monte_carlo/hypersphere_monte_carlo.html">
HYPERSPHERE_MONTE_CARLO</a>,
a C++ library which
applies a Monte Carlo method to estimate the integral of a function
on the surface of the unit hypersphere in M dimensions;
</p>
<p>
<a href = "../../cpp_src/line_monte_carlo/line_monte_carlo.html">
LINE_MONTE_CARLO</a>,
a C++ library which
applies a Monte Carlo method to estimate the integral of a function
over the length of the unit line in 1D;
</p>
<p>
<a href = "../../cpp_src/polygon_monte_carlo/polygon_monte_carlo.html">
POLYGON_MONTE_CARLO</a>,
a C++ library which
applies a Monte Carlo method to estimate the integral of a function
over the interior of a polygon in 2D.
</p>
<p>
<a href = "../../cpp_src/pyramid_felippa_rule/pyramid_felippa_rule.html">
PYRAMID_FELIPPA_RULE</a>,
a C++ library which
returns Felippa's quadratures rules for approximating integrals
over the interior of a pyramid in 3D.
</p>
<p>
<a href = "../../cpp_src/pyramid_grid/pyramid_grid.html">
PYRAMID_GRID</a>,
a C++ library which
computes a grid of points
over the interior of the unit pyramid in 3D;
</p>
<p>
<a href = "../../cpp_src/pyramid_integrals/pyramid_integrals.html">
PYRAMID_INTEGRALS</a>,
a C++ library which
returns the exact value of the integral of any monomial
over the interior of the unit pyramid in 3D.
</p>
<p>
<a href = "../../cpp_src/pyramid_rule/pyramid_rule.html">
PYRAMID_RULE</a>,
a C++ library which
computes quadrature rules
over the interior of the unit pyramid in 3D.
</p>
<p>
<a href = "../../cpp_src/simplex_monte_carlo/simplex_monte_carlo.html">
SIMPLEX_MONTE_CARLO</a>,
a C++ library which
uses the Monte Carlo method to estimate integrals
over the interior of the unit simplex in M dimensions.
</p>
<p>
<a href = "../../cpp_src/sphere_monte_carlo/sphere_monte_carlo.html">
SPHERE_MONTE_CARLO</a>,
a C++ library which
applies a Monte Carlo method to estimate the integral of a function
on the surface of the unit sphere in 3D;
</p>
<p>
<a href = "../../cpp_src/sphere_triangle_monte_carlo/sphere_triangle_monte_carlo.html">
SPHERE_TRIANGLE_MONTE_CARLO</a>,
a C++ library which
applies a Monte Carlo method to estimate the integral of a function
over a spherical triangle on the surface of the unit sphere in 3D;
</p>
<p>
<a href = "../../cpp_src/square_monte_carlo/square_monte_carlo.html">
SQUARE_MONTE_CARLO</a>,
a C++ library which
applies a Monte Carlo method to estimate the integral of a function
over the interior of the unit square in 2D;
</p>
<p>
<a href = "../../cpp_src/tetrahedron_monte_carlo/tetrahedron_monte_carlo.html">
TETRAHEDRON_MONTE_CARLO</a>,
a C++ library which
uses the Monte Carlo method to estimate integrals
over the interior of the unit tetrahedron in 3D.
</p>
<p>
<a href = "../../cpp_src/triangle_monte_carlo/triangle_monte_carlo.html">
TRIANGLE_MONTE_CARLO</a>,
a C++ library which
uses the Monte Carlo method to estimate integrals
over the interior of a triangle in 2D.
</p>
<p>
<a href = "../../cpp_src/wedge_monte_carlo/wedge_monte_carlo.html">
WEDGE_MONTE_CARLO</a>,
a C++ library which
uses the Monte Carlo method to estimate integrals
over the interior of the unit wedge in 3D.
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "pyramid_monte_carlo.cpp">pyramid_monte_carlo.cpp</a>, the source code.
</li>
<li>
<a href = "pyramid_monte_carlo.hpp">pyramid_monte_carlo.hpp</a>, the include file.
</li>
<li>
<a href = "pyramid_monte_carlo.sh">pyramid_monte_carlo.sh</a>,
BASH commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "pyramid_monte_carlo_prb.cpp">pyramid_monte_carlo_prb.cpp</a>,
a sample calling program.
</li>
<li>
<a href = "pyramid_monte_carlo_prb.sh">pyramid_monte_carlo_prb.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "pyramid_monte_carlo_prb_output.txt">pyramid_monte_carlo_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MONOMIAL_VALUE</b> evaluates a monomial.
</li>
<li>
<b>PYRAMID01_INTEGRAL:</b> monomial integral in a unit pyramid.
</li>
<li>
<b>PYRAMID01_SAMPLE:</b> sample the unit pyramid.
</li>
<li>
<b>PYRAMID01_VOLUME:</b> volume of a unit pyramid with square base.
</li>
<li>
<b>R8_CHOOSE</b> computes the binomial coefficient C(N,K) as an R8.
</li>
<li>
<b>R8_MOP</b> returns the I-th power of -1 as an R8.
</li>
<li>
<b>R8MAT_TRANSPOSE_PRINT</b> prints an R8MAT, transposed.
</li>
<li>
<b>R8MAT_TRANSPOSE_PRINT_SOME</b> prints some of an R8MAT, transposed.
</li>
<li>
<b>R8MAT_UNIFORM_01</b> fills an R8MAT with unit pseudorandom numbers.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</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 13 August 2014.
</i>
<!-- John Burkardt -->
</body>
<!-- Initial HTML skeleton created by HTMLINDEX. -->
</html>