forked from johannesgerer/jburkardt-cpp
-
Notifications
You must be signed in to change notification settings - Fork 0
/
sparse_count.html
215 lines (188 loc) · 5.54 KB
/
sparse_count.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
<html>
<head>
<title>
SPARSE_COUNT - Sparse Grids Using a Single Factor
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
SPARSE_COUNT <br> Sparse Grids Using a Single Factor
</h1>
<hr>
<p>
<b>SPARSE_COUNT</b>
is a C++ library which
contains routines for the analysis and construction of sparse grids
in which a fixed family of 1D quadrature rules is used for all spatial
dimensions.
</p>
<p>
By contrast, library <b>MIXED</b> allows different rules to
be used in different dimensions.
</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>SPARSE_COUNT</b> is available in
<a href = "../../cpp_src/sparse_count/sparse_count.html">a C++ version</a> and
<a href = "../../f_src/sparse_count/sparse_count.html">a FORTRAN90 version</a> and
<a href = "../../m_src/sparse_count/sparse_count.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/sparse_grid_mixed/sparse_grid_mixed.html">
MIXED</a>,
a library which
creates a sparse grid dataset based on a mixed set of 1D factor rules.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Volker Barthelmann, Erich Novak, Klaus Ritter,<br>
High Dimensional Polynomial Interpolation on Sparse Grids,<br>
Advances in Computational Mathematics,<br>
Volume 12, Number 4, 2000, pages 273-288.
</li>
<li>
Thomas Gerstner, Michael Griebel,<br>
Numerical Integration Using Sparse Grids,<br>
Numerical Algorithms,<br>
Volume 18, Number 3-4, 1998, pages 209-232.
</li>
<li>
Albert Nijenhuis, Herbert Wilf,<br>
Combinatorial Algorithms for Computers and Calculators,<br>
Second Edition,<br>
Academic Press, 1978,<br>
ISBN: 0-12-519260-6,<br>
LC: QA164.N54.
</li>
<li>
Fabio Nobile, Raul Tempone, Clayton Webster,<br>
A Sparse Grid Stochastic Collocation Method for Partial Differential
Equations with Random Input Data,<br>
SIAM Journal on Numerical Analysis,<br>
Volume 46, Number 5, 2008, pages 2309-2345.
</li>
<li>
Sergey Smolyak,<br>
Quadrature and Interpolation Formulas for Tensor Products of
Certain Classes of Functions,<br>
Doklady Akademii Nauk SSSR,<br>
Volume 4, 1963, pages 240-243.
</li>
<li>
Dennis Stanton, Dennis White,<br>
Constructive Combinatorics,<br>
Springer, 1986,<br>
ISBN: 0387963472,<br>
LC: QA164.S79.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "sparse_count.cpp">sparse_count.cpp</a>, the source code.
</li>
<li>
<a href = "sparse_count.hpp">sparse_count.hpp</a>,
the include file.
</li>
<li>
<a href = "sparse_count.sh">sparse_count.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "sparse_count_prb.cpp">sparse_count_prb.cpp</a>,
a sample calling program.
</li>
<li>
<a href = "sparse_count_prb.sh">sparse_count_prb.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "sparse_count_prb_output.txt">sparse_count_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>CC_S_SIZE:</b> Clenshaw Curtis Slow Exponential Growth.
</li>
<li>
<b>CFN_E_SIZE;</b> Closed Fully Nested, Exponential Growth.
</li>
<li>
<b>COMP_NEXT</b> computes the compositions of the integer N into K parts.
</li>
<li>
<b>F2_S_SIZE:</b> Fejer Type 2 Slow Growth.
</li>
<li>
<b>GP_S_SIZE:</b> Gauss Patterson, Slow Growth.
</li>
<li>
<b>I4_CHOOSE</b> computes the binomial coefficient C(N,K).
</li>
<li>
<b>OFN_E_SIZE:</b> Open Fully Nested, Exponential Growth.
</li>
<li>
<b>ONN_E_SIZE:</b> Open Non Nested, Exponential Growth.
</li>
<li>
<b>ONN_L_SIZE:</b> Open Non Nested, Linear Growth.
</li>
<li>
<b>OWN_E_SIZE:</b> Open Weakly Nested, Exponential Growth.
</li>
<li>
<b>OWN_L2_SIZE:</b> Open Weakly Nested, Linear 2 Growth.
</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 25 April 2014.
</i>
<!-- John Burkardt -->
</body>
<!-- Initial HTML skeleton created by HTMLINDEX. -->
</html>