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<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 MATLAB 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>SPARSE_GRID_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 = "../../m_src/sparse_grid_mixed/sparse_grid_mixed.html">
SPARSE_GRID_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 = "comp_next.m">comp_next.m</a>
computes the compositions of the integer N into K parts.
</li>
<li>
<a href = "i4_choose.m">i4_choose.m</a>
computes the binomial coefficient C(N,K).
</li>
<li>
<a href = "cc_se_size.m">cc_se_size.m</a>
Clenshaw Curtis Slow Exponential Growth.
</li>
<li>
<a href = "cfn_e_nvec_from_lvec.m">cfn_e_nvec_from_lvec.m</a>
Closed Fully Nested, Exponential Growth,
return 1D rule sizes based on 1D rule levels.
</li>
<li>
<a href = "cfn_e_size.m">cfn_e_size.m</a>
Closed Fully Nested, Exponential Growth,
merge repeated points.
</li>
<li>
<a href = "cfn_e_size_total.m">cfn_e_size_total.m</a>
Closed Fully Nested, Exponential Growth,
don't merge repeated points.
</li>
<li>
<a href = "f2_se_size.m">f2_se_size.m</a>
Fejer Type 2 Slow Growth.
</li>
<li>
<a href = "gp_se_size.m">gp_se_size.m</a>
Gauss Patterson, Slow Growth.
</li>
<li>
<a href = "ofn_e_size.m">ofn_e_size.m</a>
Open Fully Nested, Exponential Growth.
</li>
<li>
<a href = "onn_e_size.m">onn_e_size.m</a>
Open Non Nested, Exponential Growth.
</li>
<li>
<a href = "onn_l_size.m">onn_l_size.m</a>
Open Non Nested, Linear Growth.
</li>
<li>
<a href = "own_e_size.m">own_e_size.m</a>
Open Weakly Nested, Exponential Growth.
</li>
<li>
<a href = "own_l2_size.m">own_l2_size.m</a>
Open Weakly Nested, Linear 2 Growth.
</li>
<li>
<a href = "own_o_size.m">own_o_size.m</a>
Open Weakly Nested, Odd Growth.
</li>
<li>
<a href = "timestamp.m">timestamp.m</a>
prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "sparse_count_test.m">sparse_count_test.m</a>,
a sample calling program.
</li>
<li>
<a href = "sparse_count_test01.m">sparse_count_test01.m</a>,
tests CC_SE_SIZE.
</li>
<li>
<a href = "sparse_count_test02.m">sparse_count_test02.m</a>,
tests CFN_E_SIZE.
</li>
<li>
<a href = "sparse_count_test025.m">sparse_count_test025.m</a>,
tests CFN_E_SIZE_TOTAL.
</li>
<li>
<a href = "sparse_count_test03.m">sparse_count_test03.m</a>,
tests F2_SE_SIZE.
</li>
<li>
<a href = "sparse_count_test04.m">sparse_count_test04.m</a>,
tests GP_SE_SIZE.
</li>
<li>
<a href = "sparse_count_test05.m">sparse_count_test05.m</a>,
tests OFN_E_SIZE.
</li>
<li>
<a href = "sparse_count_test06.m">sparse_count_test06.m</a>,
tests ONN_E_SIZE.
</li>
<li>
<a href = "sparse_count_test07.m">sparse_count_test07.m</a>,
tests ONN_L_SIZE.
</li>
<li>
<a href = "sparse_count_test08.m">sparse_count_test08.m</a>,
tests OWN_E_SIZE.
</li>
<li>
<a href = "sparse_count_test09.m">sparse_count_test09.m</a>,
tests OWN_L_SIZE.
</li>
<li>
<a href = "sparse_count_test10.m">sparse_count_test10.m</a>,
tests OWN_O_SIZE.
</li>
<li>
<a href = "sparse_count_test_output.txt">sparse_count_test_output.txt</a>,
the output file.
</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 25 May 2014.
</i>
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</body>
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</html>