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<html>
<head>
<title>
SANDIA_SGMGG - Sparse Grid Mixed Growth, Generalized Construction
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
SANDIA_SGMGG <br> Sparse Grid Mixed Growth, Generalized Construction
</h1>
<hr>
<p>
<b>SANDIA_SGMGG</b>
is a FORTRAN90 library which
contains some experimental code for the investigation of sparse
grids constructed in a generalized fashion, in which the set of
indices corresponding to a sparse grid is chosen in a generalized
way, rather than being defined by a linear constraint.
</p>
<p>
The sparse grid is associated with a data structure, whose management
is a significant part of the computation.
</p>
<p>
We assume we are working in a space of dimension <b>ND</b>. An
index vector is a list of <b>ND</b> nonnegative integers, which
represent the level of quadrature in each dimension. A single
index vector can be used to construct a product rule.
</p>
<p>
A sparse grid can be thought of as a weighted summation of product
rules; our represention of a sparse grid will then consist of a list
of <b>NI</b> index vectors, which we can regard as an <b>ND</b> by
<b>NI</b> array.
</p>
<p>
Not every collection of index vectors will be admissible. For our
purposes, a collection of index vectors is admissible if each vector
in the set is admissible. An index vector that is part of a collection
is admissible if it is the 0 vector, or every vector formed by
decrementing exactly one entry by 1 is an admissible vector in the set.
</p>
<p>
Here is an example of an admissible collection of index vectors in 2D:
<pre>
(0,3)
(0,2) (1,2)
(0,1) (1,1)
(0,0) (1,0) (2,0) (3,0) (4,0)
</pre>
For the 2D case, an index is admissible if every possible index below
or to the left of it is also in the set.
</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>SANDIA_SGMGG</b> is available in
<a href = "../../cpp_src/sandia_sgmgg/sandia_sgmgg.html">a C++ version</a> and
<a href = "../../f_src/sandia_sgmgg/sandia_sgmgg.html">a FORTRAN90 version</a> and
<a href = "../../m_src/sandia_sgmgg/sandia_sgmgg.html">a MATLAB version.</a>
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/sgmga/sgmga.html">
SGMGA</a>,
a FORTRAN90 library which
creates sparse grids based on a mixture of 1D quadrature rules,
allowing anisotropic weights for each dimension.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Thomas Gerstner, Michael Griebel,<br>
Dimension-adaptive tensor-product quadrature,<br>
Computing,<br>
Volume 71, Number 1, August 2003, pages 65-87.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "sandia_sgmgg.f90">sandia_sgmgg.f90</a>, the source code.
</li>
<li>
<a href = "sandia_sgmgg.sh">sandia_sgmgg.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "sandia_sgmgg_prb.f90">sandia_sgmgg_prb.f90</a>,
a sample calling program.
</li>
<li>
<a href = "sandia_sgmgg_prb.sh">sandia_sgmgg_prb.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "sandia_sgmgg_prb_output.txt">sandia_sgmgg_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>I4_MODP</b> returns the nonnegative remainder of I4 division.
</li>
<li>
<b>I4_WRAP</b> forces an I4 to lie between given limits by wrapping.
</li>
<li>
<b>I4MAT_TRANSPOSE_PRINT</b> prints an I4MAT, transposed.
</li>
<li>
<b>I4MAT_TRANSPOSE_PRINT_SOME</b> prints some of the transpose of an I4MAT.
</li>
<li>
<b>I4VEC_PRINT</b> prints an I4VEC.
</li>
<li>
<b>R8_UNIFORM_01</b> returns a unit pseudorandom R8.
</li>
<li>
<b>R8VEC_INDEXED_HEAP_D</b> creates a descending heap from an indexed R8VEC.
</li>
<li>
<b>R8VEC_INDEXED_HEAP_D_EXTRACT:</b> extract from heap descending indexed R8VEC.
</li>
<li>
<b>R8VEC_INDEXED_HEAP_D_INSERT:</b> insert value into heap descending indexed R8VEC.
</li>
<li>
<b>R8VEC_INDEXED_HEAP_D_MAX:</b> maximum value in heap descending indexed R8VEC.
</li>
<li>
<b>SANDIA_SGMGG_COEF_INC2</b> computes tentative coefficient changes.
</li>
<li>
<b>SANDIA_SGMGG_COEF_NAIVE</b> returns the combinatorial coefficients.
</li>
<li>
<b>SANDIA_SGMGG_NEIGHBOR_NAIVE</b> returns the immediate forward neighbor vector.
</li>
<li>
<b>SGMGG_PRINT</b> prints out an SGMGG data structure.
</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 = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 23 August 2011.
</i>
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