jburkardt-m/sparse_grid_hermite_dataset/sparse_grid_hermite_dataset.html at master · johannesgerer/jburkardt-m · GitHub

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<html>

  <head>
    <title>
      SPARSE_GRID_HERMITE_DATASET - Create Gauss-Hermite Sparse Grid Dataset
    </title>
  </head>

  <body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">

    <h1 align = "center">
      SPARSE_GRID_HERMITE_DATASET <br> Create Gauss-Hermite Sparse Grid Dataset
    </h1>

    <hr>

    <p>
      <b>SPARSE_GRID_HERMITE_DATASET</b>
      is a MATLAB program which
      creates a Gauss-Hermite sparse grid dataset.
    </p>

    <h3 align = "center">
      Usage:
    </h3>

    <p>
      <blockquote>
        <b>sparse_grid_hermite_dataset</b> ( <i>dim_num</i>, <i>level_max</i> )
      </blockquote>
      where
      <ul>
        <li>
          <i>dim_num</i> is the spatial dimension, typically between 2 and 10;
        </li>
        <li>
          <i>level_max</i> is the sparse grid level, typically between 0 and 6,
          which controls the number of points
          in the grid.  The 1D rules used will have order 2^(level_max)+1.
        </li>
      </ul>
    </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_GRID_HERMITE_DATASET</b> is available in
      <a href = "../../cpp_src/sparse_grid_hermite_dataset/sparse_grid_hermite_dataset.html">a C++ version</a> and
      <a href = "../../f_src/sparse_grid_hermite_dataset/sparse_grid_hermite_dataset.html">a FORTRAN90 version</a> and
      <a href = "../../m_src/sparse_grid_hermite_dataset/sparse_grid_hermite_dataset.html">a MATLAB version.</a>
    </p>

    <h3 align = "center">
      Related Data and Programs:
    </h3>

    <p>
      <a href = "../../m_src/cc_display/cc_display.html">
      CC_DISPLAY</a>,
      a MATLAB library which
      can compute and display Clenshaw Curtis grids in two dimensions,
      as well as sparse grids formed from sums of Clenshaw Curtis grids.
    </p>

    <p>
      <a href = "../../m_src/grid_display/grid_display.html">
      GRID_DISPLAY</a>,
      a MATLAB library which
      can display a 2D or 3D grid or sparse grid.
    </p>

    <p>
      <a href = "../../datasets/quadrature_rules/quadrature_rules.html">
      QUADRATURE_RULES</a>,
      a dataset directory which
      defines quadrature rules;
      a number of examples of sparse grid quadrature rules are included.
    </p>

    <p>
      <a href = "../../m_src/quadrule/quadrule.html">
      QUADRULE</a>,
      a MATLAB library which
      defines quadrature rules for
      various intervals and weight functions.
    </p>

    <p>
      <a href = "../../m_src/sgmga/sgmga.html">
      SGMGA</a>,
      a MATLAB library which
      creates sparse grids based on a mixture of 1D quadrature rules,
      allowing anisotropic weights for each dimension.
    </p>

    <p>
      <a href = "../../c_src/smolpack/smolpack.html">
      SMOLPACK</a>,
      a C library which
      implements Novak and Ritter's method for estimating the integral
      of a function over a multidimensional hypercube using sparse grids.
    </p>

    <p>
      <a href = "../../datasets/sparse_grid_cc/sparse_grid_cc.html">
      SPARSE_GRID_CC</a>,
      a dataset directory which
      contains the abscissas of sparse
      grids based on a Clenshaw Curtis rule.
    </p>

    <p>
      <a href = "../../m_src/sparse_grid_cc_dataset/sparse_grid_cc_dataset.html">
      SPARSE_GRID_CC_DATASET</a>,
      a MATLAB program which
      creates a sparse grid dataset based on Clenshaw-Curtis rules.
    </p>

    <p>
      <a href = "../../datasets/sparse_grid_f2/sparse_grid_f2.html">
      SPARSE_GRID_F2</a>,
      a dataset directory which
      contains the abscissas of sparse
      grids based on a Fejer Type 2 rule.
    </p>

    <p>
      <a href = "../../m_src/sparse_grid_gl_dataset/sparse_grid_gl_dataset.html">
      SPARSE_GRID_GL_DATASET</a>,
      a MATLAB program which
      creates a sparse grid dataset based on Gauss-Legendre rules.
    </p>

    <p>
      <a href = "../../datasets/sparse_grid_gp/sparse_grid_gp.html">
      SPARSE_GRID_GP</a>,
      a dataset directory which
      contains the abscissas of sparse
      grids based on a Gauss Patterson rule.
    </p>

    <p>
      <a href = "../../m_src/sparse_grid_hermite/sparse_grid_hermite.html">
      SPARSE_GRID_HERMITE</a>,
      a MATLAB library which
      can create a Gauss-Hermite sparse grid.
    </p>

    <p>
      <a href = "../../datasets/sparse_grid_hermite/sparse_grid_hermite.html">
      SPARSE_GRID_HERMITE</a>,
      a dataset directory which
      contains Gauss-Hermite sparse grids.
    </p>

    <p>
      <a href = "../../m_src/sparse_grid_hw/sparse_grid_hw.html">
      SPARSE_GRID_HW</a>,
      a MATLAB library which
      creates sparse grids based on Gauss-Legendre, Gauss-Hermite,
      Gauss-Patterson, or a nested variation of Gauss-Hermite rules,
      by Florian Heiss and Viktor Winschel.
    </p>

    <p>
      <a href = "../../m_src/sparse_grid_mixed_dataset/sparse_grid_mixed_dataset.html">
      SPARSE_GRID_MIXED_DATASET</a>,
      a MATLAB program which
      creates a sparse grid dataset based on a mixture of 1D rules.
    </p>

    <p>
      <a href = "../../datasets/sparse_grid_ncc/sparse_grid_ncc.html">
      SPARSE_GRID_NCC</a>,
      a dataset directory of files which
      contain the abscissas of sparse
      grids based on a Newton Cotes closed rule.
    </p>

    <p>
      <a href = "../../datasets/sparse_grid_nco/sparse_grid_nco.html">
      SPARSE_GRID_NCO</a>,
      a dataset directory of files which
      contain the abscissas of sparse
      grids based on a Newton Cotes open rule.
    </p>

    <p>
      <a href = "../../m_src/sparse_grid_open_dataset/sparse_grid_open_dataset.html">
      SPARSE_GRID_OPEN_DATASET</a>,
      a MATLAB program which
      creates a sparse grid dataset based on
      open rules (Fejer 2, Gauss-Patterson, Newton-Cotes-Open).
    </p>

    <p>
      <a href = "../../m_src/toms847/toms847.html">
      TOMS847</a>,
      a MATLAB program which
      uses sparse grids to carry out multilinear hierarchical interpolation.
      It is commonly known as SPINTERP, and is by Andreas Klimke.
    </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_grid_hermite_dataset.m">
          sparse_grid_hermite_dataset.m</a>
          the source code.
        </li>
      </ul>
    </p>

    <h3 align = "center">
      Examples and Tests:
    </h3>

    <p>
      Here are the three quadrature files created by the command
      <blockquote><b>
        sparse_grid_hermite_dataset 2 3
      </b></blockquote>
      <ul>
        <li>
          <a href = "sparse_grid_hermite_dataset_output.txt">
          sparse_grid_hermite_dataset_output.txt</a>,
          the printed output from the program.
        </li>
        <li>
          <a href = "herm_d2_level3_r.txt">herm_d2_level3_r.txt</a>,
          the "R" or "region" file.
        </li>
        <li>
          <a href = "herm_d2_level3_w.txt">herm_d2_level3_w.txt</a>,
          the "W" or "weight" file.
        </li>
        <li>
          <a href = "herm_d2_level3_x.txt">herm_d2_level3_x.txt</a>,
          the "X" or "abscissa" 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 10 August 2009.
    </i>

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