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<html>

  <head>
    <title>
      MXM - Matrix-Matrix Multiplication Timings
    </title>
  </head>

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

    <h1 align = "center">
      MXM <br> Matrix-Matrix Multiplication Timings
    </h1>

    <hr>

    <p>
      <b>MXM</b>
      is a MATLAB program which
      sets up a matrix-matrix multiplication problem A = B * C,
      and carries it out using
      <ul>
        <li>
          Nested DO I, J, K loops;
        </li>
        <li>
          Nested DO I, K, J loops;
        </li>
        <li>
          Nested DO J, I, K loops;
        </li>
        <li>
          Nested DO J, K, I loops;
        </li>
        <li>
          Nested DO K, I, J loops;
        </li>
        <li>
          Nested DO K, J, I loops;
        </li>
        <li>
          the MATLAB "star" operator: A = B * C;
        </li>
      </ul>
    </p>

    <p>
      The user is allowed to specify N1, N2, and N3, which define
      the matrix sizes.
    </p>

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

    <p>
      <blockquote>
        <b>mxm</b> <i>n1</i> <i>n2</i> <i>n3</i>
      </blockquote>
      where
      <ul>
        <li>
          <b>n1</b> is the number of rows in B.
        </li>
        <li>
          <b>n2</b> is the number of columns in B and rows in C.
        </li>
        <li>
          <b>n3</b> is the number of columns in C;
        </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>MXM</b> is available in
      <a href = "../../c_src/mxm/mxm.html">a C version</a> and
      <a href = "../../cpp_src/mxm/mxm.html">a C++ version</a> and
      <a href = "../../f77_src/mxm/mxm.html">a FORTRAN77 version</a> and
      <a href = "../../f_src/mxm/mxm.html">a FORTRAN90 version</a> and
      <a href = "../../m_src/mxm/mxm.html">a MATLAB version</a>.
    </p>

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

    <p>
      <a href = "../../m_src/linpack_bench/linpack_bench.html">
      LINPACK_BENCH</a>,
      a MATLAB program which
      measures the time needed to factor and solve a "large" (N=1000)
      dense linear system of equations, and is used as a benchmark.
    </p>

    <p>
      <a href = "../../m_src/mxv/mxv.html">
      MXV</a>,
      a MATLAB program which
      compares the performance of (DO I, DO J) loops, (DO J, DO I ) loops,
      and MATMUL for computing the product of an MxN matrix A and an N vector X.
    </p>

    <p>
      <a href = "../../m_src/sum_million/sum_million.m">
      SUM_MILLION</a>,
      a MATLAB program which
      sums the integers from 1 to 1,000,000, as a demonstration of how
      to rate a computer's speed;
    </p>

    <p>
      <a href = "../../m_src/timer/timer.html">
      TIMER</a>,
      MATLAB programs which
      demonstrate how to compute CPU time or elapsed time.
    </p>

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

    <p>
      <ol>
        <li>
          John Burkardt, Paul Puglielli,<br>
          Pittsburgh Supercomputing Center,<br>
          <a href = "../../presentations/matmul.pdf">
          MATMUL: An Interactive Matrix Multiplication Benchmark
          </a>
        </li>
      </ol>
    </p>

    <h3 align = "center">
      Source Code:
    </h3>

    <p>
      <ul>
        <li>
          <a href = "mxm.m">mxm.m</a>, the source code.
        </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 08 October 2010.
    </i>

    <!-- John Burkardt -->

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