blas3/blas3.html

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      BLAS3 - Basic Linear Algebra Subprograms - Level 3
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      BLAS3 <br> 
      Basic Linear Algebra Subprograms - Level 3
    </h1>

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    <p>
      <b>BLAS3</b>
      is a MATLAB library which
      implements the Level 3 BLAS, or Basic Linear Algebra Subprograms.
    </p>

    <p>
      The BLAS are a small core library of linear algebra utilities,
      which can be highly optimized for various architectures.  Software
      that relies on the BLAS is thus highly portable, and will typically
      run very efficiently.
    </p>

    <p>
      The Level 3 BLAS are primarily for use in matrix-matrix operations,
      such as matrix multiplication.
      In certain cases, they may also be used to operate on the rows
      or columns of a two-dimensional array.
    </p>

    <p>
      The Level 3 BLAS were originally written in FORTRAN77.  This version
      of the library only contains a subset of the BLAS3 library (at
      the moment, mainly just DGEMM).  Arrays are stored according to the
      FORTRAN convention.  Thus, an M by N mathematical array might be stored 
      in a double precision FORTRAN array called "A" that is declared as 
      <pre>
        double precision a(lda,sda)
      </pre>
      where LDA is the "leading" dimension and SDA is the "second" dimension.
      It is natural for LDA to equal M, but it is only necessary that 
      M <= LDA.  The matrix is stored as a vector of concatenated column 
      vectors, and the dimension statement is used to determine that columns 
      should be LDA units long.  Thus, a typical entry A(I,J) of the 
      mathematical matrix is actually stored in the location FORTRAN
      vector location I+(J-1)*LDA.  Of course, in C, this location would be
      I-1+(J-1)*LDA.
    </p>

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      Licensing:
    </h3>

    <p>
      The computer code and data files made available on this
      web page are distributed under
      <a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
    </p>

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      Languages:
    </h3>

    <p>
      <b>BLAS3</b> is available in
      <a href = "../../c_src/blas/blas.html">a C version</a> and
      <a href = "../../cpp_src/blas/blas.html">a C++ version</a> and
      <a href = "../../f77_src/blas/blas.html">a FORTRAN77 version</a> and
      <a href = "../../f_src/blas/blas.html">a FORTRAN90 version</a> and
      <a href = "../../m_src/blas/blas.html">a MATLAB version.</a> 
    </p>

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      Related Data and Programs:
    </h3>

    <p>
      <a href = "../../m_src/blas0/blas0.html">
      BLAS0</a>,
      a MATLAB library which
      contains auxilliary functions for the Basic Linear Algebra Subprograms 
      (BLAS).
    </p>

    <p>
      <a href = "../../m_src/blas1_c/blas1_c.html">
      BLAS1_C</a>,
      a MATLAB library which
      contains basic linear algebra routines for vector-vector operations,
      using single precision complex arithmetic.
    </p>

    <p>
      <a href = "../../m_src/blas1_d/blas1_d.html">
      BLAS1_D</a>,
      a MATLAB library which
      contains basic linear algebra routines for vector-vector operations,
      using double precision real arithmetic.
    </p>

    <p>
      <a href = "../../m_src/blas1_s/blas1_s.html">
      BLAS1_S</a>,
      a MATLAB library which
      contains basic linear algebra routines for vector-vector operations,
      using single precision real arithmetic.
    </p>

    <p>
      <a href = "../../m_src/blas1_z/blas1_z.html">
      BLAS1_Z</a>,
      a MATLAB library which
      contains basic linear algebra routines for vector-vector operations,
      using double precision complex arithmetic.
    </p>

    <p>
      <a href = "../../m_src/blas2/blas2.html">
      BLAS2</a>,
      a MATLAB library which
      contains basic linear algebra subprograms (BLAS) 
      for matrix-vector operations;
    </p>

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      Reference:
    </h3>

    <p>
      <ol>
        <li>
          Thomas Coleman, Charles vanLoan,<br>
          Handbook for Matrix Computations,<br>
          SIAM, 1988,<br>
          ISBN13: 978-0-898712-27-8,<br>
          LC: QA188.C65.
        </li>
        <li>
          Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart,<br>
          LINPACK User's Guide,<br>
          SIAM, 1979,<br>
          ISBN13: 978-0-898711-72-1,<br>
          LC: QA214.L56.
        </li>
        <li>
          Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh,<br>
          Algorithm 539:
          Basic Linear Algebra Subprograms for Fortran Usage,<br>
          ACM Transactions on Mathematical Software,<br>
          Volume 5, Number 3, September 1979, pages 308-323.
        </li>
      </ol>
    </p>

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      Source Code:
    </h3>

    <p>
      <ul>
        <li>
          <a href = "dgemm.m">dgemm.m</a>, 
          computes C = alpha * A * B and related operations.
        </li>
        <li>
          <a href = "dtrmm.m">dtrmm.m</a>, 
          performs B:=A*B or B:=B*A, A triangular, B rectangular.
        </li>
        <li>
          <a href = "dtrsm.m">dtrsm.m</a>, 
          solves A*X=alpha*B or X*A=alpha*B, for triangular A, rectangular B.
        </li>
        <li>
          <a href = "sgemm.m">sgemm.m</a>, 
          computes C = alpha * A * B and related operations.
        </li>
        <li>
          <a href = "strmm.m">strmm.m</a>, 
          performs B:=A*B or B:=B*A, A triangular, B rectangular.
        </li>
        <li>
          <a href = "strsm.m">strsm.m</a>, 
          solves A*X=alpha*B or X*A=alpha*B, for triangular A, rectangular B.
        </li>
      </ul>
    </p>

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      Examples and Tests:
    </h3>

    <p>
      <ul>
        <li>
          <a href = "blas3_test.m">blas3_test.m</a>
          a sample calling program.
        </li>
        <li>
          <a href = "blas3_test01.m">blas3_test01.m</a>,
          tests DGEMM.
        </li>
        <li>
          <a href = "blas3_test02.m">blas3_test02.m</a>,
          tests DTRMM.
        </li>
        <li>
          <a href = "blas3_test03.m">blas3_test03.m</a>,
          tests DTRSM.
        </li>
        <li>
          <a href = "blas3_test_output.txt">blas3_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>

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    <i>
      Last revised on 05 April 2014.
    </i>

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