sparsekit.html

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  <head>
    <title>
      SPARSEKIT - Sparse Matrix Utility Package
    </title>
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  <body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">

    <h1 align = "center">
      SPARSEKIT <br> Sparse Matrix Utility Package
    </h1>

    <hr>

    <p>
      <b>SPARSEKIT</b>
      is a FORTRAN77 library which
      carries out a number of
      operations on sparse matrices, particularly conversion between
      various sparse formats.
    </p>

    <p>
      <b>SPARSEKIT</b> can manipulate sparse matrices in a variety of formats,
      and can convert from one to another.  For example, a matrix can be
      converted from the generalized diagonal format used by ELLPACK and
      ITPACK to the format used by the Harwell-Boeing Sparse Matrix
      Collection or into LINPACK banded format.
    </p>

    <p>
      Utilities available include converting data structures, printing simple
      statistics on a matrix, plotting a matrix profile, performing basic
      linear algebra operations (similar to the BLAS for dense matrix),
      and so on.
    </p>

    <p>
      Matrix formats that are recognized include:
      <ul>
        <li>
          <b>BND</b>, the LINPACK format for general banded matrices.
        </li>
        <li>
          <b>BSR</b>, block row sparse format.
        </li>
        <li>
          <b>COO</b>, coordinate format.
        </li>
        <li>
          <b>CSC</b>, compressed sparse column format.
        </li>
        <li>
          <b>CSR</b>, compressed sparse row format.
        </li>
        <li>
          <b>DIA</b>, the diagonal sparse matrix format (NOT a diagonal matrix!).
        </li>
        <li>
          <b>DIAG</b>, a diagonal matrix, stored as a vector.
        </li>
        <li>
          <b>DNS</b>, dense storage, also called full storage.
        </li>
        <li>
          <b>ELL</b>, ELLPACK/ITPACK, the format used by ELLPACK and ITPACK.
        </li>
        <li>
          <b>HB</b>, Harwell-Boeing format.  (Actually, CSR format plus auxilliary data)
        </li>
        <li>
          <b>JAD</b>, the jagged diagonal format.
        </li>
        <li>
          <b>LNK</b>, linked storage format.
        </li>
        <li>
          <b>MSC</b>, modified sparse column format.
        </li>
        <li>
          <b>MSR</b>, modified sparse row format.
        </li>
        <li>
          <b>SSK</b>, Symmetric skyline format.
        </li>
        <li>
          <b>SSR</b>, Symmetric sparse row format.
        </li>
      </ul>
    </p>

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

    <p>
      <b>SPARSEKIT</b> is available in
      <a href = "../../f77_src/sparsekit/sparsekit.html">a FORTRAN77 version</a> and
      <a href = "../../f_src/sparsekit/sparsekit.html">a FORTRAN90 version</a>.
    </p>

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

    <p>
      <a href = "../../c_src/csparse/csparse.html">
      CSPARSE</a>,
      a C library which
      carries out the direct solution of sparse linear systems.
    </p>

    <p>
      <a href = "../../f_src/dlap/dlap.html">
      DLAP</a>,
      a FORTRAN90 library which
      solves sparse linear systems.
    </p>

    <p>
      <a href = "../../f_src/hb_io/hb_io.html">
      HB_IO</a>,
      a FORTRAN90 library which
      reads and writes sparse linear
      systems stored in the Harwell-Boeing Sparse Matrix format.
    </p>

    <p>
      <a href = "../../f77_src/hb_to_st/hb_to_st.html">
      HB_TO_ST</a>,
      a FORTRAN77 program which
      converts the sparse matrix information stored in a Harwell-Boeing
      file into a sparse triplet file.
    </p>

    <p>
      <a href = "../../f77_src/mgmres/mgmres.html">
      MGMRES</a>,
      a FORTRAN77 library which
      applies the restarted GMRES algorithm
      to solve a sparse linear system.
    </p>

    <p>
      <a href = "../../f_src/mm_io/mm_io.html">
      MM_IO</a>,
      a FORTRAN90 library which
      reads and writes sparse linear
      systems stored in the Matrix Market format.
    </p>

    <p>
      <a href = "../../data/sparse_cc/sparse_cc.html">
      SPARSE_CC</a>,
      a data directory which
      contains a description and examples of the CC format,
      ("compressed column") for storing a sparse matrix,
      including a way to write the matrix as a set of three files.
    </p>

    <p>
      <a href = "../../data/sparse_cr/sparse_cr.html">
      SPARSE_CR</a>,
      a data directory which
      contains a description and examples of the CR format,
      ("compressed row") for storing a sparse matrix,
      including a way to write the matrix as a set of three files.
    </p>

    <p>
      <a href = "../../f_src/sparsepak/sparsepak.html">
      SPARSEPAK</a>,
      a FORTRAN90 library which
      reorders and solves sparse linear systems.
    </p>

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

    <p>
      <ol>
        <li>
          Efstratios Gallopoulos, Youcef Saad,<br>
          Efficient solution of parabolic equations by Krylov
          approximation methods,<br>
          RIACS Technical Report, 90-14.
        </li>
        <li>
          Noborou Kikuchi,<br>
          Finite element methods in mechanics,<br>
          Cambridge University Press, 1986.
        </li>
        <li>
          David Kincaid, Thomas Oppe, John Respess, David Young,<br>
          ITPACKV 2C User's Guide,<br>
          Technical Report CNA-191.<br>
          Center for Numerical Analysis,<br>
          University of Texas at Austin, 1984.
        </li>
        <li>
          Donald Knuth,<br>
          The Art of Computer Programming,<br>
          Volume 3: Sorting and Searching,<br>
          Addison-Wesley, 1973.
        </li>
        <li>
          Ole Osterby, Zahari Zlatev,<br>
          Direct Methods for Sparse Matrices,<br>
          Springer-Verlag 1983.
        </li>
        <li>
          Youcef Saad,<br>
          Sparsekit: a basic tool kit for sparse matrix computations,<br>
          Technical Report, Computer Science Department,<br>
          University of Minnesota, June 1994.
        </li>
        <li>
          Youcef Saad,<br>
          Analysis of some Krylov subspace approximations to the
          matrix exponential operator,<br>
          RIACS Technical Report, 90-14.
        </li>
        <li>
          Yousef Saad,<br>
          Iterative Methods for Sparse Linear Systems,<br>
          Second Edition,<br>
          SIAM, 2003,<br>
          ISBN: 0898715342.
        </li>
        <li>
          Zahari Zlatev, Kjeld Schaumburg, Jerzy Wasniewski,<br>
          A testing Scheme for Subroutines Solving Large Linear Problems,<br>
          Computers and Chemistry,<br>
          Volume 5, Number 2-3, pages 91-100, 1981.
        </li>
      </ol>
    </p>

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

    <p>
      <ul>
        <li>
          <a href = "sparsekit.f">sparsekit.f</a>, the source code.
        </li>
        <li>
          <a href = "sparsekit.sh">sparsekit.sh</a>,
          commands to compile the source code.
        </li>
      </ul>
    </p>

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

    <p>
      Sample problem 1:
      <ul>
        <li>
          <a href = "sparsekit_prb01.f">sparsekit_prb01.f</a>,
          a sample calling program.
        </li>
        <li>
          <a href = "sparsekit_prb01.sh">sparsekit_prb01.sh</a>,
          commands to compile and run the sample program.
        </li>
        <li>
          <a href = "sparsekit_prb01_output.txt">sparsekit_prb01_output.txt</a>,
          the output file.
        </li>
      </ul>
    </p>

    <p>
      Sample problem 2:
      <ul>
        <li>
          <a href = "sparsekit_prb02.f">sparsekit_prb02.f</a>,
          a sample calling program.
        </li>
        <li>
          <a href = "sparsekit_prb02.sh">sparsekit_prb02.sh</a>,
          commands to compile and run the sample program.
        </li>
        <li>
          <a href = "sparsekit_prb02_output.txt">sparsekit_prb02_output.txt</a>,
          the output file.
        </li>
      </ul>
    </p>

    <p>
      Sample problem 3:
      <ul>
        <li>
          <a href = "sparsekit_prb03.f">sparsekit_prb03.f</a>,
          a sample calling program.
        </li>
        <li>
          <a href = "sparsekit_prb03.sh">sparsekit_prb03.sh</a>,
          commands to compile and run the sample program.
        </li>
        <li>
          <a href = "sparsekit_prb03_output.txt">sparsekit_prb03_output.txt</a>,
          the output file.
        </li>
      </ul>
    </p>

    <p>
      Sample problem 4 takes a banded matrix of order 16, stored
      as a dense matrix, converts it to CSR format and sorted CSR
      format.
      <ul>
        <li>
          <a href = "sparsekit_prb04.f">sparsekit_prb04.f</a>,
          a sample calling program.
        </li>
        <li>
          <a href = "sparsekit_prb04.sh">sparsekit_prb04.sh</a>,
          commands to compile and run the sample program.
        </li>
        <li>
          <a href = "sparsekit_prb04_output.txt">sparsekit_prb04_output.txt</a>,
          the output file.
        </li>
      </ul>
    </p>

    <p>
      Sample problem 5:
      <ul>
        <li>
          <a href = "sparsekit_prb05.f">sparsekit_prb05.f</a>,
          a sample calling program.
        </li>
        <li>
          <a href = "sparsekit_prb05.sh">sparsekit_prb05.sh</a>,
          commands to compile and run the sample program.
        </li>
        <li>
          <a href = "sparsekit_prb05_output.txt">sparsekit_prb05_output.txt</a>,
          the output file.
        </li>
      </ul>
    </p>

    <p>
      Sample problem 6:
      <ul>
        <li>
          <a href = "sparsekit_prb06.f">sparsekit_prb06.f</a>,
          a sample calling program.
        </li>
        <li>
          <a href = "sparsekit_prb06.sh">sparsekit_prb06.sh</a>,
          commands to compile and run the sample program.
        </li>
        <li>
          <a href = "sparsekit_prb06_output.txt">sparsekit_prb06_output.txt</a>,
          the output file.
        </li>
      </ul>
    </p>

    <p>
      Sample problem 7:
      <ul>
        <li>
          <a href = "sparsekit_prb07.f">sparsekit_prb07.f</a>,
          a sample calling program.
        </li>
        <li>
          <a href = "sparsekit_prb07.sh">sparsekit_prb07.sh</a>,
          commands to compile and run the sample program.
        </li>
        <li>
          <a href = "sparsekit_prb07_output.txt">sparsekit_prb07_output.txt</a>,
          the output file.
        </li>
      </ul>
    </p>

    <p>
      Sample problem 8 generates three sample matrices from the
      Zlatev set, and writes them to Harwell-Boeing format files:
      <ul>
        <li>
          <a href = "sparsekit_prb08.f">sparsekit_prb08.f</a>,
          a sample calling program.
        </li>
        <li>
          <a href = "sparsekit_prb08.sh">sparsekit_prb08.sh</a>,
          commands to compile and run the sample program.
        </li>
        <li>
          <a href = "sparsekit_prb08_output.txt">sparsekit_prb08_output.txt</a>,
          the output ffile.
        </li>
        <li>
          <a href = "zlatev1_hb.txt">zlatev1_hb.txt</a>,
          Zlatev sample matrix 1.
        </li>
        <li>
          <a href = "zlatev2_hb.txt">zlatev2_hb.txt</a>,
          Zlatev sample matrix 2.
        </li>
        <li>
          <a href = "zlatev3_hb.txt">zlatev3_hb.txt</a>,
          Zlatev sample matrix 3.
        </li>
      </ul>
    </p>

    <p>
      Sample problem 9:
      <ul>
        <li>
          <a href = "sparsekit_prb09.f">sparsekit_prb09.f</a>,
          a sample calling program.
        </li>
        <li>
          <a href = "sparsekit_prb09.sh">sparsekit_prb09.sh</a>,
          commands to compile and run the sample program.
        </li>
        <li>
          <a href = "sparsekit_prb09_output.txt">sparsekit_prb09_output.txt</a>,
          the output file.
        </li>
      </ul>
    </p>

    <p>
      Sample problem 10:
      <ul>
        <li>
          <a href = "sparsekit_prb10.f">sparsekit_prb10.f</a>,
          a sample calling program.
        </li>
        <li>
          <a href = "sparsekit_prb10.sh">sparsekit_prb10.sh</a>,
          commands to compile and run the sample program.
        </li>
        <li>
          <a href = "sparsekit_prb10_output.txt">sparsekit_prb10_output.txt</a>,
          the output file.
        </li>
      </ul>
    </p>

    <p>
      Sample problem 11:
      <ul>
        <li>
          <a href = "sparsekit_prb11.f">sparsekit_prb11.f</a>,
          a sample calling program.
        </li>
        <li>
          <a href = "sparsekit_prb11.sh">sparsekit_prb11.sh</a>,
          commands to compile and run the sample program.
        </li>
        <li>
          <a href = "sparsekit_prb11_output.txt">sparsekit_prb11_output.txt</a>,
          the output file.
        </li>
      </ul>
    </p>

    <p>
      Sample problem 12:
      <ul>
        <li>
          <a href = "sparsekit_prb12.f">sparsekit_prb12.f</a>,
          a sample calling program.
        </li>
        <li>
          <a href = "sparsekit_prb12.sh">sparsekit_prb12.sh</a>,
          commands to compile and run the sample program.
        </li>
        <li>
          <a href = "sparsekit_prb12_output.txt">sparsekit_prb12_output.txt</a>,
          the output file.
        </li>
      </ul>
    </p>

    <p>
      Sample problem 13:
      <ul>
        <li>
          <a href = "sparsekit_prb13.f">sparsekit_prb13.f</a>,
          a sample calling program.
        </li>
        <li>
          <a href = "sparsekit_prb13.sh">sparsekit_prb13.sh</a>,
          commands to compile and run the sample program.
        </li>
        <li>
          <a href = "sparsekit_prb13_output.txt">sparsekit_prb13_output.txt</a>,
          the output file.
        </li>
      </ul>
    </p>

    <p>
      Sample problem 14 generates a sample CSR matrix and
      converts it to an NCF (nonsymmetric coordinate format)
      used by NSPCG.
      <ul>
        <li>
          <a href = "sparsekit_prb14.f">sparsekit_prb14.f</a>,
          a sample calling program.
        </li>
        <li>
          <a href = "sparsekit_prb14.sh">sparsekit_prb14.sh</a>,
          commands to compile and run the sample program.
        </li>
        <li>
          <a href = "sparsekit_prb14_output.txt">sparsekit_prb14_output.txt</a>,
          the output file.
        </li>
      </ul>
    </p>

    <h3 align = "center">
      List of Routines:
    </h3>

    <p>
      <ul>
        <li>
          <b>AMASK</b> extracts a sparse matrix from a masked input matrix.
        </li>
        <li>
          <b>AMUB</b> performs the matrix product C = A * B.
        </li>
        <li>
          <b>AMUBDG</b> gets the number of nonzero elements in each row of A * B.
        </li>
        <li>
          <b>AMUDIA</b> performs the matrix by matrix product B = A * Diag  (in place)
        </li>
        <li>
          <b>AMUX</b> multiplies a CSR matrix A times a vector.
        </li>
        <li>
          <b>AMUXD</b> multiplies a DIA matrix times a vector.
        </li>
        <li>
          <b>AMUXE</b> multiplies an ELL matrix times a vector.
        </li>
        <li>
          <b>AMUXJ</b> multiplies a JAD matrix times a vector.
        </li>
        <li>
          <b>APLB</b> performs the CSR matrix sum C = A + B.
        </li>
        <li>
          <b>APLB1</b> performs the sum C = A + B for sorted CSR matrices.
        </li>
        <li>
          <b>APLBDG</b> gets the number of nonzero elements in each row of A + B.
        </li>
        <li>
          <b>APLDIA</b> adds a diagonal matrix to a general sparse matrix:  B = A + Diag.
        </li>
        <li>
          <b>APLSB</b> performs the matrix linear combination C = A + s * B.
        </li>
        <li>
          <b>APLSB1</b> performs the operation C = A + s * B for sorted CSR matrices.
        </li>
        <li>
          <b>APLSBT</b> performs the matrix sum C = A + B'.
        </li>
        <li>
          <b>APLSCA</b> adds a scalar to the diagonal entries of a sparse matrix A :=A + s I
        </li>
        <li>
          <b>APMBT</b> performs the matrix sum  C = A + B' or C = A - B'.
        </li>
        <li>
          <b>ASSMB1</b> assembles a finite element matrix in the CSR format.
        </li>
        <li>
          <b>ASSMBO</b> assembles a finite element matrix.
        </li>
        <li>
          <b>ATMUX</b> computes A' * x for a CSR matrix A.
        </li>
        <li>
          <b>BLKCHK</b> checks whether the input matrix is a block matrix.
        </li>
        <li>
          <b>BLKFND</b> determines the block structure of a matrix.
        </li>
        <li>
          <b>BNDCSR</b> converts Banded Linpack format to Compressed Sparse Row format.
        </li>
        <li>
          <b>BOUND</b> counts the number of boundary points.
        </li>
        <li>
          <b>BSORT2</b> returns the NCUT largest elements of an array, using bubble sort.
        </li>
        <li>
          <b>BSRCSR</b> converts Block Sparse Row to Compressed Sparse Row (CSR) format.
        </li>
        <li>
          <b>BSTEN</b> calculates block stencil values.
        </li>
        <li>
          <b>CHECKREF</b> returns the expected number of new nodes and elements.
        </li>
        <li>
          <b>CHKELMT</b> checks the labeling within each element and reorders if necessary.
        </li>
        <li>
          <b>CNRMS</b> gets the norms of each column of A.
        </li>
        <li>
          <b>COICSR</b> converts COO to CSR in place.
        </li>
        <li>
          <b>COOCSR</b> converts COO to CSR.
        </li>
        <li>
          <b>COOELL</b> converts coordinate format to Ellpack/Itpack format.
        </li>
        <li>
          <b>COPMAT</b> copies the matrix A, JA, IA, into the matrix AO, JAO, IAO.
        </li>
        <li>
          <b>CPERM</b> permutes the columns of a matrix.
        </li>
        <li>
          <b>CSCAL</b> scales the columns of A such that their norms are one.
        </li>
        <li>
          <b>CSORT</b> sorts the elements of a CSR matrix.
        </li>
        <li>
          <b>CSRBND</b> converts Compressed Sparse Row to Banded Linpack format.
        </li>
        <li>
          <b>CSRBSR</b> converts Compressed Sparse Row to Block Sparse Row.
        </li>
        <li>
          <b>CSRCOO</b> converts Compressed Sparse Row to Coordinate format.
        </li>
        <li>
          <b>CSRCSC</b> converts Compressed Sparse Row to Compressed Sparse Column.
        </li>
        <li>
          <b>CSRDIA</b> converts Compressed Sparse Row to diagonal format.
        </li>
        <li>
          <b>CSRDNS</b> converts Compressed Sparse Row to Dense format.
        </li>
        <li>
          <b>CSRELL</b> converts Compressed Sparse Row to Ellpack/Itpack format.
        </li>
        <li>
          <b>CSRJAD</b> converts Compressed Sparse Row to Jagged Diagonal storage.
        </li>
        <li>
          <b>CSRLNK</b> converts Compressed Sparse Row to Linked storage format.
        </li>
        <li>
          <b>CSRMSR</b> converts Compressed Sparse Row to Modified Sparse Row.
        </li>
        <li>
          <b>CSRNCF</b> converts CSR to NSPCG NCF format.
        </li>
        <li>
          <b>CSRSSK</b> converts Compressed Sparse Row to Symmetric Skyline Format.
        </li>
        <li>
          <b>CSRSSR</b> converts Compressed Sparse Row to Symmetric Sparse Row.
        </li>
        <li>
          <b>DAXPY</b> computes constant times a vector plus a vector.
        </li>
        <li>
          <b>DCN</b> generates sparse square matrices of type D(N,C).
        </li>
        <li>
          <b>DCSORT</b> computes a sorting permutation for a vector.
        </li>
        <li>
          <b>DDOT</b> forms the dot product of two vectors.
        </li>
        <li>
          <b>DIACSR</b> converts diagonal format to compressed sparse row.
        </li>
        <li>
          <b>DIAMUA</b> performs the matrix by matrix product B = Diag * A.
        </li>
        <li>
          <b>DIAPOS</b> returns the positions of the diagonal elements of a sparse matrix.
        </li>
        <li>
          <b>DINFO1</b> computes and prints matrix statistics.
        </li>
        <li>
          <b>DIRIC</b> accounts for Dirichlet boundary conditions.
        </li>
        <li>
          <b>DLAUNY</b> is a simple, nonoptimal Delaunay triangulation code.
        </li>
        <li>
          <b>DNSCSR</b> converts Dense to Compressed Row Sparse format.
        </li>
        <li>
          <b>DPERM</b> permutes the rows and columns of a matrix stored in CSR format.
        </li>
        <li>
          <b>DSCALDG</b> scales rows by a diagonal factor.
        </li>
        <li>
          <b>DUMP</b> writes the matrix to a file.
        </li>
        <li>
          <b>DVPERM</b> performs an in-place permutation of a double precision vector.
        </li>
        <li>
          <b>ECN</b> generates sparse (square) matrices of the type E(N,C).
        </li>
        <li>
          <b>ELLCSR</b> converts Ellpack/Itpack to Compressed Sparse Row.
        </li>
        <li>
          <b>ESTIF3</b> constructs an element stiffness matrix using 3 node triangles.
        </li>
        <li>
          <b>EXPHES</b> computes the Arnoldi basis.
        </li>
        <li>
          <b>EXPPRO</b> computes an approximation to the vector
        </li>
        <li>
          <b>EXPPROD</b> computes an approximation to the vector
        </li>
        <li>
          <b>EXTBDG</b> extracts the main diagonal blocks of a matrix.
        </li>
        <li>
          <b>FILTER</b> copies a matrix, dropping small elements.
        </li>
        <li>
          <b>GEN57BL</b> computes the sparse matrix for an elliptic operator.
        </li>
        <li>
          <b>GEN57PT</b> computes the compressed sparse matrix for an elliptic operator.
        </li>
        <li>
          <b>GENFEA</b> generates finite element matrices for heat conduction problems.
        </li>
        <li>
          <b>GENFEU</b> generates finite element matrices for heat conduction problems.
        </li>
        <li>
          <b>GETBWD</b> gets the bandwidth of lower part and upper part of A.
        </li>
        <li>
          <b>GETDIA</b> extracts a given diagonal from a matrix stored in CSR format.
        </li>
        <li>
          <b>GETELM</b> returns the element A(I,J) of a CSR matrix A.
        </li>
        <li>
          <b>GETL</b> extracts the lower triangular part of a matrix.
        </li>
        <li>
          <b>GETSTEN</b> calculates the stencil for centered elliptic discretization.
        </li>
        <li>
          <b>GETU</b> extracts the upper triangular part of a matrix.
        </li>
        <li>
          <b>GRADI3</b> constructs the first derivative of the shape functions.
        </li>
        <li>
          <b>HES</b> computes exp ( H dt) * y  where H = Hessenberg matrix (hh)
        </li>
        <li>
          <b>HSOURC</b> assembles the load vector F from element contributions in FS.
        </li>
        <li>
          <b>ILU0</b> is an ILU(0) preconditioner.
        </li>
        <li>
          <b>ILUT</b> is an ILUT preconditioner.
        </li>
        <li>
          <b>INFDIA</b> obtains information on the diagonals of A.
        </li>
        <li>
          <b>IVPERM</b> performs an in-place permutation of an integer vector.
        </li>
        <li>
          <b>JADSCR</b> converts Jagged Diagonal Storage to Compressed Sparse Row.
        </li>
        <li>
          <b>LDSOL</b> solves L * x = y, for L a triangular matrix in MSR format.
        </li>
        <li>
          <b>LDSOLC</b> solves L*x = y;    L = nonunit Low. Triang. MSC format
        </li>
        <li>
          <b>LDSOLL</b> solves L*x = y; L = triangular.
        </li>
        <li>
          <b>LEVELS</b> gets the level structure of a lower triangular matrix.
        </li>
        <li>
          <b>LNKCSR</b> converts linked list storage to Compressed Sparse Row format.
        </li>
        <li>
          <b>LSOL</b> solves L*x = y ; L = lower unit triang. /  CSR format
        </li>
        <li>
          <b>LSOLC</b> solves L*x = y where L = unit lower triang. CSC format
        </li>
        <li>
          <b>LUSOL0</b> performs forward and backward solves for LU matrix produced by ILUT.
        </li>
        <li>
          <b>MARKGEN</b> is a matrix generator for a Markov random walk on a triang. grid
        </li>
        <li>
          <b>MATRF2</b> generates sparse (rectangular or square) matrices.
        </li>
        <li>
          <b>MGSR</b> is a modified Gram - Schmidt with partial reorthogonalization.
        </li>
        <li>
          <b>MILU0</b> is a simple milu(0) preconditioner.
        </li>
        <li>
          <b>MSRCSR</b> converts Modified Sparse Row to Compressed Sparse Row.
        </li>
        <li>
          <b>OPE</b> sparse matrix * vector multiplication
        </li>
        <li>
          <b>PGMRES</b> is an ILUT - Preconditioned GMRES solver.
        </li>
        <li>
          <b>PLTMT</b> creates a 'pic' plot of a matrix.
        </li>
        <li>
          <b>PLTMTPS</b> creates a PostScript plot of a sparse matrix.
        </li>
        <li>
          <b>PROJECT</b> computes the matrix-vector product w = U * v.
        </li>
        <li>
          <b>PRTMT</b> writes a matrix in Harwell-Boeing format into a file.
        </li>
        <li>
          <b>READMT</b> reads a Harwell/Boeing sparse matrix file.
        </li>
        <li>
          <b>REFALL</b> refines a finite element grid using triangular elements.
        </li>
        <li>
          <b>RETMX</b> returns in dd(*) the max absolute value of elements in row *.
        </li>
        <li>
          <b>RNRMS</b> gets the norms of each row of A. (choice of three norms)
        </li>
        <li>
          <b>RPERM</b> permutes the rows of a matrix in CSR format.
        </li>
        <li>
          <b>RSCAL</b> normalizes the rows of A.
        </li>
        <li>
          <b>SSKSSR</b> converts Symmetric Skyline Format to Symmetric Sparse Row format.
        </li>
        <li>
          <b>SSRCSR</b> converts Symmetric Sparse Row to (regular) Compressed Sparse Row.
        </li>
        <li>
          <b>SUBMAT</b> extracts the submatrix A(i1:i2,j1:j2).
        </li>
        <li>
          <b>TIMESTAMP</b> prints out the current YMDHMS date as a timestamp.
        </li>
        <li>
          <b>TRANSP</b> carries out in-place transposition routine.
        </li>
        <li>
          <b>UDSOL</b> solves U*x = y;   U = upper triangular in MSR format
        </li>
        <li>
          <b>UDSOLC</b> solves U * x = y, for upper triangular U in MSC format.
        </li>
        <li>
          <b>UNASSBL</b> ?
        </li>
        <li>
          <b>USOL</b> solves   U x = y    U = unit upper triangular.
        </li>
        <li>
          <b>USOLC</b> solves U * x = y for unit upper triangular U in CSC format.
        </li>
      </ul>
    </p>

    <p>
      You can go up one level to <a href = "../f77_src.html">
      the FORTRAN77 source codes</a>.
    </p>

    <hr>

    <i>
      Last revised on 26 October 2008.
    </i>

    <!-- John Burkardt -->

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