TESTING/MATGEN/slatm3.f(3)

NAME
TESTING/MATGEN/slatm3.f

SYNOPSIS

  Functions/Subroutines
real function slatm3 (m, n, i, j, isub, jsub, kl, ku, idist, iseed, d, igrade, dl, dr, ipvtng, iwork, sparse)
SLATM3

Function/Subroutine Documentation

  real function slatm3 (integer m, integer n, integer i, integer j, integer isub, integer jsub, integer kl, integer ku, integer idist, integer, dimension( 4 ) iseed, real, dimension( * ) d, integer igrade, real, dimension( * ) dl, real, dimension( * ) dr, integer ipvtng, integer, dimension( * ) iwork, real sparse)

SLATM3

Purpose:

        SLATM3 returns the (ISUB,JSUB) entry of a random matrix of
        dimension (M, N) described by the other parameters. (ISUB,JSUB)
        is the final position of the (I,J) entry after pivoting
        according to IPVTNG and IWORK. SLATM3 is called by the
        SLATMR routine in order to build random test matrices. No error
        checking on parameters is done, because this routine is called in
        a tight loop by SLATMR which has already checked the parameters.
        Use of SLATM3 differs from SLATM2 in the order in which the random
        number generator is called to fill in random matrix entries.
        With SLATM2, the generator is called to fill in the pivoted matrix
        columnwise. With SLATM3, the generator is called to fill in the
        matrix columnwise, after which it is pivoted. Thus, SLATM3 can
        be used to construct random matrices which differ only in their
        order of rows and/or columns. SLATM2 is used to construct band
        matrices while avoiding calling the random number generator for
        entries outside the band (and therefore generating random numbers
        in different orders for different pivot orders).
        The matrix whose (ISUB,JSUB) entry is returned is constructed as
        follows (this routine only computes one entry):
          If ISUB is outside (1..M) or JSUB is outside (1..N), return zero
             (this is convenient for generating matrices in band format).
          Generate a matrix A with random entries of distribution IDIST.
          Set the diagonal to D.
          Grade the matrix, if desired, from the left (by DL) and/or
             from the right (by DR or DL) as specified by IGRADE.
          Permute, if desired, the rows and/or columns as specified by
             IPVTNG and IWORK.
          Band the matrix to have lower bandwidth KL and upper
             bandwidth KU.
          Set random entries to zero as specified by SPARSE.

Parameters
    M

              M is INTEGER
               Number of rows of matrix. Not modified.

    N

              N is INTEGER
               Number of columns of matrix. Not modified.

    I

              I is INTEGER
               Row of unpivoted entry to be returned. Not modified.

    J

              J is INTEGER
               Column of unpivoted entry to be returned. Not modified.

    ISUB

              ISUB is INTEGER
               Row of pivoted entry to be returned. Changed on exit.

    JSUB

              JSUB is INTEGER
               Column of pivoted entry to be returned. Changed on exit.

    KL

              KL is INTEGER
               Lower bandwidth. Not modified.

    KU

              KU is INTEGER
               Upper bandwidth. Not modified.

    IDIST

              IDIST is INTEGER
               On entry, IDIST specifies the type of distribution to be
               used to generate a random matrix .
               1 => UNIFORM( 0, 1 )
               2 => UNIFORM( -1, 1 )
               3 => NORMAL( 0, 1 )
               Not modified.

    ISEED

              ISEED is INTEGER array of dimension ( 4 )
               Seed for random number generator.
               Changed on exit.

    D

              D is REAL array of dimension ( MIN( I , J ) )
               Diagonal entries of matrix. Not modified.

    IGRADE

              IGRADE is INTEGER
               Specifies grading of matrix as follows:
               0  => no grading
               1  => matrix premultiplied by diag( DL )
               2  => matrix postmultiplied by diag( DR )
               3  => matrix premultiplied by diag( DL ) and
                             postmultiplied by diag( DR )
               4  => matrix premultiplied by diag( DL ) and
                             postmultiplied by inv( diag( DL ) )
               5  => matrix premultiplied by diag( DL ) and
                             postmultiplied by diag( DL )
               Not modified.

    DL

              DL is REAL array ( I or J, as appropriate )
               Left scale factors for grading matrix.  Not modified.

    DR

              DR is REAL array ( I or J, as appropriate )
               Right scale factors for grading matrix.  Not modified.

    IPVTNG

              IPVTNG is INTEGER
               On entry specifies pivoting permutations as follows:
               0 => none.
               1 => row pivoting.
               2 => column pivoting.
               3 => full pivoting, i.e., on both sides.
               Not modified.

    IWORK

              IWORK is INTEGER array ( I or J, as appropriate )
               This array specifies the permutation used. The
               row (or column) originally in position K is in
               position IWORK( K ) after pivoting.
               This differs from IWORK for SLATM2. Not modified.

    SPARSE

              SPARSE is REAL between 0. and 1.
               On entry specifies the sparsity of the matrix
               if sparse matrix is to be generated.
               SPARSE should lie between 0 and 1.
               A uniform ( 0, 1 ) random number x is generated and
               compared to SPARSE; if x is larger the matrix entry
               is unchanged and if x is smaller the entry is set
               to zero. Thus on the average a fraction SPARSE of the
               entries will be set to zero.
               Not modified.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 223 of file slatm3.f.

Author

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