TESTING/MATGEN/dlatm3.f(3)

NAME
TESTING/MATGEN/dlatm3.f

SYNOPSIS

  Functions/Subroutines
double precision function dlatm3 (m, n, i, j, isub, jsub, kl, ku, idist, iseed, d, igrade, dl, dr, ipvtng, iwork, sparse)
DLATM3

Function/Subroutine Documentation

  double precision function dlatm3 (integer m, integer n, integer i, integer j, integer isub, integer jsub, integer kl, integer ku, integer idist, integer, dimension( 4 ) iseed, double precision, dimension( * ) d, integer igrade, double precision, dimension( * ) dl, double precision, dimension( * ) dr, integer ipvtng, integer, dimension( * ) iwork, double precision sparse)

DLATM3

Purpose:

    !>
    !>    DLATM3 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. DLATM3 is called by the
    !>    DLATMR 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 DLATMR which has already checked the parameters.
    !>
    !>    Use of DLATM3 differs from SLATM2 in the order in which the random
    !>    number generator is called to fill in random matrix entries.
    !>    With DLATM2, the generator is called to fill in the pivoted matrix
    !>    columnwise. With DLATM3, the generator is called to fill in the
    !>    matrix columnwise, after which it is pivoted. Thus, DLATM3 can
    !>    be used to construct random matrices which differ only in their
    !>    order of rows and/or columns. DLATM2 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 DOUBLE PRECISION 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 DOUBLE PRECISION array ( I or J, as appropriate )
    !>           Left scale factors for grading matrix.  Not modified.
    !>

    DR

    !>          DR is DOUBLE PRECISION 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 DLATM2. Not modified.
    !>

    SPARSE

    !>          SPARSE is DOUBLE PRECISION 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 dlatm3.f.

Author

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