zlatm2.f - Man Page

complex *16 function zlatm2 (m, n, i, j, kl, ku, idist, iseed, d, igrade, dl, dr, ipvtng, iwork, sparse)
ZLATM2

ZLATM2

Purpose:

    ZLATM2 returns the (I,J) entry of a random matrix of dimension
    (M, N) described by the other parameters. It is called by the
    ZLATMR 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 ZLATMR which has already checked the parameters.

    Use of ZLATM2 differs from CLATM3 in the order in which the random
    number generator is called to fill in random matrix entries.
    With ZLATM2, the generator is called to fill in the pivoted matrix
    columnwise. With ZLATM3, the generator is called to fill in the
    matrix columnwise, after which it is pivoted. Thus, ZLATM3 can
    be used to construct random matrices which differ only in their
    order of rows and/or columns. ZLATM2 is used to construct band
    matrices while avoiding calling the random number generator for
    entries outside the band (and therefore generating random numbers

    The matrix whose (I,J) entry is returned is constructed as
    follows (this routine only computes one entry):

      If I is outside (1..M) or J 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 entry to be returned. Not modified.

J

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

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 => real and imaginary parts each UNIFORM( 0, 1 )
           2 => real and imaginary parts each UNIFORM( -1, 1 )
           3 => real and imaginary parts each NORMAL( 0, 1 )
           4 => complex number uniform in DISK( 0 , 1 )
           Not modified.

ISEED

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

D

          D is COMPLEX*16 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( CONJG(DL) )
           6  => matrix premultiplied by diag( DL ) and
                         postmultiplied by diag( DL )
           Not modified.

DL

          DL is COMPLEX*16 array ( I or J, as appropriate )
           Left scale factors for grading matrix.  Not modified.

DR

          DR is COMPLEX*16 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) in position K was originally in
           position IWORK( K ).
           This differs from IWORK for ZLATM3. 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 209 of file zlatm2.f.