zlaror.f - Man Page

TESTING/MATGEN/zlaror.f

Synopsis

Functions/Subroutines

subroutine zlaror (side, init, m, n, a, lda, iseed, x, info)
ZLAROR

Function/Subroutine Documentation

subroutine zlaror (character side, character init, integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( 4 ) iseed, complex*16, dimension( * ) x, integer info)

ZLAROR

Purpose:

    ZLAROR pre- or post-multiplies an M by N matrix A by a random
    unitary matrix U, overwriting A. A may optionally be
    initialized to the identity matrix before multiplying by U.
    U is generated using the method of G.W. Stewart
    ( SIAM J. Numer. Anal. 17, 1980, pp. 403-409 ).
    (BLAS-2 version)
Parameters

SIDE

          SIDE is CHARACTER*1
           SIDE specifies whether A is multiplied on the left or right
           by U.
       SIDE = 'L'   Multiply A on the left (premultiply) by U
       SIDE = 'R'   Multiply A on the right (postmultiply) by UC>       SIDE = 'C'   Multiply A on the left by U and the right by UC>       SIDE = 'T'   Multiply A on the left by U and the right by U'
           Not modified.

INIT

          INIT is CHARACTER*1
           INIT specifies whether or not A should be initialized to
           the identity matrix.
              INIT = 'I'   Initialize A to (a section of) the
                           identity matrix before applying U.
              INIT = 'N'   No initialization.  Apply U to the
                           input matrix A.

           INIT = 'I' may be used to generate square (i.e., unitary)
           or rectangular orthogonal matrices (orthogonality being
           in the sense of ZDOTC):

           For square matrices, M=N, and SIDE many be either 'L' or
           'R'; the rows will be orthogonal to each other, as will the
           columns.
           For rectangular matrices where M < N, SIDE = 'R' will
           produce a dense matrix whose rows will be orthogonal and
           whose columns will not, while SIDE = 'L' will produce a
           matrix whose rows will be orthogonal, and whose first M
           columns will be orthogonal, the remaining columns being
           zero.
           For matrices where M > N, just use the previous
           explanation, interchanging 'L' and 'R' and 'rows' and
           'columns'.

           Not modified.

M

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

N

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

A

           A is COMPLEX*16 array, dimension ( LDA, N )
           Input and output array. Overwritten by U A ( if SIDE = 'L' )
           or by A U ( if SIDE = 'R' )
           or by U A U* ( if SIDE = 'C')
           or by U A U' ( if SIDE = 'T') on exit.

LDA

          LDA is INTEGER
           Leading dimension of A. Must be at least MAX ( 1, M ).
           Not modified.

ISEED

          ISEED is INTEGER array, dimension ( 4 )
           On entry ISEED specifies the seed of the random number
           generator. The array elements should be between 0 and 4095;
           if not they will be reduced mod 4096.  Also, ISEED(4) must
           be odd.  The random number generator uses a linear
           congruential sequence limited to small integers, and so
           should produce machine independent random numbers. The
           values of ISEED are changed on exit, and can be used in the
           next call to ZLAROR to continue the same random number
           sequence.
           Modified.

X

          X is COMPLEX*16 array, dimension ( 3*MAX( M, N ) )
           Workspace. Of length:
               2*M + N if SIDE = 'L',
               2*N + M if SIDE = 'R',
               3*N     if SIDE = 'C' or 'T'.
           Modified.

INFO

          INFO is INTEGER
           An error flag.  It is set to:
            0  if no error.
            1  if ZLARND returned a bad random number (installation
               problem)
           -1  if SIDE is not L, R, C, or T.
           -3  if M is negative.
           -4  if N is negative or if SIDE is C or T and N is not equal
               to M.
           -6  if LDA is less than M.
Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 157 of file zlaror.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

The man page zlaror(3) is an alias of zlaror.f(3).

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK