slaror.f - Man Page

subroutine slaror (side, init, m, n, a, lda, iseed, x, info)
SLAROR

SLAROR

Purpose:

 SLAROR pre- or post-multiplies an M by N matrix A by a random
 orthogonal 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, 403-409).

Parameters

SIDE

          SIDE is CHARACTER*1
          Specifies whether A is multiplied on the left or right by U.
          = 'L':         Multiply A on the left (premultiply) by U
          = 'R':         Multiply A on the right (postmultiply) by U'
          = 'C' or 'T':  Multiply A on the left by U and the right
                          by U' (Here, U' means U-transpose.)

INIT

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

          INIT = 'I' may be used to generate square or rectangular
          orthogonal matrices:

          For M = N and SIDE = 'L' or 'R', the rows will be orthogonal
          to each other, as will the columns.

          If M < N, SIDE = 'R' produces a dense matrix whose rows are
          orthogonal and whose columns are not, while SIDE = 'L'
          produces a matrix whose rows are orthogonal, and whose first
          M columns are orthogonal, and whose remaining columns are
          zero.

          If M > N, SIDE = 'L' produces a dense matrix whose columns
          are orthogonal and whose rows are not, while SIDE = 'R'
          produces a matrix whose columns are orthogonal, and whose
          first M rows are orthogonal, and whose remaining rows are
          zero.

M

          M is INTEGER
          The number of rows of A.

N

          N is INTEGER
          The number of columns of A.

A

          A is REAL array, dimension (LDA, N)
          On entry, the array A.
          On exit, overwritten by U A ( if SIDE = 'L' ),
           or by A U ( if SIDE = 'R' ),
           or by U A U' ( if SIDE = 'C' or 'T').

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).

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 SLAROR to continue the same random number
          sequence.

X

          X is REAL 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'.

INFO

          INFO is INTEGER
          An error flag.  It is set to:
          = 0:  normal return
          < 0:  if INFO = -k, the k-th argument had an illegal value
          = 1:  if the random numbers generated by SLARND are bad.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 145 of file slaror.f.