dlaror.f3

!>
!> DLAROR 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).
!> 

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 DOUBLE PRECISION 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 DLAROR to continue the same random number
!>          sequence.
!> 

X

!>          X is DOUBLE PRECISION 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 DLARND are bad.
!> 

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