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).

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.

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