SLAROR
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
November 2006
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).
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).
Arguments
| SIDE |
(input) 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 |
(input) 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 |
(input) INTEGER
The number of rows of A.
|
| N |
(input) INTEGER
The number of columns of A.
|
| A |
(input/output) 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 |
(input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
|
| ISEED |
(input/output) 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 |
(workspace) 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 |
(output) 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. |