ZLAROR
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
June 2010
June 2010
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)
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)
Arguments
| SIDE |
(input) 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 U* SIDE = 'C' Multiply A on the left by U and the right by U* SIDE = 'T' Multiply A on the left by U and the right by U' Not modified. |
| INIT |
(input) 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 |
(input) INTEGER
Number of rows of A. Not modified.
|
| N |
(input) INTEGER
Number of columns of A. Not modified.
|
| A |
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 |
(input) INTEGER
Leading dimension of A. Must be at least MAX ( 1, M ).
Not modified. |
| 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 ZLAROR to continue the same random number sequence. Modified. |
| X |
(workspace) 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 |
(output) 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. |