Visible to Intel only — GUID: GUID-6B37CE8F-1F71-46BD-9A9C-CAB9272BB823
Visible to Intel only — GUID: GUID-6B37CE8F-1F71-46BD-9A9C-CAB9272BB823
?laror
Pre- or post-multiplies an m-by-n matrix by a random orthogonal/unitary matrix.
Syntax
call slaror( side, init, m, n, a, lda, iseed, x, info )
call dlaror( side, init, m, n, a, lda, iseed, x, info )
call claror( side, init, m, n, a, lda, iseed, x, info )
call zlaror( side, init, m, n, a, lda, iseed, x, info )
Include Files
- mkl.fi
Description
The routine ?laror pre- or post-multiplies an m-by-n matrix A by a random orthogonal or 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, 403-409).
Input Parameters
- side
-
CHARACTER*1. Specifies whether A is multiplied by U on the left or right.
for slaror and dlaror:
If side = 'L', multiply A on the left (premultiply) by U.
If side = 'R', multiply A on the right (postmultiply) by UT.
If side = 'C' or 'T', multiply A on the left by U and the right by UT.
for claror and zlaror:
If side = 'L', multiply A on the left (premultiply) by U.
If side = 'R', multiply A on the right (postmultiply) by UC>.
If side = 'C', multiply A on the left by U and the right by UC>
Ifside = 'T', multiply A on the left by U and the right by UT.
- init
-
CHARACTER*1. Specifies whether or not a should be initialized to the identity matrix.
If init = 'I', initialize a to (a section of) the identity matrix before applying U.
If init = 'N', no initialization. Apply U to the input matrix A.
init = 'I' generates square or rectangular orthogonal matrices:
For m = n and side = 'L' or 'R', the rows and the columns are orthogonal to each other.
For rectangular matrices where m < n:
If side = 'R', ?laror produces a dense matrix in which rows are orthogonal and columns are not.
If side= 'L', ?laror produces a matrix in which rows are orthogonal, first m columns are orthogonal, and remaining columns are zero.
For rectangular matrices where m > n:
If side = 'L', ?laror produces a dense matrix in which columns are orthogonal and rows are not.
If side = 'R', ?laror produces a matrix in which columns are orthogonal, first m rows are orthogonal, and remaining rows are zero.
- m
-
INTEGER. The number of rows of A.
- n
-
INTEGER. The number of columns of A.
- a
-
REAL for slaror,
DOUBLE PRECISION for dlaror,
COMPLEX for claror,
DOUBLE COMPLEX for zlaror,
Array, size lda by n.
- lda
-
INTEGER. The leading dimension of the array a.
lda≥ max(1, m).
- iseed
-
INTEGER. Array, size (4).
On entry, specifies the seed of the random number generator. The array elements must be between 0 and 4095; if not they are reduced mod 4096. Also, iseed(4) must be odd.
- x
-
REAL for slaror,
DOUBLE PRECISION for dlaror,
COMPLEX for claror,
DOUBLE COMPLEX for zlaror,
Workspace array, size (3*max( m, n )) .
Value of side Length of workspace 'L' 2*m + n 'R' 2*n + m 'C' or 'T' 3*n
Output Parameters
- a
-
On exit, overwritten
by UA ( if side = 'L' ),
by AU ( if side = 'R' ),
by UAUT ( if side = 'C' or 'T').
- iseed
-
The values of iseed are changed on exit, and can be used in the next call to continue the same random number sequence.
- info
-
INTEGER. Array, size (4).
For slaror and dlaror:
If info = 0, the execution is successful.
If info < 0, the i -th parameter had an illegal value.
If info = 1, the random numbers generated by ?laror are bad.
For claror and zlaror:
If info = 0, the execution is successful.
If info = -1, side is not 'L', 'R', 'C', or 'T'.
If info = -3, if m is negative.
If info = -4, if m is negative or if side is 'C' or 'T' and n is not equal to m .
If info = -6, if lda is less than m .