# dlaror.f - Man Page

TESTING/MATGEN/dlaror.f

## Synopsis

### Functions/Subroutines

subroutine **dlaror** (side, init, m, n, a, lda, iseed, x, info)**DLAROR**

## Function/Subroutine Documentation

### subroutine dlaror (character side, character init, integer m, integer n, double precision, dimension( lda, * ) a, integer lda, integer, dimension( 4 ) iseed, double precision, dimension( * ) x, integer info)

**DLAROR**

**Purpose:**

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).

**Parameters***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.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **145** of file **dlaror.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dlaror(3) is an alias of dlaror.f(3).

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK