# 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