# claror.f - Man Page

TESTING/MATGEN/claror.f

## Synopsis

### Functions/Subroutines

subroutine claror (side, init, m, n, a, lda, iseed, x, info)
CLAROR

## Function/Subroutine Documentation

### subroutine claror (character side, character init, integer m, integer n, complex, dimension( lda, * ) a, integer lda, integer, dimension( 4 ) iseed, complex, dimension( * ) x, integer info)

CLAROR

Purpose:

```    CLAROR 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)```
Parameters

SIDE

```          SIDE is 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 UC>       SIDE = 'C'   Multiply A on the left by U and the right by UC>       SIDE = 'T'   Multiply A on the left by U and the right by U'
Not modified.```

INIT

```          INIT is 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 CDOTC):

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

```          M is INTEGER
Number of rows of A. Not modified.```

N

```          N is INTEGER
Number of columns of A. Not modified.```

A

```          A is COMPLEX 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

```          LDA is INTEGER
Leading dimension of A. Must be at least MAX ( 1, M ).
Not modified.```

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 CLAROR to continue the same random number
sequence.
Modified.```

X

```          X is COMPLEX 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

```          INFO is INTEGER
An error flag.  It is set to:
0  if no error.
1  if CLARND 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.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 157 of file claror.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

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