# 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

Univ. of Colorado Denver

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