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SUBROUTINE DLARGE( N, A, LDA, ISEED, WORK, INFO )
*
* -- LAPACK auxiliary test routine (version 3.1)
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
* November 2006
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, N
* ..
* .. Array Arguments ..
INTEGER ISEED( 4 )
DOUBLE PRECISION A( LDA, * ), WORK( * )
* ..
*
* Purpose
* =======
*
* DLARGE pre- and post-multiplies a real general n by n matrix A
* with a random orthogonal matrix: A = U*D*U'.
*
* Arguments
* =========
*
* N (input) INTEGER
* The order of the matrix A. N >= 0.
*
* A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
* On entry, the original n by n matrix A.
* On exit, A is overwritten by U*A*U' for some random
* orthogonal matrix U.
*
* LDA (input) INTEGER
* The leading dimension of the array A. LDA >= N.
*
* ISEED (input/output) INTEGER array, dimension (4)
* On entry, the seed of the random number generator; the array
* elements must be between 0 and 4095, and ISEED(4) must be
* odd.
* On exit, the seed is updated.
*
* WORK (workspace) DOUBLE PRECISION array, dimension (2*N)
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = -i, the i-th argument had an illegal value
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
* ..
* .. Local Scalars ..
INTEGER I
DOUBLE PRECISION TAU, WA, WB, WN
* ..
* .. External Subroutines ..
EXTERNAL DGEMV, DGER, DLARNV, DSCAL, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, SIGN
* ..
* .. External Functions ..
DOUBLE PRECISION DNRM2
EXTERNAL DNRM2
* ..
* .. Executable Statements ..
*
* Test the input arguments
*
INFO = 0
IF( N.LT.0 ) THEN
INFO = -1
ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
INFO = -3
END IF
IF( INFO.LT.0 ) THEN
CALL XERBLA( 'DLARGE', -INFO )
RETURN
END IF
*
* pre- and post-multiply A by random orthogonal matrix
*
DO 10 I = N, 1, -1
*
* generate random reflection
*
CALL DLARNV( 3, ISEED, N-I+1, WORK )
WN = DNRM2( N-I+1, WORK, 1 )
WA = SIGN( WN, WORK( 1 ) )
IF( WN.EQ.ZERO ) THEN
TAU = ZERO
ELSE
WB = WORK( 1 ) + WA
CALL DSCAL( N-I, ONE / WB, WORK( 2 ), 1 )
WORK( 1 ) = ONE
TAU = WB / WA
END IF
*
* multiply A(i:n,1:n) by random reflection from the left
*
CALL DGEMV( 'Transpose', N-I+1, N, ONE, A( I, 1 ), LDA, WORK,
$ 1, ZERO, WORK( N+1 ), 1 )
CALL DGER( N-I+1, N, -TAU, WORK, 1, WORK( N+1 ), 1, A( I, 1 ),
$ LDA )
*
* multiply A(1:n,i:n) by random reflection from the right
*
CALL DGEMV( 'No transpose', N, N-I+1, ONE, A( 1, I ), LDA,
$ WORK, 1, ZERO, WORK( N+1 ), 1 )
CALL DGER( N, N-I+1, -TAU, WORK( N+1 ), 1, WORK, 1, A( 1, I ),
$ LDA )
10 CONTINUE
RETURN
*
* End of DLARGE
*
END
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