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*> \brief \b SLARGE
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE SLARGE( N, A, LDA, ISEED, WORK, INFO )
*
* .. Scalar Arguments ..
* INTEGER INFO, LDA, N
* ..
* .. Array Arguments ..
* INTEGER ISEED( 4 )
* REAL A( LDA, * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> SLARGE pre- and post-multiplies a real general n by n matrix A
*> with a random orthogonal matrix: A = U*D*U'.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*> A is REAL 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.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= N.
*> \endverbatim
*>
*> \param[in,out] ISEED
*> \verbatim
*> ISEED is 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.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is REAL array, dimension (2*N)
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup real_matgen
*
* =====================================================================
SUBROUTINE SLARGE( N, A, LDA, ISEED, WORK, INFO )
*
* -- LAPACK auxiliary routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, N
* ..
* .. Array Arguments ..
INTEGER ISEED( 4 )
REAL A( LDA, * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
* ..
* .. Local Scalars ..
INTEGER I
REAL TAU, WA, WB, WN
* ..
* .. External Subroutines ..
EXTERNAL SGEMV, SGER, SLARNV, SSCAL, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, SIGN
* ..
* .. External Functions ..
REAL SNRM2
EXTERNAL SNRM2
* ..
* .. 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( 'SLARGE', -INFO )
RETURN
END IF
*
* pre- and post-multiply A by random orthogonal matrix
*
DO 10 I = N, 1, -1
*
* generate random reflection
*
CALL SLARNV( 3, ISEED, N-I+1, WORK )
WN = SNRM2( N-I+1, WORK, 1 )
WA = SIGN( WN, WORK( 1 ) )
IF( WN.EQ.ZERO ) THEN
TAU = ZERO
ELSE
WB = WORK( 1 ) + WA
CALL SSCAL( 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 SGEMV( 'Transpose', N-I+1, N, ONE, A( I, 1 ), LDA, WORK,
$ 1, ZERO, WORK( N+1 ), 1 )
CALL SGER( 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 SGEMV( 'No transpose', N, N-I+1, ONE, A( 1, I ), LDA,
$ WORK, 1, ZERO, WORK( N+1 ), 1 )
CALL SGER( N, N-I+1, -TAU, WORK( N+1 ), 1, WORK, 1, A( 1, I ),
$ LDA )
10 CONTINUE
RETURN
*
* End of SLARGE
*
END
|
