*> \brief \b DLARGE * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DLARGE( N, A, LDA, ISEED, WORK, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, LDA, N * .. * .. Array Arguments .. * INTEGER ISEED( 4 ) * DOUBLE PRECISION A( LDA, * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLARGE 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 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. *> \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 DOUBLE PRECISION 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. * *> \ingroup double_matgen * * ===================================================================== SUBROUTINE DLARGE( N, A, LDA, ISEED, WORK, INFO ) * * -- LAPACK auxiliary routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. INTEGER INFO, LDA, N * .. * .. Array Arguments .. INTEGER ISEED( 4 ) DOUBLE PRECISION A( LDA, * ), WORK( * ) * .. * * ===================================================================== * * .. 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