Julie
bc6a755be4
This is really old school, but a lot of times we have users sending us copy pasting of codes, and that is the only way to know the version of the code.
175 lines
4.4 KiB
FortranFixed
175 lines
4.4 KiB
FortranFixed
*> \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.
|
|
*
|
|
*> \date December 2016
|
|
*
|
|
*> \ingroup double_matgen
|
|
*
|
|
* =====================================================================
|
|
SUBROUTINE DLARGE( N, A, LDA, ISEED, WORK, INFO )
|
|
*
|
|
* -- LAPACK auxiliary routine (version 3.7.0) --
|
|
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
|
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
|
* December 2016
|
|
*
|
|
* .. 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
|