175 lines
4.4 KiB
Fortran
175 lines
4.4 KiB
Fortran
*> \brief \b SLARGE
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE SLARGE( N, A, LDA, ISEED, WORK, INFO )
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*
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* .. Scalar Arguments ..
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* INTEGER INFO, LDA, N
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* ..
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* .. Array Arguments ..
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* INTEGER ISEED( 4 )
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* REAL A( LDA, * ), WORK( * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> SLARGE pre- and post-multiplies a real general n by n matrix A
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*> with a random orthogonal matrix: A = U*D*U'.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The order of the matrix A. N >= 0.
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*> \endverbatim
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*>
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*> \param[in,out] A
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*> \verbatim
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*> A is REAL array, dimension (LDA,N)
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*> On entry, the original n by n matrix A.
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*> On exit, A is overwritten by U*A*U' for some random
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*> orthogonal matrix U.
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> The leading dimension of the array A. LDA >= N.
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*> \endverbatim
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*>
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*> \param[in,out] ISEED
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*> \verbatim
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*> ISEED is INTEGER array, dimension (4)
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*> On entry, the seed of the random number generator; the array
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*> elements must be between 0 and 4095, and ISEED(4) must be
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*> odd.
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*> On exit, the seed is updated.
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is REAL array, dimension (2*N)
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*> \endverbatim
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*>
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*> \param[out] INFO
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*> \verbatim
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*> INFO is INTEGER
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*> = 0: successful exit
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*> < 0: if INFO = -i, the i-th argument had an illegal value
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \date December 2016
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*
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*> \ingroup real_matgen
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*
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* =====================================================================
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SUBROUTINE SLARGE( N, A, LDA, ISEED, WORK, INFO )
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*
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* -- LAPACK auxiliary routine (version 3.7.0) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* December 2016
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*
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* .. Scalar Arguments ..
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INTEGER INFO, LDA, N
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* ..
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* .. Array Arguments ..
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INTEGER ISEED( 4 )
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REAL A( LDA, * ), WORK( * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ZERO, ONE
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PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
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* ..
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* .. Local Scalars ..
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INTEGER I
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REAL TAU, WA, WB, WN
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* ..
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* .. External Subroutines ..
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EXTERNAL SGEMV, SGER, SLARNV, SSCAL, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, SIGN
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* ..
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* .. External Functions ..
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REAL SNRM2
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EXTERNAL SNRM2
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* ..
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* .. Executable Statements ..
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*
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* Test the input arguments
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*
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INFO = 0
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IF( N.LT.0 ) THEN
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INFO = -1
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ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
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INFO = -3
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END IF
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IF( INFO.LT.0 ) THEN
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CALL XERBLA( 'SLARGE', -INFO )
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RETURN
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END IF
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*
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* pre- and post-multiply A by random orthogonal matrix
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*
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DO 10 I = N, 1, -1
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*
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* generate random reflection
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*
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CALL SLARNV( 3, ISEED, N-I+1, WORK )
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WN = SNRM2( N-I+1, WORK, 1 )
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WA = SIGN( WN, WORK( 1 ) )
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IF( WN.EQ.ZERO ) THEN
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TAU = ZERO
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ELSE
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WB = WORK( 1 ) + WA
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CALL SSCAL( N-I, ONE / WB, WORK( 2 ), 1 )
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WORK( 1 ) = ONE
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TAU = WB / WA
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END IF
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*
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* multiply A(i:n,1:n) by random reflection from the left
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*
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CALL SGEMV( 'Transpose', N-I+1, N, ONE, A( I, 1 ), LDA, WORK,
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$ 1, ZERO, WORK( N+1 ), 1 )
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CALL SGER( N-I+1, N, -TAU, WORK, 1, WORK( N+1 ), 1, A( I, 1 ),
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$ LDA )
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*
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* multiply A(1:n,i:n) by random reflection from the right
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*
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CALL SGEMV( 'No transpose', N, N-I+1, ONE, A( 1, I ), LDA,
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$ WORK, 1, ZERO, WORK( N+1 ), 1 )
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CALL SGER( N, N-I+1, -TAU, WORK( N+1 ), 1, WORK, 1, A( 1, I ),
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$ LDA )
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10 CONTINUE
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RETURN
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*
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* End of SLARGE
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*
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END
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