181 lines
4.3 KiB
Fortran
181 lines
4.3 KiB
Fortran
*> \brief \b SRZT01
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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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* REAL FUNCTION SRZT01( M, N, A, AF, LDA, TAU, WORK,
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* LWORK )
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*
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* .. Scalar Arguments ..
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* INTEGER LDA, LWORK, M, N
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* ..
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* .. Array Arguments ..
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* REAL A( LDA, * ), AF( LDA, * ), TAU( * ),
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* $ WORK( LWORK )
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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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*> SRZT01 returns
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*> || A - R*Q || / ( M * eps * ||A|| )
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*> for an upper trapezoidal A that was factored with STZRZF.
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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] M
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*> \verbatim
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*> M is INTEGER
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*> The number of rows of the matrices A and AF.
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*> \endverbatim
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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 number of columns of the matrices A and AF.
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*> \endverbatim
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*>
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*> \param[in] A
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*> \verbatim
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*> A is REAL array, dimension (LDA,N)
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*> The original upper trapezoidal M by N matrix A.
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*> \endverbatim
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*>
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*> \param[in] AF
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*> \verbatim
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*> AF is REAL array, dimension (LDA,N)
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*> The output of STZRZF for input matrix A.
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*> The lower triangle is not referenced.
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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 arrays A and AF.
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*> \endverbatim
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*>
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*> \param[in] TAU
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*> \verbatim
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*> TAU is REAL array, dimension (M)
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*> Details of the Householder transformations as returned by
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*> STZRZF.
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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 (LWORK)
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*> \endverbatim
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*>
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*> \param[in] LWORK
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*> \verbatim
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*> LWORK is INTEGER
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*> The length of the array WORK. LWORK >= m*n + m*nb.
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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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*> \ingroup single_lin
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*
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* =====================================================================
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REAL FUNCTION SRZT01( M, N, A, AF, LDA, TAU, WORK,
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$ LWORK )
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*
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* -- LAPACK test routine --
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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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*
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* .. Scalar Arguments ..
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INTEGER LDA, LWORK, M, N
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* ..
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* .. Array Arguments ..
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REAL A( LDA, * ), AF( LDA, * ), TAU( * ),
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$ WORK( LWORK )
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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, INFO, J
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REAL NORMA
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* ..
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* .. Local Arrays ..
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REAL RWORK( 1 )
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* ..
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* .. External Functions ..
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REAL SLAMCH, SLANGE
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EXTERNAL SLAMCH, SLANGE
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* ..
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* .. External Subroutines ..
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EXTERNAL SAXPY, SLASET, SORMRZ, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, REAL
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* ..
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* .. Executable Statements ..
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*
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SRZT01 = ZERO
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*
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IF( LWORK.LT.M*N+M ) THEN
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CALL XERBLA( 'SRZT01', 8 )
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( M.LE.0 .OR. N.LE.0 )
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$ RETURN
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*
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NORMA = SLANGE( 'One-norm', M, N, A, LDA, RWORK )
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*
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* Copy upper triangle R
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*
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CALL SLASET( 'Full', M, N, ZERO, ZERO, WORK, M )
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DO 20 J = 1, M
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DO 10 I = 1, J
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WORK( ( J-1 )*M+I ) = AF( I, J )
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10 CONTINUE
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20 CONTINUE
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*
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* R = R * P(1) * ... *P(m)
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*
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CALL SORMRZ( 'Right', 'No transpose', M, N, M, N-M, AF, LDA, TAU,
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$ WORK, M, WORK( M*N+1 ), LWORK-M*N, INFO )
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*
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* R = R - A
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*
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DO 30 I = 1, N
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CALL SAXPY( M, -ONE, A( 1, I ), 1, WORK( ( I-1 )*M+1 ), 1 )
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30 CONTINUE
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*
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SRZT01 = SLANGE( 'One-norm', M, N, WORK, M, RWORK )
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*
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SRZT01 = SRZT01 / ( SLAMCH( 'Epsilon' )*REAL( MAX( M, N ) ) )
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IF( NORMA.NE.ZERO )
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$ SRZT01 = SRZT01 / NORMA
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*
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RETURN
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*
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* End of SRZT01
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*
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END
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