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.
296 lines
8.7 KiB
FortranFixed
296 lines
8.7 KiB
FortranFixed
*> \brief \b CPPT05
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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 CPPT05( UPLO, N, NRHS, AP, B, LDB, X, LDX, XACT,
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* LDXACT, FERR, BERR, RESLTS )
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*
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* .. Scalar Arguments ..
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* CHARACTER UPLO
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* INTEGER LDB, LDX, LDXACT, N, NRHS
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* ..
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* .. Array Arguments ..
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* REAL BERR( * ), FERR( * ), RESLTS( * )
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* COMPLEX AP( * ), B( LDB, * ), X( LDX, * ),
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* $ XACT( LDXACT, * )
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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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*> CPPT05 tests the error bounds from iterative refinement for the
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*> computed solution to a system of equations A*X = B, where A is a
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*> Hermitian matrix in packed storage format.
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*>
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*> RESLTS(1) = test of the error bound
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*> = norm(X - XACT) / ( norm(X) * FERR )
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*>
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*> A large value is returned if this ratio is not less than one.
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*>
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*> RESLTS(2) = residual from the iterative refinement routine
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*> = the maximum of BERR / ( (n+1)*EPS + (*) ), where
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*> (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
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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] UPLO
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*> \verbatim
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*> UPLO is CHARACTER*1
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*> Specifies whether the upper or lower triangular part of the
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*> Hermitian matrix A is stored.
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*> = 'U': Upper triangular
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*> = 'L': Lower triangular
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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 rows of the matrices X, B, and XACT, and the
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*> order of the matrix A. N >= 0.
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*> \endverbatim
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*>
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*> \param[in] NRHS
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*> \verbatim
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*> NRHS is INTEGER
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*> The number of columns of the matrices X, B, and XACT.
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*> NRHS >= 0.
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*> \endverbatim
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*>
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*> \param[in] AP
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*> \verbatim
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*> AP is COMPLEX array, dimension (N*(N+1)/2)
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*> The upper or lower triangle of the Hermitian matrix A, packed
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*> columnwise in a linear array. The j-th column of A is stored
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*> in the array AP as follows:
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*> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
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*> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
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*> \endverbatim
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*>
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*> \param[in] B
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*> \verbatim
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*> B is COMPLEX array, dimension (LDB,NRHS)
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*> The right hand side vectors for the system of linear
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*> equations.
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*> \endverbatim
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*>
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*> \param[in] LDB
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*> \verbatim
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*> LDB is INTEGER
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*> The leading dimension of the array B. LDB >= max(1,N).
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*> \endverbatim
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*>
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*> \param[in] X
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*> \verbatim
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*> X is COMPLEX array, dimension (LDX,NRHS)
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*> The computed solution vectors. Each vector is stored as a
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*> column of the matrix X.
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*> \endverbatim
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*>
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*> \param[in] LDX
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*> \verbatim
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*> LDX is INTEGER
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*> The leading dimension of the array X. LDX >= max(1,N).
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*> \endverbatim
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*>
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*> \param[in] XACT
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*> \verbatim
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*> XACT is COMPLEX array, dimension (LDX,NRHS)
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*> The exact solution vectors. Each vector is stored as a
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*> column of the matrix XACT.
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*> \endverbatim
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*>
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*> \param[in] LDXACT
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*> \verbatim
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*> LDXACT is INTEGER
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*> The leading dimension of the array XACT. LDXACT >= max(1,N).
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*> \endverbatim
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*>
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*> \param[in] FERR
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*> \verbatim
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*> FERR is REAL array, dimension (NRHS)
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*> The estimated forward error bounds for each solution vector
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*> X. If XTRUE is the true solution, FERR bounds the magnitude
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*> of the largest entry in (X - XTRUE) divided by the magnitude
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*> of the largest entry in X.
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*> \endverbatim
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*>
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*> \param[in] BERR
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*> \verbatim
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*> BERR is REAL array, dimension (NRHS)
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*> The componentwise relative backward error of each solution
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*> vector (i.e., the smallest relative change in any entry of A
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*> or B that makes X an exact solution).
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*> \endverbatim
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*>
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*> \param[out] RESLTS
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*> \verbatim
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*> RESLTS is REAL array, dimension (2)
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*> The maximum over the NRHS solution vectors of the ratios:
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*> RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
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*> RESLTS(2) = BERR / ( (n+1)*EPS + (*) )
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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 complex_lin
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*
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* =====================================================================
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SUBROUTINE CPPT05( UPLO, N, NRHS, AP, B, LDB, X, LDX, XACT,
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$ LDXACT, FERR, BERR, RESLTS )
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*
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* -- LAPACK test 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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CHARACTER UPLO
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INTEGER LDB, LDX, LDXACT, N, NRHS
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* ..
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* .. Array Arguments ..
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REAL BERR( * ), FERR( * ), RESLTS( * )
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COMPLEX AP( * ), B( LDB, * ), X( LDX, * ),
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$ XACT( LDXACT, * )
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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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LOGICAL UPPER
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INTEGER I, IMAX, J, JC, K
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REAL AXBI, DIFF, EPS, ERRBND, OVFL, TMP, UNFL, XNORM
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COMPLEX ZDUM
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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INTEGER ICAMAX
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REAL SLAMCH
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EXTERNAL LSAME, ICAMAX, SLAMCH
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, AIMAG, MAX, MIN, REAL
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* ..
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* .. Statement Functions ..
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REAL CABS1
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* ..
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* .. Statement Function definitions ..
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CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) )
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* ..
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* .. Executable Statements ..
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*
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* Quick exit if N = 0 or NRHS = 0.
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*
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IF( N.LE.0 .OR. NRHS.LE.0 ) THEN
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RESLTS( 1 ) = ZERO
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RESLTS( 2 ) = ZERO
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RETURN
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END IF
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*
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EPS = SLAMCH( 'Epsilon' )
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UNFL = SLAMCH( 'Safe minimum' )
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OVFL = ONE / UNFL
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UPPER = LSAME( UPLO, 'U' )
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*
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* Test 1: Compute the maximum of
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* norm(X - XACT) / ( norm(X) * FERR )
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* over all the vectors X and XACT using the infinity-norm.
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*
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ERRBND = ZERO
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DO 30 J = 1, NRHS
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IMAX = ICAMAX( N, X( 1, J ), 1 )
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XNORM = MAX( CABS1( X( IMAX, J ) ), UNFL )
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DIFF = ZERO
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DO 10 I = 1, N
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DIFF = MAX( DIFF, CABS1( X( I, J )-XACT( I, J ) ) )
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10 CONTINUE
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*
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IF( XNORM.GT.ONE ) THEN
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GO TO 20
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ELSE IF( DIFF.LE.OVFL*XNORM ) THEN
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GO TO 20
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ELSE
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ERRBND = ONE / EPS
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GO TO 30
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END IF
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*
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20 CONTINUE
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IF( DIFF / XNORM.LE.FERR( J ) ) THEN
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ERRBND = MAX( ERRBND, ( DIFF / XNORM ) / FERR( J ) )
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ELSE
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ERRBND = ONE / EPS
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END IF
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30 CONTINUE
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RESLTS( 1 ) = ERRBND
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*
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* Test 2: Compute the maximum of BERR / ( (n+1)*EPS + (*) ), where
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* (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
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*
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DO 90 K = 1, NRHS
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DO 80 I = 1, N
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TMP = CABS1( B( I, K ) )
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IF( UPPER ) THEN
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JC = ( ( I-1 )*I ) / 2
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DO 40 J = 1, I - 1
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TMP = TMP + CABS1( AP( JC+J ) )*CABS1( X( J, K ) )
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40 CONTINUE
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TMP = TMP + ABS( REAL( AP( JC+I ) ) )*CABS1( X( I, K ) )
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JC = JC + I + I
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DO 50 J = I + 1, N
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TMP = TMP + CABS1( AP( JC ) )*CABS1( X( J, K ) )
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JC = JC + J
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50 CONTINUE
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ELSE
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JC = I
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DO 60 J = 1, I - 1
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TMP = TMP + CABS1( AP( JC ) )*CABS1( X( J, K ) )
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JC = JC + N - J
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60 CONTINUE
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TMP = TMP + ABS( REAL( AP( JC ) ) )*CABS1( X( I, K ) )
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DO 70 J = I + 1, N
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TMP = TMP + CABS1( AP( JC+J-I ) )*CABS1( X( J, K ) )
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70 CONTINUE
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END IF
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IF( I.EQ.1 ) THEN
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AXBI = TMP
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ELSE
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AXBI = MIN( AXBI, TMP )
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END IF
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80 CONTINUE
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TMP = BERR( K ) / ( ( N+1 )*EPS+( N+1 )*UNFL /
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$ MAX( AXBI, ( N+1 )*UNFL ) )
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IF( K.EQ.1 ) THEN
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RESLTS( 2 ) = TMP
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ELSE
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RESLTS( 2 ) = MAX( RESLTS( 2 ), TMP )
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END IF
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90 CONTINUE
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*
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RETURN
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*
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* End of CPPT05
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*
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END
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