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181 lines
4.5 KiB
181 lines
4.5 KiB
2 years ago
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*> \brief \b DPTT02
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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 DPTT02( N, NRHS, D, E, X, LDX, B, LDB, RESID )
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*
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* .. Scalar Arguments ..
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* INTEGER LDB, LDX, N, NRHS
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* DOUBLE PRECISION RESID
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* ..
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* .. Array Arguments ..
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* DOUBLE PRECISION B( LDB, * ), D( * ), E( * ), X( LDX, * )
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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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*> DPTT02 computes the residual for the solution to a symmetric
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*> tridiagonal system of equations:
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*> RESID = norm(B - A*X) / (norm(A) * norm(X) * EPS),
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*> where EPS is the machine epsilon.
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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.
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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 right hand sides, i.e., the number of columns
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*> of the matrices B and X. NRHS >= 0.
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*> \endverbatim
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*>
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*> \param[in] D
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*> \verbatim
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*> D is DOUBLE PRECISION array, dimension (N)
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*> The n diagonal elements of the tridiagonal matrix A.
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*> \endverbatim
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*>
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*> \param[in] E
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*> \verbatim
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*> E is DOUBLE PRECISION array, dimension (N-1)
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*> The (n-1) subdiagonal elements of the tridiagonal matrix A.
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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 DOUBLE PRECISION array, dimension (LDX,NRHS)
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*> The n by nrhs matrix of solution vectors 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,out] B
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*> \verbatim
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*> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
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*> On entry, the n by nrhs matrix of right hand side vectors B.
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*> On exit, B is overwritten with the difference B - A*X.
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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[out] RESID
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*> \verbatim
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*> RESID is DOUBLE PRECISION
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*> norm(B - A*X) / (norm(A) * norm(X) * 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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*> \ingroup double_lin
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*
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* =====================================================================
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SUBROUTINE DPTT02( N, NRHS, D, E, X, LDX, B, LDB, RESID )
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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 LDB, LDX, N, NRHS
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DOUBLE PRECISION RESID
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION B( LDB, * ), D( * ), E( * ), X( LDX, * )
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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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DOUBLE PRECISION ONE, ZERO
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PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
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* ..
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* .. Local Scalars ..
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INTEGER J
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DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
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* ..
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* .. External Functions ..
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DOUBLE PRECISION DASUM, DLAMCH, DLANST
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EXTERNAL DASUM, DLAMCH, DLANST
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX
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* ..
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* .. External Subroutines ..
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EXTERNAL DLAPTM
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* ..
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* .. Executable Statements ..
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*
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* Quick return if possible
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*
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IF( N.LE.0 ) THEN
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RESID = ZERO
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RETURN
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END IF
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*
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* Compute the 1-norm of the tridiagonal matrix A.
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*
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ANORM = DLANST( '1', N, D, E )
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*
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* Exit with RESID = 1/EPS if ANORM = 0.
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*
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EPS = DLAMCH( 'Epsilon' )
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IF( ANORM.LE.ZERO ) THEN
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RESID = ONE / EPS
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RETURN
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END IF
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*
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* Compute B - A*X.
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*
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CALL DLAPTM( N, NRHS, -ONE, D, E, X, LDX, ONE, B, LDB )
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*
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* Compute the maximum over the number of right hand sides of
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* norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
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*
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RESID = ZERO
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DO 10 J = 1, NRHS
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BNORM = DASUM( N, B( 1, J ), 1 )
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XNORM = DASUM( N, X( 1, J ), 1 )
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IF( XNORM.LE.ZERO ) THEN
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RESID = ONE / EPS
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ELSE
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RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS )
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END IF
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10 CONTINUE
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*
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RETURN
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*
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* End of DPTT02
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*
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END
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