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258 lines
6.6 KiB
258 lines
6.6 KiB
2 years ago
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*> \brief \b SGTT01
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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 SGTT01( N, DL, D, DU, DLF, DF, DUF, DU2, IPIV, WORK,
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* LDWORK, RWORK, RESID )
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*
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* .. Scalar Arguments ..
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* INTEGER LDWORK, N
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* REAL RESID
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* ..
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* .. Array Arguments ..
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* INTEGER IPIV( * )
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* REAL D( * ), DF( * ), DL( * ), DLF( * ), DU( * ),
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* $ DU2( * ), DUF( * ), RWORK( * ),
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* $ WORK( LDWORK, * )
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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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*> SGTT01 reconstructs a tridiagonal matrix A from its LU factorization
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*> and computes the residual
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*> norm(L*U - A) / ( norm(A) * 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. N >= 0.
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*> \endverbatim
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*>
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*> \param[in] DL
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*> \verbatim
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*> DL is REAL array, dimension (N-1)
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*> The (n-1) sub-diagonal elements of A.
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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 REAL array, dimension (N)
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*> The diagonal elements of A.
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*> \endverbatim
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*>
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*> \param[in] DU
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*> \verbatim
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*> DU is REAL array, dimension (N-1)
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*> The (n-1) super-diagonal elements of A.
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*> \endverbatim
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*>
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*> \param[in] DLF
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*> \verbatim
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*> DLF is REAL array, dimension (N-1)
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*> The (n-1) multipliers that define the matrix L from the
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*> LU factorization of A.
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*> \endverbatim
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*>
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*> \param[in] DF
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*> \verbatim
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*> DF is REAL array, dimension (N)
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*> The n diagonal elements of the upper triangular matrix U from
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*> the LU factorization of A.
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*> \endverbatim
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*>
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*> \param[in] DUF
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*> \verbatim
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*> DUF is REAL array, dimension (N-1)
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*> The (n-1) elements of the first super-diagonal of U.
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*> \endverbatim
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*>
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*> \param[in] DU2
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*> \verbatim
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*> DU2 is REAL array, dimension (N-2)
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*> The (n-2) elements of the second super-diagonal of U.
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*> \endverbatim
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*>
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*> \param[in] IPIV
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*> \verbatim
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*> IPIV is INTEGER array, dimension (N)
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*> The pivot indices; for 1 <= i <= n, row i of the matrix was
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*> interchanged with row IPIV(i). IPIV(i) will always be either
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*> i or i+1; IPIV(i) = i indicates a row interchange was not
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*> required.
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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 (LDWORK,N)
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*> \endverbatim
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*>
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*> \param[in] LDWORK
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*> \verbatim
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*> LDWORK is INTEGER
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*> The leading dimension of the array WORK. LDWORK >= max(1,N).
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*> \endverbatim
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*>
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*> \param[out] RWORK
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*> \verbatim
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*> RWORK is REAL array, dimension (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 REAL
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*> The scaled residual: norm(L*U - A) / (norm(A) * 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 single_lin
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*
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* =====================================================================
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SUBROUTINE SGTT01( N, DL, D, DU, DLF, DF, DUF, DU2, IPIV, WORK,
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$ LDWORK, RWORK, 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 LDWORK, N
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REAL RESID
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* ..
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* .. Array Arguments ..
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INTEGER IPIV( * )
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REAL D( * ), DF( * ), DL( * ), DLF( * ), DU( * ),
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$ DU2( * ), DUF( * ), RWORK( * ),
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$ WORK( LDWORK, * )
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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 ONE, ZERO
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PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
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* ..
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* .. Local Scalars ..
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INTEGER I, IP, J, LASTJ
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REAL ANORM, EPS, LI
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* ..
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* .. External Functions ..
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REAL SLAMCH, SLANGT, SLANHS
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EXTERNAL SLAMCH, SLANGT, SLANHS
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MIN
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* ..
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* .. External Subroutines ..
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EXTERNAL SAXPY, SSWAP
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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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EPS = SLAMCH( 'Epsilon' )
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*
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* Copy the matrix U to WORK.
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*
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DO 20 J = 1, N
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DO 10 I = 1, N
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WORK( I, J ) = ZERO
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10 CONTINUE
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20 CONTINUE
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DO 30 I = 1, N
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IF( I.EQ.1 ) THEN
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WORK( I, I ) = DF( I )
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IF( N.GE.2 )
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$ WORK( I, I+1 ) = DUF( I )
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IF( N.GE.3 )
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$ WORK( I, I+2 ) = DU2( I )
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ELSE IF( I.EQ.N ) THEN
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WORK( I, I ) = DF( I )
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ELSE
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WORK( I, I ) = DF( I )
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WORK( I, I+1 ) = DUF( I )
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IF( I.LT.N-1 )
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$ WORK( I, I+2 ) = DU2( I )
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END IF
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30 CONTINUE
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*
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* Multiply on the left by L.
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*
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LASTJ = N
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DO 40 I = N - 1, 1, -1
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LI = DLF( I )
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CALL SAXPY( LASTJ-I+1, LI, WORK( I, I ), LDWORK,
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$ WORK( I+1, I ), LDWORK )
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IP = IPIV( I )
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IF( IP.EQ.I ) THEN
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LASTJ = MIN( I+2, N )
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ELSE
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CALL SSWAP( LASTJ-I+1, WORK( I, I ), LDWORK, WORK( I+1, I ),
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$ LDWORK )
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END IF
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40 CONTINUE
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*
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* Subtract the matrix A.
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*
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WORK( 1, 1 ) = WORK( 1, 1 ) - D( 1 )
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IF( N.GT.1 ) THEN
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WORK( 1, 2 ) = WORK( 1, 2 ) - DU( 1 )
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WORK( N, N-1 ) = WORK( N, N-1 ) - DL( N-1 )
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WORK( N, N ) = WORK( N, N ) - D( N )
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DO 50 I = 2, N - 1
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WORK( I, I-1 ) = WORK( I, I-1 ) - DL( I-1 )
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WORK( I, I ) = WORK( I, I ) - D( I )
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WORK( I, I+1 ) = WORK( I, I+1 ) - DU( I )
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50 CONTINUE
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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 = SLANGT( '1', N, DL, D, DU )
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*
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* Compute the 1-norm of WORK, which is only guaranteed to be
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* upper Hessenberg.
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*
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RESID = SLANHS( '1', N, WORK, LDWORK, RWORK )
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*
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* Compute norm(L*U - A) / (norm(A) * EPS)
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*
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IF( ANORM.LE.ZERO ) THEN
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IF( RESID.NE.ZERO )
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$ RESID = ONE / EPS
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ELSE
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RESID = ( RESID / ANORM ) / EPS
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END IF
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*
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RETURN
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*
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* End of SGTT01
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*
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END
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