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206 lines
5.2 KiB
206 lines
5.2 KiB
2 years ago
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*> \brief \b SGTT02
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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 SGTT02( TRANS, N, NRHS, DL, D, DU, X, LDX, B, LDB,
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* RESID )
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*
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* .. Scalar Arguments ..
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* CHARACTER TRANS
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* INTEGER LDB, LDX, N, NRHS
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* REAL RESID
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* ..
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* .. Array Arguments ..
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* REAL B( LDB, * ), D( * ), DL( * ), DU( * ),
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* $ 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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*> SGTT02 computes the residual for the solution to a tridiagonal
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*> system of equations:
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*> RESID = norm(B - op(A)*X) / (norm(op(A)) * norm(X) * EPS),
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*> where EPS is the machine epsilon.
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*> The norm used is the 1-norm.
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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] TRANS
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*> \verbatim
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*> TRANS is CHARACTER
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*> Specifies the form of the residual.
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*> = 'N': B - A * X (No transpose)
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*> = 'T': B - A**T * X (Transpose)
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*> = 'C': B - A**H * X (Conjugate transpose = Transpose)
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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 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 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] 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] X
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*> \verbatim
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*> X is REAL array, dimension (LDX,NRHS)
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*> The computed 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 REAL array, dimension (LDB,NRHS)
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*> On entry, the right hand side vectors for the system of
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*> linear equations.
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*> On exit, B is overwritten with the difference B - op(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 REAL
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*> norm(B - op(A)*X) / (norm(op(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 single_lin
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*
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* =====================================================================
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SUBROUTINE SGTT02( TRANS, N, NRHS, DL, D, DU, X, LDX, B, LDB,
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$ 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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CHARACTER TRANS
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INTEGER LDB, LDX, N, NRHS
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REAL RESID
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* ..
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* .. Array Arguments ..
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REAL B( LDB, * ), D( * ), DL( * ), DU( * ),
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$ 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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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 J
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REAL ANORM, BNORM, EPS, XNORM
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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REAL SASUM, SLAMCH, SLANGT
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EXTERNAL LSAME, SASUM, SLAMCH, SLANGT
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* ..
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* .. External Subroutines ..
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EXTERNAL SLAGTM
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX
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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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RESID = ZERO
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IF( N.LE.0 .OR. NRHS.EQ.0 )
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$ RETURN
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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 - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ).
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*
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IF( LSAME( TRANS, 'N' ) ) THEN
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ANORM = SLANGT( '1', N, DL, D, DU )
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ELSE
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ANORM = SLANGT( 'I', N, DL, D, DU )
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END IF
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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 = SLAMCH( '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 - op(A)*X and store in B.
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*
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CALL SLAGTM( TRANS, N, NRHS, -ONE, DL, D, DU, X, LDX, ONE, B,
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$ LDB )
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*
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DO 10 J = 1, NRHS
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BNORM = SASUM( N, B( 1, J ), 1 )
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XNORM = SASUM( 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 SGTT02
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*
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END
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