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237 lines
6.6 KiB
237 lines
6.6 KiB
2 years ago
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*> \brief \b DTBT02
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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 DTBT02( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, X,
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* LDX, B, LDB, WORK, RESID )
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*
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* .. Scalar Arguments ..
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* CHARACTER DIAG, TRANS, UPLO
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* INTEGER KD, LDAB, 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 AB( LDAB, * ), B( LDB, * ), WORK( * ),
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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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*> DTBT02 computes the residual for the computed solution to a
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*> triangular system of linear equations op(A)*X = B, when A is a
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*> triangular band matrix. The test ratio is the maximum over
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*> norm(b - op(A)*x) / ( ||op(A)||_1 * norm(x) * EPS ),
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*> where op(A) = A or A**T, b is the column of B, x is the solution
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*> vector, and 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] UPLO
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*> \verbatim
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*> UPLO is CHARACTER*1
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*> Specifies whether the matrix A is upper or lower triangular.
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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] TRANS
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*> \verbatim
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*> TRANS is CHARACTER*1
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*> Specifies the operation applied to A.
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*> = 'N': A * X = B (No transpose)
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*> = 'T': A**T * X = B (Transpose)
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*> = 'C': A**H * X = B (Conjugate transpose = Transpose)
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*> \endverbatim
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*>
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*> \param[in] DIAG
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*> \verbatim
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*> DIAG is CHARACTER*1
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*> Specifies whether or not the matrix A is unit triangular.
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*> = 'N': Non-unit triangular
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*> = 'U': Unit 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 order of the matrix A. N >= 0.
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*> \endverbatim
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*>
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*> \param[in] KD
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*> \verbatim
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*> KD is INTEGER
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*> The number of superdiagonals or subdiagonals of the
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*> triangular band matrix A. KD >= 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 X and B. NRHS >= 0.
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*> \endverbatim
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*>
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*> \param[in] AB
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*> \verbatim
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*> AB is DOUBLE PRECISION array, dimension (LDAB,N)
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*> The upper or lower triangular band matrix A, stored in the
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*> first kd+1 rows of the array. The j-th column of A is stored
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*> in the j-th column of the array AB as follows:
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*> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
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*> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
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*> \endverbatim
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*>
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*> \param[in] LDAB
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*> \verbatim
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*> LDAB is INTEGER
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*> The leading dimension of the array AB. LDAB >= KD+1.
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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 computed solution 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] 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] B
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*> \verbatim
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*> B is DOUBLE PRECISION 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[out] WORK
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*> \verbatim
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*> WORK is DOUBLE PRECISION 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 DOUBLE PRECISION
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*> The maximum over the number of right hand sides of
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*> norm(op(A)*x - b) / ( 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 double_lin
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*
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* =====================================================================
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SUBROUTINE DTBT02( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, X,
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$ LDX, B, LDB, WORK, 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 DIAG, TRANS, UPLO
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INTEGER KD, LDAB, 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 AB( LDAB, * ), B( LDB, * ), WORK( * ),
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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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DOUBLE PRECISION ZERO, ONE
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PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+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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LOGICAL LSAME
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DOUBLE PRECISION DASUM, DLAMCH, DLANTB
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EXTERNAL LSAME, DASUM, DLAMCH, DLANTB
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* ..
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* .. External Subroutines ..
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EXTERNAL DAXPY, DCOPY, DTBMV
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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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IF( N.LE.0 .OR. NRHS.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 op(A).
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*
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IF( LSAME( TRANS, 'N' ) ) THEN
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ANORM = DLANTB( '1', UPLO, DIAG, N, KD, AB, LDAB, WORK )
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ELSE
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ANORM = DLANTB( 'I', UPLO, DIAG, N, KD, AB, LDAB, WORK )
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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 = 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 the maximum over the number of right hand sides of
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* norm(op(A)*x - b) / ( norm(op(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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CALL DCOPY( N, X( 1, J ), 1, WORK, 1 )
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CALL DTBMV( UPLO, TRANS, DIAG, N, KD, AB, LDAB, WORK, 1 )
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CALL DAXPY( N, -ONE, B( 1, J ), 1, WORK, 1 )
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BNORM = DASUM( N, WORK, 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 DTBT02
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*
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END
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