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*> \brief \b DGBT02
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE DGBT02( TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B,
* LDB, RWORK, RESID )
*
* .. Scalar Arguments ..
* CHARACTER TRANS
* INTEGER KL, KU, LDA, LDB, LDX, M, N, NRHS
* DOUBLE PRECISION RESID
* ..
* .. Array Arguments ..
* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), X( LDX, * ),
* RWORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DGBT02 computes the residual for a solution of a banded system of
*> equations op(A)*X = B:
*> RESID = norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ),
*> where op(A) = A or A**T, depending on TRANS, and EPS is the
*> machine epsilon.
*> The norm used is the 1-norm.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] TRANS
*> \verbatim
*> TRANS is CHARACTER*1
*> Specifies the form of the system of equations:
*> = 'N': A * X = B (No transpose)
*> = 'T': A**T * X = B (Transpose)
*> = 'C': A**H * X = B (Conjugate transpose = Transpose)
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of rows of the matrix A. M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of columns of the matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in] KL
*> \verbatim
*> KL is INTEGER
*> The number of subdiagonals within the band of A. KL >= 0.
*> \endverbatim
*>
*> \param[in] KU
*> \verbatim
*> KU is INTEGER
*> The number of superdiagonals within the band of A. KU >= 0.
*> \endverbatim
*>
*> \param[in] NRHS
*> \verbatim
*> NRHS is INTEGER
*> The number of columns of B. NRHS >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is DOUBLE PRECISION array, dimension (LDA,N)
*> The original matrix A in band storage, stored in rows 1 to
*> KL+KU+1.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,KL+KU+1).
*> \endverbatim
*>
*> \param[in] X
*> \verbatim
*> X is DOUBLE PRECISION array, dimension (LDX,NRHS)
*> The computed solution vectors for the system of linear
*> equations.
*> \endverbatim
*>
*> \param[in] LDX
*> \verbatim
*> LDX is INTEGER
*> The leading dimension of the array X. If TRANS = 'N',
*> LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,M).
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
*> On entry, the right hand side vectors for the system of
*> linear equations.
*> On exit, B is overwritten with the difference B - A*X.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. IF TRANS = 'N',
*> LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N).
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*> RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK)),
*> where LRWORK >= M when TRANS = 'T' or 'C'; otherwise, RWORK
*> is not referenced.
*> \endverbatim
*
*> \param[out] RESID
*> \verbatim
*> RESID is DOUBLE PRECISION
*> The maximum over the number of right hand sides of
*> norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ).
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup double_lin
*
* =====================================================================
SUBROUTINE DGBT02( TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B,
$ LDB, RWORK, RESID )
*
* -- LAPACK test routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
CHARACTER TRANS
INTEGER KL, KU, LDA, LDB, LDX, M, N, NRHS
DOUBLE PRECISION RESID
* ..
* .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), B( LDB, * ), X( LDX, * ),
$ RWORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
* ..
* .. Local Scalars ..
INTEGER I1, I2, J, KD, N1
DOUBLE PRECISION ANORM, BNORM, EPS, TEMP, XNORM
* ..
* .. External Functions ..
LOGICAL DISNAN, LSAME
DOUBLE PRECISION DASUM, DLAMCH
EXTERNAL DASUM, DISNAN, DLAMCH, LSAME
* ..
* .. External Subroutines ..
EXTERNAL DGBMV
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, MIN
* ..
* .. Executable Statements ..
*
* Quick return if N = 0 pr NRHS = 0
*
IF( M.LE.0 .OR. N.LE.0 .OR. NRHS.LE.0 ) THEN
RESID = ZERO
RETURN
END IF
*
* Exit with RESID = 1/EPS if ANORM = 0.
*
EPS = DLAMCH( 'Epsilon' )
ANORM = ZERO
IF( LSAME( TRANS, 'N' ) ) THEN
*
* Find norm1(A).
*
KD = KU + 1
DO 10 J = 1, N
I1 = MAX( KD+1-J, 1 )
I2 = MIN( KD+M-J, KL+KD )
IF( I2.GE.I1 ) THEN
TEMP = DASUM( I2-I1+1, A( I1, J ), 1 )
IF( ANORM.LT.TEMP .OR. DISNAN( TEMP ) ) ANORM = TEMP
END IF
10 CONTINUE
ELSE
*
* Find normI(A).
*
DO 12 I1 = 1, M
RWORK( I1 ) = ZERO
12 CONTINUE
DO 16 J = 1, N
KD = KU + 1 - J
DO 14 I1 = MAX( 1, J-KU ), MIN( M, J+KL )
RWORK( I1 ) = RWORK( I1 ) + ABS( A( KD+I1, J ) )
14 CONTINUE
16 CONTINUE
DO 18 I1 = 1, M
TEMP = RWORK( I1 )
IF( ANORM.LT.TEMP .OR. DISNAN( TEMP ) ) ANORM = TEMP
18 CONTINUE
END IF
IF( ANORM.LE.ZERO ) THEN
RESID = ONE / EPS
RETURN
END IF
*
IF( LSAME( TRANS, 'T' ) .OR. LSAME( TRANS, 'C' ) ) THEN
N1 = N
ELSE
N1 = M
END IF
*
* Compute B - op(A)*X
*
DO 20 J = 1, NRHS
CALL DGBMV( TRANS, M, N, KL, KU, -ONE, A, LDA, X( 1, J ), 1,
$ ONE, B( 1, J ), 1 )
20 CONTINUE
*
* Compute the maximum over the number of right hand sides of
* norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ).
*
RESID = ZERO
DO 30 J = 1, NRHS
BNORM = DASUM( N1, B( 1, J ), 1 )
XNORM = DASUM( N1, X( 1, J ), 1 )
IF( XNORM.LE.ZERO ) THEN
RESID = ONE / EPS
ELSE
RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS )
END IF
30 CONTINUE
*
RETURN
*
* End of DGBT02
*
END
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