numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
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| lapack/TESTING/LIN/dgbt02.f | 7217B | -rw-r--r-- |
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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