*> \brief \b DPBTRS * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DPBTRS + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER INFO, KD, LDAB, LDB, N, NRHS * .. * .. Array Arguments .. * DOUBLE PRECISION AB( LDAB, * ), B( LDB, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DPBTRS solves a system of linear equations A*X = B with a symmetric *> positive definite band matrix A using the Cholesky factorization *> A = U**T*U or A = L*L**T computed by DPBTRF. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': Upper triangular factor stored in AB; *> = 'L': Lower triangular factor stored in AB. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in] KD *> \verbatim *> KD is INTEGER *> The number of superdiagonals of the matrix A if UPLO = 'U', *> or the number of subdiagonals if UPLO = 'L'. KD >= 0. *> \endverbatim *> *> \param[in] NRHS *> \verbatim *> NRHS is INTEGER *> The number of right hand sides, i.e., the number of columns *> of the matrix B. NRHS >= 0. *> \endverbatim *> *> \param[in] AB *> \verbatim *> AB is DOUBLE PRECISION array, dimension (LDAB,N) *> The triangular factor U or L from the Cholesky factorization *> A = U**T*U or A = L*L**T of the band matrix A, stored in the *> first KD+1 rows of the array. The j-th column of U or L is *> stored in the j-th column of the array AB as follows: *> if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j; *> if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd). *> \endverbatim *> *> \param[in] LDAB *> \verbatim *> LDAB is INTEGER *> The leading dimension of the array AB. LDAB >= KD+1. *> \endverbatim *> *> \param[in,out] B *> \verbatim *> B is DOUBLE PRECISION array, dimension (LDB,NRHS) *> On entry, the right hand side matrix B. *> On exit, the solution matrix X. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> The leading dimension of the array B. LDB >= max(1,N). *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup doubleOTHERcomputational * * ===================================================================== SUBROUTINE DPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER INFO, KD, LDAB, LDB, N, NRHS * .. * .. Array Arguments .. DOUBLE PRECISION AB( LDAB, * ), B( LDB, * ) * .. * * ===================================================================== * * .. Local Scalars .. LOGICAL UPPER INTEGER J * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL DTBSV, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 UPPER = LSAME( UPLO, 'U' ) IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( KD.LT.0 ) THEN INFO = -3 ELSE IF( NRHS.LT.0 ) THEN INFO = -4 ELSE IF( LDAB.LT.KD+1 ) THEN INFO = -6 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN INFO = -8 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DPBTRS', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 .OR. NRHS.EQ.0 ) \$ RETURN * IF( UPPER ) THEN * * Solve A*X = B where A = U**T *U. * DO 10 J = 1, NRHS * * Solve U**T *X = B, overwriting B with X. * CALL DTBSV( 'Upper', 'Transpose', 'Non-unit', N, KD, AB, \$ LDAB, B( 1, J ), 1 ) * * Solve U*X = B, overwriting B with X. * CALL DTBSV( 'Upper', 'No transpose', 'Non-unit', N, KD, AB, \$ LDAB, B( 1, J ), 1 ) 10 CONTINUE ELSE * * Solve A*X = B where A = L*L**T. * DO 20 J = 1, NRHS * * Solve L*X = B, overwriting B with X. * CALL DTBSV( 'Lower', 'No transpose', 'Non-unit', N, KD, AB, \$ LDAB, B( 1, J ), 1 ) * * Solve L**T *X = B, overwriting B with X. * CALL DTBSV( 'Lower', 'Transpose', 'Non-unit', N, KD, AB, \$ LDAB, B( 1, J ), 1 ) 20 CONTINUE END IF * RETURN * * End of DPBTRS * END