221 lines
5.9 KiB
Fortran
221 lines
5.9 KiB
Fortran
*> \brief \b DPBTRS
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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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*> \htmlonly
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*> Download DPBTRS + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpbtrs.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dpbtrs.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpbtrs.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE DPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
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*
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* .. Scalar Arguments ..
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* CHARACTER UPLO
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* INTEGER INFO, KD, LDAB, LDB, N, NRHS
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* ..
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* .. Array Arguments ..
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* DOUBLE PRECISION AB( LDAB, * ), B( LDB, * )
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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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*> DPBTRS solves a system of linear equations A*X = B with a symmetric
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*> positive definite band matrix A using the Cholesky factorization
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*> A = U**T*U or A = L*L**T computed by DPBTRF.
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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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*> = 'U': Upper triangular factor stored in AB;
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*> = 'L': Lower triangular factor stored in AB.
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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 of the matrix A if UPLO = 'U',
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*> or the number of subdiagonals if UPLO = 'L'. 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 matrix 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 triangular factor U or L from the Cholesky factorization
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*> A = U**T*U or A = L*L**T of the band matrix A, stored in the
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*> first KD+1 rows of the array. The j-th column of U or L is
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*> stored in the j-th column of the array AB as follows:
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*> if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
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*> if UPLO ='L', AB(1+i-j,j) = L(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,out] B
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*> \verbatim
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*> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
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*> On entry, the right hand side matrix B.
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*> On exit, the solution matrix 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] INFO
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*> \verbatim
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*> INFO is INTEGER
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*> = 0: successful exit
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*> < 0: if INFO = -i, the i-th argument had an illegal value
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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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*> \date December 2016
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*
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*> \ingroup doubleOTHERcomputational
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*
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* =====================================================================
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SUBROUTINE DPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
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*
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* -- LAPACK computational routine (version 3.7.0) --
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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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* December 2016
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*
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* .. Scalar Arguments ..
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CHARACTER UPLO
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INTEGER INFO, KD, LDAB, LDB, N, NRHS
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION AB( LDAB, * ), B( LDB, * )
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* ..
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*
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* =====================================================================
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*
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* .. Local Scalars ..
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LOGICAL UPPER
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INTEGER J
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. External Subroutines ..
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EXTERNAL DTBSV, XERBLA
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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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* Test the input parameters.
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*
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INFO = 0
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UPPER = LSAME( UPLO, 'U' )
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IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
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INFO = -1
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ELSE IF( N.LT.0 ) THEN
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INFO = -2
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ELSE IF( KD.LT.0 ) THEN
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INFO = -3
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ELSE IF( NRHS.LT.0 ) THEN
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INFO = -4
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ELSE IF( LDAB.LT.KD+1 ) THEN
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INFO = -6
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ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
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INFO = -8
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'DPBTRS', -INFO )
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( N.EQ.0 .OR. NRHS.EQ.0 )
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$ RETURN
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*
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IF( UPPER ) THEN
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*
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* Solve A*X = B where A = U**T *U.
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*
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DO 10 J = 1, NRHS
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*
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* Solve U**T *X = B, overwriting B with X.
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*
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CALL DTBSV( 'Upper', 'Transpose', 'Non-unit', N, KD, AB,
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$ LDAB, B( 1, J ), 1 )
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*
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* Solve U*X = B, overwriting B with X.
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*
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CALL DTBSV( 'Upper', 'No transpose', 'Non-unit', N, KD, AB,
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$ LDAB, B( 1, J ), 1 )
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10 CONTINUE
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ELSE
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*
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* Solve A*X = B where A = L*L**T.
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*
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DO 20 J = 1, NRHS
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*
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* Solve L*X = B, overwriting B with X.
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*
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CALL DTBSV( 'Lower', 'No transpose', 'Non-unit', N, KD, AB,
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$ LDAB, B( 1, J ), 1 )
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*
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* Solve L**T *X = B, overwriting B with X.
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*
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CALL DTBSV( 'Lower', 'Transpose', 'Non-unit', N, KD, AB,
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$ LDAB, B( 1, J ), 1 )
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20 CONTINUE
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END IF
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*
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RETURN
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*
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* End of DPBTRS
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*
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END
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