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*> \brief <b> DGBSV computes the solution to system of linear equations A * X = B for GB matrices</b>
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> Download DGBSV + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgbsv.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgbsv.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgbsv.f">
*> [TXT]</a>
*
* Definition
* ==========
*
* SUBROUTINE DGBSV( N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO )
*
* .. Scalar Arguments ..
* INTEGER INFO, KL, KU, LDAB, LDB, N, NRHS
* ..
* .. Array Arguments ..
* INTEGER IPIV( * )
* DOUBLE PRECISION AB( LDAB, * ), B( LDB, * )
* ..
*
* Purpose
* =======
*
*>\details \b Purpose:
*>\verbatim
*>
*> DGBSV computes the solution to a real system of linear equations
*> A * X = B, where A is a band matrix of order N with KL subdiagonals
*> and KU superdiagonals, and X and B are N-by-NRHS matrices.
*>
*> The LU decomposition with partial pivoting and row interchanges is
*> used to factor A as A = L * U, where L is a product of permutation
*> and unit lower triangular matrices with KL subdiagonals, and U is
*> upper triangular with KL+KU superdiagonals. The factored form of A
*> is then used to solve the system of equations A * X = B.
*>
*>\endverbatim
*
* Arguments
* =========
*
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of linear equations, i.e., the order 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 right hand sides, i.e., the number of columns
*> of the matrix B. NRHS >= 0.
*> \endverbatim
*>
*> \param[in,out] AB
*> \verbatim
*> AB is DOUBLE PRECISION array, dimension (LDAB,N)
*> On entry, the matrix A in band storage, in rows KL+1 to
*> 2*KL+KU+1; rows 1 to KL of the array need not be set.
*> The j-th column of A is stored in the j-th column of the
*> array AB as follows:
*> AB(KL+KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+KL)
*> On exit, details of the factorization: U is stored as an
*> upper triangular band matrix with KL+KU superdiagonals in
*> rows 1 to KL+KU+1, and the multipliers used during the
*> factorization are stored in rows KL+KU+2 to 2*KL+KU+1.
*> See below for further details.
*> \endverbatim
*>
*> \param[in] LDAB
*> \verbatim
*> LDAB is INTEGER
*> The leading dimension of the array AB. LDAB >= 2*KL+KU+1.
*> \endverbatim
*>
*> \param[out] IPIV
*> \verbatim
*> IPIV is INTEGER array, dimension (N)
*> The pivot indices that define the permutation matrix P;
*> row i of the matrix was interchanged with row IPIV(i).
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
*> On entry, the N-by-NRHS right hand side matrix B.
*> On exit, if INFO = 0, the N-by-NRHS 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
*> > 0: if INFO = i, U(i,i) is exactly zero. The factorization
*> has been completed, but the factor U is exactly
*> singular, and the solution has not been computed.
*> \endverbatim
*>
*
* Authors
* =======
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup doubleGBsolve
*
*
* Further Details
* ===============
*>\details \b Further \b Details
*> \verbatim
*>
*> The band storage scheme is illustrated by the following example, when
*> M = N = 6, KL = 2, KU = 1:
*>
*> On entry: On exit:
*>
*> * * * + + + * * * u14 u25 u36
*> * * + + + + * * u13 u24 u35 u46
*> * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56
*> a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66
*> a21 a32 a43 a54 a65 * m21 m32 m43 m54 m65 *
*> a31 a42 a53 a64 * * m31 m42 m53 m64 * *
*>
*> Array elements marked * are not used by the routine; elements marked
*> + need not be set on entry, but are required by the routine to store
*> elements of U because of fill-in resulting from the row interchanges.
*>
*> \endverbatim
*>
* =====================================================================
SUBROUTINE DGBSV( N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO )
*
* -- LAPACK solve routine (version 3.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
INTEGER INFO, KL, KU, LDAB, LDB, N, NRHS
* ..
* .. Array Arguments ..
INTEGER IPIV( * )
DOUBLE PRECISION AB( LDAB, * ), B( LDB, * )
* ..
*
* =====================================================================
*
* .. External Subroutines ..
EXTERNAL DGBTRF, DGBTRS, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
IF( N.LT.0 ) THEN
INFO = -1
ELSE IF( KL.LT.0 ) THEN
INFO = -2
ELSE IF( KU.LT.0 ) THEN
INFO = -3
ELSE IF( NRHS.LT.0 ) THEN
INFO = -4
ELSE IF( LDAB.LT.2*KL+KU+1 ) THEN
INFO = -6
ELSE IF( LDB.LT.MAX( N, 1 ) ) THEN
INFO = -9
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DGBSV ', -INFO )
RETURN
END IF
*
* Compute the LU factorization of the band matrix A.
*
CALL DGBTRF( N, N, KL, KU, AB, LDAB, IPIV, INFO )
IF( INFO.EQ.0 ) THEN
*
* Solve the system A*X = B, overwriting B with X.
*
CALL DGBTRS( 'No transpose', N, KL, KU, NRHS, AB, LDAB, IPIV,
$ B, LDB, INFO )
END IF
RETURN
*
* End of DGBSV
*
END
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