*> \brief \b SGBTRS
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
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*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE SGBTRS( TRANS, N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB,
* INFO )
*
* .. Scalar Arguments ..
* CHARACTER TRANS
* INTEGER INFO, KL, KU, LDAB, LDB, N, NRHS
* ..
* .. Array Arguments ..
* INTEGER IPIV( * )
* REAL AB( LDAB, * ), B( LDB, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> SGBTRS solves a system of linear equations
*> A * X = B or A**T * X = B
*> with a general band matrix A using the LU factorization computed
*> by SGBTRF.
*> \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**T* X = B (Conjugate transpose = Transpose)
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> 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] AB
*> \verbatim
*> AB is REAL array, dimension (LDAB,N)
*> Details of the LU factorization of the band matrix A, as
*> computed by SGBTRF. 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.
*> \endverbatim
*>
*> \param[in] LDAB
*> \verbatim
*> LDAB is INTEGER
*> The leading dimension of the array AB. LDAB >= 2*KL+KU+1.
*> \endverbatim
*>
*> \param[in] IPIV
*> \verbatim
*> IPIV is INTEGER array, dimension (N)
*> The pivot indices; for 1 <= i <= N, row i of the matrix was
*> interchanged with row IPIV(i).
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> B is REAL 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.
*
*> \ingroup realGBcomputational
*
* =====================================================================
SUBROUTINE SGBTRS( TRANS, N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB,
$ INFO )
*
* -- LAPACK computational 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 INFO, KL, KU, LDAB, LDB, N, NRHS
* ..
* .. Array Arguments ..
INTEGER IPIV( * )
REAL AB( LDAB, * ), B( LDB, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ONE
PARAMETER ( ONE = 1.0E+0 )
* ..
* .. Local Scalars ..
LOGICAL LNOTI, NOTRAN
INTEGER I, J, KD, L, LM
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL SGEMV, SGER, SSWAP, STBSV, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
NOTRAN = LSAME( TRANS, 'N' )
IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) .AND. .NOT.
$ LSAME( TRANS, 'C' ) ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( KL.LT.0 ) THEN
INFO = -3
ELSE IF( KU.LT.0 ) THEN
INFO = -4
ELSE IF( NRHS.LT.0 ) THEN
INFO = -5
ELSE IF( LDAB.LT.( 2*KL+KU+1 ) ) THEN
INFO = -7
ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
INFO = -10
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'SGBTRS', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 .OR. NRHS.EQ.0 )
$ RETURN
*
KD = KU + KL + 1
LNOTI = KL.GT.0
*
IF( NOTRAN ) THEN
*
* Solve A*X = B.
*
* Solve L*X = B, overwriting B with X.
*
* L is represented as a product of permutations and unit lower
* triangular matrices L = P(1) * L(1) * ... * P(n-1) * L(n-1),
* where each transformation L(i) is a rank-one modification of
* the identity matrix.
*
IF( LNOTI ) THEN
DO 10 J = 1, N - 1
LM = MIN( KL, N-J )
L = IPIV( J )
IF( L.NE.J )
$ CALL SSWAP( NRHS, B( L, 1 ), LDB, B( J, 1 ), LDB )
CALL SGER( LM, NRHS, -ONE, AB( KD+1, J ), 1, B( J, 1 ),
$ LDB, B( J+1, 1 ), LDB )
10 CONTINUE
END IF
*
DO 20 I = 1, NRHS
*
* Solve U*X = B, overwriting B with X.
*
CALL STBSV( 'Upper', 'No transpose', 'Non-unit', N, KL+KU,
$ AB, LDAB, B( 1, I ), 1 )
20 CONTINUE
*
ELSE
*
* Solve A**T*X = B.
*
DO 30 I = 1, NRHS
*
* Solve U**T*X = B, overwriting B with X.
*
CALL STBSV( 'Upper', 'Transpose', 'Non-unit', N, KL+KU, AB,
$ LDAB, B( 1, I ), 1 )
30 CONTINUE
*
* Solve L**T*X = B, overwriting B with X.
*
IF( LNOTI ) THEN
DO 40 J = N - 1, 1, -1
LM = MIN( KL, N-J )
CALL SGEMV( 'Transpose', LM, NRHS, -ONE, B( J+1, 1 ),
$ LDB, AB( KD+1, J ), 1, ONE, B( J, 1 ), LDB )
L = IPIV( J )
IF( L.NE.J )
$ CALL SSWAP( NRHS, B( L, 1 ), LDB, B( J, 1 ), LDB )
40 CONTINUE
END IF
END IF
RETURN
*
* End of SGBTRS
*
END