*> \brief \b SGBTRS * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download SGBTRS + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \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