*> \brief CGBSV computes the solution to system of linear equations A * X = B for GB matrices (simple driver) * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download CGBSV + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE CGBSV( N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, KL, KU, LDAB, LDB, N, NRHS * .. * .. Array Arguments .. * INTEGER IPIV( * ) * COMPLEX AB( LDAB, * ), B( LDB, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> CGBSV computes the solution to a complex 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 COMPLEX 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 COMPLEX 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. * *> \ingroup complexGBsolve * *> \par Further 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 CGBSV( N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO ) * * -- LAPACK driver routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. INTEGER INFO, KL, KU, LDAB, LDB, N, NRHS * .. * .. Array Arguments .. INTEGER IPIV( * ) COMPLEX AB( LDAB, * ), B( LDB, * ) * .. * * ===================================================================== * * .. External Subroutines .. EXTERNAL CGBTRF, CGBTRS, 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( 'CGBSV ', -INFO ) RETURN END IF * * Compute the LU factorization of the band matrix A. * CALL CGBTRF( N, N, KL, KU, AB, LDAB, IPIV, INFO ) IF( INFO.EQ.0 ) THEN * * Solve the system A*X = B, overwriting B with X. * CALL CGBTRS( 'No transpose', N, KL, KU, NRHS, AB, LDAB, IPIV, $ B, LDB, INFO ) END IF RETURN * * End of CGBSV * END