*> \brief SPBSV computes the solution to system of linear equations A * X = B for OTHER matrices * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download SPBSV + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE SPBSV( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER INFO, KD, LDAB, LDB, N, NRHS * .. * .. Array Arguments .. * REAL AB( LDAB, * ), B( LDB, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> SPBSV computes the solution to a real system of linear equations *> A * X = B, *> where A is an N-by-N symmetric positive definite band matrix and X *> and B are N-by-NRHS matrices. *> *> The Cholesky decomposition is used to factor A as *> A = U**T * U, if UPLO = 'U', or *> A = L * L**T, if UPLO = 'L', *> where U is an upper triangular band matrix, and L is a lower *> triangular band matrix, with the same number of superdiagonals or *> subdiagonals as A. The factored form of A is then used to solve the *> system of equations A * X = B. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': Upper triangle of A is stored; *> = 'L': Lower triangle of A is stored. *> \endverbatim *> *> \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] KD *> \verbatim *> KD is INTEGER *> The number of superdiagonals of the matrix A if UPLO = 'U', *> or the number of subdiagonals if UPLO = 'L'. KD >= 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 REAL array, dimension (LDAB,N) *> On entry, the upper or lower triangle of the symmetric band *> matrix A, stored in the first KD+1 rows of the array. The *> j-th column of A is stored in the j-th column of the array AB *> as follows: *> if UPLO = 'U', AB(KD+1+i-j,j) = A(i,j) for max(1,j-KD)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(N,j+KD). *> See below for further details. *> *> On exit, if INFO = 0, the triangular factor U or L from the *> Cholesky factorization A = U**T*U or A = L*L**T of the band *> matrix A, in the same storage format as A. *> \endverbatim *> *> \param[in] LDAB *> \verbatim *> LDAB is INTEGER *> The leading dimension of the array AB. LDAB >= KD+1. *> \endverbatim *> *> \param[in,out] B *> \verbatim *> B is REAL 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, the leading minor of order i of A is not *> positive definite, so the factorization could not be *> completed, 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 realOTHERsolve * *> \par Further Details: * ===================== *> *> \verbatim *> *> The band storage scheme is illustrated by the following example, when *> N = 6, KD = 2, and UPLO = 'U': *> *> On entry: On exit: *> *> * * a13 a24 a35 a46 * * 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 *> *> Similarly, if UPLO = 'L' the format of A is as follows: *> *> On entry: On exit: *> *> a11 a22 a33 a44 a55 a66 l11 l22 l33 l44 l55 l66 *> a21 a32 a43 a54 a65 * l21 l32 l43 l54 l65 * *> a31 a42 a53 a64 * * l31 l42 l53 l64 * * *> *> Array elements marked * are not used by the routine. *> \endverbatim *> * ===================================================================== SUBROUTINE SPBSV( UPLO, N, KD, NRHS, AB, LDAB, 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 .. CHARACTER UPLO INTEGER INFO, KD, LDAB, LDB, N, NRHS * .. * .. Array Arguments .. REAL AB( LDAB, * ), B( LDB, * ) * .. * * ===================================================================== * * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL SPBTRF, SPBTRS, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( KD.LT.0 ) THEN INFO = -3 ELSE IF( NRHS.LT.0 ) THEN INFO = -4 ELSE IF( LDAB.LT.KD+1 ) THEN INFO = -6 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN INFO = -8 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'SPBSV ', -INFO ) RETURN END IF * * Compute the Cholesky factorization A = U**T*U or A = L*L**T. * CALL SPBTRF( UPLO, N, KD, AB, LDAB, INFO ) IF( INFO.EQ.0 ) THEN * * Solve the system A*X = B, overwriting B with X. * CALL SPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO ) * END IF RETURN * * End of SPBSV * END