You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
226 lines
6.7 KiB
226 lines
6.7 KiB
*> \brief <b> SPBSV computes the solution to system of linear equations A * X = B for OTHER matrices</b>
|
|
*
|
|
* =========== DOCUMENTATION ===========
|
|
*
|
|
* Online html documentation available at
|
|
* http://www.netlib.org/lapack/explore-html/
|
|
*
|
|
*> \htmlonly
|
|
*> Download SPBSV + dependencies
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/spbsv.f">
|
|
*> [TGZ]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/spbsv.f">
|
|
*> [ZIP]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/spbsv.f">
|
|
*> [TXT]</a>
|
|
*> \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 principal minor of order i
|
|
*> of A is not positive, 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
|
|
|