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*> \brief \b SPBTRS
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition
* ==========
*
* SUBROUTINE SPBTRS( 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, * )
* ..
*
* Purpose
* =======
*
*>\details \b Purpose:
*>\verbatim
*>
*> SPBTRS solves a system of linear equations A*X = B with a symmetric
*> positive definite band matrix A using the Cholesky factorization
*> A = U**T*U or A = L*L**T computed by SPBTRF.
*>
*>\endverbatim
*
* Arguments
* =========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> = 'U': Upper triangular factor stored in AB;
*> = 'L': Lower triangular factor stored in AB.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> 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] AB
*> \verbatim
*> AB is REAL array, dimension (LDAB,N)
*> The triangular factor U or L from the Cholesky factorization
*> A = U**T*U or A = L*L**T of the band matrix A, stored in the
*> first KD+1 rows of the array. The j-th column of U or L is
*> stored in the j-th column of the array AB as follows:
*> if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
*> if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).
*> \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 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.
*
*> \date November 2011
*
*> \ingroup realOTHERcomputational
*
* =====================================================================
SUBROUTINE SPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
*
* -- LAPACK computational routine (version 3.3.1) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER INFO, KD, LDAB, LDB, N, NRHS
* ..
* .. Array Arguments ..
REAL AB( LDAB, * ), B( LDB, * )
* ..
*
* =====================================================================
*
* .. Local Scalars ..
LOGICAL UPPER
INTEGER J
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL STBSV, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
UPPER = LSAME( UPLO, 'U' )
IF( .NOT.UPPER .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( 'SPBTRS', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 .OR. NRHS.EQ.0 )
$ RETURN
*
IF( UPPER ) THEN
*
* Solve A*X = B where A = U**T *U.
*
DO 10 J = 1, NRHS
*
* Solve U**T *X = B, overwriting B with X.
*
CALL STBSV( 'Upper', 'Transpose', 'Non-unit', N, KD, AB,
$ LDAB, B( 1, J ), 1 )
*
* Solve U*X = B, overwriting B with X.
*
CALL STBSV( 'Upper', 'No transpose', 'Non-unit', N, KD, AB,
$ LDAB, B( 1, J ), 1 )
10 CONTINUE
ELSE
*
* Solve A*X = B where A = L*L**T.
*
DO 20 J = 1, NRHS
*
* Solve L*X = B, overwriting B with X.
*
CALL STBSV( 'Lower', 'No transpose', 'Non-unit', N, KD, AB,
$ LDAB, B( 1, J ), 1 )
*
* Solve L**T *X = B, overwriting B with X.
*
CALL STBSV( 'Lower', 'Transpose', 'Non-unit', N, KD, AB,
$ LDAB, B( 1, J ), 1 )
20 CONTINUE
END IF
*
RETURN
*
* End of SPBTRS
*
END
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