spbtrs.f

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*> \brief \b SPBTRS
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
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*> \endhtmlonly
*
*  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, * )
*       ..
*
*
*> \par 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.
*
*> \ingroup pbtrs
*
*  =====================================================================
      SUBROUTINE spbtrs( UPLO, N, KD, NRHS, AB, LDAB, 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          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