dtbtrs.f

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*> \brief \b DTBTRS
*
*  =========== DOCUMENTATION ===========
*
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*            http://www.netlib.org/lapack/explore-html/
*
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*
*  Definition:
*  ===========
*
*       SUBROUTINE DTBTRS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B,
*                          LDB, INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          DIAG, TRANS, UPLO
*       INTEGER            INFO, KD, LDAB, LDB, N, NRHS
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   AB( LDAB, * ), B( LDB, * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DTBTRS solves a triangular system of the form
*>
*>    A * X = B  or  A**T * X = B,
*>
*> where A is a triangular band matrix of order N, and B is an N-by-NRHS matrix.
*>
*> This subroutine verifies that A is nonsingular, but callers should note that only exact
*> singularity is detected. It is conceivable for one or more diagonal elements of A to be
*> subnormally tiny numbers without this subroutine signalling an error.
*>
*> If a possible loss of numerical precision due to near-singular matrices is a concern, the
*> caller should verify that A is nonsingular within some tolerance before calling this subroutine.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] UPLO
*> \verbatim
*>          UPLO is CHARACTER*1
*>          = 'U':  A is upper triangular;
*>          = 'L':  A is lower triangular.
*> \endverbatim
*>
*> \param[in] TRANS
*> \verbatim
*>          TRANS is CHARACTER*1
*>          Specifies the form the system of equations:
*>          = 'N':  A * X = B  (No transpose)
*>          = 'T':  A**T * X = B  (Transpose)
*>          = 'C':  A**H * X = B  (Conjugate transpose = Transpose)
*> \endverbatim
*>
*> \param[in] DIAG
*> \verbatim
*>          DIAG is CHARACTER*1
*>          = 'N':  A is non-unit triangular;
*>          = 'U':  A is unit triangular.
*> \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 or subdiagonals of the
*>          triangular band matrix A.  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 DOUBLE PRECISION array, dimension (LDAB,N)
*>          The upper or lower triangular band matrix A, stored in the
*>          first kd+1 rows of AB.  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).
*>          If DIAG = 'U', the diagonal elements of A are not referenced
*>          and are assumed to be 1.
*> \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 DOUBLE PRECISION array, dimension (LDB,NRHS)
*>          On entry, the right hand side matrix B.
*>          On exit, if INFO = 0, 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
*>          > 0:  if INFO = i, the i-th diagonal element of A is exactly zero,
*>                indicating that the matrix is singular and the
*>                solutions X have not been computed.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup tbtrs
*
*  =====================================================================
      SUBROUTINE dtbtrs( UPLO, TRANS, DIAG, 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          DIAG, TRANS, UPLO
      INTEGER            INFO, KD, LDAB, LDB, N, NRHS
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   AB( LDAB, * ), B( LDB, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO
      parameter( zero = 0.0d+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            NOUNIT, UPPER
      INTEGER            J
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           lsame
*     ..
*     .. External Subroutines ..
      EXTERNAL           dtbsv, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      info = 0
      nounit = lsame( diag, 'N' )
      upper = lsame( uplo, 'U' )
      IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
         info = -1
      ELSE IF( .NOT.lsame( trans, 'N' ) .AND. .NOT.
     $         lsame( trans, 'T' ) .AND.
     $                .NOT.lsame( trans, 'C' ) ) THEN
         info = -2
      ELSE IF( .NOT.nounit .AND. .NOT.lsame( diag, 'U' ) ) THEN
         info = -3
      ELSE IF( n.LT.0 ) THEN
         info = -4
      ELSE IF( kd.LT.0 ) THEN
         info = -5
      ELSE IF( nrhs.LT.0 ) THEN
         info = -6
      ELSE IF( ldab.LT.kd+1 ) THEN
         info = -8
      ELSE IF( ldb.LT.max( 1, n ) ) THEN
         info = -10
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'DTBTRS', -info )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( n.EQ.0 )
     $   RETURN
*
*     Check for singularity.
*
      IF( nounit ) THEN
         IF( upper ) THEN
            DO 10 info = 1, n
               IF( ab( kd+1, info ).EQ.zero )
     $            RETURN
   10       CONTINUE
         ELSE
            DO 20 info = 1, n
               IF( ab( 1, info ).EQ.zero )
     $            RETURN
   20       CONTINUE
         END IF
      END IF
      info = 0
*
*     Solve A * X = B  or  A**T * X = B.
*
      DO 30 j = 1, nrhs
         CALL dtbsv( uplo, trans, diag, n, kd, ab, ldab, b( 1, j ),
     $               1 )
   30 CONTINUE
*
      RETURN
*
*     End of DTBTRS
*
      END