      SUBROUTINE DGBTRS( TRANS, N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB,
     $                   INFO )
*
*  -- LAPACK routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     March 31, 1993
*
*     .. Scalar Arguments ..
      CHARACTER          TRANS
      INTEGER            INFO, KL, KU, LDAB, LDB, N, NRHS
*     ..
*     .. Array Arguments ..
      INTEGER            IPIV( * )
      DOUBLE PRECISION   AB( LDAB, * ), B( LDB, * )
*     ..
*
*  Purpose
*  =======
*
*  DGBTRS solves a system of linear equations
*     A * X = B  or  A' * X = B
*  with a general band matrix A using the LU factorization computed
*  by DGBTRF.
*
*  Arguments
*  =========
*
*  TRANS   (input) CHARACTER*1
*          Specifies the form of the system of equations.
*          = 'N':  A * X = B  (No transpose)
*          = 'T':  A'* X = B  (Transpose)
*          = 'C':  A'* X = B  (Conjugate transpose = Transpose)
*
*  N       (input) INTEGER
*          The order of the matrix A.  N >= 0.
*
*  KL      (input) INTEGER
*          The number of subdiagonals within the band of A.  KL >= 0.
*
*  KU      (input) INTEGER
*          The number of superdiagonals within the band of A.  KU >= 0.
*
*  NRHS    (input) INTEGER
*          The number of right hand sides, i.e., the number of columns
*          of the matrix B.  NRHS >= 0.
*
*  AB      (input) DOUBLE PRECISION array, dimension (LDAB,N)
*          Details of the LU factorization of the band matrix A, as
*          computed by DGBTRF.  U is stored as an upper triangular band
*          matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
*          the multipliers used during the factorization are stored in
*          rows KL+KU+2 to 2*KL+KU+1.
*
*  LDAB    (input) INTEGER
*          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.
*
*  IPIV    (input) INTEGER array, dimension (N)
*          The pivot indices; for 1 <= i <= N, row i of the matrix was
*          interchanged with row IPIV(i).
*
*  B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
*          On entry, the right hand side matrix B.
*          On exit, the solution matrix X.
*
*  LDB     (input) INTEGER
*          The leading dimension of the array B.  LDB >= max(1,N).
*
*  INFO    (output) INTEGER
*          = 0:  successful exit
*          < 0: if INFO = -i, the i-th argument had an illegal value
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE
      PARAMETER          ( ONE = 1.0D+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            LNOTI, NOTRAN
      INTEGER            I, J, KD, L, LM
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL           DGEMV, DGER, DSWAP, DTBSV, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX, MIN
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO = 0
      NOTRAN = LSAME( TRANS, 'N' )
      IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) .AND. .NOT.
     $    LSAME( TRANS, 'C' ) ) THEN
         INFO = -1
      ELSE IF( N.LT.0 ) THEN
         INFO = -2
      ELSE IF( KL.LT.0 ) THEN
         INFO = -3
      ELSE IF( KU.LT.0 ) THEN
         INFO = -4
      ELSE IF( NRHS.LT.0 ) THEN
         INFO = -5
      ELSE IF( LDAB.LT.( 2*KL+KU+1 ) ) THEN
         INFO = -7
      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
         INFO = -10
      END IF
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'DGBTRS', -INFO )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( N.EQ.0 .OR. NRHS.EQ.0 )
     $   RETURN
*
      KD = KU + KL + 1
      LNOTI = KL.GT.0
*
      IF( NOTRAN ) THEN
*
*        Solve  A*X = B.
*
*        Solve L*X = B, overwriting B with X.
*
*        L is represented as a product of permutations and unit lower
*        triangular matrices L = P(1) * L(1) * ... * P(n-1) * L(n-1),
*        where each transformation L(i) is a rank-one modification of
*        the identity matrix.
*
         IF( LNOTI ) THEN
            DO 10 J = 1, N - 1
               LM = MIN( KL, N-J )
               L = IPIV( J )
               IF( L.NE.J )
     $            CALL DSWAP( NRHS, B( L, 1 ), LDB, B( J, 1 ), LDB )
               CALL DGER( LM, NRHS, -ONE, AB( KD+1, J ), 1, B( J, 1 ),
     $                    LDB, B( J+1, 1 ), LDB )
   10       CONTINUE
         END IF
*
         DO 20 I = 1, NRHS
*
*           Solve U*X = B, overwriting B with X.
*
            CALL DTBSV( 'Upper', 'No transpose', 'Non-unit', N, KL+KU,
     $                  AB, LDAB, B( 1, I ), 1 )
   20    CONTINUE
*
      ELSE
*
*        Solve A'*X = B.
*
         DO 30 I = 1, NRHS
*
*           Solve U'*X = B, overwriting B with X.
*
            CALL DTBSV( 'Upper', 'Transpose', 'Non-unit', N, KL+KU, AB,
     $                  LDAB, B( 1, I ), 1 )
   30    CONTINUE
*
*        Solve L'*X = B, overwriting B with X.
*
         IF( LNOTI ) THEN
            DO 40 J = N - 1, 1, -1
               LM = MIN( KL, N-J )
               CALL DGEMV( 'Transpose', LM, NRHS, -ONE, B( J+1, 1 ),
     $                     LDB, AB( KD+1, J ), 1, ONE, B( J, 1 ), LDB )
               L = IPIV( J )
               IF( L.NE.J )
     $            CALL DSWAP( NRHS, B( L, 1 ), LDB, B( J, 1 ), LDB )
   40       CONTINUE
         END IF
      END IF
      RETURN
*
*     End of DGBTRS
*
      END
