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dgbtrs

 NAME
      DGBTRS - solve a system of linear equations  A * X = B or A'
      * X = B with a general band matrix A using the LU factoriza-
      tion computed by DGBTRF

 SYNOPSIS
      SUBROUTINE DGBTRS( TRANS, N, KL, KU, NRHS, AB, LDAB, IPIV,
                         B, LDB, INFO )

          CHARACTER      TRANS

          INTEGER        INFO, KL, KU, LDAB, LDB, N, NRHS

          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).

 (LDB,NRHS)
      B       (input/output) DOUBLE PRECISION array, dimension
              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