DGBTRS  -  solve a system of linear equations A * X = B or
       A' * X = B with a general band matrix A using the LU  fac­
       torization 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 factor­
       ization 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 = Trans­
               pose)

       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.

               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 ille­
               gal value


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