ZGBTRS  -  solve  a  system of linear equations A * X = B,
       A**T * X = B, or A**H * X = B with a general band matrix A
       using the LU factorization computed by ZGBTRF


SYNOPSIS

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

           CHARACTER      TRANS

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

           INTEGER        IPIV( * )

           COMPLEX*16     AB( LDAB, * ), B( LDB, * )


PURPOSE

       ZGBTRS solves a system of linear equations A * X = B, A**T
       *  X  =  B,  or  A**H * X = B with a general band matrix A
       using the LU factorization computed by ZGBTRF.


ARGUMENTS

       TRANS   (input) CHARACTER*1
               Specifies the form of the system of equations.   =
               'N':  A * X = B     (No transpose)
               = 'T':  A**T * X = B  (Transpose)
               = 'C':  A**H * X = B  (Conjugate 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) COMPLEX*16 array, dimension (LDAB,N)
               Details of the LU factorization of the band matrix
               A, as computed by ZGBTRF.  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 >=


       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) COMPLEX*16 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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