ZGBTRS(3)      LAPACK routine of NEC Numeric Library Collection      ZGBTRS(3)



NAME
       ZGBTRS

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



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)
                     TRANS is 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)
                     N is INTEGER
                     The order of the matrix A.  N >= 0.

           KL        (input)
                     KL is INTEGER
                     The number of subdiagonals within the band of A.  KL >= 0.

           KU        (input)
                     KU is INTEGER
                     The number of superdiagonals within the band of A.  KU >= 0.

           NRHS      (input)
                     NRHS is INTEGER
                     The number of right hand sides, i.e., the number of columns
                     of the matrix B.  NRHS >= 0.

           AB        (input)
                     AB is 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)
                     LDAB is INTEGER
                     The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.

           IPIV      (input)
                     IPIV is 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)
                     B is COMPLEX*16 array, dimension (LDB,NRHS)
                     On entry, the right hand side matrix B.
                     On exit, the solution matrix X.

           LDB       (input)
                     LDB is INTEGER
                     The leading dimension of the array B.  LDB >= max(1,N).

           INFO      (output)
                     INFO is INTEGER
                     = 0:  successful exit
                     < 0:  if INFO = -i, the i-th argument had an illegal value



LAPACK routine                  31 October 2017                      ZGBTRS(3)