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



NAME
       DGBTRS

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



PURPOSE
            DGBTRS solves a system of linear equations
               A * X = B  or  A**T * X = B
            with a general band matrix A using the LU factorization computed
            by DGBTRF.




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**T* X = B  (Conjugate transpose = 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 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)
                     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 DOUBLE PRECISION 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                      DGBTRS(3)