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NAME

        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  com‐
                puted  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 >= 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) 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 illegal value
 

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