```ZGBTRS(l)		LAPACK routine (version	1.1)		    ZGBTRS(l)

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 com-
puted	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 >= 2*KL+KU+1.

IPIV	  (input) INTEGER array, dimension (N)
The pivot indices; for 1 <= i	<= N, row i of the matrix was inter-
changed 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

```

Back to the listing of computational routines for linear equations