# zgbtrs (l) - Linux Man Pages

## NAME

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

## 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
B,  A**T B,  or  A**H 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. = aqNaq: A * X = B (No transpose)
= aqTaq: A**T * X = B (Transpose)
= aqCaq: 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 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