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 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

  —  LAPACK version 2.0  —  08 October 1994