# zgtsv (l) - Linux Man Pages

## NAME

ZGTSV - solves the equation A*X = B,

## SYNOPSIS

SUBROUTINE ZGTSV(
N, NRHS, DL, D, DU, B, LDB, INFO )

INTEGER INFO, LDB, N, NRHS

COMPLEX*16 B( LDB, * ), D( * ), DL( * ), DU( * )

## PURPOSE

ZGTSV solves the equation where A is an N-by-N tridiagonal matrix, by Gaussian elimination with partial pivoting.
Note that the equation Aaq*X = B may be solved by interchanging the order of the arguments DU and DL.

## ARGUMENTS

N (input) INTEGER
The order of the matrix A. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
DL (input/output) COMPLEX*16 array, dimension (N-1)
On entry, DL must contain the (n-1) subdiagonal elements of A. On exit, DL is overwritten by the (n-2) elements of the second superdiagonal of the upper triangular matrix U from the LU factorization of A, in DL(1), ..., DL(n-2).
D (input/output) COMPLEX*16 array, dimension (N)
On entry, D must contain the diagonal elements of A. On exit, D is overwritten by the n diagonal elements of U.
DU (input/output) COMPLEX*16 array, dimension (N-1)
On entry, DU must contain the (n-1) superdiagonal elements of A. On exit, DU is overwritten by the (n-1) elements of the first superdiagonal of U.
B (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
On entry, the N-by-NRHS right hand side matrix B. On exit, if INFO = 0, the N-by-NRHS 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
> 0: if INFO = i, U(i,i) is exactly zero, and the solution has not been computed. The factorization has not been completed unless i = N.