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# zgtsv

```
NAME
ZGTSV - solve 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 elimi-
nation with partial pivoting.

Note that the equation  A'*X = B  may be solved by inter-
changing 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 ele-
ments 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)
= 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.
```