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# LAPACK-3

## man page of LAPACK-3

### LAPACK-3: solves the equation A*X = B,

```NAME
LAPACK-3 - 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  A'*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.

LAPACK routine (version 3.2)     March 2011                       LAPACK-3(3)
```