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# dpttrf

```
NAME
DPTTRF - compute the factorization of a real symmetric posi-
tive definite tridiagonal matrix A

SYNOPSIS
SUBROUTINE DPTTRF( N, D, E, INFO )

INTEGER        INFO, N

DOUBLE         PRECISION D( * ), E( * )

PURPOSE
DPTTRF computes the factorization of a real symmetric posi-
tive definite tridiagonal matrix A.

If the subdiagonal elements of A are supplied in the array
E, the factorization has the form A = L*D*L**T, where D is
diagonal and L is unit lower bidiagonal; if the superdiago-
nal elements of A are supplied, it has the form A =
U**T*D*U, where U is unit upper bidiagonal.  (The two forms
are equivalent if A is real.)

ARGUMENTS
N       (input) INTEGER
The order of the matrix A.  N >= 0.

D       (input/output) DOUBLE PRECISION array, dimension (N)
On entry, the n diagonal elements of the tridiagonal
matrix A.  On exit, the n diagonal elements of the
diagonal matrix D from the L*D*L**T factorization of
A.

E       (input/output) DOUBLE PRECISION array, dimension (N-
1)
On entry, the (n-1) off-diagonal elements of the
tridiagonal matrix A.  On exit, the (n-1) off-
diagonal elements of the unit bidiagonal factor L or
U from the factorization of A.

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal
value
> 0:  if INFO = i, the leading minor of order i is
not positive definite; if i < N, the factorization
could not be completed, while if i = N, the factori-
zation was completed, but D(N) = 0.
```