NAME¶

SPTTRF - computes the L*D*L' factorization of a real symmetric positive definite tridiagonal matrix A

SYNOPSIS¶

SUBROUTINE SPTTRF(

N, D, E, INFO )

INTEGER INFO, N REAL D( * ), E( * )

PURPOSE¶

SPTTRF computes the L*D*L' factorization of a real symmetric positive definite tridiagonal matrix A. The factorization may also be regarded as having the form A = U'*D*U.

ARGUMENTS¶

N (input) INTEGER

The order of the matrix A. N >= 0.

D (input/output) REAL 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' factorization of A.

E (input/output) REAL array, dimension (N-1)

On entry, the (n-1) subdiagonal elements of the tridiagonal matrix A. On exit, the (n-1) subdiagonal elements of the unit bidiagonal factor L from the L*D*L' factorization of A. E can also be regarded as the superdiagonal of the unit bidiagonal factor U from the U'*D*U factorization of A.

INFO (output) INTEGER

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