SGTTRF - compute an LU factorization of a real tridiagonal
matrix A using elimination with partial pivoting and row
interchanges
SYNOPSIS
SUBROUTINE SGTTRF( N, DL, D, DU, DU2, IPIV, INFO )
INTEGER INFO, N
INTEGER IPIV( * )
REAL D( * ), DL( * ), DU( * ), DU2( * )
PURPOSE
SGTTRF computes an LU factorization of a real tridiagonal
matrix A using elimination with partial pivoting and row
interchanges. The factorization has the form
A = L * U
where L is a product of permutation and unit lower bidiag
onal matrices and U is upper triangular with nonzeros in
only the main diagonal and first two superdiagonals.
ARGUMENTS
N (input) INTEGER
The order of the matrix A.
DL (input/output) REAL array, dimension (N-1)
On entry, DL must contain the (n-1) sub-diagonal
elements of A.
On exit, DL is overwritten by the (n-1) multipli
ers that define the matrix L from the LU factor
ization of A.
D (input/output) REAL array, dimension (N)
On entry, D must contain the diagonal elements of
A.
On exit, D is overwritten by the n diagonal ele
ments of the upper triangular matrix U from the LU
factorization of A.
DU (input/output) REAL array, dimension (N-1)
On entry, DU must contain the (n-1) super-diagonal
elements of A.
On exit, DU is overwritten by the (n-1) elements
of the first super-diagonal of U.
DU2 (output) REAL array, dimension (N-2)
On exit, DU2 is overwritten by the (n-2) elements
of the second super-diagonal of U.
The pivot indices; for 1 <= i <= n, row i of the
matrix was interchanged with row IPIV(i). IPIV(i)
will always be either i or i+1; IPIV(i) = i indi
cates a row interchange was not required.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -k, the k-th argument had an ille
gal value
> 0: if INFO = k, U(k,k) is exactly zero. The
factorization has been completed, but the factor U
is exactly singular, and division by zero will
occur if it is used to solve a system of equa
tions.
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