---
name: "dgttrf"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/dgttrf/3lapack"
---

# dgttrf(3lapack)

computes an LU factorization of a real tridiagonal matrix A using elimination with partial pivoting and row interchanges

## NAME

DGTTRF - computes an LU factorization of a real tridiagonal matrix A using elimination with partial pivoting and row interchanges

## SYNOPSIS

- SUBROUTINE DGTTRF(

  N, DL, D, DU, DU2, IPIV, INFO )

- INTEGER

  INFO, N

- INTEGER

  IPIV( \* )

- DOUBLE

  PRECISION D( \* ), DL( \* ), DU( \* ), DU2( \* )

## PURPOSE

DGTTRF 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 bidiagonal 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) DOUBLE PRECISION 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) multipliers that define the matrix L from the LU factorization of A.

- D (input/output) DOUBLE PRECISION array, dimension (N)

  On entry, D must contain the diagonal elements of A. On exit, D is overwritten by the n diagonal elements of the upper triangular matrix U from the LU factorization of A.

- DU (input/output) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (N-2)

  On exit, DU2 is overwritten by the (n-2) elements of the second super-diagonal of U.

- IPIV (output) INTEGER array, dimension (N)

  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 indicates a row interchange was not required.

- INFO (output) INTEGER

  \= 0:  successful exit\
   \< 0:  if INFO = -k, the k-th argument had an illegal 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 equations.