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## man page of LAPACK-3

### LAPACK-3: computes an LU factorization of a complex tridiagonal matrix A using elimination with partial pivoting and row

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LAPACK-3 - computes an LU factorization of a complex tridiagonal matrix A using elimination with partial pivoting and row interchanges## SYNOPSIS

SUBROUTINE ZGTTRF( N, DL, D, DU, DU2, IPIV, INFO ) INTEGER INFO, N INTEGER IPIV( * ) COMPLEX*16 D( * ), DL( * ), DU( * ), DU2( * )## PURPOSE

ZGTTRF computes an LU factorization of a complex 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) COMPLEX*16 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) 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 the upper triangular matrix U from the LU factorization of A. DU (input/output) COMPLEX*16 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) COMPLEX*16 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. LAPACK routine (version 3.2) March 2011 LAPACK-3(3)

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