◆ zgttrf()

LU factorization of a complex tridiagonal matrix

Purpose: This routine 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 super-diagonals.

Parameters

[in]	n	Order of the matrix A. (n >= 0) (If n = 0, returns without computation)
[in,out]	dl[]	Array dl[ldl] (ldl >= n - 1) [in] n-1 sub-diagonal elements of A. [out] n-1 multipliers that define the matrix L from the LU factorization of A.
[in,out]	d[]	Array d[ld] (ld >= n) [in] Diagonal elements of A. [out] n diagonal elements of the upper triangular matrix U from the LU factorization of A.
[in,out]	du[]	Array du[ldu] (ldu >= n - 1) [in] n-1 super-diagonal elements of A. [out] n-1 elements of the first super-diagonal of U.
[out]	du2[]	Array du2[ldu2] (ldu2 >= n - 2) n-2 elements of the second super-diagonal of U.
[out]	ipiv[]	Array ipiv[lipiv] (lipiv >= n) Pivot indices; for 1 <= i <= n, row i of the matrix was interchanged with row ipiv[i-1]. ipiv[i-1] will always be either i or i+1; ipiv[i-1] = i indicates a row interchange was not required.
[out]	info	= 0: Successful exit = -1: The argument n had an illegal value (n < 0) = i > 0: The i-th diagonal element of the factor U 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.