.TH CGTTRF 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) " .SH NAME CGTTRF - an LU factorization of a complex tridiagonal matrix A using elimination with partial pivoting and row interchanges .SH SYNOPSIS .TP 19 SUBROUTINE CGTTRF( N, DL, D, DU, DU2, IPIV, INFO ) .TP 19 .ti +4 INTEGER INFO, N .TP 19 .ti +4 INTEGER IPIV( * ) .TP 19 .ti +4 COMPLEX D( * ), DL( * ), DU( * ), DU2( * ) .SH PURPOSE CGTTRF computes an LU factorization of a complex tridiagonal matrix A using elimination with partial pivoting and row interchanges. The factorization has the form .br A = L * U .br 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. .br .SH ARGUMENTS .TP 8 N (input) INTEGER The order of the matrix A. .TP 8 DL (input/output) COMPLEX 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. .TP 8 D (input/output) COMPLEX 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. .TP 8 DU (input/output) COMPLEX 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. .TP 8 DU2 (output) COMPLEX array, dimension (N-2) On exit, DU2 is overwritten by the (n-2) elements of the second super-diagonal of U. .TP 8 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. .TP 8 INFO (output) INTEGER = 0: successful exit .br < 0: if INFO = -k, the k-th argument had an illegal value .br > 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.