NAME

zgttrf - compute an LU factorization of a complex tridiagonal matrix A using elimination with partial pivoting and row interchanges

SYNOPSIS

  SUBROUTINE ZGTTRF( N, LOW, DIAG, UP1, UP2, IPIVOT, INFO)
  DOUBLE COMPLEX LOW(*), DIAG(*), UP1(*), UP2(*)
  INTEGER N, INFO
  INTEGER IPIVOT(*)

  SUBROUTINE ZGTTRF_64( N, LOW, DIAG, UP1, UP2, IPIVOT, INFO)
  DOUBLE COMPLEX LOW(*), DIAG(*), UP1(*), UP2(*)
  INTEGER*8 N, INFO
  INTEGER*8 IPIVOT(*)

F95 INTERFACE

  SUBROUTINE GTTRF( [N], LOW, DIAG, UP1, UP2, IPIVOT, [INFO])
  COMPLEX(8), DIMENSION(:) :: LOW, DIAG, UP1, UP2
  INTEGER :: N, INFO
  INTEGER, DIMENSION(:) :: IPIVOT

  SUBROUTINE GTTRF_64( [N], LOW, DIAG, UP1, UP2, IPIVOT, [INFO])
  COMPLEX(8), DIMENSION(:) :: LOW, DIAG, UP1, UP2
  INTEGER(8) :: N, INFO
  INTEGER(8), DIMENSION(:) :: IPIVOT

C INTERFACE

#include <sunperf.h>

void zgttrf(int n, doublecomplex *low, doublecomplex *diag, doublecomplex *up1, doublecomplex *up2, int *ipivot, int *info);

void zgttrf_64(long n, doublecomplex *low, doublecomplex *diag, doublecomplex *up1, doublecomplex *up2, long *ipivot, long *info);

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)
The order of the matrix A.
LOW (input/output)
On entry, LOW must contain the (n-1) sub-diagonal elements of A.
On exit, LOW is overwritten by the (n-1) multipliers that define the matrix L from the LU factorization of A.
DIAG (input/output)
On entry, DIAG must contain the diagonal elements of A.
On exit, DIAG is overwritten by the n diagonal elements of the upper triangular matrix U from the LU factorization of A.
UP1 (input/output)
On entry, UP1 must contain the (n-1) super-diagonal elements of A.
On exit, UP1 is overwritten by the (n-1) elements of the first super-diagonal of U.
UP2 (output)
On exit, UP2 is overwritten by the (n-2) elements of the second super-diagonal of U.
IPIVOT (output)
The pivot indices; for 1 < = i < = n, row i of the matrix was interchanged with row IPIVOT(i). IPIVOT(i) will always be either i or i+1; IPIVOT(i) = i indicates a row interchange was not required.

INFO (output)

 = 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.