• NAME
• SYNOPSIS
• F95 INTERFACE
• C INTERFACE
• PURPOSE
• ARGUMENTS

NAME

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

SYNOPSIS

  SUBROUTINE SGTTRF( N, LOW, DIAG, UP1, UP2, IPIVOT, INFO)
  INTEGER N, INFO
  INTEGER IPIVOT(*)
  REAL LOW(*), DIAG(*), UP1(*), UP2(*)

  SUBROUTINE SGTTRF_64( N, LOW, DIAG, UP1, UP2, IPIVOT, INFO)
  INTEGER*8 N, INFO
  INTEGER*8 IPIVOT(*)
  REAL LOW(*), DIAG(*), UP1(*), UP2(*)

F95 INTERFACE

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

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

C INTERFACE

#include <sunperf.h>

void sgttrf(int n, float *low, float *diag, float *up1, float *up2, int *ipivot, int *info);

void sgttrf_64(long n, float *low, float *diag, float *up1, float *up2, long *ipivot, long *info);

PURPOSE

sgttrf 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)
  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.