Developer Reference for Intel® oneAPI Math Kernel Library for C

ID 766684
Date 3/31/2023
Public

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?gttrf

Computes the LU factorization of a tridiagonal matrix.

Syntax

lapack_int LAPACKE_sgttrf (lapack_int n , float * dl , float * d , float * du , float * du2 , lapack_int * ipiv );

lapack_int LAPACKE_dgttrf (lapack_int n , double * dl , double * d , double * du , double * du2 , lapack_int * ipiv );

lapack_int LAPACKE_cgttrf (lapack_int n , lapack_complex_float * dl , lapack_complex_float * d , lapack_complex_float * du , lapack_complex_float * du2 , lapack_int * ipiv );

lapack_int LAPACKE_zgttrf (lapack_int n , lapack_complex_double * dl , lapack_complex_double * d , lapack_complex_double * du , lapack_complex_double * du2 , lapack_int * ipiv );

Include Files
  • mkl.h
Description

The routine computes the LU factorization of a real or 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 nonzeroes in only the main diagonal and first two superdiagonals.

Input Parameters

n

The order of the matrix A; n 0.

dl, d, du

Arrays containing elements of A.

The array dl of dimension (n - 1) contains the subdiagonal elements of A.

The array d of dimension n contains the diagonal elements of A.

The array du of dimension (n - 1) contains the superdiagonal elements of A.

Output Parameters

dl

Overwritten by the (n-1) multipliers that define the matrix L from the LU factorization of A.

d

Overwritten by the n diagonal elements of the upper triangular matrix U from the LU factorization of A.

du

Overwritten by the (n-1) elements of the first superdiagonal of U.

du2

Array, dimension (n -2). On exit, du2 contains (n-2) elements of the second superdiagonal of U.

ipiv

Array, dimension (n). The pivot indices: for 1 ≤ in, row i was interchanged with row ipiv[i-1]. ipiv[i-1] is always i or i+1; ipiv[i-1] = i indicates a row interchange was not required.

Return Values

This function returns a value info.

If info = 0, the execution is successful.

If info = -i, parameter i had an illegal value.

If info = i, uiiis 0. The factorization has been completed, but U is exactly singular. Division by zero will occur if you use the factor U for solving a system of linear equations.

Application Notes

?gbtrs

to solve A*X = B or AT*X = B or AH*X = B

?gbcon

to estimate the condition number of A.