?gttrf

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 3/31/2023

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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

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 ≤ `i` ≤ n, 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, u_iiis 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 `AX = B` or `A^TX = B` or `A^H*X = B`
?gbcon	to estimate the condition number of `A`.

Parent topic: Matrix Factorization: LAPACK Computational Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for C

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