?gttrf

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 10/15/2026

Version

Public

?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: Specifies the order of the matrix A . The value of n must be at least zero.

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 , \(U_{ii}\) is 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.

LAPACK 95 Interface Notes

There exist FORTRAN 77 and FORTRAN 95 interfaces for this routine. See the Intel® oneMKL Fortran Developer Reference for details.

Application Notes

?gbtrs (Solves a system of linear equations with an LU-factored band coefficient matrix, with multiple right-hand sides.)

to solve \(A X = B\) or \(A^{T} X = B\) or \(A^{H} X = B\)

?gbcon (Estimates the reciprocal of the condition number of a band matrix in the 1-norm or the infinity-norm.)

to estimate the condition number of \(A\) .

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?gttrf

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values

LAPACK 95 Interface Notes

Application Notes