?gttrf

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 12/16/2022

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?gttrf

Computes the LU factorization of a tridiagonal matrix.

Syntax

call sgttrf( n, dl, d, du, du2, ipiv, info )

call dgttrf( n, dl, d, du, du2, ipiv, info )

call cgttrf( n, dl, d, du, du2, ipiv, info )

call zgttrf( n, dl, d, du, du2, ipiv, info )

call gttrf( dl, d, du, du2 [, ipiv] [,info] )

Include Files

mkl.fi, lapack.f90

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

INTEGER. The order of the matrix A; n≥ 0.

dl, d, du

REAL for sgttrf

DOUBLE PRECISION for dgttrf

COMPLEX for cgttrf

DOUBLE COMPLEX for zgttrf.

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`. The matrix `L` has unit diagonal elements, and the `(n-1)` elements of dl form the subdiagonal. All other elements of `L` are zero.
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	REAL for sgttrf DOUBLE PRECISION for dgttrf COMPLEX for cgttrf DOUBLE COMPLEX for zgttrf. Array, dimension `(n -2)`. On exit, `du2` contains `(n-2)` elements of the second superdiagonal of `U`.
ipiv	INTEGER. Array, dimension (n). The pivot indices: for 1 ≤ `i` ≤ n, row `i` was interchanged with row ipiv(`i`). ipiv(`i`) is always `i` or `i`+1; ipiv(`i`) = `i` indicates a row interchange was not required.
info	INTEGER. If `info = 0`, the execution is successful. If `info = -i`, the `i`-th parameter 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

Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or reconstructible arguments, see LAPACK 95 Interface Conventions.

Specific details for the routine gttrf interface are as follows:

dl	Holds the vector of length (`n`-1).
d	Holds the vector of length `n`.
du	Holds the vector of length (`n`-1).
du2	Holds the vector of length (`n`-2).
ipiv	Holds the vector of length `n`.

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 Fortran

?gttrf