?pttrf

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 12/16/2022

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?pttrf

Computes the factorization of a symmetric (Hermitian) positive-definite tridiagonal matrix.

Syntax

lapack_int LAPACKE_spttrf( lapack_int n, float* d, float* e );

lapack_int LAPACKE_dpttrf( lapack_int n, double* d, double* e );

lapack_int LAPACKE_cpttrf( lapack_int n, float* d, lapack_complex_float* e );

lapack_int LAPACKE_zpttrf( lapack_int n, double* d, lapack_complex_double* e );

Include Files

mkl.h

Description

The routine forms the factorization of a symmetric positive-definite or, for complex data, Hermitian positive-definite tridiagonal matrix A:

A = L*D*L^T for real flavors, or

A = L*D*L^H for complex flavors,

where D is diagonal and L is unit lower bidiagonal. The factorization may also be regarded as having the form A = U^T*D*U for real flavors, or A = U^H*D*U for complex flavors, where U is unit upper bidiagonal.

Input Parameters

n	The order of the matrix `A`; `n`≥ 0.
d	Array, dimension (`n`). Contains the diagonal elements of `A`.
e	Array, dimension (`n` -1). Contains the subdiagonal elements of `A`.

Output Parameters

d	Overwritten by the `n` diagonal elements of the diagonal matrix `D` from the `LDL`^T (for real flavors) or `LDL`^H (for complex flavors) factorization of `A`.
e	Overwritten by the `(n - 1)` sub-diagonal elements of the unit bidiagonal factor `L` or `U` from the factorization of `A`.

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, the leading minor of order i (and therefore the matrix A itself) is not positive-definite; if i < n, the factorization could not be completed, while if i = n, the factorization was completed, but d[n - 1] ≤ 0.

Parent topic: Matrix Factorization: LAPACK Computational Routines

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?pttrf