?pttrf

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 4/28/2026

Version

Public

?pttrf

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

Syntax

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

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

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

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

Include Files

mkl.h

Description

spttrf dpttrf cpttrf zpttrf pttrf

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 \(L*D*L^T\) (for real flavors) or \(L*D*L^H\) (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 .

LAPACK 95 Interface Notes

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

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?pttrf

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values

LAPACK 95 Interface Notes