?pptrf

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 3/31/2023

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?pptrf

Computes the Cholesky factorization of a symmetric (Hermitian) positive-definite matrix using packed storage.

Syntax

lapack_int LAPACKE_spptrf (int matrix_layout , char uplo , lapack_int n , float * ap );

lapack_int LAPACKE_dpptrf (int matrix_layout , char uplo , lapack_int n , double * ap );

lapack_int LAPACKE_cpptrf (int matrix_layout , char uplo , lapack_int n , lapack_complex_float * ap );

lapack_int LAPACKE_zpptrf (int matrix_layout , char uplo , lapack_int n , lapack_complex_double * ap );

Include Files

mkl.h

Description

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

`A = U^TU` for real data, `A = U^HU` for complex data	if `uplo='U'`
`A = LL^T` for real data, `A = LL^H` for complex data	if `uplo='L'`

where L is a lower triangular matrix and U is upper triangular.

NOTE:

This routine supports the Progress Routine feature. See Progress Function for details.

Input Parameters

matrix_layout	Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).
uplo	Must be 'U' or 'L'. Indicates whether the upper or lower triangular part of `A` is packed in the array `ap`, and how `A` is factored: If `uplo` = 'U', the array `ap` stores the upper triangular part of the matrix `A`, and `A` is factored as `U`^H`U`. If `uplo` = 'L', the array `ap` stores the lower triangular part of the matrix `A`; `A` is factored as `LL`^H.
n	The order of matrix `A`; `n`≥ 0.
ap	Array, size at least max(1, `n`(`n`+1)/2). The array `ap` contains either the upper or the lower triangular part of the matrix `A` (as specified by `uplo`) in packed storage (see Matrix Storage Schemes).

Output Parameters

ap	Overwritten by the Cholesky factor `U` or `L`, as specified by `uplo`.

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, and the factorization could not be completed. This may indicate an error in forming the matrix A.

Application Notes

If uplo = 'U', the computed factor U is the exact factor of a perturbed matrix A + E, where

c(n) is a modest linear function of n, and ε is the machine precision.

A similar estimate holds for uplo = 'L'.

The total number of floating-point operations is approximately (1/3)n³ for real flavors and (4/3)n³ for complex flavors.

After calling this routine, you can call the following routines:

?pptrs	to solve `A*X = B`
?ppcon	to estimate the condition number of `A`
?pptri	to compute the inverse of `A`.

Parent topic: Matrix Factorization: LAPACK Computational Routines

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