?potrf2

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 3/22/2024

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?potrf2

Computes Cholesky factorization using a recursive algorithm.

Syntax

lapack_int LAPACKE_spotrf2 (int matrix_layout, char uplo, lapack_int n, float * a, lapack_int lda);

lapack_int LAPACKE_dpotrf2 (int matrix_layout, char uplo, lapack_int n, double * a, lapack_int lda);

lapack_int LAPACKE_cpotrf2 (int matrix_layout, char uplo, lapack_int n, lapack_complex_float * a, lapack_int lda);

lapack_int LAPACKE_zpotrf2 (int matrix_layout, char uplo, lapack_int n, lapack_complex_double * a, lapack_int lda);

Include Files

mkl.h

Description

?potrf2 computes the Cholesky factorization of a real or complex symmetric positive definite matrix A using the recursive algorithm.

The factorization has the form

for real flavors:

A = U^T * U, if uplo = 'U', or

A = L * L^T, if uplo = 'L',

for complex flavors:

A = U^H * U, if uplo = 'U',

or A = L * L^H, if uplo = 'L',

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

This is the recursive version of the algorithm. It divides the matrix into four submatrices:

where A11 is n1 by n1 and A22 is n2 by n2, with n1 = n/2 and n2 = n-n1.

The subroutine calls itself to factor A11. Update and scale A21 or A12, update A22 then call itself to factor A22.

Input Parameters

matrix_layout

Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).

uplo

= 'U': Upper triangle of A is stored;

= 'L': Lower triangle of A is stored.

n

The order of the matrix A.

n≥ 0.

a

Array, size (lda*n).

On entry, the symmetric matrix A.

If uplo = 'U', the leading n-by-n upper triangular part of a contains the upper triangular part of the matrix A, and the strictly lower triangular part of a is not referenced.

If uplo = 'L', the leading n-by-n lower triangular part of a contains the lower triangular part of the matrix A, and the strictly upper triangular part of a is not referenced.

lda

The leading dimension of the array a.

lda≥ max(1,n).

Output Parameters

a	On exit, if info = 0, the factor `U` or `L` from the Cholesky factorization. For real flavors: `A` = `U`^T`U` or `A` = `L``L`^T; For complex flavors: `A` = `U`^H`U` or `A` = `L``L`^H.

Return Values

This function returns a value info.

= 0: successful exit

< 0: if info = -i, the i-th argument had an illegal value

> 0: if info = i, the leading minor of order i is not positive definite, and the factorization could not be completed.

Parent topic: Matrix Factorization: LAPACK Computational Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?potrf2

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values