?potrf2

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 10/15/2026

Version

Public

?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:

\[\begin{split}A = \begin{pmatrix} A_{11} & A_{12} \\ A_{21} & A_{22} \end{pmatrix}\end{split}\]

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: Specifies the order of the matrix A . The value of n must be at least zero.

a

REAL for spotrf2 DOUBLE PRECISION for dpotrf2 COMPLEX for cpotrf2 DOUBLE COMPLEX for zpotrf2

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.

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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