?potrf2

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

?potrf2

Computes Cholesky factorization using a recursive algorithm.

Syntax

call spotrf2 ( uplo , n , a , lda , info )

call dpotrf2 ( uplo , n , a , lda , info )

call cpotrf2 ( uplo , n , a , lda , info )

call zpotrf2 ( uplo , n , a , lda , info )

Include Files

mkl.fi

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:

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

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

uplo

CHARACTER*1. = ‘U’: Upper triangle of A is stored;

= ‘L’: Lower triangle of A is stored.

n

INTEGER. The order of the matrix A .

n ≥ 0.

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

INTEGER. 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 \(A = L L^H\) .

info

INTEGER.

= 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.

Return Values

No return value, info is an Output Parameter.

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?potrf2

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values