?pftrf

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 10/15/2026

Version

Public

?pftrf

Computes the Cholesky factorization of a symmetric (Hermitian) positive-definite matrix using the Rectangular Full Packed (RFP) format .

Syntax

lapack_int LAPACKE_spftrf(int matrix_layout, char transr, char uplo, lapack_int n,
                          float *a);

lapack_int LAPACKE_dpftrf(int matrix_layout, char transr, char uplo, lapack_int n,
                          double *a);

lapack_int LAPACKE_cpftrf(int matrix_layout, char transr, char uplo, lapack_int n,
                          lapack_complex_float *a);

lapack_int LAPACKE_zpftrf(int matrix_layout, char transr, char uplo, lapack_int n,
                          lapack_complex_double *a);

Include Files

mkl.h

Description

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

`\(A = U^{T}U\)` for real data, `\(A = U^{H}U\)` 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.

The matrix \(A\) is in the Rectangular Full Packed (RFP) format. For the description of the RFP format, see Matrix Storage Schemes .

This is the block version of the algorithm, calling Level 3 BLAS.

Input Parameters

matrix_layout

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

transr

Must be ‘N’ , ‘T’ (for real data) or ‘C’ (for complex data).

If transr = ‘N’ , the Normal transr of RFP A is stored.

If transr = ‘T’ , the Transpose transr of RFP A is stored.

If transr = ‘C’ , the Conjugate-Transpose transr of RFP A is stored.

uplo

Must be ‘U’ or ‘L’ .

Indicates whether the upper or lower triangular part of A is stored:

If uplo = ‘U’ , the array a stores the upper triangular part of the matrix A .

If uplo = ‘L’ , the array a stores the lower triangular part of the matrix A .

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

a

Array, size (n*(n+1)/2) . The array a contains the matrix A in the RFP format.

Output Parameters

a

a is overwritten by the Cholesky factor U or L , as specified by uplo and trans .

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 .

NOTE:

Matrix Storage Schemes

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?pftrf

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values