?pftrf

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

?pftrf

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

Syntax

call spftrf ( transr , uplo , n , a , info )

call dpftrf ( transr , uplo , n , a , info )

call cpftrf ( transr , uplo , n , a , info )

call zpftrf ( transr , uplo , n , a , info )

Include Files

mkl.fi , mkl_lapack.f90

Description

spftrf dpftrf cpftrf zpftrf

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

transr

CHARACTER*1 . 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

CHARACTER*1 . 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

INTEGER . The order of the matrix A ; n ≥ 0.

a

REAL for spftrf

DOUBLE PRECISION for dpftrf

COMPLEX for cpftrf

DOUBLE COMPLEX for zpftrf .

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 .

info

INTEGER .

If info=0 , the execution is successful.
If info = -i , the i -th parameter 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 .

Return Values

No return value, info is an Output Parameter.

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?pftrf

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values