?pstrf

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

?pstrf

Computes the Cholesky factorization with complete pivoting of a real symmetric (complex Hermitian) positive semidefinite matrix.

Syntax

call spstrf ( uplo , n , a , lda , piv , rank , tol , work , info )

call dpstrf ( uplo , n , a , lda , piv , rank , tol , work , info )

call cpstrf ( uplo , n , a , lda , piv , rank , tol , work , info )

call zpstrf ( uplo , n , a , lda , piv , rank , tol , work , info )

Include Files

mkl.fi , mkl_lapack.f90

Description

spstrf dpstrf cpstrf zpstrf pstrf

The routine computes the Cholesky factorization with complete pivoting of a real symmetric (complex Hermitian) positive semidefinite matrix. The form of the factorization is:

\(P^{T} * A * P = U^{T} * U\) , if uplo = ‘U’ for real flavors,
\(P^{T} * A * P = U^{H} * U\) , if uplo = ‘U’ for complex flavors,
\(P^{T} * A * P = L * L^{T}\) , if uplo = ‘L’ for real flavors,
\(P^{T} * A * P = L * L^{H}\) , if uplo = ‘L’ for complex flavors,

where \(P\) is a permutation matrix stored as vector piv , and \(U\) and \(L\) are upper and lower triangular matrices, respectively.

This algorithm does not attempt to check that \(A\) is positive semidefinite. This version of the algorithm calls level 3 BLAS.

Input Parameters

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 , and the strictly lower triangular part of the matrix is not referenced.

If uplo = 'L' , the array a stores the lower triangular part of the matrix A , and the strictly upper triangular part of the matrix is not referenced.

n

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

a

REAL for spstrf

DOUBLE PRECISION for dpstrf

COMPLEX for cpstrf

DOUBLE COMPLEX for zpstrf .

Array a , size (lda,*) . The array a contains either the upper or the lower triangular part of the matrix A (see uplo ). The second dimension of a must be at least max(1, n) .

work

REAL for spstrf and cpstrf

DOUBLE PRECISION for dpstrf and zpstrf .

work(*) is a workspace array. The dimension of work is at least max(1,2*n) .

tol

REAL for single precision flavors

DOUBLE PRECISION for double precision flavors.

User defined tolerance. If tol < 0, then \(n * \varepsilon * max(A_{kk})\), where \(\varepsilon\) is the machine precision, will be used (see Error Analysis for the definition of machine precision). The algorithm terminates at the (k-1) -st step, if the pivot ≤ tol .

lda

INTEGER . The leading dimension of a ; at least max(1, n) .

Output Parameters

a

If info = 0 , the factor U or L from the Cholesky factorization is as described in Description .

piv

INTEGER .

Array, size at least max(1, n) . The array piv is such that the nonzero entries are \(P_{piv(k),k}\) (1 ≤ k ≤ n ).

rank

INTEGER .

The rank of a given by the number of steps the algorithm completed.

info

INTEGER .

If info = 0 , the execution is successful.
If info = -k , the k- th argument had an illegal value.
If info > 0 , the matrix A is either rank deficient with a computed rank as returned in rank , or is not positive semidefinite.

Return Values

No return value, info is an Output Parameter.

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?pstrf

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values