?pstf2

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

Download PDF

ID 766686

Date 4/28/2026

Version

Public

?pstf2

Computes the Cholesky factorization with complete pivoting of a real symmetric or complex Hermitian positive semi-definite matrix.

Syntax

call spstf 2( uplo , n , a , lda , piv , rank , tol , work , info )

call dpstf2 ( uplo , n , a , lda , piv , rank , tol , work , info )

call cpstf 2( uplo , n , a , lda , piv , rank , tol , work , info )

call zpstf2 ( uplo , n , a , lda , piv , rank , tol , work , info )

Include Files

mkl.fi

Description

spstf2 dpstf2 cpstf2 zpstf2

The real flavors spstf2 and dpstf2 compute the Cholesky factorization with complete pivoting of a real symmetric positive semi-definite matrix A . The complex flavors cpstf2 and zpstf2 compute the Cholesky factorization with complete pivoting of a complex Hermitian positive semi-definite matrix A . The factorization has the form:

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 U is an upper triangular matrix and L is lower triangular, and P is stored as vector piv .

This algorithm does not check that A is positive semi-definite. This version of the algorithm calls level 2 BLAS .

Input Parameters

uplo: CHARACTER*1 . Specifies whether the upper or lower triangular part of the symmetric or Hermitian matrix A is stored: * = ‘U’: Upper triangular, * = ‘L’: Lower triangular.
n: INTEGER . The order of the matrix A . n≥ 0 .
a: REAL for spstf2 , DOUBLE PRECISION for dpstf2 , COMPLEX for cpstf2 , DOUBLE COMPLEX for zpstf2 . Array, DIMENSION ( lda, *) . On entry, the symmetric matrix A . * If uplo = ‘U’, the leading n -by- n upper triangular part of the array 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 the array a contains the lower triangular part of the matrix A , and the strictly upper triangular part of a is not referenced.
tol: REAL for spstf2 and cpstf2 , DOUBLE PRECISION for dpstf2 and zpstf2 . A user-defined tolerance. * If tol < 0, n*ulp*max(A(k,k)) will be used ( ulp is the Unit in the Last Place, or Unit of Least Precision). The algorithm terminates at the ( k - 1)-st step if the pivot is not greater than tol .
lda: INTEGER . The leading dimension of the matrix A.lda ≥ max (1, n ).
work: REAL for spstf2 and cpstf2 , DOUBLE PRECISION for dpstf2 and zpstf2 . Workspace array, DIMENSION at least max (1, 2*n).

Output Parameters

piv: INTEGER . Array. DIMENSION at least max(1,n) . piv is such that the non-zero entries are P(piv(k),k) = 1.
a: On exit, if info = 0, the factor U or L from the Cholesky factorization stored the same way as the matrix A is stored on entry.
rank: INTEGER . The rank of A , determined by the number of steps the algorithm completed.

info

INTEGER .

< 0: if info = - k , the k -th parameter had an illegal value,
=0: the algorithm completed successfully,
> 0: the matrix A is rank-deficient with the computed rank, returned in rank , or indefinite.

Select Your Language

Using Intel.com Search

Quick Links

Recent Searches

Advanced Search

Only search in

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?pstf2

Syntax

Include Files

Description

Input Parameters

Output Parameters