naginterfaces.library.lapacklin.dpstrf¶
- naginterfaces.library.lapacklin.dpstrf(uplo, n, a, tol=- 1)[source]¶
dpstrf
computes the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix.For full information please refer to the NAG Library document for f07kd
https://support.nag.com/numeric/nl/nagdoc_30.1/flhtml/f07/f07kdf.html
- Parameters
- uplostr, length 1
Specifies whether the upper or lower triangular part of is stored and how is to be factorized.
The upper triangular part of is stored and is factorized as , where is upper triangular.
The lower triangular part of is stored and is factorized as , where is lower triangular.
- nint
, the order of the matrix .
- afloat, array-like, shape
The symmetric positive semidefinite matrix .
- tolfloat, optional
User defined tolerance. If , will be used. The algorithm terminates at the th step if the th step pivot .
- Returns
- afloat, ndarray, shape
If , the first rows of the upper triangle of are overwritten with the nonzero elements of the Cholesky factor , and the remaining rows of the triangle are destroyed.
If , the first columns of the lower triangle of are overwritten with the nonzero elements of the Cholesky factor , and the remaining columns of the triangle are destroyed.
- pivint, ndarray, shape
is such that the nonzero entries of are , for .
- rankint
The computed rank of given by the number of steps the algorithm completed.
- Raises
- NagValueError
- (errno )
On entry, error in parameter .
Constraint: or .
- (errno )
On entry, error in parameter .
Constraint: .
- Warns
- NagAlgorithmicWarning
- (errno )
The matrix is not positive definite. It is either positive semidefinite with computed rank as returned in and less than , or it may be indefinite, see Further Comments.
- Notes
dpstrf
forms the Cholesky factorization of a real symmetric positive semidefinite matrix either as if or if , where is a permutation matrix, is an upper triangular matrix and is lower triangular.This algorithm does not attempt to check that is positive semidefinite.
- References
Higham, N J, 2002, Accuracy and Stability of Numerical Algorithms, (2nd Edition), SIAM, Philadelphia
Lucas, C, 2004, LAPACK-style codes for Level 2 and 3 pivoted Cholesky factorizations, LAPACK Working Note No. 161. Technical Report CS-04-522, Department of Computer Science, University of Tennessee, 107 Ayres Hall, Knoxville, TN 37996-1301, USA, https://www.netlib.org/lapack/lawnspdf/lawn161.pdf