naginterfaces.library.lapacklin.dpptrf

naginterfaces.library.lapacklin.dpptrf(uplo, n, ap)

dpptrf computes the Cholesky factorization of a real symmetric positive definite matrix, using packed storage.

For full information please refer to the NAG Library document for f07gd

https://support.nag.com/numeric/nl/nagdoc_30/flhtml/f07/f07gdf.html

Parameters

uplostr, length 1

Specifies whether the upper or lower triangular part of $A$ is stored and how $A$ is to be factorized.

$uplo=\text{'U'}$

The upper triangular part of $A$ is stored and $A$ is factorized as $U^{T}U$, where $U$ is upper triangular.

$uplo=\text{'L'}$

The lower triangular part of $A$ is stored and $A$ is factorized as $L{L}^T$, where $L$ is lower triangular.

nint

$n$, the order of the matrix $A$.

apfloat, array-like, shape $(n\times (n+1)/2)$

The $n\times n$ symmetric matrix $A$, packed by columns.

Returns

apfloat, ndarray, shape $(n\times (n+1)/2)$

If no exception or warning is raised, the factor $U$ or $L$ from the Cholesky factorization $A=U^{T}U$ or $A=L{L}^T$, in the same storage format as $A$.

Raises

NagValueError

(errno $-1$)

On entry, error in parameter $uplo$.

Constraint: $uplo=\text{'U'}$ or $\text{'L'}$.

(errno $-2$)

On entry, error in parameter $n$.

Constraint: $n\ge 0$.

(errno $i>0$)

The leading minor of order $⟨value⟩$ is not positive definite and the factorization could not be completed. Hence $A$ itself is not positive definite. This may indicate an error in forming the matrix $A$. To factorize a symmetric matrix which is not positive definite, call dsptrf() instead.

Notes

dpptrf forms the Cholesky factorization of a real symmetric positive definite matrix $A$ either as $A=U^{T}U$ if $uplo=\text{'U'}$ or $A=L{L}^T$ if $uplo=\text{'L'}$, where $U$ is an upper triangular matrix and $L$ is lower triangular, using packed storage.

References

Demmel, J W, 1989, On floating-point errors in Cholesky, LAPACK Working Note No. 14, University of Tennessee, Knoxville, https://www.netlib.org/lapack/lawnspdf/lawn14.pdf

Golub, G H and Van Loan, C F, 1996, Matrix Computations, (3rd Edition), Johns Hopkins University Press, Baltimore