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NAG[f07gdc] NAG[nag_dpptrf] - Cholesky factorization of real symmetric positive-definite matrix, packed storage
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Calling Sequence
f07gdc(uplo, n, ap, 'fail'=fail)
nag_dpptrf(. . .)
Parameters
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uplo - String;
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On entry: indicates whether the upper or lower triangular part of is stored and how is factorized.
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Constraint: "Nag_Upper" or "Nag_Lower". .
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n - integer;
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On entry: , the order of the matrix .
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Constraint: . .
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ap - Vector(1..dim, datatype=float[8]);
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Note: the dimension, dim, of the array ap must be at least .
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On entry: the symmetric positive-definite matrix , packed by rows or columns. The storage of elements depends on the storage order and uplo arguments as follows:
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'fail'=fail - table; (optional)
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The NAG error argument, see the documentation for NagError.
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Description
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Purpose
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nag_dpptrf (f07gdc) computes the Cholesky factorization of a real symmetric positive-definite matrix, using packed storage.
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Error Indicators and Warnings
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"NE_BAD_PARAM"
On entry, argument had an illegal value.
"NE_INT"
On entry, . Constraint: .
"NE_INTERNAL_ERROR"
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please consult NAG for assistance.
"NE_POS_DEF"
The leading minor of order is not positive-definite and the factorization could not be completed. Hence itself is not positive-definite. This may indicate an error in forming the matrix . To factorize a matrix which is not positive-definite, call f07pdc (nag_dsptrf) instead.
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Further Comments
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The total number of floating-point operations is approximately .
A call to nag_dpptrf (f07gdc) may be followed by calls to the functions:
The complex analogue of this function is f07grc (nag_zpptrf).
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Examples
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>
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uplo := "Nag_Lower":
n := 4:
ap := Vector([4.16, -3.12, 5.03, 0.5600000000000001, -0.83, 0.76, -0.1, 1.18, 0.34, 1.18], datatype=float[8], order='C_order'):
NAG:-f07gdc(uplo, n, ap):
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See Also
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Demmel J W (1989) On floating-point errors in Cholesky LAPACK Working Note No. 14 University of Tennessee, Knoxville
Golub G H and Van Loan C F (1996) Matrix Computations (3rd Edition) Johns Hopkins University Press, Baltimore
f07 Chapter Introduction.
NAG Toolbox Overview.
NAG Web Site.
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