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NAG[f07frc] NAG[nag_zpotrf] - Cholesky factorization of complex Hermitian positive-definite matrix
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Calling Sequence
f07frc(uplo, a, 'n'=n, 'fail'=fail)
nag_zpotrf(. . .)
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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a - Matrix(1..dim1, 1..dim2, datatype=complex[8], order=order);
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Note: this array may be supplied in Fortran_order or C_order , as specified by order. All array parameters must use a consistent order.
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If  , the upper triangle of  must be stored and the elements of the array below the diagonal are not referenced.
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If  , the lower triangle of  must be stored and the elements of the array above the diagonal are not referenced.
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'n'=n - integer; (optional)
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Default value: the dimension of the array a.
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On entry:  , the order of the matrix  .
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Constraint:  . .
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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_zpotrf (f07frc) computes the Cholesky factorization of a complex Hermitian positive-definite matrix.
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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 f07mrc (nag_zhetrf) instead.
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Further Comments
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The total number of real floating-point operations is approximately  .
A call to nag_zpotrf (f07frc) may be followed by calls to the functions:
The real analogue of this function is f07fdc (nag_dpotrf).
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Examples
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uplo := "Nag_Lower":
n := 4:
a := Matrix([[3.23 +0*I , 0 +0*I , 0 +0*I , 0 +0*I ], [1.51 +1.92*I , 3.58 +0*I , 0 +0*I , 0 +0*I ], [1.9 -0.84*I , -0.23 -1.11*I , 4.09 +0*I , 0 +0*I ], [0.42 -2.5*I , -1.18 -1.37*I , 2.33 +0.14*I , 4.29 +0*I ]], datatype=complex[8], order='C_order'):
NAG:-f07frc(uplo, a, 'n' = n):
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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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