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NAG[f01bnc] NAG[nag_complex_cholesky] -  factorization of complex Hermitian positive-definite matrix
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Calling Sequence
f01bnc(a, p, 'n'=n, 'tda'=tda, 'fail'=fail)
nag_complex_cholesky(. . .)
Parameters
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a - Matrix(1..n, 1..tda, datatype=complex[8], order=C_order);
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On exit: the off-diagonal elements of the upper triangular matrix  . The lower triangle of  is unchanged.
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p - Vector(1..n, datatype=float[8]);
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On exit: the reciprocals of the real diagonal elements of  .
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'n'=n - integer; (optional)
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Default value: the first dimension of the arrays a, p and the second dimension of the arrays a, pthe array a.
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On entry:  , the order of the matrix  .
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Constraint:  . .
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'tda'=tda - integer; (optional)
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On entry: the second dimension of the array a as declared in the function from which nag_complex_cholesky (f01bnc) is called.
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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_complex_cholesky (f01bnc) computes a Cholesky factorization of a complex positive-definite Hermitian matrix.
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Description
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nag_complex_cholesky (f01bnc) computes the Cholesky factorization of a complex positive-definite Hermitian matrix  , where  is a complex upper triangular matrix with real diagonal elements.
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Error Indicators and Warnings
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"NE_DIAG_IMAG_NON_ZERO"
Matrix diagonal element ![a[< >+1][< >+1]](/support/helpjp/helpview.aspx?si=10063/file08038/math131.png) has non-zero imaginary part.
"NE_INT_ARG_LT"
On entry, n must not be less than 1:  .
"NE_NOT_POS_DEF"
The matrix is not positive-definite, possibly due to rounding errors.
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Further Comments
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The time taken by nag_complex_cholesky (f01bnc) is approximately proportional to  .
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Examples
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>
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n := 4:
tda := 4:
a := Matrix([[15 +0*I , 0 +0*I , 0 +0*I , 0 +0*I ], [1 +2*I , 20 +0*I , 0 +0*I , 0 +0*I ], [2 +0*I , -2 -1*I , 18 +0*I , 0 +0*I ], [-4 -3*I , 3 +3*I , -1 -2*I , 26 +0*I ]], datatype=complex[8], order='C_order'):
p := Vector(4, datatype=float[8]):
NAG:-f01bnc(a, p, 'n' = n, 'tda' = tda):
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