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NAG[f03aec] NAG[nag_real_cholesky] -  factorization and determinant of real symmetric positive-definite matrix
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Calling Sequence
f03aec(a, p, detf, dete, 'n'=n, 'tda'=tda, 'fail'=fail)
nag_real_cholesky(. . .)
Parameters
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a - Matrix(1..n, 1..tda, datatype=float[8], order=C_order);
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On exit: the sub-diagonal elements of the lower triangular matrix  . The upper 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 diagonal elements of  .
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detf - assignable;
dete - assignable;
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Note: On exit the variable detf will have a value of type float, dete will have a value of type integer.
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On exit: the determinant of  is given by  . It is given in this form to avoid overflow or underflow.
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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_real_cholesky (f03aec) 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_real_cholesky (f03aec) computes a Cholesky factorization of a real symmetric positive-definite matrix, and evaluates the determinant.
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Description
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nag_real_cholesky (f03aec) computes the Cholesky factorization of a real symmetric positive-definite matrix  where  is lower triangular. The determinant is the product of the squares of the diagonal elements of  .
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Error Indicators and Warnings
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"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. The factorization could not be completed. detf and dete are set to zero.
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Accuracy
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The accuracy of the determinant depends on the conditioning of the original matrix. For a detailed error analysis see page 25 of Wilkinson and Reinsch (1971).
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Further Comments
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The time taken by nag_real_cholesky (f03aec) is approximately proportional to  .
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Examples
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>
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n := 4:
tda := 4:
a := Matrix([[6, 7, 6, 5], [7, 11, 8, 7], [6, 8, 11, 9], [5, 7, 9, 11]], datatype=float[8], order='C_order'):
p := Vector(4, datatype=float[8]):
NAG:-f03aec(a, p, detf, dete, 'n' = n, 'tda' = tda):
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