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NAG[f03afc] NAG[nag_real_lu] -  factorization and determinant of real matrix
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Calling Sequence
f03afc(a, pivot, detf, dete, 'n'=n, 'tda'=tda, 'fail'=fail)
nag_real_lu(. . .)
Parameters
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a - Matrix(1..n, 1..tda, datatype=float[8], order=C_order);
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pivot - Vector(1..n, datatype=integer[kernelopts('wordsize')/8]);
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On exit: ![pivot[i]](/support/helpjp/helpview.aspx?si=10092/file08062/math58.png) gives the row index of the  th pivot.
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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, pivot and the second dimension of the arrays a, pivotthe 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_lu (f03afc) 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_lu (f03afc) computes an  factorization of a real matrix, with partial pivoting, and evaluates the determinant.
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Error Indicators and Warnings
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"NE_ALLOC_FAIL"
Dynamic memory allocation failed.
"NE_INT_ARG_LT"
On entry, n must not be less than 1:  .
"NE_SINGULAR"
The matrix  is singular, 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 Wilkinson and Reinsch (1971).
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Further Comments
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The time taken by nag_real_lu (f03afc) is approximately proportional to  .
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Examples
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>
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n := 3:
tda := 3:
a := Matrix([[33, 16, 72], [-24, -10, -57], [-8, -4, -17]], datatype=float[8], order='C_order'):
pivot := Vector(3, datatype=integer[kernelopts('wordsize')/8]):
NAG:-f03afc(a, pivot, detf, dete, 'n' = n, 'tda' = tda):
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