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NAG[f03ahc] NAG[nag_complex_lu] -  factorization and determinant of complex matrix
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Calling Sequence
f03ahc(a, pivot, det, dete, 'n'=n, 'tda'=tda, 'fail'=fail)
nag_complex_lu(. . .)
Parameters
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a - Matrix(1..n, 1..tda, datatype=complex[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=10097/file08063/math58.png) gives the row index of the  th pivot.
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det - assignable;
dete - assignable;
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Note: On exit the variable det will have a value of type complex, 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 and 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_complex_lu (f03ahc) 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_lu (f03ahc) computes an  factorization of a complex 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.  ,  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_complex_lu (f03ahc) is approximately proportional to  .
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Examples
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>
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n := 3:
tda := 3:
a := Matrix([[2 +0*I , 1 +2*I , 2 +10*I ], [1 +1*I , 1 +3*I , -5 +14*I ], [1 +1*I , 0 +5*I , -7 +20*I ]], datatype=complex[8], order='C_order'):
pivot := Vector(3, datatype=integer[kernelopts('wordsize')/8]):
NAG:-f03ahc(a, pivot, det, dete, 'n' = n, 'tda' = tda):
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