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NAG[f02afc] NAG[nag_real_eigenvalues] - All eigenvalues of real matrix
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Calling Sequence
f02afc(a, r, iter, 'n'=n, 'tda'=tda, 'fail'=fail)
nag_real_eigenvalues(. . .)
Parameters
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a - Matrix(1..n, 1..tda, datatype=float[8], order=C_order);
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On exit: the array is overwritten.
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r - Vector(1..n, datatype=complex[8]);
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On exit: the eigenvalues.
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iter - Vector(1..n, datatype=integer[kernelopts('wordsize')/8]);
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Note: the eigenvalues are found in reverse order, starting with the  th.
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'n'=n - integer; (optional)
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Default value: the first dimension of the arrays a, r, iter and the second dimension of the arrays a, r, iterthe 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_eigenvalues (f02afc) 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_eigenvalues (f02afc) calculates all the eigenvalues of a real unsymmetric matrix.
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Description
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The matrix  is first balanced and then reduced to upper Hessenberg form using stabilised elementary similarity transformations. The eigenvalues are then found using the  algorithm for real Hessenberg matrices.
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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_TOO_MANY_ITERATIONS"
More than  iterations are required to isolate all the eigenvalues.
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Accuracy
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The accuracy of the results depends on the original matrix and the multiplicity of the roots. For a detailed error analysis see pages 352 and 367 Wilkinson and Reinsch (1971).
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Further Comments
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The time taken by nag_real_eigenvalues (f02afc) is approximately proportional to  .
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Examples
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>
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n := 4:
tda := 4:
a := Matrix([[1.5, 0.1, 4.5, -1.5], [-22.5, 3.5, 12.5, -2.5], [-2.5, 0.3, 4.5, -2.5], [-2.5, 0.1, 4.5, 2.5]], datatype=float[8], order='C_order'):
r := Vector(4, datatype=complex[8]):
iter := Vector(4, datatype=integer[kernelopts('wordsize')/8]):
NAG:-f02afc(a, r, iter, 'n' = n, 'tda' = tda):
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