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NAG[f02awc] NAG[nag_hermitian_eigenvalues] - All eigenvalues of complex Hermitian matrix
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Calling Sequence
f02awc(a, r, 'n'=n, 'tda'=tda, 'fail'=fail)
nag_hermitian_eigenvalues(. . .)
Parameters
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a - Matrix(1..n, 1..tda, datatype=complex[8], order=C_order);
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On exit: the array is overwritten.
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r - Vector(1..n, datatype=float[8]);
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On exit: the eigenvalues in ascending order.
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'n'=n - integer; (optional)
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Default value: the first dimension of the arrays a, r and the second dimension of the arrays a, rthe 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_hermitian_eigenvalues (f02awc) 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_hermitian_eigenvalues (f02awc) calculates all the eigenvalues of a complex Hermitian matrix.
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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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For a detailed error analysis see page 235 of Wilkinson and Reinsch (1971).
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Further Comments
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The time taken by nag_hermitian_eigenvalues (f02awc) is approximately proportional to  .
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Examples
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>
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n := 4:
tda := 4:
a := Matrix([[0.5 +0*I , 0 +0*I , 1.84 +1.38*I , 2.08 -1.56*I ], [0 +0*I , 0.5 +0*I , 1.12 +0.84*I , -0.5600000000000001 +0.42*I ], [1.84 -1.38*I , 1.12 -0.84*I , 0.5 +0*I , 0 +0*I ], [2.08 +1.56*I , -0.5600000000000001 -0.42*I , 0 +0*I , 0.5 +0*I ]], datatype=complex[8], order='C_order'):
r := Vector(4, datatype=float[8]):
NAG:-f02awc(a, r, 'n' = n, 'tda' = tda):
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