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NAG[f02aac] NAG[nag_real_symm_eigenvalues] - All eigenvalues of real symmetric matrix
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Calling Sequence
f02aac(a, r, 'n'=n, 'tda'=tda, 'fail'=fail)
nag_real_symm_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 elements of  below the diagonal are overwritten, and the rest of the array is unchanged.
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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_real_symm_eigenvalues (f02aac) 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_symm_eigenvalues (f02aac) calculates all the eigenvalues of a real symmetric matrix.
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Description
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nag_real_symm_eigenvalues (f02aac) reduces the real symmetric matrix  to a real symmetric tridiagonal matrix using Householder's method. The eigenvalues of the tridiagonal matrix are then determined using the  algorithm.
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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 eigenvalues depends on the sensitivity of the matrix to rounding errors produced in tridiagonalisation. For a detailed error analysis see pages 222 and 235 of Wilkinson and Reinsch (1971).
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Further Comments
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The time taken by nag_real_symm_eigenvalues (f02aac) 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, 2.3, -2.6], [0, 0.5, -1.4, -0.7], [2.3, -1.4, 0.5, 0], [-2.6, -0.7, 0, 0.5]], datatype=float[8], order='C_order'):
r := Vector(4, datatype=float[8]):
NAG:-f02aac(a, r, 'n' = n, 'tda' = tda):
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