NAG Library Function Document

nag_hermitian_eigenvalues (f02awc)

1: n – IntegerInput: On entry: $n$ , the order of the matrix $A$ .
Constraint: $n \geq 1$ .
2: a[ $n \times tda$ ] – ComplexInput/Output: Note: the $(i, j)$ th element of the matrix $A$ is stored in $a [(i - 1) \times tda + j - 1]$ .

On entry: the elements of the lower triangle of the $n$ by $n$ complex Hermitian matrix $A$ . Elements of the array above the diagonal need not be set.

On exit: a is overwritten.
3: tda – IntegerInput: On entry: the stride separating matrix column elements in the array a.

Constraint: $tda \geq n$ .
4: r[n] – doubleOutput: On exit: the eigenvalues in ascending order.
5: fail – NagError *Input/Output: The NAG error argument (see Section 3.6 in the Essential Introduction).

6 Error Indicators and Warnings

NE_2_INT_ARG_LT: On entry, $tda = ⟨value⟩$ while $n = ⟨value⟩$ . These arguments must satisfy $tda \geq n$ .
NE_ALLOC_FAIL: Dynamic memory allocation failed.
NE_INT_ARG_LT: On entry, $n = ⟨value⟩$ .
Constraint: $n \geq 1$ .
NE_TOO_MANY_ITERATIONS: More than $⟨value⟩$ iterations are required to isolate all the eigenvalues.

For a detailed error analysis see page 235 of Wilkinson and Reinsch (1971).

Not applicable.

The time taken by nag_hermitian_eigenvalues (f02awc) is approximately proportional to

n^{3}

To calculate all the eigenvalues of the complex Hermitian matrix:

(\begin{matrix} 0.50 & 0.00 & 1.84 + 1.38 i & 2.08 - 1.56 i \\ 0.00 & 0.50 & 1.12 + 0.84 i & - 0.56 + 0.42 i \\ 1.84 - 1.38 i & 1.12 - 0.84 i & 0.50 & 0.00 \\ 2.08 + 1.56 i & - 0.56 - 0.42 i & 0.00 & 0.50 \end{matrix}) .