NAG Library Function Document

nag_real_eigenvalues (f02afc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:    $\mathbf{n}$ – IntegerInput

On entry: $n$, the order of the matrix $A$.

Constraint: $\mathbf{n}\ge 1$.

2:    $\mathbf{a}\left[\mathbf{n}\times \mathbf{tda}\right]$ – doubleInput/Output

Note: the $\left(i,j\right)$th element of the matrix $A$ is stored in $\mathbf{a}\left[\left(i-1\right)\times \mathbf{tda}+j-1\right]$.

On entry: the $n$ by $n$ matrix $A$.

On exit: a is overwritten.

3:    $\mathbf{tda}$ – IntegerInput

On entry: the stride separating matrix column elements in the array a.

Constraint: $\mathbf{tda}\ge \mathbf{n}$.

4:    $\mathbf{r}\left[\mathbf{n}\right]$ – ComplexOutput

On exit: the eigenvalues.

5:    $\mathbf{iter}\left[\mathbf{n}\right]$ – IntegerOutput

On exit: $\mathbf{iter}\left[i-1\right]$ contains the number of iterations used to find the $i$th eigenvalue. If $\mathbf{iter}\left[i-1\right]$ is negative, the $i$th eigenvalue is the second of a pair found simultaneously.

Note: the eigenvalues are found in reverse order, starting with the $n$th.

6:    $\mathbf{fail}$ – 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, $\mathbf{tda}=〈\mathit{\text{value}}〉$ while $\mathbf{n}=〈\mathit{\text{value}}〉$. These arguments must satisfy $\mathbf{tda}\ge \mathbf{n}$.

NE_ALLOC_FAIL

Dynamic memory allocation failed.

NE_INT_ARG_LT

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 1$.

NE_TOO_MANY_ITERATIONS

More than $〈\mathit{\text{value}}〉$ iterations are required to isolate all the eigenvalues.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (f02afce.c)

10.2  Program Data

Program Data (f02afce.d)

10.3  Program Results

Program Results (f02afce.r)