NAG Library Function Document

nag_hermitian_eigensystem (f02axc)

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:    $\mathbf{a}\left[\mathbf{n}\times \mathbf{tda}\right]$ – const ComplexInput

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. See also Section 9.

3:    $\mathbf{tda}$ – IntegerInput

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

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

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

On exit: the eigenvalues in ascending order.

5:    $\mathbf{v}\left[\mathbf{n}\times \mathbf{tdv}\right]$ – ComplexOutput

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

On exit: the eigenvectors, stored by columns. The $i$th column corresponds to the $i$th eigenvector. The eigenvectors are normalized so that the sum of the squares of the moduli of the elements is equal to 1 and the element of largest modulus is real. See also Section 9.

6:    $\mathbf{tdv}$ – IntegerInput

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

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

7:    $\mathbf{fail}$ – 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 $\mathbf{tda}\ge \mathbf{n}$.

On entry, $\mathbf{tdv}=〈\mathit{\text{value}}〉$ while $\mathbf{n}=〈\mathit{\text{value}}〉$. These arguments must satisfy $\mathbf{tdv}\ge \mathbf{n}$.

NE_ALLOC_FAIL

Dynamic memory allocation failed.

NE_DIAG_IMAG_NON_ZERO

Matrix diagonal element $\mathbf{a}\left[\left(〈\mathit{\text{value}}〉\right)\times \mathbf{tda}+〈\mathit{\text{value}}〉\right]$ has nonzero imaginary part.

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 (f02axce.c)

10.2  Program Data

Program Data (f02axce.d)

10.3  Program Results

Program Results (f02axce.r)