NAG Library Routine Document

f08fnf  (zheev)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{jobz}$ – Character(1)Input

On entry: indicates whether eigenvectors are computed.

$\mathbf{jobz}=\text{'N'}$

Only eigenvalues are computed.

$\mathbf{jobz}=\text{'V'}$

Eigenvalues and eigenvectors are computed.

Constraint: $\mathbf{jobz}=\text{'N'}$ or $\text{'V'}$.

2:     $\mathbf{uplo}$ – Character(1)Input

On entry: if $\mathbf{uplo}=\text{'U'}$, the upper triangular part of $A$ is stored.

If $\mathbf{uplo}=\text{'L'}$, the lower triangular part of $A$ is stored.

Constraint: $\mathbf{uplo}=\text{'U'}$ or $\text{'L'}$.

3:     $\mathbf{n}$ – IntegerInput

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

Constraint: $\mathbf{n}\ge 0$.

4:     $\mathbf{a}\left(\mathbf{lda},*\right)$ – Complex (Kind=nag_wp) arrayInput/Output

Note: the second dimension of the array a must be at least $\max \left(1,\mathbf{n}\right)$.

On entry: the $n$ by $n$ Hermitian matrix $A$.

• If $\mathbf{uplo}=\text{'U'}$, the upper triangular part of $A$ must be stored and the elements of the array below the diagonal are not referenced.
• If $\mathbf{uplo}=\text{'L'}$, the lower triangular part of $A$ must be stored and the elements of the array above the diagonal are not referenced.

On exit: if $\mathbf{jobz}=\text{'V'}$, a contains the orthonormal eigenvectors of the matrix $A$.

If $\mathbf{jobz}=\text{'N'}$ then on exit the lower triangle (if $\mathbf{uplo}=\text{'L'}$) or the upper triangle (if $\mathbf{uplo}=\text{'U'}$) of a, including the diagonal, is overwritten.

5:     $\mathbf{lda}$ – IntegerInput

On entry: the first dimension of the array a as declared in the (sub)program from which f08fnf (zheev) is called.

Constraint: $\mathbf{lda}\ge \max \left(1,\mathbf{n}\right)$.

6:     $\mathbf{w}\left(\mathbf{n}\right)$ – Real (Kind=nag_wp) arrayOutput

On exit: the eigenvalues in ascending order.

7:     $\mathbf{work}\left(\max \left(1,\mathbf{lwork}\right)\right)$ – Complex (Kind=nag_wp) arrayWorkspace

On exit: if $\mathbf{info}=\mathbf{0}$, the real part of $\mathbf{work}\left(1\right)$ contains the minimum value of lwork required for optimal performance.

8:     $\mathbf{lwork}$ – IntegerInput

On entry: the dimension of the array work as declared in the (sub)program from which f08fnf (zheev) is called.

If $\mathbf{lwork}=-1$, a workspace query is assumed; the routine only calculates the optimal size of the work array, returns this value as the first entry of the work array, and no error message related to lwork is issued.

Suggested value: for optimal performance, $\mathbf{lwork}\ge \left(\mathit{nb}+1\right)\times \mathbf{n}$, where $\mathit{nb}$ is the optimal block size for f08fsf (zhetrd).

Constraint: $\mathbf{lwork}\ge \max \left(1,2\times \mathbf{n}-1\right)$.

9:     $\mathbf{rwork}\left(*\right)$ – Real (Kind=nag_wp) arrayWorkspace

Note: the dimension of the array rwork must be at least $\max \left(1,3\times \mathbf{n}-2\right)$.

10:   $\mathbf{info}$ – IntegerOutput

On exit: $\mathbf{info}=0$ unless the routine detects an error (see Section 6).

6

Error Indicators and Warnings

$\mathbf{info}<0$

If $\mathbf{info}=-i$, argument $i$ had an illegal value. An explanatory message is output, and execution of the program is terminated.

$\mathbf{info}>0$

If $\mathbf{info}=i$, the algorithm failed to converge; $i$ off-diagonal elements of an intermediate tridiagonal form did not converge to zero.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (f08fnfe.f90)

10.2

Program Data

Program Data (f08fnfe.d)

10.3

Program Results

Program Results (f08fnfe.r)