NAG CL Interface
f08jac (dstev)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{order}$ – Nag_OrderType Input

On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by $\mathbf{order}=\mathrm{Nag\_RowMajor}$. See Section 3.1.3 in the Introduction to the NAG Library CL Interface for a more detailed explanation of the use of this argument.

Constraint: $\mathbf{order}=\mathrm{Nag\_RowMajor}$ or $\mathrm{Nag\_ColMajor}$.

2: $\mathbf{job}$ – Nag_JobType Input

On entry: indicates whether eigenvectors are computed.

$\mathbf{job}=\mathrm{Nag\_EigVals}$

Only eigenvalues are computed.

$\mathbf{job}=\mathrm{Nag\_DoBoth}$

Eigenvalues and eigenvectors are computed.

Constraint: $\mathbf{job}=\mathrm{Nag\_EigVals}$ or $\mathrm{Nag\_DoBoth}$.

3: $\mathbf{n}$ – Integer Input

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

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

4: $\mathbf{d}\left[\mathit{dim}\right]$ – double Input/Output

Note: the dimension, dim, of the array d must be at least $\max (1,\mathbf{n})$.

On entry: the $n$ diagonal elements of the tridiagonal matrix $A$.

On exit: if $\mathbf{fail}\mathbf{.}\mathbf{code}=$ NE_NOERROR, the eigenvalues in ascending order.

5: $\mathbf{e}\left[\mathit{dim}\right]$ – double Input/Output

Note: the dimension, dim, of the array e must be at least $\max (1,\mathbf{n}-1)$.

On entry: the $(n-1)$ subdiagonal elements of the tridiagonal matrix $A$.

On exit: the contents of e are destroyed.

6: $\mathbf{z}\left[\mathit{dim}\right]$ – double Output

Note: the dimension, dim, of the array z must be at least

• $\max (1,\mathbf{pdz}\times \mathbf{n})$ when $\mathbf{job}=\mathrm{Nag\_DoBoth}$;
• $1$ otherwise.

The $(i,j)$th element of the matrix $Z$ is stored in

• $\mathbf{z}\left[(j-1)\times \mathbf{pdz}+i-1\right]$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\mathbf{z}\left[(i-1)\times \mathbf{pdz}+j-1\right]$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

On exit: if $\mathbf{job}=\mathrm{Nag\_DoBoth}$, then if $\mathbf{fail}\mathbf{.}\mathbf{code}=$ NE_NOERROR, z contains the orthonormal eigenvectors of the matrix $A$, with the $i$th column of $Z$ holding the eigenvector associated with $\mathbf{d}\left[i-1\right]$.

If $\mathbf{job}=\mathrm{Nag\_EigVals}$, z is not referenced.

7: $\mathbf{pdz}$ – Integer Input

On entry: the stride separating row or column elements (depending on the value of order) in the array z.

Constraints:

• if $\mathbf{job}=\mathrm{Nag\_DoBoth}$, $\mathbf{pdz}\ge \max (1,\mathbf{n})$;
• otherwise $\mathbf{pdz}\ge 1$.

8: $\mathbf{fail}$ – NagError * Input/Output

The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.

NE_BAD_PARAM

On entry, argument $⟨\mathit{\text{value}}⟩$ had an illegal value.

NE_CONVERGENCE

The algorithm failed to converge; $⟨\mathit{\text{value}}⟩$ off-diagonal elements of e did not converge to zero.

NE_ENUM_INT_2

On entry, $\mathbf{job}=⟨\mathit{\text{value}}⟩$, $\mathbf{pdz}=⟨\mathit{\text{value}}⟩$ and $\mathbf{n}=⟨\mathit{\text{value}}⟩$.
Constraint: if $\mathbf{job}=\mathrm{Nag\_DoBoth}$, $\mathbf{pdz}\ge \max (1,\mathbf{n})$;
otherwise $\mathbf{pdz}\ge 1$.

NE_INT

On entry, $\mathbf{n}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{n}\ge 0$.

On entry, $\mathbf{pdz}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{pdz}>0$.

NE_INTERNAL_ERROR

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results