NAG CL Interface
f01emc (real_​gen_​matrix_​fun_​usd)

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: $\mathbf{n}$ – Integer Input

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

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

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

Note: the dimension, dim, of the array a must be at least $\mathbf{pda}\times \mathbf{n}$.

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

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

On entry: the $n\times n$ matrix $A$.

On exit: the $n\times n$ matrix, $f\left(A\right)$.

4: $\mathbf{pda}$ – Integer Input

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

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

5: $\mathbf{f}$ – function, supplied by the user External Function

Given an integer $m$, the function f evaluates $f^{\left(m\right)}\left(z_i\right)$ at a number of points $z_i$.

The specification of f is:

copy

void  f (Integer m, Integer *iflag, Integer nz, const Complex z[], Complex fz[], Nag_Comm *comm)

1: $\mathbf{m}$ – Integer Input

On entry: the order, $m$, of the derivative required.

If $\mathbf{m}=0$, $f\left(z_i\right)$ should be returned. For $\mathbf{m}>0$, $f^{\left(m\right)}\left(z_i\right)$ should be returned.

2: $\mathbf{iflag}$ – Integer * Input/Output

On entry: iflag will be zero.

On exit: iflag should either be unchanged from its entry value of zero, or may be set nonzero to indicate that there is a problem in evaluating the function $f\left(z\right)$; for instance $f\left(z_i\right)$ may not be defined for a particular $z_i$. If iflag is returned as nonzero then f01emc will terminate the computation, with $\mathbf{fail}\mathbf{.}\mathbf{code}=$ NE_INT, NE_INT_2 or NE_USER_STOP.

3: $\mathbf{nz}$ – Integer Input

On entry: $n_z$, the number of function or derivative values required.

4: $\mathbf{z}\left[\mathit{dim}\right]$ – const Complex Input

On entry: the $n_z$ points $z_1,z_2,\dots ,z_{n_z}$ at which the function $f$ is to be evaluated.

5: $\mathbf{fz}\left[\mathit{dim}\right]$ – Complex Output

On exit: the $n_z$ function or derivative values. $\mathbf{fz}\left[\mathit{i}-1\right]$ should return the value $f^{\left(m\right)}\left(z_{\mathit{i}}\right)$, for $\mathit{i}=1,2,\dots ,n_z$. If $z_i$ lies on the real line, then so must $f^{\left(m\right)}\left(z_i\right)$.

6: $\mathbf{comm}$ – Nag_Comm *

Pointer to structure of type Nag_Comm; the following members are relevant to f.

user – double *

iuser – Integer *

p – Pointer 

The type Pointer will be void *. Before calling f01emc you may allocate memory and initialize these pointers with various quantities for use by f when called from f01emc (see Section 3.1.1 in the Introduction to the NAG Library CL Interface).

Note: f should not return floating-point NaN (Not a Number) or infinity values, since these are not handled by f01emc. If your code inadvertently does return any NaNs or infinities, f01emc is likely to produce unexpected results.

6: $\mathbf{comm}$ – Nag_Comm *

The NAG communication argument (see Section 3.1.1 in the Introduction to the NAG Library CL Interface).

7: $\mathbf{iflag}$ – Integer * Output

On exit: $\mathbf{iflag}=0$, unless iflag has been set nonzero inside f, in which case iflag will be the value set and fail will be set to $\mathbf{fail}\mathbf{.}\mathbf{code}=$ NE_INT, NE_INT_2 or NE_USER_STOP.

8: $\mathbf{imnorm}$ – double * Output

On exit: if $A$ has complex eigenvalues, f01emc will use complex arithmetic to compute $f\left(A\right)$. The imaginary part is discarded at the end of the computation, because it will theoretically vanish. imnorm contains the $1$-norm of the imaginary part, which should be used to check that the function has given a reliable answer.

If $A$ has real eigenvalues, f01emc uses real arithmetic and $\mathbf{imnorm}=0$.

9: $\mathbf{fail}$ – 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

A Taylor series failed to converge.

NE_INT

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

NE_INT_2

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

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.

An unexpected internal error occurred when ordering the eigenvalues of $A$. Please contact NAG.

There was an error whilst reordering the Schur form of $A$.
Note:  this failure should not occur and suggests that the function has been called incorrectly.

The routine was unable to compute the Schur decomposition of $A$.
Note:  this failure should not occur and suggests that the function has been called incorrectly.

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.

NE_USER_STOP

Termination requested in f.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results