NAG CL Interface
f01kcc (complex_​gen_​matrix_​cond_​usd)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{n}$ – Integer Input

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

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

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

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

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

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

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

3: $\mathbf{pda}$ – Integer Input

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

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

4: $\mathbf{f}$ – 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:

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 $f\left(z\right)$ may not be defined. If iflag is returned as nonzero then f01kcc will terminate the computation, with $\mathbf{fail}\mathbf{.}\mathbf{code}=$ 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 $\mathit{i}=1,2,\dots ,n_z$.

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 f01kcc you may allocate memory and initialize these pointers with various quantities for use by f when called from f01kcc (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 f01kcc. If your code inadvertently does return any NaNs or infinities, f01kcc is likely to produce unexpected results.

5: $\mathbf{comm}$ – Nag_Comm *

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

6: $\mathbf{iflag}$ – 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_USER_STOP.

7: $\mathbf{conda}$ – double * Output

On exit: an estimate of the absolute condition number of $f$ at $A$.

8: $\mathbf{norma}$ – double * Output

On exit: the $1$-norm of $A$.

9: $\mathbf{normfa}$ – double * Output

On exit: the $1$-norm of $f\left(A\right)$.

10: $\mathbf{fail}$ – 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_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 internal error occurred when estimating the norm of the Fréchet derivative of $f$ at $A$. Please contact NAG.

An internal error occurred when evaluating the matrix function $f\left(A\right)$. You can investigate further by calling f01fmc with the matrix $A$ and the function $f$.

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

iflag has been set nonzero by the user-supplied function.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results