NAG CL Interface
c05mbc (sys_​func_​aa)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

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

f must return the values of the functions $f_k$ at a point $x$.

The specification of f is:

copy

void  f (Integer n, const double x[], double fvec[], Nag_Comm *comm, Integer *iflag)

1: $\mathbf{n}$ – Integer Input

On entry: $n$, the number of equations.

2: $\mathbf{x}\left[\mathbf{n}\right]$ – const double Input

On entry: the components of the point $x$ at which the functions must be evaluated.

3: $\mathbf{fvec}\left[\mathbf{n}\right]$ – double Output

On exit: the function values $f_k\left(x\right)$ (unless iflag is set to a negative value by f).

4: $\mathbf{comm}$ – 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 c05mbc you may allocate memory and initialize these pointers with various quantities for use by f when called from c05mbc (see Section 3.1.1 in the Introduction to the NAG Library CL Interface).

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

On entry: $\mathbf{iflag}\ge 0$.

On exit: in general, iflag should not be reset by f. If, however, you wish to terminate execution (perhaps because some illegal point x has been reached), iflag should be set to a negative integer. This value will be returned through fail.

Note: f should not return floating-point NaN (Not a Number) or infinity values, since these are not handled by c05mbc. If your code inadvertently does return any NaNs or infinities, c05mbc is likely to produce unexpected results.

2: $\mathbf{n}$ – Integer Input

On entry: $n$, the number of equations.

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

3: $\mathbf{x}\left[\mathbf{n}\right]$ – double Input/Output

On entry: an initial guess at the solution vector, ${\hat{x}}_0$.

On exit: the final estimate of the solution vector.

4: $\mathbf{fvec}\left[\mathbf{n}\right]$ – double Output

On exit: the function values at the final point, x.

5: $\mathbf{atol}$ – double Input

On entry: the absolute convergence criterion; see rtol.

Suggested value: $\sqrt{\epsilon }$, where $\epsilon$ is the machine precision returned by X02AJC.

Constraint: $\mathbf{atol}\ge 0.0$.

6: $\mathbf{rtol}$ – double Input

On entry: the relative convergence criterion. At each iteration $\Vert f\left({\hat{x}}_i\right)\Vert$ is computed. The iteration is deemed to have converged if $\Vert f\left({\hat{x}}_i\right)\Vert \le \max (\mathbf{atol},\mathbf{rtol}\times \Vert f\left({\hat{x}}_0\right)\Vert )$.

Suggested value: $\sqrt{\epsilon }$, where $\epsilon$ is the machine precision returned by X02AJC.

Constraint: $\mathbf{rtol}\ge 0.0$.

7: $\mathbf{m}$ – Integer Input

On entry: $m$, the number of previous iterates to use in Anderson acceleration. If $m=0$, Anderson acceleration is not used.

Suggested value: $\mathbf{m}=4$.

Constraint: $0\le \mathbf{m}\le \mathbf{n}$.

8: $\mathbf{cndtol}$ – double Input

On entry: the maximum allowable condition number for the triangular $QR$ factor generated during Anderson acceleration. At each iteration, if the condition number exceeds cndtol, columns are deleted until it is sufficiently small.

If $\mathbf{cndtol}=0.0$, no condition number tests are performed.

Suggested value: $\mathbf{cndtol}=0.0$. If condition number tests are required, a suggested value is $\mathbf{cndtol}=1.0/\sqrt{\epsilon }$.

Constraint: $\mathbf{cndtol}\ge 0.0$.

9: $\mathbf{astart}$ – Integer Input

On entry: the number of iterations by which to delay the start of Anderson acceleration.

Suggested value: $\mathbf{astart}=0$.

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

10: $\mathbf{comm}$ – Nag_Comm *

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

11: $\mathbf{fail}$ – 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

An error occurred in evaluating the $QR$ decomposition during Anderson acceleration. This may be due to slow convergence of the iteration. Try setting the value of cndtol. If condition number tests are already performed, try decreasing cndtol.

NE_DIVERGENCE

The iteration has diverged and subsequent iterates are too large to be computed in floating-point arithmetic.

NE_INT

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

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

NE_INT_2

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

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.

NE_NO_IMPROVEMENT

The iteration is not making good progress. This failure exit may indicate that the system does not have a zero, or that the solution is very close to the origin. Rerunning c05mbc from a different starting point may avoid the region of difficulty.

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_REAL

On entry, $\mathbf{atol}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{atol}\ge 0.0$.

On entry, $\mathbf{cndtol}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{cndtol}\ge 0.0$.

On entry, $\mathbf{rtol}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{rtol}\ge 0.0$.

NE_TOO_MANY_FEVALS

There have been at least $200\times (\mathbf{n}+1)$ calls to f. Consider restarting the calculation from the point held in x.

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