NAG FL Interface
c05mbf (sys_​func_​aa)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{fcn}$ – Subroutine, supplied by the user. External Procedure

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

The specification of fcn is:

Fortran Interface

Subroutine fcn ( n, x, fvec, iuser, ruser, cpuser, iflag) Integer, Intent (In) :: n Integer, Intent (Inout) :: iuser(*), iflag Real (Kind=nag_wp), Intent (In) :: x(n) Real (Kind=nag_wp), Intent (Inout) :: ruser(*) Real (Kind=nag_wp), Intent (Out) :: fvec(n) Type (c_ptr), Intent (In) :: cpuser

C Header Interface

void  fcn_ (const Integer *n, const double x[], double fvec[], Integer iuser[], double ruser[], void **cpuser, Integer *iflag)

C++ Header Interface

#include <nag.h> extern "C" { void  fcn_ (const Integer &n, const double x[], double fvec[], Integer iuser[], double ruser[], void *&cpuser, Integer &iflag) }

1: $\mathbf{n}$ – Integer Input

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

2: $\mathbf{x}\left(\mathbf{n}\right)$ – Real (Kind=nag_wp) array Input

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

3: $\mathbf{fvec}\left(\mathbf{n}\right)$ – Real (Kind=nag_wp) array Output

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

4: $\mathbf{iuser}\left(*\right)$ – Integer array User Workspace

5: $\mathbf{ruser}\left(*\right)$ – Real (Kind=nag_wp) array User Workspace

6: $\mathbf{cpuser}$ – Type (c_ptr) User Workspace

fcn is called with the arguments iuser, ruser and cpuser as supplied to c05mbf. You should use the arrays iuser and ruser, and the data handle cpuser to supply information to fcn.

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

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

On exit: in general, iflag should not be reset by fcn. 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 ifail.

fcn must either be a module subprogram USEd by, or declared as EXTERNAL in, the (sub)program from which c05mbf is called. Arguments denoted as Input must not be changed by this procedure.

Note: fcn should not return floating-point NaN (Not a Number) or infinity values, since these are not handled by c05mbf. If your code inadvertently does return any NaNs or infinities, c05mbf is likely to produce unexpected results.

2: $\mathbf{n}$ – Integer Input

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

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

3: $\mathbf{x}\left(\mathbf{n}\right)$ – Real (Kind=nag_wp) array Input/Output

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

On exit: the final estimate of the solution vector.

4: $\mathbf{fvec}\left(\mathbf{n}\right)$ – Real (Kind=nag_wp) array Output

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

5: $\mathbf{atol}$ – Real (Kind=nag_wp) Input

On entry: the absolute convergence criterion; see rtol.

Suggested value: $\sqrt{\epsilon }$, where $\epsilon$ is the machine precision returned by x02ajf.

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

6: $\mathbf{rtol}$ – Real (Kind=nag_wp) Input

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

Suggested value: $\sqrt{\epsilon }$, where $\epsilon$ is the machine precision returned by x02ajf.

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: $\mathbf{cndtol}$ – Real (Kind=nag_wp) 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: $\mathbf{iuser}\left(*\right)$ – Integer array User Workspace

11: $\mathbf{ruser}\left(*\right)$ – Real (Kind=nag_wp) array User Workspace

12: $\mathbf{cpuser}$ – Type (c_ptr) User Workspace

iuser, ruser and cpuser are not used by c05mbf, but are passed directly to fcn and may be used to pass information to this routine. If you do not need to reference cpuser, it should be initialized to c_null_ptr.

13: $\mathbf{ifail}$ – Integer Input/Output

On entry: ifail must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this argument you should refer to Section 4 in the Introduction to the NAG Library FL Interface for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this argument, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of ifail on exit.

On exit: $\mathbf{ifail}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

$\mathbf{ifail}=1$

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

$\mathbf{ifail}=2$

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

$\mathbf{ifail}=3$

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

$\mathbf{ifail}=4$

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

$\mathbf{ifail}=5$

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

$\mathbf{ifail}=6$

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

$\mathbf{ifail}=7$

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.

$\mathbf{ifail}=8$

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 c05mbf from a different starting point may avoid the region of difficulty.

$\mathbf{ifail}=9$

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

$\mathbf{ifail}=10$

iflag was set negative in fcn. $\mathbf{iflag}=〈\mathit{\text{value}}〉$.

$\mathbf{ifail}=11$

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

$\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 8 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 9 in the Introduction to the NAG Library FL 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