NAG CL Interface
e04cbc (uncon_​simplex)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{n}$ – Integer Input

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

Constraint: $\mathbf{n}\ge 1$.

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

On entry: a guess at the position of the minimum. Note that the problem should be scaled so that the values of the $\mathbf{x}\left[i-1\right]$ are of order unity.

On exit: the value of $\mathbf{x}$ corresponding to the function value in f.

3: $\mathbf{f}$ – double * Output

On exit: the lowest function value found.

4: $\mathbf{tolf}$ – double Input

On entry: the error tolerable in the function values, in the following sense. If $f_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,n+1$, are the individual function values at the vertices of the current simplex, and if $f_m$ is the mean of these values, then you can request that e04cbc should terminate if

$$\sqrt{\frac{1}{n+1}\sum _{i=1}^{n+1}{(f_i-f_m)}^2}<\mathbf{tolf}\text{.}$$

(1)

You may specify $\mathbf{tolf}=0$ if you wish to use only the termination criterion (2) on the spatial values: see the description of tolx.

Constraint: $\mathbf{tolf}$ must be greater than or equal to the machine precision (see Chapter X02), or if tolf equals zero, then tolx must be greater than or equal to the machine precision.

5: $\mathbf{tolx}$ – double Input

On entry: the error tolerable in the spatial values, in the following sense. If $LV$ denotes the ‘linearized’ volume of the current simplex, and if ${LV}_{\mathrm{init}}$ denotes the ‘linearized’ volume of the initial simplex, then you can request that e04cbc should terminate if

$$\frac{LV}{{LV}_{\mathrm{init}}}<\mathbf{tolx}\text{.}$$

(2)

You may specify $\mathbf{tolx}=0$ if you wish to use only the termination criterion (1) on function values: see the description of tolf.

Constraint: $\mathbf{tolx}$ must be greater than or equal to the machine precision (see Chapter X02), or if tolx equals zero, then tolf must be greater than or equal to the machine precision.

6: $\mathbf{funct}$ – function, supplied by the user External Function

funct must evaluate the function $F$ at a specified point. It should be tested separately before being used in conjunction with e04cbc.

The specification of funct is:

copy

void  funct (Integer n, const double xc[], double *fc, Nag_Comm *comm)

1: $\mathbf{n}$ – Integer Input

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

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

On entry: the point at which the function value is required.

3: $\mathbf{fc}$ – double * Output

On exit: the value of the function $F$ at the current point $\mathbf{x}$.

4: $\mathbf{comm}$ – Nag_Comm *

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

user – double *

iuser – Integer *

p – Pointer 

The type Pointer will be void *. Before calling e04cbc you may allocate memory and initialize these pointers with various quantities for use by funct when called from e04cbc (see Section 3.1.1 in the Introduction to the NAG Library CL Interface).

Note: funct should not return floating-point NaN (Not a Number) or infinity values, since these are not handled by e04cbc. If your code inadvertently does return any NaNs or infinities, e04cbc is likely to produce unexpected results.

7: $\mathbf{monit}$ – function, supplied by the user External Function

monit may be used to monitor the optimization process. It is invoked once every iteration.

If no monitoring is required, monit may be specified as NULLFN.

The specification of monit is:

copy

void  monit (double fmin, double fmax, const double sim[], Integer n, Integer ncall, double serror, double vratio, Nag_Comm *comm)

1: $\mathbf{fmin}$ – double Input

On entry: the smallest function value in the current simplex.

2: $\mathbf{fmax}$ – double Input

On entry: the largest function value in the current simplex.

3: $\mathbf{sim}\left[(\mathbf{n}+1)\times \mathbf{n}\right]$ – const double Input

On entry: the $n+1$ position vectors of the current simplex, where $\mathbf{sim}\left[(j-1)\times (n+1)+i-1\right]$ is the $j$th coordinate of the $i$th position vector.

4: $\mathbf{n}$ – Integer Input

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

5: $\mathbf{ncall}$ – Integer Input

On entry: the number of times that funct has been called so far.

6: $\mathbf{serror}$ – double Input

On entry: the current value of the standard deviation in function values used in termination test (1).

7: $\mathbf{vratio}$ – double Input

On entry: the current value of the linearized volume ratio used in termination test (2).

8: $\mathbf{comm}$ – Nag_Comm *

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

user – double *

iuser – Integer *

p – Pointer 

The type Pointer will be void *. Before calling e04cbc you may allocate memory and initialize these pointers with various quantities for use by monit when called from e04cbc (see Section 3.1.1 in the Introduction to the NAG Library CL Interface).

8: $\mathbf{maxcal}$ – Integer Input

On entry: the maximum number of function evaluations to be allowed.

Constraint: $\mathbf{maxcal}\ge 1$.

9: $\mathbf{comm}$ – Nag_Comm *

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

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, $\mathbf{maxcal}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{maxcal}\ge 1$.

On entry, $\mathbf{n}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{n}\ge 1$.

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.

NE_REAL

On entry, $\mathbf{tolf}=0.0$ and $\mathbf{tolx}=⟨\mathit{\text{value}}⟩$.
Constraint: if $\mathbf{tolf}=0.0$ then $\mathbf{tolx}$ is greater than or equal to the machine precision.

On entry, $\mathbf{tolx}=0.0$ and $\mathbf{tolf}=⟨\mathit{\text{value}}⟩$.
Constraint: if $\mathbf{tolx}=0.0$ then $\mathbf{tolf}$ is greater than or equal to the machine precision.

NE_REAL_2

On entry, $\mathbf{tolf}=⟨\mathit{\text{value}}⟩$ and $\mathbf{tolx}=⟨\mathit{\text{value}}⟩$.
Constraint: if $\mathbf{tolf}\ne 0.0$ and $\mathbf{tolx}\ne 0.0$ then both should be greater than or equal to the machine precision.

NW_TOO_MANY_FEVALS

maxcal function evaluations have been completed without any other termination test passing. Check the coding of funct before increasing the value of maxcal.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results