NAG FL Interface
e04hcf (check_​deriv)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{n}$ – Integer Input

On entry: the number $n$ of independent variables in the objective function.

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

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

funct must evaluate the function and its first derivatives at a given point. (The minimization routines mentioned in Section 3 gives you the option of resetting arguments of funct to cause the minimization process to terminate immediately. e04hcf will also terminate immediately, without finishing the checking process, if the argument in question is reset.)

The specification of funct is:

Fortran Interface

Subroutine funct ( iflag, n, xc, fc, gc, iw, liw, w, lw) Integer, Intent (In) :: n, liw, lw Integer, Intent (Inout) :: iflag, iw(liw) Real (Kind=nag_wp), Intent (In) :: xc(n) Real (Kind=nag_wp), Intent (Inout) :: w(lw) Real (Kind=nag_wp), Intent (Out) :: fc, gc(n)

C Header Interface

void  funct_ (Integer *iflag, const Integer *n, const double xc[], double *fc, double gc[], Integer iw[], const Integer *liw, double w[], const Integer *lw)

C++ Header Interface

#include <nag.h> extern "C" { void  funct_ (Integer &iflag, const Integer &n, const double xc[], double &fc, double gc[], Integer iw[], const Integer &liw, double w[], const Integer &lw) }

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

On entry: will be set to $2$.

On exit: if you reset iflag to a negative number in funct and return control to e04hcf, e04hcf will terminate immediately with ifail set to your setting of iflag.

2: $\mathbf{n}$ – Integer Input

On entry: the number $n$ of variables.

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

On entry: the point $x$ at which $F$ and its derivatives are required.

4: $\mathbf{fc}$ – Real (Kind=nag_wp) Output

On exit: unless funct resets iflag, fc must be set to the value of the function $F$ at the current point $x$.

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

On exit: unless funct resets iflag, $\mathbf{gc}\left(\mathit{j}\right)$ must be set to the value of the first derivative $\frac{\partial F}{\partial x_{\mathit{j}}}$ at the point $x$, for $\mathit{j}=1,2,\dots ,n$.

6: $\mathbf{iw}\left(\mathbf{liw}\right)$ – Integer array Workspace

7: $\mathbf{liw}$ – Integer Input

8: $\mathbf{w}\left(\mathbf{lw}\right)$ – Real (Kind=nag_wp) array Workspace

9: $\mathbf{lw}$ – Integer Input

These arguments are present so that funct will be of the form required by the minimization routines mentioned in Section 3. funct is called with e04hcf's arguments iw, liw, w, lw as these arguments. If the advice given in the minimization routine documents is being followed, you will have no reason to examine or change any elements of iw or w. In any case, funct must not change the first $3\times \mathbf{n}$ elements of w.

funct must either be a module subprogram USEd by, or declared as EXTERNAL in, the (sub)program from which e04hcf is called. Arguments denoted as Input must not be changed by this procedure.

Note: funct should not return floating-point NaN (Not a Number) or infinity values, since these are not handled by e04hcf. If your code inadvertently does return any NaNs or infinities, e04hcf is likely to produce unexpected results.

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

On entry: $\mathbf{x}\left(\mathit{j}\right)$, for $\mathit{j}=1,2,\dots ,n$, must be set to the coordinates of a suitable point at which to check the derivatives calculated by funct. ‘Obvious’ settings, such as $0.0$ or $1.0$, should not be used since, at such particular points, incorrect terms may take correct values (particularly zero), so that errors could go undetected. Similarly, it is preferable that no two elements of x should be the same.

4: $\mathbf{f}$ – Real (Kind=nag_wp) Output

On exit: unless you set iflag negative in the first call of funct, f contains the value of the objective function $F\left(x\right)$ at the point given by you in x.

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

On exit: unless you set iflag negative in the first call of funct, $\mathbf{g}\left(\mathit{j}\right)$ contains the value of the derivative $\frac{\partial F}{\partial x_{\mathit{j}}}$ at the point given in x, as calculated by funct, for $\mathit{j}=1,2,\dots ,n$.

6: $\mathbf{iw}\left(\mathbf{liw}\right)$ – Integer array Workspace

7: $\mathbf{liw}$ – Integer Input

This array is in the argument list so that it can be used by other library routines for passing integer quantities to funct. It is not examined or changed by e04hcf. Generally, you must provide an array iw but are advised not to use it.

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

8: $\mathbf{w}\left(\mathbf{lw}\right)$ – Real (Kind=nag_wp) array Workspace

9: $\mathbf{lw}$ – Integer Input

On entry: the dimension of the array w as declared in the (sub)program from which e04hcf is called.

Constraint: $\mathbf{lw}\ge 3\times \mathbf{n}$.

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

On entry: ifail must be set to $0$, $-1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.

A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $-1$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $-1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $-1$ is recommended since useful values can be provided in some output arguments even when $\mathbf{ifail}\ne \mathbf{0}$ on exit. When the value $-\mathbf{1}$ 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, $\mathbf{liw}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{liw}\ge 1$.

On entry, $\mathbf{lw}=〈\mathit{\text{value}}〉$ and $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{lw}\ge 3\times \mathbf{n}$.

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

$\mathbf{ifail}=2$

Large errors were found in the derivatives of $F$ computed by funct.

$\mathbf{ifail}<0$

User requested termination by setting iflag negative in funct.

$\mathbf{ifail}=-99$

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