NAG Library Routine Document

C05AWF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     $\mathrm{X}$ – REAL (KIND=nag_wp)Input/Output

On entry: an initial approximation to the zero.

On exit: the final approximation to the zero, unless $\mathbf{IFAIL}=\mathbf{1}$, $\mathbf{2}$ or $\mathbf{5}$, in which case it contains no useful information.

2:     $\mathrm{EPS}$ – REAL (KIND=nag_wp)Input

On entry: an absolute tolerance to control the accuracy to which the zero is determined. In general, the smaller the value of EPS the more accurate X will be as an approximation to $\alpha$. Indeed, for very small positive values of EPS, it is likely that the final approximation will satisfy $\left|\mathbf{X}-\alpha \right|<\mathbf{EPS}$. You are advised to call the routine with more than one value for EPS to check the accuracy obtained.

Constraint: $\mathbf{EPS}>0.0$.

3:     $\mathrm{ETA}$ – REAL (KIND=nag_wp)Input

On entry: a value such that if $\left|f\left(x\right)\right|<\mathbf{ETA}$, $x$ is accepted as the zero. ETA may be specified as $0.0$ (see Section 7).

4:     $\mathrm{F}$ – REAL (KIND=nag_wp) FUNCTION, supplied by the user.External Procedure

F must evaluate the function $f$ whose zero is to be determined.

The specification of F is:

FUNCTION F ( X, IUSER, RUSER) REAL (KIND=nag_wp) F INTEGER  IUSER(*) REAL (KIND=nag_wp)  X, RUSER(*)

1:     $\mathrm{X}$ – REAL (KIND=nag_wp)Input

On entry: the point at which the function must be evaluated.

2:     $\mathrm{IUSER}\left(*\right)$ – INTEGER arrayUser Workspace

3:     $\mathrm{RUSER}\left(*\right)$ – REAL (KIND=nag_wp) arrayUser Workspace

F is called with the parameters IUSER and RUSER as supplied to C05AWF. You are free to use the arrays IUSER and RUSER to supply information to F as an alternative to using COMMON global variables.

F must either be a module subprogram USEd by, or declared as EXTERNAL in, the (sub)program from which C05AWF is called. Parameters denoted as Input must not be changed by this procedure.

5:     $\mathrm{NFMAX}$ – INTEGERInput

On entry: the maximum permitted number of calls to F from C05AWF. If F is inexpensive to evaluate, NFMAX should be given a large value (say $>1000$).

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

6:     $\mathrm{IUSER}\left(*\right)$ – INTEGER arrayUser Workspace

7:     $\mathrm{RUSER}\left(*\right)$ – REAL (KIND=nag_wp) arrayUser Workspace

IUSER and RUSER are not used by C05AWF, but are passed directly to F and may be used to pass information to this routine as an alternative to using COMMON global variables.

8:     $\mathrm{IFAIL}$ – INTEGERInput/Output

On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction 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 parameter, 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, $\mathbf{EPS}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{EPS}>0.0$.

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

$\mathbf{IFAIL}=2$

Internal scale factor invalid for this problem. Consider using C05AXF instead and setting SCAL.

$\mathbf{IFAIL}=3$

Either F has no zero near X or too much accuracy has been requested. Check the coding of F or increase EPS.

$\mathbf{IFAIL}=4$

More than NFMAX calls have been made to F.

NFMAX may be too small for the problem (because X is too far away from the zero), or F has no zero near X, or too much accuracy has been requested in calculating the zero. Increase NFMAX, check the coding of F or increase EPS.

$\mathbf{IFAIL}=5$

A serious error occurred in an internal call to an auxiliary routine.

$\mathbf{IFAIL}=-99$

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

See Section 3.8 in the Essential Introduction for further information.

$\mathbf{IFAIL}=-399$

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

See Section 3.7 in the Essential Introduction for further information.

$\mathbf{IFAIL}=-999$

Dynamic memory allocation failed.

See Section 3.6 in the Essential Introduction for further information.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (c05awfe.f90)

10.2  Program Data

10.3  Program Results

Program Results (c05awfe.r)