NAG Library Routine Document

c05ayf  (contfn_brent)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{a}$ – Real (Kind=nag_wp)Input

On entry: $a$, the lower bound of the interval.

2:     $\mathbf{b}$ – Real (Kind=nag_wp)Input

On entry: $b$, the upper bound of the interval.

Constraint: $\mathbf{b}\ne \mathbf{a}$.

3:     $\mathbf{eps}$ – Real (Kind=nag_wp)Input

On entry: the termination tolerance on $x$ (see Section 3).

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

4:     $\mathbf{eta}$ – Real (Kind=nag_wp)Input

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

5:     $\mathbf{f}$ – 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:

Fortran Interface

Function f ( x, iuser, ruser) Real (Kind=nag_wp) :: f Integer, Intent (Inout) :: iuser(*) Real (Kind=nag_wp), Intent (In) :: x Real (Kind=nag_wp), Intent (Inout) :: ruser(*)

C Header Interface

#include nagmk26.h double  f ( const double *x, Integer iuser[], double ruser[])

1:     $\mathbf{x}$ – Real (Kind=nag_wp)Input

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

2:     $\mathbf{iuser}\left(*\right)$ – Integer arrayUser Workspace

3:     $\mathbf{ruser}\left(*\right)$ – Real (Kind=nag_wp) arrayUser Workspace

f is called with the arguments iuser and ruser as supplied to c05ayf. You should use the arrays iuser and ruser to supply information to f.

f must either be a module subprogram USEd by, or declared as EXTERNAL in, the (sub)program from which c05ayf is called. Arguments denoted as Input must not be changed by this procedure.

Note: f should not return floating-point NaN (Not a Number) or infinity values, since these are not handled by c05ayf. If your code inadvertently does return any NaNs or infinities, c05ayf is likely to produce unexpected results.

6:     $\mathbf{x}$ – Real (Kind=nag_wp)Output

On exit: if $\mathbf{ifail}=\mathbf{0}$ or $\mathbf{2}$, x is the final approximation to the zero. If $\mathbf{ifail}=\mathbf{3}$, x is likely to be a pole of $f\left(x\right)$. Otherwise, x contains no useful information.

7:     $\mathbf{iuser}\left(*\right)$ – Integer arrayUser Workspace

8:     $\mathbf{ruser}\left(*\right)$ – Real (Kind=nag_wp) arrayUser Workspace

iuser and ruser are not used by c05ayf, but are passed directly to f and may be used to pass information to this routine.

9:     $\mathbf{ifail}$ – IntegerInput/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 3.4 in How to Use the NAG Library and its Documentation 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, $\mathbf{a}=〈\mathit{\text{value}}〉$ and $\mathbf{b}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{a}\ne \mathbf{b}$.

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

On entry, $\mathbf{f}\left(\mathbf{a}\right)$ and $\mathbf{f}\left(\mathbf{b}\right)$ have the same sign with neither equalling $0.0$: $\mathbf{f}\left(\mathbf{a}\right)=〈\mathit{\text{value}}〉$ and $\mathbf{f}\left(\mathbf{b}\right)=〈\mathit{\text{value}}〉$.

$\mathbf{ifail}=2$

No further improvement in the solution is possible. eps is too small: $\mathbf{eps}=〈\mathit{\text{value}}〉$. The final value of x returned is an accurate approximation to the zero.

$\mathbf{ifail}=3$

The function values in the interval $\left[\mathbf{a},\mathbf{b}\right]$ might contain a pole rather than a zero. Reducing eps may help in distinguishing between a pole and a zero.

$\mathbf{ifail}=-99$

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

See Section 3.9 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-399$

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

See Section 3.8 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (c05ayfe.f90)

10.2

Program Data

10.3

Program Results

Program Results (c05ayfe.r)