naginterfaces.library.roots.contfn_​cntin

naginterfaces.library.roots.contfn_cntin(x, f, eps=1.1102230246251565e-13, eta=0.0, nfmax=1000, data=None)[source]

contfn_cntin attempts to locate a zero of a continuous function using a continuation method based on a secant iteration.

For full information please refer to the NAG Library document for c05aw

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/c05/c05awf.html

Parameters
xfloat

An initial approximation to the zero.

fcallable retval = f(x, data=None)

must evaluate the function whose zero is to be determined.

Parameters
xfloat

The point at which the function must be evaluated.

dataarbitrary, optional, modifiable in place

User-communication data for callback functions.

Returns
retvalfloat

The value of evaluated at .

epsfloat, optional

An absolute tolerance to control the accuracy to which the zero is determined. In general, the smaller the value of the more accurate will be as an approximation to . Indeed, for very small positive values of , it is likely that the final approximation will satisfy . You are advised to call the function with more than one value for to check the accuracy obtained.

etafloat, optional

A value such that if , is accepted as the zero. may be specified as (see Accuracy).

nfmaxint, optional

The maximum permitted number of calls to from contfn_cntin. If is inexpensive to evaluate, should be given a large value (say ).

dataarbitrary, optional

User-communication data for callback functions.

Returns
xfloat

The final approximation to the zero, unless = 1 or 2, in which case it contains no useful information.

Raises
NagValueError
(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

Internal scale factor invalid for this problem. Consider using contfn_cntin_rcomm() instead and setting .

(errno )

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

(errno )

More than calls have been made to .

Notes

contfn_cntin attempts to obtain an approximation to a simple zero of the function given an initial approximation to . The zero is found by a call to contfn_cntin_rcomm() whose specification should be consulted for details of the method used.

The approximation to the zero is determined so that at least one of the following criteria is satisfied:

  1. ,

  2. .