naginterfaces.library.roots.contfn_brent_interval(x, f, h=0.1, eps=1.1102230246251565e-13, eta=0.0, data=None)[source]

contfn_brent_interval locates a simple zero of a continuous function from a given starting value. It uses a binary search to locate an interval containing a zero of the function, then Brent’s method, which is a combination of nonlinear interpolation, linear extrapolation and bisection, to locate the zero precisely.

For full information please refer to the NAG Library document for c05au


An initial approximation to the zero.

fcallable retval = f(x, data=None)

must evaluate the function whose zero is to be determined.


The point at which the function must be evaluated.

dataarbitrary, optional, modifiable in place

User-communication data for callback functions.


The value of at the specified point.

hfloat, optional

A step length for use in the binary search for an interval containing the zero. The maximum interval searched is .

epsfloat, optional

The termination tolerance on (see Notes).

etafloat, optional

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

dataarbitrary, optional

User-communication data for callback functions.


If the function exits successfully or = 4, is the final approximation to the zero.

If = 3, is likely to be a pole of .

Otherwise, contains no useful information.


The lower bound of the interval resulting from the binary search


The upper bound of the interval resulting from the binary search

(errno )

On entry, .

Constraint: .

(errno )

On entry, and .

Constraint: (to machine accuracy).

(errno )

An interval containing the zero could not be found. Increasing and calling contfn_brent_interval again will increase the range searched for the zero. Decreasing and calling contfn_brent_interval again will refine the mesh used in the search for the zero.

(errno )

Solution may be a pole rather than a zero.

(errno )

The tolerance has been set too small for the problem being solved. However, the value returned is a good approximation to the zero. .


contfn_brent_interval attempts to locate an interval containing a simple zero of the function by a binary search starting from the initial point and using repeated calls to contfn_interval_rcomm(). If this search succeeds, then the zero is determined to a user-specified accuracy by a call to contfn_brent(). The specifications of functions contfn_interval_rcomm() and contfn_brent() should be consulted for details of the methods used.

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

  1. ,

  2. .


Brent, R P, 1973, Algorithms for Minimization Without Derivatives, Prentice–Hall