emmy.numerical.roots.bisect — org.mentat/emmy 0.32.0

This namespace contains implementations of a number of methods for root-finding on real-valued functions of one argument.

NOTE: This namespace is not yet stable: Expect these functions to change as new root-finding methods are added.

*bisect-break* clj/s

Controls the default behavior of bisect's search. See bisect's docstring for more info.

all-methods clj/s

Set of all methods allowed as :method options to bisect.

bisect clj/s

(bisect f a b)

(bisect f
        a
        b
        {:keys [eps maxiter maxfun callback]
         :or {eps u/machine-epsilon maxiter 1000 callback (constantly nil)}
         :as opts})

Given some function f and (inclusive) lower and upper bounds a and b on the domain, attempts to find a root of f in that range, i.e., a value x for which (f x) is equal to 0.

Supports the following optional keyword arguments:

:method: can be :bisection, :secant or :mixed. See the Methods section below for a description of each. Defaults to :mixed

:eps: defaults to [[emmy.value/machine-epsilon]].

:callback: if supplied, the supplied f will be invoked at each intermediate point with the iteration count and the values of x and f(x) at each search step.

:maxiter: maximum number of iterations allowed for the minimizer. Defaults to 1000.

:maxfun maximum number of times the function can be evaluated before exiting. Defaults to (inc maxiter).

:n-break defaults to the dynamically bindable *bisect-break* (which defaults to 60). Bind *bisect-break* to modify the behavior of the :mixed method (see below) when it's used inside a nested routine. Ignored if method is not :mixed.

Methods

• :bisection causes bisect to use the Bisection method; at each iteration, the midpoint between the bounds is chosen as the next point.

• :secant uses the Secant method; each candidate point is chosen by taking the root of a line drawn between the two endpoints [a (f a)] and [b (f b)]. This method is most useful when the bounds are close to the root.

• :mixed uses :bisection up until :n-break iterations and :secant beyond. This can be useful for narrowing down a very wide range close to the root, and then switching in to a faster search method.

search-for-roots clj/s

(search-for-roots f a b dx)

(search-for-roots f a b dx opts)

Given a smooth function f and (inclusive) lower and upper bounds a and b on the domain, attempts to find all roots of f, i.e., a vector of values x_n such that each (f x_n) is equal to 0.

search-for-roots first attempts to cut the (inclusive) range [a, b] into pieces at most dx wide; then bisect is used to search each segment for a root.

All opts supplied are passed on to bisect.