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/**

* @file

* @brief Find real roots of a function in a specified interval [a, b], where f(a)*f(b) < 0

* @details Given a function f(x) and an interval [a, b], where f(a) * f(b) < 0, find an approximation of the root

* by calculating the middle m = (a + b) / 2, checking f(m) * f(a) and f(m) * f(b) and then by choosing the

* negative product that means Bolzano's theorem is applied,, define the new interval with these points. Repeat until

* we get the precision we want [Wikipedia](https://en.wikipedia.org/wiki/Bisection_method)

* @author [ggkogkou](https://github.com/ggkogkou)

const findRoot = (a, b, func, numberOfIterations) => {

// Check if a given real value belongs to the function's domain

const belongsToDomain = (x, f) => {

const res = f(x)

return !Number.isNaN(res)

}

if (!belongsToDomain(a, func) || !belongsToDomain(b, func))

throw Error("Given interval is not a valid subset of function's domain")

// Bolzano theorem

const hasRoot = (a, b, func) => {

return func(a) * func(b) <= 0

}

if (hasRoot(a, b, func) === false) {

throw Error(

'Product f(a)*f(b) has to be negative so that Bolzano theorem is applied'

)

}

// Declare m

const m = (a + b) / 2

// Recursion terminal condition

if (numberOfIterations === 0) {

return m

}

// Find the products of f(m) and f(a), f(b)

const fm = func(m)

const prod1 = fm * func(a)

const prod2 = fm * func(b)

// Depending on the sign of the products above, decide which position will m fill (a's or b's)

if (prod2 <= 0) return findRoot(m, b, func, --numberOfIterations)

return findRoot(a, m, func, --numberOfIterations)

}

export { findRoot }