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Added bisection method #827

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Merged
raklaptudirm merged 2 commits into TheAlgorithms:master from ggkogkou:bisection_branch
Oct 31, 2021
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1 change: 1 addition & 0 deletions DIRECTORY.md
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* [BinaryConvert](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/BinaryConvert.js)
* [BinaryExponentiationIterative](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/BinaryExponentiationIterative.js)
* [BinaryExponentiationRecursive](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/BinaryExponentiationRecursive.js)
* [BisectionMethod](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/BisectionMethod.js)
* [CheckKishnamurthyNumber](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/CheckKishnamurthyNumber.js)
* [Coordinate](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/Coordinate.js)
* [CoPrimeCheck](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/CoPrimeCheck.js)
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46 changes: 46 additions & 0 deletions Maths/BisectionMethod.js
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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 (prod1 > 0 && prod2 < 0) return findRoot(m, b, func, --numberOfIterations)
else if (prod1 < 0 && prod2 > 0) return findRoot(a, m, func, --numberOfIterations)
else throw Error('Unexpected behavior')
}

export { findRoot }
16 changes: 16 additions & 0 deletions Maths/test/BisectionMethod.test.js
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import { findRoot } from '../BisectionMethod'

test('Equation f(x) = x^2 - 3*x + 2 = 0, has root x = 1 in [a, b] = [0, 1.5]', () => {
const root = findRoot(0, 1.5, (x) => { return Math.pow(x, 2) - 3 * x + 2 }, 8)
expect(root).toBe(0.9990234375)
})

test('Equation f(x) = ln(x) + sqrt(x) + π*x^2 = 0, has root x = 0.36247037 in [a, b] = [0, 10]', () => {
const root = findRoot(0, 10, (x) => { return Math.log(x) + Math.sqrt(x) + Math.PI * Math.pow(x, 2) }, 32)
expect(Number(Number(root).toPrecision(8))).toBe(0.36247037)
})

test('Equation f(x) = sqrt(x) + e^(2*x) - 8*x = 0, has root x = 0.93945851 in [a, b] = [0.5, 100]', () => {
const root = findRoot(0.5, 100, (x) => { return Math.exp(2 * x) + Math.sqrt(x) - 8 * x }, 32)
expect(Number(Number(root).toPrecision(8))).toBe(0.93945851)
})

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