diff --git a/DIRECTORY.md b/DIRECTORY.md index c61257f942..c1bdd15ed8 100644 --- a/DIRECTORY.md +++ b/DIRECTORY.md @@ -145,6 +145,7 @@ * [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) diff --git a/Maths/BisectionMethod.js b/Maths/BisectionMethod.js new file mode 100644 index 0000000000..79254ddc87 --- /dev/null +++ b/Maths/BisectionMethod.js @@ -0,0 +1,46 @@ +/** + * + * @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 } diff --git a/Maths/test/BisectionMethod.test.js b/Maths/test/BisectionMethod.test.js new file mode 100644 index 0000000000..9c34a79dd2 --- /dev/null +++ b/Maths/test/BisectionMethod.test.js @@ -0,0 +1,16 @@ +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) +})