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fix: hadnle zeros at the endpoints in BisectionMethod (#1640)

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* fix: hadnle zeros at the endpoints

* style: use simpler syntax express polynomials

Co-authored-by: appgurueu <34514239+appgurueu@users.noreply.github.com>

---------

Co-authored-by: appgurueu <34514239+appgurueu@users.noreply.github.com>
This commit is contained in:
Piotr Idzik
2024-04-03 17:18:45 +02:00
committed by GitHub
parent 702840b4c8
commit 34a663aca7
2 changed files with 14 additions and 13 deletions
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9
Maths/BisectionMethod.js
View File

@ -23,7 +23,7 @@ const findRoot = (a, b, func, numberOfIterations) => {
// Bolzano theorem // Bolzano theorem
const hasRoot = (a, b, func) => { const hasRoot = (a, b, func) => {
return func(a) * func(b) < 0 return func(a) * func(b) <= 0
} }
if (hasRoot(a, b, func) === false) { if (hasRoot(a, b, func) === false) {
throw Error( throw Error(
@ -45,10 +45,9 @@ const findRoot = (a, b, func, numberOfIterations) => {
const prod2 = fm * func(b) const prod2 = fm * func(b)
// Depending on the sign of the products above, decide which position will m fill (a's or b's) // 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) if (prod2 <= 0) return findRoot(m, b, func, --numberOfIterations)
else if (prod1 < 0 && prod2 > 0)
return findRoot(a, m, func, --numberOfIterations) return findRoot(a, m, func, --numberOfIterations)
else throw Error('Unexpected behavior')
} }
export { findRoot } export { findRoot }

18
Maths/test/BisectionMethod.test.js
View File

@ -1,14 +1,7 @@
import { findRoot } from '../BisectionMethod' import { findRoot } from '../BisectionMethod'
test('Equation f(x) = x^2 - 3*x + 2 = 0, has root x = 1 in [a, b] = [0, 1.5]', () => { test('Equation f(x) = x^2 - 3*x + 2 = 0, has root x = 1 in [a, b] = [0, 1.5]', () => {
const root = findRoot( const root = findRoot(0, 1.5, (x) => x ** 2 - 3 * x + 2, 8)
0,
1.5,
(x) => {
return Math.pow(x, 2) - 3 * x + 2
},
8
)
expect(root).toBe(0.9990234375) expect(root).toBe(0.9990234375)
}) })
@ -35,3 +28,12 @@ test('Equation f(x) = sqrt(x) + e^(2*x) - 8*x = 0, has root x = 0.93945851 in [a
) )
expect(Number(Number(root).toPrecision(8))).toBe(0.93945851) expect(Number(Number(root).toPrecision(8))).toBe(0.93945851)
}) })
test('Equation f(x) = x^3 = 0, has root x = 0.0 in [a, b] = [-1.0, 1.0]', () => {
const root = findRoot(-1.0, 1.0, (x) => x ** 3, 32)
expect(root).toBeCloseTo(0.0, 5)
})
test('Throws an error when function does not change sign', () => {
expect(() => findRoot(-1.0, 1.0, (x) => x ** 2, 10)).toThrowError()
})