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fix: hadnle zeros at the endpoints in BisectionMethod
(#1640)
* 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>
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@ -23,7 +23,7 @@ const findRoot = (a, b, func, numberOfIterations) => {
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// Bolzano theorem
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const hasRoot = (a, b, func) => {
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return func(a) * func(b) < 0
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return func(a) * func(b) <= 0
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}
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if (hasRoot(a, b, func) === false) {
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throw Error(
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@ -45,10 +45,9 @@ const findRoot = (a, b, func, numberOfIterations) => {
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const prod2 = fm * func(b)
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// Depending on the sign of the products above, decide which position will m fill (a's or b's)
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if (prod1 > 0 && prod2 < 0) return findRoot(m, b, func, --numberOfIterations)
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else if (prod1 < 0 && prod2 > 0)
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return findRoot(a, m, func, --numberOfIterations)
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else throw Error('Unexpected behavior')
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if (prod2 <= 0) return findRoot(m, b, func, --numberOfIterations)
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return findRoot(a, m, func, --numberOfIterations)
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}
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export { findRoot }
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@ -1,14 +1,7 @@
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import { findRoot } from '../BisectionMethod'
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test('Equation f(x) = x^2 - 3*x + 2 = 0, has root x = 1 in [a, b] = [0, 1.5]', () => {
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const root = findRoot(
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0,
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1.5,
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(x) => {
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return Math.pow(x, 2) - 3 * x + 2
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},
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8
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)
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const root = findRoot(0, 1.5, (x) => x ** 2 - 3 * x + 2, 8)
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expect(root).toBe(0.9990234375)
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})
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@ -35,3 +28,12 @@ test('Equation f(x) = sqrt(x) + e^(2*x) - 8*x = 0, has root x = 0.93945851 in [a
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)
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expect(Number(Number(root).toPrecision(8))).toBe(0.93945851)
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})
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test('Equation f(x) = x^3 = 0, has root x = 0.0 in [a, b] = [-1.0, 1.0]', () => {
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const root = findRoot(-1.0, 1.0, (x) => x ** 3, 32)
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expect(root).toBeCloseTo(0.0, 5)
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})
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test('Throws an error when function does not change sign', () => {
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expect(() => findRoot(-1.0, 1.0, (x) => x ** 2, 10)).toThrowError()
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})
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