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Commit 7722870

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ggkogkouggkogkougithub-actionsraklaptudirm
authored
merge: Created composite Simpson's integration method. Tests included. (#819)
* Created composite Simpson's integration method.Tests included * Minor corrections * Auto-update DIRECTORY.md * Styled with standard.js * chore: remove blank line * chore: remove blank line Co-authored-by: ggkogkou <ggkogkou@ggkogkou.gr> Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com> Co-authored-by: Rak Laptudirm <raklaptudirm@gmail.com>
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‎DIRECTORY.md‎

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* [ReverseNumber](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/ReverseNumber.js)
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* [ReversePolishNotation](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/ReversePolishNotation.js)
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* [SieveOfEratosthenes](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/SieveOfEratosthenes.js)
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* [SimpsonIntegration](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/SimpsonIntegration.js)
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* [Softmax](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/Softmax.js)
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* [SquareRoot](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/SquareRoot.js)
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* [SumOfDigits](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/SumOfDigits.js)

‎Maths/SimpsonIntegration.js‎

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/*
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*
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* @file
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* @title Composite Simpson's rule for definite integral evaluation
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* @author: [ggkogkou](https://github.com/ggkogkou)
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* @brief Calculate definite integrals using composite Simpson's numerical method
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*
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* @details The idea is to split the interval in an EVEN number N of intervals and use as interpolation points the xi
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* for which it applies that xi = x0 + i*h, where h is a step defined as h = (b-a)/N where a and b are the
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* first and last points of the interval of the integration [a, b].
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*
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* We create a table of the xi and their corresponding f(xi) values and we evaluate the integral by the formula:
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* I = h/3 * {f(x0) + 4*f(x1) + 2*f(x2) + ... + 2*f(xN-2) + 4*f(xN-1) + f(xN)}
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*
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* That means that the first and last indexed i f(xi) are multiplied by 1,
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* the odd indexed f(xi) by 4 and the even by 2.
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*
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* N must be even number and a<b. By increasing N, we also increase precision
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*
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* More info: [Wikipedia link](https://en.wikipedia.org/wiki/Simpson%27s_rule#Composite_Simpson's_rule)
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*
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*/
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function integralEvaluation (N, a, b, func) {
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// Check if N is an even integer
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let isNEven = true
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if (N % 2 !== 0) isNEven = false
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if (!Number.isInteger(N) || Number.isNaN(a) || Number.isNaN(b)) { throw new TypeError('Expected integer N and finite a, b') }
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if (!isNEven) { throw Error('N is not an even number') }
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if (N <= 0) { throw Error('N has to be >= 2') }
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// Check if a < b
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if (a > b) { throw Error('a must be less or equal than b') }
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if (a === b) return 0
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// Calculate the step h
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const h = (b - a) / N
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// Find interpolation points
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let xi = a // initialize xi = x0
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const pointsArray = []
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// Find the sum {f(x0) + 4*f(x1) + 2*f(x2) + ... + 2*f(xN-2) + 4*f(xN-1) + f(xN)}
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let temp
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for (let i = 0; i < N + 1; i++) {
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if (i === 0 || i === N) temp = func(xi)
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else if (i % 2 === 0) temp = 2 * func(xi)
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else temp = 4 * func(xi)
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pointsArray.push(temp)
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xi += h
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}
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// Calculate the integral
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let result = h / 3
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temp = 0
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for (let i = 0; i < pointsArray.length; i++) temp += pointsArray[i]
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result *= temp
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if (Number.isNaN(result)) { throw Error('Result is NaN. The input interval doesnt belong to the functions domain') }
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return result
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}
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export { integralEvaluation }
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import { integralEvaluation } from '../SimpsonIntegration'
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test('Should return the integral of f(x) = sqrt(x) in [1, 3] to be equal 2.797434', () => {
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const result = integralEvaluation(16, 1, 3, (x) => { return Math.sqrt(x) })
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expect(Number(result.toPrecision(7))).toBe(2.797434)
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})
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test('Should return the integral of f(x) = sqrt(x) + x^2 in [1, 3] to be equal 11.46410161', () => {
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const result = integralEvaluation(64, 1, 3, (x) => { return Math.sqrt(x) + Math.pow(x, 2) })
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expect(Number(result.toPrecision(10))).toBe(11.46410161)
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})
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test('Should return the integral of f(x) = log(x) + Pi*x^3 in [5, 12] to be equal 15809.9141543', () => {
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const result = integralEvaluation(128, 5, 12, (x) => { return Math.log(x) + Math.PI * Math.pow(x, 3) })
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expect(Number(result.toPrecision(12))).toBe(15809.9141543)
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})

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