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Commit 1cd3b86

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ggkogkouggkogkougithub-actions
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merge: Created midpoint integration numerical method (#822)
* Created midpoint integration numerical method * Auto-update DIRECTORY.md * Added resources link * Fixed doxumentation * Fixed spelling error Co-authored-by: ggkogkou <ggkogkou@ggkogkou.gr> Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
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‎DIRECTORY.md‎

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* [MatrixExponentiationRecursive](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/MatrixExponentiationRecursive.js)
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* [MatrixMultiplication](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/MatrixMultiplication.js)
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* [MeanSquareError](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/MeanSquareError.js)
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* [MidpointIntegration](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/MidpointIntegration.js)
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* [ModularBinaryExponentiationRecursive](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/ModularBinaryExponentiationRecursive.js)
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* [NumberOfDigits](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/NumberOfDigits.js)
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* [Palindrome](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/Palindrome.js)

‎Maths/MidpointIntegration.js‎

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/**
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*
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* @title Midpoint rule for definite integral evaluation
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* @author [ggkogkou](https://github.com/ggkogkou)
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* @brief Calculate definite integrals with midpoint method
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*
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* @details The idea is to split the interval in a 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 * {f(x0+h/2) + f(x1+h/2) + ... + f(xN-1+h/2)}
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*
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* N must be > 0 and a<b. By increasing N, we also increase precision
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*
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* [More info link](https://tutorial.math.lamar.edu/classes/calcii/approximatingdefintegrals.aspx)
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*
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*/
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function integralEvaluation (N, a, b, func) {
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// Check if all restrictions are satisfied for the given N, a, b
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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 (N <= 0) { throw Error('N has to be >= 2') } // check if N > 0
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if (a > b) { throw Error('a must be less or equal than b') } // Check if a < b
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if (a === b) return 0 // If a === b integral is zero
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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+h/2) + f(x1+h/2) + ... + f(xN-1+h/2)}
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let temp
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for (let i = 0; i < N; i++) {
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temp = func(xi + h / 2)
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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
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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 does not 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 '../MidpointIntegration'
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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(10000, 1, 3, (x) => { return Math.sqrt(x) })
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expect(Number(result.toPrecision(6))).toBe(2.79743)
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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(10000, 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(20000, 5, 12, (x) => { return Math.log(x) + Math.PI * Math.pow(x, 3) })
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expect(Number(result.toPrecision(10))).toBe(15809.91415)
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})

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