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* chore: Switch to Node 20 + Vitest * chore: migrate to vitest mock functions * chore: code style (switch to prettier) * test: re-enable long-running test Seems the switch to Node 20 and Vitest has vastly improved the code's and / or the test's runtime! see #1193 * chore: code style * chore: fix failing tests * Updated Documentation in README.md * Update contribution guidelines to state usage of Prettier * fix: set prettier printWidth back to 80 * chore: apply updated code style automatically * fix: set prettier line endings to lf again * chore: apply updated code style automatically --------- Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com> Co-authored-by: Lars Müller <34514239+appgurueu@users.noreply.github.com>
79 lines
2.2 KiB
JavaScript
79 lines
2.2 KiB
JavaScript
/*
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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)) {
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throw new TypeError('Expected integer N and finite a, b')
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}
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if (!isNEven) {
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throw Error('N is not an even number')
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}
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if (N <= 0) {
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throw Error('N has to be >= 2')
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}
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// Check if a < b
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if (a > b) {
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throw Error('a must be less or equal than b')
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}
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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 = pointsArray.reduce((acc, currValue) => acc + currValue, 0)
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result *= temp
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if (Number.isNaN(result)) {
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throw Error(
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"Result is NaN. The input interval doesn't belong to the functions domain"
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)
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}
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return result
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}
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export { integralEvaluation }
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