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86d333ee94
* 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>
64 lines
1.9 KiB
JavaScript
64 lines
1.9 KiB
JavaScript
/**
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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)) {
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throw new TypeError('Expected integer N and finite a, b')
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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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} // check if N > 0
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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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} // 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 = 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 does not 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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