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preview", + "test": "jest", + "coverage": "jest --coverage" }, "devDependencies": { + "@babel/core": "^7.18.6", + "@babel/preset-env": "^7.18.6", + "@babel/preset-typescript": "^7.18.6", "@types/dat.gui": "^0.7.7", + "@types/jest": "^28.1.3", "@types/three": "^0.139.0", - "tailwindcss": "^3.0.24", - "typescript": "^4.5.4", + "babel-jest": "^28.1.1", + "jest": "^28.1.1", + "typescript": "^4.7.4", "vite": "^2.9.5" }, "dependencies": { "dat.gui": "^0.7.9", + "mathjs": "^10.6.4", "three": "^0.139.2" } } diff --git a/src/simulation/Integrators.ts b/src/simulation/Integrators.ts new file mode 100644 index 0000000000000000000000000000000000000000..33324467dd2eec4b1cd375ed47623cb68e7dd748 --- /dev/null +++ b/src/simulation/Integrators.ts @@ -0,0 +1,23 @@ +export function Euler(x: Array<number>, h: number, f: (x: Array<number>) => Array<number>): Array<number> { + let y = f(x); + let x_new = x.map((_, i) => x[i] + h * y[i]); + return x_new; +} + +export function Midpoint(x: Array<number>, h: number, f: (x: Array<number>) => Array<number>): Array<number> { + let euler_step = Euler(x, h / 2, f); + let y = f(euler_step); + let x_new = x.map((_, i) => x[i] + h * y[i]); + return x_new; +} + +export function Runge_Kutta(x: Array<number>, h: number, f: (x: Array<number>) => Array<number>): Array<number> { + let k1 = f(x); + let k2 = f(x.map((_, i) => x[i] + h / 2 * k1[i])); + let k3 = f(x.map((_, i) => x[i] + h / 2 * k2[i])); + let k4 = f(x.map((_, i) => x[i] + h * k3[i])); + let x_new = x.map((_, i) => x[i] + h / 6 * (k1[i] + 2 * k2[i] + 2 * k3[i] + k4[i])); + return x_new; +} + + diff --git a/tests/Integrators.test.ts b/tests/Integrators.test.ts new file mode 100644 index 0000000000000000000000000000000000000000..94050ccde9d37c70a73eb2b8cbdefaf29a8fe7d6 --- /dev/null +++ b/tests/Integrators.test.ts @@ -0,0 +1,115 @@ +import * as Integrator from "../src/simulation/Integrators"; +import * as math from "mathjs"; +import * as fs from "fs"; +// select a differential equation with a known solution + +// format numbers to a fixed number of decimal places +function format_number(number: number, decimal_places: number): string { + return number.toFixed(decimal_places); +} + +// find minimum for decimal places +function decimal_places(n: number): number { + let decimal_places = 0; + while (n < 1) { + n = n * 10; + decimal_places++; + } + return decimal_places+1; +} + +function min_elem(arrs: Array<Array<number>>): number { + let min = arrs[0][0]; + for (let i = 0; i < arrs.length; i++) { + for (let j = 0; j < arrs[i].length; j++) { + if (arrs[i][j] < min) { + min = arrs[i][j]; + } + } + } + return min; +} + +function write_table(result: Array<number>, exact: Array<number>, error: Array<number>, title: string, bins: number, decimal_places: number): void { + let table = [["x", "exact", "result", "error"]]; + for (let i = 0; i < result.length; i++) { + table.push([format_number(i / bins, decimal_places), format_number(exact[i], decimal_places), format_number(result[i], decimal_places), format_number(error[i], decimal_places)]); + } + + let table_string = ""; + for (let i = 0; i < table.length; i++) { + for (let j = 0; j < table[i].length; j++) { + table_string += table[i][j]; + if (j < table[i].length - 1) table_string += " | "; + } + table_string += "\n"; + } + + fs.writeFileSync(`${title}.txt`, table_string); +} + +function calculate_error(result: Array<number>, exact: Array<number>): Array<number> { + let error: Array<number> = []; + for (let i = 0; i < result.length; i++) { + error.push(Math.abs(result[i] - exact[i])); + } + return error; +} + +describe("Integrators", () => { + + let k = 0.5 + let c = 2 + let g = (x: number): number => c * math.exp(-k * x); + let init_value = g(0); + + // find the next y value for function g(x) + let f = (x: Array<number>): Array<number> => [-k * x[0]]; + + // compare values betwenn [0, 1] + let bins = 100; + let h = 1 / bins; + + // calculate the exact solution + let exact: Array<number> = []; + for(let i = 0; i <= bins; i++) { + let x = i / bins; + let y = g(x); + exact.push(y); + } + + // evaluation loop + function eval_func(integrator: (x: Array<number>, h: number, f: (x: Array<number>) => Array<number>) => Array<number>, init: number): Array<number> { + let result: Array<number> = [init]; + let x = [init] + for(let i = 0; i < bins; i++) { + x = integrator(x, h, f); + result.push(x[0]); + } + return result; + } + + let max_error = 0.1; + + // calculate the Euler solution + it("Euler", () => { + let result = eval_func(Integrator.Euler, init_value); + let error = calculate_error(result, exact); + error.forEach((e, i) => { expect(e).toBeLessThan(max_error); }); + write_table(result, exact, error, "Euler", bins, 5); + }); + + it("Midpoint", () => { + let result = eval_func(Integrator.Midpoint, init_value); + let error = calculate_error(result, exact); + error.forEach((e, i) => { expect(e).toBeLessThan(max_error); }); + write_table(result, exact, error, "Midpoint", bins, 10); + }); + + it("Runge-Kutta", () => { + let result = eval_func(Integrator.Runge_Kutta, init_value); + let error = calculate_error(result, exact); + error.forEach((e, i) => { expect(e).toBeLessThan(max_error); }); + write_table(result, exact, error, "Runge-Kutta", bins, 20); + }); +}); \ No newline at end of file diff --git a/tsconfig.json b/tsconfig.json deleted file mode 100644 index fbd022532d3096ebfe0740835100c45cbe246b9c..0000000000000000000000000000000000000000 --- a/tsconfig.json +++ /dev/null @@ -1,20 +0,0 @@ -{ - "compilerOptions": { - "target": "ESNext", - "useDefineForClassFields": true, - "module": "ESNext", - "lib": ["ESNext", "DOM"], - "moduleResolution": "Node", - "strict": true, - "sourceMap": true, - "resolveJsonModule": true, - "isolatedModules": true, - "esModuleInterop": true, - "noEmit": true, - "noUnusedLocals": true, - "noUnusedParameters": true, - "noImplicitReturns": true, - "skipLibCheck": true - }, - "include": ["src"] -}