Initial and only commit :)

Author: FlyN-Nick

index.ts

@@ -0,0 +1,142 @@
+// Calculus Bisection Class Project 
+// Author: Nicholas Assaderaghi (FlyN Nick)
+// Why did I write this in TypeScript: I felt like it :) 
+
+/**
+ * Bisection function. 
+ * Finds the root of a function within given range.
+ * 
+ * Things that may cause this to be unsuccessfull/error:
+ * #1: Root is not within given range. 
+ * #2: Function changes signs more than once within given range.
+ * #3: The given minimum is greater than the given maximum. 
+ * #4: There are x within given range where f(x) is undefined. 
+ * 
+ * @param {(x: number) => any} func - function you want to find the root of. 
+ * @param {number} givenMin - min of given range.
+ * @param {number} givenMax - max of given range.
+ * @param {bool} annoyingConsoleLogs - (optional) really annoying console log ever iteration. 
+ * @param {number} maxIter - (optional) max number of iterations 
+ */
+function bisection(func: (x: number) => number, givenMin: number, givenMax: number, maxIter=100, annoyingConsoleLogs=false): number | [number, number] | "ERROR"
+{
+ let posSlope = true; 
+ let min = givenMin;
+ let max = givenMax;
+ let iter = 0; 
+ 
+ console.log("---------------------------------------------------------------");
+
+ if (givenMin > givenMax) 
+ {
+ console.log("You seem to have mixed the min and max...");
+ return "ERROR"; 
+ }
+ else if (givenMin == givenMax)
+ {
+ console.log("The min and max given were the same...");
+ return "ERROR"; 
+ }
+
+ if (func(min) > func(min+max/2)) { posSlope = false; }
+
+ while (iter != maxIter) 
+ {
+ iter++; 
+ let guess = (min+max)/2;
+
+ if ((func(guess) < 0 && posSlope) || (func(guess) > 0 && !posSlope)) 
+ {
+ if (guess == min)
+ { 
+ console.log(`Stopped at iteration #${iter}`);
+ console.log(`Root not found.\nRange: (${min}, ${max}).`); 
+ return [min, max]; 
+ }
+ min = guess; 
+ }
+ else if ((func(guess) > 0 && posSlope) || (func(guess) < 0 && !posSlope)) 
+ { 
+ if (guess == max) 
+ { 
+ console.log(`Stopped at iteration #${iter}`);
+ console.log(`Root not found.\nRange: (${min}, ${max}).`); 
+ return [min, max]; 
+ }
+ max = guess; 
+ }
+ else 
+ {
+ console.log(`Root: ${guess}.\nIterations it took: ${iter}.`);
+ return guess;
+ }
+ if (annoyingConsoleLogs) 
+ { 
+ console.log(`Iteration #${iter}:\n\tCurrent range: (${min}, ${max})`); 
+ }
+ }
+ 
+ console.log(`Root not found (maximum iterations reached).\nRange: (${min}, ${max}).`);
+
+ console.log("Remember, this algorithm will only work if:\n\t#1: The root is within the range.\n\t#2: The function changes sign once within the interval.");
+
+ return [min, max];
+}
+
+/** 
+ * Just testing if everything generally works.
+ * This is not an in-depth test (does not test all error scenarios). 
+ */
+function testBisectionFunction() 
+{
+ console.log("TESTING BISECTION FUNCTION!");
+ /** Test linear function: (2x -19). */
+ const linFunc = (x: number) => { return 2*x-19; }
+
+ /** Test polynomial function: (x^2 + x - 5). */
+ const polyFunc = (x: number) => { return x**2+x-5; } 
+
+ /** First test trigonometric function: sin(1/x). */
+ const trigFuncOne = (x: number) => { return Math.sin(1/x); }
+
+ /** Second test trigonometric function: sin(x)/x. */
+ const trigFuncTwo = (x: number) => { return Math.sin(x)/x; }
+
+ const returnedVals: (number | [number, number] | "ERROR")[] = 
+ [
+ bisection(linFunc, 100, -100),
+ bisection(linFunc, -100, 100),
+ bisection(polyFunc, 0, 21),
+ bisection(trigFuncOne, 0.212, 0.637, 100000),
+ bisection(trigFuncTwo, 0.1, 4.25, 1000/*, true*/) // those console logs really are annoying... 
+ ]
+
+ console.log("---------------------------------------------------------------");
+ console.log(`\nReturned values from bisection function:\n[`);
+
+ // should I have just used a regular for loop: yes. 
+ let len = returnedVals.length; 
+ let i = 0;
+ for (const returnedVal of returnedVals)
+ {
+ i++;
+ let toPrint;
+ switch (typeof returnedVal)
+ {
+ case 'string':
+ toPrint = `\t"${returnedVal}"`;
+ break;
+ case 'number': 
+ toPrint = `\t${returnedVal}`;
+ break;
+ default:
+ toPrint = `\t[${returnedVal[0]}, ${returnedVal[1]}]`;
+ }
+ if (i != len) { toPrint += ','; }
+ console.log(toPrint);
+ }
+
+ console.log(`]`);
+}
+
+testBisectionFunction();

tsconfig.json

@@ -0,0 +1,17 @@
+{
+ "compilerOptions": 
+ {
+ "target": "es6",
+ "lib": ["esnext", "dom"],
+ "module": "commonjs",
+ "moduleResolution": "node",
+ "strict": true,
+ "jsx": "react",
+ "allowJs": false,
+ "sourceMap": true,
+ "inlineSources": true,
+ "types": ["node"],
+ "allowSyntheticDefaultImports": true,
+ "experimentalDecorators": true
+ }
+}