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Making it a npm package.
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‎.DS_Store‎

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‎bisection.ts‎

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// Calculus Bisection Class Project
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// Author: Nicholas Assaderaghi (FlyN Nick)
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// Why did I write this in TypeScript: I felt like it :)
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/** Returns the value of an expressios given x. */
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function convert(f: ((x: number) => number) | string, x: number): number
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{
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if (typeof f == 'string') { return eval(f); }
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else { return f(x); }
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}
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/**
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* Bisection function.
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* Finds the root of a function within given range.
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*
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* Things that may cause this to be unsuccessfull/error:
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* #1: Root is not within given range.
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* #2: Function changes signs more than once within given range.
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* #3: The given minimum is greater than the given maximum.
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* #4: There are x within given range where f(x) is undefined.
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*
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* @param {(x: number) => any} f - function you want to find the root of.
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* @param {number} min - min of given range.
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* @param {number} max - max of given range.
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* @param {bool} annoyingConsoleLogs - (optional) really annoying console log ever iteration.
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* @param {number} maxIter - (optional) max number of iterations
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*/
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export function bisection(f: ((x: number) => number) | string, min: number, max: number, maxIter=100, annoyingConsoleLogs=false): number | [number, number] | 'ERROR'
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{
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console.log("---------------------------------------------------------------");
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if (min > max)
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{
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console.log("You seem to have mixed the min and max...");
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return 'ERROR';
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}
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else if (min == max && convert(f, min) == 0)
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{
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console.log("Wow, the given min and max were the same and were the root. Kinda seems like this was on purpose...");
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return min;
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}
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else if (min == max)
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{
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console.log("Wow, the given min and max were the same but were not the root. Kinda seems like this was on purpose...");
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return 'ERROR';
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}
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else if (convert(f, min) == 0)
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{
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console.log("Wow, the lower bound of the given range was the root. Kinda seems like this was on purpose...");
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return min;
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}
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else if (convert(f, max) == 0)
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{
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console.log("Wow, the upper bound of the given range was the root. Kinda seems like this was on purpose...");
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return max;
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}
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let posSlope = true;
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if (convert(f, min) > convert(f, (min+max/2))) { posSlope = false; }
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let iter = 0;
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while (iter != maxIter)
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{
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iter++;
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let guess = (min+max)/2;
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if ((convert(f, guess) < 0 && posSlope) || (convert(f, guess) > 0 && !posSlope))
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{
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if (guess == min)
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{
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console.log(`Stopped at iteration #${iter}.`);
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console.log(`Root not found.\nRange: (${min}, ${max}).`);
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return [min, max];
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}
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min = guess;
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}
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else if ((convert(f, guess) > 0 && posSlope) || (convert(f, guess) < 0 && !posSlope))
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{
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if (guess == max)
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{
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console.log(`Stopped at iteration #${iter}.`);
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console.log(`Root not found.\nRange: (${min}, ${max}).`);
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return [min, max];
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}
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max = guess;
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}
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else
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{
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console.log(`Root: ${guess}.\nIterations it took: ${iter}.`);
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return guess;
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}
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if (annoyingConsoleLogs)
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{
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console.log(`Iteration #${iter}:\n\tCurrent range: (${min}, ${max})`);
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}
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}
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console.log(`Root not found (maximum iterations reached).\nRange: (${min}, ${max}).`);
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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.`);
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return [min, max];
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}
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/**
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* Just testing if everything generally works.
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* This is not an in-depth test (does not test all error scenarios).
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*/
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export function testBisectionFunction()
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{
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console.log(`TESTING BISECTION FUNCTION!\n`);
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/** Test linear function: (2x -19). */
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const linFunc = (x: number) => { return 2*x-19; }
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/** Test linear function in string format. */
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const linFuncString = '2*x-19';
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/** Test polynomial function: (x^2 + x - 5). */
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const polyFunc = (x: number) => { return x**2+x-5; }
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/** First test trigonometric function: sin(1/x). */
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const trigFuncOne = (x: number) => { return Math.sin(1/x); }
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/** Second test trigonometric function: sin(x)/x. */
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const trigFuncTwo = (x: number) => { return Math.sin(x)/x; }
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const returnedVals: (number | [number, number] | 'ERROR')[] =
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[
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bisection(linFunc, 9.5, 9.5), // root is both given min and max
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bisection(linFunc, 5, 5), // given min and max are the same, but not the root
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bisection(linFunc, 9.5, 10), // root is the given min
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bisection(linFunc, 9, 9.5), // root is the given max
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bisection(linFunc, -100, 0), // root not within range
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bisection(linFunc, 100, -100), // upper and lower switched
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bisection(linFuncString, -100, 100),
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bisection(polyFunc, 0, 21),
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bisection(trigFuncOne, 0.212, 0.637, 100000),
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bisection(trigFuncTwo, 0.1, 4.25, 1000/*, true*/) // those console logs really are annoying...
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]
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console.log("---------------------------------------------------------------");
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console.log(`\nReturned values from bisection function:\n[`);
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// should I have just used a regular for loop: yes.
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let len = returnedVals.length;
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let i = 0;
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for (const returnedVal of returnedVals)
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{
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i++;
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let toPrint;
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switch (typeof returnedVal)
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{
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case 'string':
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toPrint = `\t${returnedVal}`;
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break;
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case 'number':
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toPrint = `\t${returnedVal}`;
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break;
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default:
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toPrint = `\t[${returnedVal[0]}, ${returnedVal[1]}]`;
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}
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if (i != len) { toPrint += ','; }
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else { toPrint += `\n]`; }
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console.log(toPrint);
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}
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}
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//testBisectionFunction();

‎index.ts‎

Lines changed: 1 addition & 169 deletions
Original file line numberDiff line numberDiff line change
@@ -1,169 +1 @@
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// Calculus Bisection Class Project
2-
// Author: Nicholas Assaderaghi (FlyN Nick)
3-
// Why did I write this in TypeScript: I felt like it :)
4-
5-
/** Returns the value of an expressios given x. */
6-
function convert(f: ((x: number) => number) | string, x: number): number
7-
{
8-
if (typeof f == 'string') { return eval(f); }
9-
else { return f(x); }
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}
11-
12-
/**
13-
* Bisection function.
14-
* Finds the root of a function within given range.
15-
*
16-
* Things that may cause this to be unsuccessfull/error:
17-
* #1: Root is not within given range.
18-
* #2: Function changes signs more than once within given range.
19-
* #3: The given minimum is greater than the given maximum.
20-
* #4: There are x within given range where f(x) is undefined.
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*
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* @param {(x: number) => any} f - function you want to find the root of.
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* @param {number} min - min of given range.
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* @param {number} max - max of given range.
25-
* @param {bool} annoyingConsoleLogs - (optional) really annoying console log ever iteration.
26-
* @param {number} maxIter - (optional) max number of iterations
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*/
28-
function bisection(f: ((x: number) => number) | string, min: number, max: number, maxIter=100, annoyingConsoleLogs=false): number | [number, number] | 'ERROR'
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{
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console.log("---------------------------------------------------------------");
31-
32-
if (min > max)
33-
{
34-
console.log("You seem to have mixed the min and max...");
35-
return 'ERROR';
36-
}
37-
else if (min == max && convert(f, min) == 0)
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{
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console.log("Wow, the given min and max were the same and were the root. Kinda seems like this was on purpose...");
40-
return min;
41-
}
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else if (min == max)
43-
{
44-
console.log("Wow, the given min and max were the same but were not the root. Kinda seems like this was on purpose...");
45-
return 'ERROR';
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}
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else if (convert(f, min) == 0)
48-
{
49-
console.log("Wow, the lower bound of the given range was the root. Kinda seems like this was on purpose...");
50-
return min;
51-
}
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else if (convert(f, max) == 0)
53-
{
54-
console.log("Wow, the upper bound of the given range was the root. Kinda seems like this was on purpose...");
55-
return max;
56-
}
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let posSlope = true;
59-
if (convert(f, min) > convert(f, (min+max/2))) { posSlope = false; }
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let iter = 0;
62-
while (iter != maxIter)
63-
{
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iter++;
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let guess = (min+max)/2;
66-
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if ((convert(f, guess) < 0 && posSlope) || (convert(f, guess) > 0 && !posSlope))
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{
69-
if (guess == min)
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{
71-
console.log(`Stopped at iteration #${iter}.`);
72-
console.log(`Root not found.\nRange: (${min}, ${max}).`);
73-
return [min, max];
74-
}
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min = guess;
76-
}
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else if ((convert(f, guess) > 0 && posSlope) || (convert(f, guess) < 0 && !posSlope))
78-
{
79-
if (guess == max)
80-
{
81-
console.log(`Stopped at iteration #${iter}.`);
82-
console.log(`Root not found.\nRange: (${min}, ${max}).`);
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return [min, max];
84-
}
85-
max = guess;
86-
}
87-
else
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{
89-
console.log(`Root: ${guess}.\nIterations it took: ${iter}.`);
90-
return guess;
91-
}
92-
if (annoyingConsoleLogs)
93-
{
94-
console.log(`Iteration #${iter}:\n\tCurrent range: (${min}, ${max})`);
95-
}
96-
}
97-
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console.log(`Root not found (maximum iterations reached).\nRange: (${min}, ${max}).`);
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100-
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.`);
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return [min, max];
103-
}
104-
105-
/**
106-
* Just testing if everything generally works.
107-
* This is not an in-depth test (does not test all error scenarios).
108-
*/
109-
function testBisectionFunction()
110-
{
111-
console.log(`TESTING BISECTION FUNCTION!\n`);
112-
113-
/** Test linear function: (2x -19). */
114-
const linFunc = (x: number) => { return 2*x-19; }
115-
116-
/** Test linear function in string format. */
117-
const linFuncString = '2*x-19';
118-
119-
/** Test polynomial function: (x^2 + x - 5). */
120-
const polyFunc = (x: number) => { return x**2+x-5; }
121-
122-
/** First test trigonometric function: sin(1/x). */
123-
const trigFuncOne = (x: number) => { return Math.sin(1/x); }
124-
125-
/** Second test trigonometric function: sin(x)/x. */
126-
const trigFuncTwo = (x: number) => { return Math.sin(x)/x; }
127-
128-
const returnedVals: (number | [number, number] | 'ERROR')[] =
129-
[
130-
bisection(linFunc, 9.5, 9.5), // root is both given min and max
131-
bisection(linFunc, 5, 5), // given min and max are the same, but not the root
132-
bisection(linFunc, 9.5, 10), // root is the given min
133-
bisection(linFunc, 9, 9.5), // root is the given max
134-
bisection(linFunc, -100, 0), // root not within range
135-
bisection(linFunc, 100, -100), // upper and lower switched
136-
bisection(linFuncString, -100, 100),
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bisection(polyFunc, 0, 21),
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bisection(trigFuncOne, 0.212, 0.637, 100000),
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bisection(trigFuncTwo, 0.1, 4.25, 1000/*, true*/) // those console logs really are annoying...
140-
]
141-
142-
console.log("---------------------------------------------------------------");
143-
console.log(`\nReturned values from bisection function:\n[`);
144-
145-
// should I have just used a regular for loop: yes.
146-
let len = returnedVals.length;
147-
let i = 0;
148-
for (const returnedVal of returnedVals)
149-
{
150-
i++;
151-
let toPrint;
152-
switch (typeof returnedVal)
153-
{
154-
case 'string':
155-
toPrint = `\t${returnedVal}`;
156-
break;
157-
case 'number':
158-
toPrint = `\t${returnedVal}`;
159-
break;
160-
default:
161-
toPrint = `\t[${returnedVal[0]}, ${returnedVal[1]}]`;
162-
}
163-
if (i != len) { toPrint += ','; }
164-
else { toPrint += `\n]`; }
165-
console.log(toPrint);
166-
}
167-
}
168-
169-
testBisectionFunction();
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export { bisection, testBisectionFunction } from './bisection';

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