DMleadgen
46d973904b
Next.js website for Rocky Mountain Vending company featuring: - Product catalog with Stripe integration - Service areas and parts pages - Admin dashboard with Clerk authentication - SEO optimized pages with JSON-LD structured data Co-authored-by: Cursor <cursoragent@cursor.com>
111 lines
2 KiB
Text
111 lines
2 KiB
Text
/*
|
|
Fraction.js v5.0.0 10/1/2024
|
|
https://raw.org/article/rational-numbers-in-javascript/
|
|
|
|
Copyright (c) 2024, Robert Eisele (https://raw.org/)
|
|
Licensed under the MIT license.
|
|
*/
|
|
const Fraction = require('fraction.js');
|
|
|
|
/*
|
|
We have the polynom f(x) = 1/3x_1^2 + x_2^2 + x_1 * x_2 + 3
|
|
|
|
The gradient of f(x):
|
|
|
|
grad(x) = | x_1^2+x_2 |
|
|
| 2x_2+x_1 |
|
|
|
|
And thus the Hesse-Matrix H:
|
|
| 2x_1 1 |
|
|
| 1 2 |
|
|
|
|
The inverse Hesse-Matrix H^-1 is
|
|
| -2 / (1-4x_1) 1 / (1 - 4x_1) |
|
|
| 1 / (1 - 4x_1) -2x_1 / (1 - 4x_1) |
|
|
|
|
We now want to find lim ->oo x[n], with the starting element of (3 2)^T
|
|
|
|
*/
|
|
|
|
// Get the Hesse Matrix
|
|
function H(x) {
|
|
|
|
var z = Fraction(1).sub(Fraction(4).mul(x[0]));
|
|
|
|
return [
|
|
Fraction(-2).div(z),
|
|
Fraction(1).div(z),
|
|
Fraction(1).div(z),
|
|
Fraction(-2).mul(x[0]).div(z),
|
|
];
|
|
}
|
|
|
|
// Get the gradient of f(x)
|
|
function grad(x) {
|
|
|
|
return [
|
|
Fraction(x[0]).mul(x[0]).add(x[1]),
|
|
Fraction(2).mul(x[1]).add(x[0])
|
|
];
|
|
}
|
|
|
|
// A simple matrix multiplication helper
|
|
function matrMult(m, v) {
|
|
|
|
return [
|
|
Fraction(m[0]).mul(v[0]).add(Fraction(m[1]).mul(v[1])),
|
|
Fraction(m[2]).mul(v[0]).add(Fraction(m[3]).mul(v[1]))
|
|
];
|
|
}
|
|
|
|
// A simple vector subtraction helper
|
|
function vecSub(a, b) {
|
|
|
|
return [
|
|
Fraction(a[0]).sub(b[0]),
|
|
Fraction(a[1]).sub(b[1])
|
|
];
|
|
}
|
|
|
|
// Main function, gets a vector and the actual index
|
|
function run(V, j) {
|
|
|
|
var t = H(V);
|
|
//console.log("H(X)");
|
|
for (var i in t) {
|
|
|
|
// console.log(t[i].toFraction());
|
|
}
|
|
|
|
var s = grad(V);
|
|
//console.log("vf(X)");
|
|
for (var i in s) {
|
|
|
|
// console.log(s[i].toFraction());
|
|
}
|
|
|
|
//console.log("multiplication");
|
|
var r = matrMult(t, s);
|
|
for (var i in r) {
|
|
|
|
// console.log(r[i].toFraction());
|
|
}
|
|
|
|
var R = (vecSub(V, r));
|
|
|
|
console.log("X" + j);
|
|
console.log(R[0].toFraction(), "= " + R[0].valueOf());
|
|
console.log(R[1].toFraction(), "= " + R[1].valueOf());
|
|
console.log("\n");
|
|
|
|
return R;
|
|
}
|
|
|
|
|
|
// Set the starting vector
|
|
var v = [3, 2];
|
|
|
|
for (var i = 0; i < 15; i++) {
|
|
|
|
v = run(v, i);
|
|
}
|