113 lines
2.1 KiB
JavaScript
113 lines
2.1 KiB
JavaScript
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/**
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* @license Fraction.js v2.4.1 01/06/2015
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* http://www.xarg.org/2014/03/rational-numbers-in-javascript/
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*
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* Copyright (c) 2015, Robert Eisele (robert@xarg.org)
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* Dual licensed under the MIT or GPL Version 2 licenses.
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**/
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var Fraction = require('../fraction.min.js');
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/*
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We have the polynom f(x) = 1/3x_1^2 + x_2^2 + x_1 * x_2 + 3
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The gradient of f(x):
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grad(x) = | x_1^2+x_2 |
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| 2x_2+x_1 |
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And thus the Hesse-Matrix H:
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| 2x_1 1 |
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| 1 2 |
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The inverse Hesse-Matrix H^-1 is
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| -2 / (1-4x_1) 1 / (1 - 4x_1) |
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| 1 / (1 - 4x_1) -2x_1 / (1 - 4x_1) |
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We now want to find lim ->oo x[n], with the starting element of (3 2)^T
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*/
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// Get the Hesse Matrix
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function H(x) {
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var z = new Fraction(1).sub(new Fraction(4).mul(x[0]));
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return [
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new Fraction(-2).div(z),
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new Fraction(1).div(z),
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new Fraction(1).div(z),
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new Fraction(-2).mul(x[0]).div(z),
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];
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}
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// Get the gradient of f(x)
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function grad(x) {
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return [
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new Fraction(x[0]).mul(x[0]).add(x[1]),
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new Fraction(2).mul(x[1]).add(x[0])
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];
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}
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// A simple matrix multiplication helper
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function matrMult(m, v) {
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return [
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new Fraction(m[0]).mul(v[0]).add(new Fraction(m[1]).mul(v[1])),
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new Fraction(m[2]).mul(v[0]).add(new Fraction(m[3]).mul(v[1]))
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];
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}
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// A simple vector subtraction helper
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function vecSub(a, b) {
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return [
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new Fraction(a[0]).sub(b[0]),
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new Fraction(a[1]).sub(b[1])
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];
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}
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// Main function, gets a vector and the actual index
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function run(V, j) {
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var t = H(V);
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//console.log("H(X)");
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for (var i in t) {
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// console.log(t[i].toFraction());
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}
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var s = grad(V);
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//console.log("vf(X)");
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for (var i in s) {
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// console.log(s[i].toFraction());
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}
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//console.log("multiplikation");
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var r = matrMult(t, s);
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for (var i in r) {
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// console.log(r[i].toFraction());
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}
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var R = (vecSub(V, r));
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console.log("X"+j);
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console.log(R[0].toFraction(), "= "+R[0].valueOf());
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console.log(R[1].toFraction(), "= "+R[1].valueOf());
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console.log("\n");
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return R;
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}
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// Set the starting vector
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var v = [3, 2];
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for (var i = 0; i < 15; i++) {
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v = run(v, i);
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}
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