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114
linear-algebra-javascript/README.md
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linear-algebra-javascript/README.md
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# Linear algebra library for JavaScript
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This library contains some useful classes and functions for dealing with linear algebra in JavaScript.
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The library was orginal written in **TypeScript** and then compiles into pure JavaScript.
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---
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## Overview
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- class Vector : This class represents a vector of arbitray size and operations on it.
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- constructor Vector(N) : creates a zero vector of size N
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- constructor Vector(N, components) : creates a vector of size N with the given components.
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- createUnitBasis(pos) : converts this vector in a unit basis vector and returns it.
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- component(pos) : returns the specified component (indexing at 0)
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- changeComponent(pos, value) : change the specified component.
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- toString() : returns a string representation of this vector.
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- size() : returns the size of the vector. (not the eulidean length!)
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- eulideanLength() : computes the eulidean length of this vector.
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- add(other) : vector addition, returns the rersult.
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- sub(other) : vector subtraction, returns the rersult.
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- dot(other) : computes the dot-product and returns it.
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- scalar(s) : scalar (s) multiplication. returns the result.
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- norm() : normalizes this vector and returns it.
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- equal(other) : returns true if the vectors are equal, otherwise false.
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- function unitBasisVector(N,pos) : returns a unit basis vector of size N with a One on position 'pos'
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- function randomVectorInt(N,a,b) : returns a random vector with integer components (between 'a' and 'b') of size N.
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- function randomVectorFloat(N,a,b) : returns a random vector with floating point components (between 'a' and 'b') of size N.
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- class Matrix : This class represents a matrix of arbitrary size and operations on it.
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- constructor(rows, cols) : creates a zero matrix of dimension rows x cols.
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- constructor(rows, cols, components) : creates a matrix with fix numbers of dimension rows x cols.
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- component(x,y) : returns the specified component.
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- changeComponent(x,y,value) : changes the specified component with the new value 'value'.
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- toString() : returns a string representation of this matrix.
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- dimension() : returns the dimension of this matrix as number arras [rows,cols].
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- add(other) : returns the result of the matrix addition.
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- equal(other) : returns true if the matrices are equal, otherwise false.
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- scalar(c) : returns the result of the matrix-scalar multiplication.
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---
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## Documentation
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The module is well documented in its source code. Look in the TypeScript file ```la_lib.ts```.
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---
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## Usage
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You will find the library in the **src** directory its called ```la_lib.js```. You simply need to
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include this library in your project **(you don't install anything)**. After that:
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```js
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var x = LinearAlgebra.Vector(...);
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```
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The namespace LinearAlgebra contains useful classes and functions for dealing with linear algebra under JavaScript.
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Some examples:
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```js
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// ---------------------------- Examples ------------------------------------------
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// creates vectors
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var x = new LinearAlgebra.Vector(5, [1, 2, 3, 4, 5]);
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var y = new LinearAlgebra.Vector(5, [1, 2, 3, 4, 5]);
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// prints size of the vector
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console.log(x.size()); // ==> 5
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// changes the 2-th component with 7
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//x.changeComponent(2,7);
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// print the 2-th component.
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console.log(x.component(2)); // ==> 3
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// prints the full vector as string.
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console.log(x.toString()); // ==> (1,2,3,4,5)
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// vector addition
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console.log(x.add(y).toString()); // ==> (2,3,6,8,10)
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//console.log(x.createUnitBasis(1).toString());
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// computes the dot-product
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console.log(x.dot(y)); // ==> 55
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// computes and prints the scalar-product
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console.log(x.scalar(5).toString()); // ==> (5,10,15,20,25)
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// creates a unit basis vector
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console.log(LinearAlgebra.unitBasisVector(3, 0).toString()); // ==> (1,0,0)
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// creates random vectors
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console.log(LinearAlgebra.randomVectorInt(3, 0, 5).toString());
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console.log(LinearAlgebra.randomVectorFloat(3, 0, 5).toString());
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```
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---
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## Tests
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Go in the directory of the project and type in:
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```npm install```
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```npm test```
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The test-suite use the JavaScript test-framework **mocha**.
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---
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## Contributing
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You can contribute to this project. Feel free and pull request some new features or documention.
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**TODO:** Global functions for special matrices.
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**TODO:** Documention of the classes and functions.
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171
linear-algebra-javascript/package-lock.json
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||||||
17
linear-algebra-javascript/package.json
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linear-algebra-javascript/package.json
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|||||||
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{
|
||||||
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"name": "linear-algebra-javascript",
|
||||||
|
"version": "1.0.0",
|
||||||
|
"description": "simple linear algebra library for JavaScript",
|
||||||
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"main": "index.js",
|
||||||
|
"directories": {
|
||||||
|
"test": "test"
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||||||
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},
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||||||
|
"scripts": {
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||||||
|
"test": "mocha"
|
||||||
|
},
|
||||||
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"author": "Christian Bender",
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||||||
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"license": "MIT",
|
||||||
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"dependencies": {
|
||||||
|
"mocha": "^5.0.2"
|
||||||
|
}
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||||||
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}
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||||||
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linear-algebra-javascript/src/la_lib.js
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325
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|
|||||||
|
/*
|
||||||
|
author: Christian Bender
|
||||||
|
license: MIT-license
|
||||||
|
|
||||||
|
The namespace LinearAlgebra contains useful classes and functions for dealing with
|
||||||
|
linear algebra under JavaScript.
|
||||||
|
*/
|
||||||
|
var LinearAlgebra;
|
||||||
|
(function (LinearAlgebra) {
|
||||||
|
/*
|
||||||
|
class: Vector
|
||||||
|
This class represents a vector of arbitrary size and operations on it.
|
||||||
|
*/
|
||||||
|
var Vector = /** @class */ (function () {
|
||||||
|
// constructor
|
||||||
|
function Vector(N, comps) {
|
||||||
|
if (comps === void 0) { comps = []; }
|
||||||
|
this.components = new Array(N);
|
||||||
|
if (comps.length == 0) {
|
||||||
|
for (var i = 0; i < N; i++) {
|
||||||
|
this.components[i] = 0.0;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
else {
|
||||||
|
if (N == comps.length) {
|
||||||
|
this.components = comps;
|
||||||
|
}
|
||||||
|
else {
|
||||||
|
throw "Vector: invalide size!";
|
||||||
|
}
|
||||||
|
}
|
||||||
|
} // end of constructor
|
||||||
|
// returns the size of this vector.
|
||||||
|
// not the eulidean length!
|
||||||
|
Vector.prototype.size = function () {
|
||||||
|
return this.components.length;
|
||||||
|
};
|
||||||
|
// computes the eulidean length.
|
||||||
|
Vector.prototype.eulideanLength = function () {
|
||||||
|
var sum = 0;
|
||||||
|
for (var i = 0; i < this.components.length; i++) {
|
||||||
|
sum += this.components[i] * this.components[i];
|
||||||
|
}
|
||||||
|
return Math.sqrt(sum);
|
||||||
|
};
|
||||||
|
// getter for the components of the vector.
|
||||||
|
// returns a specified component (index)
|
||||||
|
Vector.prototype.component = function (index) {
|
||||||
|
return this.components[index];
|
||||||
|
};
|
||||||
|
// setter for a specified component of this vector.
|
||||||
|
Vector.prototype.changeComponent = function (index, value) {
|
||||||
|
if (index >= 0 && index < this.components.length) {
|
||||||
|
this.components[index] = value;
|
||||||
|
}
|
||||||
|
else {
|
||||||
|
throw "changeComponent: index out of bounds!";
|
||||||
|
}
|
||||||
|
};
|
||||||
|
// vector addition
|
||||||
|
Vector.prototype.add = function (other) {
|
||||||
|
if (this.size() == other.size()) {
|
||||||
|
var SIZE = this.size();
|
||||||
|
var ans = new Vector(SIZE);
|
||||||
|
for (var i = 0; i < SIZE; i++) {
|
||||||
|
ans.changeComponent(i, (this.components[i] + other.component(i)));
|
||||||
|
}
|
||||||
|
return ans;
|
||||||
|
}
|
||||||
|
else {
|
||||||
|
throw "add: vector must have same size!";
|
||||||
|
}
|
||||||
|
};
|
||||||
|
// vector subtraction
|
||||||
|
Vector.prototype.sub = function (other) {
|
||||||
|
if (this.size() == other.size()) {
|
||||||
|
var SIZE = this.size();
|
||||||
|
var ans = new Vector(SIZE);
|
||||||
|
for (var i = 0; i < SIZE; i++) {
|
||||||
|
ans.changeComponent(i, (this.components[i] - other.component(i)));
|
||||||
|
}
|
||||||
|
return ans;
|
||||||
|
}
|
||||||
|
else {
|
||||||
|
throw "add: vector must have same size!";
|
||||||
|
}
|
||||||
|
};
|
||||||
|
// dot-product
|
||||||
|
Vector.prototype.dot = function (other) {
|
||||||
|
var sum = 0;
|
||||||
|
if (other.size() == this.size()) {
|
||||||
|
var SIZE = other.size();
|
||||||
|
for (var i = 0; i < SIZE; i++) {
|
||||||
|
sum += this.components[i] * other.component(i);
|
||||||
|
}
|
||||||
|
return sum;
|
||||||
|
}
|
||||||
|
else {
|
||||||
|
throw "dot: vectors must have same size!";
|
||||||
|
}
|
||||||
|
};
|
||||||
|
// scalar multiplication
|
||||||
|
Vector.prototype.scalar = function (s) {
|
||||||
|
var SIZE = this.size();
|
||||||
|
var ans = new Vector(SIZE);
|
||||||
|
for (var i = 0; i < SIZE; i++) {
|
||||||
|
ans.changeComponent(i, (this.components[i] * s));
|
||||||
|
}
|
||||||
|
return ans;
|
||||||
|
};
|
||||||
|
// returns a string representation of this vector.
|
||||||
|
Vector.prototype.toString = function () {
|
||||||
|
var ans = "(";
|
||||||
|
var SIZE = this.components.length;
|
||||||
|
for (var i = 0; i < SIZE; i++) {
|
||||||
|
if (i < SIZE - 1) {
|
||||||
|
ans += this.components[i] + ",";
|
||||||
|
}
|
||||||
|
else {
|
||||||
|
ans += this.components[i] + ")";
|
||||||
|
}
|
||||||
|
}
|
||||||
|
return ans;
|
||||||
|
};
|
||||||
|
// converts this vector in a unit basis vector and returns it.
|
||||||
|
// the One is on position 'pos'
|
||||||
|
Vector.prototype.createUnitBasis = function (pos) {
|
||||||
|
if (pos >= 0 && pos < this.components.length) {
|
||||||
|
for (var i = 0; i < this.components.length; i++) {
|
||||||
|
if (i == pos) {
|
||||||
|
this.components[i] = 1.0;
|
||||||
|
}
|
||||||
|
else {
|
||||||
|
this.components[i] = 0.0;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
else {
|
||||||
|
throw "createUnitBasis: index out of bounds";
|
||||||
|
}
|
||||||
|
return this;
|
||||||
|
};
|
||||||
|
// normalizes this vector and returns it.
|
||||||
|
Vector.prototype.norm = function () {
|
||||||
|
var SIZE = this.size();
|
||||||
|
var quotient = 1.0 / this.eulideanLength();
|
||||||
|
for (var i = 0; i < SIZE; i++) {
|
||||||
|
this.components[i] = this.components[i] * quotient;
|
||||||
|
}
|
||||||
|
return this;
|
||||||
|
};
|
||||||
|
// returns true if the vectors are equal otherwise false.
|
||||||
|
Vector.prototype.equal = function (other) {
|
||||||
|
var ans = true;
|
||||||
|
var SIZE = this.size();
|
||||||
|
var EPSILON = 0.001;
|
||||||
|
if (SIZE == other.size()) {
|
||||||
|
for (var i = 0; i < SIZE; i++) {
|
||||||
|
if (Math.abs(this.components[i] - other.component(i)) > EPSILON) {
|
||||||
|
ans = false;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
else {
|
||||||
|
ans = false;
|
||||||
|
}
|
||||||
|
return ans;
|
||||||
|
};
|
||||||
|
return Vector;
|
||||||
|
}()); // end of class Vector
|
||||||
|
LinearAlgebra.Vector = Vector;
|
||||||
|
// -------------- global functions ---------------------------------
|
||||||
|
// returns a unit basis vector of size N with a One on position 'pos'
|
||||||
|
function unitBasisVector(N, pos) {
|
||||||
|
var ans = new Vector(N);
|
||||||
|
for (var i = 0; i < N; i++) {
|
||||||
|
if (i == pos) {
|
||||||
|
ans.changeComponent(i, 1.0);
|
||||||
|
}
|
||||||
|
else {
|
||||||
|
ans.changeComponent(i, 0);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
return ans;
|
||||||
|
}
|
||||||
|
LinearAlgebra.unitBasisVector = unitBasisVector;
|
||||||
|
// returns a random vector with integer components (between 'a' and 'b') of size N.
|
||||||
|
function randomVectorInt(N, a, b) {
|
||||||
|
var ans = new Vector(N);
|
||||||
|
for (var i = 0; i < N; i++) {
|
||||||
|
ans.changeComponent(i, (Math.floor((Math.random() * b) + a)));
|
||||||
|
}
|
||||||
|
return ans;
|
||||||
|
}
|
||||||
|
LinearAlgebra.randomVectorInt = randomVectorInt;
|
||||||
|
// returns a random vector with floating point components (between 'a' and 'b') of size N.
|
||||||
|
function randomVectorFloat(N, a, b) {
|
||||||
|
var ans = new Vector(N);
|
||||||
|
for (var i = 0; i < N; i++) {
|
||||||
|
ans.changeComponent(i, ((Math.random() * b) + a));
|
||||||
|
}
|
||||||
|
return ans;
|
||||||
|
}
|
||||||
|
LinearAlgebra.randomVectorFloat = randomVectorFloat;
|
||||||
|
// ------------------ end of global functions -----------------------------
|
||||||
|
/*
|
||||||
|
class: Matrix
|
||||||
|
This class represents a matrix of arbitrary size and operations on it.
|
||||||
|
*/
|
||||||
|
var Matrix = /** @class */ (function () {
|
||||||
|
// constructor for zero-matrix or fix number matrix.
|
||||||
|
function Matrix(row, col, comps) {
|
||||||
|
if (comps === void 0) { comps = []; }
|
||||||
|
if (comps.length == 0) {
|
||||||
|
this.matrix = new Array();
|
||||||
|
var rowVector = new Array();
|
||||||
|
for (var i = 0; i < row; i++) {
|
||||||
|
for (var j = 0; j < col; j++) {
|
||||||
|
rowVector[j] = 0;
|
||||||
|
}
|
||||||
|
this.matrix[i] = rowVector;
|
||||||
|
rowVector = new Array();
|
||||||
|
}
|
||||||
|
}
|
||||||
|
else {
|
||||||
|
this.matrix = comps;
|
||||||
|
}
|
||||||
|
this.rows = row;
|
||||||
|
this.cols = col;
|
||||||
|
}
|
||||||
|
// returns the specified component.
|
||||||
|
Matrix.prototype.component = function (x, y) {
|
||||||
|
if (x >= 0 && x < this.rows && y >= 0 && y < this.cols) {
|
||||||
|
return this.matrix[x][y];
|
||||||
|
}
|
||||||
|
else {
|
||||||
|
throw new Error("component: index out of bounds");
|
||||||
|
}
|
||||||
|
};
|
||||||
|
// changes the specified component with value 'value'.
|
||||||
|
Matrix.prototype.changeComponent = function (x, y, value) {
|
||||||
|
if (x >= 0 && x < this.rows && y >= 0 && y < this.cols) {
|
||||||
|
this.matrix[x][y] = value;
|
||||||
|
}
|
||||||
|
else {
|
||||||
|
throw new Error("changeComponent: index out of bounds");
|
||||||
|
}
|
||||||
|
};
|
||||||
|
// returns a string representation of this matrix.
|
||||||
|
Matrix.prototype.toString = function () {
|
||||||
|
var ans = "";
|
||||||
|
for (var i = 0; i < this.rows; i++) {
|
||||||
|
ans += "|";
|
||||||
|
for (var j = 0; j < this.cols; j++) {
|
||||||
|
if (j < this.cols - 1) {
|
||||||
|
ans += this.matrix[i][j] + ",";
|
||||||
|
}
|
||||||
|
else {
|
||||||
|
if (i < this.rows - 1) {
|
||||||
|
ans += this.matrix[i][j] + "|\n";
|
||||||
|
}
|
||||||
|
else {
|
||||||
|
ans += this.matrix[i][j] + "|";
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
return ans;
|
||||||
|
};
|
||||||
|
// returns the dimension rows x cols as number array
|
||||||
|
Matrix.prototype.dimension = function () {
|
||||||
|
var ans = new Array();
|
||||||
|
ans[0] = this.rows;
|
||||||
|
ans[1] = this.cols;
|
||||||
|
return ans;
|
||||||
|
};
|
||||||
|
// matrix addition. returns the result.
|
||||||
|
Matrix.prototype.add = function (other) {
|
||||||
|
if (this.rows == other.dimension()[0]
|
||||||
|
&& this.cols == other.dimension()[1]) {
|
||||||
|
var ans = new Matrix(this.rows, this.cols);
|
||||||
|
for (var i = 0; i < this.rows; i++) {
|
||||||
|
for (var j = 0; j < this.cols; j++) {
|
||||||
|
ans.changeComponent(i, j, (this.matrix[i][j] + other.component(i, j)));
|
||||||
|
}
|
||||||
|
}
|
||||||
|
return ans;
|
||||||
|
}
|
||||||
|
else {
|
||||||
|
throw new Error("add: matrices must have same dimension!");
|
||||||
|
}
|
||||||
|
};
|
||||||
|
// returns true if the matrices are equal, otherwise false.
|
||||||
|
Matrix.prototype.equal = function (other) {
|
||||||
|
var ans = true;
|
||||||
|
var EPSILON = 0.001;
|
||||||
|
if (this.rows == other.dimension()[0]
|
||||||
|
&& this.cols == other.dimension()[1]) {
|
||||||
|
for (var i = 0; i < this.rows; i++) {
|
||||||
|
for (var j = 0; j < this.cols; j++) {
|
||||||
|
if (Math.abs(this.matrix[i][j] - other.component(i, j)) > EPSILON) {
|
||||||
|
ans = false;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
else {
|
||||||
|
ans = false;
|
||||||
|
}
|
||||||
|
return ans;
|
||||||
|
};
|
||||||
|
// matrix-scalar multiplication
|
||||||
|
Matrix.prototype.scalar = function (c) {
|
||||||
|
var ans = new Matrix(this.rows, this.cols);
|
||||||
|
for (var i = 0; i < this.rows; i++) {
|
||||||
|
for (var j = 0; j < this.cols; j++) {
|
||||||
|
ans.changeComponent(i, j, (this.matrix[i][j] * c));
|
||||||
|
}
|
||||||
|
}
|
||||||
|
return ans;
|
||||||
|
};
|
||||||
|
return Matrix;
|
||||||
|
}()); // end of class Matrix
|
||||||
|
LinearAlgebra.Matrix = Matrix;
|
||||||
|
})(LinearAlgebra || (LinearAlgebra = {})); // end of namespace LinearAlgebra
|
||||||
342
linear-algebra-javascript/src/la_lib.ts
Normal file
342
linear-algebra-javascript/src/la_lib.ts
Normal file
@ -0,0 +1,342 @@
|
|||||||
|
/*
|
||||||
|
author: Christian Bender
|
||||||
|
license: MIT-license
|
||||||
|
|
||||||
|
The namespace LinearAlgebra contains useful classes and functions for dealing with
|
||||||
|
linear algebra under JavaScript.
|
||||||
|
*/
|
||||||
|
|
||||||
|
namespace LinearAlgebra {
|
||||||
|
/*
|
||||||
|
class: Vector
|
||||||
|
This class represents a vector of arbitrary size and operations on it.
|
||||||
|
*/
|
||||||
|
export class Vector {
|
||||||
|
|
||||||
|
// the vector components
|
||||||
|
private components: number[];
|
||||||
|
|
||||||
|
// constructor
|
||||||
|
constructor(N: number, comps: number[] = []) {
|
||||||
|
this.components = new Array(N);
|
||||||
|
if (comps.length == 0) { // creates a zero vector of size N
|
||||||
|
for (var i = 0; i < N; i++) {
|
||||||
|
this.components[i] = 0.0;
|
||||||
|
}
|
||||||
|
} else { // assigns the components
|
||||||
|
if (N == comps.length) {
|
||||||
|
this.components = comps;
|
||||||
|
} else {
|
||||||
|
throw "Vector: invalide size!";
|
||||||
|
}
|
||||||
|
|
||||||
|
}
|
||||||
|
} // end of constructor
|
||||||
|
|
||||||
|
// returns the size of this vector.
|
||||||
|
// not the eulidean length!
|
||||||
|
size(): number {
|
||||||
|
return this.components.length;
|
||||||
|
}
|
||||||
|
|
||||||
|
// computes the eulidean length.
|
||||||
|
eulideanLength(): number {
|
||||||
|
var sum: number = 0;
|
||||||
|
for (var i = 0; i < this.components.length; i++) {
|
||||||
|
sum += this.components[i] * this.components[i];
|
||||||
|
}
|
||||||
|
return Math.sqrt(sum);
|
||||||
|
}
|
||||||
|
|
||||||
|
// getter for the components of the vector.
|
||||||
|
// returns a specified component (index)
|
||||||
|
component(index: number): number {
|
||||||
|
return this.components[index];
|
||||||
|
}
|
||||||
|
|
||||||
|
// setter for a specified component of this vector.
|
||||||
|
changeComponent(index: number, value: number): void {
|
||||||
|
if (index >= 0 && index < this.components.length) {
|
||||||
|
this.components[index] = value;
|
||||||
|
} else { // error case
|
||||||
|
throw "changeComponent: index out of bounds!";
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
// vector addition
|
||||||
|
add(other: Vector): Vector {
|
||||||
|
if (this.size() == other.size()) {
|
||||||
|
var SIZE = this.size();
|
||||||
|
var ans: Vector = new Vector(SIZE);
|
||||||
|
for (var i = 0; i < SIZE; i++) {
|
||||||
|
ans.changeComponent(i, (this.components[i] + other.component(i)));
|
||||||
|
}
|
||||||
|
return ans;
|
||||||
|
} else {
|
||||||
|
throw "add: vector must have same size!";
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
// vector subtraction
|
||||||
|
sub(other: Vector): Vector {
|
||||||
|
if (this.size() == other.size()) {
|
||||||
|
var SIZE = this.size();
|
||||||
|
var ans: Vector = new Vector(SIZE);
|
||||||
|
for (var i = 0; i < SIZE; i++) {
|
||||||
|
ans.changeComponent(i, (this.components[i] - other.component(i)));
|
||||||
|
}
|
||||||
|
return ans;
|
||||||
|
} else { // error case
|
||||||
|
throw "add: vector must have same size!";
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
// dot-product
|
||||||
|
dot(other: Vector): number {
|
||||||
|
var sum: number = 0;
|
||||||
|
if (other.size() == this.size()) {
|
||||||
|
const SIZE: number = other.size();
|
||||||
|
for (var i = 0; i < SIZE; i++) {
|
||||||
|
sum += this.components[i] * other.component(i);
|
||||||
|
}
|
||||||
|
return sum;
|
||||||
|
} else { // error case
|
||||||
|
throw "dot: vectors must have same size!";
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
// scalar multiplication
|
||||||
|
scalar(s: number): Vector {
|
||||||
|
const SIZE: number = this.size();
|
||||||
|
var ans: Vector = new Vector(SIZE);
|
||||||
|
for (var i = 0; i < SIZE; i++) {
|
||||||
|
ans.changeComponent(i, (this.components[i] * s));
|
||||||
|
}
|
||||||
|
return ans;
|
||||||
|
}
|
||||||
|
|
||||||
|
// returns a string representation of this vector.
|
||||||
|
toString(): string {
|
||||||
|
var ans: string = "(";
|
||||||
|
var SIZE: number = this.components.length;
|
||||||
|
for (var i = 0; i < SIZE; i++) {
|
||||||
|
if (i < SIZE - 1) {
|
||||||
|
ans += this.components[i] + ",";
|
||||||
|
} else {
|
||||||
|
ans += this.components[i] + ")";
|
||||||
|
}
|
||||||
|
}
|
||||||
|
return ans;
|
||||||
|
}
|
||||||
|
|
||||||
|
// converts this vector in a unit basis vector and returns it.
|
||||||
|
// the One is on position 'pos'
|
||||||
|
createUnitBasis(pos: number): Vector {
|
||||||
|
if (pos >= 0 && pos < this.components.length) {
|
||||||
|
for (var i = 0; i < this.components.length; i++) {
|
||||||
|
if (i == pos) {
|
||||||
|
this.components[i] = 1.0;
|
||||||
|
} else {
|
||||||
|
this.components[i] = 0.0;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
} else { // error case
|
||||||
|
throw "createUnitBasis: index out of bounds";
|
||||||
|
}
|
||||||
|
return this;
|
||||||
|
}
|
||||||
|
|
||||||
|
// normalizes this vector and returns it.
|
||||||
|
norm(): Vector {
|
||||||
|
const SIZE: number = this.size();
|
||||||
|
var quotient = 1.0 / this.eulideanLength();
|
||||||
|
for (var i = 0; i < SIZE; i++) {
|
||||||
|
this.components[i] = this.components[i] * quotient;
|
||||||
|
}
|
||||||
|
return this;
|
||||||
|
}
|
||||||
|
|
||||||
|
// returns true if the vectors are equal otherwise false.
|
||||||
|
equal(other: Vector): boolean {
|
||||||
|
var ans: boolean = true;
|
||||||
|
const SIZE: number = this.size();
|
||||||
|
const EPSILON: number = 0.001;
|
||||||
|
if (SIZE == other.size()) {
|
||||||
|
for (var i = 0; i < SIZE; i++) {
|
||||||
|
if (Math.abs(this.components[i] - other.component(i)) > EPSILON) {
|
||||||
|
ans = false;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
} else {
|
||||||
|
ans = false;
|
||||||
|
}
|
||||||
|
return ans;
|
||||||
|
}
|
||||||
|
|
||||||
|
} // end of class Vector
|
||||||
|
|
||||||
|
// -------------- global functions ---------------------------------
|
||||||
|
|
||||||
|
// returns a unit basis vector of size N with a One on position 'pos'
|
||||||
|
export function unitBasisVector(N: number, pos: number): Vector {
|
||||||
|
var ans = new Vector(N);
|
||||||
|
for (var i = 0; i < N; i++) {
|
||||||
|
if (i == pos) {
|
||||||
|
ans.changeComponent(i, 1.0);
|
||||||
|
} else {
|
||||||
|
ans.changeComponent(i, 0);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
return ans;
|
||||||
|
}
|
||||||
|
|
||||||
|
// returns a random vector with integer components (between 'a' and 'b') of size N.
|
||||||
|
export function randomVectorInt(N: number, a: number, b: number): Vector {
|
||||||
|
var ans: Vector = new Vector(N);
|
||||||
|
for (var i = 0; i < N; i++) {
|
||||||
|
ans.changeComponent(i, (Math.floor((Math.random() * b) + a)));
|
||||||
|
}
|
||||||
|
return ans;
|
||||||
|
}
|
||||||
|
|
||||||
|
// returns a random vector with floating point components (between 'a' and 'b') of size N.
|
||||||
|
export function randomVectorFloat(N: number, a: number, b: number): Vector {
|
||||||
|
var ans: Vector = new Vector(N);
|
||||||
|
for (var i = 0; i < N; i++) {
|
||||||
|
ans.changeComponent(i, ((Math.random() * b) + a));
|
||||||
|
}
|
||||||
|
return ans;
|
||||||
|
}
|
||||||
|
|
||||||
|
// ------------------ end of global functions -----------------------------
|
||||||
|
|
||||||
|
|
||||||
|
/*
|
||||||
|
class: Matrix
|
||||||
|
This class represents a matrix of arbitrary size and operations on it.
|
||||||
|
*/
|
||||||
|
export class Matrix {
|
||||||
|
|
||||||
|
// private field that contains the actual matrix.
|
||||||
|
private matrix: number[][];
|
||||||
|
|
||||||
|
// private field for the dimension of the matrix
|
||||||
|
private rows: number;
|
||||||
|
private cols: number;
|
||||||
|
|
||||||
|
// constructor for zero-matrix or fix number matrix.
|
||||||
|
constructor(row: number, col: number, comps: number[][] = []) {
|
||||||
|
if (comps.length == 0) { // zero-matrix
|
||||||
|
this.matrix = new Array();
|
||||||
|
var rowVector: number[] = new Array();
|
||||||
|
for (var i = 0; i < row; i++) {
|
||||||
|
for (var j = 0; j < col; j++) {
|
||||||
|
rowVector[j] = 0;
|
||||||
|
}
|
||||||
|
this.matrix[i] = rowVector;
|
||||||
|
rowVector = new Array();
|
||||||
|
}
|
||||||
|
} else { // fix number matrix
|
||||||
|
this.matrix = comps;
|
||||||
|
}
|
||||||
|
this.rows = row;
|
||||||
|
this.cols = col;
|
||||||
|
}
|
||||||
|
|
||||||
|
// returns the specified component.
|
||||||
|
component(x: number, y: number): number {
|
||||||
|
if (x >= 0 && x < this.rows && y >= 0 && y < this.cols) {
|
||||||
|
return this.matrix[x][y];
|
||||||
|
} else { // error case
|
||||||
|
throw new Error("component: index out of bounds");
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
// changes the specified component with value 'value'.
|
||||||
|
changeComponent(x: number, y: number, value: number): void {
|
||||||
|
if (x >= 0 && x < this.rows && y >= 0 && y < this.cols) {
|
||||||
|
this.matrix[x][y] = value;
|
||||||
|
} else {
|
||||||
|
throw new Error("changeComponent: index out of bounds");
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
// returns a string representation of this matrix.
|
||||||
|
toString(): string {
|
||||||
|
var ans: string = "";
|
||||||
|
for (var i = 0; i < this.rows; i++) {
|
||||||
|
ans += "|";
|
||||||
|
for (var j = 0; j < this.cols; j++) {
|
||||||
|
if (j < this.cols - 1) {
|
||||||
|
ans += this.matrix[i][j] + ",";
|
||||||
|
} else {
|
||||||
|
if (i < this.rows - 1) {
|
||||||
|
ans += this.matrix[i][j] + "|\n";
|
||||||
|
} else {
|
||||||
|
ans += this.matrix[i][j] + "|";
|
||||||
|
}
|
||||||
|
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
return ans;
|
||||||
|
}
|
||||||
|
|
||||||
|
// returns the dimension rows x cols as number array
|
||||||
|
dimension(): number[] {
|
||||||
|
var ans: number[] = new Array();
|
||||||
|
ans[0] = this.rows;
|
||||||
|
ans[1] = this.cols;
|
||||||
|
return ans;
|
||||||
|
}
|
||||||
|
|
||||||
|
// matrix addition. returns the result.
|
||||||
|
add(other: Matrix): Matrix {
|
||||||
|
if (this.rows == other.dimension()[0]
|
||||||
|
&& this.cols == other.dimension()[1]) {
|
||||||
|
var ans = new Matrix(this.rows, this.cols);
|
||||||
|
for (var i = 0; i < this.rows; i++) {
|
||||||
|
for (var j = 0; j < this.cols; j++) {
|
||||||
|
ans.changeComponent(i, j, (this.matrix[i][j] + other.component(i, j)));
|
||||||
|
}
|
||||||
|
}
|
||||||
|
return ans;
|
||||||
|
} else {
|
||||||
|
throw new Error("add: matrices must have same dimension!");
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
// returns true if the matrices are equal, otherwise false.
|
||||||
|
equal(other: Matrix): boolean {
|
||||||
|
var ans: boolean = true;
|
||||||
|
const EPSILON: number = 0.001;
|
||||||
|
if (this.rows == other.dimension()[0]
|
||||||
|
&& this.cols == other.dimension()[1]) {
|
||||||
|
for (var i = 0; i < this.rows; i++) {
|
||||||
|
for (var j = 0; j < this.cols; j++) {
|
||||||
|
if (Math.abs(this.matrix[i][j] - other.component(i, j)) > EPSILON) {
|
||||||
|
ans = false;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
} else {
|
||||||
|
ans = false;
|
||||||
|
}
|
||||||
|
return ans;
|
||||||
|
}
|
||||||
|
|
||||||
|
// matrix-scalar multiplication
|
||||||
|
scalar(c: number): Matrix {
|
||||||
|
var ans = new Matrix(this.rows, this.cols);
|
||||||
|
for (var i = 0; i < this.rows; i++) {
|
||||||
|
for (var j = 0; j < this.cols; j++) {
|
||||||
|
ans.changeComponent(i, j, (this.matrix[i][j] * c));
|
||||||
|
}
|
||||||
|
}
|
||||||
|
return ans;
|
||||||
|
}
|
||||||
|
|
||||||
|
} // end of class Matrix
|
||||||
|
} // end of namespace LinearAlgebra
|
||||||
|
|
||||||
|
|
||||||
170
linear-algebra-javascript/test/test.js
Normal file
170
linear-algebra-javascript/test/test.js
Normal file
@ -0,0 +1,170 @@
|
|||||||
|
/*
|
||||||
|
author: Christian Bender
|
||||||
|
license: MIT-license
|
||||||
|
|
||||||
|
This file contains the test-suite for the linear algebra library.
|
||||||
|
The tests use javascript test-framework mocha
|
||||||
|
*/
|
||||||
|
|
||||||
|
var assert = require('assert');
|
||||||
|
var fs = require('fs');
|
||||||
|
|
||||||
|
// file is included here
|
||||||
|
eval(fs.readFileSync('src/la_lib.js') + '');
|
||||||
|
|
||||||
|
// Tests goes here
|
||||||
|
|
||||||
|
// creating some vectors
|
||||||
|
describe('Create Vectors', function () {
|
||||||
|
describe('#toString()', function () {
|
||||||
|
it('should return a string representation', function () {
|
||||||
|
assert.equal((new LinearAlgebra.Vector(3, [1, 2, 3])).toString(), "(1,2,3)");
|
||||||
|
});
|
||||||
|
});
|
||||||
|
describe("#unitBasisVector()", function () {
|
||||||
|
it("should return a unit basis vector", function () {
|
||||||
|
assert.equal(LinearAlgebra.unitBasisVector(3, 1).toString(), "(0,1,0)");
|
||||||
|
});
|
||||||
|
});
|
||||||
|
});
|
||||||
|
|
||||||
|
// operations on it.
|
||||||
|
describe("Vector operations", function () {
|
||||||
|
describe("#add()", function () {
|
||||||
|
it("should return vector (2,4,6)", function () {
|
||||||
|
var x = new LinearAlgebra.Vector(3, [1, 2, 3]);
|
||||||
|
var y = new LinearAlgebra.Vector(3, [1, 2, 3]);
|
||||||
|
assert.equal((x.add(y)).toString(), "(2,4,6)");
|
||||||
|
});
|
||||||
|
});
|
||||||
|
describe("#sub()", function () {
|
||||||
|
it("should return vector (0,0,0)", function () {
|
||||||
|
var x = new LinearAlgebra.Vector(3, [1, 2, 3]);
|
||||||
|
var y = new LinearAlgebra.Vector(3, [1, 2, 3]);
|
||||||
|
assert.equal((x.sub(y)).toString(), "(0,0,0)");
|
||||||
|
});
|
||||||
|
});
|
||||||
|
describe("#dot()", function () {
|
||||||
|
it("should return the dot-product", function () {
|
||||||
|
var x = new LinearAlgebra.Vector(3, [1, 2, 3]);
|
||||||
|
var y = new LinearAlgebra.Vector(3, [5, 6, 7]);
|
||||||
|
assert.equal(x.dot(y), 38);
|
||||||
|
});
|
||||||
|
});
|
||||||
|
describe("#scalar()", function () {
|
||||||
|
it("should return the scalar product", function () {
|
||||||
|
var x = new LinearAlgebra.Vector(3, [1, 2, 3]);
|
||||||
|
assert.equal(x.scalar(2).toString(), "(2,4,6)");
|
||||||
|
});
|
||||||
|
});
|
||||||
|
describe("#norm()", function () {
|
||||||
|
it("should return the normalizes vector", function () {
|
||||||
|
var x = new LinearAlgebra.Vector(4, [9, 0, 3, 1]);
|
||||||
|
var y = x.norm();
|
||||||
|
assert.ok(Math.abs(y.component(0) - (9.0 / Math.sqrt(91))) <= 0.01);
|
||||||
|
});
|
||||||
|
});
|
||||||
|
describe("#eulideanLength()", function () {
|
||||||
|
it("should return the eulidean length of the vector", function () {
|
||||||
|
var x = new LinearAlgebra.Vector(3, [1, 2, 2]);
|
||||||
|
assert.ok(Math.abs(x.eulideanLength() - 3) <= 0.001);
|
||||||
|
});
|
||||||
|
});
|
||||||
|
describe("#size()", function () {
|
||||||
|
it("should return the size (not eulidean length!) of the vector", function () {
|
||||||
|
var x = LinearAlgebra.randomVectorInt(10, 1, 5);
|
||||||
|
assert.equal(x.size(), 10);
|
||||||
|
});
|
||||||
|
});
|
||||||
|
describe("#equal()", function () {
|
||||||
|
it("should compares two vectors", function () {
|
||||||
|
var x = new LinearAlgebra.Vector(3, [1, 2, 2]);
|
||||||
|
var y = new LinearAlgebra.Vector(3, [1, 2, 3]);
|
||||||
|
assert.ok(x.equal(x));
|
||||||
|
assert.ok(!x.equal(y));
|
||||||
|
});
|
||||||
|
});
|
||||||
|
});
|
||||||
|
|
||||||
|
describe("Methods on vectors", function () {
|
||||||
|
describe("#component()", function () {
|
||||||
|
it("should return the specified component", function () {
|
||||||
|
var x = new LinearAlgebra.Vector(3, [1, 2, 2]);
|
||||||
|
assert.equal(x.component(1), 2);
|
||||||
|
});
|
||||||
|
});
|
||||||
|
describe("#changeComponent()", function () {
|
||||||
|
it("should return the changed vector", function () {
|
||||||
|
var x = new LinearAlgebra.Vector(3, [1, 2, 2]);
|
||||||
|
x.changeComponent(1, 5);
|
||||||
|
assert.equal(x.toString(), "(1,5,2)");
|
||||||
|
});
|
||||||
|
});
|
||||||
|
describe("#toString()", function () {
|
||||||
|
it("should return a string representation of the vector", function () {
|
||||||
|
var x = new LinearAlgebra.Vector(4, [9, 0, 3, 1]);
|
||||||
|
assert.equal(x.toString(), "(9,0,3,1)");
|
||||||
|
});
|
||||||
|
});
|
||||||
|
});
|
||||||
|
|
||||||
|
|
||||||
|
describe("class Matrix", function () {
|
||||||
|
describe("#component()", function () {
|
||||||
|
it("should return the specified component", function () {
|
||||||
|
var A = new LinearAlgebra.Matrix(2, 2);
|
||||||
|
assert.equal(A.component(0, 1), 0);
|
||||||
|
var B = new LinearAlgebra.Matrix(2, 2, [[1, 2], [3, 4]]);
|
||||||
|
assert.equal(B.component(1, 0), 3);
|
||||||
|
});
|
||||||
|
});
|
||||||
|
describe("#toString()", function () {
|
||||||
|
it("should return a string representation of the matrix", function () {
|
||||||
|
var A = new LinearAlgebra.Matrix(2, 2, [[1, 2], [3, 4]]);
|
||||||
|
assert.equal(A.toString(), "|1,2|\n|3,4|");
|
||||||
|
});
|
||||||
|
});
|
||||||
|
describe("#dimension()", function () {
|
||||||
|
it("should return the dimension of the matrix as number array", function () {
|
||||||
|
var A = new LinearAlgebra.Matrix(3, 2, [[1, 2], [3, 4], [5, 6]]);
|
||||||
|
assert.equal(A.dimension()[0], 3);
|
||||||
|
assert.equal(A.dimension()[1], 2);
|
||||||
|
});
|
||||||
|
});
|
||||||
|
describe("#changeComponent()", function () {
|
||||||
|
it("should change the specified component of the matrix", function () {
|
||||||
|
var A = new LinearAlgebra.Matrix(3, 2, [[1, 2], [3, 4], [5, 6]]);
|
||||||
|
A.changeComponent(1, 0, 5);
|
||||||
|
assert.equal(A.component(1, 0), 5);
|
||||||
|
});
|
||||||
|
});
|
||||||
|
describe("#equal()", function () {
|
||||||
|
it("should compares the matrices", function () {
|
||||||
|
var A = new LinearAlgebra.Matrix(3, 2, [[1, 2], [3, 4], [5, 6]]);
|
||||||
|
var B = new LinearAlgebra.Matrix(3, 2, [[1, 2], [3, 4], [5, 6]]);
|
||||||
|
var C = new LinearAlgebra.Matrix(2, 2, [[1, 2], [3, 4]]);
|
||||||
|
var D = new LinearAlgebra.Matrix(2, 2, [[1, 2], [5, 4]]);
|
||||||
|
assert.ok(A.equal(B));
|
||||||
|
assert.ok(!A.equal(C));
|
||||||
|
assert.ok(!C.equal(D));
|
||||||
|
});
|
||||||
|
});
|
||||||
|
describe("#add()", function () {
|
||||||
|
it("should return the result of the matrix addition", function () {
|
||||||
|
var A = new LinearAlgebra.Matrix(3, 2, [[1, 2], [3, 4], [5, 6]]);
|
||||||
|
var B = new LinearAlgebra.Matrix(3, 2, [[1, 2], [3, 4], [5, 6]]);
|
||||||
|
var C = A.add(B);
|
||||||
|
assert.equal(C.component(1, 0), 6);
|
||||||
|
assert.equal(C.component(1, 1), 8);
|
||||||
|
assert.equal(C.component(0, 0), 2);
|
||||||
|
});
|
||||||
|
});
|
||||||
|
describe("#scalar()", function () {
|
||||||
|
it("should return the result of the matrix-scalar multiplication", function () {
|
||||||
|
var A = new LinearAlgebra.Matrix(3, 2, [[1, 2], [3, 4], [5, 6]]);
|
||||||
|
var B = A.scalar(2);
|
||||||
|
var C = new LinearAlgebra.Matrix(3, 2, [[2, 4], [6, 8], [10, 12]]);
|
||||||
|
assert.ok(B.equal(C));
|
||||||
|
});
|
||||||
|
})
|
||||||
|
});
|
||||||
Reference in New Issue
Block a user