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itsvinayak
311
Linear-Algebra-Javascript/src/la_lib.js
Normal file
311
Linear-Algebra-Javascript/src/la_lib.js
Normal file
@@ -0,0 +1,311 @@
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||||
/*
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author: Christian Bender
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license: MIT-license
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The namespace LinearAlgebra contains useful classes and functions for dealing with
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linear algebra under JavaScript.
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*/
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var LinearAlgebra;
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(function (LinearAlgebra) {
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/*
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class: Vector
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This class represents a vector of arbitrary size and operations on it.
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*/
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var Vector = /** @class */ (function () {
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// constructor
|
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function Vector (N, comps) {
|
||||
if (comps === undefined) {
|
||||
comps = []
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||||
}
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||||
this.components = new Array(N)
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||||
if (comps.length === 0) {
|
||||
for (var i = 0; i < N; i++) {
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||||
this.components[i] = 0.0
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||||
}
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||||
} else {
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if (N === comps.length) {
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this.components = comps
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} else {
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throw new Error('Vector: invalide size!')
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}
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}
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} // end of constructor
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// returns the size of this vector.
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// not the eulidean length!
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Vector.prototype.size = function () {
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||||
return this.components.length
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}
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// computes the eulidean length.
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Vector.prototype.eulideanLength = function () {
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||||
var sum = 0
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||||
for (var i = 0; i < this.components.length; i++) {
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sum += this.components[i] * this.components[i]
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}
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return Math.sqrt(sum)
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}
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||||
// getter for the components of the vector.
|
||||
// returns a specified component (index)
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||||
Vector.prototype.component = function (index) {
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return this.components[index]
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}
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||||
// setter for a specified component of this vector.
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||||
Vector.prototype.changeComponent = function (index, value) {
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||||
if (index >= 0 && index < this.components.length) {
|
||||
this.components[index] = value
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||||
} else {
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||||
throw new Error('changeComponent: index out of bounds!')
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||||
}
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}
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// vector addition
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Vector.prototype.add = function (other) {
|
||||
if (this.size() === other.size()) {
|
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var SIZE = this.size()
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||||
var ans = new Vector(SIZE)
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||||
for (var i = 0; i < SIZE; i++) {
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ans.changeComponent(i, (this.components[i] + other.component(i)))
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||||
}
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return ans
|
||||
} else {
|
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throw new Error('add: vector must have same size!')
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}
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}
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||||
// vector subtraction
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Vector.prototype.sub = function (other) {
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||||
if (this.size() === other.size()) {
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var SIZE = this.size()
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var ans = new Vector(SIZE)
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||||
for (var i = 0; i < SIZE; i++) {
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ans.changeComponent(i, (this.components[i] - other.component(i)))
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}
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return ans
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} else {
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throw new Error('add: vector must have same size!')
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||||
}
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}
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// dot-product
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Vector.prototype.dot = function (other) {
|
||||
var sum = 0
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if (other.size() === this.size()) {
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var SIZE = other.size()
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for (var i = 0; i < SIZE; i++) {
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sum += this.components[i] * other.component(i)
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||||
}
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return sum
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||||
} else {
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throw new Error('dot: vectors must have same size!')
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}
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}
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// scalar multiplication
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Vector.prototype.scalar = function (s) {
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var SIZE = this.size()
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var ans = new Vector(SIZE)
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for (var i = 0; i < SIZE; i++) {
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ans.changeComponent(i, (this.components[i] * s))
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||||
}
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return ans
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}
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// returns a string representation of this vector.
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Vector.prototype.toString = function () {
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var ans = '('
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||||
var SIZE = this.components.length
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for (var i = 0; i < SIZE; i++) {
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if (i < SIZE - 1) {
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ans += this.components[i] + ','
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} else {
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ans += this.components[i] + ')'
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}
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}
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return ans
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}
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// converts this vector in a unit basis vector and returns it.
|
||||
// the One is on position 'pos'
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Vector.prototype.createUnitBasis = function (pos) {
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||||
if (pos >= 0 && pos < this.components.length) {
|
||||
for (var i = 0; i < this.components.length; i++) {
|
||||
if (i === pos) {
|
||||
this.components[i] = 1.0
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} else {
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this.components[i] = 0.0
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}
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}
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} else {
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throw new Error('createUnitBasis: index out of bounds')
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}
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return this
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}
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// normalizes this vector and returns it.
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Vector.prototype.norm = function () {
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var SIZE = this.size()
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var quotient = 1.0 / this.eulideanLength()
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for (var i = 0; i < SIZE; i++) {
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this.components[i] = this.components[i] * quotient
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}
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return this
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}
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// returns true if the vectors are equal otherwise false.
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Vector.prototype.equal = function (other) {
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var ans = true
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var SIZE = this.size()
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var EPSILON = 0.001
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if (SIZE === other.size()) {
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for (var i = 0; i < SIZE; i++) {
|
||||
if (Math.abs(this.components[i] - other.component(i)) > EPSILON) {
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ans = false
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}
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||||
}
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} else {
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ans = false
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}
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return ans
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}
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return Vector
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}()) // end of class Vector
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LinearAlgebra.Vector = Vector
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// -------------- global functions ---------------------------------
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// returns a unit basis vector of size N with a One on position 'pos'
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function unitBasisVector (N, pos) {
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var ans = new Vector(N)
|
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for (var i = 0; i < N; i++) {
|
||||
if (i === pos) {
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ans.changeComponent(i, 1.0)
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} else {
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ans.changeComponent(i, 0)
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}
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}
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return ans
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}
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LinearAlgebra.unitBasisVector = unitBasisVector
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// returns a random vector with integer components (between 'a' and 'b') of size N.
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function randomVectorInt (N, a, b) {
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var ans = new Vector(N)
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for (var i = 0; i < N; i++) {
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ans.changeComponent(i, (Math.floor((Math.random() * b) + a)))
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||||
}
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return ans
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||||
}
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LinearAlgebra.randomVectorInt = randomVectorInt
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// returns a random vector with floating point components (between 'a' and 'b') of size N.
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function randomVectorFloat (N, a, b) {
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var ans = new Vector(N)
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||||
for (var i = 0; i < N; i++) {
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||||
ans.changeComponent(i, ((Math.random() * b) + a))
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||||
}
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||||
return ans
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||||
}
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||||
LinearAlgebra.randomVectorFloat = randomVectorFloat
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||||
// ------------------ end of global functions -----------------------------
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||||
/*
|
||||
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.
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||||
function Matrix (row, col, comps) {
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||||
if (comps === undefined) {
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||||
comps = []
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||||
}
|
||||
if (comps.length === 0) {
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this.matrix = []
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var rowVector = []
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||||
for (var i = 0; i < row; i++) {
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for (var j = 0; j < col; j++) {
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rowVector[j] = 0
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}
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||||
this.matrix[i] = rowVector
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||||
rowVector = []
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||||
}
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||||
} else {
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this.matrix = comps
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||||
}
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||||
this.rows = row
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||||
this.cols = col
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||||
}
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||||
// returns the specified component.
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||||
Matrix.prototype.component = function (x, y) {
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if (x >= 0 && x < this.rows && y >= 0 && y < this.cols) {
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return this.matrix[x][y]
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} else {
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throw new Error('component: index out of bounds')
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}
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}
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||||
// changes the specified component with value 'value'.
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Matrix.prototype.changeComponent = function (x, y, value) {
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if (x >= 0 && x < this.rows && y >= 0 && y < this.cols) {
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this.matrix[x][y] = value
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||||
} else {
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||||
throw new Error('changeComponent: index out of bounds')
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}
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}
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// returns a string representation of this matrix.
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Matrix.prototype.toString = function () {
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var ans = ''
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for (var i = 0; i < this.rows; i++) {
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ans += '|'
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for (var j = 0; j < this.cols; j++) {
|
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if (j < this.cols - 1) {
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ans += this.matrix[i][j] + ','
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} else {
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if (i < this.rows - 1) {
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ans += this.matrix[i][j] + '|\n'
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||||
} else {
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ans += this.matrix[i][j] + '|'
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}
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||||
}
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}
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}
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return ans
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}
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// returns the dimension rows x cols as number array
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Matrix.prototype.dimension = function () {
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var ans = []
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ans[0] = this.rows
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||||
ans[1] = this.cols
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return ans
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}
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||||
// matrix addition. returns the result.
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||||
Matrix.prototype.add = function (other) {
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||||
if (this.rows === other.dimension()[0] &&
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this.cols === other.dimension()[1]) {
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||||
var ans = new Matrix(this.rows, this.cols)
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||||
for (var i = 0; i < this.rows; i++) {
|
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for (var j = 0; j < this.cols; j++) {
|
||||
ans.changeComponent(i, j, (this.matrix[i][j] + other.component(i, j)))
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||||
}
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||||
}
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||||
return ans
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||||
} else {
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||||
throw new Error('add: matrices must have same dimension!')
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}
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}
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// returns true if the matrices are equal, otherwise false.
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||||
Matrix.prototype.equal = function (other) {
|
||||
var ans = true
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||||
var EPSILON = 0.001
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||||
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++) {
|
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if (Math.abs(this.matrix[i][j] - other.component(i, j)) > EPSILON) {
|
||||
ans = false
|
||||
}
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||||
}
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||||
}
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} else {
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ans = false
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||||
}
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return ans
|
||||
}
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||||
// matrix-scalar multiplication
|
||||
Matrix.prototype.scalar = function (c) {
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var ans = new Matrix(this.rows, this.cols)
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for (var i = 0; i < this.rows; i++) {
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||||
for (var j = 0; j < this.cols; j++) {
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||||
ans.changeComponent(i, j, (this.matrix[i][j] * c))
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||||
}
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||||
}
|
||||
return ans
|
||||
}
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return Matrix
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||||
}()) // end of class Matrix
|
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LinearAlgebra.Matrix = Matrix
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})(LinearAlgebra || (LinearAlgebra = {})) // end of namespace LinearAlgebra
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342
Linear-Algebra-Javascript/src/la_lib.ts
Normal file
342
Linear-Algebra-Javascript/src/la_lib.ts
Normal file
@@ -0,0 +1,342 @@
|
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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.
|
||||
*/
|
||||
|
||||
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
|
||||
|
||||
|
||||
Reference in New Issue
Block a user