linalg.js/objects.js

Linear Algebra Module

function delta(i, j) {
	return i == j ? 1 : 0;
}

function Complex(a, b) {
	this.real = a = a || 0;
	this.imag = b = b || 0;
	this.toString = function() {
		if (a == 0)
			return b + 'i';
		else if (b == 0)
			return a.toString();
		else
			return '(' + a + '+' + b + 'i)';
	}
}

function complexMult(a, b) {
	return new Complex(a.real * b.real + a.imag * b.imag, a.real * b.imag + a.imag * b.real);
}

function complexExp(z, exp) {
	//Exponentiation Rapide !!!
	var z2 = z;
	for (var i = 0; i < exp; i++) {
		z2 = complexMult(z2, z);
	}
	return z2;
}

module.exports.Complex = Complex;
module.exports.complexMult = complexMult;
module.exports.complexExp = complexExp;

//Vector
function Vector(...values) {
	return new Matrix(1, values.length, function(i, j) {
		return values[i];
	});
}
module.exports.Vector = Vector;

//Matrix
function Matrix(w, h, value = 0) {
	this.width = w;
	this.height = h;
	var mat = new Array(h);
	for (var i = 0; i < h; i++) {
		mat[i] = new Array(w);
		for (var j = 0; j < w; j++) {
			mat[i][j] = typeof value === 'function' ? value(i, j) : value;
		}
	}
	this.mat = mat;
	this.get = function(i, j) {
		return mat[i][j];
	};
	this.set = function(i, j, k) {
		mat[i, j] = k;
	}
	this.transpose = function() {
		return new Matrix(h, w, function(i, j) {
			return mat[j][i];
		});
	}
	this.toString = function() {
		var str = '[';
		for (var i = 0; i < h; i++) {
			str += (i === 0 ? '' : ' ') + '[';
			for (var j = 0; j < w; j++) {
				var number = this.mat[i][j].toString();
				str += number + ' '.repeat(8 - number.length);
			}
			str += ']' + (i === h - 1 ? '' : '\n');
		}
		str += ']\n';
		return str;
	}
}

function SquareMatrix(w, value = 0) {
	return new Matrix(w, w, value);
}

function UpperTriMatrix(w, value = 0) {
	return new Matrix(w, w, function(i, j) {
		if (i < j)
			return 0;
		else return typeof value === 'function' ? value(i, j) : value;
	})
}

function LowerTriMatrix(w, value = 0) {
	return new Matrix(w, w, function(i, j) {
		if (i > j)
			return 0;
		else return typeof value === 'function' ? value(i, j) : value;
	})
}

function NullMatrix(w) {
	return new Matrix(w, w, 0);
}

function IdentityMatrix(w) {
	return new Matrix(w, w, function(i, j) {
		return delta(i, j);
	});
}

function matrixMult(matA, matB) {

	var A = matA.mat;
	var B = matB.mat;

	console.log(matA.width + ' / ' + matB.height);
	if (matA.width != matB.height) {
		console.log('Error: Matrices Are Incompatible (%dx%d & %dx%d)', matA.height, matA.width, matB.height, matB.width);
		return;
	}

	return new Matrix(matB.width, matA.height, function(i, k) {
		var c = 0;
		for (var j = 0; j < matA.width; j++) {
			c += A[i][j] * B[j][k];
		}
		return c;
	});
}

function matrixExp(mat, exp) {
	//Exponentiation Rapide ...
	if (mat.width != mat.height) return null;
	if (exp < 0)
		return null;
	else if (exp == 0)
		return new IdentityMatrix(mat.width);
	else {
		var newMat = mat;
		for (var i = 1; i < exp; i++) {
			newMat = matrixMult(newMat, mat);
		}
		return newMat;
	}
}

module.exports.Matrix = Matrix;
module.exports.UpperTriMatrix = UpperTriMatrix;
module.exports.LowerTriMatrix = LowerTriMatrix;
module.exports.IdentityMatrix = IdentityMatrix;
module.exports.NullMatrix = NullMatrix;
module.exports.matrixMult = matrixMult;
module.exports.matrixExp = matrixExp;

function Polynom(...coeffs) {
	this.polynom = coeffs;
	this.toString = function() {
		str = '';
		for (var i = coeffs.length - 1; i >= 0; i--) {
			str += coeffs[i].toString() + (i == 0 ? '' : 'X^' + i + ' + ');
		}
		return str;
	}
	this.evaluate = function(value) {
	}
}

module.exports.Polynom = Polynom;