// Computes the Inverse of a matrix
function inverse(A):Array{
	var Ainv, E, i, j, k, n, swap;
	n = A.length;
	Ainv = identity(n);
	E = identity(n);
	for(j = 0; j < n; j++){
		for(i = j; i < n; i++){
			if(i == j){
				if(A[i][j] == 0){
					for(k = j + 1; k < n; k++){
						if(A[k][j] != 0){
							swap = A[i];
							A[i] = A[k];
							A[k] = swap;
							swap = Ainv[i];
							Ainv[i] = Ainv[k];
							Ainv[k] = swap;
							k = n;
						}
					}
				}
				E[i][j] = 1 / A[i][j];
			}else{
				E[i][j] = -A[i][j];
			}
			A = multiply(E, A);
			Ainv = multiply(E, Ainv);
			E = identity(n);
		}
	}
	for(j = n - 1; j > 0; j--){
		for(i = j - 1; i > -1; i--){
			E[i][j] = -A[i][j];
			A = multiply(E, A);
			Ainv = multiply(E, Ainv);
			E = identity(n);
		}
	}
	return Ainv;
}

// Multiplies two matrices together by making use of the Dot Product
function multiply(A, B):Array{
	var M, i, j;
	B = transpose(B);
	M = new Array(A.length);
	for(i = 0; i < M.length; i++){
		M[i] = new Array(B.length);
	}
	for(i = 0; i < A.length; i++){
		for(j = 0; j < B.length; j++){
			M[i][j] = dotProduct([A[i]],[B[j]]);
		}
	}
	return M;
}

// Calculate the Transpose of a matrix
// Takes matrices of any type so long as they're enclosed in double brackets
// I.E. [[]] This applies to 1 x 1 matrices as well as row and column vectors
function transpose(A):Array{
	var T, i, j;
	T = new Array(A[0].length);
	for(i = 0; i < T.length; i++){
		T[i] = new Array(A.length);
	}
	for(i = 0; i < A.length; i++){
		for(j = 0; j < A[0].length; j++){
			T[j][i] = A[i][j];
		}
	}
	return T;
}

// Calculate the Dot Product of two vectors
// Takes two row vectors of the form [[,,,...]]
// OR column vectors of the form [[],[],...]
function dotProduct(a, b):Number{
	var product = 0;
	var i, j;
	if(a.length == 1){
		for(j = 0; j < a[0].length; j++){
			product += a[0][j] * b[0][j];
		}
	}else{
		for(i = 0; i < a.length; i++){
			product += a[i][0] * b[i][0];
		}
	}
	return product;
}

// Returns an identity matrix of Nth size
function identity(n):Array{
	var A, i, j;
	A = new Array(n);
	for(i = 0; i < n; i++){
		A[i] = new Array(n);
	}
	for(i = 0; i < n; i++){
		for(j = 0; j < n; j++){
			if(i == j){
				A[i][j] = 1;
			}else{
				A[i][j] = 0;
			}
		}
	}
	return A;
}