var img = new Image();
img.src = '../res/testimage.jpg';
img.onload = Matrix(function() {
   var U=Matrix(this), S, V, R;
   "[U,S,V]=U.SVD"            
   [15,10,5,2].forEach(j=>{
     for (var i=j; i < S.rows; i++) S[i]=0;               
     "R=U*S~*V'"
     Matrix.show(R,document.body);
   });
});

// Find the rigid transform that transforms pointset A to pointset B.
// A and B are matrices with nr_of_points rows and nr_of_dimensions columns.
// It returns a square nr_of_dimensions dimensional matrix T so that A*T=B
var findTransform = Matrix(function(A,B){
  var mA, mB, U, S, V, COV;

// Center dataset by subtracting average row..
  "mA = A-A.avg"
  "mB = B-B.avg"

// Calculate covariance matrix.
  "COV = mA'*mB"

// do SVD factorisation on covariance matrix.
  "[U,S,V] = COV.SVD"

// Find transformation that brings A to B
  "return U*V'"
});

// a skinny matrix.
  var A = Matrix([[1,2],[3,4],[5,6],[7,8]]); 

// an empty matrix.
  var B = Matrix(4,2);

// a matrix from an image, video or canvas : 
  var C = Matrix(document.getElementById('myImage'));

// Solve (x=0,x=1,y=0)
  var solution = Matrix("[[1,0],[1,0],[0,1]]\\[0,1,0]");

// add the transpose of a to b then multiply with c
  var D = Matrix("(A'+B)*C");

// Multiply B with the inverse of A : 
  var E = Matrix("B*A^-1");

// you can store these expressions as functions.
// simpy add the arguments list as second parameter.
  var solve = Matrix("(A'*A)^-1*A'*Y","A,Y"); 
  var solution2 = solve([[1,0],[1,0],[0,1]],[0,1,0]);

var sample = Matrix(function(){
  var A=[[1,0],[1,0],[0,1]];
  var Y=[0,1,0];
  "return A\Y"
});

var solve = Matrix(function(A,Y){
  var Ai = Matrix(A);
  "Ai = (A'*A)^-1*A'"
  "return Ai*Y"
});
solve([[1,0],[1,0],[0,1]],[0,1,0]);

var fitCubic = Matrix(function (data) {
  var Vandermonde = data.map(x=>[x[0]*x[0]*x[0],x[0]*x[0],x[0],1]);
  var Rhs = data.map(x=>x[1]);
  "return Vandermonde\Rhs"
});

// Linear Least squares, regularised linear least squares, weighted linear least squares.
var lls  = Matrix("A\\Y","A,Y");
var rlls = Matrix("(A'*A + l*I)^-1*A'*Y","A,Y,I,l");
var wlls = Matrix("(A'*W~*A)^-1*A'*W~*Y","A,Y,W");

// Find intersection of the system ( y=0, x=1, y=2, x=3 )
var A=[[0,1],[1,0],[0,1],[1,0]];
var Y=[0,1,2,3];

// Using linear least squares
lls(A,Y).log();

// Regularised .. importance of arg size is 0.1
rlls(A,Y,Matrix.identity(2),0.1).log();

// Weighted .. first two more important.
wlls(A,Y,[1,1,0.5,0.5]).log();