// -*- c++ -*-
//
// $COPYRIGHT$
//
//===========================================================================

#include "mtl/matrix.h"
#include "mtl/mtl.h"
#include "mtl/utils.h"  
#include "mtl/linalg_vec.h"
#include <math.h>

/*
  This example uses matrix-vector multiplication
  to rotates a vector.

  Sample Output

  Original vector: [3,4,]

  Rotated vector:  [-2,1.5,]
  
  */

using namespace mtl;
using namespace std;

int
main()
{
  //begin
  // Use the matrix generator to select a matrix type
  typedef matrix< double, 
                  rectangle<>, 
                  dense<>, 
                  column_major>::type Matrix; 
  // Use the std::vector based dense1D for our Vector type
  typedef dense1D<double> Vector;
  const int N = 2;
  double pi, theta;
  // Create the matrix object, with dimensions NxN
  Matrix rot(N, N);
  // Create two vectors of length N
  Vector vec1(N),vec2(N);

  pi = 4.0 * atan (1.0);
  theta = pi / 2.0;

  // Assign some values into Matrix rot
  rot(0,0) = cos(theta);
  rot(1,0) = sin(theta);
  rot(0,1) = -sin(theta);
  rot(1,1) = cos(theta);

  // Assign some values into vec1
  vec1[0] = 3.0;
  vec1[1] = 4.0;
  //end
  cout << endl;
  cout << "Original vector: ";
  print_vector(vec1);
  cout << endl;
  //begin

  // Compute rot*vec1*0.5 -> vec2
  // This uses the 3 argument version of mtl::mult.
  // mtl::mult(A,x,y),  A*x -> y
  // where in this example A=rot,x=(vec1*0.5), y=vec2
  mult(rot, scaled(vec1, 0.5), vec2);
  //end
  cout << "Rotated vector: ";
  print_vector(vec2);

  return 0;
}