// test_46_nl.java       compile    javac -cp . test_46_nl.java
//                        execute    java  -cp . test_46_nl
// see test_nav2_newton3.java
// needs simeq_newton3.java
// test Ai,0*x0 + Ai,1*x1 + Ai,2*x2 + Ai,3*x3 + Ai4*x0*x1 + Ai,5*x2*x3 = yi;
// 6 variables, thus need values for i=0..5
// 
public class test_46_nl
{
  int neqn = 4; // for x0, x1, x2, x3
  int nlin = 2; // for x0*x1  x2*x3
  int ntot = neqn+nlin;
  double A[][] = new double[neqn][ntot];
  //
  //coef x0     x1     x2     x3   x0*x1  x2*x3     X ,unk   Y
  // | A0,0   A0,1   A0,2   A0,3   A0,4   A0,5  | | X0    | |Y0 |
  // | A1,0   A1,1   A1,2   A1,3   A1,4   A1,5  | | X1    | |Y1 |
  // | A2,0   A2,1   A2,2   A2,3   A2,4   A2,5  |*| X2    |=|Y2 |
  // | A3,0   A3,1   A3,2   A3,3   A3,4   A3,5  | | X3    | |Y3 |
  //                                              | X0*x1 |
  //                                              | X2*x3 |
  //
  double Y[] = new double[neqn];
  double X[] = new double[ntot]; // solution A X = Y
  int var1[] = { 0,  1,  2,  3,  0,  2}; // products x0*x1 x2*x3
  int var2[] = {-1, -1, -1, -1,  1,  3};
  int var3[] = {-1, -1, -1, -1, -1, -1}; // all -1 no x0*x1*x2
  int maxitr = 25; // maximum iterations of newton method
  double b = 1.00; // stability factor
  double eps = 1.0e-6;
  Boolean debug = true;
  double x0 = 1.0; // the correct solution
  double x1 = 2.0;
  double x2 = 3.0;
  double x3 = 4.0;
  double max_err = 0.0;
    
  public test_46_nl() // constructor
  {
    System.out.println("test_46_nl.java running");
    System.out.println("neqn="+neqn+", nlin="+nlin+", ntot="+ntot);
    System.out.println("   var1,  var2,  var3 ");
    for(int i=0; i<ntot; i++)
    {
	System.out.println("["+i+"] "+var1[i]+", "+var2[i]+", "+var3[i]);
    }
    System.out.println(" ");

    init_matrix(); // A and Y

    for(int i=0; i<neqn; i++)
    {
      for(int j=0; j<ntot; j++)
      {
	System.out.println("A["+i+"]["+j+"] ="+A[i][j]);
      } // end j
      System.out.println("Y["+i+"] ="+Y[i]);
      System.out.println(" ");
    }
    System.out.println(" ");

    for(int j=0; j<ntot; j++)
    {
      X[j] = 2.5; // initial guess
    } // end j

    new simeq_newton3(neqn, nlin, A, Y, var1, var2, var3, X,
		      maxitr, b, eps, 0);    
    System.out.println("given x0="+x0+", x1="+x1+", x2="+x2);
    System.out.println("given x3="+x3+", x0*x1="+(x0*x1)+", x2*x3="+(x2*x3));
    System.out.println("solution x[0], x[1], x[2] ");
    System.out.println("solution x[3], x[4], x[5] ");
    System.out.println(X[0]+"  "+X[1]+"  "+X[2]);
    System.out.println(X[3]+"  "+X[4]+"  "+X[5]);
    System.out.println(" ");

    // check solution
    max_err = check(x0, x1, x2,  x3, neqn, X);
    System.out.println("max_err= "+max_err);

    System.out.println("test_46_nl.java finished");
  } // end test_46_nl

  void init_matrix()
  {
    // specific for test, you must generate A and then Y
    for(int i=0; i<neqn; i++)
    {
      for(int j=0; j<ntot; j++)
      {
	A[i][j] = Math.random(); // typically problem
      } // end j
      Y[i] = eqn(x0, x1, x2, x3,
		 A[i][0],  A[i][1],  A[i][2],
		 A[i][3],  A[i][4],  A[i][5]);
    } // end i
  } // end init_matrix

  double eqn(double x0, double x1, double x2 ,double x3,
	     double c0, double c1, double c2,
	     double c3, double c4, double c5)  // ntot
  {
    return c0*x0 + c1*x1 + c2*x2 + c3*x3 + c4*x0*x1 + c5*x2*x3;	
  } // end eqn

  double check(double x0, double x1, double x2 ,double x3,
	       int neqn, double X[])
  {
    double err = 0.0;
    double soln[] = new double[neqn];
    soln[0] = x0;
    soln[1] = x1;
    soln[2] = x2;
    soln[3] = x3;
    for(int i=0; i<neqn; i++)
    {
      err = Math.max(err, Math.abs(X[i]-soln[i]));
    } // end i
    return err;	
  } // end eqn

  public static void main (String[] args)
  {
    new test_46_nl();
  }
} // end test_46_nl.java