// test_phiquad2D.java   test evaluation of derivatives 

class test_phiquad2D
{
  test_phiquad2D()
  {
    double x, y, up, upp;
    double xx[] = new double[12];
    double yy[] = new double[12];
    double u[] = new double[12];
    double u2[][] = new double[12][12];
    double Q[] = new double[8];
    int i, j;
    double hx=0.15;
    int nx=10;
    double hy=0.2;
    int ny=10;
    int a1[] = new int[ 5];
    int b1[] = new int[ 1]; // first derivative 
    int a2[] = new int[ 9];
    int b2[] = new int[ 1]; // second derivative 

    double dx, dxx;
    double dy, dyy;
    double dxy;

    System.out.println("test_phiquad2D.java running");
    phiquad2D P = new phiquad2D();
    nderiv N = new nderiv();
    
    N.deriv(1, 5, 2, a1, b1);
    N.deriv(2, 9, 4, a2, b2);

    x=0.1;
    for(i=0; i<10; i++)
    {
      xx[i]=x;
      x=x+hx;
    }

    y=0.2;
    for(i=0; i<10; i++)
    {
      yy[i]=y;
      y=y+hy;
    }

    Q[0]=0.1;
    Q[1]=0.2;
    Q[2]=1.3;
    Q[3]=0.3;
    Q[4]=1.4;
    Q[5]=2.4;
    Q[6]=0.6;
    Q[7]=2.3;
    System.out.println("x1="+Q[0]+", y1="+Q[1]);
    System.out.println("x2="+Q[2]+", y2="+Q[3]);
    System.out.println("x3="+Q[4]+", y3="+Q[5]);
    System.out.println("x4="+Q[6]+", y4="+Q[7]);
    System.out.println("phi(x1,y1)="+P.phi(Q,Q[0],Q[1])+"  should be 1");
    System.out.println("phi(x2,y2)="+P.phi(Q,Q[2],Q[3])+"  should be 0");
    System.out.println("phi(x3,y3)="+P.phi(Q,Q[4],Q[5])+"  should be 0");
    System.out.println("phi(x4,y4)="+P.phi(Q,Q[6],Q[7])+"  should be 0");

    for(i=0; i<5; i++) // base phi quad 2D
    {
      for(j=0; j<5; j++)
      {
        u2[i][j]=P.phi(Q,xx[i],yy[j]); // base phi 
      }
    }
    dx=(1.0/(b1[0]*hx))*(a1[0]*u2[0][2]+a1[1]*u2[1][2]+a1[2]*u2[2][2]+
                      a1[3]*u2[3][2]+a1[4]*u2[4][2]);
    up=P.phix(Q,xx[2],yy[2]);
    System.out.println("at x="+xx[2]+", y="+yy[2]);
    System.out.println("phiquad2D,phix="+up+", dx="+dx+", err="+(up-dx));

    dy=(1.0/(b1[0]*hy))*(a1[0]*u2[2][0]+a1[1]*u2[2][1]+a1[2]*u2[2][2]+
                      a1[3]*u2[2][3]+a1[4]*u2[2][4]);
    up=P.phiy(Q,xx[2],yy[2]);
    System.out.println("at x="+xx[2]+", y="+yy[2]);
    System.out.println("phiquad2D,phiy="+up+", dy="+dy+", err="+(up-dy));


    for(i=0; i<9; i++)
    {
      for(j=0; j<9; j++)
      {
        u2[i][j]=P.phi(Q,xx[i],yy[j]); // base phi 
      }
    }

    upp=P.phixx(Q,xx[4],yy[4]);
    System.out.println("at x="+xx[4]+", y="+yy[4]);
    dxx=(1.0/(b2[0]*hx*hx))*(a2[0]*u2[0][4]+a2[1]*u2[1][4]+a2[2]*u2[2][4]+
                          a2[3]*u2[3][4]+a2[4]*u2[4][4]+a2[5]*u2[5][4]+
                          a2[6]*u2[6][4]+a2[7]*u2[7][4]+a2[8]*u2[8][4]);
    System.out.println("phiquad2D,phixx="+upp+", dxx="+dxx+", err="+(upp-dxx));

    upp=P.phiyy(Q,xx[4],yy[4]);
    dyy=(1.0/(b2[0]*hy*hy))*(a2[0]*u2[4][0]+a2[1]*u2[4][1]+a2[2]*u2[4][2]+
                          a2[3]*u2[4][3]+a2[4]*u2[4][4]+a2[5]*u2[4][5]+
                          a2[6]*u2[4][6]+a2[7]*u2[4][7]+a2[8]*u2[4][8]);
    System.out.println("at x="+xx[4]+", y="+yy[4]);
    System.out.println("phiquad2D,phiyy="+upp+", dyy="+dyy+", err="+(upp-dyy));


    for(i=0; i<5; i++)
    {
      u[i]=(1.0/(b1[0]*hy))*(a1[0]*u2[i][0]+a1[1]*u2[i][1]+a1[2]*u2[i][2]+
                             a1[3]*u2[i][3]+a1[4]*u2[i][4]);
    }
    dxy=(1.0/(b1[0]*hx))*(a1[0]*u[0]+a1[1]*u[1]+a1[2]*u[2]+a1[3]*u[3]+a1[4]*u[4]);
    up=P.phixy(Q,xx[2],yy[2]);
    System.out.println("at x="+xx[2]+", y="+yy[2]);
    System.out.println("phiquad2D,phixy="+up+", dxy="+dxy+", err="+(up-dxy));

  } // end test_phiquad2D 

  public static void main (String[] args)
  {
    new test_phiquad2D();
  }
} // end test_phiquad2D class