// Instructions:
// (1) Insert code to compute the least squares solution. Compile and
//     execute to verify the same solution as you had before.
// (2) Change the matrix by adding the column (8,1,0) and see what happens.
//
// NOTE: you will need lintool.jar in your CLASSPATH. 

import edu.gwu.lintool.*;
import org.edisonwj.draw3d.*;
import javafx.application.*;
import javafx.scene.*;
import javafx.scene.paint.*;
import javafx.stage.*;
import java.util.*;

public class LeastSquaresExample3D  extends Application {

    String title = "least squares example";

    void drawingCommands () 
    {
	// RHS b
	double[] b = {5,6,3};
	d3.setDrawColor (Color.BLUE);
	d3.drawVector (b);

	// Two columns of the matrix (just for drawing).
	double[] c1 = {6,2,0};
	double[] c2 = {4,3,0};
	d3.drawVector (c1);
	d3.drawVector (c2);

	// The matrix
	double[][] A = {
	    {6, 4},
	    {2, 3},
	    {0, 0}
        };

	// INSERT YOUR CODE HERE:
	
	// Compute the transpose of A:
	double[][] AT = 

	// Multiply A by AT (with AT on the left)
	double[][] ATA = 

	// Get the inverse of ATA:
	LinResult L = LinToolLibrary.inverse (ATA);
	if (L.Ainv == null) {
	    System.out.println ("No inverse exists for ATA");
	    System.exit (0);
	}
	MatrixTool.print (L.Ainv);

	// Compute approx solution x = ATA^-1 * A^T * b in two steps:
	// Step 1: first compute AT * b
	double[] ATb = 
	// Step 2: multiply the result on the left by ATA^-1
	double[] x = 

	System.out.println ("x[0]=" + x[0] + " x[1]=" + x[1]);

	// Use x[0],x[1] in the linear combination of c1, c2:
	double[] y = MatrixTool.add (
			MatrixTool.scalarMult (x[0], c1),
			MatrixTool.scalarMult (x[1], c2)
		     );

	// The difference vector z:
	double[] z = MatrixTool.sub (b, y);

	// Draw y and z:
	d3.setDrawColor (Color.GREEN);
	d3.drawVector (y);
	d3.setDrawColor (Color.RED);
	d3.drawArrow (y[0],y[1],y[2], b[0],b[1],b[2]);
    }

    // No need to read further
    //////////////////////////////////////////////////////////

    Draw3D d3;

    void preambleCommands ()
    {
	d3.setAmbientLight(false);
	d3.setPointLight(true);
	d3.setCumulate(false);
	d3.setSequencingOn();
	d3.setVectorRadius(1);
        d3.setArrowRadius(1);
    }

    public void start (Stage primaryStage) 
    {
	d3 = new Draw3D ();
	Scene scene = d3.buildScene ();
	preambleCommands ();
	drawingCommands ();
	d3.setStart ();
	primaryStage.setScene (scene);
	primaryStage.setTitle (title);
	primaryStage.show ();
    }

    public static void main (String[] argv)
    {
	launch (argv);
    }

}