Add new symmetric matrix class and so a new trinagular number method in Sequence class. Modify constructor and the addition routine in matrix classes. Add a new property to WObjekt to store the number of operations.

src/math/Maths.java

@@ -778,6 +778,18 @@ final public class Maths{
 		return sum;
 	}
 
+	/**
+	 * @param a
+	 * @return sum of all values in array.
+	 */
+	public static Integer sum(Integer[] a) {
+		int i;
+		Integer sum = 0;
+		for(i=0; i<a.length; i++)
+			sum += a[i];
+		return sum;
+	}
+
 	/**
 	 * @param a array
      * @param is first index

src/math/Sequence.java

@@ -2,7 +2,41 @@ package math;
 
 import math.number.Rational;
 
-class Sequence {
+public class Sequence {
+	
+	/**
+	 * Triangular numbers.
+	 * 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120 …
+	 * T<sub>n</sub> = &sum;k = 1 + 2 + 3 + 4 + &hellip; + n = 0.5*n*(n+1).
+	 * @param n
+	 * @return
+	 */
+	public static int triangularNumber(int n){
+		return polygonalNumber(3,n);
+	}
+	
+	/**
+	 * Triangular roots.
+	 * @param x
+	 * @return
+	 */
+	public static double triangularRoot(int x){
+		return (Math.sqrt(8*x+1)-1)/2;
+	}
+	
+	/**
+	 * (s-2)*n*(n-1)/2+n
+	 * @param s
+	 * @param n
+	 * @return
+	 */
+	public static int polygonalNumber(int s, int n){
+		switch(s){
+			case 3:  return n*(n+1)/2;
+			case 4:  return n*n;
+			default: return n*((s-2)*n-s)/2;
+		}
+	}
 	
 	/**
 	 *  Prints out binomial coefficients such that such that a[N][k] contains 

src/math/Series.java

@@ -124,6 +124,7 @@ public class Series{
 	
 	/**
 	 * The sum of a geometric series.
+	 * a+ar+ar<sup>2</sup>+ar<sup>3</sup>+&hellip;
 	 * @param a start term
 	 * @param r common ratio
 	 * @return sum
@@ -136,6 +137,7 @@ public class Series{
 	
 	/**
 	 * The sum of a geometric series.
+	 * a+ar+ar<sup>2</sup>+ar<sup>3</sup>+&hellip;
 	 * @param a start term
 	 * @param r common ratio
 	 * @return sum
@@ -148,6 +150,7 @@ public class Series{
 	
 	/**
 	 * The sum of a geometric series.
+	 * a+ar+ar<sup>2</sup>+ar<sup>3</sup>+&hellip;+ar<sup>n-1</sup>.
 	 * @param a start term
 	 * @param r common ratio
 	 * @param n first n terms

src/math/matrix/Diagonal2D.java

@@ -1,5 +1,7 @@
 package math.matrix;
 
+import exception.IllegalDimensionException;
+
 /**
  * 2D diagonal matrix object d<sub>ij</sub>&isin;&#x211D;, i&ne;j=0
  * with 2 rows and 2 columns
@@ -17,6 +19,12 @@ public class Diagonal2D extends Matrix2D {
 		n = 2;
 		data = new double[2];
 	}
+	
+	public Diagonal2D(double... i){
+		m = 2;
+		n = 2;
+		data = i;
+	}
 
 	/**
 	 * Generate an n-by-n identity matrix.
@@ -35,6 +43,34 @@ public class Diagonal2D extends Matrix2D {
 	public void set(int i, double d){
 		data[i] = d;
 	}
+    
+    /**
+     * Subtract two matrices of the same dimension (entrywise subtraction).
+     * The subtraction of two m-by-n matrices <b>A</b> and <b>B</b>,
+     * is again an m-by-n matrix computed by subtracting corresponding elements.
+     * @param B matrix
+     * @return <b>C</b> = <b>A</b> - <b>B</b>, entrywise subtracted matrix
+     * @throws IllegalDimensionException
+     */
+    public Matrix minus(Matrix B) throws IllegalDimensionException{
+    	checkDimensions(B);
+    	int i,j;
+        Matrix c = createAddition(B);
+//		System.out.println(this instanceof Diagonal2D);
+//		System.out.println(this);
+//		System.out.println(B instanceof Diagonal2D);
+//		System.out.println(B);
+//		System.out.println(c instanceof Diagonal2D);
+//		System.out.println(c);
+        if(B instanceof Diagonal)
+        	for(i=0; i<n; i++)
+        		c.minus(i, i, ((Diagonal) B).get(i));
+        else
+	        for(i=0; i<m; i++)
+	            for(j=0; j<n; j++)
+	                c.minus(i,j, B.get(i,j));
+        return c;
+    }
 
 	public String toString(){
 		return Matrix2D.diag(data).toString();

src/math/matrix/Matrix.java

@@ -27,7 +27,7 @@ import exception.SingularException;
  */
 public class Matrix extends WObject implements Cloneable, Serializable{
 	
-	enum Flag{Square, Symmetric} // TODO: subclass?
+	enum Flag{Square}
 	
 	/**
 	 * UID
@@ -235,7 +235,15 @@ public class Matrix extends WObject implements Cloneable, Serializable{
     	this(a.n, a.get());
     }
 	
-	public Matrix create(int m, int n){
+	private Matrix copy(){
+		if(this instanceof TensorII2D) return new TensorII2D(this);
+		if(this instanceof Matrix2D) return new Matrix2D(this);
+		if(this instanceof Matrix3D) return new Matrix3D(this);
+		if(this instanceof Diagonal) return new Diagonal(this);
+		else return new Matrix(this);
+	}
+	
+	private Matrix create(int m, int n){
 		if(this instanceof TensorII2D) return new TensorII2D();
 		if(this instanceof TensorII) return new TensorII();
 		if(this instanceof Matrix3D) return new Matrix3D(n);
@@ -245,22 +253,24 @@ public class Matrix extends WObject implements Cloneable, Serializable{
 		else return new Matrix(m,n);
 	}
 	
-	public Matrix create(int m, int n, Matrix B){
+	protected Matrix createAddition(Matrix B){
-        if(m == 2 && B.n == 2) return new TensorII2D();
+		if(this instanceof Symmetric && B instanceof Symmetric) return new Symmetric(getN());
-        if(m == 3 && B.n == 3) return new TensorII();
+		if(this instanceof Diagonal && B instanceof Diagonal) return new Diagonal(getM(),getN());
-		if(this instanceof Matrix3D) return new Matrix3D(n);
+		if(this instanceof Matrix3D && B instanceof Matrix3D) return new Matrix3D(getN());
-		if(this instanceof Matrix2D) return new Matrix2D(n);
+		if(this instanceof Matrix2D && B instanceof Matrix2D) return new Matrix2D(getN());
-		if(this instanceof Matrix3D) return new Matrix3D(n);
+		if(this instanceof TensorII2D && B instanceof TensorII2D) return new TensorII2D();
-		if(this instanceof Diagonal) return new Diagonal(m,n);
+		else return new Matrix(getM(),getN());
-		else return new Matrix(m,n);
 	}
 	
-	public Matrix create(Matrix B){
+	private Matrix createMultiplication(Matrix B){ 
-		if(this instanceof TensorII2D) return new TensorII2D(B);
+//		System.out.println(n);
-		if(this instanceof Matrix2D) return new Matrix2D(B);
+        if(m == 2 && B.n == 2) return new TensorII2D();
-		if(this instanceof Matrix3D) return new Matrix3D(B);
+        if(m == 3 && B.n == 3) return new TensorII();
-		if(this instanceof Diagonal) return new Diagonal(B);
+		if(this instanceof Matrix3D) return new Matrix3D(B.n);
-		else return new Matrix(B);
+		if(this instanceof Matrix2D) return new Matrix2D(B.n);
+		if(this instanceof Matrix3D) return new Matrix3D(B.n);
+		if(this instanceof Diagonal) return new Diagonal(m,B.n);
+		else return new Matrix(m,B.n);
 	}
 	
 	private Vector create(int n){
@@ -470,6 +480,16 @@ public class Matrix extends WObject implements Cloneable, Serializable{
 		return c;
 	}
 
+	/**
+	 * Get the element A<sub>i</sub> at given index i
+	 * @param i index
+	 * @return the value at the given index i
+	 * @throws IllegalDimensionException 
+	 */
+	protected double get(int i){
+		return data[i];
+	}
+
 	/**
 	 * Get the element A<sub>ij</sub> at given row i and column j
 	 * @param i row
@@ -797,7 +817,7 @@ public class Matrix extends WObject implements Cloneable, Serializable{
      * @param j column
      * @param b scalar
      */
-    public void plus(int i, int j, double b){
+    protected void plus(int i, int j, double b){
     	set(i,j, get(i,j)+b);
     }
 
@@ -812,14 +832,20 @@ public class Matrix extends WObject implements Cloneable, Serializable{
     public Matrix plus(Matrix B) throws IllegalDimensionException{
     	checkDimensions(B);
     	int i,j;
-        Matrix c = create(this);
+        Matrix c = createAddition(B);
+        c.newOperation();
         if(B instanceof Diagonal)
-        	for(i=0; i<n; i++)
+        	for(i=0; i<m; i++)
-        		c.plus(i, i, ((Diagonal) B).get(i));
+        		for(j=0; j<n; j++){
+        			c.set(i, j, get(i,j)+((Diagonal) B).get(i));
+        			c.operate();
+        		}
         else
         	for(i=0; i<m; i++)
-        		for(j=0; j<n; j++)
+        		for(j=0; j<n; j++){
-        			c.plus(i,j, B.get(i,j));
+        			c.set(i,j, get(i,j)+B.get(i,j));
+        			c.operate();
+        		}
         return c;
     }
 
@@ -876,16 +902,22 @@ public class Matrix extends WObject implements Cloneable, Serializable{
     public Matrix minus(Matrix B) throws IllegalDimensionException{
     	checkDimensions(B);
     	int i,j;
-        Matrix c = create(B);
+        Matrix c = createAddition(B);
-        System.out.println(this);
+		//System.out.println(this instanceof Diagonal2D);
-        System.out.println(B);
+        //System.out.println(this);
+        //System.out.println(B);
         if(B instanceof Diagonal)
-        	for(i=0; i<n; i++)
+        	for(i=0; i<m; i++)
-        		c.minus(i, i, ((Diagonal) B).get(i));
+        		for(j=0; j<n; j++){
+        			c.set(i, j, get(i,j));
+        			if(i==j)
+        				c.set(i, j, get(i,j)-((Diagonal) B).get(i));
+        		}
         else
 	        for(i=0; i<m; i++)
-	            for(j=0; j<n; j++)
+	            for(j=0; j<n; j++){
-	                c.minus(i,j, B.get(i,j));
+	                c.set(i,j, get(i,j)-B.get(i,j));
+	            }
         return c;
     }
     
@@ -1007,7 +1039,10 @@ public class Matrix extends WObject implements Cloneable, Serializable{
 	public Matrix times(Matrix B) throws IllegalDimensionException{
 		int i,j,k;
         if(n != B.m) throw new IllegalDimensionException("Inner matrix dimensions must agree.");
-        Matrix c = create(m,B.n,B);
+        Matrix c = createMultiplication(B);
+//        System.out.println("times\n" + this);
+//        System.out.println(B);
+//        System.out.println(c);
         if(B instanceof Diagonal)
         	for(i=0; i<c.m; i++)
         		for(j=0; j<c.n; j++)
@@ -1603,7 +1638,7 @@ public class Matrix extends WObject implements Cloneable, Serializable{
         	 throw new IllegalArgumentException("Illegal matrix dimensions.");
 
         // create copies of the data
-        Matrix A = create(this);
+        Matrix A = copy();
         Vector B = create(b);
 
         // Gaussian elimination with partial pivoting
@@ -1696,7 +1731,7 @@ public class Matrix extends WObject implements Cloneable, Serializable{
      */
     public Matrix eigenvalues(){
     	if(eig == null) eig();
-    	return create(eig.getD());
+    	return new Matrix(eig.getD());
     }
 
     /**
@@ -1724,7 +1759,7 @@ public class Matrix extends WObject implements Cloneable, Serializable{
      */
     public Matrix eigenvectors(){
     	if(eig == null) eig();
-    	return create(eig.getV());
+    	return new Matrix(eig.getV());
     }
 	
     /**
@@ -1886,7 +1921,7 @@ public class Matrix extends WObject implements Cloneable, Serializable{
 	 * Check if size(A) == size(B)
 	 * @throws IllegalDimensionException 
 	 **/
-	private void checkDimensions(Matrix b) throws IllegalDimensionException {
+	protected void checkDimensions(Matrix b) throws IllegalDimensionException {
 		if(b.m != m || b.n != n)
 			throw new IllegalDimensionException("Two matrices have to be the same dimension.");
 	}
@@ -2235,31 +2270,63 @@ public class Matrix extends WObject implements Cloneable, Serializable{
 	    	Matrix.setSupressErrorMessage(true);
 	    	
 	    	Matrix A, B, C, D;
+	    	boolean test;
 	
-	        A = Matrix.random(5, 5);
+	    	A = new Matrix(new double[][]{{3,1,2},{2,0,5},{1,2,3}});
-	        A.setName("A").println();
+	    	B = new Matrix(new double[][]{{3,1,2},{2,0,5},{5,1,7}});
+	    	System.out.println(A.setName("A"));
+	    	System.out.println(B.setName("B"));
+	    	
+	    	test = A.plus(B).equals(new Matrix(new double[][]{{6,2,4},{4,0,10},{6,3,10}}));
+	    	if(test) System.out.println("A+B : test successful");
+	    	else System.err.println("A+B : test faild");
+			System.out.println("Operations: "+A.plus(B).getOperationsTotal());
+//	    	System.out.println(A.plus(B));
+	    	
+	    	test = A.minus(B).equals(new Matrix(new double[][]{{0,0,0},{0,0,0},{-4,1,-4}}));
+	    	if(test) System.out.println("A-B : test successful");
+	    	else System.err.println("A-B : test faild");
+//	    	System.out.println(A.minus(B));
 	
-	        A.swap(1, 2);
+	        test = A.transpose().equals(new Matrix(new double[][]{{3,2,1},{1,0,2},{2,5,3}}));
-	        System.out.println("A.swap(1, 2)");
+	        if(test) System.out.println("A' : test successful");
-	        A.println();
+	        else System.err.println("A' : test faild");
-	
+//	        System.out.println(A.transpose());
-	        B = A.transpose();
+	        
-	        System.out.println("A' = \n" + B.setName("B"));
+	        test = A.swap(1, 2).equals(new Matrix(new double[][]{{3,1,2},{1,2,3},{2,0,5}}));
+	    	if(test) System.out.println("A.swap(1, 2) : test successful");
+	    	else System.err.println("A.swap(1, 2) : faild");
+	    	A.swap(1, 2);
+//	        A.println();
 	
 	        C = Matrix.identity(5);
-	        System.out.println("identity(5) = \n"+C.setName("C"));
+	        test = Matrix.identity(5).equals(new Diagonal(1,1,1,1,1));
+	    	if(test) System.out.println("identity(5) : test successful");
+	    	else System.err.println("identity(5) : test faild");
 	
-	        System.out.println(A);
+//	        System.out.println(A);
+	        
+	        test = A.times(B).equals(new Matrix(new double[][]{{21,5,25},{31,7,39},{22,4,33}}));
+	        if(test) System.out.println("A*B : test successful");
+	        else System.err.println("A*B : test faild");
+	        
+//	        System.out.println(A.times(B));
+//	        System.out.println(B.times(A));
 	
-	        // shouldn't be equal since AB != BA in general    
+	        // shouldn't be equal since AB != BA in general
-	        System.out.println("A*B =? B*A : \n"+A.times(B).equals(B.times(A)));
+	        test = A.times(B).equals(B.times(A));
-	        System.out.println(A);
+	        if(!test) System.out.println("A*B =? B*A : "+A.times(B).equals(B.times(A)) + " -> test successful");
+	        else System.err.println("A*B =? B*A : "+A.times(B).equals(B.times(A)) + " -> test faild");
+//	        System.out.println(A);
+	    	
+	        D = Matrix.random(5, 5);
+//	        D.setName("D").println();
 	
 	        Matrix f = Matrix.random(5, 1);
 	        System.out.println("random(5, 1) = \n"+f.setName("f"));
 	
-	        Matrix x = A.solve(f);
+	        Matrix x = D.solve(f);
-	        System.out.println("A^-1*f = \n"+x.setName("x"));
+	        System.out.println("D^-1*f = \n"+x.setName("x"));
 	        
 	    	Matrix2D a = new Matrix2D(0,1,1,0);
 	    	System.out.println(a.setName("a"));
@@ -2413,6 +2480,7 @@ public class Matrix extends WObject implements Cloneable, Serializable{
 
 	        Vector2D v = new Vector2D(1,1);
 	        Vector2D w = new Vector2D(0,1);
+	        System.out.println(v.setName("v"));
 	        P = (Matrix2D) Matrix2D.mirror(v);
 	        System.out.println("Pw = ");
 	        P.times(w).println();
@@ -2487,7 +2555,7 @@ public class Matrix extends WObject implements Cloneable, Serializable{
 	        
 	        D = new Diagonal(2.,3);
 	        System.out.println(A);
-	        System.out.println(D);
+	        System.out.println(D.setName("D"));
 	        System.out.println(A.plus(D));
 	        
 	        Matrix I = Matrix.identity(2);

src/math/matrix/Matrix2D.java

@@ -214,6 +214,7 @@ public class Matrix2D extends Matrix{
 	 */
 	public static Matrix2D mirror(Vector v) throws IllegalDimensionException{
 		// P = I - alpha v v'; alpha = 2 / (v'v)
+		//System.out.println(Diagonal2D.identity(v.n()) instanceof Diagonal2D);
 		return (Matrix2D) Diagonal2D.identity(v.n()).minus(v.tensorProduct(v).times(2/v.dot(v)));
 	}
 	

src/math/matrix/QRDecomposition.java

@@ -18,7 +18,7 @@ import math.Maths;
  * returns false.
  * @author Daniel Weschke
  */
-public class QRDecomposition implements Serializable {
+public class QRDecomposition extends Matrix implements Serializable {
 
    /**
 	 * UID

src/math/matrix/Symmetric.java

@@ -0,0 +1,104 @@
+package math.matrix;
+
+import exception.IllegalDimensionException;
+import math.Sequence;
+
+/**
+ * Symmetric matrix object d<sub>ij</sub>=d<sub>ji</sub>&isin;&#x211D;
+ * with n rows and n columns
+ * @author Daniel Weschke
+ */
+public class Symmetric extends Matrix {
+
+	/**
+	 * UID
+	 */
+	private static final long serialVersionUID = -3506578822884073555L;
+	
+	public Symmetric(int n){
+		this.m = n;
+		this.n = n;
+		data = new double[Sequence.triangularNumber(n)];
+	}
+	
+	public Symmetric(double... d){
+		this((int)Math.ceil(Sequence.triangularRoot(d.length)));
+		int i;
+        for(i=0; i<d.length; i++)
+        	set(i, d[i]);
+	}
+	
+	public Matrix set(int i, double d){
+		data[i] = d;
+		return this;
+	}
+	
+	public Matrix set(int i, int j, double d){
+		data[index(i,j)] = d;
+		return this;
+	}
+	
+	public double get(int i, int j){
+		return get(index(i,j));
+	}
+	
+	private int index(int i, int j){
+		return i>j?Sequence.triangularNumber(i)+j:i+Sequence.triangularNumber(j);
+	}
+
+    /**
+     * Adds two matrices of the same dimension (entrywise addition).
+     * The addition of two n-by-n matrices <b>A</b> and <b>B</b>,
+     * is again an n-by-n matrix computed by adding corresponding elements.
+     * @param B matrix
+     * @return <b>C</b> = <b>A</b> + <b>B</b>, entrywise summarized matrix
+     * @throws IllegalDimensionException
+     */
+    public Matrix plus(Matrix B) throws IllegalDimensionException{
+    	checkDimensions(B);
+    	int i,j;
+        Matrix c = createAddition(B);
+        c.newOperation();
+        if(B instanceof Diagonal)
+        	for(i=0; i<m; i++)
+        		for(j=i; j<n; j++){
+        			c.set(i, j, get(i,j)+((Diagonal) B).get(i));
+        			c.operate();
+        		}
+        else if(B instanceof Symmetric)
+        	for(i=0; i<m; i++)
+        		for(j=i; j<n; j++){
+        			c.set(i,j, get(i,j)+B.get(i,j));
+        			c.operate();
+        		}
+        else
+        	for(i=0; i<m; i++)
+        		for(j=0; j<n; j++){
+        			c.set(i,j, get(i,j)+B.get(i,j));
+        			c.operate();
+        		}
+//        System.out.println(this instanceof Symmetric);
+//        System.out.println(B instanceof Symmetric);
+        return c;
+    }
+	
+    public static void main(String[] args){
+		Symmetric s1 = new Symmetric(1.);
+		System.out.println(s1);
+		Symmetric s2 = new Symmetric(1., 2.);
+		System.out.println(s2);
+		Symmetric s3 = new Symmetric(1., 2., 3.);
+		System.out.println(s3);
+		Symmetric s4 = new Symmetric(1., 2., 3., 4.);
+		System.out.println(s4);
+		System.out.println(s4.get(0,2));
+		System.out.println(s4.get(2,0));
+		try {
+			System.out.println(s2.plus(s3));
+			System.out.println("Operations: "+s2.plus(s3).getOperationsTotal());
+			System.out.println(s2.minus(s3));
+		} catch (IllegalDimensionException e) {
+			e.printStackTrace();
+		}
+	}
+}

src/math/matrix/TensorII.java

@@ -11,6 +11,10 @@ public class TensorII extends Matrix3D {
 	 */
 	private static final long serialVersionUID = -5664678448598889794L;
 
+	public TensorII() {
+		super(3);
+	}
+
 	public static void main(String[] args) {
 	}
 

src/thisandthat/WObject.java

@@ -1,11 +1,52 @@
 package thisandthat;
 
+import java.util.ArrayList;
+import java.util.Arrays;
+
+import math.Maths;
+
 /**
  * @author Daniel Weschke
  */
 public class WObject {
 	private static boolean supressErrorMessage = false;
 	private String name;
+	private ArrayList<Integer> operations = new ArrayList<Integer>();
+	private Integer[] convertedArray; 
+	private boolean justConverted;
+
+	public String getName() {
+		return name;
+	}
+
+	public WObject setName(String name) {
+		this.name = name;
+		return this;
+	}
+	
+	public Integer[] getOperations(){
+		if(!justConverted){
+			Integer[] itemArray = new Integer[operations.size()];
+			convertedArray = operations.toArray(itemArray);
+			justConverted = true;
+		}
+		return convertedArray;
+	}
+	
+	public int getOperationsTotal(){
+		return Maths.sum(getOperations());
+	}
+	
+	public void newOperation(){
+		operations.add(0);
+		justConverted = false;
+	}
+	
+	public void operate(){
+		int index = operations.size()-1;
+		operations.set(index,operations.get(index)+1);
+		justConverted = false;
+	}
 
 	public static boolean isSupressErrorMessage() {
 		return supressErrorMessage;
@@ -26,15 +67,6 @@ public class WObject {
     public static <T> T last(T[] array) {
         return array[array.length - 1];
     }
-
-	public String getName() {
-		return name;
-	}
-
-	public WObject setName(String name) {
-		this.name = name;
-		return this;
-	}
 	
 	/**
 	 * The declaration of that method is:
@@ -67,6 +99,26 @@ public class WObject {
 		WObject obj = new WObject();
     	obj.setName("one");
         obj.println();
+        
+        obj.newOperation();
+        System.out.print(Arrays.toString(obj.getOperations()));
+        System.out.println(" tot: "+obj.getOperationsTotal());
+        obj.operate();
+        System.out.print(Arrays.toString(obj.getOperations()));
+        System.out.println(" tot: "+obj.getOperationsTotal());
+        obj.operate();
+        System.out.print(Arrays.toString(obj.getOperations()));
+        System.out.println(" tot: "+obj.getOperationsTotal());
+        
+        obj.newOperation();
+        System.out.print(Arrays.toString(obj.getOperations()));
+        System.out.println(" tot: "+obj.getOperationsTotal());
+        obj.operate();
+        System.out.print(Arrays.toString(obj.getOperations()));
+        System.out.println(" tot: "+obj.getOperationsTotal());
+        obj.operate();
+        System.out.print(Arrays.toString(obj.getOperations()));
+        System.out.println(" tot: "+obj.getOperationsTotal());
 	}
 
 }