First develop commit. Adding all existing files.

test/math/Eigenvalues.java

@@ -0,0 +1,40 @@
+package math;
+
+import math.matrix.EigenvalueDecomposition;
+import math.matrix.Matrix;
+import exception.IllegalDimensionException;
+
+/**
+ * Test client for computing eigenvalues and eigenvectors of a real
+ * symmetric matrix A = V D V^T.
+ */
+public class Eigenvalues {
+   public static void main(String[] args) throws IllegalDimensionException { 
+      int N = 5;
+
+      // create a symmetric positive definite matrix
+      Matrix A = Matrix.random(N, N);
+      A = A.transpose().times(A);
+
+      // compute the spectral decomposition
+      EigenvalueDecomposition e = A.eig();
+      Matrix V = e.getV();
+      Matrix D = e.getD();
+
+      System.out.print("A =");
+      A.print(9, 6);
+      System.out.print("D =");
+      D.print(9, 6);
+      System.out.print("V =");
+      V.print(9, 6);
+
+      // check that V is orthogonal
+      System.out.print("||V * V^T - I|| = ");
+      System.out.println(V.times(V.transpose()).minus(Matrix.identity(N, N)).normInf());
+
+      // check that A V = D V
+      System.out.print("||AV - DV|| = ");
+      System.out.println(A.times(V).minus(V.times(D)).normInf());
+   }
+
+}

test/math/MatrixTest.java

@@ -0,0 +1,37 @@
+package math;
+
+import math.matrix.Matrix;
+import exception.IllegalDimensionException;
+
+public class MatrixTest {
+   public static void main(String[] args) throws IllegalDimensionException { 
+      Matrix A = new Matrix(new double[][] { { 0,  1,  1 },
+                                             { 2,  4, -2 },
+                                             { 0,  3, 15 } }); 
+
+      Matrix b = new Matrix(new double[][] { {  4 },
+                                             {  2 },
+                                             { 36 } });
+      Matrix x = A.solve(b);
+      Matrix residual = A.times(x).minus(b);
+      double rnorm = residual.normInf();
+
+      System.out.println("A");
+      A.print(9, 6);                // printf("%9.6f");
+
+      System.out.println("b");
+      b.print(9, 6);
+
+      System.out.println("x");
+      x.print(9, 6);
+      System.out.println(x);
+
+      System.out.println("residual");
+      residual.print(9, 6);
+      
+      System.out.println("rnorm");
+      System.out.println(rnorm);
+
+   }
+
+}

test/math/SVD.java

@@ -0,0 +1,43 @@
+package math;
+
+import math.matrix.Matrix;
+import math.matrix.SingularValueDecomposition;
+import exception.IllegalDimensionException;
+
+/**
+ * Test client for computing singular values of a matrix.
+ */
+public class SVD {
+   public static void main(String[] args) throws IllegalDimensionException { 
+
+      // create M-by-N matrix that doesn't have full rank
+      int M = 8, N = 5;
+      Matrix B = Matrix.random(5, 3);
+      Matrix A = Matrix.random(M, N).times(B).times(B.transpose());
+      System.out.print("A = ");
+      A.print(9, 6);
+
+      // compute the singular vallue decomposition
+      System.out.println("A = U S V^T");
+      System.out.println();
+      SingularValueDecomposition s = A.svd();
+      System.out.print("U = ");
+      Matrix U = s.getU();
+      U.print(9, 6);
+      System.out.print("Sigma = ");
+      Matrix S = s.getS();
+      S.print(9, 6);
+      System.out.print("V = ");
+      Matrix V = s.getV();
+      V.print(9, 6);
+      System.out.println("rank = " + s.rank());
+      System.out.println("condition number = " + s.cond());
+      System.out.println("2-norm = " + s.norm2());
+
+      // print out singular values
+      System.out.print("singular values = ");
+      Matrix svalues = new Matrix(s.getSingularValues(), 1);
+      svalues.print(9, 6);
+   }
+
+}