Merge branch 'ellipsoid-factor' into testing

Conflicts:
	src/org/bonej/Help.java

src/org/doube/geometry/EigenCalculator.java

@@ -0,0 +1,60 @@
+package org.doube.geometry;
+
+import org.doube.jama.EigenvalueDecomposition;
+import org.doube.jama.Matrix;
+
+public class EigenCalculator {
+
+	/**
+	 * Calculate the eigenvectors and eigenvalues of a set of points by the
+	 * covariance method and eigendecomposition.
+	 * 
+	 * @param coOrdinates
+	 *            n x 3 array
+	 * @return EigenvalueDecomposition containing eigenvectors and eigenvalues
+	 * 
+	 */
+	public static EigenvalueDecomposition principalComponents(
+			double[][] coOrdinates) {
+		final int nPoints = coOrdinates.length;
+		double sumX = 0, sumY = 0, sumZ = 0;
+		//calculate the centroid of the points
+		for (int n = 0; n < nPoints; n++) {
+			sumX += coOrdinates[n][0];
+			sumY += coOrdinates[n][1];
+			sumZ += coOrdinates[n][2];
+		}
+		//centroid is the mean (x, y, z) position
+		final double centX = sumX / nPoints;
+		final double centY = sumY / nPoints;
+		final double centZ = sumZ / nPoints;
+
+		//construct the covariance matrix
+		double[][] C = new double[3][3];
+		double count = 0;
+		for (int n = 0; n < nPoints; n++) {
+			//translate so that centroid is at (0,0,0)
+			final double x = coOrdinates[n][0] - centX;
+			final double y = coOrdinates[n][1] - centY;
+			final double z = coOrdinates[n][2] - centZ;
+			C[0][0] += x * x;
+			C[1][1] += y * y;
+			C[2][2] += z * z;
+			final double xy = x * y;
+			final double xz = x * z;
+			final double yz = y * z; 
+			C[0][1] += xy;
+			C[0][2] += xz;
+			C[1][0] += xy;
+			C[1][2] += yz;
+			C[2][0] += xz;
+			C[2][1] += yz;
+			count += 1;
+		}
+		double invCount = 1 / count;
+		Matrix covarianceMatrix = new Matrix(C).times(invCount);
+		EigenvalueDecomposition E = new EigenvalueDecomposition(
+				covarianceMatrix);
+		return E;
+	}
+}