Merge branch 'optional-ml'

build.gradle

@@ -28,8 +28,13 @@ dependencies {
 	runtimeOnly 'com.googlecode.soundlibs:tritonus-share:0.3.7.4'
 	runtimeOnly 'com.googlecode.soundlibs:mp3spi:1.9.5.4'
 
+	//compileOnlyApi 'colt:colt:1.2.0'
+	api 'colt:colt:1.2.0'
+	//api 'net.sourceforge.parallelcolt:parallelcolt:0.10.1'
+
     testImplementation 'org.junit.jupiter:junit-jupiter-api:5.8.1'
-    testRuntimeOnly 'org.junit.jupiter:junit-jupiter-engine:5.8.1'
+	testImplementation 'org.junit.jupiter:junit-jupiter-params:5.8.1'
+	testRuntimeOnly 'org.junit.jupiter:junit-jupiter-engine:5.8.1'
 }
 
 test {

src/main/java/schule/ngb/zm/Constants.java

@@ -1269,7 +1269,8 @@ public class Constants {
 	}
 
 	/**
-	 * Erzeugt eine Pseudozufallszahl nach einer Gaussverteilung.
+	 * Erzeugt eine Pseudozufallszahl zwischen -1 und 1 nach einer
+	 * Normalverteilung mit Mittelwert 0 und Standardabweichung 1.
 	 *
 	 * @return Eine Zufallszahl.
 	 * @see Random#nextGaussian()

src/main/java/schule/ngb/zm/ml/DoubleMatrix.java

@@ -0,0 +1,399 @@
+package schule.ngb.zm.ml;
+
+import schule.ngb.zm.Constants;
+
+import java.util.function.DoubleUnaryOperator;
+
+/**
+ * Eine einfache Implementierung der {@link MLMatrix} zur Verwendung in
+ * {@link NeuralNetwork}s.
+ * <p>
+ * Diese Klasse stellt die interne Implementierung der Matrixoperationen dar,
+ * die zur Berechnung der Gewichte in einem {@link NeuronLayer} notwendig sind.
+ * <p>
+ * Die Klasse ist nur minimal optimiert und sollte nur für kleine Netze
+ * verwendet werden. Für größere Netze sollte auf eine der optionalen
+ * Bibliotheken wie
+ * <a href="">Colt</a> zurückgegriffen werden.
+ */
+public final class DoubleMatrix implements MLMatrix {
+
+	/**
+	 * Anzahl Zeilen der Matrix.
+	 */
+	private int rows;
+
+	/**
+	 * Anzahl Spalten der Matrix.
+	 */
+	private int columns;
+
+	/**
+	 * Die Koeffizienten der Matrix.
+	 * <p>
+	 * Um den Overhead bei Speicher und Zugriffszeiten von zweidimensionalen
+	 * Arrays zu vermeiden wird ein eindimensionales Array verwendet und die
+	 * Indizes mit Spaltenpriorität berechnet. Der Index i des Koeffizienten
+	 * {@code r,c} in Zeile {@code r} und Spalte {@code c} wird bestimmt durch
+	 * <pre>
+	 * i = c * rows + r
+	 * </pre>
+	 * <p>
+	 * Die Werte einer Spalte liegen also hintereinander im Array. Dies sollte
+	 * einen leichten Vorteil bei der {@link #colSums() Spaltensummen} geben.
+	 * Generell sollte eine Iteration über die Matrix der Form
+	 * <pre><code>
+	 * for( int j = 0; j < columns; j++ ) {
+	 *     for( int i = 0; i < rows; i++ ) {
+	 *         // ...
+	 *     }
+	 * }
+	 * </code></pre>
+	 * etwas schneller sein als
+	 * <pre><code>
+	 * for( int i = 0; i < rows; i++ ) {
+	 *     for( int j = 0; j < columns; j++ ) {
+	 *         // ...
+	 *     }
+	 * }
+	 * </code></pre>
+	 */
+	double[] coefficients;
+
+	public DoubleMatrix( int rows, int cols ) {
+		this.rows = rows;
+		this.columns = cols;
+		coefficients = new double[rows * cols];
+	}
+
+	public DoubleMatrix( double[][] coefficients ) {
+		this.rows = coefficients.length;
+		this.columns = coefficients[0].length;
+		this.coefficients = new double[rows * columns];
+		for( int j = 0; j < columns; j++ ) {
+			for( int i = 0; i < rows; i++ ) {
+				this.coefficients[idx(i, j)] = coefficients[i][j];
+			}
+		}
+	}
+
+	/**
+	 * Initialisiert diese Matrix als Kopie der angegebenen Matrix.
+	 *
+	 * @param other Die zu kopierende Matrix.
+	 */
+	public DoubleMatrix( DoubleMatrix other ) {
+		this.rows = other.rows();
+		this.columns = other.columns();
+		this.coefficients = new double[rows * columns];
+		System.arraycopy(
+			other.coefficients, 0,
+			this.coefficients, 0,
+			rows * columns);
+	}
+
+	/**
+	 * {@inheritDoc}
+	 */
+	@Override
+	public int columns() {
+		return columns;
+	}
+
+	/**
+	 * {@inheritDoc}
+	 */
+	@Override
+	public int rows() {
+		return rows;
+	}
+
+	/**
+	 * {@inheritDoc}
+	 */
+	int idx( int r, int c ) {
+		return c * rows + r;
+	}
+
+	/**
+	 * {@inheritDoc}
+	 */
+	@Override
+	public double get( int row, int col ) {
+		try {
+			return coefficients[idx(row, col)];
+		} catch( ArrayIndexOutOfBoundsException ex ) {
+			throw new IllegalArgumentException("No element at row=" + row + ", column=" + col, ex);
+		}
+	}
+
+	/**
+	 * {@inheritDoc}
+	 */
+	@Override
+	public MLMatrix set( int row, int col, double value ) {
+		try {
+			coefficients[idx(row, col)] = value;
+		} catch( ArrayIndexOutOfBoundsException ex ) {
+			throw new IllegalArgumentException("No element at row=" + row + ", column=" + col, ex);
+		}
+		return this;
+	}
+
+	/**
+	 * {@inheritDoc}
+	 */
+	@Override
+	public MLMatrix initializeRandom() {
+		return initializeRandom(-1.0, 1.0);
+	}
+
+	/**
+	 * {@inheritDoc}
+	 */
+	@Override
+	public MLMatrix initializeRandom( double lower, double upper ) {
+		applyInPlace(( d ) -> ((upper - lower) * Constants.random()) + lower);
+		return this;
+	}
+
+	/**
+	 * {@inheritDoc}
+	 */
+	@Override
+	public MLMatrix initializeOne() {
+		applyInPlace(( d ) -> 1.0);
+		return this;
+	}
+
+	/**
+	 * {@inheritDoc}
+	 */
+	@Override
+	public MLMatrix initializeZero() {
+		applyInPlace(( d ) -> 0.0);
+		return this;
+	}
+
+	/**
+	 * {@inheritDoc}
+	 */
+	@Override
+	public MLMatrix duplicate() {
+		return new DoubleMatrix(this);
+	}
+
+	/**
+	 * {@inheritDoc}
+	 */
+	@Override
+	public MLMatrix multiplyTransposed( MLMatrix B ) {
+		/*return new DoubleMatrix(IntStream.range(0, rows).parallel().mapToObj(
+			( i ) -> IntStream.range(0, B.rows()).mapToDouble(
+				( j ) -> IntStream.range(0, columns).mapToDouble(
+					( k ) -> get(i, k) * B.get(j, k)
+				).sum()
+			).toArray()
+		).toArray(double[][]::new));*/
+		DoubleMatrix result = new DoubleMatrix(rows, B.rows());
+		for( int i = 0; i < rows; i++ ) {
+			for( int j = 0; j < B.rows(); j++ ) {
+				result.coefficients[result.idx(i, j)] = 0.0;
+				for( int k = 0; k < columns; k++ ) {
+					result.coefficients[result.idx(i, j)] += get(i, k) * B.get(j, k);
+				}
+			}
+		}
+		return result;
+	}
+
+	/**
+	 * {@inheritDoc}
+	 */
+	@Override
+	public MLMatrix multiplyAddBias( final MLMatrix B, final MLMatrix C ) {
+		/*return new DoubleMatrix(IntStream.range(0, rows).parallel().mapToObj(
+			( i ) -> IntStream.range(0, B.columns()).mapToDouble(
+				( j ) -> IntStream.range(0, columns).mapToDouble(
+					( k ) -> get(i, k) * B.get(k, j)
+				).sum() + C.get(0, j)
+			).toArray()
+		).toArray(double[][]::new));*/
+		DoubleMatrix result = new DoubleMatrix(rows, B.columns());
+		for( int i = 0; i < rows; i++ ) {
+			for( int j = 0; j < B.columns(); j++ ) {
+				result.coefficients[result.idx(i, j)] = 0.0;
+				for( int k = 0; k < columns; k++ ) {
+					result.coefficients[result.idx(i, j)] += get(i, k) * B.get(k, j);
+				}
+				result.coefficients[result.idx(i, j)] += C.get(0, j);
+			}
+		}
+		return result;
+	}
+
+	/**
+	 * {@inheritDoc}
+	 */
+	@Override
+	public MLMatrix transposedMultiplyAndScale( final MLMatrix B, final double scalar ) {
+		/*return new DoubleMatrix(IntStream.range(0, columns).parallel().mapToObj(
+			( i ) -> IntStream.range(0, B.columns()).mapToDouble(
+				( j ) -> IntStream.range(0, rows).mapToDouble(
+					( k ) -> get(k, i) * B.get(k, j) * scalar
+				).sum()
+			).toArray()
+		).toArray(double[][]::new));*/
+		DoubleMatrix result = new DoubleMatrix(columns, B.columns());
+		for( int i = 0; i < columns; i++ ) {
+			for( int j = 0; j < B.columns(); j++ ) {
+				result.coefficients[result.idx(i, j)] = 0.0;
+				for( int k = 0; k < rows; k++ ) {
+					result.coefficients[result.idx(i, j)] += get(k, i) * B.get(k, j);
+				}
+				result.coefficients[result.idx(i, j)] *= scalar;
+			}
+		}
+		return result;
+	}
+
+	/**
+	 * {@inheritDoc}
+	 */
+	@Override
+	public MLMatrix add( MLMatrix B ) {
+		/*return new DoubleMatrix(IntStream.range(0, rows).parallel().mapToObj(
+			( i ) -> IntStream.range(0, columns).mapToDouble(
+				( j ) -> get(i, j) + B.get(i, j)
+			).toArray()
+		).toArray(double[][]::new));*/
+		DoubleMatrix sum = new DoubleMatrix(rows, columns);
+		for( int j = 0; j < columns; j++ ) {
+			for( int i = 0; i < rows; i++ ) {
+				sum.coefficients[idx(i, j)] = coefficients[idx(i, j)] + B.get(i, j);
+			}
+		}
+		return sum;
+	}
+
+	/**
+	 * {@inheritDoc}
+	 */
+	@Override
+	public MLMatrix addInPlace( MLMatrix B ) {
+		for( int j = 0; j < columns; j++ ) {
+			for( int i = 0; i < rows; i++ ) {
+				coefficients[idx(i, j)] += B.get(i, j);
+			}
+		}
+		return this;
+	}
+
+	/**
+	 * {@inheritDoc}
+	 */
+	@Override
+	public MLMatrix sub( MLMatrix B ) {
+		/*return new DoubleMatrix(IntStream.range(0, rows).parallel().mapToObj(
+			( i ) -> IntStream.range(0, columns).mapToDouble(
+				( j ) -> get(i, j) - B.get(i, j)
+			).toArray()
+		).toArray(double[][]::new));*/
+		DoubleMatrix diff = new DoubleMatrix(rows, columns);
+		for( int j = 0; j < columns; j++ ) {
+			for( int i = 0; i < rows; i++ ) {
+				diff.coefficients[idx(i, j)] = coefficients[idx(i, j)] - B.get(i, j);
+			}
+		}
+		return diff;
+	}
+
+	/**
+	 * {@inheritDoc}
+	 */
+	@Override
+	public MLMatrix colSums() {
+		/*DoubleMatrix colSums = new DoubleMatrix(1, columns);
+		colSums.coefficients = IntStream.range(0, columns).parallel().mapToDouble(
+			( j ) -> IntStream.range(0, rows).mapToDouble(
+				( i ) -> get(i, j)
+			).sum()
+		).toArray();
+		return colSums;*/
+		DoubleMatrix colSums = new DoubleMatrix(1, columns);
+		for( int j = 0; j < columns; j++ ) {
+			colSums.coefficients[j] = 0.0;
+			for( int i = 0; i < rows; i++ ) {
+				colSums.coefficients[j] += coefficients[idx(i, j)];
+			}
+		}
+		return colSums;
+	}
+
+	/**
+	 * {@inheritDoc}
+	 */
+	@Override
+	public MLMatrix scaleInPlace( final double scalar ) {
+		for( int i = 0; i < coefficients.length; i++ ) {
+			coefficients[i] *= scalar;
+		}
+		return this;
+	}
+
+	/**
+	 * {@inheritDoc}
+	 */
+	@Override
+	public MLMatrix scaleInPlace( final MLMatrix S ) {
+		for( int j = 0; j < columns; j++ ) {
+			for( int i = 0; i < rows; i++ ) {
+				coefficients[idx(i, j)] *= S.get(i, j);
+			}
+		}
+		return this;
+	}
+
+	/**
+	 * {@inheritDoc}
+	 */
+	@Override
+	public MLMatrix apply( DoubleUnaryOperator op ) {
+		DoubleMatrix result = new DoubleMatrix(rows, columns);
+		for( int i = 0; i < coefficients.length; i++ ) {
+			result.coefficients[i] = op.applyAsDouble(coefficients[i]);
+		}
+		return result;
+	}
+
+	/**
+	 * {@inheritDoc}
+	 */
+	@Override
+	public MLMatrix applyInPlace( DoubleUnaryOperator op ) {
+		for( int i = 0; i < coefficients.length; i++ ) {
+			coefficients[i] = op.applyAsDouble(coefficients[i]);
+		}
+		return this;
+	}
+
+	@Override
+	public String toString() {
+		StringBuilder sb = new StringBuilder();
+		sb.append(rows);
+		sb.append(" x ");
+		sb.append(columns);
+		sb.append(" Matrix");
+		sb.append('\n');
+		for( int i = 0; i < rows; i++ ) {
+			for( int j = 0; j < columns; j++ ) {
+				sb.append(get(i, j));
+				if( j < columns - 1 )
+					sb.append(' ');
+			}
+			sb.append('\n');
+		}
+		return sb.toString();
+	}
+
+}

src/main/java/schule/ngb/zm/ml/MLMatrix.java

@@ -0,0 +1,316 @@
+package schule.ngb.zm.ml;
+
+import java.util.function.DoubleUnaryOperator;
+
+/**
+ * Interface für Matrizen, die in {@link NeuralNetwork} Klassen verwendet
+ * werden.
+ * <p>
+ * Eine implementierende Klasse muss generell zwei Konstruktoren bereitstellen:
+ * <ol>
+ * <li> {@code MLMatrix(int rows, int columns)} erstellt eine Matrix mit den
+ * 		angegebenen Dimensionen und setzt alle Koeffizienten auf 0.
+ * <li> {@code MLMatrix(double[][] coefficients} erstellt eine Matrix mit der
+ * 		durch das Array gegebenen Dimensionen und setzt die Werte auf die
+ * 		jeweiligen Werte des Arrays.
+ * </ol>
+ * <p>
+ * Das Interface ist nicht dazu gedacht eine allgemeine Umsetzung für
+ * Matrizen-Algebra abzubilden, sondern soll gezielt die im Neuralen Netzwerk
+ * verwendeten Algorithmen umsetzen. Einerseits würde eine ganz allgemeine
+ * Matrizen-Klasse nicht im Rahmen der Zeichenmaschine liegen und auf der
+ * anderen Seite bietet eine Konzentration auf die verwendeten Algorithmen mehr
+ * Spielraum zur Optimierung.
+ * <p>
+ * Intern wird das Interface von {@link DoubleMatrix} implementiert. Die Klasse
+ * ist eine weitestgehend naive Implementierung der Algorithmen mit kleineren
+ * Optimierungen. Die Verwendung eines generalisierten Interfaces erlaubt aber
+ * zukünftig die optionale Integration spezialisierterer Algebra-Bibliotheken
+ * wie
+ * <a href="https://dst.lbl.gov/ACSSoftware/colt/">Colt</a>, um auch große
+ * Netze effizient berechnen zu können.
+ */
+public interface MLMatrix {
+
+	/**
+	 * Die Anzahl der Spalten der Matrix.
+	 *
+	 * @return Spaltenzahl.
+	 */
+	int columns();
+
+	/**
+	 * Die Anzahl der Zeilen der Matrix.
+	 *
+	 * @return Zeilenzahl.
+	 */
+	int rows();
+
+	/**
+	 * Gibt den Wert an der angegebenen Stelle der Matrix zurück.
+	 *
+	 * @param row Die Spaltennummer zwischen 0 und {@code rows()-1}.
+	 * @param col Die Zeilennummer zwischen 0 und {@code columns()-1}
+	 * @return Den Koeffizienten in der Zeile {@code row} und der Spalte
+	 *    {@code col}.
+	 * @throws IllegalArgumentException Falls {@code row >= rows()} oder
+	 *                                  {@code col >= columns()}.
+	 */
+	double get( int row, int col ) throws IllegalArgumentException;
+
+	/**
+	 * Setzt den Wert an der angegebenen Stelle der Matrix.
+	 *
+	 * @param row Die Spaltennummer zwischen 0 und {@code rows()-1}.
+	 * @param col Die Zeilennummer zwischen 0 und {@code columns()-1}
+	 * @param value Der neue Wert.
+	 * @return Diese Matrix selbst (method chaining).
+	 * @throws IllegalArgumentException Falls {@code row >= rows()} oder
+	 *                                  {@code col >= columns()}.
+	 */
+	MLMatrix set( int row, int col, double value ) throws IllegalArgumentException;
+
+	/**
+	 * Setzt jeden Wert in der Matrix auf eine Zufallszahl zwischen -1 und 1.
+	 * <p>
+	 * Nach Möglichkeit sollte der
+	 * {@link schule.ngb.zm.Constants#random(int, int) Zufallsgenerator der
+	 * Zeichenmaschine} verwendet werden.
+	 *
+	 * @return Diese Matrix selbst (method chaining).
+	 */
+	MLMatrix initializeRandom();
+
+	/**
+	 * Setzt jeden Wert in der Matrix auf eine Zufallszahl innerhalb der
+	 * angegebenen Grenzen.
+	 * <p>
+	 * Nach Möglichkeit sollte der
+	 * {@link schule.ngb.zm.Constants#random(int, int) Zufallsgenerator der
+	 * Zeichenmaschine} verwendet werden.
+	 *
+	 * @param lower Untere Grenze der Zufallszahlen.
+	 * @param upper Obere Grenze der Zufallszahlen.
+	 * @return Diese Matrix selbst (method chaining).
+	 */
+	MLMatrix initializeRandom( double lower, double upper );
+
+	/**
+	 * Setzt alle Werte der Matrix auf 1.
+	 *
+	 * @return Diese Matrix selbst (method chaining).
+	 */
+	MLMatrix initializeOne();
+
+	/**
+	 * Setzt alle Werte der Matrix auf 0.
+	 *
+	 * @return Diese Matrix selbst (method chaining).
+	 */
+	MLMatrix initializeZero();
+
+	/**
+	 * Erzeugt eine neue Matrix {@code C} mit dem Ergebnis der Matrixoperation
+	 * <pre>
+	 * C = this . B + V'
+	 * </pre>
+	 * wobei {@code this} dieses Matrixobjekt ist und {@code .} für die
+	 * Matrixmultiplikation steht. {@vode V'} ist die Matrix {@code V}
+	 * {@code rows()}-mal untereinander wiederholt.
+	 * <p>
+	 * Wenn diese Matrix die Dimension r x c hat, dann muss die Matrix {@code B}
+	 * die Dimension c x m haben und {@code V} eine 1 x m Matrix sein. Die
+	 * Matrix {@code V'} hat also die Dimension r x m, ebenso wie das Ergebnis
+	 * der Operation.
+	 *
+	 * @param B Eine {@code columns()} x m Matrix mit der Multipliziert wird.
+	 * @param V Eine 1 x {@code B.columns()} Matrix mit den Bias-Werten.
+	 * @return Eine {@code rows()} x m Matrix.
+	 * @throws IllegalArgumentException Falls die Dimensionen der Matrizen nicht
+	 *                                  zur Operation passen. Also
+	 *                                  {@code this.columns() != B.rows()} oder
+	 *                                  {@code B.columns() != V.columns()} oder
+	 *                                  {@code V.rows() != 1}.
+	 */
+	MLMatrix multiplyAddBias( MLMatrix B, MLMatrix V ) throws IllegalArgumentException;
+
+	/**
+	 * Erzeugt eine neue Matrix {@code C} mit dem Ergebnis der Matrixoperation
+	 * <pre>
+	 * C = this . t(B)
+	 * </pre>
+	 * wobei {@code this} dieses Matrixobjekt ist, {@code t(B)} die
+	 * Transposition der Matrix {@code B} ist und {@code .} für die
+	 * Matrixmultiplikation steht.
+	 * <p>
+	 * Wenn diese Matrix die Dimension r x c hat, dann muss die Matrix {@code B}
+	 * die Dimension m x c haben und das Ergebnis ist eine r x m Matrix.
+	 *
+	 * @param B Eine m x {@code columns()} Matrix.
+	 * @return Eine {@code rows()} x m Matrix.
+	 * @throws IllegalArgumentException Falls die Dimensionen der Matrizen nicht
+	 *                                  zur Operation passen. Also
+	 *                                  {@code this.columns() != B.columns()}.
+	 */
+	MLMatrix multiplyTransposed( MLMatrix B ) throws IllegalArgumentException;
+
+	/**
+	 * Erzeugt eine neue Matrix {@code C} mit dem Ergebnis der Matrixoperation
+	 * <pre>
+	 * C = t(this) . B * scalar
+	 * </pre>
+	 * wobei {@code this} dieses Matrixobjekt ist, {@code t(this)} die
+	 * Transposition dieser Matrix ist und {@code .} für die
+	 * Matrixmultiplikation steht. {@code *} bezeichnet die
+	 * Skalarmultiplikation, bei der jeder Wert der Matrix mit {@code scalar}
+	 * multipliziert wird.
+	 * <p>
+	 * Wenn diese Matrix die Dimension r x c hat, dann muss die Matrix {@code B}
+	 * die Dimension r x m haben und das Ergebnis ist eine c x m Matrix.
+	 *
+	 * @param B Eine m x {@code columns()} Matrix.
+	 * @return Eine {@code rows()} x m Matrix.
+	 * @throws IllegalArgumentException Falls die Dimensionen der Matrizen nicht
+	 *                                  zur Operation passen. Also
+	 *                                  {@code this.rows() != B.rows()}.
+	 */
+	MLMatrix transposedMultiplyAndScale( MLMatrix B, double scalar ) throws IllegalArgumentException;
+
+	/**
+	 * Erzeugt eine neue Matrix {@code C} mit dem Ergebnis der komponentenweisen
+	 * Matrix-Addition
+	 * <pre>
+	 * C = this + B
+	 * </pre>
+	 * wobei {@code this} dieses Matrixobjekt ist. Für ein Element {@code C_ij}
+	 * in {@code C} gilt
+	 * <pre>
+	 * C_ij = A_ij + B_ij
+	 * </pre>
+	 * <p>
+	 * Die Matrix {@code B} muss dieselbe Dimension wie diese Matrix haben.
+	 *
+	 * @param B Eine {@code rows()} x {@code columns()} Matrix.
+	 * @return Eine {@code rows()} x {@code columns()} Matrix.
+	 * @throws IllegalArgumentException Falls die Dimensionen der Matrizen nicht
+	 *                                  zur Operation passen. Also
+	 *                                  {@code this.rows() != B.rows()} oder
+	 *                                  {@code this.columns() != B.columns()}.
+	 */
+	MLMatrix add( MLMatrix B ) throws IllegalArgumentException;
+
+	/**
+	 * Setzt diese Matrix auf das Ergebnis der komponentenweisen
+	 * Matrix-Addition
+	 * <pre>
+	 * A' = A + B
+	 * </pre>
+	 * wobei {@code A} dieses Matrixobjekt ist und {@code A'} diese Matrix nach
+	 * der Operation. Für ein Element {@code A'_ij} in {@code A'} gilt
+	 * <pre>
+	 * A'_ij = A_ij + B_ij
+	 * </pre>
+	 * <p>
+	 * Die Matrix {@code B} muss dieselbe Dimension wie diese Matrix haben.
+	 *
+	 * @param B Eine {@code rows()} x {@code columns()} Matrix.
+	 * @return Eine {@code rows()} x {@code columns()} Matrix.
+	 * @throws IllegalArgumentException Falls die Dimensionen der Matrizen nicht
+	 *                                  zur Operation passen. Also
+	 *                                  {@code this.rows() != B.rows()} oder
+	 *                                  {@code this.columns() != B.columns()}.
+	 */
+	MLMatrix addInPlace( MLMatrix B ) throws IllegalArgumentException;
+
+	/**
+	 * Erzeugt eine neue Matrix {@code C} mit dem Ergebnis der komponentenweisen
+	 * Matrix-Subtraktion
+	 * <pre>
+	 * C = A - B
+	 * </pre>
+	 * wobei {@code A} dieses Matrixobjekt ist. Für ein Element {@code C_ij} in
+	 * {@code C} gilt
+	 * <pre>
+	 * C_ij = A_ij - B_ij
+	 * </pre>
+	 * <p>
+	 * Die Matrix {@code B} muss dieselbe Dimension wie diese Matrix haben.
+	 *
+	 * @param B Eine {@code rows()} x {@code columns()} Matrix.
+	 * @return Eine {@code rows()} x {@code columns()} Matrix.
+	 * @throws IllegalArgumentException Falls die Dimensionen der Matrizen nicht
+	 *                                  zur Operation passen. Also
+	 *                                  {@code this.rows() != B.rows()} oder
+	 *                                  {@code this.columns() != B.columns()}.
+	 */
+	MLMatrix sub( MLMatrix B ) throws IllegalArgumentException;
+
+	/**
+	 * Multipliziert jeden Wert dieser Matrix mit dem angegebenen Skalar.
+	 * <p>
+	 * Ist {@code A} dieses Matrixobjekt und {@code A'} diese Matrix nach der
+	 * Operation, dann gilt für ein Element {@code A'_ij} in {@code A'}
+	 * <pre>
+	 * A'_ij = A_ij * scalar
+	 * </pre>
+	 *
+	 * @param scalar Ein Skalar.
+	 * @return Diese Matrix selbst (method chaining)
+	 */
+	MLMatrix scaleInPlace( double scalar );
+
+	/**
+	 * Multipliziert jeden Wert dieser Matrix mit dem entsprechenden Wert in der
+	 * Matrix {@code S}.
+	 * <p>
+	 * Ist {@code A} dieses Matrixobjekt und {@code A'} diese Matrix nach der
+	 * Operation, dann gilt für ein Element {@code A'_ij} in {@code A'}
+	 * <pre>
+	 * A'_ij = A_ij * S_ij
+	 * </pre>
+	 *
+	 * @param S Eine {@code rows()} x {@code columns()} Matrix.
+	 * @return Diese Matrix selbst (method chaining)
+	 * @throws IllegalArgumentException Falls die Dimensionen der Matrizen nicht
+	 *                                  zur Operation passen. Also
+	 *                                  {@code this.rows() != B.rows()} oder
+	 *                                  {@code this.columns() != B.columns()}.
+	 */
+	MLMatrix scaleInPlace( MLMatrix S ) throws IllegalArgumentException;
+
+	/**
+	 * Berechnet eine neue Matrix mit nur einer Zeile, die die Spaltensummen
+	 * dieser Matrix enthalten.
+	 *
+	 * @return Eine 1 x {@code columns()} Matrix.
+	 */
+	MLMatrix colSums();
+
+	/**
+	 * Erzeugt eine neue Matrix, deren Werte gleich den Werten dieser Matrix
+	 * nach der Anwendung der angegebenen Funktion sind.
+	 *
+	 * @param op Eine Operation {@code (double) -> double}.
+	 * @return Eine {@code rows()} x {@code columns()} Matrix.
+	 */
+	MLMatrix apply( DoubleUnaryOperator op );
+
+	/**
+	 * Endet die gegebene Funktion auf jeden Wert der Matrix an.
+	 *
+	 * @param op Eine Operation {@code (double) -> double}.
+	 * @return Diese Matrix selbst (method chaining)
+	 */
+	MLMatrix applyInPlace( DoubleUnaryOperator op );
+
+	/**
+	 * Erzeugt eine neue Matrix mit denselben Dimensionen und Koeffizienten wie
+	 * diese Matrix.
+	 *
+	 * @return Eine Kopie dieser Matrix.
+	 */
+	MLMatrix duplicate();
+
+	String toString();
+
+}

src/main/java/schule/ngb/zm/ml/Matrix.java

@@ -1,82 +0,0 @@
-package schule.ngb.zm.ml;
-
-import schule.ngb.zm.Constants;
-
-import java.util.Arrays;
-
-// TODO: Move Math into Matrix class
-// TODO: Implement support for optional sci libs
-public class Matrix {
-
-	private int columns, rows;
-
-	double[][] coefficients;
-
-	public Matrix( int rows, int cols )  {
-		this.rows = rows;
-		this.columns = cols;
-		coefficients = new double[rows][cols];
-	}
-
-	public Matrix( double[][] coefficients ) {
-		this.coefficients = coefficients;
-		this.rows = coefficients.length;
-		this.columns = coefficients[0].length;
-	}
-
-	public int getColumns() {
-		return columns;
-	}
-
-	public int getRows() {
-		return rows;
-	}
-
-	public double[][] getCoefficients() {
-		return coefficients;
-	}
-
-	public double get( int row, int col ) {
-		return coefficients[row][col];
-	}
-
-	public void initializeRandom() {
-		coefficients = MLMath.matrixApply(coefficients, (d) -> Constants.randomGaussian());
-	}
-
-	public void initializeRandom( double lower, double upper ) {
-		coefficients = MLMath.matrixApply(coefficients, (d) -> ((upper-lower) * (Constants.randomGaussian()+1) * .5) + lower);
-	}
-
-	public void initializeIdentity() {
-		initializeZero();
-		for( int i = 0; i < Math.min(rows, columns); i++ ) {
-			this.coefficients[i][i] = 1.0;
-		}
-	}
-
-	public void initializeOne() {
-		coefficients = MLMath.matrixApply(coefficients, (d) -> 1.0);
-	}
-
-	public void initializeZero() {
-		coefficients = MLMath.matrixApply(coefficients, (d) -> 0.0);
-	}
-
-	@Override
-	public String toString() {
-		//return Arrays.deepToString(coefficients);
-		StringBuilder sb = new StringBuilder();
-		sb.append('[');
-		sb.append('\n');
-		for( int i = 0; i < coefficients.length; i++ ) {
-			sb.append('\t');
-			sb.append(Arrays.toString(coefficients[i]));
-			sb.append('\n');
-		}
-		sb.append(']');
-
-		return sb.toString();
-	}
-
-}

src/main/java/schule/ngb/zm/ml/MatrixFactory.java

@@ -0,0 +1,246 @@
+package schule.ngb.zm.ml;
+
+import cern.colt.matrix.DoubleFactory2D;
+import schule.ngb.zm.Constants;
+import schule.ngb.zm.util.Log;
+
+import java.util.function.DoubleUnaryOperator;
+
+/**
+ * Zentrale Klasse zur Erstellung neuer Matrizen. Generell sollten neue Matrizen
+ * nicht direkt erstellt werden, sondern durch den Aufruf von
+ * {@link #create(int, int)} oder {@link #create(double[][])}. Die Fabrik
+ * ermittelt automatisch die beste verfügbare Implementierung und initialisiert
+ * eine entsprechende Implementierung von {@link MLMatrix}.
+ * <p>
+ * Derzeit werden die optionale Bibliothek <a
+ * href="https://dst.lbl.gov/ACSSoftware/colt/">Colt</a> und die interne
+ * Implementierung {@link DoubleMatrix} unterstützt.
+ */
+public class MatrixFactory {
+
+	/**
+	 * Erstellt eine neue Matrix mit den angegebenen Dimensionen und
+	 * initialisiert alle Werte mit 0.
+	 *
+	 * @param rows Anzahl der Zeilen.
+	 * @param cols Anzahl der Spalten.
+	 * @return Eine {@code rows} x {@code cols} Matrix.
+	 */
+	public static final MLMatrix create( int rows, int cols ) {
+		try {
+			return getMatrixType().getDeclaredConstructor(int.class, int.class).newInstance(rows, cols);
+		} catch( Exception ex ) {
+			LOG.error(ex, "Could not initialize matrix implementation for class <%s>. Using internal implementation.", matrixType);
+		}
+		return new DoubleMatrix(rows, cols);
+	}
+
+	/**
+	 * Erstellt eine neue Matrix mit den Dimensionen des angegebenen Arrays und
+	 * initialisiert die Werte mit den entsprechenden Werten des Arrays.
+	 *
+	 * @param values Die Werte der Matrix.
+	 * @return Eine {@code values.length} x {@code values[0].length} Matrix mit
+	 * 	den Werten des Arrays.
+	 */
+	public static final MLMatrix create( double[][] values ) {
+		try {
+			return getMatrixType().getDeclaredConstructor(double[][].class).newInstance((Object) values);
+		} catch( Exception ex ) {
+			LOG.error(ex, "Could not initialize matrix implementation for class <%s>. Using internal implementation.", matrixType);
+		}
+		return new DoubleMatrix(values);
+	}
+
+	/**
+	 * Die verwendete {@link MLMatrix} Implementierung, aus der Matrizen erzeugt
+	 * werden.
+	 */
+	static Class<? extends MLMatrix> matrixType = null;
+
+	/**
+	 * Ermittelt die beste verfügbare Implementierung von {@link MLMatrix}.
+	 *
+	 * @return Die verwendete {@link MLMatrix} Implementierung.
+	 */
+	private static final Class<? extends MLMatrix> getMatrixType() {
+		if( matrixType == null ) {
+			try {
+				Class<?> clazz = Class.forName("cern.colt.matrix.impl.DenseDoubleMatrix2D", false, MatrixFactory.class.getClassLoader());
+				matrixType = ColtMatrix.class;
+				LOG.info("Colt library found. Using <cern.colt.matrix.impl.DenseDoubleMatrix2D> as matrix implementation.");
+			} catch( ClassNotFoundException e ) {
+				LOG.info("Colt library not found. Falling back on internal implementation.");
+				matrixType = DoubleMatrix.class;
+			}
+		}
+		return matrixType;
+	}
+
+	private static final Log LOG = Log.getLogger(MatrixFactory.class);
+
+	/**
+	 * Interner Wrapper der DoubleMatrix2D Klasse aus der Colt Bibliothek, um
+	 * das {@link MLMatrix} Interface zu implementieren.
+	 */
+	static class ColtMatrix implements MLMatrix {
+
+		cern.colt.matrix.DoubleMatrix2D matrix;
+
+		public ColtMatrix( double[][] doubles ) {
+			matrix = new cern.colt.matrix.impl.DenseDoubleMatrix2D(doubles);
+		}
+
+		public ColtMatrix( int rows, int cols ) {
+			matrix = new cern.colt.matrix.impl.DenseDoubleMatrix2D(rows, cols);
+		}
+
+		public ColtMatrix( ColtMatrix matrix ) {
+			this.matrix = matrix.matrix.copy();
+		}
+
+		@Override
+		public int columns() {
+			return matrix.columns();
+		}
+
+		@Override
+		public int rows() {
+			return matrix.rows();
+		}
+
+		@Override
+		public double get( int row, int col ) {
+			return matrix.get(row, col);
+		}
+
+		@Override
+		public MLMatrix set( int row, int col, double value ) {
+			matrix.set(row, col, value);
+			return this;
+		}
+
+		@Override
+		public MLMatrix initializeRandom() {
+			return initializeRandom(-1.0, 1.0);
+		}
+
+		@Override
+		public MLMatrix initializeRandom( double lower, double upper ) {
+			matrix.assign(( d ) -> ((upper - lower) * Constants.random()) + lower);
+			return this;
+		}
+
+		@Override
+		public MLMatrix initializeOne() {
+			this.matrix.assign(1.0);
+			return this;
+		}
+
+		@Override
+		public MLMatrix initializeZero() {
+			this.matrix.assign(0.0);
+			return this;
+		}
+
+		@Override
+		public MLMatrix duplicate() {
+			ColtMatrix newMatrix = new ColtMatrix(matrix.rows(), matrix.columns());
+			newMatrix.matrix.assign(this.matrix);
+			return newMatrix;
+		}
+
+		@Override
+		public MLMatrix multiplyTransposed( MLMatrix B ) {
+			ColtMatrix CB = (ColtMatrix) B;
+			ColtMatrix newMatrix = new ColtMatrix(0, 0);
+			newMatrix.matrix = matrix.zMult(CB.matrix, null, 1.0, 0.0, false, true);
+			return newMatrix;
+		}
+
+		@Override
+		public MLMatrix multiplyAddBias( MLMatrix B, MLMatrix C ) {
+			ColtMatrix CB = (ColtMatrix) B;
+			ColtMatrix newMatrix = new ColtMatrix(0, 0);
+			newMatrix.matrix = DoubleFactory2D.dense.repeat(((ColtMatrix) C).matrix, rows(), 1);
+			matrix.zMult(CB.matrix, newMatrix.matrix, 1.0, 1.0, false, false);
+			return newMatrix;
+		}
+
+		@Override
+		public MLMatrix transposedMultiplyAndScale( final MLMatrix B, final double scalar ) {
+			ColtMatrix CB = (ColtMatrix) B;
+			ColtMatrix newMatrix = new ColtMatrix(0, 0);
+			newMatrix.matrix = matrix.zMult(CB.matrix, null, scalar, 0.0, true, false);
+			return newMatrix;
+		}
+
+		@Override
+		public MLMatrix add( MLMatrix B ) {
+			ColtMatrix CB = (ColtMatrix) B;
+			ColtMatrix newMatrix = new ColtMatrix(this);
+			newMatrix.matrix.assign(CB.matrix, ( d1, d2 ) -> d1 + d2);
+			return newMatrix;
+		}
+
+		@Override
+		public MLMatrix addInPlace( MLMatrix B ) {
+			ColtMatrix CB = (ColtMatrix) B;
+			matrix.assign(CB.matrix, ( d1, d2 ) -> d1 + d2);
+			return this;
+		}
+
+		@Override
+		public MLMatrix sub( MLMatrix B ) {
+			ColtMatrix CB = (ColtMatrix) B;
+			ColtMatrix newMatrix = new ColtMatrix(this);
+			newMatrix.matrix.assign(CB.matrix, ( d1, d2 ) -> d1 - d2);
+			return newMatrix;
+		}
+
+		@Override
+		public MLMatrix colSums() {
+			double[][] sums = new double[1][matrix.columns()];
+			for( int c = 0; c < matrix.columns(); c++ ) {
+				for( int r = 0; r < matrix.rows(); r++ ) {
+					sums[0][c] += matrix.getQuick(r, c);
+				}
+			}
+			return new ColtMatrix(sums);
+		}
+
+		@Override
+		public MLMatrix scaleInPlace( double scalar ) {
+			this.matrix.assign(( d ) -> d * scalar);
+			return this;
+		}
+
+		@Override
+		public MLMatrix scaleInPlace( MLMatrix S ) {
+			this.matrix.forEachNonZero(( r, c, d ) -> d * S.get(r, c));
+			return this;
+		}
+
+		@Override
+		public MLMatrix apply( DoubleUnaryOperator op ) {
+			ColtMatrix newMatrix = new ColtMatrix(matrix.rows(), matrix.columns());
+			newMatrix.matrix.assign(matrix);
+			newMatrix.matrix.assign(( d ) -> op.applyAsDouble(d));
+			return newMatrix;
+		}
+
+		@Override
+		public MLMatrix applyInPlace( DoubleUnaryOperator op ) {
+			this.matrix.assign(( d ) -> op.applyAsDouble(d));
+			return this;
+		}
+
+		@Override
+		public String toString() {
+			return matrix.toString();
+		}
+
+	}
+
+}

src/main/java/schule/ngb/zm/ml/NeuralNetwork.java

@@ -15,7 +15,7 @@ public class NeuralNetwork {
 			Writer writer = ResourceStreamProvider.getWriter(source);
 			PrintWriter out = new PrintWriter(writer)
 		) {
-			for( NeuronLayer layer: network.layers ) {
+			for( NeuronLayer layer : network.layers ) {
 				out.print(layer.getNeuronCount());
 				out.print(' ');
 				out.print(layer.getInputCount());
@@ -23,20 +23,44 @@ public class NeuralNetwork {
 
 				for( int i = 0; i < layer.getInputCount(); i++ ) {
 					for( int j = 0; j < layer.getNeuronCount(); j++ ) {
-						out.print(layer.weights.coefficients[i][j]);
+						out.print(layer.weights.get(i, j));
 						out.print(' ');
 					}
 					out.println();
 				}
 				for( int j = 0; j < layer.getNeuronCount(); j++ ) {
-					out.print(layer.biases[j]);
+					out.print(layer.biases.get(0, j));
 					out.print(' ');
 				}
 				out.println();
 			}
 			out.flush();
 		} catch( IOException ex ) {
-			LOG.warn(ex, "");
+			LOG.error(ex, "");
+		}
+	}
+
+	public static void saveToDataFile( String source, NeuralNetwork network ) {
+		try(
+			OutputStream stream = ResourceStreamProvider.getOutputStream(source);
+			DataOutputStream out = new DataOutputStream(stream)
+		) {
+			for( NeuronLayer layer : network.layers ) {
+				out.writeInt(layer.getNeuronCount());
+				out.writeInt(layer.getInputCount());
+
+				for( int i = 0; i < layer.getInputCount(); i++ ) {
+					for( int j = 0; j < layer.getNeuronCount(); j++ ) {
+						out.writeDouble(layer.weights.get(i, j));
+					}
+				}
+				for( int j = 0; j < layer.getNeuronCount(); j++ ) {
+					out.writeDouble(layer.biases.get(0, j));
+				}
+			}
+			out.flush();
+		} catch( IOException ex ) {
+			LOG.error(ex, "");
 		}
 	}
 
@@ -56,13 +80,13 @@ public class NeuralNetwork {
 				for( int i = 0; i < inputs; i++ ) {
 					split = in.readLine().split(" ");
 					for( int j = 0; j < neurons; j++ ) {
-						layer.weights.coefficients[i][j] = Double.parseDouble(split[j]);
+						layer.weights.set(i, j, Double.parseDouble(split[j]));
 					}
 				}
 				// Load Biases
 				split = in.readLine().split(" ");
 				for( int j = 0; j < neurons; j++ ) {
-					layer.biases[j] = Double.parseDouble(split[j]);
+					layer.biases.set(0, j, Double.parseDouble(split[j]));
 				}
 
 				layers.add(layer);
@@ -70,29 +94,30 @@ public class NeuralNetwork {
 
 			return new NeuralNetwork(layers);
 		} catch( IOException | NoSuchElementException ex ) {
-			LOG.warn(ex, "Could not load neural network from source <%s>", source);
+			LOG.error(ex, "Could not load neural network from source <%s>", source);
 		}
 		return null;
 	}
 
-	/*public static NeuralNetwork loadFromFile( String source ) {
+	public static NeuralNetwork loadFromDataFile( String source ) {
 		try(
 			InputStream stream = ResourceStreamProvider.getInputStream(source);
-			Scanner in = new Scanner(stream)
+			DataInputStream in = new DataInputStream(stream)
 		) {
 			List<NeuronLayer> layers = new LinkedList<>();
-			while( in.hasNext() ) {
-				int neurons = in.nextInt();
-				int inputs = in.nextInt();
+			while( in.available() > 0 ) {
+				int neurons = in.readInt();
+				int inputs = in.readInt();
 
 				NeuronLayer layer = new NeuronLayer(neurons, inputs);
 				for( int i = 0; i < inputs; i++ ) {
 					for( int j = 0; j < neurons; j++ ) {
-						layer.weights.coefficients[i][j] = in.nextDouble();
+						layer.weights.set(i, j, in.readDouble());
 					}
 				}
+				// Load Biases
 				for( int j = 0; j < neurons; j++ ) {
-					layer.biases[j] = in.nextDouble();
+					layer.biases.set(0, j, in.readDouble());
 				}
 
 				layers.add(layer);
@@ -100,14 +125,14 @@ public class NeuralNetwork {
 
 			return new NeuralNetwork(layers);
 		} catch( IOException | NoSuchElementException ex ) {
-			LOG.warn(ex, "Could not load neural network from source <%s>", source);
+			LOG.error(ex, "Could not load neural network from source <%s>", source);
 		}
 		return null;
-	}*/
+	}
 
 	private NeuronLayer[] layers;
 
-	private double[][] output;
+	private MLMatrix output;
 
 	private double learningRate = 0.1;
 
@@ -128,7 +153,7 @@ public class NeuralNetwork {
 		for( int i = 0; i < layers.size(); i++ ) {
 			this.layers[i] = layers.get(i);
 			if( i > 0 ) {
-				this.layers[i-1].setNextLayer(this.layers[i]);
+				this.layers[i - 1].setNextLayer(this.layers[i]);
 			}
 		}
 	}
@@ -138,7 +163,7 @@ public class NeuralNetwork {
 		for( int i = 0; i < layers.length; i++ ) {
 			this.layers[i] = layers[i];
 			if( i > 0 ) {
-				this.layers[i-1].setNextLayer(this.layers[i]);
+				this.layers[i - 1].setNextLayer(this.layers[i]);
 			}
 		}
 	}
@@ -146,6 +171,7 @@ public class NeuralNetwork {
 	public int getLayerCount() {
 		return layers.length;
 	}
+
 	public NeuronLayer[] getLayers() {
 		return layers;
 	}
@@ -162,17 +188,25 @@ public class NeuralNetwork {
 		this.learningRate = pLearningRate;
 	}
 
-	public double[][] getOutput() {
+	public MLMatrix getOutput() {
 		return output;
 	}
 
-	public double[][] predict( double[][] inputs ) {
+	public MLMatrix predict( double[][] inputs ) {
 		//this.output = layers[1].apply(layers[0].apply(inputs));
+		return predict(MatrixFactory.create(inputs));
+	}
+
+	public MLMatrix predict( MLMatrix inputs ) {
 		this.output = layers[0].apply(inputs);
 		return this.output;
 	}
 
 	public void learn( double[][] expected ) {
+		learn(MatrixFactory.create(expected));
+	}
+
+	public void learn( MLMatrix expected ) {
 		layers[layers.length - 1].backprop(expected, learningRate);
 	}
 

src/main/java/schule/ngb/zm/ml/NeuronLayer.java

@@ -1,50 +1,66 @@
 package schule.ngb.zm.ml;
 
-import java.util.Arrays;
 import java.util.function.DoubleUnaryOperator;
 import java.util.function.Function;
 
-public class NeuronLayer implements Function<double[][], double[][]> {
+/**
+ * Implementierung einer Neuronenebene in einem Neuonalen Netz.
+ * <p>
+ * Eine Ebene besteht aus einer Anzahl an <em>Neuronen</em> die jeweils eine
+ * Anzahl <em>Eingänge</em> haben. Die Eingänge erhalten als Signal die Ausgabe
+ * der vorherigen Ebene und berechnen die Ausgabe des jeweiligen Neurons.
+ */
+public class NeuronLayer implements Function<MLMatrix, MLMatrix> {
+
+	public static NeuronLayer fromArray( double[][] weights, boolean transpose ) {
+		NeuronLayer layer;
+		if( transpose ) {
+			layer = new NeuronLayer(weights.length, weights[0].length);
+		} else {
+			layer = new NeuronLayer(weights[0].length, weights.length);
+		}
 
-	public static NeuronLayer fromArray( double[][] weights ) {
-		NeuronLayer layer = new NeuronLayer(weights[0].length, weights.length);
 		for( int i = 0; i < weights[0].length; i++ ) {
 			for( int j = 0; j < weights.length; j++ ) {
-				layer.weights.coefficients[i][j] = weights[i][j];
+				if( transpose ) {
+					layer.weights.set(j, i, weights[i][j]);
+				} else {
+					layer.weights.set(i, j, weights[i][j]);
+				}
 			}
 		}
+
 		return layer;
 	}
 
-	public static NeuronLayer fromArray( double[][] weights, double[] biases ) {
-		NeuronLayer layer = new NeuronLayer(weights[0].length, weights.length);
-		for( int i = 0; i < weights[0].length; i++ ) {
-			for( int j = 0; j < weights.length; j++ ) {
-				layer.weights.coefficients[i][j] = weights[i][j];
-			}
-		}
+	public static NeuronLayer fromArray( double[][] weights, double[] biases, boolean transpose ) {
+		NeuronLayer layer = fromArray(weights, transpose);
+
 		for( int j = 0; j < biases.length; j++ ) {
-			layer.biases[j] = biases[j];
+			layer.biases.set(0, j, biases[j]);
 		}
+
 		return layer;
 	}
-	
-	Matrix weights;
 
-	double[] biases;
+	MLMatrix weights;
+
+	MLMatrix biases;
 
 	NeuronLayer previous, next;
 
 	DoubleUnaryOperator activationFunction, activationFunctionDerivative;
 
-	double[][] lastOutput, lastInput;
+	MLMatrix lastOutput, lastInput;
 
 	public NeuronLayer( int neurons, int inputs ) {
-		weights = new Matrix(inputs, neurons);
-		weights.initializeRandom(-1, 1);
+		weights = MatrixFactory
+			.create(inputs, neurons)
+			.initializeRandom();
 
-		biases = new double[neurons];
-		Arrays.fill(biases, 0.0); // TODO: Random?
+		biases = MatrixFactory
+			.create(1, neurons)
+			.initializeZero();
 
 		activationFunction = MLMath::sigmoid;
 		activationFunctionDerivative = MLMath::sigmoidDerivative;
@@ -85,45 +101,42 @@ public class NeuronLayer implements Function<double[][], double[][]> {
 		}
 	}
 
-	public Matrix getWeights() {
+	public MLMatrix getWeights() {
 		return weights;
 	}
 
+	public MLMatrix getBiases() {
+		return biases;
+	}
+
 	public int getNeuronCount() {
-		return weights.coefficients[0].length;
+		return weights.columns();
 	}
 
 	public int getInputCount() {
-		return weights.coefficients.length;
+		return weights.rows();
 	}
 
-	public double[][] getLastOutput() {
+	public MLMatrix getLastOutput() {
 		return lastOutput;
 	}
 
-	public void setWeights( double[][] newWeights ) {
-		weights.coefficients = MLMath.copyMatrix(newWeights);
-	}
-
-	public void adjustWeights( double[][] adjustment ) {
-		weights.coefficients = MLMath.matrixAdd(weights.coefficients, adjustment);
+	public void setWeights( MLMatrix newWeights ) {
+		weights = newWeights.duplicate();
 	}
 
 	@Override
 	public String toString() {
-		return weights.toString() + "\n" + Arrays.toString(biases);
+		return "weights:\n" + weights.toString() + "\nbiases:\n" + biases.toString();
 	}
 
 	@Override
-	public double[][] apply( double[][] inputs ) {
-		lastInput = inputs;
-		lastOutput = MLMath.matrixApply(
-			MLMath.biasAdd(
-				MLMath.matrixMultiply(inputs, weights.coefficients),
-				biases
-			),
-			activationFunction
-		);
+	public MLMatrix apply( MLMatrix inputs ) {
+		lastInput = inputs.duplicate();
+		lastOutput = inputs
+			.multiplyAddBias(weights, biases)
+			.applyInPlace(activationFunction);
+
 		if( next != null ) {
 			return next.apply(lastOutput);
 		} else {
@@ -132,36 +145,41 @@ public class NeuronLayer implements Function<double[][], double[][]> {
 	}
 
 	@Override
-	public <V> Function<V, double[][]> compose( Function<? super V, ? extends double[][]> before ) {
+	public <V> Function<V, MLMatrix> compose( Function<? super V, ? extends MLMatrix> before ) {
 		return ( in ) -> apply(before.apply(in));
 	}
 
 	@Override
-	public <V> Function<double[][], V> andThen( Function<? super double[][], ? extends V> after ) {
+	public <V> Function<MLMatrix, V> andThen( Function<? super MLMatrix, ? extends V> after ) {
 		return ( in ) -> after.apply(apply(in));
 	}
 
-	public void backprop( double[][] expected, double learningRate ) {
-		double[][] error, delta, adjustment;
+	public void backprop( MLMatrix expected, double learningRate ) {
+		MLMatrix error, adjustment;
 		if( next == null ) {
-			error = MLMath.matrixSub(expected, this.lastOutput);
+			error = expected.sub(lastOutput);
 		} else {
-			error = MLMath.matrixMultiply(expected, MLMath.matrixTranspose(next.weights.coefficients));
+			error = expected.multiplyTransposed(next.weights);
 		}
 
-		delta = MLMath.matrixScale(error, MLMath.matrixApply(this.lastOutput, this.activationFunctionDerivative));
+		error.scaleInPlace(
+			lastOutput.apply(this.activationFunctionDerivative)
+		);
 		// Hier schon leraningRate anwenden?
 		// See https://towardsdatascience.com/understanding-and-implementing-neural-networks-in-java-from-scratch-61421bb6352c
 		//delta = MLMath.matrixApply(delta, ( x ) -> learningRate * x);
 		if( previous != null ) {
-			previous.backprop(delta, learningRate);
+			previous.backprop(error, learningRate);
 		}
 
-		biases = MLMath.biasAdjust(biases, MLMath.matrixApply(delta, ( x ) -> learningRate * x));
+		biases.addInPlace(
+			error.colSums().scaleInPlace(
+				-learningRate / (double) error.rows()
+			)
+		);
 
-		adjustment = MLMath.matrixMultiply(MLMath.matrixTranspose(lastInput), delta);
-		adjustment = MLMath.matrixApply(adjustment, ( x ) -> learningRate * x);
-		this.adjustWeights(adjustment);
+		adjustment = lastInput.transposedMultiplyAndScale(error, learningRate);
+		weights.addInPlace(adjustment);
 	}
 
 }

src/test/java/schule/ngb/zm/ml/MLMatrixTest.java

@@ -0,0 +1,426 @@
+package schule.ngb.zm.ml;
+
+import org.junit.jupiter.api.BeforeEach;
+import org.junit.jupiter.api.Test;
+import org.junit.jupiter.api.TestInfo;
+import org.junit.jupiter.params.ParameterizedTest;
+import org.junit.jupiter.params.provider.ValueSource;
+import schule.ngb.zm.util.Timer;
+
+import static org.junit.jupiter.api.Assertions.*;
+
+class MLMatrixTest {
+
+	private TestInfo info;
+
+	@BeforeEach
+	void saveTestInfo( TestInfo info ) {
+		this.info = info;
+	}
+
+	@ParameterizedTest
+	@ValueSource( classes = {DoubleMatrix.class, MatrixFactory.ColtMatrix.class} )
+	void get( Class<? extends MLMatrix> mType ) {
+		MatrixFactory.matrixType = mType;
+
+		MLMatrix M = MatrixFactory.create(new double[][]{
+			{1, 2, 3},
+			{4, 5, 6}
+		});
+
+		assertEquals(mType, M.getClass());
+
+		assertEquals(1.0, M.get(0,0));
+		assertEquals(4.0, M.get(1,0));
+		assertEquals(6.0, M.get(1,2));
+	}
+
+	@ParameterizedTest
+	@ValueSource( classes = {DoubleMatrix.class, MatrixFactory.ColtMatrix.class} )
+	void initializeOne( Class<? extends MLMatrix> mType ) {
+		MatrixFactory.matrixType = mType;
+
+		MLMatrix m = MatrixFactory.create(4, 4);
+		m.initializeOne();
+
+		assertEquals(mType, m.getClass());
+
+		for( int i = 0; i < m.rows(); i++ ) {
+			for( int j = 0; j < m.columns(); j++ ) {
+				assertEquals(1.0, m.get(i, j));
+			}
+		}
+	}
+
+	@ParameterizedTest
+	@ValueSource( classes = {DoubleMatrix.class, MatrixFactory.ColtMatrix.class} )
+	void initializeZero( Class<? extends MLMatrix> mType ) {
+		MatrixFactory.matrixType = mType;
+
+		MLMatrix m = MatrixFactory.create(4, 4);
+		m.initializeZero();
+
+		assertEquals(mType, m.getClass());
+
+		for( int i = 0; i < m.rows(); i++ ) {
+			for( int j = 0; j < m.columns(); j++ ) {
+				assertEquals(0.0, m.get(i, j));
+			}
+		}
+	}
+
+	@ParameterizedTest
+	@ValueSource( classes = {DoubleMatrix.class, MatrixFactory.ColtMatrix.class} )
+	void initializeRandom( Class<? extends MLMatrix> mType ) {
+		MatrixFactory.matrixType = mType;
+
+		MLMatrix m = MatrixFactory.create(4, 4);
+		m.initializeRandom();
+
+		assertEquals(mType, m.getClass());
+
+		for( int i = 0; i < m.rows(); i++ ) {
+			for( int j = 0; j < m.columns(); j++ ) {
+				double d = m.get(i, j);
+				assertTrue(-1.0 <= d && d < 1.0);
+			}
+		}
+	}
+
+	@ParameterizedTest
+	@ValueSource( classes = {DoubleMatrix.class, MatrixFactory.ColtMatrix.class} )
+	void multiplyTransposed( Class<? extends MLMatrix> mType ) {
+		MatrixFactory.matrixType = mType;
+
+		MLMatrix A = MatrixFactory.create(new double[][]{
+			{1.0, 2.0, 3.0, 4.0},
+			{1.0, 2.0, 3.0, 4.0},
+			{1.0, 2.0, 3.0, 4.0}
+		});
+		MLMatrix B = MatrixFactory.create(new double[][]{
+			{1, 3, 5, 7},
+			{2, 4, 6, 8}
+		});
+
+		MLMatrix C = A.multiplyTransposed(B);
+
+		assertEquals(mType, A.getClass());
+		assertEquals(mType, B.getClass());
+		assertEquals(mType, C.getClass());
+
+		assertEquals(3, C.rows());
+		assertEquals(2, C.columns());
+		for( int i = 0; i < C.rows(); i++ ) {
+			assertEquals(50.0, C.get(i, 0));
+			assertEquals(60.0, C.get(i, 1));
+		}
+	}
+
+	@ParameterizedTest
+	@ValueSource( classes = {DoubleMatrix.class, MatrixFactory.ColtMatrix.class} )
+	void multiplyAddBias( Class<? extends MLMatrix> mType ) {
+		MatrixFactory.matrixType = mType;
+
+		MLMatrix A = MatrixFactory.create(new double[][]{
+			{1.0, 2.0, 3.0, 4.0},
+			{1.0, 2.0, 3.0, 4.0},
+			{1.0, 2.0, 3.0, 4.0}
+		});
+		MLMatrix B = MatrixFactory.create(new double[][]{
+			{1.0, 2.0},
+			{3.0, 4.0},
+			{5.0, 6.0},
+			{7.0, 8.0}
+		});
+		MLMatrix V = MatrixFactory.create(new double[][]{
+			{1000.0, 2000.0}
+		});
+
+		MLMatrix C = A.multiplyAddBias(B, V);
+
+		assertEquals(mType, A.getClass());
+		assertEquals(mType, B.getClass());
+		assertEquals(mType, C.getClass());
+		assertEquals(mType, V.getClass());
+
+		assertEquals(3, C.rows());
+		assertEquals(2, C.columns());
+		for( int i = 0; i < C.rows(); i++ ) {
+			assertEquals(1050.0, C.get(i, 0));
+			assertEquals(2060.0, C.get(i, 1));
+		}
+	}
+
+	@ParameterizedTest
+	@ValueSource( classes = {DoubleMatrix.class, MatrixFactory.ColtMatrix.class} )
+	void transposedMultiplyAndScale( Class<? extends MLMatrix> mType ) {
+		MatrixFactory.matrixType = mType;
+
+		MLMatrix A = MatrixFactory.create(new double[][]{
+			{1, 1, 1},
+			{2, 2, 2},
+			{3, 3, 3},
+			{4, 4, 4}
+		});
+		MLMatrix B = MatrixFactory.create(new double[][]{
+			{1.0, 2.0},
+			{3.0, 4.0},
+			{5.0, 6.0},
+			{7.0, 8.0}
+		});
+
+		MLMatrix C = A.transposedMultiplyAndScale(B, 2.0);
+
+		assertEquals(mType, A.getClass());
+		assertEquals(mType, B.getClass());
+		assertEquals(mType, C.getClass());
+
+		assertEquals(3, C.rows());
+		assertEquals(2, C.columns());
+		for( int i = 0; i < C.rows(); i++ ) {
+			assertEquals(100.0, C.get(i, 0));
+			assertEquals(120.0, C.get(i, 1));
+		}
+	}
+
+	@ParameterizedTest
+	@ValueSource( classes = {DoubleMatrix.class, MatrixFactory.ColtMatrix.class} )
+	void apply( Class<? extends MLMatrix> mType ) {
+		MatrixFactory.matrixType = mType;
+
+		MLMatrix M = MatrixFactory.create(new double[][]{
+			{1, 1, 1},
+			{2, 2, 2},
+			{3, 3, 3},
+			{4, 4, 4}
+		});
+
+		MLMatrix R = M.apply(( d ) -> d * d);
+
+		assertEquals(mType, M.getClass());
+		assertEquals(mType, R.getClass());
+		assertNotSame(M, R);
+
+		for( int i = 0; i < M.rows(); i++ ) {
+			for( int j = 0; j < M.columns(); j++ ) {
+				assertEquals(
+					(i + 1) * (i + 1), R.get(i, j),
+					msg("(%d,%d)", "apply", i, j)
+				);
+			}
+		}
+
+		MLMatrix M2 = M.applyInPlace(( d ) -> d * d * d);
+		assertSame(M, M2);
+		for( int i = 0; i < M.rows(); i++ ) {
+			for( int j = 0; j < M.columns(); j++ ) {
+				assertEquals(
+					(i + 1) * (i + 1) * (i + 1), M.get(i, j),
+					msg("(%d,%d)", "applyInPlace", i, j)
+				);
+			}
+		}
+	}
+
+	@ParameterizedTest
+	@ValueSource( classes = {DoubleMatrix.class, MatrixFactory.ColtMatrix.class} )
+	void add( Class<? extends MLMatrix> mType ) {
+		MatrixFactory.matrixType = mType;
+
+		MLMatrix M = MatrixFactory.create(new double[][]{
+			{1, 1, 1},
+			{2, 2, 2},
+			{3, 3, 3},
+			{4, 4, 4}
+		});
+
+		MLMatrix R = M.add(M);
+
+		assertEquals(mType, M.getClass());
+		assertEquals(mType, R.getClass());
+		assertNotSame(M, R);
+
+		for( int i = 0; i < M.rows(); i++ ) {
+			for( int j = 0; j < M.columns(); j++ ) {
+				assertEquals(
+					(i + 1) + (i + 1), R.get(i, j),
+					msg("(%d,%d)", "add", i, j)
+				);
+			}
+		}
+
+		MLMatrix M2 = M.addInPlace(R);
+		assertSame(M, M2);
+		for( int i = 0; i < M.rows(); i++ ) {
+			for( int j = 0; j < M.columns(); j++ ) {
+				assertEquals(
+					(i + 1) + (i + 1) + (i + 1), M.get(i, j),
+					msg("(%d,%d)", "addInPlace", i, j)
+				);
+			}
+		}
+	}
+
+	@ParameterizedTest
+	@ValueSource( classes = {DoubleMatrix.class, MatrixFactory.ColtMatrix.class} )
+	void sub( Class<? extends MLMatrix> mType ) {
+		MatrixFactory.matrixType = mType;
+
+		MLMatrix M = MatrixFactory.create(new double[][]{
+			{1, 1, 1},
+			{2, 2, 2},
+			{3, 3, 3},
+			{4, 4, 4}
+		});
+
+		MLMatrix R = M.sub(M);
+
+		assertEquals(mType, M.getClass());
+		assertEquals(mType, R.getClass());
+		assertNotSame(M, R);
+
+		for( int i = 0; i < M.rows(); i++ ) {
+			for( int j = 0; j < M.columns(); j++ ) {
+				assertEquals(
+					0.0, R.get(i, j),
+					msg("(%d,%d)", "sub", i, j)
+				);
+			}
+		}
+	}
+
+	@ParameterizedTest
+	@ValueSource( classes = {DoubleMatrix.class, MatrixFactory.ColtMatrix.class} )
+	void colSums( Class<? extends MLMatrix> mType ) {
+		MatrixFactory.matrixType = mType;
+
+		MLMatrix M = MatrixFactory.create(new double[][]{
+			{1, 2, 3},
+			{1, 2, 3},
+			{1, 2, 3},
+			{1, 2, 3}
+		});
+
+		MLMatrix R = M.colSums();
+
+		assertEquals(mType, M.getClass());
+		assertEquals(mType, R.getClass());
+		assertNotSame(M, R);
+
+		assertEquals(1, R.rows());
+		assertEquals(3, R.columns());
+		for( int j = 0; j < M.columns(); j++ ) {
+			assertEquals(
+				(j+1)*4, R.get(0, j),
+				msg("(%d,%d)", "colSums", 0, j)
+			);
+		}
+	}
+
+
+	@ParameterizedTest
+	@ValueSource( classes = {DoubleMatrix.class, MatrixFactory.ColtMatrix.class} )
+	void duplicate( Class<? extends MLMatrix> mType ) {
+		MatrixFactory.matrixType = mType;
+
+		MLMatrix M = MatrixFactory.create(new double[][]{
+			{1, 2, 3},
+			{1, 2, 3},
+			{1, 2, 3},
+			{1, 2, 3}
+		});
+
+		MLMatrix R = M.duplicate();
+
+		assertEquals(mType, M.getClass());
+		assertEquals(mType, R.getClass());
+		assertNotSame(M, R);
+
+		for( int i = 0; i < M.rows(); i++ ) {
+			for( int j = 0; j < M.columns(); j++ ) {
+				assertEquals(
+					M.get(i, j), R.get(i, j),
+					msg("(%d,%d)", "duplicate", i, j)
+				);
+			}
+		}
+	}
+
+	@ParameterizedTest
+	@ValueSource( classes = {DoubleMatrix.class, MatrixFactory.ColtMatrix.class} )
+	void scale( Class<? extends MLMatrix> mType ) {
+		MatrixFactory.matrixType = mType;
+
+		MLMatrix M = MatrixFactory.create(new double[][]{
+			{1, 1, 1},
+			{2, 2, 2},
+			{3, 3, 3},
+			{4, 4, 4}
+		});
+
+		MLMatrix M2 = M.scaleInPlace(2.0);
+
+		assertEquals(mType, M.getClass());
+		assertEquals(mType, M2.getClass());
+		assertSame(M, M2);
+
+		for( int i = 0; i < M.rows(); i++ ) {
+			for( int j = 0; j < M.columns(); j++ ) {
+				assertEquals(
+					(i+1)*2.0, M2.get(i, j),
+					msg("(%d,%d)", "scaleInPlace", i, j)
+				);
+			}
+		}
+
+		MLMatrix M3 = M.scaleInPlace(M);
+		assertSame(M, M3);
+		for( int i = 0; i < M.rows(); i++ ) {
+			for( int j = 0; j < M.columns(); j++ ) {
+				assertEquals(
+					((i+1)*2.0)*((i+1)*2.0), M.get(i, j),
+					msg("(%d,%d)", "addInPlace", i, j)
+				);
+			}
+		}
+	}
+
+	private String msg( String msg, String methodName, Object... args ) {
+		String testName = this.info.getTestMethod().get().getName();
+		String className = MatrixFactory.matrixType.getSimpleName();
+		return String.format("[" + testName + "(" + className + ") " + methodName + "()] " + msg, args);
+	}
+
+	//@ParameterizedTest
+	//@ValueSource( classes = {MatrixFactory.ColtMatrix.class, DoubleMatrix.class} )
+	void speed( Class<? extends MLMatrix> mType ) {
+		MatrixFactory.matrixType = mType;
+
+		int N = 10;
+		int rows  = 1000;
+		int cols  = 1000;
+
+		Timer timer = new Timer();
+
+		MLMatrix M = MatrixFactory.create(rows, cols);
+		timer.start();
+		for( int i = 0; i < N; i++ ) {
+			M.initializeRandom();
+		}
+		timer.stop();
+		System.err.println(msg("%d iterations: %d ms", "initializeRandom", N, timer.getMillis()));
+
+		timer.reset();
+
+		MLMatrix B = MatrixFactory.create(rows*2, M.columns());
+		B.initializeRandom();
+
+		timer.start();
+		for( int i = 0; i < N; i++ ) {
+			M.multiplyTransposed(B);
+		}
+		timer.stop();
+		System.err.println(msg("%d iterations: %d ms", "multiplyTransposed", N, timer.getMillis()));
+	}
+
+}

src/test/java/schule/ngb/zm/ml/MatrixTest.java

@@ -1,57 +0,0 @@
-package schule.ngb.zm.ml;
-
-import org.junit.jupiter.api.Test;
-
-import java.util.Arrays;
-
-import static org.junit.jupiter.api.Assertions.*;
-
-class MatrixTest {
-
-	@Test
-	void initializeIdentity() {
-		Matrix m = new Matrix(4, 4);
-		m.initializeIdentity();
-
-		assertArrayEquals(new double[]{1.0, 0.0, 0.0, 0.0}, m.coefficients[0]);
-		assertArrayEquals(new double[]{0.0, 1.0, 0.0, 0.0}, m.coefficients[1]);
-		assertArrayEquals(new double[]{0.0, 0.0, 1.0, 0.0}, m.coefficients[2]);
-		assertArrayEquals(new double[]{0.0, 0.0, 0.0, 1.0}, m.coefficients[3]);
-	}
-
-	@Test
-	void initializeOne() {
-		Matrix m = new Matrix(4, 4);
-		m.initializeOne();
-
-		double[] ones = new double[]{1.0, 1.0, 1.0, 1.0};
-		assertArrayEquals(ones, m.coefficients[0]);
-		assertArrayEquals(ones, m.coefficients[1]);
-		assertArrayEquals(ones, m.coefficients[2]);
-		assertArrayEquals(ones, m.coefficients[3]);
-	}
-
-	@Test
-	void initializeZero() {
-		Matrix m = new Matrix(4, 4);
-		m.initializeZero();
-
-		double[] zeros = new double[]{0.0, 0.0, 0.0, 0.0};
-		assertArrayEquals(zeros, m.coefficients[0]);
-		assertArrayEquals(zeros, m.coefficients[1]);
-		assertArrayEquals(zeros, m.coefficients[2]);
-		assertArrayEquals(zeros, m.coefficients[3]);
-	}
-
-	@Test
-	void initializeRandom() {
-		Matrix m = new Matrix(4, 4);
-		m.initializeRandom(-1, 1);
-
-		assertTrue(Arrays.stream(m.coefficients[0]).allMatch((d) -> -1.0 <= d && d < 1.0));
-		assertTrue(Arrays.stream(m.coefficients[1]).allMatch((d) -> -1.0 <= d && d < 1.0));
-		assertTrue(Arrays.stream(m.coefficients[2]).allMatch((d) -> -1.0 <= d && d < 1.0));
-		assertTrue(Arrays.stream(m.coefficients[3]).allMatch((d) -> -1.0 <= d && d < 1.0));
-	}
-
-}

src/test/java/schule/ngb/zm/ml/NeuralNetworkTest.java

@@ -2,15 +2,14 @@ package schule.ngb.zm.ml;
 
 import org.junit.jupiter.api.BeforeAll;
 import org.junit.jupiter.api.Test;
+import schule.ngb.zm.Constants;
 import schule.ngb.zm.util.Log;
+import schule.ngb.zm.util.Timer;
 
-import java.io.File;
 import java.util.ArrayList;
 import java.util.List;
 import java.util.Random;
 
-import static org.junit.jupiter.api.Assertions.*;
-
 class NeuralNetworkTest {
 
 	@BeforeAll
@@ -18,7 +17,14 @@ class NeuralNetworkTest {
 		Log.enableGlobalDebugging();
 	}
 
-	@Test
+	@BeforeAll
+	static void setupMatrixLibrary() {
+		Constants.setSeed(1001);
+		//MatrixFactory.matrixType = MatrixFactory.ColtMatrix.class;
+		MatrixFactory.matrixType = DoubleMatrix.class;
+	}
+
+	/*@Test
 	void readWrite() {
 		// XOR Dataset
 		NeuralNetwork net = new NeuralNetwork(2, 4, 1);
@@ -53,7 +59,7 @@ class NeuralNetworkTest {
 		}
 
 		assertArrayEquals(net.predict(inputs), net2.predict(inputs));
-	}
+	}*/
 
 	@Test
 	void learnXor() {
@@ -78,14 +84,14 @@ class NeuralNetworkTest {
 		}
 
 		// calculate predictions
-		double[][] predictions = net.predict(inputs);
+		MLMatrix predictions = net.predict(inputs);
 		for( int i = 0; i < 4; i++ ) {
-			int parsed_pred = predictions[i][0] < 0.5 ? 0 : 1;
+			int parsed_pred = predictions.get(i, 0) < 0.5 ? 0 : 1;
 
 			System.out.printf(
 				"{%.0f, %.0f} = %.4f (%d) -> %s\n",
 				inputs[i][0], inputs[i][1],
-				predictions[i][0],
+				predictions.get(i, 0),
 				parsed_pred,
 				parsed_pred == outputs[i][0] ? "correct" : "miss"
 			);
@@ -109,12 +115,16 @@ class NeuralNetworkTest {
 		for( int i = 0; i < trainingData.size(); i++ ) {
 			inputs[i][0] = trainingData.get(i).a;
 			inputs[i][1] = trainingData.get(i).b;
-			outputs[i][0] = trainingData.get(i).result;
+			outputs[i][0] = trainingData.get(i).getResult();
 		}
 
+		Timer timer = new Timer();
+
 		System.out.println("Training the neural net to learn "+OPERATION+"...");
+		timer.start();
 		net.train(inputs, outputs, TRAINING_CYCLES);
-		System.out.println("    finished training");
+		timer.stop();
+		System.out.println("    finished training (" + timer.getMillis() + "ms)");
 
 		for( int i = 1; i <= net.getLayerCount(); i++ ) {
 			System.out.println("Layer " +i + " weights");
@@ -136,19 +146,18 @@ class NeuralNetworkTest {
 		System.out.printf(
 			"Prediction on data (%.2f, %.2f) was %.4f, expected %.2f (of by %.4f)\n",
 			data.a, data.b,
-			net.getOutput()[0][0],
-			data.result,
-			net.getOutput()[0][0] - data.result
+			net.getOutput().get(0, 0),
+			data.getResult(),
+			net.getOutput().get(0, 0) - data.getResult()
 		);
 	}
 
 	private List<TestData> createTrainingSet( int trainingSetSize, CalcType operation ) {
-		Random random = new Random();
 		List<TestData> tuples = new ArrayList<>();
 
 		for( int i = 0; i < trainingSetSize; i++ ) {
-			double s1 = random.nextDouble() * 0.5;
-			double s2 = random.nextDouble() * 0.5;
+			double s1 = Constants.random() * 0.5;
+			double s2 = Constants.random() * 0.5;
 
 			switch( operation ) {
 				case ADD:
@@ -181,7 +190,6 @@ class NeuralNetworkTest {
 
 		double a;
 		double b;
-		double result;
 		CalcType type;
 
 		TestData( double a, double b ) {
@@ -189,6 +197,8 @@ class NeuralNetworkTest {
 			this.b = b;
 		}
 
+		abstract double getResult();
+
 	}
 
 	private static final class AddData extends TestData {
@@ -197,7 +207,9 @@ class NeuralNetworkTest {
 
 		public AddData( double a, double b ) {
 			super(a, b);
-			result = a + b;
+		}
+		double getResult() {
+			return a+b;
 		}
 
 	}
@@ -208,7 +220,9 @@ class NeuralNetworkTest {
 
 		public SubData( double a, double b ) {
 			super(a, b);
-			result = a - b;
+		}
+		double getResult() {
+			return a-b;
 		}
 
 	}
@@ -219,7 +233,9 @@ class NeuralNetworkTest {
 
 		public MulData( double a, double b ) {
 			super(a, b);
-			result = a * b;
+		}
+		double getResult() {
+			return a*b;
 		}
 
 	}
@@ -233,7 +249,9 @@ class NeuralNetworkTest {
 			if( b == 0.0 ) {
 				b = .1;
 			}
-			result = a / b;
+		}
+		double getResult() {
+			return a/b;
 		}
 
 	}
@@ -244,7 +262,12 @@ class NeuralNetworkTest {
 
 		public ModData( double b, double a ) {
 			super(b, a);
-			result = a % b;
+			if( b == 0.0 ) {
+				b = .1;
+			}
+		}
+		double getResult() {
+			return a%b;
 		}
 
 	}