Examples of aima.core.util.math.Matrix

aima.core.util.math.Matrix
Jama = Java Matrix class.
The Java Matrix Class provides the fundamental operations of numerical linear algebra. Various constructors create Matrices from two dimensional arrays of double precision floating point numbers. Various "gets" and "sets" provide access to submatrices and matrix elements. Several methods implement basic matrix arithmetic, including matrix addition and multiplication, matrix norms, and element-by-element array operations. Methods for reading and printing matrices are also included. All the operations in this version of the Matrix Class involve real matrices. Complex matrices may be handled in a future version.
Five fundamental matrix decompositions, which consist of pairs or triples of matrices, permutation vectors, and the like, produce results in five decomposition classes. These decompositions are accessed by the Matrix class to compute solutions of simultaneous linear equations, determinants, inverses and other matrix functions. The five decompositions are:
- Cholesky Decomposition of symmetric, positive definite matrices.
- LU Decomposition of rectangular matrices.
- QR Decomposition of rectangular matrices.
- Singular Value Decomposition of rectangular matrices.
- Eigenvalue Decomposition of both symmetric and nonsymmetric square matrices.
Example of use:
Solve a linear system A x = b and compute the residual norm, ||b - A x||.
```
 double[][] vals = { { 1., 2., 3 }, { 4., 5., 6. }, { 7., 8., 10. } }; Matrix A = new Matrix(vals); Matrix b = Matrix.random(3, 1); Matrix x = A.solve(b); Matrix r = A.times(x).minus(b); double rnorm = r.normInf(); 
```
@author The MathWorks, Inc. and the National Institute of Standards andTechnology. @version 5 August 1998


  @Test
  public void testFeedForward() {
    // example 11.14 of Neural Network Design by Hagan, Demuth and Beale
    // lots of tedious tests necessary to ensure nn is fundamentally correct
    Matrix weightMatrix1 = new Matrix(2, 1);
    weightMatrix1.set(0, 0, -0.27);
    weightMatrix1.set(1, 0, -0.41);


    Vector biasVector1 = new Vector(2);
    biasVector1.setValue(0, -0.48);
    biasVector1.setValue(1, -0.13);


    Layer layer1 = new Layer(weightMatrix1, biasVector1,
        new LogSigActivationFunction());


    Vector inputVector1 = new Vector(1);
    inputVector1.setValue(0, 1);


    Vector expected = new Vector(2);
    expected.setValue(0, 0.321);
    expected.setValue(1, 0.368);


    Vector result1 = layer1.feedForward(inputVector1);
    Assert.assertEquals(expected.getValue(0), result1.getValue(0), 0.001);
    Assert.assertEquals(expected.getValue(1), result1.getValue(1), 0.001);


    Matrix weightMatrix2 = new Matrix(1, 2);
    weightMatrix2.set(0, 0, 0.09);
    weightMatrix2.set(0, 1, -0.17);


    Vector biasVector2 = new Vector(1);
    biasVector2.setValue(0, 0.48);


    Layer layer2 = new Layer(weightMatrix2, biasVector2,

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    Assert.assertEquals(0.446, result2.getValue(0), 0.001);
  }


  @Test
  public void testSensitivityMatrixCalculationFromErrorVector() {
    Matrix weightMatrix1 = new Matrix(2, 1);
    weightMatrix1.set(0, 0, -0.27);
    weightMatrix1.set(1, 0, -0.41);


    Vector biasVector1 = new Vector(2);
    biasVector1.setValue(0, -0.48);
    biasVector1.setValue(1, -0.13);


    Layer layer1 = new Layer(weightMatrix1, biasVector1,
        new LogSigActivationFunction());


    Vector inputVector1 = new Vector(1);
    inputVector1.setValue(0, 1);


    layer1.feedForward(inputVector1);


    Matrix weightMatrix2 = new Matrix(1, 2);
    weightMatrix2.set(0, 0, 0.09);
    weightMatrix2.set(0, 1, -0.17);


    Vector biasVector2 = new Vector(1);
    biasVector2.setValue(0, 0.48);


    Layer layer2 = new Layer(weightMatrix2, biasVector2,
        new PureLinearActivationFunction());
    Vector inputVector2 = layer1.getLastActivationValues();
    layer2.feedForward(inputVector2);


    Vector errorVector = new Vector(1);
    errorVector.setValue(0, 1.261);
    LayerSensitivity layer2Sensitivity = new LayerSensitivity(layer2);
    layer2Sensitivity.sensitivityMatrixFromErrorMatrix(errorVector);


    Matrix sensitivityMatrix = layer2Sensitivity.getSensitivityMatrix();
    Assert.assertEquals(-2.522, sensitivityMatrix.get(0, 0), 0.0001);
  }

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    Assert.assertEquals(-2.522, sensitivityMatrix.get(0, 0), 0.0001);
  }


  @Test
  public void testSensitivityMatrixCalculationFromSucceedingLayer() {
    Matrix weightMatrix1 = new Matrix(2, 1);
    weightMatrix1.set(0, 0, -0.27);
    weightMatrix1.set(1, 0, -0.41);


    Vector biasVector1 = new Vector(2);
    biasVector1.setValue(0, -0.48);
    biasVector1.setValue(1, -0.13);


    Layer layer1 = new Layer(weightMatrix1, biasVector1,
        new LogSigActivationFunction());
    LayerSensitivity layer1Sensitivity = new LayerSensitivity(layer1);


    Vector inputVector1 = new Vector(1);
    inputVector1.setValue(0, 1);


    layer1.feedForward(inputVector1);


    Matrix weightMatrix2 = new Matrix(1, 2);
    weightMatrix2.set(0, 0, 0.09);
    weightMatrix2.set(0, 1, -0.17);


    Vector biasVector2 = new Vector(1);
    biasVector2.setValue(0, 0.48);


    Layer layer2 = new Layer(weightMatrix2, biasVector2,
        new PureLinearActivationFunction());
    Vector inputVector2 = layer1.getLastActivationValues();
    layer2.feedForward(inputVector2);


    Vector errorVector = new Vector(1);
    errorVector.setValue(0, 1.261);
    LayerSensitivity layer2Sensitivity = new LayerSensitivity(layer2);
    layer2Sensitivity.sensitivityMatrixFromErrorMatrix(errorVector);


    layer1Sensitivity
        .sensitivityMatrixFromSucceedingLayer(layer2Sensitivity);
    Matrix sensitivityMatrix = layer1Sensitivity.getSensitivityMatrix();


    Assert.assertEquals(2, sensitivityMatrix.getRowDimension());
    Assert.assertEquals(1, sensitivityMatrix.getColumnDimension());
    Assert.assertEquals(-0.0495, sensitivityMatrix.get(0, 0), 0.001);
    Assert.assertEquals(0.0997, sensitivityMatrix.get(1, 0), 0.001);
  }

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    Assert.assertEquals(0.0997, sensitivityMatrix.get(1, 0), 0.001);
  }


  @Test
  public void testWeightUpdateMatrixesFormedCorrectly() {
    Matrix weightMatrix1 = new Matrix(2, 1);
    weightMatrix1.set(0, 0, -0.27);
    weightMatrix1.set(1, 0, -0.41);


    Vector biasVector1 = new Vector(2);
    biasVector1.setValue(0, -0.48);
    biasVector1.setValue(1, -0.13);


    Layer layer1 = new Layer(weightMatrix1, biasVector1,
        new LogSigActivationFunction());
    LayerSensitivity layer1Sensitivity = new LayerSensitivity(layer1);


    Vector inputVector1 = new Vector(1);
    inputVector1.setValue(0, 1);


    layer1.feedForward(inputVector1);


    Matrix weightMatrix2 = new Matrix(1, 2);
    weightMatrix2.set(0, 0, 0.09);
    weightMatrix2.set(0, 1, -0.17);


    Vector biasVector2 = new Vector(1);
    biasVector2.setValue(0, 0.48);


    Layer layer2 = new Layer(weightMatrix2, biasVector2,
        new PureLinearActivationFunction());
    Vector inputVector2 = layer1.getLastActivationValues();
    layer2.feedForward(inputVector2);


    Vector errorVector = new Vector(1);
    errorVector.setValue(0, 1.261);
    LayerSensitivity layer2Sensitivity = new LayerSensitivity(layer2);
    layer2Sensitivity.sensitivityMatrixFromErrorMatrix(errorVector);


    layer1Sensitivity
        .sensitivityMatrixFromSucceedingLayer(layer2Sensitivity);


    Matrix weightUpdateMatrix2 = BackPropLearning.calculateWeightUpdates(
        layer2Sensitivity, layer1.getLastActivationValues(), 0.1);
    Assert.assertEquals(0.0809, weightUpdateMatrix2.get(0, 0), 0.001);
    Assert.assertEquals(0.0928, weightUpdateMatrix2.get(0, 1), 0.001);


    Matrix lastWeightUpdateMatrix2 = layer2.getLastWeightUpdateMatrix();
    Assert.assertEquals(0.0809, lastWeightUpdateMatrix2.get(0, 0), 0.001);
    Assert.assertEquals(0.0928, lastWeightUpdateMatrix2.get(0, 1), 0.001);


    Matrix penultimateWeightUpdatematrix2 = layer2
        .getPenultimateWeightUpdateMatrix();
    Assert.assertEquals(0.0, penultimateWeightUpdatematrix2.get(0, 0),
        0.001);
    Assert.assertEquals(0.0, penultimateWeightUpdatematrix2.get(0, 1),
        0.001);


    Matrix weightUpdateMatrix1 = BackPropLearning.calculateWeightUpdates(
        layer1Sensitivity, inputVector1, 0.1);
    Assert.assertEquals(0.0049, weightUpdateMatrix1.get(0, 0), 0.001);
    Assert.assertEquals(-0.00997, weightUpdateMatrix1.get(1, 0), 0.001);


    Matrix lastWeightUpdateMatrix1 = layer1.getLastWeightUpdateMatrix();
    Assert.assertEquals(0.0049, lastWeightUpdateMatrix1.get(0, 0), 0.001);
    Assert.assertEquals(-0.00997, lastWeightUpdateMatrix1.get(1, 0), 0.001);
    Matrix penultimateWeightUpdatematrix1 = layer1
        .getPenultimateWeightUpdateMatrix();
    Assert.assertEquals(0.0, penultimateWeightUpdatematrix1.get(0, 0),
        0.001);
    Assert.assertEquals(0.0, penultimateWeightUpdatematrix1.get(1, 0),
        0.001);
  }

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        0.001);
  }


  @Test
  public void testBiasUpdateMatrixesFormedCorrectly() {
    Matrix weightMatrix1 = new Matrix(2, 1);
    weightMatrix1.set(0, 0, -0.27);
    weightMatrix1.set(1, 0, -0.41);


    Vector biasVector1 = new Vector(2);
    biasVector1.setValue(0, -0.48);
    biasVector1.setValue(1, -0.13);


    Layer layer1 = new Layer(weightMatrix1, biasVector1,
        new LogSigActivationFunction());
    LayerSensitivity layer1Sensitivity = new LayerSensitivity(layer1);


    Vector inputVector1 = new Vector(1);
    inputVector1.setValue(0, 1);


    layer1.feedForward(inputVector1);


    Matrix weightMatrix2 = new Matrix(1, 2);
    weightMatrix2.set(0, 0, 0.09);
    weightMatrix2.set(0, 1, -0.17);


    Vector biasVector2 = new Vector(1);
    biasVector2.setValue(0, 0.48);


    Layer layer2 = new Layer(weightMatrix2, biasVector2,

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        0.001);
  }


  @Test
  public void testWeightsAndBiasesUpdatedCorrectly() {
    Matrix weightMatrix1 = new Matrix(2, 1);
    weightMatrix1.set(0, 0, -0.27);
    weightMatrix1.set(1, 0, -0.41);


    Vector biasVector1 = new Vector(2);
    biasVector1.setValue(0, -0.48);
    biasVector1.setValue(1, -0.13);


    Layer layer1 = new Layer(weightMatrix1, biasVector1,
        new LogSigActivationFunction());
    LayerSensitivity layer1Sensitivity = new LayerSensitivity(layer1);


    Vector inputVector1 = new Vector(1);
    inputVector1.setValue(0, 1);


    layer1.feedForward(inputVector1);


    Matrix weightMatrix2 = new Matrix(1, 2);
    weightMatrix2.set(0, 0, 0.09);
    weightMatrix2.set(0, 1, -0.17);


    Vector biasVector2 = new Vector(1);
    biasVector2.setValue(0, 0.48);


    Layer layer2 = new Layer(weightMatrix2, biasVector2,
        new PureLinearActivationFunction());
    Vector inputVector2 = layer1.getLastActivationValues();
    layer2.feedForward(inputVector2);


    Vector errorVector = new Vector(1);
    errorVector.setValue(0, 1.261);
    LayerSensitivity layer2Sensitivity = new LayerSensitivity(layer2);
    layer2Sensitivity.sensitivityMatrixFromErrorMatrix(errorVector);


    layer1Sensitivity
        .sensitivityMatrixFromSucceedingLayer(layer2Sensitivity);


    BackPropLearning.calculateWeightUpdates(layer2Sensitivity,
        layer1.getLastActivationValues(), 0.1);


    BackPropLearning.calculateBiasUpdates(layer2Sensitivity, 0.1);


    BackPropLearning.calculateWeightUpdates(layer1Sensitivity,
        inputVector1, 0.1);


    BackPropLearning.calculateBiasUpdates(layer1Sensitivity, 0.1);


    layer2.updateWeights();
    Matrix newWeightMatrix2 = layer2.getWeightMatrix();
    Assert.assertEquals(0.171, newWeightMatrix2.get(0, 0), 0.001);
    Assert.assertEquals(-0.0772, newWeightMatrix2.get(0, 1), 0.001);


    layer2.updateBiases();
    Vector newBiasVector2 = layer2.getBiasVector();
    Assert.assertEquals(0.7322, newBiasVector2.getValue(0), 0.00001);


    layer1.updateWeights();
    Matrix newWeightMatrix1 = layer1.getWeightMatrix();


    Assert.assertEquals(-0.265, newWeightMatrix1.get(0, 0), 0.001);
    Assert.assertEquals(-0.419, newWeightMatrix1.get(1, 0), 0.001);


    layer1.updateBiases();
    Vector newBiasVector1 = layer1.getBiasVector();


    Assert.assertEquals(-0.475, newBiasVector1.getValue(0), 0.001);

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  private Matrix sensitivityMatrix;
  private final Layer layer;


  public LayerSensitivity(Layer layer) {
    Matrix weightMatrix = layer.getWeightMatrix();
    this.sensitivityMatrix = new Matrix(weightMatrix.getRowDimension(),
        weightMatrix.getColumnDimension());
    this.layer = layer;


  }

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  public Matrix getSensitivityMatrix() {
    return sensitivityMatrix;
  }


  public Matrix sensitivityMatrixFromErrorMatrix(Vector errorVector) {
    Matrix derivativeMatrix = createDerivativeMatrix(layer
        .getLastInducedField());
    Matrix calculatedSensitivityMatrix = derivativeMatrix
        .times(errorVector).times(-2.0);
    sensitivityMatrix = calculatedSensitivityMatrix.copy();
    return calculatedSensitivityMatrix;
  }

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  }


  public Matrix sensitivityMatrixFromSucceedingLayer(
      LayerSensitivity nextLayerSensitivity) {
    Layer nextLayer = nextLayerSensitivity.getLayer();
    Matrix derivativeMatrix = createDerivativeMatrix(layer
        .getLastInducedField());
    Matrix weightTranspose = nextLayer.getWeightMatrix().transpose();
    Matrix calculatedSensitivityMatrix = derivativeMatrix.times(
        weightTranspose).times(
        nextLayerSensitivity.getSensitivityMatrix());
    sensitivityMatrix = calculatedSensitivityMatrix.copy();
    return sensitivityMatrix;
  }

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public class BackPropagationTests {


  @Test
  public void testFeedForwardAndBAckLoopWorks() {
    // example 11.14 of Neural Network Design by Hagan, Demuth and Beale
    Matrix hiddenLayerWeightMatrix = new Matrix(2, 1);
    hiddenLayerWeightMatrix.set(0, 0, -0.27);
    hiddenLayerWeightMatrix.set(1, 0, -0.41);


    Vector hiddenLayerBiasVector = new Vector(2);
    hiddenLayerBiasVector.setValue(0, -0.48);
    hiddenLayerBiasVector.setValue(1, -0.13);


    Vector input = new Vector(1);
    input.setValue(0, 1);


    Matrix outputLayerWeightMatrix = new Matrix(1, 2);
    outputLayerWeightMatrix.set(0, 0, 0.09);
    outputLayerWeightMatrix.set(0, 1, -0.17);


    Vector outputLayerBiasVector = new Vector(1);
    outputLayerBiasVector.setValue(0, 0.48);


    Vector error = new Vector(1);
    error.setValue(0, 1.261);


    double learningRate = 0.1;
    double momentumFactor = 0.0;
    FeedForwardNeuralNetwork ffnn = new FeedForwardNeuralNetwork(
        hiddenLayerWeightMatrix, hiddenLayerBiasVector,
        outputLayerWeightMatrix, outputLayerBiasVector);
    ffnn.setTrainingScheme(new BackPropLearning(learningRate,
        momentumFactor));
    ffnn.processInput(input);
    ffnn.processError(error);


    Matrix finalHiddenLayerWeights = ffnn.getHiddenLayerWeights();
    Assert.assertEquals(-0.265, finalHiddenLayerWeights.get(0, 0), 0.001);
    Assert.assertEquals(-0.419, finalHiddenLayerWeights.get(1, 0), 0.001);


    Vector hiddenLayerBias = ffnn.getHiddenLayerBias();
    Assert.assertEquals(-0.475, hiddenLayerBias.getValue(0), 0.001);
    Assert.assertEquals(-0.1399, hiddenLayerBias.getValue(1), 0.001);


    Matrix finalOutputLayerWeights = ffnn.getOutputLayerWeights();
    Assert.assertEquals(0.171, finalOutputLayerWeights.get(0, 0), 0.001);
    Assert.assertEquals(-0.0772, finalOutputLayerWeights.get(0, 1), 0.001);


    Vector outputLayerBias = ffnn.getOutputLayerBias();
    Assert.assertEquals(0.7322, outputLayerBias.getValue(0), 0.001);
  }

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Related Classes of aima.core.util.math.Matrix

aima.core.learning.neural.BackPropLearning

aima.core.learning.neural.Layer

aima.core.learning.neural.LayerSensitivity

aima.core.learning.neural.Perceptron

aima.core.probability.example.HMMExampleFactory

aima.core.probability.hmm.exact.FixedLagSmoothing

aima.core.probability.hmm.exact.HMMForwardBackward

aima.core.probability.hmm.exact.HMMForwardBackwardConstantSpace

aima.core.probability.hmm.FixedLagSmoothing

aima.core.probability.hmm.HiddenMarkovModel

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