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 testFeedForwardAndBAckLoopWorksWithMomentum() {
    // 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 = 0.5;
    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(-0.2675, finalHiddenLayerWeights.get(0, 0), 0.001);
    Assert.assertEquals(-0.4149, finalHiddenLayerWeights.get(1, 0), 0.001);


    Vector hiddenLayerBias = ffnn.getHiddenLayerBias();
    Assert.assertEquals(-0.4775, hiddenLayerBias.getValue(0), 0.001);
    Assert.assertEquals(-0.1349, hiddenLayerBias.getValue(1), 0.001);


    Matrix finalOutputLayerWeights = ffnn.getOutputLayerWeights();
    Assert.assertEquals(0.1304, finalOutputLayerWeights.get(0, 0), 0.001);
    Assert.assertEquals(-0.1235, finalOutputLayerWeights.get(0, 1), 0.001);


    Vector outputLayerBias = ffnn.getOutputLayerBias();
    Assert.assertEquals(0.6061, outputLayerBias.getValue(0), 0.001);
  }

Examples of aima.core.util.math.Matrix

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