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

  public List<CategoricalDistribution> forwardBackward(
      List<List<AssignmentProposition>> ev, CategoricalDistribution prior) {
    // local variables: fv, a vector of forward messages for steps 0,...,t
    List<Matrix> fv = new ArrayList<Matrix>(ev.size() + 1);
    // b, a representation of the backward message, initially all 1s
    Matrix b = hmm.createUnitMessage();
    // sv, a vector of smoothed estimates for steps 1,...,t
    List<Matrix> sv = new ArrayList<Matrix>(ev.size());


    // fv[0] <- prior
    fv.add(hmm.convert(prior));

View Full Code Here

  public Matrix getEvidence(List<AssignmentProposition> evidence) {
    if (evidence.size() != 1) {
      throw new IllegalArgumentException(
          "Only a single evidence observation value should be provided.");
    }
    Matrix e = sensorModel.get(evidence.get(0).getValue());
    if (null == e) {
      throw new IllegalArgumentException(
          "Evidence does not map to sensor model.");
    }
    return e;

View Full Code Here


  @Override
  public Matrix createUnitMessage() {
    double[] values = new double[stateVariableDomain.size()];
    Arrays.fill(values, 1.0);
    return new Matrix(values, values.length);
  }

View Full Code Here

  }


  @Override
  public Matrix convert(CategoricalDistribution fromCD) {
    double[] values = fromCD.getValues();
    return new Matrix(values, values.length);
  }

View Full Code Here

  }


  @Override
  public Matrix normalize(Matrix m) {
    double[] values = m.getRowPackedCopy();
    return new Matrix(Util.normalize(values), values.length);
  }

View Full Code Here

  // START-ForwardBackwardInference
  @Override
  public List<CategoricalDistribution> forwardBackward(
      List<List<AssignmentProposition>> ev, CategoricalDistribution prior) {
    // local variables: f, the forward message <- prior
    Matrix f = hmm.convert(prior);
    // b, a representation of the backward message, initially all 1s
    Matrix b = hmm.createUnitMessage();
    // sv, a vector of smoothed estimates for steps 1,...,t
    List<Matrix> sv = new ArrayList<Matrix>(ev.size());


    // for i = 1 to t do
    for (int i = 0; i < ev.size(); i++) {
      // fv[i] <- FORWARD(fv[i-1], ev[i])
      f = forward(f, hmm.getEvidence(ev.get(i)));
    }
    // for i = t downto 1 do
    for (int i = ev.size() - 1; i >= 0; i--) {
      // sv[i] <- NORMALIZE(fv[i] * b)
      sv.add(0, hmm.normalize(f.arrayTimes(b)));
      Matrix e = hmm.getEvidence(ev.get(i));
      // b <- BACKWARD(b, ev[i])
      b = backward(b, e);
      // f1:t <-
      // NORMALIZE((T<sup>T<sup>)<sup>-1</sup>O<sup>-1</sup><sub>t+1</sub>f<sub>1:t+1</sub>)
      f = forwardRecover(e, f);

View Full Code Here

   */
  public CategoricalDistribution fixedLagSmoothing(
      List<AssignmentProposition> et) {
    // local variables: <b>O</b><sub>t-d</sub>, <b>O</b><sub>t</sub>,
    // diagonal matrices containing the sensor model information
    Matrix O_tmd, O_t;


    // add e<sub>t</sub> to the end of e<sub>t-d:t</sub>
    e_tmd_to_t.add(hmm.getEvidence(et));
    // <b>O</b><sub>t</sub> <- diagonal matrix containing
    // <b>P</b>(e<sub>t</sub> | X<sub>t</sub>)
    O_t = e_tmd_to_t.get(e_tmd_to_t.size() - 1);
    // if t > d then
    if (t > d) {
      // remove e<sub>t-d-1</sub> from the beginning of e<sub>t-d:t</sub>
      e_tmd_to_t.remove(0);
      // <b>O</b><sub>t-d</sub> <- diagonal matrix containing
      // <b>P</b>(e<sub>t-d</sub> | X<sub>t-d</sub>)
      O_tmd = e_tmd_to_t.get(0);
      // <b>f</b> <- FORWARD(<b>f</b>, e<sub>t-d</sub>)
      f = forward(f, O_tmd);
      // <b>B</b> <-
      // <b>O</b><sup>-1</sup><sub>t-d</sub><b>B</b><b>T</b><b>O</b><sub>t</sub>
      B = O_tmd.inverse().times(hmm.getTransitionModel().inverse())
          .times(B).times(hmm.getTransitionModel()).times(O_t);
    } else {
      // else <b>B</b> <- <b>BTO</b><sub>t</sub>
      B = B.times(hmm.getTransitionModel()).times(O_t);
    }

View Full Code Here

 * 
 */
public class HMMExampleFactory {


  public static HiddenMarkovModel getUmbrellaWorldModel() {
    Matrix transitionModel = new Matrix(new double[][] { { 0.7, 0.3 },
        { 0.3, 0.7 } });
    Map<Object, Matrix> sensorModel = new HashMap<Object, Matrix>();
    sensorModel.put(Boolean.TRUE, new Matrix(new double[][] { { 0.9, 0.0 },
        { 0.0, 0.2 } }));
    sensorModel.put(Boolean.FALSE, new Matrix(new double[][] {
        { 0.1, 0.0 }, { 0.0, 0.8 } }));
    Matrix prior = new Matrix(new double[] { 0.5, 0.5 }, 2);
    return new HMM(ExampleRV.RAIN_t_RV, transitionModel, sensorModel, prior);
  }

View Full Code Here

    lastInput = input;
    return layer.feedForward(input);
  }


  public void processError(Vector error) {
    Matrix weightUpdate = error.times(lastInput.transpose());
    layer.acceptNewWeightUpdate(weightUpdate);


    Vector biasUpdate = layer.getBiasVector().plus(error);
    layer.acceptNewBiasUpdate(biasUpdate);

View Full Code Here


  public Layer(Matrix weightMatrix, Vector biasVector, ActivationFunction af) {


    activationFunction = af;
    this.weightMatrix = weightMatrix;
    lastWeightUpdateMatrix = new Matrix(weightMatrix.getRowDimension(),
        weightMatrix.getColumnDimension());
    penultimateWeightUpdateMatrix = new Matrix(
        weightMatrix.getRowDimension(),
        weightMatrix.getColumnDimension());


    this.biasVector = biasVector;
    lastBiasUpdateVector = new Vector(biasVector.getRowDimension());

View Full Code Here

0 1 2 3 4

TOP

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

All source code are property of their respective owners. Java is a trademark of Sun Microsystems, Inc and owned by ORACLE Inc. Contact coftware#gmail.com.