/** {@inheritDoc} */
 public double[] gradient(double x, double[] parameters) {
   final double a = parameters[0];
   final double omega = parameters[1];
   final double phi = parameters[2];
   final double alpha = omega * x + phi;
   final double cosAlpha = FastMath.cos(alpha);
   final double sinAlpha = FastMath.sin(alpha);
   return new double[] {cosAlpha, -a * x * sinAlpha, -a * sinAlpha};
 }
 /**
  * Calculates the Nth generalized harmonic number. See <a
  * href="http://mathworld.wolfram.com/HarmonicSeries.html">Harmonic Series</a>.
  *
  * @param n the term in the series to calculate (must be &ge; 1)
  * @param m the exponent; special case m == 1.0 is the harmonic series
  * @return the nth generalized harmonic number
  */
 private double generalizedHarmonic(final int n, final double m) {
   double value = 0;
   for (int k = n; k > 0; --k) {
     value += 1.0 / FastMath.pow(k, m);
   }
   return value;
 }
  public static NullStates getNullState(Context context) {
    final VehicleState state = context.getState();
    // final Observation obs = context.getObservation();
    final BlockStateObservation blockStateObs = state.getBlockStateObservation();
    EVehiclePhase phase = state.getJourneyState().getPhase();

    if (blockStateObs == null) {
      return NullStates.NULL_STATE;
    } else {

      final boolean hasScheduledTime =
          FastMath.abs(state.getBlockStateObservation().getScheduleDeviation()) > 0d;

      if (!hasScheduledTime) {
        return NullStates.NULL_STATE;
      }

      if (!state.getBlockStateObservation().isSnapped()
          && ((EVehiclePhase.DEADHEAD_AFTER == phase
                  && state.getBlockStateObservation().getScheduleDeviation() == 0d)
              || EVehiclePhase.AT_BASE == phase
              || (EVehiclePhase.DEADHEAD_BEFORE == phase
                  && state.getBlockStateObservation().getScheduleDeviation() == 0d)
              || (EVehiclePhase.LAYOVER_BEFORE == phase)
                  && state.getBlockStateObservation().getScheduleDeviation() == 0d)) {
        return NullStates.NULL_STATE;
      }

      return NullStates.NON_NULL_STATE;
    }
  }
  /**
   * The probability mass function P(X = x) for a Zipf distribution.
   *
   * @param x the value at which the probability density function is evaluated.
   * @return the value of the probability mass function at x
   */
  public double probability(final int x) {
    if (x <= 0 || x > numberOfElements) {
      return 0.0;
    }

    return (1.0 / FastMath.pow(x, exponent)) / generalizedHarmonic(numberOfElements, exponent);
  }
Example #5
0
  /**
   * Get a vector orthogonal to the instance.
   *
   * <p>There are an infinite number of normalized vectors orthogonal to the instance. This method
   * picks up one of them almost arbitrarily. It is useful when one needs to compute a reference
   * frame with one of the axes in a predefined direction. The following example shows how to build
   * a frame having the k axis aligned with the known vector u :
   *
   * <pre><code>
   *   Vector3D k = u.normalize();
   *   Vector3D i = k.orthogonal();
   *   Vector3D j = Vector3D.crossProduct(k, i);
   * </code></pre>
   *
   * @return a new normalized vector orthogonal to the instance
   * @exception ArithmeticException if the norm of the instance is null
   */
  public Vector3D orthogonal() {

    double threshold = 0.6 * getNorm();
    if (threshold == 0) {
      throw MathRuntimeException.createArithmeticException(LocalizedFormats.ZERO_NORM);
    }

    if ((x >= -threshold) && (x <= threshold)) {
      double inverse = 1 / FastMath.sqrt(y * y + z * z);
      return new Vector3D(0, inverse * z, -inverse * y);
    } else if ((y >= -threshold) && (y <= threshold)) {
      double inverse = 1 / FastMath.sqrt(x * x + z * z);
      return new Vector3D(-inverse * z, 0, inverse * x);
    }
    double inverse = 1 / FastMath.sqrt(x * x + y * y);
    return new Vector3D(inverse * y, -inverse * x, 0);
  }
 /**
  * Returns the next pseudorandom, Gaussian ("normally") distributed {@code double} value with mean
  * {@code 0.0} and standard deviation {@code 1.0} from this random number generator's sequence.
  *
  * <p>The default implementation uses the <em>Polar Method</em> due to G.E.P. Box, M.E. Muller and
  * G. Marsaglia, as described in D. Knuth, <u>The Art of Computer Programming</u>, 3.4.1C.
  *
  * <p>The algorithm generates a pair of independent random values. One of these is cached for
  * reuse, so the full algorithm is not executed on each activation. Implementations that do not
  * override this method should make sure to call {@link #clear} to clear the cached value in the
  * implementation of {@link #setSeed(long)}.
  *
  * @return the next pseudorandom, Gaussian ("normally") distributed {@code double} value with mean
  *     {@code 0.0} and standard deviation {@code 1.0} from this random number generator's sequence
  */
 public double nextGaussian() {
   if (!Double.isNaN(cachedNormalDeviate)) {
     double dev = cachedNormalDeviate;
     cachedNormalDeviate = Double.NaN;
     return dev;
   }
   double v1 = 0;
   double v2 = 0;
   double s = 1;
   while (s >= 1) {
     v1 = 2 * nextDouble() - 1;
     v2 = 2 * nextDouble() - 1;
     s = v1 * v1 + v2 * v2;
   }
   if (s != 0) {
     s = FastMath.sqrt(-2 * FastMath.log(s) / s);
   }
   cachedNormalDeviate = v2 * s;
   return v1 * s;
 }
Example #7
0
  /**
   * Compute the angular separation between two vectors.
   *
   * <p>This method computes the angular separation between two vectors using the dot product for
   * well separated vectors and the cross product for almost aligned vectors. This allows to have a
   * good accuracy in all cases, even for vectors very close to each other.
   *
   * @param v1 first vector
   * @param v2 second vector
   * @return angular separation between v1 and v2
   * @exception ArithmeticException if either vector has a null norm
   */
  public static double angle(Vector3D v1, Vector3D v2) {

    double normProduct = v1.getNorm() * v2.getNorm();
    if (normProduct == 0) {
      throw MathRuntimeException.createArithmeticException(LocalizedFormats.ZERO_NORM);
    }

    double dot = dotProduct(v1, v2);
    double threshold = normProduct * 0.9999;
    if ((dot < -threshold) || (dot > threshold)) {
      // the vectors are almost aligned, compute using the sine
      Vector3D v3 = crossProduct(v1, v2);
      if (dot >= 0) {
        return FastMath.asin(v3.getNorm() / normProduct);
      }
      return FastMath.PI - FastMath.asin(v3.getNorm() / normProduct);
    }

    // the vectors are sufficiently separated to use the cosine
    return FastMath.acos(dot / normProduct);
  }
Example #8
0
  private void calculateBlbSum(
      double[] sample,
      double samplingRate,
      double bagExp,
      final int numberOfBags,
      final int numberOfBootstraps,
      Mean perbootstrapTime,
      Mean perbagTime) {
    bagSums = new double[numberOfBags];
    int bag_size = (int) FastMath.ceil(FastMath.pow(sample.length, bagExp));
    int[] index = new int[sample.length];
    for (int ii = 0; ii < sample.length; ii++) {
      index[ii] = ii;
    }
    int[] origIndex = index.clone();
    long bootstrapTime = 0;
    Mean actualSum = new Mean();
    for (int ii = 0; ii < numberOfBags; ii++) {
      SamplingUtilities.KnuthShuffle(index);
      double[] sampleBag = new double[bag_size];
      for (int jj = 0; jj < bag_size; jj++) {
        sampleBag[jj] = sample[index[jj]];
      }
      BootstrapSum sum =
          new BootstrapSum(sampleBag, samplingRate, numberOfBootstraps, sample.length);
      bagSums[ii] = sum.Sum();
      actualSum.increment(bagSums[ii]);
      perbootstrapTime.increment(sum.getMeanTime());
      bootstrapTime += sum.getTimes()[sum.getTimes().length - 1];
      perbagTime.increment(sum.getTimes()[sum.getTimes().length - 1]);
      index = origIndex.clone();
    }

    meanSum = actualSum.getResult();

    totalTime = bootstrapTime;
  }
Example #9
0
 /**
  * Get the elevation of the vector.
  *
  * @return elevation (&delta;) of the vector, between -&pi;/2 and +&pi;/2
  * @see #Vector3D(double, double)
  */
 public double getDelta() {
   return FastMath.asin(z / getNorm());
 }
Example #10
0
 /**
  * Get the azimuth of the vector.
  *
  * @return azimuth (&alpha;) of the vector, between -&pi; and +&pi;
  * @see #Vector3D(double, double)
  */
 public double getAlpha() {
   return FastMath.atan2(y, x);
 }
Example #11
0
 /**
  * Get the L<sub>&infin;</sub> norm for the vector.
  *
  * @return L<sub>&infin;</sub> norm for the vector
  */
 public double getNormInf() {
   return FastMath.max(FastMath.max(FastMath.abs(x), FastMath.abs(y)), FastMath.abs(z));
 }
Example #12
0
 /**
  * Get the L<sub>2</sub> norm for the vector.
  *
  * @return euclidian norm for the vector
  */
 public double getNorm() {
   return FastMath.sqrt(x * x + y * y + z * z);
 }
Example #13
0
 /**
  * Get the L<sub>1</sub> norm for the vector.
  *
  * @return L<sub>1</sub> norm for the vector
  */
 public double getNorm1() {
   return FastMath.abs(x) + FastMath.abs(y) + FastMath.abs(z);
 }
Example #14
0
 /**
  * Returns a <code>double</code> whose value is <tt>(this<sup>exponent</sup>)</tt>, returning the
  * result in reduced form.
  *
  * @param exponent exponent to which this <code>BigFraction</code> is to be raised.
  * @return <tt>this<sup>exponent</sup></tt>.
  */
 public double pow(final double exponent) {
   return FastMath.pow(numerator.doubleValue(), exponent)
       / FastMath.pow(denominator.doubleValue(), exponent);
 }
Example #15
0
  private void costantiniUnwrap() throws LPException {

    final int ny = wrappedPhase.rows - 1; // start from Zero!
    final int nx = wrappedPhase.columns - 1; // start from Zero!

    if (wrappedPhase.isVector()) throw new IllegalArgumentException("Input must be 2D array");
    if (wrappedPhase.rows < 2 || wrappedPhase.columns < 2)
      throw new IllegalArgumentException("Size of input must be larger than 2");

    // Default weight
    DoubleMatrix w1 = DoubleMatrix.ones(ny + 1, 1);
    w1.put(0, 0.5);
    w1.put(w1.length - 1, 0.5);
    DoubleMatrix w2 = DoubleMatrix.ones(1, nx + 1);
    w2.put(0, 0.5);
    w2.put(w2.length - 1, 0.5);
    DoubleMatrix weight = w1.mmul(w2);

    DoubleMatrix i, j, I_J, IP1_J, I_JP1;
    DoubleMatrix Psi1, Psi2;
    DoubleMatrix[] ROWS;

    // Compute partial derivative Psi1, eqt (1,3)
    i = intRangeDoubleMatrix(0, ny - 1);
    j = intRangeDoubleMatrix(0, nx);
    ROWS = grid2D(i, j);
    I_J = JblasUtils.sub2ind(wrappedPhase.rows, ROWS[0], ROWS[1]);
    IP1_J = JblasUtils.sub2ind(wrappedPhase.rows, ROWS[0].add(1), ROWS[1]);
    Psi1 =
        JblasUtils.getMatrixFromIdx(wrappedPhase, IP1_J)
            .sub(JblasUtils.getMatrixFromIdx(wrappedPhase, I_J));
    Psi1 = UnwrapUtils.wrapDoubleMatrix(Psi1);

    // Compute partial derivative Psi2, eqt (2,4)
    i = intRangeDoubleMatrix(0, ny);
    j = intRangeDoubleMatrix(0, nx - 1);
    ROWS = grid2D(i, j);
    I_J = JblasUtils.sub2ind(wrappedPhase.rows, ROWS[0], ROWS[1]);
    I_JP1 = JblasUtils.sub2ind(wrappedPhase.rows, ROWS[0], ROWS[1].add(1));
    Psi2 =
        JblasUtils.getMatrixFromIdx(wrappedPhase, I_JP1)
            .sub(JblasUtils.getMatrixFromIdx(wrappedPhase, I_J));
    Psi2 = UnwrapUtils.wrapDoubleMatrix(Psi2);

    // Compute beq
    DoubleMatrix beq = DoubleMatrix.zeros(ny, nx);
    i = intRangeDoubleMatrix(0, ny - 1);
    j = intRangeDoubleMatrix(0, nx - 1);
    ROWS = grid2D(i, j);
    I_J = JblasUtils.sub2ind(Psi1.rows, ROWS[0], ROWS[1]);
    I_JP1 = JblasUtils.sub2ind(Psi1.rows, ROWS[0], ROWS[1].add(1));
    beq.addi(JblasUtils.getMatrixFromIdx(Psi1, I_JP1).sub(JblasUtils.getMatrixFromIdx(Psi1, I_J)));
    I_J = JblasUtils.sub2ind(Psi2.rows, ROWS[0], ROWS[1]);
    I_JP1 = JblasUtils.sub2ind(Psi2.rows, ROWS[0].add(1), ROWS[1]);
    beq.subi(JblasUtils.getMatrixFromIdx(Psi2, I_JP1).sub(JblasUtils.getMatrixFromIdx(Psi2, I_J)));
    beq.muli(-1 / (2 * Constants._PI));
    for (int k = 0; k < beq.length; k++) {
      beq.put(k, Math.round(beq.get(k)));
    }
    beq.reshape(beq.length, 1);

    logger.debug("Constraint matrix");
    i = intRangeDoubleMatrix(0, ny - 1);
    j = intRangeDoubleMatrix(0, nx - 1);
    ROWS = grid2D(i, j);
    DoubleMatrix ROW_I_J = JblasUtils.sub2ind(i.length, ROWS[0], ROWS[1]);
    int nS0 = nx * ny;

    // Use by S1p, S1m
    DoubleMatrix[] COLS;
    COLS = grid2D(i, j);
    DoubleMatrix COL_IJ_1 = JblasUtils.sub2ind(i.length, COLS[0], COLS[1]);
    COLS = grid2D(i, j.add(1));
    DoubleMatrix COL_I_JP1 = JblasUtils.sub2ind(i.length, COLS[0], COLS[1]);
    int nS1 = (nx + 1) * (ny);

    // SOAPBinding.Use by S2p, S2m
    COLS = grid2D(i, j);
    DoubleMatrix COL_IJ_2 = JblasUtils.sub2ind(i.length + 1, COLS[0], COLS[1]);
    COLS = grid2D(i.add(1), j);
    DoubleMatrix COL_IP1_J = JblasUtils.sub2ind(i.length + 1, COLS[0], COLS[1]);
    int nS2 = nx * (ny + 1);

    // Equality constraint matrix (Aeq)
    /*
        S1p = + sparse(ROW_I_J, COL_I_JP1,1,nS0,nS1) ...
              - sparse(ROW_I_J, COL_IJ_1,1,nS0,nS1);
        S1m = -S1p;

        S2p = - sparse(ROW_I_J, COL_IP1_J,1,nS0,nS2) ...
              + sparse(ROW_I_J, COL_IJ_2,1,nS0,nS2);
        S2m = -S2p;
    */

    // ToDo: Aeq matrix should be sparse from it's initialization, look into JblasMatrix factory for
    // howto
    // ...otherwise even a data set of eg 40x40 pixels will exhaust heap:
    // ...    dimension of Aeq (equality constraints) matrix for 30x30 input is 1521x6240 matrix
    // ...    dimension of Aeq (                    ) matrix for 50x50 input is 2401x9800
    // ...    dimension of Aeq (                    ) matrix for 512x512 input is 261121x1046528
    DoubleMatrix S1p =
        JblasUtils.setUpMatrixFromIdx(nS0, nS1, ROW_I_J, COL_I_JP1)
            .sub(JblasUtils.setUpMatrixFromIdx(nS0, nS1, ROW_I_J, COL_IJ_1));
    DoubleMatrix S1m = S1p.neg();

    DoubleMatrix S2p =
        JblasUtils.setUpMatrixFromIdx(nS0, nS2, ROW_I_J, COL_IP1_J)
            .neg()
            .add(JblasUtils.setUpMatrixFromIdx(nS0, nS2, ROW_I_J, COL_IJ_2));
    DoubleMatrix S2m = S2p.neg();

    DoubleMatrix Aeq =
        concatHorizontally(concatHorizontally(S1p, S1m), concatHorizontally(S2p, S2m));

    final int nObs = Aeq.columns;
    final int nUnkn = Aeq.rows;

    DoubleMatrix c1 = JblasUtils.getMatrixFromRange(0, ny, 0, weight.columns, weight);
    DoubleMatrix c2 = JblasUtils.getMatrixFromRange(0, weight.rows, 0, nx, weight);

    c1.reshape(c1.length, 1);
    c2.reshape(c2.length, 1);

    DoubleMatrix cost =
        DoubleMatrix.concatVertically(
            DoubleMatrix.concatVertically(c1, c1), DoubleMatrix.concatVertically(c2, c2));

    logger.debug("Minimum network flow resolution");

    StopWatch clockLP = new StopWatch();
    LinearProgram lp = new LinearProgram(cost.data);
    lp.setMinProblem(true);

    boolean[] integerBool = new boolean[nObs];
    double[] lowerBound = new double[nObs];
    double[] upperBound = new double[nObs];

    for (int k = 0; k < nUnkn; k++) {
      lp.addConstraint(new LinearEqualsConstraint(Aeq.getRow(k).toArray(), beq.get(k), "cost"));
    }

    for (int k = 0; k < nObs; k++) {
      integerBool[k] = true;
      lowerBound[k] = 0;
      upperBound[k] = 99999;
    }

    // setup bounds and integer nature
    lp.setIsinteger(integerBool);
    lp.setUpperbound(upperBound);
    lp.setLowerbound(lowerBound);
    LinearProgramSolver solver = SolverFactory.newDefault();

    //        double[] solution;
    //        solution = solver.solve(lp);
    DoubleMatrix solution = new DoubleMatrix(solver.solve(lp));

    clockLP.stop();
    logger.debug("Total GLPK time: {} [sec]", (double) (clockLP.getElapsedTime()) / 1000);

    // Displatch the LP solution
    int offset;

    int[] idx1p = JblasUtils.intRangeIntArray(0, nS1 - 1);
    DoubleMatrix x1p = solution.get(idx1p);
    x1p.reshape(ny, nx + 1);
    offset = idx1p[nS1 - 1] + 1;

    int[] idx1m = JblasUtils.intRangeIntArray(offset, offset + nS1 - 1);
    DoubleMatrix x1m = solution.get(idx1m);
    x1m.reshape(ny, nx + 1);
    offset = idx1m[idx1m.length - 1] + 1;

    int[] idx2p = JblasUtils.intRangeIntArray(offset, offset + nS2 - 1);
    DoubleMatrix x2p = solution.get(idx2p);
    x2p.reshape(ny + 1, nx);
    offset = idx2p[idx2p.length - 1] + 1;

    int[] idx2m = JblasUtils.intRangeIntArray(offset, offset + nS2 - 1);
    DoubleMatrix x2m = solution.get(idx2m);
    x2m.reshape(ny + 1, nx);

    // Compute the derivative jumps, eqt (20,21)
    DoubleMatrix k1 = x1p.sub(x1m);
    DoubleMatrix k2 = x2p.sub(x2m);

    // (?) Round to integer solution
    if (roundK == true) {
      for (int idx = 0; idx < k1.length; idx++) {
        k1.put(idx, FastMath.floor(k1.get(idx)));
      }
      for (int idx = 0; idx < k2.length; idx++) {
        k2.put(idx, FastMath.floor(k2.get(idx)));
      }
    }

    // Sum the jumps with the wrapped partial derivatives, eqt (10,11)
    k1.reshape(ny, nx + 1);
    k2.reshape(ny + 1, nx);
    k1.addi(Psi1.div(Constants._TWO_PI));
    k2.addi(Psi2.div(Constants._TWO_PI));

    // Integrate the partial derivatives, eqt (6)
    // cumsum() method in JblasTester -> see cumsum_demo() in JblasTester.cumsum_demo()
    DoubleMatrix k2_temp = DoubleMatrix.concatHorizontally(DoubleMatrix.zeros(1), k2.getRow(0));
    k2_temp = JblasUtils.cumsum(k2_temp, 1);
    DoubleMatrix k = DoubleMatrix.concatVertically(k2_temp, k1);
    k = JblasUtils.cumsum(k, 1);

    // Unwrap - final solution
    unwrappedPhase = k.mul(Constants._TWO_PI);
  }
Example #16
0
 /**
  * Compute the distance between two vectors according to the L<sub>2</sub> norm.
  *
  * <p>Calling this method is equivalent to calling: <code>v1.subtract(v2).getNorm()</code> except
  * that no intermediate vector is built
  *
  * @param v1 first vector
  * @param v2 second vector
  * @return the distance between v1 and v2 according to the L<sub>2</sub> norm
  */
 public static double distance(Vector3D v1, Vector3D v2) {
   final double dx = v2.x - v1.x;
   final double dy = v2.y - v1.y;
   final double dz = v2.z - v1.z;
   return FastMath.sqrt(dx * dx + dy * dy + dz * dz);
 }
public class DenseFeatureMatrix {
  int inputSize;
  int outputSize;
  INDArray features;
  INDArray featuresT;
  GradientStore gradientStore = new GradientStore();
  double l2 = GlobalParameters.l2regularizerLambdaDefault;
  double learningRate = GlobalParameters.learningRateDefault;

  // adagrad vars
  boolean useAdagrad = GlobalParameters.useAdagradDefault;
  INDArray adagradQuotient;
  double adagradEps = 0.001;
  double adagradMax = 10;

  // gaussian noise
  double noiseVar = GlobalParameters.noiseDevDefault;
  double noiseVarSqrt = FastMath.sqrt(noiseVar);;
  HashMap<Integer, INDArray> currentNoise = new HashMap<Integer, INDArray>();

  // momentum vars
  boolean useMomentum = GlobalParameters.useMomentumDefault;
  INDArray momentumPrevUpdate;
  double momentum = GlobalParameters.momentumDefault;

  // adadelta vars
  boolean useAdadelta = GlobalParameters.useAdadeltaDefault;
  INDArray adadeltaRMSGradient;
  INDArray adadeltaRMSUpdate;
  double adadeltaMomentum = GlobalParameters.adadeltaMomentumDefault;
  double adadeltaEps = GlobalParameters.adadeltaEpsDefault;

  // commit
  int commitMethod = GlobalParameters.commitMethodDefault;

  public DenseFeatureMatrix(
      int inputSize, int outputSize, boolean useAdagrad, boolean useMomentum, boolean useAdadelta) {
    if (inputSize == 1) {
      throw new RuntimeException("input size = 1: use vector instead");
    }
    this.inputSize = inputSize;
    this.outputSize = outputSize;
    this.useAdadelta = useAdadelta;
    this.useAdagrad = useAdagrad;
    this.useMomentum = useMomentum;
    if (useAdagrad) {
      adagradQuotient = Nd4j.zeros(inputSize, outputSize);
      adagradQuotient.addi(adagradEps);
    }
    if (useMomentum) {
      momentumPrevUpdate = Nd4j.zeros(inputSize, outputSize);
    }
    if (useAdadelta) {
      adadeltaRMSGradient = Nd4j.zeros(inputSize, outputSize);
      adadeltaRMSUpdate = Nd4j.zeros(inputSize, outputSize);
    }
  }

  public DenseFeatureMatrix(int inputSize, int outputSize) {
    if (inputSize == 1) {
      throw new RuntimeException("input size = 1: use vector instead");
    }
    this.inputSize = inputSize;
    this.outputSize = outputSize;
    if (useAdagrad) {
      adagradQuotient = Nd4j.zeros(inputSize, outputSize);
      adagradQuotient.addi(adagradEps);
    }
    if (useMomentum) {
      momentumPrevUpdate = Nd4j.zeros(inputSize, outputSize);
    }
    if (useAdadelta) {
      adadeltaRMSGradient = Nd4j.zeros(inputSize, outputSize);
      adadeltaRMSUpdate = Nd4j.zeros(inputSize, outputSize);
    }
  }

  public void initialize(double[][] vals) {
    features = Nd4j.create(vals);
    featuresT = features.transpose();
  }

  public void initializeUniform(double min, double max) {
    double[][] featuresMatrixStub = new double[inputSize][outputSize];
    RandomUtils.initializeRandomMatrix(featuresMatrixStub, min, max, 1);
    features = Nd4j.create(featuresMatrixStub);
    featuresT = features.transpose();
  }

  public void normalizedInitializationHtan(int fanin, int fanout) {
    double max = Math.sqrt(6.0d / (fanout + fanin));
    double[][] featuresMatrixStub = new double[inputSize][outputSize];
    RandomUtils.initializeRandomMatrix(featuresMatrixStub, -max, max, 1);

    features = Nd4j.create(featuresMatrixStub);
    featuresT = features.transpose();
  }

  public void normalizedInitializationSigmoid(int fanin, int fanout) {
    double max = 4 * Math.sqrt(6.0d / (fanin + fanout));
    double[][] featuresMatrixStub = new double[inputSize][outputSize];
    RandomUtils.initializeRandomMatrix(featuresMatrixStub, -max, max, 1);
    features = Nd4j.create(featuresMatrixStub);
    featuresT = features.transpose();
  }

  public INDArray getWeights() {
    return features;
  }

  public INDArray getTranspose() {
    return featuresT;
  }

  public void storeGradients(int processId, INDArray gradient) {
    gradientStore.addGradient(processId, gradient);
  }

  public void storeInputsAndOutputs(int id, INDArray x, INDArray yGrad) {
    gradientStore.addInputAndOutput(id, x, yGrad);
  }

  public void checkinGradients(int id) {
    gradientStore.computeGradientAndAdd(id);
  }

  public void update() {
    INDArray gradient = null;
    if (commitMethod == 0) {
      gradient = gradientStore.getGradientAvg();
    } else {
      gradient = gradientStore.getGradientSum();
    }
    if (gradient == null) return;
    INDArray gradientL2 = gradient.sub(features.mul(l2));
    if (useAdagrad) {
      getAdagradGradient(gradientL2);
      features.addi(gradientL2.mul(learningRate));
    } else if (useMomentum) {
      getMomentumGradient(gradientL2);
      features.addi(gradientL2.mul(learningRate));
    } else if (useAdadelta) {
      getAdadeltaGradient(gradientL2);
      features.addi(gradientL2);
    } else {
      features.addi(gradientL2.mul(learningRate));
    }
    capValues(GlobalParameters.maxVal);
    featuresT = features.transpose();
    gradientStore.init();
  }

  protected void getAdagradGradient(INDArray gradient) {
    adagradQuotient.addi(gradient.mul(gradient));
    for (int i = 0; i < inputSize; i++) {
      for (int j = 0; j < outputSize; j++) {
        double adagradQ = adagradQuotient.getDouble(i, j);
        if (adagradMax < adagradQ) {
          adagradQuotient.putScalar(new int[] {i, j}, adagradMax);
          adagradQ = adagradMax;
        }
        gradient.putScalar(new int[] {i, j}, gradient.getDouble(i, j) / Math.sqrt(adagradQ));
      }
    }
  }

  protected void getAdadeltaGradient(INDArray gradient) {
    adadeltaRMSGradient =
        adadeltaRMSGradient
            .mul(adadeltaMomentum)
            .add(gradient.mul(gradient).mul(1 - adadeltaMomentum));
    gradient.muli(
        Transforms.sqrt(adadeltaRMSUpdate.add(adadeltaEps))
            .div(Transforms.sqrt(adadeltaRMSGradient.add(adadeltaEps))));
    adadeltaRMSUpdate.mul(adadeltaMomentum).add(gradient.mul(gradient).mul(1 - adadeltaMomentum));
  }

  protected void getMomentumGradient(INDArray gradient) {
    INDArray momemtumUpdate = momentumPrevUpdate.mul(momentum);
    gradient.addi(momemtumUpdate);
    momentumPrevUpdate = gradient.dup();
  }

  public INDArray genGaussianNoise(int id) {
    if (!currentNoise.containsKey(id)) {
      INDArray zeroMean = Nd4j.zeros(inputSize, outputSize);

      currentNoise.put(id, Sampling.normal(RandomUtils.getRandomGenerator(id), zeroMean, noiseVar));
    } else {
      RealDistribution reals =
          new NormalDistribution(
              RandomUtils.getRandomGenerator(id),
              0,
              noiseVarSqrt,
              NormalDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
      INDArrayUtils.shiftLeft(
          currentNoise.get(id),
          inputSize,
          outputSize,
          RandomUtils.getRandomGenerator(id).nextInt(inputSize * outputSize),
          reals.sample());
    }

    //		currentNoise = Sampling.normal(RandomUtils.getRandomGenerator(id), zeroMean, noiseVar);

    return currentNoise.get(id);
  }

  public void capValues(double max) {
    INDArray linear = features.linearView();
    for (int i = 0; i < linear.size(0); i++) {
      linear.putScalar(i, Math.max(-max, Math.min(max, linear.getDouble(i))));
    }
  }

  public void save(PrintStream out) {
    out.println(inputSize);
    out.println(outputSize);
    out.println(useAdagrad);
    out.println(adagradEps);
    out.println(adagradMax);
    out.println(noiseVar);
    out.println(useMomentum);
    out.println(momentum);
    out.println(useAdadelta);
    out.println(adadeltaEps);
    out.println(adadeltaMomentum);
    saveMatrix(features, out);
    if (useAdagrad) {
      saveMatrix(adagradQuotient, out);
    }
    if (useMomentum) {
      saveMatrix(momentumPrevUpdate, out);
    }
    if (useAdadelta) {
      saveMatrix(adadeltaRMSGradient, out);
      saveMatrix(adadeltaRMSUpdate, out);
    }
  }

  public void saveMatrix(INDArray matrix, PrintStream out) {
    for (int row = 0; row < inputSize; row++) {
      for (int col = 0; col < outputSize; col++) {
        double val = matrix.getDouble(row, col);
        if (col < outputSize - 1) {
          out.print(val + " ");
        } else {
          out.println(val);
        }
      }
    }
  }

  public static DenseFeatureMatrix load(BufferedReader in) {
    try {
      int inputSize = Integer.parseInt(in.readLine());
      int outputSize = Integer.parseInt(in.readLine());
      DenseFeatureMatrix matrix = new DenseFeatureMatrix(inputSize, outputSize);
      matrix.useAdagrad = Boolean.parseBoolean(in.readLine());
      matrix.adagradEps = Double.parseDouble(in.readLine());
      matrix.adagradMax = Double.parseDouble(in.readLine());
      matrix.noiseVar = Double.parseDouble(in.readLine());
      matrix.useMomentum = Boolean.parseBoolean(in.readLine());
      matrix.momentum = Double.parseDouble(in.readLine());
      matrix.useAdadelta = Boolean.parseBoolean(in.readLine());
      matrix.adadeltaEps = Double.parseDouble(in.readLine());
      matrix.adadeltaMomentum = Double.parseDouble(in.readLine());
      matrix.features = loadMatrix(in, inputSize, outputSize);
      if (matrix.useAdagrad) {
        matrix.adagradQuotient = loadMatrix(in, inputSize, outputSize);
      }
      if (matrix.useMomentum) {
        matrix.momentumPrevUpdate = loadMatrix(in, inputSize, outputSize);
      }
      if (matrix.useAdadelta) {
        matrix.adadeltaRMSGradient = loadMatrix(in, inputSize, outputSize);
        matrix.adadeltaRMSUpdate = loadMatrix(in, inputSize, outputSize);
      }
      matrix.featuresT = matrix.features.transpose();
      return matrix;
    } catch (Exception e) {
      throw new RuntimeException(e);
    }
  }

  public static INDArray loadMatrix(BufferedReader in, int inputSize, int outputSize)
      throws IOException {
    INDArray matrix = Nd4j.create(inputSize, outputSize);
    for (int row = 0; row < inputSize; row++) {
      String[] vals = in.readLine().split("\\s+");
      for (int col = 0; col < outputSize; col++) {
        matrix.putScalar(new int[] {row, col}, Double.parseDouble(vals[col]));
      }
    }
    return matrix;
  }

  public void setL2(double l2) {
    this.l2 = l2;
  }

  public static void main(String[] args) {
    DenseFeatureMatrix matrix = new DenseFeatureMatrix(1, 5);
    matrix.initializeUniform(-0.1, 0.1);
    matrix.save(IOUtils.getPrintStream("/tmp/file"));

    DenseFeatureMatrix.load(IOUtils.getReader("/tmp/file")).save(System.err);
  }

  public void normalize() {
    features.divi(features.sum(0).getDouble(0) * inputSize);
    featuresT = features.transpose();
  }
}
 /** {@inheritDoc} */
 public double value(double x, double[] parameters) {
   final double a = parameters[0];
   final double omega = parameters[1];
   final double phi = parameters[2];
   return a * FastMath.cos(omega * x + phi);
 }
Example #19
0
  public static void main(String[] args) {
    TreeMap<Double, List<int[]>> voiceLeadingMap = new TreeMap<Double, List<int[]>>();
    //		List<int[]> vl = voiceLeading2Voices();
    //		List<int[]> vl = voiceLeading3Voices();
    //		System.out.println(vl.size());

    //		for (int[] is : vl) {
    //			System.out.print("[" );
    //			for (int i : is) {
    //				System.out.print(i + ",");
    //			}
    //			System.out.print("]" );
    //			System.out.println();
    //		}

    //		for (int[] is : vl) {
    //			double vlDegree = Utilities.round(analyseVoiceLeading(is),3);
    //			List<int[]> ch = voiceLeadingMap.get(vlDegree);
    //			if(ch == null){
    //				voiceLeadingMap.put(vlDegree, ch = new ArrayList<int[]>());
    //			}
    //			ch.add(is);
    //
    //		}
    //
    //		Set<Double> keys = voiceLeadingMap.keySet();
    //		for (Double key : keys) {
    //			List<int[]> ch = voiceLeadingMap.get(key);
    ////			System.out.println();
    //			System.out.println("size group: " + ch.size());
    //			for (int[] is : ch) {
    //				System.out.print(" vl : " + key);
    //				System.out.print("[" );
    //				for (int i : is) {
    //					System.out.print(i + ",");
    //				}
    //				System.out.print("]" );
    ////				System.out.println();
    //			}
    //			System.out.println();
    //
    //		}
    double[] firstChord = {60.0, 50.0, 60.0};
    double[] secondChord = {60.0, 55.0, 0.0};

    double sum = 0;
    for (int i = 0; i < firstChord.length; i++) {
      if (firstChord[i] != 0 && secondChord[i] != 0) {
        sum += FastMath.abs(firstChord[i] - secondChord[i]);
      }
    }

    //		double smoothnes = MathUtils.distance1(vec1,vec2);
    System.out.println("smoothness: " + sum);

    Note[] chord1 = new Note[4];
    chord1[0] = new Note(60, 1.0);
    chord1[1] = new Note(60, 1.0);
    chord1[2] = new Note(60, 1.0);
    chord1[3] = new Note(60, 1.0);
    Note[] chord2 = new Note[4];
    chord2[0] = new Note(60, 1.0);
    chord2[1] = new Note(70, 1.0);
    chord2[2] = new Note(70, 1.0);
    chord2[3] = new Note(60, 1.0);
    // Calculates the L2 (Euclidean) distance between two points.
    double euclideanDistance = euclideanDistance(chord1, chord2);
    System.out.println("euclideanDistance: " + euclideanDistance);
    // Smoothness: Calculates the L1 (sum of abs) distance between two points.
    double smoothness = taxiCab(chord1, chord2);
    System.out.println("smoothness: " + smoothness);
    // Calculates the L infinite (max of abs) distance between two points.
    double lInfDistance = infiniteDistance(chord1, chord2);
    System.out.println("lInfDistance: " + lInfDistance);
  }
Example #20
0
 /**
  * Compute the distance between two vectors according to the L<sub>1</sub> norm.
  *
  * <p>Calling this method is equivalent to calling: <code>v1.subtract(v2).getNorm1()</code> except
  * that no intermediate vector is built
  *
  * @param v1 first vector
  * @param v2 second vector
  * @return the distance between v1 and v2 according to the L<sub>1</sub> norm
  */
 public static double distance1(Vector3D v1, Vector3D v2) {
   final double dx = FastMath.abs(v2.x - v1.x);
   final double dy = FastMath.abs(v2.y - v1.y);
   final double dz = FastMath.abs(v2.z - v1.z);
   return dx + dy + dz;
 }
Example #21
0
  /**
   * Create a fraction given the double value and either the maximum error allowed or the maximum
   * number of denominator digits.
   *
   * <p>NOTE: This constructor is called with EITHER - a valid epsilon value and the maxDenominator
   * set to Integer.MAX_VALUE (that way the maxDenominator has no effect). OR - a valid
   * maxDenominator value and the epsilon value set to zero (that way epsilon only has effect if
   * there is an exact match before the maxDenominator value is reached).
   *
   * <p>It has been done this way so that the same code can be (re)used for both scenarios. However
   * this could be confusing to users if it were part of the public API and this constructor should
   * therefore remain PRIVATE. See JIRA issue ticket MATH-181 for more details:
   *
   * <p>https://issues.apache.org/jira/browse/MATH-181
   *
   * @param value the double value to convert to a fraction.
   * @param epsilon maximum error allowed. The resulting fraction is within <code>epsilon</code> of
   *     <code>value</code>, in absolute terms.
   * @param maxDenominator maximum denominator value allowed.
   * @param maxIterations maximum number of convergents.
   * @throws FractionConversionException if the continued fraction failed to converge.
   */
  private BigFraction(
      final double value, final double epsilon, final int maxDenominator, int maxIterations)
      throws FractionConversionException {
    long overflow = Integer.MAX_VALUE;
    double r0 = value;
    long a0 = (long) FastMath.floor(r0);
    if (a0 > overflow) {
      throw new FractionConversionException(value, a0, 1l);
    }

    // check for (almost) integer arguments, which should not go
    // to iterations.
    if (FastMath.abs(a0 - value) < epsilon) {
      numerator = BigInteger.valueOf(a0);
      denominator = BigInteger.ONE;
      return;
    }

    long p0 = 1;
    long q0 = 0;
    long p1 = a0;
    long q1 = 1;

    long p2 = 0;
    long q2 = 1;

    int n = 0;
    boolean stop = false;
    do {
      ++n;
      final double r1 = 1.0 / (r0 - a0);
      final long a1 = (long) FastMath.floor(r1);
      p2 = (a1 * p1) + p0;
      q2 = (a1 * q1) + q0;
      if ((p2 > overflow) || (q2 > overflow)) {
        throw new FractionConversionException(value, p2, q2);
      }

      final double convergent = (double) p2 / (double) q2;
      if ((n < maxIterations)
          && (FastMath.abs(convergent - value) > epsilon)
          && (q2 < maxDenominator)) {
        p0 = p1;
        p1 = p2;
        q0 = q1;
        q1 = q2;
        a0 = a1;
        r0 = r1;
      } else {
        stop = true;
      }
    } while (!stop);

    if (n >= maxIterations) {
      throw new FractionConversionException(value, maxIterations);
    }

    if (q2 < maxDenominator) {
      numerator = BigInteger.valueOf(p2);
      denominator = BigInteger.valueOf(q2);
    } else {
      numerator = BigInteger.valueOf(p1);
      denominator = BigInteger.valueOf(q1);
    }
  }
Example #22
0
 /**
  * Compute the distance between two vectors according to the L<sub>&infin;</sub> norm.
  *
  * <p>Calling this method is equivalent to calling: <code>v1.subtract(v2).getNormInf()</code>
  * except that no intermediate vector is built
  *
  * @param v1 first vector
  * @param v2 second vector
  * @return the distance between v1 and v2 according to the L<sub>&infin;</sub> norm
  */
 public static double distanceInf(Vector3D v1, Vector3D v2) {
   final double dx = FastMath.abs(v2.x - v1.x);
   final double dy = FastMath.abs(v2.y - v1.y);
   final double dz = FastMath.abs(v2.z - v1.z);
   return FastMath.max(FastMath.max(dx, dy), dz);
 }
  /** {@inheritDoc} */
  @Override
  public void integrate(final ExpandableStatefulODE equations, final double t)
      throws MathIllegalStateException, MathIllegalArgumentException {

    sanityChecks(equations, t);
    setEquations(equations);
    final boolean forward = t > equations.getTime();

    // create some internal working arrays
    final double[] y0 = equations.getCompleteState();
    final double[] y = y0.clone();
    final int stages = c.length + 1;
    final double[][] yDotK = new double[stages][y.length];
    final double[] yTmp = y0.clone();
    final double[] yDotTmp = new double[y.length];

    // set up an interpolator sharing the integrator arrays
    final RungeKuttaStepInterpolator interpolator = (RungeKuttaStepInterpolator) prototype.copy();
    interpolator.reinitialize(
        this, yTmp, yDotK, forward, equations.getPrimaryMapper(), equations.getSecondaryMappers());
    interpolator.storeTime(equations.getTime());

    // set up integration control objects
    stepStart = equations.getTime();
    double hNew = 0;
    boolean firstTime = true;
    initIntegration(equations.getTime(), y0, t);

    // main integration loop
    isLastStep = false;
    do {

      interpolator.shift();

      // iterate over step size, ensuring local normalized error is smaller than 1
      double error = 10;
      while (error >= 1.0) {

        if (firstTime || !fsal) {
          // first stage
          computeDerivatives(stepStart, y, yDotK[0]);
        }

        if (firstTime) {
          final double[] scale = new double[mainSetDimension];
          if (vecAbsoluteTolerance == null) {
            for (int i = 0; i < scale.length; ++i) {
              scale[i] = scalAbsoluteTolerance + scalRelativeTolerance * FastMath.abs(y[i]);
            }
          } else {
            for (int i = 0; i < scale.length; ++i) {
              scale[i] = vecAbsoluteTolerance[i] + vecRelativeTolerance[i] * FastMath.abs(y[i]);
            }
          }
          hNew = initializeStep(forward, getOrder(), scale, stepStart, y, yDotK[0], yTmp, yDotK[1]);
          firstTime = false;
        }

        stepSize = hNew;
        if (forward) {
          if (stepStart + stepSize >= t) {
            stepSize = t - stepStart;
          }
        } else {
          if (stepStart + stepSize <= t) {
            stepSize = t - stepStart;
          }
        }

        // next stages
        for (int k = 1; k < stages; ++k) {

          for (int j = 0; j < y0.length; ++j) {
            double sum = a[k - 1][0] * yDotK[0][j];
            for (int l = 1; l < k; ++l) {
              sum += a[k - 1][l] * yDotK[l][j];
            }
            yTmp[j] = y[j] + stepSize * sum;
          }

          computeDerivatives(stepStart + c[k - 1] * stepSize, yTmp, yDotK[k]);
        }

        // estimate the state at the end of the step
        for (int j = 0; j < y0.length; ++j) {
          double sum = b[0] * yDotK[0][j];
          for (int l = 1; l < stages; ++l) {
            sum += b[l] * yDotK[l][j];
          }
          yTmp[j] = y[j] + stepSize * sum;
        }

        // estimate the error at the end of the step
        error = estimateError(yDotK, y, yTmp, stepSize);
        if (error >= 1.0) {
          // reject the step and attempt to reduce error by stepsize control
          final double factor =
              FastMath.min(
                  maxGrowth, FastMath.max(minReduction, safety * FastMath.pow(error, exp)));
          hNew = filterStep(stepSize * factor, forward, false);
        }
      }

      // local error is small enough: accept the step, trigger events and step handlers
      interpolator.storeTime(stepStart + stepSize);
      System.arraycopy(yTmp, 0, y, 0, y0.length);
      System.arraycopy(yDotK[stages - 1], 0, yDotTmp, 0, y0.length);
      stepStart = acceptStep(interpolator, y, yDotTmp, t);
      System.arraycopy(y, 0, yTmp, 0, y.length);

      if (!isLastStep) {

        // prepare next step
        interpolator.storeTime(stepStart);

        if (fsal) {
          // save the last evaluation for the next step
          System.arraycopy(yDotTmp, 0, yDotK[0], 0, y0.length);
        }

        // stepsize control for next step
        final double factor =
            FastMath.min(maxGrowth, FastMath.max(minReduction, safety * FastMath.pow(error, exp)));
        final double scaledH = stepSize * factor;
        final double nextT = stepStart + scaledH;
        final boolean nextIsLast = forward ? (nextT >= t) : (nextT <= t);
        hNew = filterStep(scaledH, forward, nextIsLast);

        final double filteredNextT = stepStart + hNew;
        final boolean filteredNextIsLast = forward ? (filteredNextT >= t) : (filteredNextT <= t);
        if (filteredNextIsLast) {
          hNew = t - stepStart;
        }
      }

    } while (!isLastStep);

    // dispatch results
    equations.setTime(stepStart);
    equations.setCompleteState(y);

    resetInternalState();
  }
Example #24
0
 /**
  * Simple constructor. Build a vector from its azimuthal coordinates
  *
  * @param alpha azimuth (&alpha;) around Z (0 is +X, &pi;/2 is +Y, &pi; is -X and 3&pi;/2 is -Y)
  * @param delta elevation (&delta;) above (XY) plane, from -&pi;/2 to +&pi;/2
  * @see #getAlpha()
  * @see #getDelta()
  */
 public Vector3D(double alpha, double delta) {
   double cosDelta = FastMath.cos(delta);
   this.x = FastMath.cos(alpha) * cosDelta;
   this.y = FastMath.sin(alpha) * cosDelta;
   this.z = FastMath.sin(delta);
 }
Example #25
0
  /** {@inheritDoc} */
  protected final double doSolve() {
    // Get initial solution
    double x0 = getMin();
    double x1 = getMax();
    double f0 = computeObjectiveValue(x0);
    double f1 = computeObjectiveValue(x1);

    // If one of the bounds is the exact root, return it. Since these are
    // not under-approximations or over-approximations, we can return them
    // regardless of the allowed solutions.
    if (f0 == 0.0) {
      return x0;
    }
    if (f1 == 0.0) {
      return x1;
    }

    // Verify bracketing of initial solution.
    verifyBracketing(x0, x1);

    // Get accuracies.
    final double ftol = getFunctionValueAccuracy();
    final double atol = getAbsoluteAccuracy();
    final double rtol = getRelativeAccuracy();

    // Keep track of inverted intervals, meaning that the left bound is
    // larger than the right bound.
    boolean inverted = false;

    // Keep finding better approximations.
    while (true) {
      // Calculate the next approximation.
      final double x = x1 - ((f1 * (x1 - x0)) / (f1 - f0));
      final double fx = computeObjectiveValue(x);

      // If the new approximation is the exact root, return it. Since
      // this is not an under-approximation or an over-approximation,
      // we can return it regardless of the allowed solutions.
      if (fx == 0.0) {
        return x;
      }

      // Update the bounds with the new approximation.
      if (f1 * fx < 0) {
        // The value of x1 has switched to the other bound, thus inverting
        // the interval.
        x0 = x1;
        f0 = f1;
        inverted = !inverted;
      } else {
        switch (method) {
          case ILLINOIS:
            f0 *= 0.5;
            break;
          case PEGASUS:
            f0 *= f1 / (f1 + fx);
            break;
          case REGULA_FALSI:
            // Nothing.
            break;
          default:
            // Should never happen.
            throw new MathInternalError();
        }
      }
      // Update from [x0, x1] to [x0, x].
      x1 = x;
      f1 = fx;

      // If the function value of the last approximation is too small,
      // given the function value accuracy, then we can't get closer to
      // the root than we already are.
      if (FastMath.abs(f1) <= ftol) {
        switch (allowed) {
          case ANY_SIDE:
            return x1;
          case LEFT_SIDE:
            if (inverted) {
              return x1;
            }
            break;
          case RIGHT_SIDE:
            if (!inverted) {
              return x1;
            }
            break;
          case BELOW_SIDE:
            if (f1 <= 0) {
              return x1;
            }
            break;
          case ABOVE_SIDE:
            if (f1 >= 0) {
              return x1;
            }
            break;
          default:
            throw new MathInternalError();
        }
      }

      // If the current interval is within the given accuracies, we
      // are satisfied with the current approximation.
      if (FastMath.abs(x1 - x0) < FastMath.max(rtol * FastMath.abs(x1), atol)) {
        switch (allowed) {
          case ANY_SIDE:
            return x1;
          case LEFT_SIDE:
            return inverted ? x1 : x0;
          case RIGHT_SIDE:
            return inverted ? x0 : x1;
          case BELOW_SIDE:
            return (f1 <= 0) ? x1 : x0;
          case ABOVE_SIDE:
            return (f1 >= 0) ? x1 : x0;
          default:
            throw new MathInternalError();
        }
      }
    }
  }