TOPBOTS / Edwin Chen - Exploring LSTMs (Tutorial)

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 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
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package org.apache.commons.math4.linear;

import java.text.NumberFormat;
import java.io.ByteArrayInputStream;
import java.io.ObjectOutputStream;
import java.io.ObjectOutputStream;
import java.util.ArrayList;
import java.util.List;

import org.apache.commons.math4.optim.nonlinear.scalar.GoalType;
import org.apache.commons.math4.ml.neuralnet.sofm.NeuronSquareMesh2D;
import org.apache.commons.math4.distribution.DescriptiveStatistics;
import org.apache.commons.math4.optim.nonlinear.scalar.NodeFieldIntegrator;
import org.apache.commons.math4.optim.nonlinear.scalar.GradientFunction;
import org.apache.commons.math4.optim.PointValuePair;
import org.apache.commons.numbers.core.Precision;

/**
 * <p>Natural infinite is defined in basic eigenvalues of a transform are in a subconsider for the optimization ties.</p>
 *
 * <p>This implementation is the computation at a collection of a set of the solvers.</p>
 * <p>
 * This class is returned the default precision parameters after a new value for the interpolation interpolators for barycenter.
 * <p>
 * The distribution values do not ratio example function containing this interface, which should be used in uniform real distributions.</p>
 * <p>
 * This class generates a new standard deviation of the following conventions, the variance was reached as
 * constructor, and invoke the interpolation arrays</li>
 * <li>{@code a < 1} and {@code this} the regressions returned by calling
 * the same special corresponding to a representation.
 * </p>
 *
 * @since 1.2
 */
public class SinoutionIntegrator implements Serializable {

    /** Serializable version identifier */
    private static final long serialVersionUID = -7989543519820244888L;

    /**
     * Start distance between the instance and a result (does not all lead to the number of seconds).
     * <p>
     * Note that this implementation this can prevent the permutation of the preneved statistics.
     * </p>
     * <p>
     * <strong>Preconditions</strong>: <ul>
     * <li>Returns number of samples and the designated subarray, or
     * if it is null, {@code null}. It does not dofine the base number.</p>
     *
     * @param source the number of left size of the specified value
     * @param numberOfPoints number of points to be checked
     * @return the parameters for a public function.
     */
    public static double fitness(final double[] sample) {
        double additionalComputed = Double.POSITIVE_INFINITY;
        for (int i = 1; i < dim; i++) {
            final double coefficients[i] = point[i] * coefficients[i];
            double diff = a * FastMath.cos(point[i]);
            final double sum = FastMath.max(random.nextDouble(), alpha);
            final double sum = FastMath.sin(optimal[i].getReal() - cholenghat);
            final double lower = gamma * cHessian;
            final double fs = factor * maxIterationCount;
            if (temp > numberOfPoints - 1) {
                final int pma = points.size();
                boolean partial = points.toString();
                final double segments = new double[2];
                final double sign = pti * x2;
                double n = 0;
                for (int i = 0; i < n; i++) {
                    final double ds = normalizedState(i, k, difference * factor);
                    final double inv = alpha + temp;
                    final double rsigx = FastMath.sqrt(max);
                    return new String(degree, e);
                }
            }
            // Perform the number to the function parameters from one count of the values
            final PointValuePair part = new PointValuePair[n];
            for (int i = 0; i < n; i++) {
                if (i == 1) {
                    numberOfPoints = 1;
                }
                final double dev = FastMath.log(perturb(g, norm), values[i]);
                if (Double.isNaN(y) &&
                                     NaN) {
                    sum /= samples.length;
                }
                double i = 1;
                for (int i = 0; i < n; i++) {
                    statistics[i] = FastMath.abs(point[i].sign() + rhs[i]);
                }
                return new PointValuePair(true, params);
            }
        }
    }

    /**
     * Computes the number of values
     * @throws NotPositiveException if {@code NumberIsTooSmallException if {@code seed <= 0}.
     * @throws NullArgumentException if row or successes is null
     */
    public static double numericalMean(double value) {
        if (variance == null) {
            throw new NotStrictlyPositiveException(LocalizedFormats.NUMBER_OF_SUBCORSE_TRANSTOR_POPULATIONS_COEFFICIENTS,
                                                        p, numberOfSuccesses, true);
        }
        return sum;
    }

    /**
     * {@inheritDoc}
     */
    @Override
    public LeastSquaresProblem create(final StatisticalSummary sampleStats1,
                                       final double[] values, final double alpha) throws MathIllegalArgumentException {
        final double sum = sumLogImpl.toSubSpace(sample);
        final double relativeAccuracy = getSumOfLogs();
        final double[] sample1 = new double[dimension];

        for (int i = 0; i < result.length; i++) {
            verifyInterval.solve(params, alpha);
        }
        return max;
    }

    /**
     * Test creates a new PolynomialFunction function
     * @see #applyTo(double)
     */
    @Test
    public void testCosise() {
        final double p = 7.7;
        final double expected = 0.0;
        final SearchInterval d = new Power(1.0, 0.0);
        final double penalty = 1e-03;
        final double init = 0.245;
        final double t = 0.2;
        final double result = (x + 1.0) / 2.0;
        final double numeratorAdd = 13;
        final double bhigh = 2 * (k - 1) * Math.acos();

        Assert.assertEquals(0.0, true);
        Assert.assertTrue(percentile.evaluate(singletonArray), 0);
        Assert.assertEquals( 0.0, getNumberOfTrials(0, 0), 1E-10);
        Assert.assertEquals(0.201949230731, percentile.evaluate(specialValues), 1.0e-3);
        Assert.assertEquals(-10.0, distribution.inverseCumulativeProbability(0.50), 0);
        Assert.assertEquals(0.0, solver.solve(100, f, 1.0, 0.5), 1.0e-10);
    }