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Java example source code file (SparseGradient.java)

This example Java source code file (SparseGradient.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

class, dimensionmismatchexception, double, field, fieldelement, hashmap, map, override, realfieldelement, serializable, sign, sparsegradient, util

The SparseGradient.java Java example source code

/*
 * 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.
 */
package org.apache.commons.math3.analysis.differentiation;

import java.io.Serializable;
import java.util.Collections;
import java.util.HashMap;
import java.util.Map;

import org.apache.commons.math3.Field;
import org.apache.commons.math3.FieldElement;
import org.apache.commons.math3.RealFieldElement;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.util.MathArrays;
import org.apache.commons.math3.util.MathUtils;
import org.apache.commons.math3.util.Precision;

/**
 * First derivative computation with large number of variables.
 * <p>
 * This class plays a similar role to {@link DerivativeStructure}, with
 * a focus on efficiency when dealing with large number of independent variables
 * and most computation depend only on a few of them, and when only first derivative
 * is desired. When these conditions are met, this class should be much faster than
 * {@link DerivativeStructure} and use less memory.
 * </p>
 *
 * @since 3.3
 */
public class SparseGradient implements RealFieldElement<SparseGradient>, Serializable {

    /** Serializable UID. */
    private static final long serialVersionUID = 20131025L;

    /** Value of the calculation. */
    private double value;

    /** Stored derivative, each key representing a different independent variable. */
    private final Map<Integer, Double> derivatives;

    /** Internal constructor.
     * @param value value of the function
     * @param derivatives derivatives map, a deep copy will be performed,
     * so the map given here will remain safe from changes in the new instance,
     * may be null to create an empty derivatives map, i.e. a constant value
     */
    private SparseGradient(final double value, final Map<Integer, Double> derivatives) {
        this.value = value;
        this.derivatives = new HashMap<Integer, Double>();
        if (derivatives != null) {
            this.derivatives.putAll(derivatives);
        }
    }

    /** Internal constructor.
     * @param value value of the function
     * @param scale scaling factor to apply to all derivatives
     * @param derivatives derivatives map, a deep copy will be performed,
     * so the map given here will remain safe from changes in the new instance,
     * may be null to create an empty derivatives map, i.e. a constant value
     */
    private SparseGradient(final double value, final double scale,
                             final Map<Integer, Double> derivatives) {
        this.value = value;
        this.derivatives = new HashMap<Integer, Double>();
        if (derivatives != null) {
            for (final Map.Entry<Integer, Double> entry : derivatives.entrySet()) {
                this.derivatives.put(entry.getKey(), scale * entry.getValue());
            }
        }
    }

    /** Factory method creating a constant.
     * @param value value of the constant
     * @return a new instance
     */
    public static SparseGradient createConstant(final double value) {
        return new SparseGradient(value, Collections.<Integer, Double> emptyMap());
    }

    /** Factory method creating an independent variable.
     * @param idx index of the variable
     * @param value value of the variable
     * @return a new instance
     */
    public static SparseGradient createVariable(final int idx, final double value) {
        return new SparseGradient(value, Collections.singletonMap(idx, 1.0));
    }

    /**
     * Find the number of variables.
     * @return number of variables
     */
    public int numVars() {
        return derivatives.size();
    }

    /**
     * Get the derivative with respect to a particular index variable.
     *
     * @param index index to differentiate with.
     * @return derivative with respect to a particular index variable
     */
    public double getDerivative(final int index) {
        final Double out = derivatives.get(index);
        return (out == null) ? 0.0 : out;
    }

    /**
     * Get the value of the function.
     * @return value of the function.
     */
    public double getValue() {
        return value;
    }

    /** {@inheritDoc} */
    public double getReal() {
        return value;
    }

    /** {@inheritDoc} */
    public SparseGradient add(final SparseGradient a) {
        final SparseGradient out = new SparseGradient(value + a.value, derivatives);
        for (Map.Entry<Integer, Double> entry : a.derivatives.entrySet()) {
            final int id = entry.getKey();
            final Double old = out.derivatives.get(id);
            if (old == null) {
                out.derivatives.put(id, entry.getValue());
            } else {
                out.derivatives.put(id, old + entry.getValue());
            }
        }

        return out;
    }

    /**
     * Add in place.
     * <p>
     * This method is designed to be faster when used multiple times in a loop.
     * </p>
     * <p>
     * The instance is changed here, in order to not change the
     * instance the {@link #add(SparseGradient)} method should
     * be used.
     * </p>
     * @param a instance to add
     */
    public void addInPlace(final SparseGradient a) {
        value += a.value;
        for (final Map.Entry<Integer, Double> entry : a.derivatives.entrySet()) {
            final int id = entry.getKey();
            final Double old = derivatives.get(id);
            if (old == null) {
                derivatives.put(id, entry.getValue());
            } else {
                derivatives.put(id, old + entry.getValue());
            }
        }
    }

    /** {@inheritDoc} */
    public SparseGradient add(final double c) {
        final SparseGradient out = new SparseGradient(value + c, derivatives);
        return out;
    }

    /** {@inheritDoc} */
    public SparseGradient subtract(final SparseGradient a) {
        final SparseGradient out = new SparseGradient(value - a.value, derivatives);
        for (Map.Entry<Integer, Double> entry : a.derivatives.entrySet()) {
            final int id = entry.getKey();
            final Double old = out.derivatives.get(id);
            if (old == null) {
                out.derivatives.put(id, -entry.getValue());
            } else {
                out.derivatives.put(id, old - entry.getValue());
            }
        }
        return out;
    }

    /** {@inheritDoc} */
    public SparseGradient subtract(double c) {
        return new SparseGradient(value - c, derivatives);
    }

    /** {@inheritDoc} */
    public SparseGradient multiply(final SparseGradient a) {
        final SparseGradient out =
            new SparseGradient(value * a.value, Collections.<Integer, Double> emptyMap());

        // Derivatives.
        for (Map.Entry<Integer, Double> entry : derivatives.entrySet()) {
            out.derivatives.put(entry.getKey(), a.value * entry.getValue());
        }
        for (Map.Entry<Integer, Double> entry : a.derivatives.entrySet()) {
            final int id = entry.getKey();
            final Double old = out.derivatives.get(id);
            if (old == null) {
                out.derivatives.put(id, value * entry.getValue());
            } else {
                out.derivatives.put(id, old + value * entry.getValue());
            }
        }
        return out;
    }

    /**
     * Multiply in place.
     * <p>
     * This method is designed to be faster when used multiple times in a loop.
     * </p>
     * <p>
     * The instance is changed here, in order to not change the
     * instance the {@link #add(SparseGradient)} method should
     * be used.
     * </p>
     * @param a instance to multiply
     */
    public void multiplyInPlace(final SparseGradient a) {
        // Derivatives.
        for (Map.Entry<Integer, Double> entry : derivatives.entrySet()) {
            derivatives.put(entry.getKey(), a.value * entry.getValue());
        }
        for (Map.Entry<Integer, Double> entry : a.derivatives.entrySet()) {
            final int id = entry.getKey();
            final Double old = derivatives.get(id);
            if (old == null) {
                derivatives.put(id, value * entry.getValue());
            } else {
                derivatives.put(id, old + value * entry.getValue());
            }
        }
        value *= a.value;
    }

    /** {@inheritDoc} */
    public SparseGradient multiply(final double c) {
        return new SparseGradient(value * c, c, derivatives);
    }

    /** {@inheritDoc} */
    public SparseGradient multiply(final int n) {
        return new SparseGradient(value * n, n, derivatives);
    }

    /** {@inheritDoc} */
    public SparseGradient divide(final SparseGradient a) {
        final SparseGradient out = new SparseGradient(value / a.value, Collections.<Integer, Double> emptyMap());

        // Derivatives.
        for (Map.Entry<Integer, Double> entry : derivatives.entrySet()) {
            out.derivatives.put(entry.getKey(), entry.getValue() / a.value);
        }
        for (Map.Entry<Integer, Double> entry : a.derivatives.entrySet()) {
            final int id = entry.getKey();
            final Double old = out.derivatives.get(id);
            if (old == null) {
                out.derivatives.put(id, -out.value / a.value * entry.getValue());
            } else {
                out.derivatives.put(id, old - out.value / a.value * entry.getValue());
            }
        }
        return out;
    }

    /** {@inheritDoc} */
    public SparseGradient divide(final double c) {
        return new SparseGradient(value / c, 1.0 / c, derivatives);
    }

    /** {@inheritDoc} */
    public SparseGradient negate() {
        return new SparseGradient(-value, -1.0, derivatives);
    }

    /** {@inheritDoc} */
    public Field<SparseGradient> getField() {
        return new Field<SparseGradient>() {

            /** {@inheritDoc} */
            public SparseGradient getZero() {
                return createConstant(0);
            }

            /** {@inheritDoc} */
            public SparseGradient getOne() {
                return createConstant(1);
            }

            /** {@inheritDoc} */
            public Class<? extends FieldElement getRuntimeClass() {
                return SparseGradient.class;
            }

        };
    }

    /** {@inheritDoc} */
    public SparseGradient remainder(final double a) {
        return new SparseGradient(FastMath.IEEEremainder(value, a), derivatives);
    }

    /** {@inheritDoc} */
    public SparseGradient remainder(final SparseGradient a) {

        // compute k such that lhs % rhs = lhs - k rhs
        final double rem = FastMath.IEEEremainder(value, a.value);
        final double k   = FastMath.rint((value - rem) / a.value);

        return subtract(a.multiply(k));

    }

    /** {@inheritDoc} */
    public SparseGradient abs() {
        if (Double.doubleToLongBits(value) < 0) {
            // we use the bits representation to also handle -0.0
            return negate();
        } else {
            return this;
        }
    }

    /** {@inheritDoc} */
    public SparseGradient ceil() {
        return createConstant(FastMath.ceil(value));
    }

    /** {@inheritDoc} */
    public SparseGradient floor() {
        return createConstant(FastMath.floor(value));
    }

    /** {@inheritDoc} */
    public SparseGradient rint() {
        return createConstant(FastMath.rint(value));
    }

    /** {@inheritDoc} */
    public long round() {
        return FastMath.round(value);
    }

    /** {@inheritDoc} */
    public SparseGradient signum() {
        return createConstant(FastMath.signum(value));
    }

    /** {@inheritDoc} */
    public SparseGradient copySign(final SparseGradient sign) {
        final long m = Double.doubleToLongBits(value);
        final long s = Double.doubleToLongBits(sign.value);
        if ((m >= 0 && s >= 0) || (m < 0 && s < 0)) { // Sign is currently OK
            return this;
        }
        return negate(); // flip sign
    }

    /** {@inheritDoc} */
    public SparseGradient copySign(final double sign) {
        final long m = Double.doubleToLongBits(value);
        final long s = Double.doubleToLongBits(sign);
        if ((m >= 0 && s >= 0) || (m < 0 && s < 0)) { // Sign is currently OK
            return this;
        }
        return negate(); // flip sign
    }

    /** {@inheritDoc} */
    public SparseGradient scalb(final int n) {
        final SparseGradient out = new SparseGradient(FastMath.scalb(value, n), Collections.<Integer, Double> emptyMap());
        for (Map.Entry<Integer, Double> entry : derivatives.entrySet()) {
            out.derivatives.put(entry.getKey(), FastMath.scalb(entry.getValue(), n));
        }
        return out;
    }

    /** {@inheritDoc} */
    public SparseGradient hypot(final SparseGradient y) {
        if (Double.isInfinite(value) || Double.isInfinite(y.value)) {
            return createConstant(Double.POSITIVE_INFINITY);
        } else if (Double.isNaN(value) || Double.isNaN(y.value)) {
            return createConstant(Double.NaN);
        } else {

            final int expX = FastMath.getExponent(value);
            final int expY = FastMath.getExponent(y.value);
            if (expX > expY + 27) {
                // y is negligible with respect to x
                return abs();
            } else if (expY > expX + 27) {
                // x is negligible with respect to y
                return y.abs();
            } else {

                // find an intermediate scale to avoid both overflow and underflow
                final int middleExp = (expX + expY) / 2;

                // scale parameters without losing precision
                final SparseGradient scaledX = scalb(-middleExp);
                final SparseGradient scaledY = y.scalb(-middleExp);

                // compute scaled hypotenuse
                final SparseGradient scaledH =
                        scaledX.multiply(scaledX).add(scaledY.multiply(scaledY)).sqrt();

                // remove scaling
                return scaledH.scalb(middleExp);

            }

        }
    }

    /**
     * Returns the hypotenuse of a triangle with sides {@code x} and {@code y}
     * - sqrt(<i>x2 +y2)
     * avoiding intermediate overflow or underflow.
     *
     * <ul>
     * <li> If either argument is infinite, then the result is positive infinity.
     * <li> else, if either argument is NaN then the result is NaN.
     * </ul>
     *
     * @param x a value
     * @param y a value
     * @return sqrt(<i>x2 +y2)
     */
    public static SparseGradient hypot(final SparseGradient x, final SparseGradient y) {
        return x.hypot(y);
    }

    /** {@inheritDoc} */
    public SparseGradient reciprocal() {
        return new SparseGradient(1.0 / value, -1.0 / (value * value), derivatives);
    }

    /** {@inheritDoc} */
    public SparseGradient sqrt() {
        final double sqrt = FastMath.sqrt(value);
        return new SparseGradient(sqrt, 0.5 / sqrt, derivatives);
    }

    /** {@inheritDoc} */
    public SparseGradient cbrt() {
        final double cbrt = FastMath.cbrt(value);
        return new SparseGradient(cbrt, 1.0 / (3 * cbrt * cbrt), derivatives);
    }

    /** {@inheritDoc} */
    public SparseGradient rootN(final int n) {
        if (n == 2) {
            return sqrt();
        } else if (n == 3) {
            return cbrt();
        } else {
            final double root = FastMath.pow(value, 1.0 / n);
            return new SparseGradient(root, 1.0 / (n * FastMath.pow(root, n - 1)), derivatives);
        }
    }

    /** {@inheritDoc} */
    public SparseGradient pow(final double p) {
        return new SparseGradient(FastMath.pow(value,  p), p * FastMath.pow(value,  p - 1), derivatives);
    }

    /** {@inheritDoc} */
    public SparseGradient pow(final int n) {
        if (n == 0) {
            return getField().getOne();
        } else {
            final double valueNm1 = FastMath.pow(value,  n - 1);
            return new SparseGradient(value * valueNm1, n * valueNm1, derivatives);
        }
    }

    /** {@inheritDoc} */
    public SparseGradient pow(final SparseGradient e) {
        return log().multiply(e).exp();
    }

    /** Compute a<sup>x where a is a double and x a {@link SparseGradient}
     * @param a number to exponentiate
     * @param x power to apply
     * @return a<sup>x
     */
    public static SparseGradient pow(final double a, final SparseGradient x) {
        if (a == 0) {
            if (x.value == 0) {
                return x.compose(1.0, Double.NEGATIVE_INFINITY);
            } else if (x.value < 0) {
                return x.compose(Double.NaN, Double.NaN);
            } else {
                return x.getField().getZero();
            }
        } else {
            final double ax = FastMath.pow(a, x.value);
            return new SparseGradient(ax, ax * FastMath.log(a), x.derivatives);
        }
    }

    /** {@inheritDoc} */
    public SparseGradient exp() {
        final double e = FastMath.exp(value);
        return new SparseGradient(e, e, derivatives);
    }

    /** {@inheritDoc} */
    public SparseGradient expm1() {
        return new SparseGradient(FastMath.expm1(value), FastMath.exp(value), derivatives);
    }

    /** {@inheritDoc} */
    public SparseGradient log() {
        return new SparseGradient(FastMath.log(value), 1.0 / value, derivatives);
    }

    /** Base 10 logarithm.
     * @return base 10 logarithm of the instance
     */
    public SparseGradient log10() {
        return new SparseGradient(FastMath.log10(value), 1.0 / (FastMath.log(10.0) * value), derivatives);
    }

    /** {@inheritDoc} */
    public SparseGradient log1p() {
        return new SparseGradient(FastMath.log1p(value), 1.0 / (1.0 + value), derivatives);
    }

    /** {@inheritDoc} */
    public SparseGradient cos() {
        return new SparseGradient(FastMath.cos(value), -FastMath.sin(value), derivatives);
    }

    /** {@inheritDoc} */
    public SparseGradient sin() {
        return new SparseGradient(FastMath.sin(value), FastMath.cos(value), derivatives);
    }

    /** {@inheritDoc} */
    public SparseGradient tan() {
        final double t = FastMath.tan(value);
        return new SparseGradient(t, 1 + t * t, derivatives);
    }

    /** {@inheritDoc} */
    public SparseGradient acos() {
        return new SparseGradient(FastMath.acos(value), -1.0 / FastMath.sqrt(1 - value * value), derivatives);
    }

    /** {@inheritDoc} */
    public SparseGradient asin() {
        return new SparseGradient(FastMath.asin(value), 1.0 / FastMath.sqrt(1 - value * value), derivatives);
    }

    /** {@inheritDoc} */
    public SparseGradient atan() {
        return new SparseGradient(FastMath.atan(value), 1.0 / (1 + value * value), derivatives);
    }

    /** {@inheritDoc} */
    public SparseGradient atan2(final SparseGradient x) {

        // compute r = sqrt(x^2+y^2)
        final SparseGradient r = multiply(this).add(x.multiply(x)).sqrt();

        final SparseGradient a;
        if (x.value >= 0) {

            // compute atan2(y, x) = 2 atan(y / (r + x))
            a = divide(r.add(x)).atan().multiply(2);

        } else {

            // compute atan2(y, x) = +/- pi - 2 atan(y / (r - x))
            final SparseGradient tmp = divide(r.subtract(x)).atan().multiply(-2);
            a = tmp.add(tmp.value <= 0 ? -FastMath.PI : FastMath.PI);

        }

        // fix value to take special cases (+0/+0, +0/-0, -0/+0, -0/-0, +/-infinity) correctly
        a.value = FastMath.atan2(value, x.value);

        return a;

    }

    /** Two arguments arc tangent operation.
     * @param y first argument of the arc tangent
     * @param x second argument of the arc tangent
     * @return atan2(y, x)
     */
    public static SparseGradient atan2(final SparseGradient y, final SparseGradient x) {
        return y.atan2(x);
    }

    /** {@inheritDoc} */
    public SparseGradient cosh() {
        return new SparseGradient(FastMath.cosh(value), FastMath.sinh(value), derivatives);
    }

    /** {@inheritDoc} */
    public SparseGradient sinh() {
        return new SparseGradient(FastMath.sinh(value), FastMath.cosh(value), derivatives);
    }

    /** {@inheritDoc} */
    public SparseGradient tanh() {
        final double t = FastMath.tanh(value);
        return new SparseGradient(t, 1 - t * t, derivatives);
    }

    /** {@inheritDoc} */
    public SparseGradient acosh() {
        return new SparseGradient(FastMath.acosh(value), 1.0 / FastMath.sqrt(value * value - 1.0), derivatives);
    }

    /** {@inheritDoc} */
    public SparseGradient asinh() {
        return new SparseGradient(FastMath.asinh(value), 1.0 / FastMath.sqrt(value * value + 1.0), derivatives);
    }

    /** {@inheritDoc} */
    public SparseGradient atanh() {
        return new SparseGradient(FastMath.atanh(value), 1.0 / (1.0 - value * value), derivatives);
    }

    /** Convert radians to degrees, with error of less than 0.5 ULP
     *  @return instance converted into degrees
     */
    public SparseGradient toDegrees() {
        return new SparseGradient(FastMath.toDegrees(value), FastMath.toDegrees(1.0), derivatives);
    }

    /** Convert degrees to radians, with error of less than 0.5 ULP
     *  @return instance converted into radians
     */
    public SparseGradient toRadians() {
        return new SparseGradient(FastMath.toRadians(value), FastMath.toRadians(1.0), derivatives);
    }

    /** Evaluate Taylor expansion of a sparse gradient.
     * @param delta parameters offsets (Δx, Δy, ...)
     * @return value of the Taylor expansion at x + Δx, y + Δy, ...
     */
    public double taylor(final double ... delta) {
        double y = value;
        for (int i = 0; i < delta.length; ++i) {
            y += delta[i] * getDerivative(i);
        }
        return y;
    }

    /** Compute composition of the instance by a univariate function.
     * @param f0 value of the function at (i.e. f({@link #getValue()}))
     * @param f1 first derivative of the function at
     * the current point (i.e. f'({@link #getValue()}))
     * @return f(this)
    */
    public SparseGradient compose(final double f0, final double f1) {
        return new SparseGradient(f0, f1, derivatives);
    }

    /** {@inheritDoc} */
    public SparseGradient linearCombination(final SparseGradient[] a,
                                              final SparseGradient[] b)
        throws DimensionMismatchException {

        // compute a simple value, with all partial derivatives
        SparseGradient out = a[0].getField().getZero();
        for (int i = 0; i < a.length; ++i) {
            out = out.add(a[i].multiply(b[i]));
        }

        // recompute an accurate value, taking care of cancellations
        final double[] aDouble = new double[a.length];
        for (int i = 0; i < a.length; ++i) {
            aDouble[i] = a[i].getValue();
        }
        final double[] bDouble = new double[b.length];
        for (int i = 0; i < b.length; ++i) {
            bDouble[i] = b[i].getValue();
        }
        out.value = MathArrays.linearCombination(aDouble, bDouble);

        return out;

    }

    /** {@inheritDoc} */
    public SparseGradient linearCombination(final double[] a, final SparseGradient[] b) {

        // compute a simple value, with all partial derivatives
        SparseGradient out = b[0].getField().getZero();
        for (int i = 0; i < a.length; ++i) {
            out = out.add(b[i].multiply(a[i]));
        }

        // recompute an accurate value, taking care of cancellations
        final double[] bDouble = new double[b.length];
        for (int i = 0; i < b.length; ++i) {
            bDouble[i] = b[i].getValue();
        }
        out.value = MathArrays.linearCombination(a, bDouble);

        return out;

    }

    /** {@inheritDoc} */
    public SparseGradient linearCombination(final SparseGradient a1, final SparseGradient b1,
                                              final SparseGradient a2, final SparseGradient b2) {

        // compute a simple value, with all partial derivatives
        SparseGradient out = a1.multiply(b1).add(a2.multiply(b2));

        // recompute an accurate value, taking care of cancellations
        out.value = MathArrays.linearCombination(a1.value, b1.value, a2.value, b2.value);

        return out;

    }

    /** {@inheritDoc} */
    public SparseGradient linearCombination(final double a1, final SparseGradient b1,
                                              final double a2, final SparseGradient b2) {

        // compute a simple value, with all partial derivatives
        SparseGradient out = b1.multiply(a1).add(b2.multiply(a2));

        // recompute an accurate value, taking care of cancellations
        out.value = MathArrays.linearCombination(a1, b1.value, a2, b2.value);

        return out;

    }

    /** {@inheritDoc} */
    public SparseGradient linearCombination(final SparseGradient a1, final SparseGradient b1,
                                              final SparseGradient a2, final SparseGradient b2,
                                              final SparseGradient a3, final SparseGradient b3) {

        // compute a simple value, with all partial derivatives
        SparseGradient out = a1.multiply(b1).add(a2.multiply(b2)).add(a3.multiply(b3));

        // recompute an accurate value, taking care of cancellations
        out.value = MathArrays.linearCombination(a1.value, b1.value,
                                                 a2.value, b2.value,
                                                 a3.value, b3.value);

        return out;

    }

    /** {@inheritDoc} */
    public SparseGradient linearCombination(final double a1, final SparseGradient b1,
                                              final double a2, final SparseGradient b2,
                                              final double a3, final SparseGradient b3) {

        // compute a simple value, with all partial derivatives
        SparseGradient out = b1.multiply(a1).add(b2.multiply(a2)).add(b3.multiply(a3));

        // recompute an accurate value, taking care of cancellations
        out.value = MathArrays.linearCombination(a1, b1.value,
                                                 a2, b2.value,
                                                 a3, b3.value);

        return out;

    }

    /** {@inheritDoc} */
    public SparseGradient linearCombination(final SparseGradient a1, final SparseGradient b1,
                                              final SparseGradient a2, final SparseGradient b2,
                                              final SparseGradient a3, final SparseGradient b3,
                                              final SparseGradient a4, final SparseGradient b4) {

        // compute a simple value, with all partial derivatives
        SparseGradient out = a1.multiply(b1).add(a2.multiply(b2)).add(a3.multiply(b3)).add(a4.multiply(b4));

        // recompute an accurate value, taking care of cancellations
        out.value = MathArrays.linearCombination(a1.value, b1.value,
                                                 a2.value, b2.value,
                                                 a3.value, b3.value,
                                                 a4.value, b4.value);

        return out;

    }

    /** {@inheritDoc} */
    public SparseGradient linearCombination(final double a1, final SparseGradient b1,
                                              final double a2, final SparseGradient b2,
                                              final double a3, final SparseGradient b3,
                                              final double a4, final SparseGradient b4) {

        // compute a simple value, with all partial derivatives
        SparseGradient out = b1.multiply(a1).add(b2.multiply(a2)).add(b3.multiply(a3)).add(b4.multiply(a4));

        // recompute an accurate value, taking care of cancellations
        out.value = MathArrays.linearCombination(a1, b1.value,
                                                 a2, b2.value,
                                                 a3, b3.value,
                                                 a4, b4.value);

        return out;

    }

    /**
     * Test for the equality of two sparse gradients.
     * <p>
     * Sparse gradients are considered equal if they have the same value
     * and the same derivatives.
     * </p>
     * @param other Object to test for equality to this
     * @return true if two sparse gradients are equal
     */
    @Override
    public boolean equals(Object other) {

        if (this == other) {
            return true;
        }

        if (other instanceof SparseGradient) {
            final SparseGradient rhs = (SparseGradient)other;
            if (!Precision.equals(value, rhs.value, 1)) {
                return false;
            }
            if (derivatives.size() != rhs.derivatives.size()) {
                return false;
            }
            for (final Map.Entry<Integer, Double> entry : derivatives.entrySet()) {
                if (!rhs.derivatives.containsKey(entry.getKey())) {
                    return false;
                }
                if (!Precision.equals(entry.getValue(), rhs.derivatives.get(entry.getKey()), 1)) {
                    return false;
                }
            }
            return true;
        }

        return false;

    }

    /**
     * Get a hashCode for the derivative structure.
     * @return a hash code value for this object
     * @since 3.2
     */
    @Override
    public int hashCode() {
        return 743 + 809 * MathUtils.hash(value) + 167 * derivatives.hashCode();
    }

}

Other Java examples (source code examples)

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my book on functional programming

 

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