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The Apache Commons Math project is a library of lightweight, self-contained mathematics and statistics components addressing the most common practical problems not immediately available in the Java programming language or commons-lang.
/*
* 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;
import org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
import org.apache.commons.math3.analysis.differentiation.MultivariateDifferentiableFunction;
import org.apache.commons.math3.analysis.differentiation.MultivariateDifferentiableVectorFunction;
import org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
import org.apache.commons.math3.analysis.function.Identity;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.NotStrictlyPositiveException;
import org.apache.commons.math3.exception.NumberIsTooLargeException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
/**
* Utilities for manipulating function objects.
*
* @version $Id: FunctionUtils.java 1401837 2012-10-24 19:39:45Z luc $
* @since 3.0
*/
public class FunctionUtils {
/**
* Class only contains static methods.
*/
private FunctionUtils() {}
/**
* Composes functions.
*
* The functions in the argument list are composed sequentially, in the
* given order. For example, compose(f1,f2,f3) acts like f1(f2(f3(x))).
*
* @param f List of functions.
* @return the composite function.
*/
public static UnivariateFunction compose(final UnivariateFunction ... f) {
return new UnivariateFunction() {
/** {@inheritDoc} */
public double value(double x) {
double r = x;
for (int i = f.length - 1; i >= 0; i--) {
r = f[i].value(r);
}
return r;
}
};
}
/**
* Composes functions.
*
* The functions in the argument list are composed sequentially, in the
* given order. For example, compose(f1,f2,f3) acts like f1(f2(f3(x))).
*
* @param f List of functions.
* @return the composite function.
* @since 3.1
*/
public static UnivariateDifferentiableFunction compose(final UnivariateDifferentiableFunction ... f) {
return new UnivariateDifferentiableFunction() {
/** {@inheritDoc} */
public double value(final double t) {
double r = t;
for (int i = f.length - 1; i >= 0; i--) {
r = f[i].value(r);
}
return r;
}
/** {@inheritDoc} */
public DerivativeStructure value(final DerivativeStructure t) {
DerivativeStructure r = t;
for (int i = f.length - 1; i >= 0; i--) {
r = f[i].value(r);
}
return r;
}
};
}
/**
* Composes functions.
*
* The functions in the argument list are composed sequentially, in the
* given order. For example, compose(f1,f2,f3) acts like f1(f2(f3(x))).
*
* @param f List of functions.
* @return the composite function.
* @deprecated as of 3.1 replaced by {@link #compose(UnivariateDifferentiableFunction...)}
*/
public static DifferentiableUnivariateFunction compose(final DifferentiableUnivariateFunction ... f) {
return new DifferentiableUnivariateFunction() {
/** {@inheritDoc} */
public double value(double x) {
double r = x;
for (int i = f.length - 1; i >= 0; i--) {
r = f[i].value(r);
}
return r;
}
/** {@inheritDoc} */
public UnivariateFunction derivative() {
return new UnivariateFunction() {
/** {@inheritDoc} */
public double value(double x) {
double p = 1;
double r = x;
for (int i = f.length - 1; i >= 0; i--) {
p *= f[i].derivative().value(r);
r = f[i].value(r);
}
return p;
}
};
}
};
}
/**
* Adds functions.
*
* @param f List of functions.
* @return a function that computes the sum of the functions.
*/
public static UnivariateFunction add(final UnivariateFunction ... f) {
return new UnivariateFunction() {
/** {@inheritDoc} */
public double value(double x) {
double r = f[0].value(x);
for (int i = 1; i < f.length; i++) {
r += f[i].value(x);
}
return r;
}
};
}
/**
* Adds functions.
*
* @param f List of functions.
* @return a function that computes the sum of the functions.
* @since 3.1
*/
public static UnivariateDifferentiableFunction add(final UnivariateDifferentiableFunction ... f) {
return new UnivariateDifferentiableFunction() {
/** {@inheritDoc} */
public double value(final double t) {
double r = f[0].value(t);
for (int i = 1; i < f.length; i++) {
r += f[i].value(t);
}
return r;
}
/** {@inheritDoc} */
public DerivativeStructure value(final DerivativeStructure t) {
DerivativeStructure r = f[0].value(t);
for (int i = 1; i < f.length; i++) {
r = r.add(f[i].value(t));
}
return r;
}
};
}
/**
* Adds functions.
*
* @param f List of functions.
* @return a function that computes the sum of the functions.
* @deprecated as of 3.1 replaced by {@link #add(UnivariateDifferentiableFunction...)}
*/
@Deprecated
public static DifferentiableUnivariateFunction add(final DifferentiableUnivariateFunction ... f) {
return new DifferentiableUnivariateFunction() {
/** {@inheritDoc} */
public double value(double x) {
double r = f[0].value(x);
for (int i = 1; i < f.length; i++) {
r += f[i].value(x);
}
return r;
}
/** {@inheritDoc} */
public UnivariateFunction derivative() {
return new UnivariateFunction() {
/** {@inheritDoc} */
public double value(double x) {
double r = f[0].derivative().value(x);
for (int i = 1; i < f.length; i++) {
r += f[i].derivative().value(x);
}
return r;
}
};
}
};
}
/**
* Multiplies functions.
*
* @param f List of functions.
* @return a function that computes the product of the functions.
*/
public static UnivariateFunction multiply(final UnivariateFunction ... f) {
return new UnivariateFunction() {
/** {@inheritDoc} */
public double value(double x) {
double r = f[0].value(x);
for (int i = 1; i < f.length; i++) {
r *= f[i].value(x);
}
return r;
}
};
}
/**
* Multiplies functions.
*
* @param f List of functions.
* @return a function that computes the product of the functions.
* @since 3.1
*/
public static UnivariateDifferentiableFunction multiply(final UnivariateDifferentiableFunction ... f) {
return new UnivariateDifferentiableFunction() {
/** {@inheritDoc} */
public double value(final double t) {
double r = f[0].value(t);
for (int i = 1; i < f.length; i++) {
r *= f[i].value(t);
}
return r;
}
/** {@inheritDoc} */
public DerivativeStructure value(final DerivativeStructure t) {
DerivativeStructure r = f[0].value(t);
for (int i = 1; i < f.length; i++) {
r = r.multiply(f[i].value(t));
}
return r;
}
};
}
/**
* Multiplies functions.
*
* @param f List of functions.
* @return a function that computes the product of the functions.
* @deprecated as of 3.1 replaced by {@link #multiply(UnivariateDifferentiableFunction...)}
*/
public static DifferentiableUnivariateFunction multiply(final DifferentiableUnivariateFunction ... f) {
return new DifferentiableUnivariateFunction() {
/** {@inheritDoc} */
public double value(double x) {
double r = f[0].value(x);
for (int i = 1; i < f.length; i++) {
r *= f[i].value(x);
}
return r;
}
/** {@inheritDoc} */
public UnivariateFunction derivative() {
return new UnivariateFunction() {
/** {@inheritDoc} */
public double value(double x) {
double sum = 0;
for (int i = 0; i < f.length; i++) {
double prod = f[i].derivative().value(x);
for (int j = 0; j < f.length; j++) {
if (i != j) {
prod *= f[j].value(x);
}
}
sum += prod;
}
return sum;
}
};
}
};
}
/**
* Returns the univariate function
* {@code h(x) = combiner(f(x), g(x))}.
*
* @param combiner Combiner function.
* @param f Function.
* @param g Function.
* @return the composite function.
*/
public static UnivariateFunction combine(final BivariateFunction combiner,
final UnivariateFunction f,
final UnivariateFunction g) {
return new UnivariateFunction() {
/** {@inheritDoc} */
public double value(double x) {
return combiner.value(f.value(x), g.value(x));
}
};
}
/**
* Returns a MultivariateFunction h(x[]) defined by
* h(x[]) = combiner(...combiner(combiner(initialValue,f(x[0])),f(x[1]))...),f(x[x.length-1]))
*
*
* @param combiner Combiner function.
* @param f Function.
* @param initialValue Initial value.
* @return a collector function.
*/
public static MultivariateFunction collector(final BivariateFunction combiner,
final UnivariateFunction f,
final double initialValue) {
return new MultivariateFunction() {
/** {@inheritDoc} */
public double value(double[] point) {
double result = combiner.value(initialValue, f.value(point[0]));
for (int i = 1; i < point.length; i++) {
result = combiner.value(result, f.value(point[i]));
}
return result;
}
};
}
/**
* Returns a MultivariateFunction h(x[]) defined by
* h(x[]) = combiner(...combiner(combiner(initialValue,x[0]),x[1])...),x[x.length-1])
*
*
* @param combiner Combiner function.
* @param initialValue Initial value.
* @return a collector function.
*/
public static MultivariateFunction collector(final BivariateFunction combiner,
final double initialValue) {
return collector(combiner, new Identity(), initialValue);
}
/**
* Creates a unary function by fixing the first argument of a binary function.
*
* @param f Binary function.
* @param fixed Value to which the first argument of {@code f} is set.
* @return the unary function h(x) = f(fixed, x)
*/
public static UnivariateFunction fix1stArgument(final BivariateFunction f,
final double fixed) {
return new UnivariateFunction() {
/** {@inheritDoc} */
public double value(double x) {
return f.value(fixed, x);
}
};
}
/**
* Creates a unary function by fixing the second argument of a binary function.
*
* @param f Binary function.
* @param fixed Value to which the second argument of {@code f} is set.
* @return the unary function h(x) = f(x, fixed)
*/
public static UnivariateFunction fix2ndArgument(final BivariateFunction f,
final double fixed) {
return new UnivariateFunction() {
/** {@inheritDoc} */
public double value(double x) {
return f.value(x, fixed);
}
};
}
/**
* Samples the specified univariate real function on the specified interval.
*
* The interval is divided equally into {@code n} sections and sample points
* are taken from {@code min} to {@code max - (max - min) / n}; therefore
* {@code f} is not sampled at the upper bound {@code max}.
*
* @param f Function to be sampled
* @param min Lower bound of the interval (included).
* @param max Upper bound of the interval (excluded).
* @param n Number of sample points.
* @return the array of samples.
* @throws NumberIsTooLargeException if the lower bound {@code min} is
* greater than, or equal to the upper bound {@code max}.
* @throws NotStrictlyPositiveException if the number of sample points
* {@code n} is negative.
*/
public static double[] sample(UnivariateFunction f,
double min, double max, int n) {
if (n <= 0) {
throw new NotStrictlyPositiveException(
LocalizedFormats.NOT_POSITIVE_NUMBER_OF_SAMPLES,
Integer.valueOf(n));
}
if (min >= max) {
throw new NumberIsTooLargeException(min, max, false);
}
final double[] s = new double[n];
final double h = (max - min) / n;
for (int i = 0; i < n; i++) {
s[i] = f.value(min + i * h);
}
return s;
}
/** Convert a {@link UnivariateDifferentiableFunction} into a {@link DifferentiableUnivariateFunction}.
* @param f function to convert
* @return converted function
* @deprecated this conversion method is temporary in version 3.1, as the {@link
* DifferentiableUnivariateFunction} interface itself is deprecated
*/
@Deprecated
public static DifferentiableUnivariateFunction toDifferentiableUnivariateFunction(final UnivariateDifferentiableFunction f) {
return new DifferentiableUnivariateFunction() {
/** {@inheritDoc} */
public double value(final double x) {
return f.value(x);
}
/** {@inheritDoc} */
public UnivariateFunction derivative() {
return new UnivariateFunction() {
/** {@inheritDoc} */
public double value(final double x) {
return f.value(new DerivativeStructure(1, 1, 0, x)).getPartialDerivative(1);
}
};
}
};
}
/** Convert a {@link DifferentiableUnivariateFunction} into a {@link UnivariateDifferentiableFunction}.
*
* Note that the converted function is able to handle {@link DerivativeStructure} up to order one.
* If the function is called with higher order, a {@link NumberIsTooLargeException} will be thrown.
*
* @param f function to convert
* @return converted function
* @deprecated this conversion method is temporary in version 3.1, as the {@link
* DifferentiableUnivariateFunction} interface itself is deprecated
*/
@Deprecated
public static UnivariateDifferentiableFunction toUnivariateDifferential(final DifferentiableUnivariateFunction f) {
return new UnivariateDifferentiableFunction() {
/** {@inheritDoc} */
public double value(final double x) {
return f.value(x);
}
/** {@inheritDoc}
* @exception NumberIsTooLargeException if derivation order is greater than 1
*/
public DerivativeStructure value(final DerivativeStructure t)
throws NumberIsTooLargeException {
switch (t.getOrder()) {
case 0 :
return new DerivativeStructure(t.getFreeParameters(), 0, f.value(t.getValue()));
case 1 : {
final int parameters = t.getFreeParameters();
final double[] derivatives = new double[parameters + 1];
derivatives[0] = f.value(t.getValue());
final double fPrime = f.derivative().value(t.getValue());
int[] orders = new int[parameters];
for (int i = 0; i < parameters; ++i) {
orders[i] = 1;
derivatives[i + 1] = fPrime * t.getPartialDerivative(orders);
orders[i] = 0;
}
return new DerivativeStructure(parameters, 1, derivatives);
}
default :
throw new NumberIsTooLargeException(t.getOrder(), 1, true);
}
}
};
}
/** Convert a {@link MultivariateDifferentiableFunction} into a {@link DifferentiableMultivariateFunction}.
* @param f function to convert
* @return converted function
* @deprecated this conversion method is temporary in version 3.1, as the {@link
* DifferentiableMultivariateFunction} interface itself is deprecated
*/
@Deprecated
public static DifferentiableMultivariateFunction toDifferentiableMultivariateFunction(final MultivariateDifferentiableFunction f) {
return new DifferentiableMultivariateFunction() {
/** {@inheritDoc} */
public double value(final double[] x) {
return f.value(x);
}
/** {@inheritDoc} */
public MultivariateFunction partialDerivative(final int k) {
return new MultivariateFunction() {
/** {@inheritDoc} */
public double value(final double[] x) {
final int n = x.length;
// delegate computation to underlying function
final DerivativeStructure[] dsX = new DerivativeStructure[n];
for (int i = 0; i < n; ++i) {
if (i == k) {
dsX[i] = new DerivativeStructure(1, 1, 0, x[i]);
} else {
dsX[i] = new DerivativeStructure(1, 1, x[i]);
}
}
final DerivativeStructure y = f.value(dsX);
// extract partial derivative
return y.getPartialDerivative(1);
}
};
}
public MultivariateVectorFunction gradient() {
return new MultivariateVectorFunction() {
/** {@inheritDoc} */
public double[] value(final double[] x) {
final int n = x.length;
// delegate computation to underlying function
final DerivativeStructure[] dsX = new DerivativeStructure[n];
for (int i = 0; i < n; ++i) {
dsX[i] = new DerivativeStructure(n, 1, i, x[i]);
}
final DerivativeStructure y = f.value(dsX);
// extract gradient
final double[] gradient = new double[n];
final int[] orders = new int[n];
for (int i = 0; i < n; ++i) {
orders[i] = 1;
gradient[i] = y.getPartialDerivative(orders);
orders[i] = 0;
}
return gradient;
}
};
}
};
}
/** Convert a {@link DifferentiableMultivariateFunction} into a {@link MultivariateDifferentiableFunction}.
*
* Note that the converted function is able to handle {@link DerivativeStructure} elements
* that all have the same number of free parameters and order, and with order at most 1.
* If the function is called with inconsistent numbers of free parameters or higher order, a
* {@link DimensionMismatchException} or a {@link NumberIsTooLargeException} will be thrown.
*
* @param f function to convert
* @return converted function
* @deprecated this conversion method is temporary in version 3.1, as the {@link
* DifferentiableMultivariateFunction} interface itself is deprecated
*/
@Deprecated
public static MultivariateDifferentiableFunction toMultivariateDifferentiableFunction(final DifferentiableMultivariateFunction f) {
return new MultivariateDifferentiableFunction() {
/** {@inheritDoc} */
public double value(final double[] x) {
return f.value(x);
}
/** {@inheritDoc}
* @exception DimensionMismatchException if number of parameters or derivation
* order are higher than 1
*/
public DerivativeStructure value(final DerivativeStructure[] t)
throws DimensionMismatchException, NumberIsTooLargeException {
// check parameters and orders limits
final int parameters = t[0].getFreeParameters();
final int order = t[0].getOrder();
final int n = t.length;
if (order > 1) {
throw new NumberIsTooLargeException(order, 1, true);
}
// check all elements in the array are consistent
for (int i = 0; i < n; ++i) {
if (t[i].getFreeParameters() != parameters) {
throw new DimensionMismatchException(t[i].getFreeParameters(), parameters);
}
if (t[i].getOrder() != order) {
throw new DimensionMismatchException(t[i].getOrder(), order);
}
}
// delegate computation to underlying function
final double[] point = new double[n];
for (int i = 0; i < n; ++i) {
point[i] = t[i].getValue();
}
final double value = f.value(point);
final double[] gradient = f.gradient().value(point);
// merge value and gradient into one DerivativeStructure
final double[] derivatives = new double[parameters + 1];
derivatives[0] = value;
final int[] orders = new int[parameters];
for (int i = 0; i < parameters; ++i) {
orders[i] = 1;
for (int j = 0; j < n; ++j) {
derivatives[i + 1] += gradient[j] * t[j].getPartialDerivative(orders);
}
orders[i] = 0;
}
return new DerivativeStructure(parameters, order, derivatives);
}
};
}
/** Convert a {@link MultivariateDifferentiableVectorFunction} into a {@link DifferentiableMultivariateVectorFunction}.
* @param f function to convert
* @return converted function
* @deprecated this conversion method is temporary in version 3.1, as the {@link
* DifferentiableMultivariateVectorFunction} interface itself is deprecated
*/
@Deprecated
public static DifferentiableMultivariateVectorFunction toDifferentiableMultivariateVectorFunction(final MultivariateDifferentiableVectorFunction f) {
return new DifferentiableMultivariateVectorFunction() {
/** {@inheritDoc} */
public double[] value(final double[] x) {
return f.value(x);
}
public MultivariateMatrixFunction jacobian() {
return new MultivariateMatrixFunction() {
/** {@inheritDoc} */
public double[][] value(final double[] x) {
final int n = x.length;
// delegate computation to underlying function
final DerivativeStructure[] dsX = new DerivativeStructure[n];
for (int i = 0; i < n; ++i) {
dsX[i] = new DerivativeStructure(n, 1, i, x[i]);
}
final DerivativeStructure[] y = f.value(dsX);
// extract Jacobian
final double[][] jacobian = new double[y.length][n];
final int[] orders = new int[n];
for (int i = 0; i < y.length; ++i) {
for (int j = 0; j < n; ++j) {
orders[j] = 1;
jacobian[i][j] = y[i].getPartialDerivative(orders);
orders[j] = 0;
}
}
return jacobian;
}
};
}
};
}
/** Convert a {@link DifferentiableMultivariateVectorFunction} into a {@link MultivariateDifferentiableVectorFunction}.
*
* Note that the converted function is able to handle {@link DerivativeStructure} elements
* that all have the same number of free parameters and order, and with order at most 1.
* If the function is called with inconsistent numbers of free parameters or higher order, a
* {@link DimensionMismatchException} or a {@link NumberIsTooLargeException} will be thrown.
*
* @param f function to convert
* @return converted function
* @deprecated this conversion method is temporary in version 3.1, as the {@link
* DifferentiableMultivariateFunction} interface itself is deprecated
*/
@Deprecated
public static MultivariateDifferentiableVectorFunction toMultivariateDifferentiableVectorFunction(final DifferentiableMultivariateVectorFunction f) {
return new MultivariateDifferentiableVectorFunction() {
/** {@inheritDoc} */
public double[] value(final double[] x) {
return f.value(x);
}
/** {@inheritDoc}
* @exception DimensionMismatchException if number of parameters or derivation
* order are higher than 1
*/
public DerivativeStructure[] value(final DerivativeStructure[] t)
throws DimensionMismatchException, NumberIsTooLargeException {
// check parameters and orders limits
final int parameters = t[0].getFreeParameters();
final int order = t[0].getOrder();
final int n = t.length;
if (order > 1) {
throw new NumberIsTooLargeException(order, 1, true);
}
// check all elements in the array are consistent
for (int i = 0; i < n; ++i) {
if (t[i].getFreeParameters() != parameters) {
throw new DimensionMismatchException(t[i].getFreeParameters(), parameters);
}
if (t[i].getOrder() != order) {
throw new DimensionMismatchException(t[i].getOrder(), order);
}
}
// delegate computation to underlying function
final double[] point = new double[n];
for (int i = 0; i < n; ++i) {
point[i] = t[i].getValue();
}
final double[] value = f.value(point);
final double[][] jacobian = f.jacobian().value(point);
// merge value and Jacobian into a DerivativeStructure array
final DerivativeStructure[] merged = new DerivativeStructure[value.length];
for (int k = 0; k < merged.length; ++k) {
final double[] derivatives = new double[parameters + 1];
derivatives[0] = value[k];
final int[] orders = new int[parameters];
for (int i = 0; i < parameters; ++i) {
orders[i] = 1;
for (int j = 0; j < n; ++j) {
derivatives[i + 1] += jacobian[k][j] * t[j].getPartialDerivative(orders);
}
orders[i] = 0;
}
merged[k] = new DerivativeStructure(parameters, order, derivatives);
}
return merged;
}
};
}
}