FieldPolynomialFunction.java
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* Licensed to the Hipparchus project under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The Hipparchus project 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
*
* https://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
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package org.hipparchus.analysis.polynomials;
import org.hipparchus.CalculusFieldElement;
import org.hipparchus.Field;
import org.hipparchus.analysis.CalculusFieldUnivariateFunction;
import org.hipparchus.exception.LocalizedCoreFormats;
import org.hipparchus.exception.MathIllegalArgumentException;
import org.hipparchus.exception.NullArgumentException;
import org.hipparchus.util.FastMath;
import org.hipparchus.util.MathArrays;
import org.hipparchus.util.MathUtils;
/**
* Immutable representation of a real polynomial function with real coefficients.
* <p>
* <a href="http://mathworld.wolfram.com/HornersMethod.html">Horner's Method</a>
* is used to evaluate the function.</p>
* @param <T> the type of the field elements
* @since 1.5
*
*/
public class FieldPolynomialFunction<T extends CalculusFieldElement<T>> implements CalculusFieldUnivariateFunction<T> {
/**
* The coefficients of the polynomial, ordered by degree -- i.e.,
* coefficients[0] is the constant term and coefficients[n] is the
* coefficient of x^n where n is the degree of the polynomial.
*/
private final T[] coefficients;
/**
* Construct a polynomial with the given coefficients. The first element
* of the coefficients array is the constant term. Higher degree
* coefficients follow in sequence. The degree of the resulting polynomial
* is the index of the last non-null element of the array, or 0 if all elements
* are null.
* <p>
* The constructor makes a copy of the input array and assigns the copy to
* the coefficients property.</p>
*
* @param c Polynomial coefficients.
* @throws NullArgumentException if {@code c} is {@code null}.
* @throws MathIllegalArgumentException if {@code c} is empty.
*/
public FieldPolynomialFunction(final T[] c)
throws MathIllegalArgumentException, NullArgumentException {
super();
MathUtils.checkNotNull(c);
int n = c.length;
if (n == 0) {
throw new MathIllegalArgumentException(LocalizedCoreFormats.EMPTY_POLYNOMIALS_COEFFICIENTS_ARRAY);
}
while ((n > 1) && (c[n - 1].isZero())) {
--n;
}
this.coefficients = MathArrays.buildArray(c[0].getField(), n);
System.arraycopy(c, 0, this.coefficients, 0, n);
}
/**
* Compute the value of the function for the given argument.
* <p>
* The value returned is </p><p>
* {@code coefficients[n] * x^n + ... + coefficients[1] * x + coefficients[0]}
* </p>
*
* @param x Argument for which the function value should be computed.
* @return the value of the polynomial at the given point.
*
* @see org.hipparchus.analysis.UnivariateFunction#value(double)
*/
public T value(double x) {
return evaluate(coefficients, getField().getZero().add(x));
}
/**
* Compute the value of the function for the given argument.
* <p>
* The value returned is </p><p>
* {@code coefficients[n] * x^n + ... + coefficients[1] * x + coefficients[0]}
* </p>
*
* @param x Argument for which the function value should be computed.
* @return the value of the polynomial at the given point.
*
* @see org.hipparchus.analysis.UnivariateFunction#value(double)
*/
@Override
public T value(T x) {
return evaluate(coefficients, x);
}
/** Get the {@link Field} to which the instance belongs.
* @return {@link Field} to which the instance belongs
*/
public Field<T> getField() {
return coefficients[0].getField();
}
/**
* Returns the degree of the polynomial.
*
* @return the degree of the polynomial.
*/
public int degree() {
return coefficients.length - 1;
}
/**
* Returns a copy of the coefficients array.
* <p>
* Changes made to the returned copy will not affect the coefficients of
* the polynomial.</p>
*
* @return a fresh copy of the coefficients array.
*/
public T[] getCoefficients() {
return coefficients.clone();
}
/**
* Uses Horner's Method to evaluate the polynomial with the given coefficients at
* the argument.
*
* @param coefficients Coefficients of the polynomial to evaluate.
* @param argument Input value.
* @param <T> the type of the field elements
* @return the value of the polynomial.
* @throws MathIllegalArgumentException if {@code coefficients} is empty.
* @throws NullArgumentException if {@code coefficients} is {@code null}.
*/
protected static <T extends CalculusFieldElement<T>> T evaluate(T[] coefficients, T argument)
throws MathIllegalArgumentException, NullArgumentException {
MathUtils.checkNotNull(coefficients);
int n = coefficients.length;
if (n == 0) {
throw new MathIllegalArgumentException(LocalizedCoreFormats.EMPTY_POLYNOMIALS_COEFFICIENTS_ARRAY);
}
T result = coefficients[n - 1];
for (int j = n - 2; j >= 0; j--) {
result = argument.multiply(result).add(coefficients[j]);
}
return result;
}
/**
* Add a polynomial to the instance.
*
* @param p Polynomial to add.
* @return a new polynomial which is the sum of the instance and {@code p}.
*/
public FieldPolynomialFunction<T> add(final FieldPolynomialFunction<T> p) {
// identify the lowest degree polynomial
final int lowLength = FastMath.min(coefficients.length, p.coefficients.length);
final int highLength = FastMath.max(coefficients.length, p.coefficients.length);
// build the coefficients array
T[] newCoefficients = MathArrays.buildArray(getField(), highLength);
for (int i = 0; i < lowLength; ++i) {
newCoefficients[i] = coefficients[i].add(p.coefficients[i]);
}
System.arraycopy((coefficients.length < p.coefficients.length) ?
p.coefficients : coefficients,
lowLength,
newCoefficients, lowLength,
highLength - lowLength);
return new FieldPolynomialFunction<>(newCoefficients);
}
/**
* Subtract a polynomial from the instance.
*
* @param p Polynomial to subtract.
* @return a new polynomial which is the instance minus {@code p}.
*/
public FieldPolynomialFunction<T> subtract(final FieldPolynomialFunction<T> p) {
// identify the lowest degree polynomial
int lowLength = FastMath.min(coefficients.length, p.coefficients.length);
int highLength = FastMath.max(coefficients.length, p.coefficients.length);
// build the coefficients array
T[] newCoefficients = MathArrays.buildArray(getField(), highLength);
for (int i = 0; i < lowLength; ++i) {
newCoefficients[i] = coefficients[i].subtract(p.coefficients[i]);
}
if (coefficients.length < p.coefficients.length) {
for (int i = lowLength; i < highLength; ++i) {
newCoefficients[i] = p.coefficients[i].negate();
}
} else {
System.arraycopy(coefficients, lowLength, newCoefficients, lowLength,
highLength - lowLength);
}
return new FieldPolynomialFunction<>(newCoefficients);
}
/**
* Negate the instance.
*
* @return a new polynomial with all coefficients negated
*/
public FieldPolynomialFunction<T> negate() {
final T[] newCoefficients = MathArrays.buildArray(getField(), coefficients.length);
for (int i = 0; i < coefficients.length; ++i) {
newCoefficients[i] = coefficients[i].negate();
}
return new FieldPolynomialFunction<>(newCoefficients);
}
/**
* Multiply the instance by a polynomial.
*
* @param p Polynomial to multiply by.
* @return a new polynomial equal to this times {@code p}
*/
public FieldPolynomialFunction<T> multiply(final FieldPolynomialFunction<T> p) {
final Field<T> field = getField();
final T[] newCoefficients = MathArrays.buildArray(field, coefficients.length + p.coefficients.length - 1);
for (int i = 0; i < newCoefficients.length; ++i) {
newCoefficients[i] = field.getZero();
for (int j = FastMath.max(0, i + 1 - p.coefficients.length);
j < FastMath.min(coefficients.length, i + 1);
++j) {
newCoefficients[i] = newCoefficients[i].add(coefficients[j].multiply(p.coefficients[i-j]));
}
}
return new FieldPolynomialFunction<>(newCoefficients);
}
/**
* Returns the coefficients of the derivative of the polynomial with the given coefficients.
*
* @param coefficients Coefficients of the polynomial to differentiate.
* @param <T> the type of the field elements
* @return the coefficients of the derivative or {@code null} if coefficients has length 1.
* @throws MathIllegalArgumentException if {@code coefficients} is empty.
* @throws NullArgumentException if {@code coefficients} is {@code null}.
*/
protected static <T extends CalculusFieldElement<T>> T[] differentiate(T[] coefficients)
throws MathIllegalArgumentException, NullArgumentException {
MathUtils.checkNotNull(coefficients);
int n = coefficients.length;
if (n == 0) {
throw new MathIllegalArgumentException(LocalizedCoreFormats.EMPTY_POLYNOMIALS_COEFFICIENTS_ARRAY);
}
final Field<T> field = coefficients[0].getField();
final T[] result = MathArrays.buildArray(field, FastMath.max(1, n - 1));
if (n == 1) {
result[0] = field.getZero();
} else {
for (int i = n - 1; i > 0; i--) {
result[i - 1] = coefficients[i].multiply(i);
}
}
return result;
}
/**
* Returns an anti-derivative of this polynomial, with 0 constant term.
*
* @return a polynomial whose derivative has the same coefficients as this polynomial
*/
public FieldPolynomialFunction<T> antiDerivative() {
final Field<T> field = getField();
final int d = degree();
final T[] anti = MathArrays.buildArray(field, d + 2);
anti[0] = field.getZero();
for (int i = 1; i <= d + 1; i++) {
anti[i] = coefficients[i - 1].multiply(1.0 / i);
}
return new FieldPolynomialFunction<>(anti);
}
/**
* Returns the definite integral of this polymomial over the given interval.
* <p>
* [lower, upper] must describe a finite interval (neither can be infinite
* and lower must be less than or equal to upper).
*
* @param lower lower bound for the integration
* @param upper upper bound for the integration
* @return the integral of this polymomial over the given interval
* @throws MathIllegalArgumentException if the bounds do not describe a finite interval
*/
public T integrate(final double lower, final double upper) {
final T zero = getField().getZero();
return integrate(zero.add(lower), zero.add(upper));
}
/**
* Returns the definite integral of this polymomial over the given interval.
* <p>
* [lower, upper] must describe a finite interval (neither can be infinite
* and lower must be less than or equal to upper).
*
* @param lower lower bound for the integration
* @param upper upper bound for the integration
* @return the integral of this polymomial over the given interval
* @throws MathIllegalArgumentException if the bounds do not describe a finite interval
*/
public T integrate(final T lower, final T upper) {
if (Double.isInfinite(lower.getReal()) || Double.isInfinite(upper.getReal())) {
throw new MathIllegalArgumentException(LocalizedCoreFormats.INFINITE_BOUND);
}
if (lower.getReal() > upper.getReal()) {
throw new MathIllegalArgumentException(LocalizedCoreFormats.LOWER_BOUND_NOT_BELOW_UPPER_BOUND);
}
final FieldPolynomialFunction<T> anti = antiDerivative();
return anti.value(upper).subtract(anti.value(lower));
}
/**
* Returns the derivative as a {@link FieldPolynomialFunction}.
*
* @return the derivative polynomial.
*/
public FieldPolynomialFunction<T> polynomialDerivative() {
return new FieldPolynomialFunction<>(differentiate(coefficients));
}
}