UnivariateDerivative1.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,
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* See the License for the specific language governing permissions and
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package org.hipparchus.analysis.differentiation;
import org.hipparchus.exception.LocalizedCoreFormats;
import org.hipparchus.exception.MathIllegalArgumentException;
import org.hipparchus.util.FastMath;
import org.hipparchus.util.MathArrays;
import org.hipparchus.util.MathUtils;
/** Class representing both the value and the differentials of a function.
* <p>This class is a stripped-down version of {@link DerivativeStructure}
* with only one {@link DerivativeStructure#getFreeParameters() free parameter}
* and {@link DerivativeStructure#getOrder() derivation order} also limited to one.
* It should have less overhead than {@link DerivativeStructure} in its domain.</p>
* <p>This class is an implementation of Rall's numbers. Rall's numbers are an
* extension to the real numbers used throughout mathematical expressions; they hold
* the derivative together with the value of a function.</p>
* <p>{@link UnivariateDerivative1} instances can be used directly thanks to
* the arithmetic operators to the mathematical functions provided as
* methods by this class (+, -, *, /, %, sin, cos ...).</p>
* <p>Implementing complex expressions by hand using these classes is
* a tedious and error-prone task but has the advantage of having no limitation
* on the derivation order despite not requiring users to compute the derivatives by
* themselves.</p>
* <p>Instances of this class are guaranteed to be immutable.</p>
* @see DerivativeStructure
* @see UnivariateDerivative2
* @see Gradient
* @see FieldDerivativeStructure
* @see FieldUnivariateDerivative1
* @see FieldUnivariateDerivative2
* @see FieldGradient
* @since 1.7
*/
public class UnivariateDerivative1 extends UnivariateDerivative<UnivariateDerivative1>
implements Derivative1<UnivariateDerivative1> {
/** The constant value of π as a {@code UnivariateDerivative1}.
* @since 2.0
*/
public static final UnivariateDerivative1 PI = new UnivariateDerivative1(FastMath.PI, 0.0);
/** Serializable UID. */
private static final long serialVersionUID = 20200519L;
/** Value of the function. */
private final double f0;
/** First derivative of the function. */
private final double f1;
/** Build an instance with values and derivative.
* @param f0 value of the function
* @param f1 first derivative of the function
*/
public UnivariateDerivative1(final double f0, final double f1) {
this.f0 = f0;
this.f1 = f1;
}
/** Build an instance from a {@link DerivativeStructure}.
* @param ds derivative structure
* @exception MathIllegalArgumentException if either {@code ds} parameters
* is not 1 or {@code ds} order is not 1
*/
public UnivariateDerivative1(final DerivativeStructure ds) throws MathIllegalArgumentException {
MathUtils.checkDimension(ds.getFreeParameters(), 1);
MathUtils.checkDimension(ds.getOrder(), 1);
this.f0 = ds.getValue();
this.f1 = ds.getPartialDerivative(1);
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative1 newInstance(final double value) {
return new UnivariateDerivative1(value, 0.0);
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative1 withValue(final double value) {
return new UnivariateDerivative1(value, f1);
}
/** {@inheritDoc} */
@Override
public double getValue() {
return f0;
}
/** {@inheritDoc} */
@Override
public double getDerivative(final int n) {
switch (n) {
case 0 :
return f0;
case 1 :
return f1;
default :
throw new MathIllegalArgumentException(LocalizedCoreFormats.DERIVATION_ORDER_NOT_ALLOWED, n);
}
}
/** Get the first derivative.
* @return first derivative
* @see #getValue()
*/
public double getFirstDerivative() {
return f1;
}
/** {@inheritDoc} */
@Override
public DerivativeStructure toDerivativeStructure() {
return getField().getConversionFactory().build(f0, f1);
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative1 add(final UnivariateDerivative1 a) {
return new UnivariateDerivative1(f0 + a.f0, f1 + a.f1);
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative1 subtract(final UnivariateDerivative1 a) {
return new UnivariateDerivative1(f0 - a.f0, f1 - a.f1);
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative1 multiply(final int n) {
return new UnivariateDerivative1(f0 * n, f1 * n);
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative1 multiply(final double a) {
return new UnivariateDerivative1(f0 * a, f1 * a);
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative1 multiply(final UnivariateDerivative1 a) {
return new UnivariateDerivative1(f0 * a.f0,
MathArrays.linearCombination(f1, a.f0, f0, a.f1));
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative1 divide(final double a) {
final double inv1 = 1.0 / a;
return new UnivariateDerivative1(f0 * inv1, f1 * inv1);
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative1 divide(final UnivariateDerivative1 a) {
final double inv1 = 1.0 / a.f0;
final double inv2 = inv1 * inv1;
return new UnivariateDerivative1(f0 * inv1,
MathArrays.linearCombination(f1, a.f0, -f0, a.f1) * inv2);
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative1 remainder(final UnivariateDerivative1 a) {
// compute k such that lhs % rhs = lhs - k rhs
final double rem = FastMath.IEEEremainder(f0, a.f0);
final double k = FastMath.rint((f0 - rem) / a.f0);
return new UnivariateDerivative1(rem, f1 - k * a.f1);
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative1 negate() {
return new UnivariateDerivative1(-f0, -f1);
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative1 abs() {
if (Double.doubleToLongBits(f0) < 0) {
// we use the bits representation to also handle -0.0
return negate();
} else {
return this;
}
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative1 copySign(final UnivariateDerivative1 sign) {
long m = Double.doubleToLongBits(f0);
long s = Double.doubleToLongBits(sign.f0);
if ((m >= 0 && s >= 0) || (m < 0 && s < 0)) { // Sign is currently OK
return this;
}
return negate(); // flip sign
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative1 copySign(final double sign) {
long m = Double.doubleToLongBits(f0);
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} */
@Override
public UnivariateDerivative1 scalb(final int n) {
return new UnivariateDerivative1(FastMath.scalb(f0, n), FastMath.scalb(f1, n));
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative1 hypot(final UnivariateDerivative1 y) {
if (Double.isInfinite(f0) || Double.isInfinite(y.f0)) {
return new UnivariateDerivative1(Double.POSITIVE_INFINITY, 0.0);
} else if (Double.isNaN(f0) || Double.isNaN(y.f0)) {
return new UnivariateDerivative1(Double.NaN, 0.0);
} else {
final int expX = getExponent();
final int expY = y.getExponent();
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 UnivariateDerivative1 scaledX = scalb(-middleExp);
final UnivariateDerivative1 scaledY = y.scalb(-middleExp);
// compute scaled hypotenuse
final UnivariateDerivative1 scaledH =
scaledX.multiply(scaledX).add(scaledY.multiply(scaledY)).sqrt();
// remove scaling
return scaledH.scalb(middleExp);
}
}
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative1 compose(final double... f) {
MathUtils.checkDimension(f.length, getOrder() + 1);
return compose(f[0], f[1]);
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative1 compose(final double ff0, final double ff1) {
return new UnivariateDerivative1(ff0, this.f1 * ff1);
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative1Field getField() {
return UnivariateDerivative1Field.getInstance();
}
/** Compute a<sup>x</sup> where a is a double and x a {@link UnivariateDerivative1}
* @param a number to exponentiate
* @param x power to apply
* @return a<sup>x</sup>
*/
public static UnivariateDerivative1 pow(final double a, final UnivariateDerivative1 x) {
if (a == 0) {
return x.getField().getZero();
} else {
final double aX = FastMath.pow(a, x.f0);
return new UnivariateDerivative1(aX, FastMath.log(a) * aX * x.f1);
}
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative1 pow(final double p) {
if (p == 0) {
return getField().getOne();
} else {
final double f0Pm1 = FastMath.pow(f0, p - 1);
return compose(f0Pm1 * f0, p * f0Pm1);
}
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative1 pow(final int n) {
if (n == 0) {
return getField().getOne();
} else {
final double f0Nm1 = FastMath.pow(f0, n - 1);
return compose(f0Nm1 * f0, n * f0Nm1);
}
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative1 atan2(final UnivariateDerivative1 x) {
final double inv = 1.0 / (f0 * f0 + x.f0 * x.f0);
return new UnivariateDerivative1(FastMath.atan2(f0, x.f0),
MathArrays.linearCombination(x.f0, f1, -x.f1, f0) * inv);
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative1 toDegrees() {
return new UnivariateDerivative1(FastMath.toDegrees(f0), FastMath.toDegrees(f1));
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative1 toRadians() {
return new UnivariateDerivative1(FastMath.toRadians(f0), FastMath.toRadians(f1));
}
/** Evaluate Taylor expansion a univariate derivative.
* @param delta parameter offset Δx
* @return value of the Taylor expansion at x + Δx
*/
public double taylor(final double delta) {
return f0 + delta * f1;
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative1 linearCombination(final UnivariateDerivative1[] a, final UnivariateDerivative1[] b) {
// extract values and first derivatives
final int n = a.length;
final double[] a0 = new double[n];
final double[] b0 = new double[n];
final double[] a1 = new double[2 * n];
final double[] b1 = new double[2 * n];
for (int i = 0; i < n; ++i) {
final UnivariateDerivative1 ai = a[i];
final UnivariateDerivative1 bi = b[i];
a0[i] = ai.f0;
b0[i] = bi.f0;
a1[2 * i] = ai.f0;
a1[2 * i + 1] = ai.f1;
b1[2 * i] = bi.f1;
b1[2 * i + 1] = bi.f0;
}
return new UnivariateDerivative1(MathArrays.linearCombination(a0, b0),
MathArrays.linearCombination(a1, b1));
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative1 linearCombination(final double[] a, final UnivariateDerivative1[] b) {
// extract values and first derivatives
final int n = b.length;
final double[] b0 = new double[n];
final double[] b1 = new double[n];
for (int i = 0; i < n; ++i) {
b0[i] = b[i].f0;
b1[i] = b[i].f1;
}
return new UnivariateDerivative1(MathArrays.linearCombination(a, b0),
MathArrays.linearCombination(a, b1));
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative1 linearCombination(final UnivariateDerivative1 a1, final UnivariateDerivative1 b1,
final UnivariateDerivative1 a2, final UnivariateDerivative1 b2) {
return new UnivariateDerivative1(MathArrays.linearCombination(a1.f0, b1.f0,
a2.f0, b2.f0),
MathArrays.linearCombination(a1.f0, b1.f1,
a1.f1, b1.f0,
a2.f0, b2.f1,
a2.f1, b2.f0));
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative1 linearCombination(final double a1, final UnivariateDerivative1 b1,
final double a2, final UnivariateDerivative1 b2) {
return new UnivariateDerivative1(MathArrays.linearCombination(a1, b1.f0,
a2, b2.f0),
MathArrays.linearCombination(a1, b1.f1,
a2, b2.f1));
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative1 linearCombination(final UnivariateDerivative1 a1, final UnivariateDerivative1 b1,
final UnivariateDerivative1 a2, final UnivariateDerivative1 b2,
final UnivariateDerivative1 a3, final UnivariateDerivative1 b3) {
return new UnivariateDerivative1(MathArrays.linearCombination(a1.f0, b1.f0,
a2.f0, b2.f0,
a3.f0, b3.f0),
MathArrays.linearCombination(new double[] {
a1.f0, a1.f1,
a2.f0, a2.f1,
a3.f0, a3.f1
}, new double[] {
b1.f1, b1.f0,
b2.f1, b2.f0,
b3.f1, b3.f0
}));
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative1 linearCombination(final double a1, final UnivariateDerivative1 b1,
final double a2, final UnivariateDerivative1 b2,
final double a3, final UnivariateDerivative1 b3) {
return new UnivariateDerivative1(MathArrays.linearCombination(a1, b1.f0,
a2, b2.f0,
a3, b3.f0),
MathArrays.linearCombination(a1, b1.f1,
a2, b2.f1,
a3, b3.f1));
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative1 linearCombination(final UnivariateDerivative1 a1, final UnivariateDerivative1 b1,
final UnivariateDerivative1 a2, final UnivariateDerivative1 b2,
final UnivariateDerivative1 a3, final UnivariateDerivative1 b3,
final UnivariateDerivative1 a4, final UnivariateDerivative1 b4) {
return new UnivariateDerivative1(MathArrays.linearCombination(a1.f0, b1.f0,
a2.f0, b2.f0,
a3.f0, b3.f0,
a4.f0, b4.f0),
MathArrays.linearCombination(new double[] {
a1.f0, a1.f1,
a2.f0, a2.f1,
a3.f0, a3.f1,
a4.f0, a4.f1
}, new double[] {
b1.f1, b1.f0,
b2.f1, b2.f0,
b3.f1, b3.f0,
b4.f1, b4.f0
}));
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative1 linearCombination(final double a1, final UnivariateDerivative1 b1,
final double a2, final UnivariateDerivative1 b2,
final double a3, final UnivariateDerivative1 b3,
final double a4, final UnivariateDerivative1 b4) {
return new UnivariateDerivative1(MathArrays.linearCombination(a1, b1.f0,
a2, b2.f0,
a3, b3.f0,
a4, b4.f0),
MathArrays.linearCombination(a1, b1.f1,
a2, b2.f1,
a3, b3.f1,
a4, b4.f1));
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative1 getPi() {
return PI;
}
/** Test for the equality of two univariate derivatives.
* <p>
* univariate derivatives are considered equal if they have the same derivatives.
* </p>
* @param other Object to test for equality to this
* @return true if two univariate derivatives are equal
*/
@Override
public boolean equals(Object other) {
if (this == other) {
return true;
}
if (other instanceof UnivariateDerivative1) {
final UnivariateDerivative1 rhs = (UnivariateDerivative1) other;
return f0 == rhs.f0 && f1 == rhs.f1;
}
return false;
}
/** Get a hashCode for the univariate derivative.
* @return a hash code value for this object
*/
@Override
public int hashCode() {
return 453 - 19 * Double.hashCode(f0) + 37 * Double.hashCode(f1);
}
/** {@inheritDoc}
* <p>
* Comparison performed considering that derivatives are intrinsically linked to monomials in the corresponding
* Taylor expansion and that the higher the degree, the smaller the term.
* </p>
* @since 3.0
*/
@Override
public int compareTo(final UnivariateDerivative1 o) {
final int cF0 = Double.compare(f0, o.getReal());
if (cF0 == 0) {
return Double.compare(f1, o.getFirstDerivative());
} else {
return cF0;
}
}
}