UnivariateDerivative2.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.differentiation;
import org.hipparchus.exception.LocalizedCoreFormats;
import org.hipparchus.exception.MathIllegalArgumentException;
import org.hipparchus.util.FastMath;
import org.hipparchus.util.FieldSinCos;
import org.hipparchus.util.FieldSinhCosh;
import org.hipparchus.util.MathArrays;
import org.hipparchus.util.MathUtils;
import org.hipparchus.util.SinCos;
import org.hipparchus.util.SinhCosh;
/** 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 two.
* 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 UnivariateDerivative2} 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 FieldUnivariateDerivative2
* @see FieldUnivariateDerivative2
* @see FieldGradient
* @since 1.7
*/
public class UnivariateDerivative2 extends UnivariateDerivative<UnivariateDerivative2> {
/** The constant value of π as a {@code UnivariateDerivative2}.
* @since 2.0
*/
public static final UnivariateDerivative2 PI = new UnivariateDerivative2(FastMath.PI, 0.0, 0.0);
/** Serializable UID. */
private static final long serialVersionUID = 20200520L;
/** Value of the function. */
private final double f0;
/** First derivative of the function. */
private final double f1;
/** Second derivative of the function. */
private final double f2;
/** Build an instance with values and derivative.
* @param f0 value of the function
* @param f1 first derivative of the function
* @param f2 second derivative of the function
*/
public UnivariateDerivative2(final double f0, final double f1, final double f2) {
this.f0 = f0;
this.f1 = f1;
this.f2 = f2;
}
/** 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 2
*/
public UnivariateDerivative2(final DerivativeStructure ds) throws MathIllegalArgumentException {
MathUtils.checkDimension(ds.getFreeParameters(), 1);
MathUtils.checkDimension(ds.getOrder(), 2);
this.f0 = ds.getValue();
this.f1 = ds.getPartialDerivative(1);
this.f2 = ds.getPartialDerivative(2);
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 newInstance(final double value) {
return new UnivariateDerivative2(value, 0.0, 0.0);
}
@Override
public UnivariateDerivative2 withValue(final double value) {
return new UnivariateDerivative2(value, f1, f2);
}
/** {@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;
case 2 :
return f2;
default :
throw new MathIllegalArgumentException(LocalizedCoreFormats.DERIVATION_ORDER_NOT_ALLOWED, n);
}
}
/** {@inheritDoc} */
@Override
public int getOrder() {
return 2;
}
/** Get the first derivative.
* @return first derivative
* @see #getValue()
* @see #getSecondDerivative()
*/
public double getFirstDerivative() {
return f1;
}
/** Get the second derivative.
* @return second derivative
* @see #getValue()
* @see #getFirstDerivative()
*/
public double getSecondDerivative() {
return f2;
}
/** {@inheritDoc} */
@Override
public DerivativeStructure toDerivativeStructure() {
return getField().getConversionFactory().build(f0, f1, f2);
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 add(final UnivariateDerivative2 a) {
return new UnivariateDerivative2(f0 + a.f0, f1 + a.f1, f2 + a.f2);
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 subtract(final UnivariateDerivative2 a) {
return new UnivariateDerivative2(f0 - a.f0, f1 - a.f1, f2 - a.f2);
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 multiply(final int n) {
return new UnivariateDerivative2(f0 * n, f1 * n, f2 * n);
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 multiply(final double a) {
return new UnivariateDerivative2(f0 * a, f1 * a, f2 * a);
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 multiply(final UnivariateDerivative2 a) {
return new UnivariateDerivative2(f0 * a.f0,
MathArrays.linearCombination(f1, a.f0, f0, a.f1),
MathArrays.linearCombination(f2, a.f0, 2 * f1, a.f1, f0, a.f2));
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 square() {
return new UnivariateDerivative2(f0 * f0, 2 * f0 * f1, 2 * (f0 * f2 + f1 * f1));
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 divide(final double a) {
final double inv1 = 1.0 / a;
return new UnivariateDerivative2(f0 * inv1, f1 * inv1, f2 * inv1);
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 divide(final UnivariateDerivative2 a) {
final double inv1 = 1.0 / a.f0;
final double inv2 = inv1 * inv1;
final double inv3 = inv1 * inv2;
return new UnivariateDerivative2(f0 * inv1,
MathArrays.linearCombination(f1, a.f0, -f0, a.f1) * inv2,
MathArrays.linearCombination(f2, a.f0 * a.f0,
-2 * f1, a.f0 * a.f1,
2 * f0, a.f1 * a.f1,
-f0, a.f0 * a.f2) * inv3);
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 remainder(final UnivariateDerivative2 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 UnivariateDerivative2(rem, f1 - k * a.f1, f2 - k * a.f2);
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 negate() {
return new UnivariateDerivative2(-f0, -f1, -f2);
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 abs() {
if (Double.doubleToLongBits(f0) < 0) {
// we use the bits representation to also handle -0.0
return negate();
} else {
return this;
}
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 copySign(final UnivariateDerivative2 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 UnivariateDerivative2 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 UnivariateDerivative2 scalb(final int n) {
return new UnivariateDerivative2(FastMath.scalb(f0, n), FastMath.scalb(f1, n), FastMath.scalb(f2, n));
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 hypot(final UnivariateDerivative2 y) {
if (Double.isInfinite(f0) || Double.isInfinite(y.f0)) {
return new UnivariateDerivative2(Double.POSITIVE_INFINITY, 0.0, 0.0);
} else if (Double.isNaN(f0) || Double.isNaN(y.f0)) {
return new UnivariateDerivative2(Double.NaN, 0.0, 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 UnivariateDerivative2 scaledX = scalb(-middleExp);
final UnivariateDerivative2 scaledY = y.scalb(-middleExp);
// compute scaled hypotenuse
final UnivariateDerivative2 scaledH =
scaledX.multiply(scaledX).add(scaledY.multiply(scaledY)).sqrt();
// remove scaling
return scaledH.scalb(middleExp);
}
}
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 reciprocal() {
final double inv1 = 1.0 / f0;
final double inv2 = inv1 * inv1;
final double inv3 = inv1 * inv2;
return new UnivariateDerivative2(inv1, -f1 * inv2, MathArrays.linearCombination(2 * f1, f1, -f0, f2) * inv3);
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 compose(final double... f) {
MathUtils.checkDimension(f.length, getOrder() + 1);
return new UnivariateDerivative2(f[0],
f[1] * f1,
MathArrays.linearCombination(f[1], f2, f[2], f1 * f1));
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 sqrt() {
final double s0 = FastMath.sqrt(f0);
final double s0twice = 2. * s0;
final double s1 = f1 / s0twice;
final double s2 = (f2 - 2. * s1 * s1) / s0twice;
return new UnivariateDerivative2(s0, s1, s2);
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 cbrt() {
final double c = FastMath.cbrt(f0);
final double c2 = c * c;
return compose(c, 1 / (3 * c2), -1 / (4.5 * c2 * f0));
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 rootN(final int n) {
if (n == 2) {
return sqrt();
} else if (n == 3) {
return cbrt();
} else {
final double r = FastMath.pow(f0, 1.0 / n);
final double z = n * FastMath.pow(r, n - 1);
return compose(r, 1 / z, (1 - n) / (z * z * r));
}
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2Field getField() {
return UnivariateDerivative2Field.getInstance();
}
/** Compute a<sup>x</sup> where a is a double and x a {@link UnivariateDerivative2}
* @param a number to exponentiate
* @param x power to apply
* @return a<sup>x</sup>
*/
public static UnivariateDerivative2 pow(final double a, final UnivariateDerivative2 x) {
if (a == 0) {
return x.getField().getZero();
} else {
final double aX = FastMath.pow(a, x.f0);
final double lnA = FastMath.log(a);
final double aXlnA = aX * lnA;
return new UnivariateDerivative2(aX, aXlnA * x.f1, aXlnA * (x.f1 * x.f1 * lnA + x.f2));
}
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 pow(final double p) {
if (p == 0) {
return getField().getOne();
} else {
final double f0Pm2 = FastMath.pow(f0, p - 2);
final double f0Pm1 = f0Pm2 * f0;
final double f0P = f0Pm1 * f0;
return compose(f0P, p * f0Pm1, p * (p - 1) * f0Pm2);
}
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 pow(final int n) {
if (n == 0) {
return getField().getOne();
} else {
final double f0Nm2 = FastMath.pow(f0, n - 2);
final double f0Nm1 = f0Nm2 * f0;
final double f0N = f0Nm1 * f0;
return compose(f0N, n * f0Nm1, n * (n - 1) * f0Nm2);
}
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 exp() {
final double exp = FastMath.exp(f0);
return compose(exp, exp, exp);
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 expm1() {
final double exp = FastMath.exp(f0);
final double expM1 = FastMath.expm1(f0);
return compose(expM1, exp, exp);
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 log() {
final double inv = 1 / f0;
return compose(FastMath.log(f0), inv, -inv * inv);
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 log1p() {
final double inv = 1 / (1 + f0);
return compose(FastMath.log1p(f0), inv, -inv * inv);
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 log10() {
final double invF0 = 1 / f0;
final double inv = invF0 / FastMath.log(10.0);
return compose(FastMath.log10(f0), inv, -inv * invF0);
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 cos() {
final SinCos sinCos = FastMath.sinCos(f0);
return compose(sinCos.cos(), -sinCos.sin(), -sinCos.cos());
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 sin() {
final SinCos sinCos = FastMath.sinCos(f0);
return compose(sinCos.sin(), sinCos.cos(), -sinCos.sin());
}
/** {@inheritDoc} */
@Override
public FieldSinCos<UnivariateDerivative2> sinCos() {
final SinCos sinCos = FastMath.sinCos(f0);
return new FieldSinCos<>(compose(sinCos.sin(), sinCos.cos(), -sinCos.sin()),
compose(sinCos.cos(), -sinCos.sin(), -sinCos.cos()));
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 tan() {
final double tan = FastMath.tan(f0);
final double sec2 = 1 + tan * tan;
return compose(tan, sec2, 2 * sec2 * tan);
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 acos() {
final double inv = 1.0 / (1 - f0 * f0);
final double mS = -FastMath.sqrt(inv);
return compose(FastMath.acos(f0), mS, mS * f0 * inv);
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 asin() {
final double inv = 1.0 / (1 - f0 * f0);
final double s = FastMath.sqrt(inv);
return compose(FastMath.asin(f0), s, s * f0 * inv);
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 atan() {
final double inv = 1 / (1 + f0 * f0);
return compose(FastMath.atan(f0), inv, -2 * f0 * inv * inv);
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 atan2(final UnivariateDerivative2 x) {
final double x2 = x.f0 * x.f0;
final double f02 = f0 + f0;
final double inv = 1.0 / (f0 * f0 + x2);
final double atan0 = FastMath.atan2(f0, x.f0);
final double atan1 = MathArrays.linearCombination(x.f0, f1, -x.f1, f0) * inv;
final double c = MathArrays.linearCombination(f2, x2,
-2 * f1, x.f0 * x.f1,
f02, x.f1 * x.f1,
-f0, x.f0 * x.f2) * inv;
return new UnivariateDerivative2(atan0, atan1, (c - f02 * atan1 * atan1) / x.f0);
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 cosh() {
final double c = FastMath.cosh(f0);
final double s = FastMath.sinh(f0);
return compose(c, s, c);
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 sinh() {
final double c = FastMath.cosh(f0);
final double s = FastMath.sinh(f0);
return compose(s, c, s);
}
/** {@inheritDoc} */
@Override
public FieldSinhCosh<UnivariateDerivative2> sinhCosh() {
final SinhCosh sinhCosh = FastMath.sinhCosh(f0);
return new FieldSinhCosh<>(compose(sinhCosh.sinh(), sinhCosh.cosh(), sinhCosh.sinh()),
compose(sinhCosh.cosh(), sinhCosh.sinh(), sinhCosh.cosh()));
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 tanh() {
final double tanh = FastMath.tanh(f0);
final double sech2 = 1 - tanh * tanh;
return compose(tanh, sech2, -2 * sech2 * tanh);
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 acosh() {
final double inv = 1 / (f0 * f0 - 1);
final double s = FastMath.sqrt(inv);
return compose(FastMath.acosh(f0), s, -f0 * s * inv);
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 asinh() {
final double inv = 1 / (f0 * f0 + 1);
final double s = FastMath.sqrt(inv);
return compose(FastMath.asinh(f0), s, -f0 * s * inv);
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 atanh() {
final double inv = 1 / (1 - f0 * f0);
return compose(FastMath.atanh(f0), inv, 2 * f0 * inv * inv);
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 toDegrees() {
return new UnivariateDerivative2(FastMath.toDegrees(f0), FastMath.toDegrees(f1), FastMath.toDegrees(f2));
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 toRadians() {
return new UnivariateDerivative2(FastMath.toRadians(f0), FastMath.toRadians(f1), FastMath.toRadians(f2));
}
/** 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 + 0.5 * delta * f2);
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 linearCombination(final UnivariateDerivative2[] a, final UnivariateDerivative2[] b) {
// extract values and 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];
final double[] a2 = new double[3 * n];
final double[] b2 = new double[3 * n];
for (int i = 0; i < n; ++i) {
final UnivariateDerivative2 ai = a[i];
final UnivariateDerivative2 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;
a2[3 * i] = ai.f0;
a2[3 * i + 1] = ai.f1 + ai.f1;
a2[3 * i + 2] = ai.f2;
b2[3 * i] = bi.f2;
b2[3 * i + 1] = bi.f1;
b2[3 * i + 2] = bi.f0;
}
return new UnivariateDerivative2(MathArrays.linearCombination(a0, b0),
MathArrays.linearCombination(a1, b1),
MathArrays.linearCombination(a2, b2));
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 linearCombination(final double[] a, final UnivariateDerivative2[] b) {
// extract values and derivatives
final int n = b.length;
final double[] b0 = new double[n];
final double[] b1 = new double[n];
final double[] b2 = new double[n];
for (int i = 0; i < n; ++i) {
b0[i] = b[i].f0;
b1[i] = b[i].f1;
b2[i] = b[i].f2;
}
return new UnivariateDerivative2(MathArrays.linearCombination(a, b0),
MathArrays.linearCombination(a, b1),
MathArrays.linearCombination(a, b2));
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 linearCombination(final UnivariateDerivative2 a1, final UnivariateDerivative2 b1,
final UnivariateDerivative2 a2, final UnivariateDerivative2 b2) {
return new UnivariateDerivative2(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),
MathArrays.linearCombination(new double[] {
a1.f0, 2 * a1.f1, a1.f2,
a2.f0, 2 * a2.f1, a2.f2
}, new double[] {
b1.f2, b1.f1, b1.f0,
b2.f2, b2.f1, b2.f0
}));
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 linearCombination(final double a1, final UnivariateDerivative2 b1,
final double a2, final UnivariateDerivative2 b2) {
return new UnivariateDerivative2(MathArrays.linearCombination(a1, b1.f0,
a2, b2.f0),
MathArrays.linearCombination(a1, b1.f1,
a2, b2.f1),
MathArrays.linearCombination(a1, b1.f2,
a2, b2.f2));
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 linearCombination(final UnivariateDerivative2 a1, final UnivariateDerivative2 b1,
final UnivariateDerivative2 a2, final UnivariateDerivative2 b2,
final UnivariateDerivative2 a3, final UnivariateDerivative2 b3) {
return new UnivariateDerivative2(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
}),
MathArrays.linearCombination(new double[] {
a1.f0, 2 * a1.f1, a1.f2,
a2.f0, 2 * a2.f1, a2.f2,
a3.f0, 2 * a3.f1, a3.f2
}, new double[] {
b1.f2, b1.f1, b1.f0,
b2.f2, b2.f1, b2.f0,
b3.f2, b3.f1, b3.f0
}));
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 linearCombination(final double a1, final UnivariateDerivative2 b1,
final double a2, final UnivariateDerivative2 b2,
final double a3, final UnivariateDerivative2 b3) {
return new UnivariateDerivative2(MathArrays.linearCombination(a1, b1.f0,
a2, b2.f0,
a3, b3.f0),
MathArrays.linearCombination(a1, b1.f1,
a2, b2.f1,
a3, b3.f1),
MathArrays.linearCombination(a1, b1.f2,
a2, b2.f2,
a3, b3.f2));
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 linearCombination(final UnivariateDerivative2 a1, final UnivariateDerivative2 b1,
final UnivariateDerivative2 a2, final UnivariateDerivative2 b2,
final UnivariateDerivative2 a3, final UnivariateDerivative2 b3,
final UnivariateDerivative2 a4, final UnivariateDerivative2 b4) {
return new UnivariateDerivative2(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
}),
MathArrays.linearCombination(new double[] {
a1.f0, 2 * a1.f1, a1.f2,
a2.f0, 2 * a2.f1, a2.f2,
a3.f0, 2 * a3.f1, a3.f2,
a4.f0, 2 * a4.f1, a4.f2
}, new double[] {
b1.f2, b1.f1, b1.f0,
b2.f2, b2.f1, b2.f0,
b3.f2, b3.f1, b3.f0,
b4.f2, b4.f1, b4.f0
}));
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 linearCombination(final double a1, final UnivariateDerivative2 b1,
final double a2, final UnivariateDerivative2 b2,
final double a3, final UnivariateDerivative2 b3,
final double a4, final UnivariateDerivative2 b4) {
return new UnivariateDerivative2(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),
MathArrays.linearCombination(a1, b1.f2,
a2, b2.f2,
a3, b3.f2,
a4, b4.f2));
}
/** {@inheritDoc} */
@Override
public UnivariateDerivative2 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 UnivariateDerivative2) {
final UnivariateDerivative2 rhs = (UnivariateDerivative2) other;
return f0 == rhs.f0 && f1 == rhs.f1 && f2 == rhs.f2;
}
return false;
}
/** Get a hashCode for the univariate derivative.
* @return a hash code value for this object
*/
@Override
public int hashCode() {
return 317 - 41 * Double.hashCode(f0) + 57 * Double.hashCode(f1) - 103 * Double.hashCode(f2);
}
/** {@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 UnivariateDerivative2 o) {
final int cF0 = Double.compare(f0, o.getReal());
if (cF0 == 0) {
final int cF1 = Double.compare(f1, o.getFirstDerivative());
if (cF1 == 0) {
return Double.compare(f2, o.getSecondDerivative());
} else {
return cF1;
}
} else {
return cF0;
}
}
}