Derivative1.java
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* 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.CalculusFieldElement;
import org.hipparchus.util.FastMath;
import org.hipparchus.util.SinCos;
import org.hipparchus.util.SinhCosh;
import org.hipparchus.util.FieldSinCos;
import org.hipparchus.util.FieldSinhCosh;
/** Interface representing an object holding partial derivatives up to first order.
* @param <T> the type of the field elements
* @see Derivative
* @see UnivariateDerivative1
* @see Gradient
* @see SparseGradient
* @since 3.1
*/
public interface Derivative1<T extends CalculusFieldElement<T>> extends Derivative<T> {
/** {@inheritDoc} */
@Override
default int getOrder() {
return 1;
}
/** Compute composition of the instance by a univariate function differentiable at order 1.
* @param f0 value of function
* @param f1 first-order derivative
* @return f(this)
*/
T compose(double f0, double f1);
/** {@inheritDoc} */
@Override
default T square() {
final double f0 = getValue();
return compose(f0 * f0, 2 * f0);
}
/** {@inheritDoc} */
@Override
default T reciprocal () {
final double inv1 = 1.0 / getValue();
final double inv2 = -inv1 * inv1;
return compose(inv1, inv2);
}
/** {@inheritDoc} */
@Override
default T sqrt() {
final double s = FastMath.sqrt(getValue());
return compose(s, 1 / (2 * s));
}
/** {@inheritDoc} */
@Override
default T cbrt() {
final double c = FastMath.cbrt(getValue());
return compose(c, 1 / (3 * c * c));
}
/** {@inheritDoc} */
@Override
default T rootN(int n) {
if (n == 2) {
return sqrt();
} else if (n == 3) {
return cbrt();
} else {
final double r = FastMath.pow(getValue(), 1.0 / n);
return compose(r, 1 / (n * FastMath.pow(r, n - 1)));
}
}
/** {@inheritDoc} */
@Override
default T exp() {
final double exp = FastMath.exp(getValue());
return compose(exp, exp);
}
/** {@inheritDoc} */
@Override
default T expm1() {
final double exp = FastMath.exp(getValue());
final double expM1 = FastMath.expm1(getValue());
return compose(expM1, exp);
}
/** {@inheritDoc} */
@Override
default T log() {
return compose(FastMath.log(getValue()), 1 / getValue());
}
/** {@inheritDoc} */
@Override
default T log1p() {
return compose(FastMath.log1p(getValue()), 1 / (1 + getValue()));
}
/** {@inheritDoc} */
@Override
default T log10() {
return compose(FastMath.log10(getValue()), 1 / (getValue() * FastMath.log(10.0)));
}
/** {@inheritDoc} */
@Override
default T cos() {
final SinCos sinCos = FastMath.sinCos(getValue());
return compose(sinCos.cos(), -sinCos.sin());
}
/** {@inheritDoc} */
@Override
default T sin() {
final SinCos sinCos = FastMath.sinCos(getValue());
return compose(sinCos.sin(), sinCos.cos());
}
/** {@inheritDoc} */
@Override
default FieldSinCos<T> sinCos() {
final SinCos sinCos = FastMath.sinCos(getValue());
return new FieldSinCos<>(compose(sinCos.sin(), sinCos.cos()),
compose(sinCos.cos(), -sinCos.sin()));
}
/** {@inheritDoc} */
@Override
default T tan() {
final double tan = FastMath.tan(getValue());
return compose(tan, 1 + tan * tan);
}
/** {@inheritDoc} */
@Override
default T acos() {
final double f0 = getValue();
return compose(FastMath.acos(f0), -1 / FastMath.sqrt(1 - f0 * f0));
}
/** {@inheritDoc} */
@Override
default T asin() {
final double f0 = getValue();
return compose(FastMath.asin(f0), 1 / FastMath.sqrt(1 - f0 * f0));
}
/** {@inheritDoc} */
@Override
default T atan() {
final double f0 = getValue();
return compose(FastMath.atan(f0), 1 / (1 + f0 * f0));
}
/** {@inheritDoc} */
@Override
default T cosh() {
return compose(FastMath.cosh(getValue()), FastMath.sinh(getValue()));
}
/** {@inheritDoc} */
@Override
default T sinh() {
return compose(FastMath.sinh(getValue()), FastMath.cosh(getValue()));
}
/** {@inheritDoc} */
@Override
default FieldSinhCosh<T> sinhCosh() {
final SinhCosh sinhCosh = FastMath.sinhCosh(getValue());
return new FieldSinhCosh<>(compose(sinhCosh.sinh(), sinhCosh.cosh()),
compose(sinhCosh.cosh(), sinhCosh.sinh()));
}
/** {@inheritDoc} */
@Override
default T tanh() {
final double tanh = FastMath.tanh(getValue());
return compose(tanh, 1 - tanh * tanh);
}
/** {@inheritDoc} */
@Override
default T acosh() {
final double f0 = getValue();
return compose(FastMath.acosh(f0), 1 / FastMath.sqrt(f0 * f0 - 1));
}
/** {@inheritDoc} */
@Override
default T asinh() {
final double f0 = getValue();
return compose(FastMath.asinh(f0), 1 / FastMath.sqrt(f0 * f0 + 1));
}
/** {@inheritDoc} */
@Override
default T atanh() {
final double f0 = getValue();
return compose(FastMath.atanh(f0), 1 / (1 - f0 * f0));
}
}