Derivative.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
* limitations under the License.
*/
package org.hipparchus.analysis.differentiation;
import org.hipparchus.CalculusFieldElement;
import org.hipparchus.exception.MathIllegalArgumentException;
import org.hipparchus.util.FastMath;
/** Interface representing both the value and the differentials of a function.
* @param <T> the type of the field elements
* @since 1.7
*/
public interface Derivative<T extends CalculusFieldElement<T>> extends CalculusFieldElement<T>, DifferentialAlgebra {
/** {@inheritDoc} */
@Override
default double getReal() {
return getValue();
}
/** Get the value part of the function.
* @return value part of the value of the function
*/
double getValue();
/** Create a new object with new value (zeroth-order derivative, as passed as input)
* and same derivatives of order one and above.
* <p>
* This default implementation is there so that no API gets broken
* by the next release, which is not a major one. Custom inheritors
* should probably overwrite it.
* </p>
* @param value zeroth-order derivative of new represented function
* @return new object with changed value
* @since 3.1
*/
default T withValue(double value) {
return add(newInstance(value - getValue()));
}
/** Get a partial derivative.
* @param orders derivation orders with respect to each variable (if all orders are 0,
* the value is returned)
* @return partial derivative
* @see #getValue()
* @exception MathIllegalArgumentException if the numbers of variables does not
* match the instance
* @exception MathIllegalArgumentException if sum of derivation orders is larger
* than the instance limits
*/
double getPartialDerivative(int ... orders)
throws MathIllegalArgumentException;
/** {@inheritDoc} */
@Override
default T add(double a) {
return withValue(getValue() + a);
}
/** {@inheritDoc} */
@Override
default T subtract(double a) {
return withValue(getValue() - a);
}
/** Compute composition of the instance by a univariate function.
* @param f array of value and derivatives of the function at
* the current point (i.e. [f({@link #getValue()}),
* f'({@link #getValue()}), f''({@link #getValue()})...]).
* @return f(this)
* @exception MathIllegalArgumentException if the number of derivatives
* in the array is not equal to {@link #getOrder() order} + 1
*/
T compose(double... f)
throws MathIllegalArgumentException;
/** {@inheritDoc} */
@Override
default T log10() {
return log().divide(FastMath.log(10.));
}
/** {@inheritDoc} */
@Override
default T pow(T e) {
return log().multiply(e).exp();
}
/** {@inheritDoc} */
@Override
default T cosh() {
return (exp().add(negate().exp())).divide(2);
}
/** {@inheritDoc} */
@Override
default T sinh() {
return (exp().subtract(negate().exp())).divide(2);
}
/** {@inheritDoc} */
@Override
default T acos() {
return asin().negate().add(getPi().divide(2));
}
/** {@inheritDoc} */
@Override
default int getExponent() {
return FastMath.getExponent(getValue());
}
/** {@inheritDoc} */
@Override
default T remainder(double a) {
return withValue(FastMath.IEEEremainder(getValue(), a));
}
}