/*
    * 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.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));
     }
 
 }