/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF 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
 *
 *      http://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.apache.commons.math.analysis;

/**
 * Extension of {@link MultivariateRealFunction} representing a differentiable
 * multivariate real function.
 * 
 * @version $Revision$ $Date$
 * @since 2.0
 */
public interface DifferentiableMultivariateRealFunction extends MultivariateRealFunction {

	/**
	 * Returns the partial derivative of the function with respect to a point
	 * coordinate.
	 * <p>
	 * The partial derivative is defined with respect to point coordinate
	 * x<sub>k</sub>. If the partial derivatives with respect to all coordinates
	 * are needed, it may be more efficient to use the {@link #gradient()}
	 * method which will compute them all at once.
	 * </p>
	 * 
	 * @param k
	 *            index of the coordinate with respect to which the partial
	 *            derivative is computed
	 * @return the partial derivative function with respect to k<sup>th</sup>
	 *         point coordinate
	 */
	MultivariateRealFunction partialDerivative(int k);

	/**
	 * Returns the gradient function.
	 * <p>
	 * If only one partial derivative with respect to a specific coordinate is
	 * needed, it may be more efficient to use the
	 * {@link #partialDerivative(int)} method which will compute only the
	 * specified component.
	 * </p>
	 * 
	 * @return the gradient function
	 */
	MultivariateVectorialFunction gradient();

}
