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 *
 *      http://www.apache.org/licenses/LICENSE-2.0
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package org.apache.commons.math3.analysis;

Extension of MultivariateFunction representing a differentiable multivariate real function. 
Since:
2.0
Deprecated:
as of 3.1 replaced by MultivariateDifferentiableFunction/**
 * Extension of {@link MultivariateFunction} representing a differentiable
 * multivariate real function.
 * @since 2.0
 * @deprecated as of 3.1 replaced by {@link org.apache.commons.math3.analysis.differentiation.MultivariateDifferentiableFunction}
 */
@Deprecated
public interface DifferentiableMultivariateFunction extends MultivariateFunction {

    
Returns the partial derivative of the function with respect to a point coordinate.

The partial derivative is defined with respect to point coordinate
xk. If the partial derivatives with respect to all coordinates are needed, it may be more efficient to use the gradient() method which will compute them all at once. 
Params:
k – index of the coordinate with respect to which the partial
derivative is computed
Returns:
the partial derivative function with respect to kth point coordinate/**
     * 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
     */
    MultivariateFunction partialDerivative(int k);

    
Returns the gradient function.
If only one partial derivative with respect to a specific coordinate is needed, it may be more efficient to use the partialDerivative(int) method which will compute only the specified component.
Returns:
the gradient function/**
     * 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
     */
    MultivariateVectorFunction gradient();

}