Package dev.nm.analysis.differentiation.multivariate

Class MultivariateFiniteDifference

java.lang.Object
dev.nm.analysis.function.rn2r1.AbstractRealScalarFunction
dev.nm.analysis.differentiation.multivariate.MultivariateFiniteDifference
All Implemented Interfaces:
Function<Vector,Double>, RealScalarFunction
public class MultivariateFiniteDifference extends AbstractRealScalarFunction
A partial derivative of a multivariate function is the derivative with respect to one of the variables with the others held constant. This implementation applies recursively the (first order) finite difference on the function. For example, \[ {\partial^2 \over \partial x_1 \partial x_2} = {\partial \over \partial x_2}({\partial \over \partial x_1}) \] Each of the two univariate derivatives is computed using the central difference method.
See Also:

  • Constructor Details

    • MultivariateFiniteDifference

      public MultivariateFiniteDifference(RealScalarFunction f, int[] varidx)
      Construct the partial derivative of a multi-variable function.

      For example, varidx = new int[]{1, 2} means \[ f_{x_1,x_2} = {\partial^2 \over \partial x_2 \partial x_1} = {\partial \over \partial x_2}({\partial \over \partial x_1}) \]

      Parameters:
      f - the real multivariate function to take derivative of
      varidx - the variable indices of the derivative, counting from 1 up to the domain dimension of f

  • Method Details

    • evaluate

      public Double evaluate(Vector x)
      Evaluate numerically the partial derivative of f at point x.

      Make sure that h and x+h are representable in floating point precision so that the difference between x+h and x is exactly h.

      Parameters:
      x - the point to evaluate the derivative at
      Returns:
      the numerical partial derivative of f at point x
      See Also:

    • evaluate

      public double evaluate(Vector x, double h)
      Evaluate numerically the partial derivative of f at point x with step size h. It could be challenging to automatically determine the step size h, esp. when |x| is near 0. It may, for example, require an analysis that involves f' and f''. The user may want to experiment with different hs by calling this function.
      Parameters:
      x - the point to evaluate the derivative of f at
      h - the step size
      Returns:
      the numerical partial derivative of f at point x with step size h