com.numericalmethod.suanshu.analysis.differentiation.multivariate

Class FiniteDifference

java.lang.Object

com.numericalmethod.suanshu.analysis.differentiation.multivariate.FiniteDifference

All Implemented Interfaces:

Function<Vector,java.lang.Double>, RealScalarFunction, java.io.Serializable

public class FiniteDifference
extends java.lang.Object
implements RealScalarFunction

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:

• Wikipedia: Partial derivative
• Wikipedia: Finite difference

, Serialized Form

Nested Class Summary

Nested classes/interfaces inherited from interface com.numericalmethod.suanshu.analysis.function.Function

Function.EvaluationException

Constructor Summary

Constructors

Constructor and Description
FiniteDifference(RealScalarFunction f, int[] varidx) Construct the partial derivative of a multi-variable function.

Method Summary

Modifier and Type	Method and Description
int	dimensionOfDomain() Get the number of variables the function has.
int	dimensionOfRange() Get the dimension of the range space of the function.
java.lang.Double	evaluate(Vector x) Evaluate numerically the partial derivative of f at point x.
double	evaluate(Vector x, double h) Evaluate numerically the partial derivative of f at point x with step size h.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

FiniteDifference

public FiniteDifference(RealScalarFunction f,
                        int[] varidx)

Construct the partial derivative of a multi-variable function.

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

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 Detail

evaluate

public java.lang.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.

Specified by:

evaluate in interface Function<Vector,java.lang.Double>

Parameters:

x - the point to evaluate the derivative at

Returns:

the numerical partial derivative of f at point x

See Also:

Wikipedia: Practical considerations

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

dimensionOfDomain

public int dimensionOfDomain()

Description copied from interface: Function

Get the number of variables the function has. For example, for a univariate function, the domain dimension is 1; for a bivariate function, the domain dimension is 2.

Specified by:

dimensionOfDomain in interface Function<Vector,java.lang.Double>

Returns:

the number of variables

dimensionOfRange

public int dimensionOfRange()

Description copied from interface: Function

Get the dimension of the range space of the function. For example, for a Rⁿ->R^m function, the dimension of the range is m.

Specified by:

dimensionOfRange in interface Function<Vector,java.lang.Double>

Returns:

the dimension of the range