com.numericalmethod.suanshu.analysis.differentiation.multivariate

Class Gradient

java.lang.Object

com.numericalmethod.suanshu.vector.doubles.dense.DenseVector

com.numericalmethod.suanshu.analysis.differentiation.multivariate.Gradient

All Implemented Interfaces:

DeepCopyable, AbelianGroup<Vector>, BanachSpace<Vector,Real>, HilbertSpace<Vector,Real>, VectorSpace<Vector,Real>, Vector, java.io.Serializable

public class Gradient
extends DenseVector

The gradient of a scalar field is a vector field which points in the direction of the greatest rate of increase of the scalar field, and of which the magnitude is the greatest rate of change. Mathematically, the gradient of a scalar function is a vector of size n, where n is the domain dimension of f. \[ \nabla{f} = {\partial f \over \partial x_1}, \dots, {\partial f \over \partial x_n} \] The gradient vector is computed numerically using the finite difference method, e.g., FiniteDifference.

See Also:

Wikipedia: Gradient, Serialized Form

Constructor Summary

Constructors

Constructor and Description
Gradient(RealScalarFunction f, Vector x) Construct the gradient vector for a multivariate function f at point x.

Method Summary

Methods inherited from class com.numericalmethod.suanshu.vector.doubles.dense.DenseVector

add, add, angle, deepCopy, divide, equals, get, hashCode, innerProduct, minus, minus, multiply, norm, norm, opposite, pow, scaled, scaled, set, set, size, toArray, toString, ZERO

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Constructor Detail

Gradient

public Gradient(RealScalarFunction f,
                Vector x)

Construct the gradient vector for a multivariate function f at point x.

Parameters:

f - a multivariate function

x - the point to evaluate the gradient of f at