Class Gradient

java.lang.Object

org.episteme.core.mathematics.analysis.vectorcalculus.Gradient

public class Gradient
extends Object

Computes the gradient of a scalar field.

The gradient is a vector field that points in the direction of the greatest rate of increase of the scalar field.

Definition: ∇f = (∂f/∂x₁, ∂f/∂x₂, ..., ∂f/∂xₙ)

Physical interpretation: - Direction of steepest ascent - Electric field: E = -∇φ(negative gradient of potential) - Force from potential: F = -∇U

Since:

1.0

Author:

Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

Constructor Summary

Constructors

Constructor	Description
Gradient()

Method Summary

Modifier and Type	Method	Description
static VectorField<PointND>	asField(ScalarField<PointND> field, Real h)	Returns a vector field representing the gradient of the scalar field.
static Vector<Real>	compute(ScalarField<PointND> field, PointND point, Real h)	Computes the gradient of a scalar field at a point using finite differences.

Methods inherited from class Object

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

Constructor Details

Gradient

public Gradient()

Method Details

compute

public static Vector<Real> compute(ScalarField<PointND> field,
 PointND point,
 Real h)

Computes the gradient of a scalar field at a point using finite differences.

Uses central difference: ∂f/∂xᵢ ≈ (f(x + h*eᵢ) - f(x - h*eᵢ)) / (2h)

Parameters:

field - the scalar field

point - the point at which to compute the gradient

h - the step size for numerical differentiation

Returns:

the gradient vector

asField

public static VectorField<PointND> asField(ScalarField<PointND> field,
 Real h)

Returns a vector field representing the gradient of the scalar field.

Parameters:

field - the scalar field

h - the step size for numerical differentiation

Returns:

the gradient as a vector field