Class NumericalDifferentiation

java.lang.Object

org.episteme.core.mathematics.analysis.differentiation.NumericalDifferentiation

public class NumericalDifferentiation
extends Object

Numerical differentiation methods.

Since:

1.0

Author:

Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

Constructor Summary

Constructors

Constructor	Description
NumericalDifferentiation()

Method Summary

Modifier and Type	Method	Description
static double	backwardDifference(DoubleUnaryOperator f, double x, double h)	Backward difference: f'(x) ≈ (f(x) - f(x-h)) / h First-order accurate: O(h)
static double	centralDifference(DoubleUnaryOperator f, double x, double h)	Central difference: f'(x) ≈ (f(x+h) - f(x-h)) / 2h Second-order accurate: O(h²)
static double	fivePointStencil(DoubleUnaryOperator f, double x, double h)	Five-point stencil: f'(x) ≈ (-f(x+2h) + 8f(x+h) - 8f(x-h) + f(x-2h)) / 12h Fourth-order accurate: O(h⁴)
static double	forwardDifference(DoubleUnaryOperator f, double x, double h)	Forward difference: f'(x) ≈ (f(x+h) - f(x)) / h First-order accurate: O(h)
static double[]	gradient(Function<double[],Double> f, double[] x, double h)	Compute gradient for multivariate function.
static double[][]	hessian(Function<double[],Double> f, double[] x, double h)	Compute Hessian matrix (second partial derivatives).
static double[][]	jacobian(Function<double[],double[]> f, double[] x, double h)	Compute Jacobian matrix for vector-valued function.
static double	laplacian(Function<double[],Double> f, double[] x, double h)	Laplacian: ∇²f = ∂²f/∂x² + ∂²f/∂y² + ...
static double	richardsonExtrapolation(DoubleUnaryOperator f, double x, double h, int order)	Richardson extrapolation for improved accuracy.
static double	secondDerivative(DoubleUnaryOperator f, double x, double h)	Second derivative using central difference: f''(x) ≈ (f(x+h) - 2f(x) + f(x-h)) / h²

Methods inherited from class Object

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

Constructor Details

NumericalDifferentiation

public NumericalDifferentiation()

Method Details

forwardDifference

public static double forwardDifference(DoubleUnaryOperator f,
 double x,
 double h)

Forward difference: f'(x) ≈ (f(x+h) - f(x)) / h First-order accurate: O(h)

backwardDifference

public static double backwardDifference(DoubleUnaryOperator f,
 double x,
 double h)

Backward difference: f'(x) ≈ (f(x) - f(x-h)) / h First-order accurate: O(h)

centralDifference

public static double centralDifference(DoubleUnaryOperator f,
 double x,
 double h)

Central difference: f'(x) ≈ (f(x+h) - f(x-h)) / 2h Second-order accurate: O(h²)

fivePointStencil

public static double fivePointStencil(DoubleUnaryOperator f,
 double x,
 double h)

Five-point stencil: f'(x) ≈ (-f(x+2h) + 8f(x+h) - 8f(x-h) + f(x-2h)) / 12h Fourth-order accurate: O(h⁴)

secondDerivative

public static double secondDerivative(DoubleUnaryOperator f,
 double x,
 double h)

Second derivative using central difference: f''(x) ≈ (f(x+h) - 2f(x) + f(x-h)) / h²

richardsonExtrapolation

public static double richardsonExtrapolation(DoubleUnaryOperator f,
 double x,
 double h,
 int order)

Richardson extrapolation for improved accuracy.

gradient

public static double[] gradient(Function<double[],Double> f,
 double[] x,
 double h)

Compute gradient for multivariate function.

Parameters:

f - Function f(x) -> y

x - Point to evaluate

h - Step size

Returns:

Gradient vector

hessian

public static double[][] hessian(Function<double[],Double> f,
 double[] x,
 double h)

Compute Hessian matrix (second partial derivatives).

jacobian

public static double[][] jacobian(Function<double[],double[]> f,
 double[] x,
 double h)

Compute Jacobian matrix for vector-valued function.

laplacian

public static double laplacian(Function<double[],Double> f,
 double[] x,
 double h)

Laplacian: ∇²f = ∂²f/∂x² + ∂²f/∂y² + ...