Uses of Interface
org.episteme.core.mathematics.analysis.Function

Packages that use Function

Package	Description
org.episteme.core.mathematics.analysis
org.episteme.core.mathematics.analysis.chaos
org.episteme.core.mathematics.analysis.fem
org.episteme.core.mathematics.analysis.integration
org.episteme.core.mathematics.analysis.ode
org.episteme.core.mathematics.analysis.pde
org.episteme.core.mathematics.analysis.rootfinding
org.episteme.core.mathematics.analysis.series
org.episteme.core.mathematics.analysis.transform
org.episteme.core.mathematics.geometry
org.episteme.core.mathematics.geometry.curves
org.episteme.core.mathematics.geometry.surfaces
org.episteme.core.mathematics.numerical.fem
org.episteme.core.mathematics.numerical.fem.providers
org.episteme.core.mathematics.optimization
org.episteme.core.mathematics.statistics
org.episteme.core.mathematics.statistics.distributions
org.episteme.core.ui.viewers.mathematics.analysis.plotting
org.episteme.core.ui.viewers.mathematics.analysis.plotting.backends
org.episteme.natural.computing.ai.evolutionary

Uses of Function in org.episteme.core.mathematics.analysis

Subinterfaces of Function in org.episteme.core.mathematics.analysis

Modifier and Type	Interface	Description
interface	Bijection<D,C>	A bijective function (one-to-one and onto mapping).
interface	ContinuousFunction<D,C>	Represents a continuous function.
interface	DifferentiableFunction<D,C>	Represents a differentiable function.
interface	IntegrableFunction<D,C>	Represents an integrable function.
interface	MultivariateFunction	Multivariate function (multiple variables: ℝⁿ → ℝ).
interface	MultivariateRealFunction	Represents a real-valued function of multiple real variables (R^n -> R).
interface	RealFunction	Represents a real-valued function of a real variable (R -> R).
interface	ScalarField<V>	Represents a scalar field: f: ℝⁿ → ℝ
interface	ScalarFunction<D>	Scalar-valued function (returns a single real number).
interface	UnivariateFunction	Univariate function (single variable: ℝ → ℝ).
interface	VectorField<V>	Represents a vector field: F: ℝⁿ → ℝⁿ
interface	VectorFunction<F extends Field<F>>	Represents a function from a vector space to another (F^n -> F^m).

Classes in org.episteme.core.mathematics.analysis that implement Function

Modifier and Type	Class	Description
class	PolynomialFunction<R>	Represents a polynomial function P(x) over a Ring R.

Methods in org.episteme.core.mathematics.analysis that return Function

Modifier and Type	Method	Description
default <V> Function<D,V>	Function.andThen(Function<? super C, ? extends V> after)	Composes this function with another (from java.util.function.Function).
default <V> Function<V,C>	Function.compose(Function<V,D> inner)	Returns the composition of this function with another function.
Function<D,C>	DifferentiableFunction.differentiate()	Returns the derivative of this function.
Function<R,R>	PolynomialFunction.differentiate()
default Function<Real,Real>	RealFunction.differentiate()
default Function<Vector<F>, Vector<F>>	VectorFunction.differentiate()	Returns the derivative of this function, which is the linear map represented by the Jacobian.
Function<D,C>	IntegrableFunction.integrate()	Returns the indefinite integral (antiderivative) of this function.
Function<R,R>	PolynomialFunction.integrate()

Methods in org.episteme.core.mathematics.analysis with parameters of type Function

Modifier and Type	Method	Description
default <V> Function<V,C>	Function.compose(Function<V,D> inner)	Returns the composition of this function with another function.

Uses of Function in org.episteme.core.mathematics.analysis.chaos

Subinterfaces of Function in org.episteme.core.mathematics.analysis.chaos

Modifier and Type	Interface	Description
interface	DiscreteMap<T>	A discrete dynamical system defined by an iterative map.

Classes in org.episteme.core.mathematics.analysis.chaos that implement Function

Modifier and Type	Class	Description
class	ArnoldCatMap	Arnold's Cat Map: x_{n+1} = (2x_n + y_n) mod 1 y_{n+1} = (x_n + y_n) mod 1
class	GingerbreadManMap	The Gingerbread Man Map - a chaotic discrete dynamical system.
class	HenonMap	The Hénon Map: x_{n+1} = 1 - a * x_n^2 + y_n y_{n+1} = b * x_n
class	LogisticMap	The Logistic Map: x_{n+1} = r * x_n * (1 - x_n).
class	StandardMap	The Standard Map (Chirikov-Taylor map): p_{n+1} = (p_n + K * sin(theta_n)) mod 2Ï€ theta_{n+1} = (theta_n + p_{n+1}) mod 2Ï€

Uses of Function in org.episteme.core.mathematics.analysis.fem

Methods in org.episteme.core.mathematics.analysis.fem with parameters of type Function

Modifier and Type	Method	Description
Vector<Real>	FEMSolver.solvePoisson(Mesh mesh, Function<Vector<Real>, Real> sourceTerm)	Solves the Poisson equation on the given mesh.

Uses of Function in org.episteme.core.mathematics.analysis.integration

Methods in org.episteme.core.mathematics.analysis.integration with parameters of type Function

Modifier and Type	Method	Description
static Real	GaussLegendre.integrate(Function<Real,Real> f, int n)	Computes the integral of f(x) over [-1, 1] using n points.
static Real	GaussLegendre.integrate(Function<Real,Real> f, Real a, Real b, int n)	Computes the integral of f(x) over [a, b] using n points.

Uses of Function in org.episteme.core.mathematics.analysis.ode

Methods in org.episteme.core.mathematics.analysis.ode with parameters of type Function

Modifier and Type	Method	Description
static Real[]	ODESolver.euler(Function<Real[],Real> f, Real t0, Real y0, Real tEnd, Real h)	Euler's method: y_{n+1} = y_n + h*f(t_n, y_n)
static Real[]	ODESolver.midpoint(Function<Real[],Real> f, Real t0, Real y0, Real tEnd, Real h)	Midpoint method (2nd order Runge-Kutta).
static Real[]	ODESolver.rungeKutta4(Function<Real[],Real> f, Real t0, Real y0, Real tEnd, Real h)	Runge-Kutta 4th order (RK4): Classical method.

Uses of Function in org.episteme.core.mathematics.analysis.pde

Methods in org.episteme.core.mathematics.analysis.pde with parameters of type Function

Modifier and Type	Method	Description
static Real[][]	FiniteDifference.heatEquation1D(Function<Real,Real> initial, Real alpha, Real L, Real T, int nx, int nt)	Solves 1D heat equation: ∂u/∂t = α ∂²u/∂x²
static Real[][]	FiniteDifference.poisson2D(Function<Real[],Real> source, int nx, int ny, Real lx, Real ly, int maxIter, Real tolerance)	Solves 2D Poisson equation: ∇²u = f on rectangular domain.
void	HeatEquationSolver.setInitialCondition(Function<Real,Real> f)	Set initial condition.
void	WaveEquationSolver.setInitialConditions(Function<Real,Real> displacement, Function<Real,Real> velocity, Real dt)	Set initial displacement and velocity.
void	WaveEquationSolver.setInitialDisplacement(Function<Real,Real> f)	Set initial displacement.
static Real[][]	FiniteDifference.waveEquation1D(Function<Real,Real> initial, Function<Real,Real> initialVelocity, Real c, Real L, Real T, int nx, int nt)	Solves 1D wave equation: ∂²u/∂t² = c² ∂²u/∂x²

Uses of Function in org.episteme.core.mathematics.analysis.rootfinding

Methods in org.episteme.core.mathematics.analysis.rootfinding with parameters of type Function

Modifier and Type	Method	Description
static Real	RootFinding.bisection(Function<Real,Real> f, Real a, Real b, Real tolerance, int maxIterations)	Bisection method (bracketing method).
static Real	RootFinding.brent(Function<Real,Real> f, Real a, Real b, Real tolerance)	Brent's method - combination of bisection, secant, and inverse quadratic interpolation.
static Real	RootFinding.newtonRaphson(Function<Real,Real> f, Function<Real,Real> df, Real initialGuess, Real tolerance, int maxIterations)	Newton-Raphson method: xₙ₊₁ = xₙ - f(xₙ)/f'(xₙ)
static Real	RootFinding.secant(Function<Real,Real> f, Real x0, Real x1, Real tolerance, int maxIterations)	Secant method: xₙ₊₁ = xₙ - f(xₙ) * (xₙ - xₙ₋₁) / (f(xₙ) - f(xₙ₋₁))

Uses of Function in org.episteme.core.mathematics.analysis.series

Subinterfaces of Function in org.episteme.core.mathematics.analysis.series

Modifier and Type	Interface	Description
interface	ConvergentSequence<T>	Represents a sequence that converges to a limit.
interface	IntegerSequence	A sequence of integers (ℤ).
interface	Sequence<T>	A mathematical sequence a(n) for n ≥ 0.

Classes in org.episteme.core.mathematics.analysis.series that implement Function

Modifier and Type	Class	Description
class	BellSequence	Bell numbers sequence (OEIS A000110).
class	CatalanSequence	Catalan numbers: C(0)=1, C(n) = (2n)!
class	FactorialSequence	Factorial sequence: n!
class	FibonacciSequence	Fibonacci sequence: F(0) = 0, F(1) = 1, F(n) = F(n-1) + F(n-2).
class	PrimePiSequence	Prime counting function π(n) (OEIS A000720).
class	PrimeSequence	Prime number sequence: 2, 3, 5, 7, 11, ...
class	RecursiveSequence<T>	Represents a sequence defined by a recurrence relation.
class	SquareSequence	Square numbers sequence: a(n) = n².
class	TriangularSequence	Triangular numbers sequence: T(n) = n(n+1)/2.

Uses of Function in org.episteme.core.mathematics.analysis.transform

Subinterfaces of Function in org.episteme.core.mathematics.analysis.transform

Modifier and Type	Interface	Description
interface	Transform<D,C>	Represents a mathematical transform (e.g., Fourier, Laplace, Wavelet).

Classes in org.episteme.core.mathematics.analysis.transform that implement Function

Modifier and Type	Class	Description
class	DiscreteFourierTransform	Discrete Fourier Transform (DFT) using Fast Fourier Transform (FFT) algorithm.

Uses of Function in org.episteme.core.mathematics.geometry

Subinterfaces of Function in org.episteme.core.mathematics.geometry

Modifier and Type	Interface	Description
interface	ParametricCurve	Represents a parametric curve in N-dimensional space.
interface	ParametricSurface	Represents a parametric surface in 3D space.

Methods in org.episteme.core.mathematics.geometry that return Function

Modifier and Type	Method	Description
default Function<Real, Vector<Real>>	ParametricCurve.differentiate()
default Function<Vector<Real>, Vector<Real>>	ParametricSurface.differentiate()

Uses of Function in org.episteme.core.mathematics.geometry.curves

Classes in org.episteme.core.mathematics.geometry.curves that implement Function

Modifier and Type	Class	Description
class	BezierCurve	Represents a Bézier curve.
class	Circle	Represents a circle as a parametric curve.
class	Ellipse	Represents an ellipse curve.
class	Helix	Represents a 3D helix (spiral) curve.

Uses of Function in org.episteme.core.mathematics.geometry.surfaces

Classes in org.episteme.core.mathematics.geometry.surfaces that implement Function

Modifier and Type	Class	Description
class	Cone	Represents a conical surface.
class	Cylinder	Represents a cylindrical surface.
class	Ellipsoid	Represents an ellipsoidal surface.
class	Paraboloid	Represents a paraboloidal surface.
class	Sphere	Represents a sphere as a parametric surface.
class	Torus	Represents a torus as a parametric surface.

Uses of Function in org.episteme.core.mathematics.numerical.fem

Methods in org.episteme.core.mathematics.numerical.fem with parameters of type Function

Modifier and Type	Method	Description
Vector<Real>	FEMProvider.solvePoisson(Mesh mesh, Function<Vector<Real>, Real> sourceTerm)

Uses of Function in org.episteme.core.mathematics.numerical.fem.providers

Methods in org.episteme.core.mathematics.numerical.fem.providers with parameters of type Function

Modifier and Type	Method	Description
Vector<Real>	MulticoreFEMProvider.solvePoisson(Mesh mesh, Function<Vector<Real>, Real> sourceTerm)

Uses of Function in org.episteme.core.mathematics.optimization

Methods in org.episteme.core.mathematics.optimization with parameters of type Function

Modifier and Type	Method	Description
static Real	Optimizer.goldenSectionSearch(Function<Real,Real> f, Real a, Real b, Real tolerance)	Golden Section Search for 1D unimodal functions.
static Real	Optimizer.gradientDescent(Function<Real,Real> f, Function<Real,Real> gradient, Real initialGuess, Real learningRate, Real tolerance, int maxIterations)	Gradient Descent: x_{n+1} = x_n - α∇f(x_n)
static Real	Optimizer.nelderMead(Function<Real,Real> f, Real[] initialSimplex, Real tolerance, int maxIterations)	Nelder-Mead Simplex algorithm for multidimensional optimization.
static Real	Optimizer.newtonOptimization(Function<Real,Real> f, Function<Real,Real> gradient, Function<Real,Real> hessian, Real initialGuess, Real tolerance, int maxIterations)	Newton's method for optimization: x_{n+1} = x_n - H^{-1}∇f(x_n)
static Real	Optimizer.simulatedAnnealing(Function<Real,Real> f, Real initialGuess, Real temperature, Real coolingRate, int maxIterations)	Simulated Annealing - global optimization.
static ToDoubleFunction<double[]>	OptimizationBridge.toDoubleFunction(Function<Real[],Real> realFunction)	Converts a Function<Real[], Real> to a ToDoubleFunction<double[]>.

Uses of Function in org.episteme.core.mathematics.statistics

Subinterfaces of Function in org.episteme.core.mathematics.statistics

Modifier and Type	Interface	Description
interface	ProbabilityDistribution	A probability distribution P(X ≤ x).

Classes in org.episteme.core.mathematics.statistics that implement Function

Modifier and Type	Class	Description
class	ContinuousDistribution	Abstract base class for continuous probability distributions.
class	DiscreteDistribution	Abstract base class for discrete probability distributions.

Uses of Function in org.episteme.core.mathematics.statistics.distributions

Classes in org.episteme.core.mathematics.statistics.distributions that implement Function

Modifier and Type	Class	Description
class	BetaDistribution
class	BinomialDistribution	Binomial distribution Bin(n, p).
class	CauchyDistribution	Cauchy distribution (also called Lorentz distribution).
class	ChiSquareDistribution
class	ExponentialDistribution	Exponential distribution Exp(λ).
class	GammaDistribution
class	GeometricDistribution
class	LogNormalDistribution	LogNormal distribution.
class	NormalDistribution	Normal (Gaussian) distribution N(μ, σ²).
class	PoissonDistribution	*
class	StudentTDistribution
class	UniformDistribution
class	WeibullDistribution	Weibull distribution.

Uses of Function in org.episteme.core.ui.viewers.mathematics.analysis.plotting

Methods in org.episteme.core.ui.viewers.mathematics.analysis.plotting with parameters of type Function

Modifier and Type	Method	Description
Plot2D	Plot2D.addFunction(Function<Real,Real> function, Real xMin, Real xMax, String label)	Adds function to plot: y = f(x)
Plot3D	Plot3D.addParametricCurve(Function<Real,Real> xFunc, Function<Real,Real> yFunc, Function<Real,Real> zFunc, Real tMin, Real tMax, String label)	Adds parametric curve: (x(t), y(t), z(t))
Plot3D	Plot3D.addSurface(Function<Real[],Real> function, Real xMin, Real xMax, Real yMin, Real yMax, String label)	Adds surface: z = f(x, y)

Uses of Function in org.episteme.core.ui.viewers.mathematics.analysis.plotting.backends

Methods in org.episteme.core.ui.viewers.mathematics.analysis.plotting.backends with parameters of type Function

Modifier and Type	Method	Description
Plot2D	JavaFXPlot2D.addFunction(Function<Real,Real> function, Real xMin, Real xMax, String label)
Plot2D	JFreeChartPlot2D.addFunction(Function<Real,Real> function, Real xMin, Real xMax, String label)
Plot2D	XChartPlot2D.addFunction(Function<Real,Real> function, Real xMin, Real xMax, String label)
Plot3D	JavaFXPlot3D.addParametricCurve(Function<Real,Real> xFunc, Function<Real,Real> yFunc, Function<Real,Real> zFunc, Real tMin, Real tMax, String label)
Plot3D	Jzy3dPlot3D.addParametricCurve(Function<Real,Real> xFunc, Function<Real,Real> yFunc, Function<Real,Real> zFunc, Real tMin, Real tMax, String label)
Plot3D	JavaFXPlot3D.addSurface(Function<Real[],Real> function, Real xMin, Real xMax, Real yMin, Real yMax, String label)
Plot3D	Jzy3dPlot3D.addSurface(Function<Real[],Real> function, Real xMin, Real xMax, Real yMin, Real yMax, String label)

Uses of Function in org.episteme.natural.computing.ai.evolutionary

Constructors in org.episteme.natural.computing.ai.evolutionary with parameters of type Function

Modifier	Constructor	Description
	EvolutionaryOptimizer(Function<Real[],Real> fitness, int dimensions, Real[] lowerBounds, Real[] upperBounds, int populationSize)
	RealChromosome(Real[] genes, Function<Real[],Real> fitnessFunction, Real[] lowerBounds, Real[] upperBounds)