Uses of Interface
org.episteme.core.mathematics.analysis.Function
Packages that use Function
Package
Description
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Uses of Function in org.episteme.core.mathematics.analysis
Subinterfaces of Function in org.episteme.core.mathematics.analysisModifier and TypeInterfaceDescriptioninterfaceBijection<D,C> A bijective function (one-to-one and onto mapping).interfaceContinuousFunction<D,C> Represents a continuous function.interfaceRepresents a differentiable function.interfaceIntegrableFunction<D,C> Represents an integrable function.interfaceMultivariate function (multiple variables: â„Ââ¿ → â„Â).interfaceRepresents a real-valued function of multiple real variables (R^n -> R).interfaceRepresents a real-valued function of a real variable (R -> R).interfaceScalarField<V>Represents a scalar field: f: â„Ââ¿ → â„ÂinterfaceScalar-valued function (returns a single real number).interfaceUnivariate function (single variable: ℠→ â„Â).interfaceVectorField<V>Represents a vector field: F: â„Ââ¿ → â„Ââ¿interfaceVectorFunction<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 FunctionModifier and TypeClassDescriptionclassRepresents a polynomial function P(x) over a Ring R.Methods in org.episteme.core.mathematics.analysis that return FunctionModifier and TypeMethodDescriptionComposes this function with another (from java.util.function.Function).Returns the composition of this function with another function.DifferentiableFunction.differentiate()Returns the derivative of this function.PolynomialFunction.differentiate()RealFunction.differentiate()VectorFunction.differentiate()Returns the derivative of this function, which is the linear map represented by the Jacobian.IntegrableFunction.integrate()Returns the indefinite integral (antiderivative) of this function.PolynomialFunction.integrate()Methods in org.episteme.core.mathematics.analysis with parameters of type Function -
Uses of Function in org.episteme.core.mathematics.analysis.chaos
Subinterfaces of Function in org.episteme.core.mathematics.analysis.chaosModifier and TypeInterfaceDescriptioninterfaceDiscreteMap<T>A discrete dynamical system defined by an iterative map.Classes in org.episteme.core.mathematics.analysis.chaos that implement FunctionModifier and TypeClassDescriptionclassArnold's Cat Map: x_{n+1} = (2x_n + y_n) mod 1 y_{n+1} = (x_n + y_n) mod 1classThe Gingerbread Man Map - a chaotic discrete dynamical system.classThe Hénon Map: x_{n+1} = 1 - a * x_n^2 + y_n y_{n+1} = b * x_nclassThe Logistic Map: x_{n+1} = r * x_n * (1 - x_n).classThe Standard Map (Chirikov-Taylor map): p_{n+1} = (p_n + K * sin(theta_n)) mod 2À theta_{n+1} = (theta_n + p_{n+1}) mod 2À -
Uses of Function in org.episteme.core.mathematics.analysis.fem
Methods in org.episteme.core.mathematics.analysis.fem with parameters of type Function -
Uses of Function in org.episteme.core.mathematics.analysis.integration
Methods in org.episteme.core.mathematics.analysis.integration with parameters of type Function -
Uses of Function in org.episteme.core.mathematics.analysis.ode
Methods in org.episteme.core.mathematics.analysis.ode with parameters of type Function -
Uses of Function in org.episteme.core.mathematics.analysis.pde
Methods in org.episteme.core.mathematics.analysis.pde with parameters of type FunctionModifier and TypeMethodDescriptionstatic 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/∂x²static 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.voidHeatEquationSolver.setInitialCondition(Function<Real, Real> f) Set initial condition.voidWaveEquationSolver.setInitialConditions(Function<Real, Real> displacement, Function<Real, Real> velocity, Real dt) Set initial displacement and velocity.voidWaveEquationSolver.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 FunctionModifier and TypeMethodDescriptionstatic RealBisection method (bracketing method).static RealBrent's method - combination of bisection, secant, and inverse quadratic interpolation.static RealRootFinding.newtonRaphson(Function<Real, Real> f, Function<Real, Real> df, Real initialGuess, Real tolerance, int maxIterations) Newton-Raphson method: xₙ₊₠= xâ‚™ - f(xâ‚™)/f'(xâ‚™)static RealSecant method: xₙ₊₠= xâ‚™ - f(xâ‚™) * (xâ‚™ - xₙ₋â‚Â) / (f(xâ‚™) - f(xₙ₋â‚Â)) -
Uses of Function in org.episteme.core.mathematics.analysis.series
Subinterfaces of Function in org.episteme.core.mathematics.analysis.seriesModifier and TypeInterfaceDescriptioninterfaceRepresents a sequence that converges to a limit.interfaceA sequence of integers (ℤ).interfaceSequence<T>A mathematical sequence a(n) for n ≥ 0.Classes in org.episteme.core.mathematics.analysis.series that implement FunctionModifier and TypeClassDescriptionclassBell numbers sequence (OEIS A000110).classCatalan numbers: C(0)=1, C(n) = (2n)!classFactorial sequence: n!classFibonacci sequence: F(0) = 0, F(1) = 1, F(n) = F(n-1) + F(n-2).classPrime counting function À(n) (OEIS A000720).classPrime number sequence: 2, 3, 5, 7, 11, ...classRepresents a sequence defined by a recurrence relation.classSquare numbers sequence: a(n) = n².classTriangular 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.transformModifier and TypeInterfaceDescriptioninterfaceTransform<D,C> Represents a mathematical transform (e.g., Fourier, Laplace, Wavelet).Classes in org.episteme.core.mathematics.analysis.transform that implement FunctionModifier and TypeClassDescriptionclassDiscrete 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.geometryModifier and TypeInterfaceDescriptioninterfaceRepresents a parametric curve in N-dimensional space.interfaceRepresents a parametric surface in 3D space.Methods in org.episteme.core.mathematics.geometry that return Function -
Uses of Function in org.episteme.core.mathematics.geometry.curves
Classes in org.episteme.core.mathematics.geometry.curves that implement FunctionModifier and TypeClassDescriptionclassRepresents a Bézier curve.classRepresents a circle as a parametric curve.classRepresents an ellipse curve.classRepresents 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 FunctionModifier and TypeClassDescriptionclassRepresents a conical surface.classRepresents a cylindrical surface.classRepresents an ellipsoidal surface.classRepresents a paraboloidal surface.classRepresents a sphere as a parametric surface.classRepresents 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 -
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 -
Uses of Function in org.episteme.core.mathematics.optimization
Methods in org.episteme.core.mathematics.optimization with parameters of type FunctionModifier and TypeMethodDescriptionstatic RealGolden Section Search for 1D unimodal functions.static RealOptimizer.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 RealOptimizer.nelderMead(Function<Real, Real> f, Real[] initialSimplex, Real tolerance, int maxIterations) Nelder-Mead Simplex algorithm for multidimensional optimization.static RealOptimizer.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 RealOptimizer.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.statisticsModifier and TypeInterfaceDescriptioninterfaceA probability distribution P(X ≤ x).Classes in org.episteme.core.mathematics.statistics that implement FunctionModifier and TypeClassDescriptionclassAbstract base class for continuous probability distributions.classAbstract 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 FunctionModifier and TypeClassDescriptionclassclassBinomial distribution Bin(n, p).classCauchy distribution (also called Lorentz distribution).classclassExponential distribution Exp(λ).classclassclassLogNormal distribution.classNormal (Gaussian) distribution N(μ, ÃÆ’²).class*classclassclassWeibull 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 FunctionModifier and TypeMethodDescriptionAdds function to plot: y = f(x)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.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 FunctionModifier and TypeMethodDescriptionJavaFXPlot3D.addParametricCurve(Function<Real, Real> xFunc, Function<Real, Real> yFunc, Function<Real, Real> zFunc, Real tMin, Real tMax, String label) Jzy3dPlot3D.addParametricCurve(Function<Real, Real> xFunc, Function<Real, Real> yFunc, Function<Real, Real> zFunc, Real tMin, Real tMax, String label) JavaFXPlot3D.addSurface(Function<Real[], Real> function, Real xMin, Real xMax, Real yMin, Real yMax, String label) 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