Uses of Interface
orbital.math.functional.Function

Packages that use Function

orbital.algorithm.evolutionary	Genetic algorithms simulate nature on a very abstract level to get solutions for sophisticated problems.
orbital.algorithm.template	A framework for general algorithmic evaluation schemes including search and planning algorithms.
orbital.math	Defines arithmetic objects and provides mathematical algorithms.
orbital.math.functional	Contains mathematical functors and extended functional operations.

Uses of Function in orbital.algorithm.evolutionary

Methods in orbital.algorithm.evolutionary that return Function

Function	GeneticAlgorithm.complexity()
Function	GeneticAlgorithm.spaceComplexity()

Uses of Function in orbital.algorithm.template

Methods in orbital.algorithm.template that return Function

Function	ParallelBranchAndBound.complexity() O(d) on parallel machines where d the solution depth.
Function	IterativeDeepeningAStar.complexity() O(bd) where b is the branching factor and d the solution depth.
Function	IterativeDeepening.complexity() O(bd) where b is the branching factor and d the solution depth.
Function	IterativeBroadening.complexity()
Function	HillClimbing.complexity() O( inf ).
Function	GaussSeidelDynamicProgramming.complexity()
Function	BranchAndBound.complexity() O(bd) where b is the branching factor and d the solution depth.
Function	AStar.complexity() O(bd) where b is the branching factor and d the solution depth.
Function	ThresholdAccepting.complexity() O( inf ).
Function	SimulatedAnnealing.complexity() O( inf ).
Function	RealTimeDynamicProgramming.complexity()
Function	IterativeExpansion.complexity() O(bd) where b is the branching factor and d the solution depth.
Function	Greedy.complexity() O(n*log n + n*f(n)) for n=|C| candidates.
Function	DynamicProgramming.complexity() O(n2)
Function	DivideAndConquer.complexity() ≈O(n*log n).
Function	DepthFirstSearch.complexity() O( inf ).
Function	BreadthFirstSearch.complexity() O(bd) where b is the branching factor and d the solution depth.
Function	Backtracking.complexity() O(nn) in the worst case.
Function	AlgorithmicTemplate.complexity() Measure for the asymptotic time complexity of the central solution operation in O-notation.
Function	ParallelBranchAndBound.spaceComplexity() O(bd) where b is the branching factor and d the solution depth.
Function	HillClimbing.spaceComplexity() O(b) where b is the branching factor and d the solution depth.
Function	GaussSeidelDynamicProgramming.spaceComplexity()
Function	AStar.spaceComplexity() O(bd) where b is the branching factor and d the solution depth.
Function	ThresholdAccepting.spaceComplexity() O(b) where b is the branching factor and d the solution depth.
Function	SimulatedAnnealing.spaceComplexity() O(b) where b is the branching factor and d the solution depth.
Function	RealTimeDynamicProgramming.spaceComplexity()
Function	IterativeExpansion.spaceComplexity() O(b*d) where b is the branching factor and d the solution depth.
Function	Greedy.spaceComplexity()
Function	DynamicProgramming.spaceComplexity()
Function	DivideAndConquer.spaceComplexity()
Function	DepthFirstSearch.spaceComplexity() O(b*d) where b is the branching factor and d the solution depth.
Function	BreadthFirstSearch.spaceComplexity() O(bd) where b is the branching factor and d the solution depth.
Function	Backtracking.spaceComplexity()
Function	AlgorithmicTemplate.spaceComplexity() Measure for the asymptotic space complexity of the central solution operation in O-notation.

Uses of Function in orbital.math

Subinterfaces of Function in orbital.math

interface	Polynomial Polynomial p in R[S] := R(S).
interface	UnivariatePolynomial (Univariate) polynomial p in R[X].

Methods in orbital.math that return Function

static Function	NumericalAlgorithms.bezierCurve(double t0, double tz, Matrix bezierNodes) Bezier curve.
static Function	NumericalAlgorithms.dSolve(BinaryFunction f, Real tau, Real eta, Real a, Real b, int steps, int order) Returns a numerical solution x of the one-dimensional differential equation x'(t) = f(t,x(t)), x(τ)=η on [a,b].
static Function	NumericalAlgorithms.dSolve(BinaryFunction f, Real tau, Real eta, Real min, Real max, int steps, Matrix butcher) Returns a numerical solution x of the one-dimensional differential equation x'(t) = f(t,x(t)), x(τ)=η on [a,b].
static Function	NumericalAlgorithms.dSolve(BinaryFunction f, Real tau, Vector eta, Real a, Real b, int steps, int order) Returns a numerical solution x of the differential equation x'(t) = f(t,x(t)), x(τ)=η on [a,b].
static Function	NumericalAlgorithms.dSolve(BinaryFunction f, Real tau, Vector eta, Real min, Real max, int steps, Matrix butcher) Returns a numerical solution x of the differential equation x'(t) = f(t,x(t)), x(τ)=η on [a,b].
static Function	AlgebraicAlgorithms.dSolve(Matrix A, Vector b, Real tau, Vector eta) Symbolically solves ordinary differential equation system.
static Function	Stat.functionalRegression(Function composedFunc, Matrix experiment) Performs linear regression to estimate a composed function with least squares.
static Function	NumericalAlgorithms.polynomialInterpolation(Matrix A) Polynomial interpolation.
static Function	NumericalAlgorithms.splineInterpolation(int k, Matrix A, int interpolationType) Spline interpolation.
static Function	NumericalAlgorithms.splineInterpolation(int k, Matrix A, int interpolationType, java.lang.Object[] config) Deprecated. Use NumericalAlgorithms.splineInterpolation(int,Matrix,int,Real,Real), or NumericalAlgorithms.splineInterpolation(int,Matrix,int) instead since they have a more reasonable argument list.
static Function	NumericalAlgorithms.splineInterpolation(int k, Matrix A, int interpolationType, Real fp_a, Real fp_b) Spline interpolation.

Methods in orbital.math with parameters of type Function

static Function	Stat.functionalRegression(Function composedFunc, Matrix experiment) Performs linear regression to estimate a composed function with least squares.
static Arithmetic	NumericalAlgorithms.integrate(Function f, Arithmetic a, Arithmetic b) Returns ≈ integral ab f dx.
static Arithmetic	MathUtilities.integrate(Function f, Arithmetic a, Arithmetic b) Returns integral ab f dx.
static Vector	Stat.regression(Function[] funcs, Matrix experiment) Performs linear regression to estimate the statistical mean according to least squares.

Uses of Function in orbital.math.functional

Subinterfaces of Function in orbital.math.functional

static interface

Function.Composite A composite function.

Fields in orbital.math.functional declared as Function

static Function	Functions.arccos arccos: [-1,1]->[0,π]; x |-> arccos x = cos-1 x.
static Function	Functions.arccot arccot: R->(0,π); x |-> arccot x = cot-1 x.
static Function	Functions.arcosh arcosh: [1, inf )->[0, inf ); x |-> arcosh x = (cosh|[0, inf ))-1 x = log(x ± sqrt x2-1).
static Function	Functions.arcoth arcoth: R\[-1,1]->R\{0}; x |-> arcoth x = coth-1 x = log((x+1) / (x-1)) / 2.
static Function	Functions.arcsin arcsin: [-1,1]->[-π/2,π/2]; x |-> arcsin x = sin-1 x.
static Function	Functions.arctan arctan: R->(-π/2,π/2); x |-> arctan x = tan-1 x.
static Function	Functions.arsinh arsinh: R->R; x |-> arsinh x = sinh-1 x = log(x + sqrt x2+1).
static Function	Functions.artanh artanh: (-1,1)->R; x |-> artanh x = tanh-1 x = log((1+x) / (1-x)) / 2.
static Function	Functions.cos cos: C->C; x |-> cos x = Σn=0 inf (-1)n * x2n / (2n)!.
static Function	Functions.cosh cosh: C->C; x |-> cosh x = (ex+e-x) / 2 = Σn=0 inf x2n / (2n)!.
static Function	Functions.cot cot: C\πZ->C; x |-> cot x = cos x / sin x = 1 / tan x.
static Function	Functions.coth coth: R\{0}->R; x |-> coth x = cosh x / sinh x = 1 / tanh x.
static Function	Functions.csc csc: R\{0}->R; x |-> csc x = 1 / sin(x).
static Function	Functions.csch csch: R\{0}->R; x |-> csch x = 1 / sinh(x).
static Function	Functions.diracDelta diracDelta δ: M\{0}->{0}; x |-> 0 if x!=0.
static Function	Functions.exp exp: C->C\{0}; x |-> ex = Σn=0 inf xn / n!.
static Function	Functions.id id: R->R; x |-> x .
static Function	Operations.inf inf inf: An->A; (xi) |-> infi {xi} = (| inf ,min|) (xi).
static Function	Operations.inverse inverse -1: A->A; x |-> x-1.
static Function	Functions.log log: C\{0}->C; x |-> loge x.
static Function	Functions.logistic logistic: A->(0,1); x |-> 1 / (1 + e-x).
static Function	Operations.minus minus −: A->A; x |-> −x.
static Function	Functions.nondet Represents a nondeterministic function.
static Function	Functions.norm norm: A->[0, inf ); x |-> ||x||.
static Function	Functions.one one: R->R; x |-> 1 .
static Function	Operations.product product Π: An->A; (xi) |-> Πi xi = (|1,|) (xi).
static Function	Functions.reciprocal reciprocal: C\{0}->C; x |-> x-1 = 1 / x.
static Function	Functions.sec sec: R->R; x |-> sec x = 1 / cos(x).
static Function	Functions.sech sech: R->R; x |-> sech x = 1/cosh(x).
static Function	Functions.sign sign: A->{-1,0,1}; x |-> -1 if x<0, x |-> 0 if x=0, x |-> 1 if x>0.
static Function	Functions.sin sin: C->C; x |-> sin x = Σn=0 inf (-1)n * x2n+1 / (2n+1)!.
static Function	Functions.sinh sinh: C->C; x |-> sinh x = (ex-e-x) / 2 = Σn=0 inf x2n+1 / (2n+1)!.
static Function	Functions.sqrt sqrt sqrt : C->C; x |-> sqrt x = x1/2.
static Function	Functions.square square: R->R; x |-> x2 .
static Function	Operations.sum sum Σ: An->A; (xi) |-> Σi xi = (|0,+|) (xi).
static Function	Operations.sup sup sup: An->A; (xi) |-> supi {xi} = (|- inf ,max|) (xi).
static Function	Functions.tan tan: C\(π/2+πZ)->C; x |-> tan x = sin x / cos x.
static Function	Functions.tanh tanh: C\(πi/2*Z)->C; x |-> tanh x = sinh x / cosh x.
static Function	Functions.zero zero: R->R; x |-> 0 .

Methods in orbital.math.functional that return Function

static Function	Functionals.bind(BinaryFunction f) Binds both arguments of a BinaryFunction together.
static Function	Functionals.bindFirst(BinaryFunction f, java.lang.Object x) Binds the first argument of a BinaryFunction to a fixed value.
static Function	Functionals.bindSecond(BinaryFunction f, java.lang.Object y) Binds the second argument of a BinaryFunction to a fixed value.
static Function	Functionals.compose(BinaryFunction f, Function g, Function h) compose: (f,g,h) |-> f º (g × h) := f(g,h) .
static Function	Functionals.compose(Function f, Function g) compose: (f,g) |-> f º g := f(g).
static Function	Functions.constant(java.lang.Object a) constant â: R->R; x |-> a .
Function	Function.derive() Derives this function and returns the resulting Function df/dx.
static Function	Functions.exp(Arithmetic b) expb: C->C\{0}; x |-> bx .
Function	Function.integrate() Integrates this function and returns the resulting indefinite integral integral f dx.
static Function	Functions.linear(Arithmetic a) linear: A->B; x |-> a*x.
static Function	Functionals.nest(Function f, int n) Nests a function n times within itself.
static Function	Functions.piecewise(Predicate[] cond, Function[] value) Get a function defined piecewise.
static Function	Functionals.pointwise(Function elemental) A function that performs an operation pointwise.
static Function	Functions.pow(Arithmetic p) powp: R->R; x |-> xp .
static Function	Functions.pow(double p)
static Function	Functions.projection(int component) projection πc: An->A; (x1,...xn)T |-> xc.
static Function	Functions.projection(int i, int j) projection πi,j: An×m->A; (xi,j) |-> xi,j.
static Function	Functions.step(Real t) step ht: A->{0,1}; x |-> 1 if x>=t, x |-> 0 if x<t.
static Function	Functions.symbolic(java.lang.String name) symbolic f:R->R; x |-> f(x).

Methods in orbital.math.functional with parameters of type Function

static Function	Functionals.compose(BinaryFunction f, Function g, Function h) compose: (f,g,h) |-> f º (g × h) := f(g,h) .
static Function	Functionals.compose(Function f, Function g) compose: (f,g) |-> f º g := f(g).
static MathFunctor	Functionals.genericCompose(Function f, java.lang.Object g) generic compose calls the compose function appropriate for the type of g.
static Matrix	Functionals.map(Function f, Matrix a)
static Tensor	Functionals.map(Function f, Tensor a) Maps a list of arguments with a function.
static Vector	Functionals.map(Function f, Vector a)
static Function	Functionals.nest(Function f, int n) Nests a function n times within itself.
static BinaryFunction	Functionals.onFirst(Function f) Applies a function on the first argument, ignoring the second.
static BinaryFunction	Functionals.onSecond(Function f) Applies a function on the second argument, ignoring the first.
static Function	Functions.piecewise(Predicate[] cond, Function[] value) Get a function defined piecewise.
static Function	Functionals.pointwise(Function elemental) A function that performs an operation pointwise.