Orbital library

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 ThresholdAccepting.complexity()
          O(∞).
 Function SimulatedAnnealing.complexity()
          O(∞).
 Function RealTimeDynamicProgramming.complexity()
           
 Function ParallelBranchAndBound.complexity()
          O(d) on parallel machines where d the solution depth.
 Function IterativeExpansion.complexity()
          O(bd) where b is the branching factor and 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(∞).
 Function Greedy.complexity()
          O(n*log n + n*f(n)) for n=|C| candidates.
 Function GaussSeidelDynamicProgramming.complexity()
           
 Function DynamicProgramming.complexity()
          O(n2)
 Function DivideAndConquer.complexity()
          ≈O(n*㏒ n).
 Function DepthFirstSearch.complexity()
          O(∞).
 Function BreadthFirstSearch.complexity()
          O(bd) where b is the branching factor and d the solution depth.
 Function BranchAndBound.complexity()
          O(bd) where b is the branching factor and d the solution depth.
 Function Backtracking.complexity()
          O(nn) in the worst case.
 Function AStar.complexity()
          O(bd) where b is the branching factor and d the solution depth.
 Function AlgorithmicTemplate.complexity()
          Measure for the asymptotic time complexity of the central solution operation in O-notation.
 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 ParallelBranchAndBound.spaceComplexity()
          O(bd) where b is the branching factor and d the solution depth.
 Function IterativeExpansion.spaceComplexity()
          O(b*d) 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 Greedy.spaceComplexity()
           
 Function GaussSeidelDynamicProgramming.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 AStar.spaceComplexity()
          O(bd) where b is the branching factor and d the solution depth.
 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∈R[S] := R(S).
 interface UnivariatePolynomial
          (Univariate) polynomial p∈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 ≈ ∫ab f dx.
static Arithmetic MathUtilities.integrate(Function f, Arithmetic a, Arithmetic b)
          Returns ∫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,∞)→[0,∞); x ↦ arcosh x = (cosh|[0,∞))-1 x = ㏒(x ± √x2-1).
static Function Functions.arcoth
          arcoth: R\[-1,1]→R\{0}; x ↦ arcoth x = coth-1 x = ㏒((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 = ㏒(x + √x2+1).
static Function Functions.artanh
          artanh: (-1,1)→R; x ↦ artanh x = tanh-1 x = ㏒((1+x) / (1-x)) / 2.
static Function Functions.cos
          cos: CC; x ↦ cos x = ∑n=0 (-1)n * x2n / (2n)!.
static Function Functions.cosh
          cosh: CC; x ↦ cosh x = (ex+e-x) / 2 = ∑n=0 x2n / (2n)!.
static Function Functions.cot
          cot: CZC; 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: CC\{0}; x ↦ ex = ∑n=0 xn / n!.
static Function Functions.id
          id: R→R; x ↦ x .
static Function Operations.inf
          inf ⊓: An→A; (xi) ↦ ⊓i {xi} = (|∞,min|) (xi).
static Function Operations.inverse
          inverse -1: A→A; x ↦ x-1.
static Function Functions.log
          ㏒: C\{0}→C; x ↦ ㏒e 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,∞); x ↦ ||x||.
static Function Functions.one
          one: R→R; x ↦ 1 .
static Function Operations.product
          product ∏: An→A; (xi) ↦ ∏i 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: CC; x ↦ sin x = ∑n=0 (-1)n * x2n+1 / (2n+1)!.
static Function Functions.sinh
          sinh: CC; x ↦ sinh x = (ex-e-x) / 2 = ∑n=0 x2n+1 / (2n+1)!.
static Function Functions.sqrt
          sqrt √ : CC; x ↦ √x = x1/2.
static Function Functions.square
          square: R→R; x ↦ x2 .
static Function Operations.sum
          sum ∑: An→A; (xi) ↦ ∑i xi = (|0,+|) (xi).
static Function Operations.sup
          sup ⊔: An→A; (xi) ↦ ⊔i {xi} = (|-∞,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 ∘ (g × h) := f(g,h) .
static Function Functionals.compose(Function f, Function g)
          compose: (f,g) ↦ f ∘ 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: CC\{0}; x ↦ bx .
 Function Function.integrate()
          Integrates this function and returns the resulting indefinite 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 ∘ (g × h) := f(g,h) .
static Function Functionals.compose(Function f, Function g)
          compose: (f,g) ↦ f ∘ 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.
 


Orbital library
1.3.0: 11 Apr 2009

Copyright © 1996-2009 André Platzer
All Rights Reserved.