# Uses of Interfacedev.nm.analysis.function.Function

Packages that use Function
• ## Uses of Function in dev.nm.analysis.curvefit.interpolation

Modifier and Type
Class
Description
class
LinearInterpolator
Define a univariate function by linearly interpolating between adjacent points.
class
NevilleTable
Neville's algorithm is a polynomial interpolation algorithm.
• ## Uses of Function in dev.nm.analysis.differentiation

Classes in dev.nm.analysis.differentiation that implement Function
Modifier and Type
Class
Description
class
Ridders
Ridders' method computes the numerical derivative of a function.
• ## Uses of Function in dev.nm.analysis.differentiation.multivariate

Modifier and Type
Class
Description
class
GradientFunction
The gradient function, g(x), evaluates the gradient of a real scalar function f at a point x.
class
HessianFunction
The Hessian function, H(x), evaluates the Hessian of a real scalar function f at a point x.
class
JacobianFunction
The Jacobian function, J(x), evaluates the Jacobian of a real vector-valued function f at a point x.
class
MultivariateFiniteDifference
A partial derivative of a multivariate function is the derivative with respect to one of the variables with the others held constant.
• ## Uses of Function in dev.nm.analysis.differentiation.univariate

Modifier and Type
Class
Description
class
DBeta
This is the first order derivative function of the Beta function w.r.t x, $${\partial \over \partial x} \mathrm{B}(x, y)$$.
class
DBetaRegularized
This is the first order derivative function of the Regularized Incomplete Beta function, BetaRegularized, w.r.t the upper limit, x.
class
DErf
This is the first order derivative function of the Error function, Erf.
class
Dfdx
The first derivative is a measure of how a function changes as its input changes.
class
DGamma
This is the first order derivative function of the Gamma function, $${d \mathrm{\Gamma}(x) \over dx}$$.
class
DGaussian
This is the first order derivative function of a Gaussian function, $${d \mathrm{\phi}(x) \over dx}$$.
class
DPolynomial
This is the first order derivative function of a Polynomial, which, again, is a polynomial.
class
FiniteDifference
A finite difference (divided by a small increment) is an approximation of the derivative of a function.
• ## Uses of Function in dev.nm.analysis.function

Classes in dev.nm.analysis.function that implement Function
Modifier and Type
Class
Description
class
SubFunction<R>
A sub-function, g, is defined over a subset of the domain of another (original) function, f.
Fields in dev.nm.analysis.function declared as Function
Modifier and Type
Field
Description
protected final Function<Vector,R>
SubFunction.f
the original, unrestricted function
Constructors in dev.nm.analysis.function with parameters of type Function
Modifier
Constructor
Description

SubFunction(Function<Vector,R> f, Map<Integer,Double> fixing)
Constructs a sub-function.
• ## Uses of Function in dev.nm.analysis.function.matrix

Modifier and Type
Interface
Description
interface
RntoMatrix
This interface is a function that maps from Rn to a Matrix space.
Classes in dev.nm.analysis.function.matrix that implement Function
Modifier and Type
Class
Description
class
R1toConstantMatrix
A constant matrix function maps a real number to a constant matrix: $$R^n \rightarrow A$$.
class
R1toMatrix
This is a function that maps from R1 to a Matrix space.
class
R2toMatrix
This is a function that maps from R2 to a Matrix space.
• ## Uses of Function in dev.nm.analysis.function.polynomial

Modifier and Type
Class
Description
class
CauchyPolynomial
The Cauchy's polynomial of a polynomial takes this form:
class
Polynomial
A polynomial is a UnivariateRealFunction that represents a finite length expression constructed from variables and constants, using the operations of addition, subtraction, multiplication, and constant non-negative whole number exponents.
class
QuadraticMonomial
A quadratic monomial has this form: x2 + ux + v.
class
ScaledPolynomial
This constructs a scaled polynomial that has neither too big or too small coefficients, hence avoiding overflow or underflow.
• ## Uses of Function in dev.nm.analysis.function.rn2r1

Modifier and Type
Interface
Description
interface
BivariateRealFunction
A bivariate real function takes two real arguments and outputs one real value.
interface
RealScalarFunction
A real valued function a $$R^n \rightarrow R$$ function, $$y = f(x_1, ..., x_n)$$.
interface
TrivariateRealFunction
A trivariate real function takes three real arguments and outputs one real value.
Classes in dev.nm.analysis.function.rn2r1 that implement Function
Modifier and Type
Class
Description
class
AbstractBivariateRealFunction
A bivariate real function takes two real arguments and outputs one real value.
class
AbstractRealScalarFunction
This abstract implementation implements dimensionOfRange() by always returning 1, and dimensionOfDomain() by returning the input argument for the dimension of domain.
class
AbstractTrivariateRealFunction
A trivariate real function takes three real arguments and outputs one real value.
class
QuadraticFunction
A quadratic function takes this form: $$f(x) = \frac{1}{2} \times x'Hx + x'p + c$$.
class
R1Projection
Projection creates a real-valued function RealScalarFunction from a vector-valued function RealVectorFunction by taking only one of its coordinate components in the vector output.
class
RealScalarSubFunction
This constructs a RealScalarFunction from another RealScalarFunction by restricting/fixing the values of a subset of variables.
• ## Uses of Function in dev.nm.analysis.function.rn2r1.univariate

Modifier and Type
Interface
Description
interface
UnivariateRealFunction
A univariate real function takes one real argument and outputs one real value.
Modifier and Type
Class
Description
class
AbstractUnivariateRealFunction
A univariate real function takes one real argument and outputs one real value.
class
ContinuedFraction
A continued fraction representation of a number has this form: $z = b_0 + \cfrac{a_1}{b_1 + \cfrac{a_2}{b_2 + \cfrac{a_3}{b_3 + \cfrac{a_4}{b_4 + \ddots\,}}}}$ ai and bi can be functions of x, which in turn makes z a function of x.
class
StepFunction
A step function (or staircase function) is a finite linear combination of indicator functions of intervals.
• ## Uses of Function in dev.nm.analysis.function.rn2rm

Modifier and Type
Interface
Description
interface
RealVectorFunction
A vector-valued function a $$R^n \rightarrow R^m$$ function, $$[y_1,...,y_m] = f(x_1,...,x_n)$$.
Classes in dev.nm.analysis.function.rn2rm that implement Function
Modifier and Type
Class
Description
class
AbstractR1RnFunction
This is a function that takes one real argument and outputs one vector value.
class
AbstractRealVectorFunction
This abstract implementation implements dimensionOfDomain() and dimensionOfRange() by returning the input arguments at constructor.
class
RealVectorSubFunction
This constructs a RealVectorFunction from another RealVectorFunction by restricting/fixing the values of a subset of variables.
• ## Uses of Function in dev.nm.analysis.function.special

Classes in dev.nm.analysis.function.special that implement Function
Modifier and Type
Class
Description
class
Rastrigin
The Rastrigin function is a non-convex function used as a performance test problem for optimization algorithms.
• ## Uses of Function in dev.nm.analysis.function.special.beta

Modifier and Type
Class
Description
class
Beta
The beta function defined as: $B(x,y) = \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)}= \int_0^1t^{x-1}(1-t)^{y-1}\,dt, x > 0, y > 0$
class
BetaRegularized
The Regularized Incomplete Beta function is defined as: $I_x(p,q) = \frac{B(x;\,p,q)}{B(p,q)} = \frac{1}{B(p,q)} \int_0^x t^{p-1}\,(1-t)^{q-1}\,dt, p > 0, q > 0$
class
BetaRegularizedInverse
The inverse of the Regularized Incomplete Beta function is defined at: $x = I^{-1}_{(p,q)}(u), 0 \le u \le 1$
class
LogBeta
This class represents the log of Beta function log(B(x, y)).
class
MultinomialBetaFunction
A multinomial Beta function is defined as: $\frac{\prod_{i=1}^K \Gamma(\alpha_i)}{\Gamma\left(\sum_{i=1}^K \alpha_i\right)},\qquad\boldsymbol{\alpha}=(\alpha_1,\cdots,\alpha_K)$
• ## Uses of Function in dev.nm.analysis.function.special.gamma

Modifier and Type
Class
Description
class
Digamma
The digamma function is defined as the logarithmic derivative of the gamma function.
class
GammaGergoNemes
The Gergo Nemes' algorithm is very simple and quick to compute the Gamma function, if accuracy is not critical.
class
GammaLanczos
Lanczos approximation provides a way to compute the Gamma function such that the accuracy can be made arbitrarily precise.
class
GammaLanczosQuick
Lanczos approximation, computations are done in double.
class
GammaLowerIncomplete
The Lower Incomplete Gamma function is defined as: $\gamma(s,x) = \int_0^x t^{s-1}\,e^{-t}\,{\rm d}t = P(s,x)\Gamma(s)$ P(s,x) is the Regularized Incomplete Gamma P function.
class
GammaRegularizedP
The Regularized Incomplete Gamma P function is defined as: $P(s,x) = \frac{\gamma(s,x)}{\Gamma(s)} = 1 - Q(s,x), s \geq 0, x \geq 0$
class
GammaRegularizedPInverse
The inverse of the Regularized Incomplete Gamma P function is defined as: $x = P^{-1}(s,u), 0 \geq u \geq 1$ When s > 1, we use the asymptotic inversion method. When s <= 1, we use an approximation of P(s,x) together with a higher-order Newton like method. In both cases, the estimated value is then improved using Halley's method, c.f., HalleyRoot.
class
GammaRegularizedQ
The Regularized Incomplete Gamma Q function is defined as: $Q(s,x)=\frac{\Gamma(s,x)}{\Gamma(s)}=1-P(s,x), s \geq 0, x \geq 0$ The algorithm used for computing the regularized incomplete Gamma Q function depends on the values of s and x.
class
GammaUpperIncomplete
The Upper Incomplete Gamma function is defined as: $\Gamma(s,x) = \int_x^{\infty} t^{s-1}\,e^{-t}\,{\rm d}t = Q(s,x) \times \Gamma(s)$ The integrand has the same form as the Gamma function, but the lower limit of the integration is a variable.
class
LogGamma
The log-Gamma function, $$\log (\Gamma(z))$$, for positive real numbers, is the log of the Gamma function.
class
Trigamma
The trigamma function is defined as the logarithmic derivative of the digamma function.
• ## Uses of Function in dev.nm.analysis.function.special.gaussian

Modifier and Type
Class
Description
class
CumulativeNormalHastings
Hastings algorithm is faster but less accurate way to compute the cumulative standard Normal.
class
CumulativeNormalInverse
The inverse of the cumulative standard Normal distribution function is defined as: $N^{-1}(u) /] class  CumulativeNormalMarsaglia Marsaglia is about 3 times slower but is more accurate to compute the cumulative standard Normal. class  Erf The Error function is defined as: \[ \operatorname{erf}(x) = \frac{2}{\sqrt{\pi}}\int_{0}^x e^{-t^2} dt$
class
Erfc
This complementary Error function is defined as: $\operatorname{erfc}(x) = 1-\operatorname{erf}(x) = \frac{2}{\sqrt{\pi}} \int_x^{\infty} e^{-t^2}\,dt$
class
ErfInverse
The inverse of the Error function is defined as: $\operatorname{erf}^{-1}(x)$
class
Gaussian
The Gaussian function is defined as: $f(x) = a e^{- { \frac{(x-b)^2 }{ 2 c^2} } }$
• ## Uses of Function in dev.nm.misc.algorithm

Methods in dev.nm.misc.algorithm with parameters of type Function
Modifier and Type
Method
Description
double[]
Bins.getBinObjectValues(Function<List<T>,Double> f)
Applies a function to the items of each bin.
Constructors in dev.nm.misc.algorithm with parameters of type Function
Modifier
Constructor
Description

BruteForce(Function<D,R> function)
Constructs a brute force search for a function.
• ## Uses of Function in dev.nm.solver.multivariate.constrained.convex.sdp.socp.problem.portfoliooptimization

Modifier and Type
Class
Description
class
MarketImpact1
Constructs the constraint coefficient arrays of a market impact term in the compact form.
class
PortfolioRiskExactSigma
Constructs the constraint coefficient arrays of the portfolio risk term in the compact form.
class
SOCPPortfolioConstraint
An SOCP constraint for portfolio optimization, e.g., market impact, is represented by a set of constraints in this form: $||A^{T}x+c||_{2}\leq b^{T}x+d$ or this form: /[ A^T x = c, x \in \Re^m /] or this form: /[ A^T x \leq c, x \in \Re^m /]
class
SOCPPortfolioObjectiveFunction
Constructs the objective function for portfolio optimization.
class
SOCPRiskConstraint

• ## Uses of Function in dev.nm.solver.multivariate.constrained.convex.sdp.socp.qp.problem

Modifier and Type
Class
Description
class
QPProblemOnlyEqualityConstraints
A quadratic programming problem with only equality constraints can be converted into a equivalent quadratic programming problem without constraints, hence a mere quadratic function.
• ## Uses of Function in dev.nm.solver.multivariate.constrained.general.penaltymethod

Modifier and Type
Class
Description
class
AbsoluteErrorPenalty
This penalty function sums up the absolute error penalties.
class
CourantPenalty
This penalty function sums up the squared error penalties.
class
FletcherPenalty
This penalty function sums up the squared costs penalties.
class
MultiplierPenalty
A multiplier penalty function allows different weights to be assigned to the constraints.
class
PenaltyFunction
A function P: Rn -> R is a penalty function for a constrained optimization problem if it has these properties.
class
SumOfPenalties
This penalty function sums up the costs from a set of constituent penalty functions.
class
ZeroPenalty
This is a dummy zero cost (no cost) penalty function.
• ## Uses of Function in dev.nm.solver.multivariate.unconstrained

Methods in dev.nm.solver.multivariate.unconstrained with parameters of type Function
Modifier and Type
Method
Description
BruteForceMinimizer<R>.Solution
BruteForceMinimizer.solve(Function<Vector,R> f)

• ## Uses of Function in dev.nm.stat.evt.evd.univariate.fitting.acer

Modifier and Type
Class
Description
class
ACERFunction
The ACER (Average Conditional Exceedance Rate) function $$\epsilon_k(\eta)$$ approximates the probability $\epsilon_k(\eta) = Pr(X_k > \eta | X_1 \le \eta, X_2 \le \eta, ..., X_{k-1} \le \eta)$ for a sequence of stochastic process observations $$X_i$$ with a k-step memory.
class
ACERInverseFunction
The inverse of the ACER function.
class
ACERLogFunction
The ACER function in log scale (base e), i.e., $$log(\epsilon_k(\eta))$$.
class
ACERReturnLevel
Given an ACER function, compute the return level $$\eta$$ for a given return period $$R$$.
• ## Uses of Function in dev.nm.stat.evt.function

Classes in dev.nm.stat.evt.function that implement Function
Modifier and Type
Class
Description
class
ReturnLevel
Given a GEV distribution of a random variable $$X$$, the return level $$\eta$$ is the value that is expected to be exceeded on average once every interval of time $$T$$, with a probability of $$1 / T$$.
class
ReturnPeriod
The return period $$R$$ of a level $$\eta$$ for a random variable $$X$$ is the mean number of trials that must be done for $$X$$ to exceed $$\eta$$.
• ## Uses of Function in dev.nm.stat.random.rng.multivariate.mcmc.proposalfunction

Modifier and Type
Class
Description
class
GaussianProposalFunction
A proposal generator where each perturbation is a random vector, where each element is drawn from a standard Normal distribution, multiplied by a scale matrix.
class
HybridMCMCProposalFunction

class
ProposalFunction
A proposal function goes from the current state to the next state, where a state is a vector.
• ## Uses of Function in dev.nm.stat.stochasticprocess.univariate.filtration

Modifier and Type
Class
Description
class
Bt
This is a FiltrationFunction that returns $$B(t_i)$$, the Brownian motion value at the i-th time point.
class
F_Sum_BtDt
This represents a function of this integral $I = \int_{0}^{1} B(t)dt$
class
F_Sum_tBtDt
This represents a function of this integral $\int_{0}^{1} (t - 0.5) * B(t) dt$
class
FiltrationFunction
A filtration function, parameterized by a fixed filtration, is a function of time, $$f(\mathfrak{F_{t_i}})$$.
• ## Uses of Function in dev.nm.stat.timeseries.linear.multivariate

Modifier and Type
Class
Description
class
MultivariateAutoCorrelationFunction
This is the auto-correlation function of a multi-dimensional time series {Xt}.
class
MultivariateAutoCovarianceFunction
This is the auto-covariance function of a multi-dimensional time series {Xt}, $K(i, j) = E((X_i - \mu_i) \times (X_j - \mu_j)')$ For a stationary process, the auto-covariance depends only on the lag, |i - j|.
• ## Uses of Function in dev.nm.stat.timeseries.linear.multivariate.stationaryprocess.arma

Modifier and Type
Class
Description
class
VARMAAutoCorrelation
Compute the Auto-Correlation Function (ACF) for a vector AutoRegressive Moving Average (ARMA) model, assuming that EXt = 0.
class
VARMAAutoCovariance
Compute the Auto-CoVariance Function (ACVF) for a vector AutoRegressive Moving Average (ARMA) model, assuming that EXt = 0.
• ## Uses of Function in dev.nm.stat.timeseries.linear.univariate

Modifier and Type
Class
Description
class
AutoCorrelationFunction
This is the auto-correlation function of a univariate time series {xt}.
class
AutoCovarianceFunction
This is the auto-covariance function of a univariate time series {xt}.
• ## Uses of Function in dev.nm.stat.timeseries.linear.univariate.sample

Modifier and Type
Class
Description
class
SampleAutoCorrelation
This is the sample Auto-Correlation Function (ACF) for a univariate data set.
class
SampleAutoCovariance
This is the sample Auto-Covariance Function (ACVF) for a univariate data set.
class
SamplePartialAutoCorrelation
This is the sample partial Auto-Correlation Function (PACF) for a univariate data set.
• ## Uses of Function in dev.nm.stat.timeseries.linear.univariate.stationaryprocess.arma

Modifier and Type
Class
Description
class
AutoCorrelation
Compute the Auto-Correlation Function (ACF) for an AutoRegressive Moving Average (ARMA) model, assuming that EXt = 0.
class
AutoCovariance
Computes the Auto-CoVariance Function (ACVF) for an AutoRegressive Moving Average (ARMA) model by recursion.
• ## Uses of Function in tech.nmfin.portfoliooptimization.lai2010.ceta

Modifier and Type
Class
Description
class
Ceta
The function C(η) to be maximized (Eq.
• ## Uses of Function in tech.nmfin.portfoliooptimization.lai2010.ceta.maximizer

Modifier and Type
Class
Description
static class
CetaMaximizer.NegCetaFunction

• ## Uses of Function in tech.nmfin.portfoliooptimization.socp.constraints

Modifier and Type
Class
Description
class
SOCPLinearBlackList
A black list means that the positions of some assets must be zero.
class
SOCPLinearMaximumLoan
A maximum loan constraint.
class
SOCPLinearSectorNeutrality
A sector neutrality means that the sum of weights for given sectors are zero.
class
SOCPLinearSelfFinancing
A self financing constraint.
class
SOCPLinearZeroValue
A zero value constraint.
class
SOCPMaximumLoan
Transforms a maximum loan constraint into the compact SOCP form.
class
SOCPNoTradingList1
Transforms a black list (not to trade a new position) constraint into the compact SOCP form.
class
SOCPSectorNeutrality
Transforms a sector neutral constraint into the compact SOCP form.
class
SOCPSelfFinancing
Transforms a self financing constraint into the compact SOCP form.
class
SOCPZeroValue
Transforms a zero value constraint into the compact SOCP form.
• ## Uses of Function in tech.nmfin.portfoliooptimization.socp.constraints.ybar

Modifier and Type
Class
Description
class
SOCPLinearSectorExposure
A sector exposure constraint.
class
SOCPNoTradingList2
Transforms a black list (not to trade a new position) constraint into the compact SOCP form.
class
SOCPSectorExposure
Transforms a sector exposure constraint into the compact SOCP form.