Uses of Class
dev.nm.analysis.function.rn2r1.AbstractRealScalarFunction

Packages that use AbstractRealScalarFunction

Package	Description
dev.nm.analysis.curvefit.interpolation
dev.nm.analysis.differentiation
dev.nm.analysis.differentiation.multivariate
dev.nm.analysis.differentiation.univariate
dev.nm.analysis.function.polynomial
dev.nm.analysis.function.rn2r1
dev.nm.analysis.function.rn2r1.univariate
dev.nm.analysis.function.special
dev.nm.analysis.function.special.beta
dev.nm.analysis.function.special.gamma
dev.nm.analysis.function.special.gaussian
dev.nm.solver.multivariate.constrained.convex.sdp.socp.qp.problem
dev.nm.stat.evt.evd.univariate.fitting.acer
dev.nm.stat.evt.function
dev.nm.stat.stochasticprocess.univariate.filtration
dev.nm.stat.timeseries.linear.univariate
dev.nm.stat.timeseries.linear.univariate.sample
dev.nm.stat.timeseries.linear.univariate.stationaryprocess.arma
tech.nmfin.portfoliooptimization.lai2010.ceta
tech.nmfin.portfoliooptimization.lai2010.ceta.maximizer

Uses of AbstractRealScalarFunction in dev.nm.analysis.curvefit.interpolation

Subclasses of AbstractRealScalarFunction 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 AbstractRealScalarFunction in dev.nm.analysis.differentiation

Subclasses of AbstractRealScalarFunction in dev.nm.analysis.differentiation

Modifier and Type	Class	Description
class	Ridders	Ridders' method computes the numerical derivative of a function.

Uses of AbstractRealScalarFunction in dev.nm.analysis.differentiation.multivariate

Subclasses of AbstractRealScalarFunction in dev.nm.analysis.differentiation.multivariate

Modifier and Type	Class	Description
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 AbstractRealScalarFunction in dev.nm.analysis.differentiation.univariate

Subclasses of AbstractRealScalarFunction 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 AbstractRealScalarFunction in dev.nm.analysis.function.polynomial

Subclasses of AbstractRealScalarFunction 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 AbstractRealScalarFunction in dev.nm.analysis.function.rn2r1

Subclasses of AbstractRealScalarFunction in dev.nm.analysis.function.rn2r1

Modifier and Type	Class	Description
class	AbstractBivariateRealFunction	A bivariate real function takes two real arguments and outputs one real value.
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.

Uses of AbstractRealScalarFunction in dev.nm.analysis.function.rn2r1.univariate

Subclasses of AbstractRealScalarFunction in dev.nm.analysis.function.rn2r1.univariate

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 AbstractRealScalarFunction in dev.nm.analysis.function.special

Subclasses of AbstractRealScalarFunction in dev.nm.analysis.function.special

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 AbstractRealScalarFunction in dev.nm.analysis.function.special.beta

Subclasses of AbstractRealScalarFunction 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 AbstractRealScalarFunction in dev.nm.analysis.function.special.gamma

Subclasses of AbstractRealScalarFunction 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 AbstractRealScalarFunction in dev.nm.analysis.function.special.gaussian

Subclasses of AbstractRealScalarFunction 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 AbstractRealScalarFunction in dev.nm.solver.multivariate.constrained.convex.sdp.socp.qp.problem

Subclasses of AbstractRealScalarFunction 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 AbstractRealScalarFunction in dev.nm.stat.evt.evd.univariate.fitting.acer

Subclasses of AbstractRealScalarFunction 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 AbstractRealScalarFunction in dev.nm.stat.evt.function

Subclasses of AbstractRealScalarFunction in dev.nm.stat.evt.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 AbstractRealScalarFunction in dev.nm.stat.stochasticprocess.univariate.filtration

Subclasses of AbstractRealScalarFunction 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 AbstractRealScalarFunction in dev.nm.stat.timeseries.linear.univariate

Subclasses of AbstractRealScalarFunction 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 AbstractRealScalarFunction in dev.nm.stat.timeseries.linear.univariate.sample

Subclasses of AbstractRealScalarFunction 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 AbstractRealScalarFunction in dev.nm.stat.timeseries.linear.univariate.stationaryprocess.arma

Subclasses of AbstractRealScalarFunction 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 AbstractRealScalarFunction in tech.nmfin.portfoliooptimization.lai2010.ceta

Subclasses of AbstractRealScalarFunction in tech.nmfin.portfoliooptimization.lai2010.ceta

Modifier and Type	Class	Description
class	Ceta	The function C(η) to be maximized (Eq.

Uses of AbstractRealScalarFunction in tech.nmfin.portfoliooptimization.lai2010.ceta.maximizer

Subclasses of AbstractRealScalarFunction in tech.nmfin.portfoliooptimization.lai2010.ceta.maximizer

Modifier and Type	Class	Description
static class	CetaMaximizer.NegCetaFunction