Uses of Class
dev.nm.analysis.function.rn2r1.AbstractRealScalarFunction
-
-
Uses of AbstractRealScalarFunction in dev.nm.analysis.curvefit.interpolation
Subclasses of AbstractRealScalarFunction in dev.nm.analysis.curvefit.interpolation Modifier and Type Class Description classLinearInterpolatorDefine a univariate function by linearly interpolating between adjacent points.classNevilleTableNeville'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 classRiddersRidders' 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 classMultivariateFiniteDifferenceA 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 classDBetaThis is the first order derivative function of theBetafunction w.r.t x, \({\partial \over \partial x} \mathrm{B}(x, y)\).classDBetaRegularizedThis is the first order derivative function of the Regularized Incomplete Beta function,BetaRegularized, w.r.t the upper limit, x.classDErfThis is the first order derivative function of the Error function,Erf.classDfdxThe first derivative is a measure of how a function changes as its input changes.classDGammaThis is the first order derivative function of the Gamma function, \({d \mathrm{\Gamma}(x) \over dx}\).classDGaussianThis is the first order derivative function of aGaussianfunction, \({d \mathrm{\phi}(x) \over dx}\).classDPolynomialThis is the first order derivative function of aPolynomial, which, again, is a polynomial.classFiniteDifferenceA 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 classCauchyPolynomialThe Cauchy's polynomial of a polynomial takes this form:classPolynomialA polynomial is aUnivariateRealFunctionthat represents a finite length expression constructed from variables and constants, using the operations of addition, subtraction, multiplication, and constant non-negative whole number exponents.classQuadraticMonomialA quadratic monomial has this form: x2 + ux + v.classScaledPolynomialThis 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 classAbstractBivariateRealFunctionA bivariate real function takes two real arguments and outputs one real value.classAbstractTrivariateRealFunctionA trivariate real function takes three real arguments and outputs one real value.classQuadraticFunctionA quadratic function takes this form: \(f(x) = \frac{1}{2} \times x'Hx + x'p + c\).classR1ProjectionProjection creates a real-valued functionRealScalarFunctionfrom a vector-valued functionRealVectorFunctionby 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 classAbstractUnivariateRealFunctionA univariate real function takes one real argument and outputs one real value.classContinuedFractionA 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.classStepFunctionA 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 classRastriginThe 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 classBetaThe beta function defined as: \[ B(x,y) = \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)}= \int_0^1t^{x-1}(1-t)^{y-1}\,dt, x > 0, y > 0 \]classBetaRegularizedThe Regularized Incomplete Beta function is defined as: \[ I_x(p,q) = \frac{B(x;\,p,q)}{B(p,q)} = \frac{1}{B(p,q)} \int_0^x t^{p-1}\,(1-t)^{q-1}\,dt, p > 0, q > 0 \]classBetaRegularizedInverseThe inverse of the Regularized Incomplete Beta function is defined at: \[ x = I^{-1}_{(p,q)}(u), 0 \le u \le 1 \]classLogBetaThis class represents the log of Beta functionlog(B(x, y)).classMultinomialBetaFunctionA 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 classDigammaThe digamma function is defined as the logarithmic derivative of the gamma function.classGammaGergoNemesThe Gergo Nemes' algorithm is very simple and quick to compute the Gamma function, if accuracy is not critical.classGammaLanczosLanczos approximation provides a way to compute the Gamma function such that the accuracy can be made arbitrarily precise.classGammaLanczosQuickLanczos approximation, computations are done indouble.classGammaLowerIncompleteThe 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.classGammaRegularizedPThe Regularized Incomplete Gamma P function is defined as: \[ P(s,x) = \frac{\gamma(s,x)}{\Gamma(s)} = 1 - Q(s,x), s \geq 0, x \geq 0 \]classGammaRegularizedPInverseThe inverse of the Regularized Incomplete Gamma P function is defined as: \[ x = P^{-1}(s,u), 0 \geq u \geq 1 \] Whens > 1, we use the asymptotic inversion method. Whens <= 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.classGammaRegularizedQThe 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.classGammaUpperIncompleteThe 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.classLogGammaThe log-Gamma function, \(\log (\Gamma(z))\), for positive real numbers, is the log of the Gamma function.classTrigammaThe 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 classCumulativeNormalHastingsHastings algorithm is faster but less accurate way to compute the cumulative standard Normal.classCumulativeNormalInverseThe inverse of the cumulative standard Normal distribution function is defined as: \[ N^{-1}(u) /]classCumulativeNormalMarsagliaMarsaglia is about 3 times slower but is more accurate to compute the cumulative standard Normal.classErfThe Error function is defined as: \[ \operatorname{erf}(x) = \frac{2}{\sqrt{\pi}}\int_{0}^x e^{-t^2} dt \]classErfcThis complementary Error function is defined as: \[ \operatorname{erfc}(x) = 1-\operatorname{erf}(x) = \frac{2}{\sqrt{\pi}} \int_x^{\infty} e^{-t^2}\,dt \]classErfInverseThe inverse of the Error function is defined as: \[ \operatorname{erf}^{-1}(x) \]classGaussianThe 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 classQPProblemOnlyEqualityConstraintsA 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 classACERFunctionThe 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.classACERInverseFunctionThe inverse of the ACER function.classACERLogFunctionThe ACER function in log scale (base e), i.e., \(log(\epsilon_k(\eta))\).classACERReturnLevelGiven 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 classReturnLevelGiven 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 \(1 / T\).classReturnPeriodThe 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 classBtThis is aFiltrationFunctionthat returns \(B(t_i)\), the Brownian motion value at the i-th time point.classF_Sum_BtDtThis represents a function of this integral \[ I = \int_{0}^{1} B(t)dt \]classF_Sum_tBtDtThis represents a function of this integral \[ \int_{0}^{1} (t - 0.5) * B(t) dt \]classFiltrationFunctionA 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 classAutoCorrelationFunctionThis is the auto-correlation function of a univariate time series {xt}.classAutoCovarianceFunctionThis 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 classSampleAutoCorrelationThis is the sample Auto-Correlation Function (ACF) for a univariate data set.classSampleAutoCovarianceThis is the sample Auto-Covariance Function (ACVF) for a univariate data set.classSamplePartialAutoCorrelationThis 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 classAutoCorrelationCompute the Auto-Correlation Function (ACF) for an AutoRegressive Moving Average (ARMA) model, assuming that EXt = 0.classAutoCovarianceComputes 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 classCetaThe 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 classCetaMaximizer.NegCetaFunction
-