Modifier and Type | Method and Description |
---|---|
static Matrix |
MatrixUtils.elementOperation(Matrix A1,
Matrix A2,
BivariateRealFunction f) |
Constructor and Description |
---|
PoissonEquation2D(double a,
double b,
BivariateRealFunction f,
BivariateRealFunction g)
Constructs a Poisson's equation problem.
|
Constructor and Description |
---|
WaveEquation2D(double beta,
double T,
double a,
double b,
BivariateRealFunction f,
BivariateRealFunction g)
Create a two-dimensional wave equation.
|
Constructor and Description |
---|
ConvectionDiffusionEquation1D(BivariateRealFunction sigma,
BivariateRealFunction mu,
BivariateRealFunction R,
double a,
double T,
UnivariateRealFunction f,
double c1,
UnivariateRealFunction g1,
double c2,
UnivariateRealFunction g2)
Constructs a convection-diffusion equation problem.
|
Constructor and Description |
---|
HeatEquation2D(double beta,
double T,
double a,
double b,
BivariateRealFunction f,
TrivariateRealFunction g)
Constructs a two-dimensional heat equation problem.
|
Modifier and Type | Class and Description |
---|---|
class |
DBeta
This is the first order derivative function of the
Beta function w.r.t x, \({\partial \over \partial x} \mathrm{B}(x, y)\). |
Modifier and Type | Class and Description |
---|---|
class |
AbstractBivariateRealFunction
A bivariate real function takes two real arguments and outputs one real value.
|
Modifier and Type | Class and Description |
---|---|
class |
Beta
The beta function defined as:
\[
B(x,y) = \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)}= \int_0^1t^{x-1}(1-t)^{y-1}\,dt, x > 0, y > 0
\]
The R equivalent function is
beta . |
class |
LogBeta
This class represents the log of Beta function
log(B(x, y)) . |
Modifier and Type | Class and Description |
---|---|
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:
\[
P(s,x) = \frac{\gamma(s,x)}{\Gamma(s)} = 1 - Q(s,x), s \geq 0, x \geq 0
\]
The R equivalent function is
pgamma . |
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.
|
Modifier and Type | Class and 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}.
|
Modifier and Type | Class and 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.
|
Modifier and Type | Class and 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.
|
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