# Statistical Tools for Toroidal Diffusions

## Documentation for package ‘sdetorus’ version 0.1.8

- DESCRIPTION file.

## Help Pages

sdetorus-package | sdetorus - Statistical Tools for Toroidal Diffusions
a1Inv | Efficient computation of Bessel related functions
alphaToA | Valid drift matrices for the Ornstein-Uhlenbeck diffusion in 2D
approxMleWn1D | Approximate MLE of the WN diffusion in 1D
approxMleWn2D | Approximate MLE of the WN diffusion in 2D
approxMleWnPairs | Approximate MLE of the WN diffusion in 2D from a sample of initial and final pairs of angles.
aToAlpha | Valid drift matrices for the Ornstein-Uhlenbeck diffusion in 2D
constBvm | Bivariate Sine von Mises density
constJp | Jones and Pewsey (2005)'s circular distribution
covstOu | Transition probability density of the univariate OU diffusion
covtMou | Transition probability density of the multivariate OU diffusion
crankNicolson1D | Crank-Nicolson finite difference scheme for the 1D Fokker-Planck equation with periodic boundaries
crankNicolson2D | Crank-Nicolson finite difference scheme for the 2D Fokker-Planck equation with periodic boundaries
dBvm | Bivariate Sine von Mises density
diffCirc | Lagged differences for circular time series
dJp | Jones and Pewsey (2005)'s circular distribution
dPsTpd | Wrapped Euler and Shoji-Ozaki pseudo-transition probability densities
driftJp | Drift for the JP diffusion
driftMixIndVm | Drift for the mivM diffusion
driftMixVm | Drift for the mivM diffusion (circular case)
driftMvm | Drift for the MvM diffusion
driftWn | Drift for the WN diffusion
driftWn1D | Drift of the WN diffusion in 1D
driftWn2D | Drift of the WN diffusion in 2D
dStatWn2D | Stationary density of a WN diffusion (with diagonal diffusion matrix) in 2D
dTpdMou | Transition probability density of the multivariate OU diffusion
dTpdOu | Transition probability density of the univariate OU diffusion
dTpdPde1D | Transition probability density in 1D by PDE solving
dTpdPde2D | Transition probability density in 2D by PDE solving
dTpdWou | Conditional probability density of the WOU process
dTpdWou1D | Approximation of the transition probability density of the WN diffusion in 1D
dTpdWou2D | Approximation of the transition probability density of the WN diffusion in 2D
dVm | Density of the von Mises
dWn1D | WN density in 1D
euler1D | Simulation of trajectories of the WN or vM diffusion in 1D
euler2D | Simulation of trajectories of the WN or MvM diffusion in 2D
forwardSweepPeriodicTridiag | Thomas algorithm for solving tridiagonal matrix systems, with optional presaving of LU decomposition
forwardSweepTridiag | Thomas algorithm for solving tridiagonal matrix systems, with optional presaving of LU decomposition
integrateSimp1D | Quadrature rules in 1D, 2D and 3D
integrateSimp2D | Quadrature rules in 1D, 2D and 3D
integrateSimp3D | Quadrature rules in 1D, 2D and 3D
linesCirc | Lines and arrows with vertical wrapping
linesTorus | Lines and arrows with wrapping in the torus
linesTorus3d | Lines and arrows with wrapping in the torus
logBesselI0Scaled | Efficient computation of Bessel related functions
logLikWouPairs | Loglikelihood of WN in 2D when only the initial and final points are observed
meantMou | Transition probability density of the multivariate OU diffusion
meantOu | Transition probability density of the univariate OU diffusion
mleMou | Maximum likelihood estimation of the multivariate OU diffusion
mleOptimWrapper | Optimization wrapper for likelihood-based procedures
mleOu | Maximum likelihood estimation of the OU diffusion
mlePde1D | MLE for toroidal process via PDE solving in 1D
mlePde2D | MLE for toroidal process via PDE solving in 2D
momentMatchWnVm | Score and moment matching of a univariate or bivariate wrapped normal by a von Mises
periodicTrapRule1D | Quadrature rules in 1D, 2D and 3D
periodicTrapRule2D | Quadrature rules in 1D, 2D and 3D
periodicTrapRule3D | Quadrature rules in 1D, 2D and 3D
psMle | Maximum pseudo-likelihood estimation by wrapped pseudo-likelihoods
rStatWn2D | Simulation from the stationary density of a WN diffusion in 2D
rTpdWn2D | Simulation from the approximated transition distribution of a WN diffusion in 2D
rTrajLangevin | Simulation of trajectories of a Langevin diffusion
rTrajMou | Simulation of trajectories for the multivariate OU diffusion
rTrajOu | Simulation of trajectories for the univariate OU diffusion
rTrajWn1D | Simulation of trajectories for the WN diffusion in 1D
rTrajWn2D | Simulation of trajectories for the WN diffusion in 2D
safeSoftMax | Safe softmax function for computing weights
scoreMatchWnBvm | Score and moment matching of a univariate or bivariate wrapped normal by a von Mises
scoreMatchWnVm | Score and moment matching of a univariate or bivariate wrapped normal by a von Mises
sdetorus | sdetorus - Statistical Tools for Toroidal Diffusions
sigmaDiff | High-frequency estimate of the diffusion matrix
solvePeriodicTridiag | Thomas algorithm for solving tridiagonal matrix systems, with optional presaving of LU decomposition
solveTridiag | Thomas algorithm for solving tridiagonal matrix systems, with optional presaving of LU decomposition
solveTridiagMatConsts | Thomas algorithm for solving tridiagonal matrix systems, with optional presaving of LU decomposition
stepAheadWn1D | Multiple simulation of trajectory ends of the WN or vM diffusion in 1D
stepAheadWn2D | Multiple simulation of trajectory ends of the WN or MvM diffusion in 2D
to2PiInt | Wrapping of radians to its principal values
toInt | Wrapping of radians to its principal values
toPiInt | Wrapping of radians to its principal values
torusAxis | Draws pretty axis labels for circular variables
torusAxis3d | Draws pretty axis labels for circular variables
unwrapCircSeries | Unwrapping of circular time series
vartOu | Transition probability density of the univariate OU diffusion