unwrapCircSeries {sdetorus}

Unwrapping of circular time series

Description

Completes a circular time series to a linear one by computing the closest wind numbers. Useful for plotting circular trajectories with crossing of boundaries.

Usage

unwrapCircSeries(x)

Arguments

x

wrapped angles. Must be a vector or a matrix, see details.

Details

If x is a matrix then the unwrapping is carried out row-wise, on each column separately.

Value

A vector or matrix containing a choice of unwrapped angles of x that maximizes linear continuity.

Examples

# Vectors
x <- c(-pi, -pi/2, pi - 0.1, -pi + 0.2)
u <- unwrapCircSeries(x)
max(abs(toPiInt(u) - x))
plot(toPiInt(x), ylim = c(-pi, pi))
for(k in -1:1) lines(u + 2 * k * pi)

# Matrices
N <- 100
set.seed(234567)
x <- t(euler2D(x0 = rbind(c(0, 0)), A = diag(c(1, 1)), sigma = rep(1, 2),
                 mu = c(pi, pi), N = N, delta = 1, type = 2)[1, , ])
u <- unwrapCircSeries(x)
max(abs(toPiInt(u) - x))
plot(x, xlim = c(-pi, pi), ylim = c(-pi, pi))
for(k1 in -3:3) for(k2 in -3:3) lines(u[, 1] + 2 * k1 * pi,
                                      u[, 2] + 2 * k2 * pi, col = gray(0.5))