ridge_fourier_fit {ridgetorus}

Fourier expansion of a given curve

Description

Computation of the Fourier expansion coefficients of a given curve.

Usage

ridge_fourier_fit(curve, K = 15, norm_prop = 1, N = 1280, at2 = TRUE)

Arguments

curve

points of the curve.

K

number of terms in the Fourier expansion. Defaults to 15.

norm_prop

percentage of explained norm. Defaults to 1.

N

number of Gaussian quadrature points, passed to Gauss_Legen_nodes. Defaults to 1280.

at2

do the atan2 fit instead of the sine fit (only using S_m)? Defaults to TRUE. at2 = FALSE is not recommended to use.

Value

The coefficients of the fit (see ridge_curve). A list with entries:

cos_a

contains a_0,a_1,\ldots,a_m.

sin_b

contains b_1,\ldots,b_m.

Examples

# Zero mean
ridge0 <- ridge_bvm(mu = c(0, 0), kappa = c(1, 2, -5), subint_1 = 5e2,
                    subint_2 = 5e2)
coefs <- ridge_fourier_fit(ridge0)
th <- seq(-pi, pi, l = 500)
plot(ridge0, xlim = c(-pi, pi), ylim = c(-pi, pi))
points(ridge_curve(th, mu = c(0, 0), coefs = coefs, at2 = TRUE), col = 3,
       cex = 0.5)

# Non-zero mean from a zero-mean ridge
mu <- c(1.4, 2)
ridge1 <- ridge_bvm(mu = mu, kappa = c(1, 2, -5), subint_1 = 5e2,
                    subint_2 = 5e2) # Just for plot
plot(ridge1, xlim = c(-pi, pi), ylim = c(-pi, pi))
points(mu[1], mu[2], col = 4, pch = "*", cex = 5)
points(ridge_curve(th, mu = mu, coefs = coefs), col = 3, cex = 0.5)

# Other zero-mean example
mu <- c(0, 0)
ridge <- ridge_bwc(mu = mu, xi = c(0.3, 0.5, 0.7), subint_1 = 5e2,
                   subint_2 = 5e2)
plot(ridge, xlim = c(-pi, pi), ylim = c(-pi, pi))
coefs <- ridge_fourier_fit(ridge)
points(ridge_curve(th, mu = mu, coefs = coefs), col = 4, cex = 0.5)

# Another zero-mean example
mu <- c(0, 0)
ridge <- ridge_bwc(mu = mu, xi = c(0.8, 0.1, 0.75), subint_1 = 5e2,
                   subint_2 = 5e2)
plot(ridge, xlim = c(-pi, pi), ylim = c(-pi, pi))
coefs <- ridge_fourier_fit(ridge)
points(ridge_curve(th, mu = mu, coefs = coefs), col = 4, cex = 0.5)