make_basis_fct: Generate basis function
In larslau/pavpop: Phase and amplitude varying population pattern models

Description Usage Arguments Details Examples

Method for generating a 'basis function' function, that outputs a functional basis.

1 2	make_basis_fct(kts = NULL, df = NULL, type = "B-spline", intercept = FALSE, control = list())

`kts`	a sequence of increasing points specifying the placement of the knots.
`df`	degrees of freedom of the spline basis. Knots are chosen equidistantly.
`type`	the type of basis function you want. Currently supported choices are `'B-spline'`, `'increasing'` and `'intercept'`. See details for more information.
`intercept`	logical. Should the basis include an intercept?
`control`	list of control parameters. Most importantly is `boundary` which contains boundary points for a B-spline basis. See details for more options.

Basis types 'Fourier' and 'wavelet' will become available soon. If needed please contact the developer.

The control argument takes a list with the following entries order and constraints and sparse

boundary: boundary knots for the basis spline.
order: order of the spline, if NULL, B-splines have order 4 (cubic spline) and I-splines (type = 'increasing') have order 3.
constraints: positivity constraints, if set to 'positive', only positive weights are allowed
sparse: logical. Should sparse matrices be used?

# Basis function knots
kts <- seq(0, 1, length = 12)[2:11]

# Construct B-spline basis function
basis_fct <- make_basis_fct(kts = kts, control = list(boundary = c(0, 1)))

# Evaluation points
t <- seq(0, 1, length = 100)
A <- basis_fct(t)
plot(t, t, type = 'n', ylim = range(A))
for (i in 1:ncol(A)) lines(t, A[, i], col = rainbow(ncol(A))[i])

# Evaluate derivatives
Ad <- basis_fct(t, TRUE)
plot(t, t, type = 'n', ylim = range(Ad))
for (i in 1:ncol(A)) lines(t, Ad[, i], col = rainbow(ncol(Ad))[i])

# Construct I-spline
# Knots should contain the left and right endpoints
kts_inc <- seq(0, 1, length = 10)
basis_fct_inc <- make_basis_fct(kts = kts_inc, type = 'increasing')
A_inc <- basis_fct_inc(t)
plot(t, t, type = 'n', ylim = range(A_inc))
for (i in 1:ncol(A_inc)) lines(t, A_inc[, i], col = rainbow(ncol(A))[i])

# Evaluate derivatives
Ad_inc <- basis_fct_inc(t, deriv = TRUE)
plot(t, t, type = 'n', ylim = range(Ad_inc))
for (i in 1:ncol(Ad_inc)) lines(t, Ad_inc[, i], col = rainbow(ncol(Ad))[i])

# Simulate data
y <- t^2 * sin(8 * t) + t
plot(t, y, type = 'l', lwd = 2, lty = 2)

# Add noise to data
y <- y + rnorm(length(y), sd = 0.1)
points(t, y, pch = 19, cex = 0.5)

# Fit B-spline to data assuming iid. noise
weights <- spline_weights(y, t, basis_fct = basis_fct)
lines(t, A %*% weights, col = 'red', lwd = 2)

# Fit increasing spline
pos_weights <- spline_weights(y, t, basis_fct = basis_fct_inc)
lines(t, A_inc %*% pos_weights, col = 'blue', lwd = 2)