integral_operator: Integral transformation of a curve using an integral operator
In fdaACF: Autocorrelation Function for Functional Time Series

Description Usage Arguments Value Examples

Compute the integral transform of the curve Y_i with respect to a given integral operator Ψ. The transformation is given by

Ψ(Y_{i})(v) = \int ψ(u,v)Y_{i}(u)du

1	integral_operator(operator_kernel, curve, v)

`operator_kernel`	Matrix with the values of the kernel surface of the integral operator. The dimension of the matrix is (g x m), where g is the number of discretization points of the input curve and m is the number of discretization points of the output curve.
`curve`	Vector containing the discretized values of a functional observation. The dimension of the matrix is (1 x m), where m is the number of points observed in the curve.
`v`	Numerical vector specifying the discretization points of the curves.

Returns a matrix the same size as curve with the transformed values.

# Example 1

v <- seq(from = 0, to = 1, length.out = 20)
set.seed(10)
curve <- sin(v) + rnorm(length(v))
operator_kernel <- 0.6*(v %*% t(v))
hat_curve <- integral_operator(operator_kernel,curve,v)