integral_operator {fdaACF}

Integral transformation of a curve using an integral operator

Description

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

\Psi(Y_{i})(v) = \int \psi(u,v)Y_{i}(u)du

Usage

integral_operator(operator_kernel, curve, v)

Arguments

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.

Value

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

Examples

# 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)