integral_operator {fdaACF}R Documentation

Integral transformation of a curve using an integral operator

Description

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

Ψ(Yi)(v)=ψ(u,v)Yi(u)du\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 (gxm)(g x m), where gg is the number of discretization points of the input curve and mm 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 (1xm)(1 x m), where mm 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)


[Package fdaACF version 1.0.0 Index]