projection_basis: Projection on the kernel basis

In ardeeshany/AFSSEN: Adaptive Function on Scalar Elastic Net

Projection on the kernel basis

Description

It computes the projection of a set of functions on the kernel basis defined by a set of eigenvalues and eigenfunctions

Usage

projection_basis(y, eigenvect, M_integ)

Arguments

y	matrix. N \times m matrix containing in row n the point-wise evaluation of the function y_n.
eigenvect	matrix. m \times J matrix containing in column j the point-wise evaluation of an eigenfunction v_j of the kernel evaluated on an equispaced time domain grid.
M_integ	scalar, integer. Number of points of the domain D of the functions (m) divided by the width of the domain |D|. Constant value used to compute the integrals.

Value

J \times N matrix (Y) containing in position (j,n) the integral of the product of the eigenfunction v_j with the function y_n, i.e. the coefficient correspondent to v_j of the projection of y_n on the kernel basis.

Y[i,j] = \int_{D} y_n(t) v_j(t) dt

Examples

data(simulation)
data(SobolevKernel)
summary(T_domain)
M_integ <- length(T_domain)/diff(range(T_domain))
projection_basis(Y_full, eigenvect, M_integ ) # projection on the J dimensional
# basis of the Y functions.

ardeeshany/AFSSEN documentation built on Aug. 28, 2022, 2:22 p.m.