coef2fd {onlinePCA}

Recover functional data from their B-spline coefficients

Description

This function computes functional data from their coefficients in a B-spline basis.

Usage

coef2fd(beta, basis, byrow = TRUE)

Arguments

beta

B-spline coefficients

basis

object created by create.basis

byrow

are the coefficients of each functional observation stored in rows (TRUE) or in columns (FALSE)?

Value

A matrix of functional data stored in the same format (row or columns) as the coefficients beta.

Note

In view of (online or offline) functional PCA, the coefficients beta are left- or right- multiplied by M^{-1/2} (depending on their row/column format)) before applying the B-spline matrix B, with M the Gram matrix associated to B.

See Also

create.basis, fd2coef

Examples

n <- 100 # number of curves
d <- 500 # number of observation points
grid <- (1:d)/d # observation points
p <- 50 # number of B-spline basis functions 

# Simulate Brownian motion
x <- matrix(rnorm(n*d,sd=1/sqrt(d)),n,d)
x <- t(apply(x,1,cumsum))

# Create B-spline basis 
mybasis <- create.basis(grid, p, 1e-4)

# Compute smooth basis coefficients 
beta <- fd2coef(x, mybasis)

# Recover smooth functional data
x.smooth <- coef2fd(beta, mybasis) 
	
# Standard PCA and Functional PCA
pca <- prcomp(x)
fpca <- prcomp(beta)