R/ppderiv.R

In fda: Functional Data Analysis

#  ---------------------------------------------------------------------

ppderiv <- function(Coeff, Deriv=0){
#PPDERIV computes the DERIV-th derivatives of the polynomials 
# with coefficients COEFF such that the i-th polynomial is
# COEFF(i,1)*x^(k-1) + COEFF(i,2)*x^(k-2) + ... + COEFF(i,k)
# It returns a matrix COEFFD with the same number of rows as COEFF, 
# but with k-DERIV columns such that the DERIV-th derivative 
# of the i-th polynomial is expressed as
# COEFFD(i,1)*x^(k-1-DERIV) + COEFFD(i,k-DERIV-1)*x + COEFFD(i,k-DERIV),
# Note that if k-DERIV < 1, then COEFFD is the zero vector,
# and if DERIV < 1 we are not differentiating.

m <- dim(Coeff)[1]  # k is the order of the polynomials.
k <- dim(Coeff)[2]  

# If DERIV is not a positive integer, we are not differentiating.
if (Deriv < 1){
    CoeffD <- as.matrix(Coeff)  
    return(CoeffD)
}

# Compute the coefficient of the DERIV-th derivative of the function

if((k-Deriv) < 1){
    CoeffD <- matrix(0,m,1)  # The derivative is zero everywhere
    return(CoeffD)
    }
else{
    # initialize COEFFD with the coefficients from COEFF we will need
    CoeffD <- Coeff[,1:(k-Deriv)]
    if (!is.matrix(CoeffD)) CoeffD <- t(as.matrix(CoeffD))
    for (j in 1:(k-2)){
        bound1 <- max(1,j-Deriv+1) 
        bound2 <- min(j,k-Deriv) 
        CoeffD[,bound1:bound2] <- (k-j)*CoeffD[,bound1:bound2] 
    }
    return(CoeffD)
}    
}