indmat.derivmat.func <- function(sp.bootind, h, d, interval)
{
# indmat.derivmat.func:
# Calculates the matrix of 2nd derivative estimates from the
# matrix sp.bootind of bootstrapped abundance indices.
# 
# sp.bootind is a matrix of the form sp.bootind.Nrep.df 
# (e.g. cb.bootind.399.10).
# Each row of the output matrix is the vector of 2nd derivative estimates
# for the abundance index curve in the corresponding row of the index 
# matrix (i.e. the curve corresponding to a particular bootstrap
# replicate). 
# See diffop.func for a full explanation of arguments  h, d, and interval.
# interval is the time lapse between consecutive index points: e.g. if 
#    the index curve measures abundance every 2 years, then interval=2. 
#    Usually interval=1. 
# h is related to window size for the second derivative estimates: usually
#    will be chosen to be the smallest possible (h=1) but try
#    experimenting with h=2 and h=3 to see if the results are any
#    different. 
# d is the order of the difference operator: can be 2, 4, or 6, 
#    representing the second derivative estimates obtained from 2nd
#    differences, 4th differences, or 6th differences (eqns 9, 10, and 11
#    in the Ecology paper).  d=6 should give the most accurate results. 
#
# The output from this function would normally be named 
# sp.bootderiv.Nrep.df, although this function is usually only called
# from within sp.plot.  
# example: 
# cb.bootderiv.399.10 <- indmat.derivmat.func(cb.bootind.399.10, 1, 6, 1)
# 
# 
	t(apply(sp.bootind, 1, diffop.func, h = h, d = d, interval = interval))
}