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### quadvar.R (2006-16)
###
### Estimation of the multifractional function of the multi-fractal Brownian field
### by the localized quadratic variations method
###
### Copyright 2006-16 Alexandre Brouste and Sophie Lambert-Lacroix
###
locquadvar <- function(Z,t,h){
## INPUT VARIABLES
#########################
## Z : matrix of size NxN
## matrix associated with the sample path of one
## multi-fractal Brownian field
## (N=2^(nblevel)+1 and Z[i,j] gives the value of
## the process at point (2^(-i*nblevel),2^(-j*nblevel)))
## t : point where H(t) must be estimated
## h : the neighborhood used to estimate H(t) is of the following form
## (2^(-i*nblevel),2^(-j*nblevel)), i,j=1,...,N such that
## |2^(-i*nblevel)-t_1|<=h and |2^(-j*nblevel)-t_2|<=h
## OUTPUT VARIABLES
##########################
## H: real in ]0,1[
## Estimation of the multifractional function of the multi-fractal Brownian field
## at the point t
## TEST ON INPUT VARIABLES
##############################
##On Z
if ((is.numeric(Z)==FALSE)||(is.matrix(Z)==FALSE)){
stop("Message from locquadvar.R: Z is not of valid type")}
if (dim(Z)[1]!=dim(Z)[2]){
stop("Message from locquadvar.R: Z is not of valid type")}
##On h
if (is.vector(h)==FALSE)
stop("Message from locquadvar.R: h is not of valid type")
if (length(h)!=1)
stop("Message from locquadvar.R: only one value can be specified for h")
if ((is.numeric(h)==FALSE)||(h<=0)){
stop("Message from locquadvar.R: h is not of valid type")}
##On t
if (is.vector(t)==FALSE)
stop("Message from locquadvar.R: t is not of valid type")
if (length(t)!=2)
stop("Message from locquadvar.R: t must be a vector of length 2")
if ((is.numeric(t)==FALSE)||(t[1]<0)||(t[2]<0)||(t[1]>1)||(t[2]>1)){
stop("Message from locquadvar.R: t is not of valid type (2)")}
#Find the points in the neighborhood of t
############################################
x1 <- max(0,t[1]-h)
x2 <- min(1,t[1]+h)
y1 <- max(0,t[2]-h)
y2 <- min(1,t[2]+h)
N <- dim(Z)[1]
M <- N-1
i1 <- floor(x1*M)+1
i2 <- floor(x2*M)+1
j1 <- floor(y1*M)+1
j2 <- floor(y2*M)+1
Vh <- Z[i1:i2,j1:j2]
#Compute the estimate
#########################
H <- quadvaraux(Vh)
return(H)}
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