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# Multisensi R package ; file basis.poly.r (last modified: 2016-02-03)
# Authors: C. Bidot, M. Lamboni, H. Monod
# Copyright INRA 2011-2018
# MaIAGE, INRA, Univ. Paris-Saclay, 78350 Jouy-en-Josas, France
#
# More about multisensi in https://CRAN.R-project.org/package=multisensi
#
# This software is governed by the CeCILL license under French law and
# abiding by the rules of distribution of free software. You can use,
# modify and/ or redistribute the software under the terms of the CeCILL
# license as circulated by CEA, CNRS and INRIA at the following URL
# "http://www.cecill.info".
#
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#===========================================================================
basis.poly <- function(simuls, basis.args=list(degree=3))
#===========================================================================
{
## fait la decomposition sur une base de polynomes definie par le parametre degree
## utilise poly()
## INPUTS
## simuls : data.frame sur laquelle faire la decomposition (sortie des simulations du modele)
## basis.args : arguments specifiques a la methode de decomposition sous forme de list
## - degree : degre maximal des polynomes (3 par defaut)
## - x.coord : coordonnees ou calculer les valeurs des polynomes (optionnel, 1:ncol(simuls) par defaut)
## OUTPUTS
## H : coefficients associes a la base de decomposition
## de taille nrow(simuls) x nbpoly (nbpoly = degree+1)
## L : matrice des vecteurs de la base de polynomes
## de taille ncol(simuls) x nbpoly
## NB : simuls ~ H %*% t(L)
## call.info : contient des indications sur la fonction utilisee, call.info$reduction="polynomial"
b.args=basis.args
# definition des valeurs par defaut des arguments
if(is.null(basis.args$degree)){
b.args$degree=3;
# cat("Warning : basis.poly argument 'degree' not given,\n default value 'degree=3' used.\n")
}
if(is.null(basis.args$x.coord)){
b.args$x.coord=seq(1,ncol(simuls));
# cat("Warning : basis.poly argument 'x.coord' not given,\n default value 'x.coord=1:",ncol(simuls),"' used.\n")
}else if(length(b.args$x.coord)!=ncol(simuls)){
stop("basis.poly argument 'x.coord' length not adequate,\n length(x.coord) must be ",ncol(simuls)," (",length(b.args$x.coord)," used).\n")
}
##calcul des polynomes
pbase=poly(b.args$x.coord,degree=b.args$degree)
# ces polynomes sont orthogonaux au poly constant mais il faut l'ajouter
# => 1/sqrt(N) pour etre norme
# cad colSums(pbase^2) = 1 1 ... 1
pbase=cbind(rep(1/sqrt(nrow(pbase)),nrow(pbase)),pbase)
colnames(pbase)[1]="0"
colnames(pbase) <- paste("Deg",colnames(pbase),sep="")
# pbase de taille ncol(simuls) x (degree +1)
#projecteur = solve( t(pbase) %*% pbase) %*% t(pbase)
# "solve" solves the equation ‘a %*% x = b’ for ‘x’
# ici a =t(pbase) %*% pbase et b=O => (t(pbase) %*% pbase) ^(-1)
# matrice pbase n'est pas carree, le calcul permet d'avoir l'inverse dans projecteur
# mais a priori comme orthonormee devrait être egale a t(pbase)
# +/- le polynome constant
# donc:
projecteur=t(pbase)
# projecteur de taille (degree+1) x ncol(simuls)
## calcul de H (H=Y.L^(-1)):
# t(L) %*% t(projecteur) = I et projecteur %*% L = I
# H*t(L) = Y => H*t(L) * t(projecteur) = Y * t(projecteur) => H = Y * t(projecteur)
coefpoly = as.matrix(simuls)%*% t(projecteur);
# coefpoly de taille nrow(simuls) x (degree+1)
return(list(H=coefpoly, # taille nrow(simuls) x (degree+1)
L=pbase, # taille ncol(simuls) x (degree+1)
call.info=list(reduction="polynomial")))
}
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