https://github.com/cran/nacopula
Tip revision: 161411bb86f97e5a8bd89091cd61d03a33c2761a authored by Martin Maechler on 06 February 2012, 00:00:00 UTC
version 0.8-0
version 0.8-0
Tip revision: 161411b
G_ak.R
## Copyright (C) 2010 Marius Hofert and Martin Maechler
##
## This program is free software; you can redistribute it and/or modify it under
## the terms of the GNU General Public License as published by the Free Software
## Foundation; either version 3 of the License, or (at your option) any later
## version.
##
## This program is distributed in the hope that it will be useful, but WITHOUT
## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
## FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
## details.
##
## You should have received a copy of the GNU General Public License along with
## this program; if not, see <http://www.gnu.org/licenses/>.
library(nacopula)
#### Testing / exploring coeffG(), the coefficients a_k for
#### the Gumbel copula's generator derivatives and copula density
###--- Part 1 ---- Investigate dsumSibuya() -----------------
## Use dsumSibuya() the way it's used from coeffG() :
dsSib <- function(d, alpha, method, log=TRUE) {
stopifnot(length(d) == 1, d >= 1, is.numeric(alpha), is.character(method))
dsumSibuya(x=d, n = 1:d, alpha=alpha, method=method, log=log)
}
(ds.MethsA <- eval(formals(dsumSibuya)$method))
ds.Meths <- ds.MethsA[ds.MethsA != "RmpfrM"]
(ds.Meths1 <- ds.Meths [ds.Meths != "Rmpfr"])
dsSibA <- function(d, alpha, methods = ds.Meths, log=TRUE) {
stopifnot(length(d) == 1, d >= 1, is.numeric(alpha))
structure(
vapply(methods, dsumSibuya, FUN.VALUE = rep.int(NA_real_, d),
x=d, n = 1:d, alpha=alpha, log=log),
alpha=alpha, log=log)
}
p.dsSib <- function(dsSmat, type="l", ...) {
stopifnot(is.matrix(dsSmat), (p <- ncol(dsSmat)) >= 1,
is.numeric(alp <- attr(dsSmat, "alpha")))
d <- nrow(dsSmat)
matplot (dsSmat, type=type, xlab = quote(k), ylab = "",
main = paste("dsumSibuya(x= (d= )", d,
", n= (k= ) 1:d, alpha=", formatC(alp),", log = ",attr(dsSmat,"log"),")",
sep=""), col=1:p, lty=1, ...)
legend("topright", colnames(dsSmat),
pch = if(type %in%c("o","b","p")) paste(1:p),
col=1:p, lty=1, bty="n")
}
str(m50..1 <- dsSibA(50, alpha = 0.1))
stopifnot(is.matrix(m50..1))
p.dsSib(m50..1)## -- now Rmpfr has no NaN anymore!
p.dsSib(dsSibA(60, alpha = 0.4))
p.dsSib(dsSibA(70, alpha = 0.4))
p.dsSib(dsSibA(80, alpha = 0.4), type="b")
p.dsSib(ds70 <- dsSibA(70, alpha = 0.1))
## more extreme:
p.dsSib(ds1c <- dsSibA(100, alpha = 0.01))
##--> For small alpha and "large" d, even Rmpfr (now "Rmpfr0")
## is not good enough...
## Look at the values *before* log(.) :
dsumSibuya(50, 1:50, alpha=0.1, method="Rmpfr")
dd <- dsumSibuya(50, 1:50, alpha=mpfr(0.1, 200), method="Rmpfr")# now -- higher prec. -- all fine!
plot(dd, log="y")
###--- Part 2 ------------------------------------------------
coeffG <- nacopula:::coeffG
### step (1): look at the a_k's, check if they can be evaluated ################
## Now, explore things seriously :
## use all methods for a set of alpha and d.vec
cGmeths <- function() {
mm <- eval(formals(coeffG)$method)
## for now - do not use deprecated,..
mm[!(mm %in% c("dsumSibuya", "dsSib.RmpfrM"))]
}
cGmeths()
## need the fixed sapply() {or R >= 2.13.x} :
if(getRversion() < "2.13")
source(system.file("Rsource", "fixup-sapply.R", package="nacopula"))
asN <- function(x, name=deparse(substitute(x))[1]) {
names(x) <- paste(name, vapply(x, format, ""), sep="=")
x
}
cG.all <- function(alpha, d.s, meths = NULL) {
if(is.null(meths)) meths <- cGmeths()
stopifnot(is.numeric(alpha), is.numeric(d.s), is.character(meths))
##
## the asN(.) below ensure nice dimnames
sapply(asN(d.s, "d"), function(d) {
cat("\nd = ", d,"\n--------\n\n")
sapply(asN(alpha), function(al) {
cat("alpha = ", format(al), "\n")
sapply(meths, coeffG, d=d, alpha=al, log=TRUE)
}, simplify = "array")
}, simplify=FALSE)
}
alph.vec <- c(.1, .3, .5, .7, .8, .9, .99, .995)## = 1 - tau
## desirable, but too long for demo:
## d.vec <- c(5,10*(1:10), 20*(6:10))
##--> smaller and fewer for now:
d.vec <- c(5,10*c(1:3, 5, 7, 10, 15))
d.vec <- c(5,10*c(1:3, 5))
options(warn = 1)# show them immediately
ak.all <- cG.all(alpha = alph.vec, d.s = d.vec)
## --> > many warnings, only for d >= 30
## d = 30, alpha in {0.1, 0.3}
## d >= 40: for all alpha
stopifnot("array" == sapply(ak.all, class))
str(head(ak.all, 3))
ak.all$`d=20`[,,"alpha=0.99"]
## TODO improve the checks, now we have the dsSib.Rmpfr version
chk1 <- function(ak.mat, tol = 1e-7) {
stopifnot(is.matrix(ak.mat), (d <- nrow(ak.mat)) >= 2)
n.meth <- ncol(ak.mat)
med <- apply(ak.mat, 1, median, na.rm=TRUE)
apply(ak.mat, 2, all.equal, target=med, tol=tol)
}
chk1(ak.all$`d=20`[,,"alpha=0.3"])
## chk1(ak.all$`d=90`[,,"alpha=0.3"])
chk.all <-
lapply(ak.all, function(ak.arr) apply(ak.arr, 3, chk1))
chk.all # quite interesting -- but is the median the truth ??
ak.all$`d=50`[,,"alpha=0.1"] ##--> we see that some "Rmpfr" results got NaN !!!
source(system.file("test-tools-1.R", package="Matrix"))#-> relErr()
relE.ak <- function(ak.mat, tol = 1e-7, trNam = "dsSib.Rmpfr") {
stopifnot(is.matrix(ak.mat), (d <- nrow(ak.mat)) >= 2,
is.numeric(true <- ak.mat[, trNam]))
n.meth <- ncol(ak.mat)
apply(ak.mat[,trNam != colnames(ak.mat)], 2, relErr, target= true)
}
relE.ak(ak.all$`d=20`[,,"alpha=0.3"])
relE.all <- lapply(ak.all, function(ak.arr) apply(ak.arr, 3, relE.ak))
print(relE.all, digits = 4) # --- wow!
## For d = 5,..85 this is fine (unless for large alpha (!) :
(a.k <- coeffG(100, 0.55, method = "horner"))
## => just works [but in the "extreme area", the numbers are not quite correct,
## e.g., a.k[53] = 4.325e+83 and Maple says 4.627673570e83]
## conclusion: large alpha's [small theta's] cause the problems!!!
## ==========
## An example showing that for "dsumSibuya" the problem is exactly *small* alphas:
plot (a.k.H <- coeffG(100, 0.01, method = "horner"), type = "l", lwd=3, log="y")
lines(a.k.J <- coeffG(100, 0.01, method = "dsSib.log"), col=2, type ="o")
lines(a.k.s <- coeffG(100, 0.01, method = "sort"), col=3, type ="l")
lines(a.k.d <- coeffG(100, 0.01, method = "direct"),
col=adjustcolor("blue"), type ="l", lwd=4)
set.seed(1)
n <- 50
d <- 100
tau <- 0.2
theta <- copGumbel@tauInv(tau)
alpha <- 1/theta
## animate this
library(animation)
library(lattice)
m <- 50 # frames
plot.list <- vector("list", m)
alpha.list <- (1:m)/(m+1)
d <- 100
for(i in 1:m){
coeffs <- coeffG(d, alpha.list[i], log=TRUE, method = "dsumSibuya")
plot.list[[i]] <-
xyplot(coeffs~1:d, type="l", xlim = c(-3,104), ylim = c(-303,374),
xlab = "k", ylab = expression(log(a[k])), aspect = 1,
main = substitute(expression(alpha == alpha.),
list(alpha. = alpha.list[i])))
}
saveHTML(for(i in 1:m) print(plot.list[[i]]))
## conclusion: seems to be better for large alpha [seems to work for alpha >= 0.78,
## including our test case by a whisker... not totally satisfactory so far]
plot(coeffs~1:100, type="l", xlim = c(-3,104), ylim = c(-303,374),
xlab = "k", ylab = expression(log(a[k])), aspect = 1,
main = substitute(expression(alpha == alpha.),
list(alpha. = alpha.list[i])))