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# Copyright (c) 2012 Michel Crucifix <michel.crucifix@uclouvain.be>
# Permission is hereby granted, free of charge, to any person obtaining
# a copy of this software and associated documentation files (the
# "Software"), to deal in the Software without restriction, including
# without limitation the rights to use, copy, modify, merge, publish,
# distribute, sublicense, and/or sell copies of the Software, and to
# permit persons to whom the Software is furnished to do so, subject
# the following conditions:
# The above copyright notice and this permission notice shall be
# incluudedin all copies or substantial portions of the Software.
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
# EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
# MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND INFRINGEMENT
# IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR
# CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
# TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
# SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
# When using this package for actual applications, always
# cite the authors of the original insolation solutions
# Berger, Loutre and/or Laskar, see details in man pages
# ------------------------------------------------------------------
# R Code developed for R version 2.15.2 (2012-10-26) -- "Trick or Treat"
# ------------------------------------------------------------------
GenerateTable2 <- function(Table1, Table4, Table5, sol='BER78')
{
#
# Re-Generates the precession amplitudes and frequencies based on
# files provided by Berger 1978
# (labelled Table 2 in the original publication)
# The present routine is an implementation of the
# original article by Berger and Loutre :
# A. Berger and M. F. Loutre, Origine des fr\'equences des \'el\'ements
# astronomiques intervenant dans l'insolation,
# Bull. Classe des Sciences, 1-3, 45-106 1990
#
if (sol == 'BER78')
{
P<- 50.439273
zeta <- 3.392506
} else if (sol == 'BER90')
{
P <- 50.41726176 # cf. eq. (31) in BER90
zeta <- 1.60075265 # cf. eq. (30) in BER90
}
## PsiBar
g <- Table4$V3
M <- Table4$V2
beta <- Table4$V4
F <- Table5$V2/60./60.*pi/180
f <- Table5$V3
delta <- Table5$V4
## division in 3 groups, as in Table 13 and Table 14 of Berger & Loutre, Ac. Roy. 1990
Fre <- c(g+P,outer(g,f,"+")+P,outer(g,f,"-")+P)
Amp <- c(M,outer(M,F,"*")/2.,outer(M,F,"*")/2. )
Pha <- c(beta+zeta,outer(beta,delta,"+")+zeta,outer(beta,delta,"-")+zeta)
## regroup similar frequencies
tol <- 0.0001
Ntrun <- 200.
Order <- order(abs(Amp),decreasing=TRUE)
Amp <- Amp[Order]
Fre <- Fre[Order]
## truncates the first 200 terms
Fre <- Fre[1:Ntrun]
Amp <- Amp[1:Ntrun]
N <- length(Fre)
for (i in 1:(N-1)) {
for (j in (i+1):N) {
if (abs(Fre[j] - Fre[i]) < tol) {
Amp[i] <- Amp[i]+Amp[j]
Amp[j] <- 0
} } }
Order <- order(abs(Amp),decreasing=TRUE)
Amp <- Amp[Order]
Fre <- Fre[Order]
Pha <- (Pha[Order]+180)%%360.
Per <- 360*60*60/Fre/1000.
Table2 <<- data.frame(Index=seq(1,length(Amp)),Amp=Amp,Fre=Fre,Pha=Pha,Per=abs(Per[Order]))
}
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