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#' Returns predictor vector for design matrix
#' @description Returns predictor vector for design matrix from 39 astronomical angular velocities.
#' @param xi Transit index
#' @param tdiff Length of input time series.
#' @return A list with the selected angular velocities, their ranks and the predictor vector (Values between -1, 1).
Funcs <- function(tdiff, xi) {
#Vector with angular velocities
rad <- 0.017453292519943
xi <- rad * xi
omegas <- vector()
omegas[ 1]<-0.0548098
omegas[ 2]<-0.2306165
omegas[ 3]<-1.0201944
omegas[ 4]<-1.8097724
omegas[ 5]<-2.0403886
omegas[ 6]<-11.5978420
omegas[ 7]<-11.7131503
omegas[ 8]<-12.3874200
omegas[ 9]<-12.6180365
omegas[10]<-12.7881545
omegas[11]<-13.5229227
omegas[12]<-13.6382309
omegas[13]<-13.6930407
omegas[14]<-13.7535391
omegas[15]<-15.9640460
omegas[16]<-24.2158785
omegas[17]<-25.1812631
omegas[18]<-25.2360729
omegas[19]<-26.2562673
omegas[20]<-27.0458453
omegas[21]<-27.1611535
omegas[22]<-27.2764618
omegas[23]<-27.3312716
omegas[24]<-36.9492232
omegas[25]<-38.7589956
omegas[26]<-38.8743038
omegas[27]<-38.9896120
omegas[28]<-40.7993844
omegas[29]<-49.4519514
omegas[30]<-50.4721458
omegas[31]<-52.5125347
omegas[32]<-52.5673444
omegas[33]<-54.5529235
omegas[34]<-62.1852961
omegas[35]<-63.9950685
omegas[36]<-64.2256849
omegas[37]<-75.7082187
omegas[38]<-77.7486076
omegas[39]<-100.9442917
# omegas[41]<-66.035455302
# omegas[42]<-75.708216801
# omegas[43]<-77.748605565
# omegas[44]<-100.944289068
omega_pos <- omegas
iranks <- vector()
iranks[ 1]<-6
iranks[ 2]<-13
iranks[ 3]<-7
iranks[ 4]<-31
iranks[ 5]<-17
iranks[ 6]<-14
iranks[ 7]<-8
iranks[ 8]<-34
iranks[ 9]<-19
iranks[10]<-39
iranks[11]<-3
iranks[12]<-4
iranks[13]<-38
iranks[14]<-21
iranks[15]<-36
iranks[16]<-11
iranks[17]<-35
iranks[18]<-1
iranks[19]<-12
iranks[20]<-33
iranks[21]<-15
iranks[22]<-2
iranks[23]<-27
iranks[24]<-10
iranks[25]<-16
iranks[26]<-24
iranks[27]<-22
iranks[28]<-23
iranks[29]<-29
iranks[30]<-5
iranks[31]<-9
iranks[32]<-37
iranks[33]<-30
iranks[34]<-25
iranks[35]<-28
iranks[36]<-26
iranks[37]<-20
iranks[38]<-18
iranks[39]<-32
# iranks[40]<-34
# iranks[41]<-42
# iranks[42]<-20
# iranks[43]<-41
# iranks[44]<-33
omega_pos_rank <- iranks
omega_sel <- vector()
omega_sel_rank <- vector()
while (length(omega_pos) > 0) {
#Find most relevant velocities
maxrank <- which.min(omega_pos_rank)
omega_pos_maxrank <- omega_pos[maxrank]
if( omega_pos_maxrank * tdiff > 360){
omega_sel <- c(omega_sel, omega_pos_maxrank)
omega_sel_rank <- c(omega_sel_rank, omega_pos_rank[maxrank])
del_index <- which((abs(omega_pos - omega_pos_maxrank) * tdiff) < 360)
omega_pos <- omega_pos[-del_index]
omega_pos_rank <- omega_pos_rank[-del_index]
} else {
omega_pos <- omega_pos[-maxrank]
omega_pos_rank <- omega_pos_rank[-maxrank]
}
}
omega_sel <- omega_sel[order(omega_sel)]
#Computing the afuncs for the selected omegas
afunc <- vector(mode = "numeric", length = 2 * length(omega_sel) + 1)
afunc[1] <- 1.00000
for(i in seq(2, 2 * length(omega_sel) + 1, 2)) {
oxi <- omega_sel[i / 2] * xi
afunc[i] <- cos(oxi)
afunc[i + 1] <- sin(oxi)
}
return(list(omega_sel, omega_sel_rank, afunc))
}
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