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bls_and_tcf_noise_change_as_depth_decrease.R
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bls_and_tcf_noise_change_as_depth_decrease.R
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#################################################################################
# Aim: Given a transit depth, run the extreme value code and related procedures
# and then plot the results.
# Notes:
# 1. This script can only be used if simulation is the intention.
# 2. This script was used for making some of the plots in the paper.
#################################################################################
library(forecast)
library('cobs')
library('boot')
library('extRemes')
library('kernlab')
library('goftest') # install.packages("goftest")
source('BLS/bls.R')
source('TCF3.0/intf_libtcf.R')
source('utils.R')
source('eva_periodogram.R')
helperGetFAP <- function(
depth, noiseType=1, ntransits=10, res=2, ofac=2,
gaussStd=1e-4, useOptimalFreqSampling=TRUE,
L=300, R=300, K=2, seedValue=465, applyGPRforBLS=FALSE
) {
set.seed(seedValue)
period <- 2
duration <- 2
# Generate light curve using the parameters.
yt <- getLightCurve(period, depth, duration, noiseType=noiseType, ntransits=ntransits, res=res, gaussStd=gaussStd, seedValue=seedValue)
y <- unlist(yt[1])
t <- unlist(yt[2])
noiseStd <- unlist(yt[3])
noiseIQR <- unlist(yt[4])
# Special case (TCF fails if absolutely no noise -- so add a very small amount of noise just to prevent any errors).
if (noiseType == 0) {
y <- y + 10^-10 * rnorm(length(y))
}
# Create frequency grid.
bfreqGrid <- getFreqGridToTest(t, period, duration, res=res, ofac=ofac, useOptimalFreqSampling=useOptimalFreqSampling, algo="BLS")
tfreqGrid <- getFreqGridToTest(t, period, duration, res=res, ofac=ofac, useOptimalFreqSampling=useOptimalFreqSampling, algo="TCF")
stopifnot(exprs={
identical(tfreqGrid, bfreqGrid)
})
boutput <- bls(if (noiseType == 2 | applyGPRforBLS) getGPRResid(t, y) else y, t, bls.plot = FALSE, per.min=min(1/bfreqGrid), per.max=max(1/bfreqGrid), nper=length(bfreqGrid))
bperResults <- c(boutput$per, boutput$depth, boutput$dur)
tfstep <- (max(tfreqGrid) - min(tfreqGrid)) / length(tfreqGrid)
tfreqs <- seq(from = min(tfreqGrid), by = tfstep, length.out = length(tfreqGrid))
tperiodsToTry <- 1 / tfreqs
tresidTCF <- getResidForTCF(y)
toutput <- tcf(tresidTCF, p.try = tperiodsToTry * res, print.output = TRUE)
tpowmax.loc = which.max(toutput$outpow)
tperResults <- c(toutput$inper[tpowmax.loc]/res, toutput$outdepth[tpowmax.loc], toutput$outdur[tpowmax.loc]/res)
# output$inper = output$inper / 2
# Standardize periodograms
nboutput <- standardizeAPeriodogram(
boutput,
periodsToTry=NULL, # This argument is only needed when algo="TCF" and not needed for algo="BLS".
algo="BLS",
mode='detrend_normalize', # Other option is 'detrend' in which case only detrending is performed, no normalization using scatter is performed.
scatterWindowLength=length(boutput$periodsTested)/10
)
bcobsxy50 <- nboutput[[2]]
ntoutput <- standardizeAPeriodogram(
toutput,
periodsToTry=tperiodsToTry, # This argument is only needed when algo="TCF" and not needed for algo="BLS".
algo="TCF",
mode='detrend_normalize', # Other option is 'detrend' in which case only detrending is performed, no normalization using scatter is performed.
scatterWindowLength=length(tperiodsToTry)/10
)
tcobsxy50 <- ntoutput[[2]]
# Call extreme value analysis code.
resultBLS <- evd(period, depth, duration, noiseType=noiseType, algo='BLS', ofac=ofac, L=L, R=R, res=res, ntransits=ntransits, gaussStd=gaussStd, FAPSNR_mode=0, seedValue=seedValue, useStandardization=TRUE, mode='detrend_normalize')
resultTCF <- evd(period, depth, duration, noiseType=noiseType, algo='TCF', ofac=ofac, L=L, R=R, res=res, ntransits=ntransits, gaussStd=gaussStd, FAPSNR_mode=0, seedValue=seedValue, useStandardization=TRUE, mode='detrend_normalize')
fapBLS <- resultBLS[1]
fapTCF <- resultTCF[1]
perResultsBLS <- resultBLS[2:4]
perResultsTCF <- resultTCF[2:4]
return (list(perResultsBLS, perResultsTCF, fapBLS, fapTCF))
}
helperGetFAPMultipleSeeds <- function(
...
) {
set.seed(42)
seeds <- sample(1:1e5, 50)
faps_BLS <- c()
faps_TCF <- c()
for (seed in seeds) {
x <- helperGetFAP(..., seedValue=seed)
fapBLS <- x[[3]]
fapTCF <- x[[4]]
faps_BLS <- c(faps_BLS, fapBLS)
faps_TCF <- c(faps_TCF, fapTCF)
}
return (c(median(faps_BLS), median(faps_TCF)))
}
blsAndTCFDepthChange <- function(
depth, noiseType=1, ntransits=10, res=2, ofac=2,
gaussStd=1e-4, useOptimalFreqSampling=TRUE,
L=300, R=300, K=2, seedValue=465, applyGPRforBLS=FALSE,
fapBLS=NaN, fapTCF=NaN
) {
set.seed(seedValue)
period <- 2
duration <- 2
# Generate light curve using the parameters.
yt <- getLightCurve(period, depth, duration, noiseType=noiseType, ntransits=ntransits, res=res, gaussStd=gaussStd, seedValue=seedValue)
y <- unlist(yt[1])
t <- unlist(yt[2])
noiseStd <- unlist(yt[3])
noiseIQR <- unlist(yt[4])
# Special case (TCF fails if absolutely no noise -- so add a very small amount of noise just to prevent any errors).
if (noiseType == 0) {
y <- y + 10^-10 * rnorm(length(y))
}
# Create frequency grid.
bfreqGrid <- getFreqGridToTest(t, period, duration, res=res, ofac=ofac, useOptimalFreqSampling=useOptimalFreqSampling, algo="BLS")
tfreqGrid <- getFreqGridToTest(t, period, duration, res=res, ofac=ofac, useOptimalFreqSampling=useOptimalFreqSampling, algo="TCF")
stopifnot(exprs={
identical(tfreqGrid, bfreqGrid)
})
boutput <- bls(if (noiseType == 2 | applyGPRforBLS) getGPRResid(t, y) else y, t, bls.plot = FALSE, per.min=min(1/bfreqGrid), per.max=max(1/bfreqGrid), nper=length(bfreqGrid))
bperResults <- c(boutput$per, boutput$depth, boutput$dur)
tfstep <- (max(tfreqGrid) - min(tfreqGrid)) / length(tfreqGrid)
tfreqs <- seq(from = min(tfreqGrid), by = tfstep, length.out = length(tfreqGrid))
tperiodsToTry <- 1 / tfreqs
tresidTCF <- getResidForTCF(y)
toutput <- tcf(tresidTCF, p.try = tperiodsToTry * res, print.output = TRUE)
tpowmax.loc = which.max(toutput$outpow)
tperResults <- c(toutput$inper[tpowmax.loc]/res, toutput$outdepth[tpowmax.loc], toutput$outdur[tpowmax.loc]/res)
# output$inper = output$inper / 2
# Standardize periodograms
nboutput <- standardizeAPeriodogram(
boutput,
periodsToTry=NULL, # This argument is only needed when algo="TCF" and not needed for algo="BLS".
algo="BLS",
mode='detrend_normalize', # Other option is 'detrend' in which case only detrending is performed, no normalization using scatter is performed.
scatterWindowLength=length(boutput$periodsTested)/10
)
bcobsxy50 <- nboutput[[2]]
ntoutput <- standardizeAPeriodogram(
toutput,
periodsToTry=tperiodsToTry, # This argument is only needed when algo="TCF" and not needed for algo="BLS".
algo="TCF",
mode='detrend_normalize', # Other option is 'detrend' in which case only detrending is performed, no normalization using scatter is performed.
scatterWindowLength=length(tperiodsToTry)/10
)
tcobsxy50 <- ntoutput[[2]]
# Call extreme value analysis code.
resultBLS <- evd(period, depth, duration, noiseType=noiseType, algo='BLS', ofac=ofac, L=L, R=R, res=res, ntransits=ntransits, gaussStd=gaussStd, FAPSNR_mode=0, seedValue=seedValue, useStandardization=TRUE, mode='detrend_normalize')
resultTCF <- evd(period, depth, duration, noiseType=noiseType, algo='TCF', ofac=ofac, L=L, R=R, res=res, ntransits=ntransits, gaussStd=gaussStd, FAPSNR_mode=0, seedValue=seedValue, useStandardization=TRUE, mode='detrend_normalize')
fapBLS <- resultBLS[1]
fapTCF <- resultTCF[1]
perResultsBLS <- resultBLS[2:4]
perResultsTCF <- resultTCF[2:4]
png(filename="depth_change_gaussian_0.02.png", width = 430, height = 320, units='mm', res = 300)
par(mar=c(5,6,4,2), cex=15)
cexVal <- 2.0
layout(matrix(c(1,1,1,1,2,2, 3,3,3,4,4,4, 5,5,5,6,6,6, 7,7,7,8,8,8, 9,9,9,10,10,10), nrow=5, ncol=6, byrow=TRUE))
# layout(mat = mat1,
# heights = c(1, 1, 1, 1), # Heights of the two rows
# widths = c(1.5, 2, 2)
# ) # Widths of the two columns
bpergram <- boutput$spec
tpergram <- toutput$outpow
plot(t/24, y, type='l', main=sprintf("Period: %.1f days, Depth: %.1f ppm, Duration: %.1f hrs | Noise: Gaussian", period, depth*1e4, duration), cex.main=cexVal, cex.lab=cexVal, cex.axis=cexVal, xlab='Time (days)', ylab='Flux')
acfEstimate <- acf(y, plot = FALSE, na.action = na.pass)
lJStats <- Box.test(y, lag = 1, type = "Ljung") # We want to see autocorrelation with each lag, hence pass lag = 1.
plot(acfEstimate, main="", cex.main=cexVal, cex.lab=cexVal, cex.axis=cexVal, xlim=c(1, 20), ylim=c(-0.2, +0.5))
text(10, 0.36, sprintf("P(Ljung-Box) = %.2f, ACF(1) = %.2f\n", lJStats[3], acfEstimate$acf[[2]]), cex=1.9)
# plot(acfEstimate, main=sprintf("P(Ljung-Box) = %.2f, ACF(1) = %.2f", lJStats[3], acfEstimate$acf[[2]]), cex.main=cexVal, cex.lab=cexVal, cex.axis=cexVal, cex=cexVal, xlim=c(1, 20), ylim=(-0.2, +0.5))
# ROW 2 #######################################################################################################
plot((10**bcobsxy50$x)/24, bpergram, type = 'l', main="BLS periodogram", log='x', xlab='Period (days) [log scale]', ylab='Power', cex.main=cexVal, cex.lab=cexVal, cex.axis=cexVal)
lines((10**bcobsxy50$x)/24, bcobsxy50$fitted, type = 'l', col='red', lwd=3.0)
# lines(cobsxy501$x, cobsxy501$fitted, type = 'l', col='cyan')
# lines(cobsxy502$x, cobsxy502$fitted, type = 'l', col='magenta')
rug((10**bcobsxy50$knots)/24)
# legend("topleft", lty = 1,
# col= c("red"), text.col = "black",
# legend=c("trend fit"), bty="n", cex=1.5, pt.cex = 1
# )
text(0.08, 3.8e-5, paste0(sprintf("Period = %.5f days, Depth = %.1f ppm\nSNR = %.1f", perResultsBLS[1]/24, perResultsBLS[2]*1e6, calculateSNR(boutput$periodsTested, bpergram))), cex=1.9, adj=0)
plot(10**(tcobsxy50$x)/24, tpergram, type = 'l', main="TCF periodogram", log='x', xlab='Period (days) [log scale]', ylab='Power', cex.main=cexVal, cex.lab=cexVal, cex.axis=cexVal)
lines((10**tcobsxy50$x)/24, tcobsxy50$fitted, type = 'l', col='red', lwd=3.0)
# lines(cobsxy501$x, cobsxy501$fitted, type = 'l', col='cyan')
# lines(cobsxy502$x, cobsxy502$fitted, type = 'l', col='magenta')
rug((10**tcobsxy50$knots)/24)
# legend("topleft", lty = 1,
# col= c("red"), text.col = "black",
# legend=c("trend fit"), bty="n", cex=1.5, pt.cex = 1
# )
text(0.08, 153, paste0(sprintf("Period = %.5f days, Depth = %.1f ppm\nSNR = %.1f", perResultsTCF[1]/24, perResultsTCF[2]*1e6, calculateSNR(tperiodsToTry * res, tpergram))), cex=1.9, adj=0)
###############################################################################################################
# print(calculateSNR(tperiodsToTry * res, tpergram))
# print(calculateSNR(boutput$periodsTested, bpergram))
# Row 3 ##############################################################################################################
# Plot histogram of original periodograms. Shows log-frequency on y-axis in histogram for better visualization.
bhist.data = hist(boutput$spec, breaks=50, plot = FALSE)
# bSkewnessBefore <- skewness(boutput$spec)
# bKurtosisBefore <- kurtosis(boutput$spec)
thist.data = hist(toutput$outpow, breaks=50, plot = FALSE)
# Compute skewness and kurtosis of the original and standardized histograms.
### Refer https://brownmath.com/stat/shape.htm for more information ###
### Note: R does NOT compute the "excess kurtosis".
# The kurtosis is calculated as follows:
# ```
# n <- length(x)
# n * sum((x - mean(x))^4)/(sum((x - mean(x))^2)^2)
# ``` Taken from https://stackoverflow.com/a/21484052
# tSkewnessBefore <- skewness(toutput$outpow)
plot(bhist.data$count, type='h', log='y', main=sprintf('BLS periodogram histogram'), cex=cexVal, cex.main=cexVal, cex.lab=cexVal, cex.axis=cexVal, xaxt="n", lwd=10, lend=2, col='grey61', xlab='Power', ylab='Count')
axis(1, at=1:length(bhist.data$mids), labels=sprintf(bhist.data$mids, fmt="%.1e"), cex.axis=cexVal)
plot(thist.data$count, type='h', log='y', main=sprintf('TCF periodogram histogram'), cex=cexVal, cex.main=cexVal, cex.lab=cexVal, cex.axis=cexVal, xaxt="n", lwd=10, lend=2, col='grey61', xlab='Power', ylab='Count')
axis(1, at=1:length(thist.data$mids), labels=sprintf(thist.data$mids, fmt="%.1e"), cex.axis=cexVal)
# tKurtosisBefore <- kurtosis(toutput$outpow)
###############################################################################################################
# Row 4 ##############################################################################################################
plot((10**bcobsxy50$x)/24, nboutput[[1]], type = 'l', main="Standardized BLS periodogram", log='x', xlab='Period (days) [log scale]', ylab='Power', cex.main=cexVal, cex.lab=cexVal, cex.axis=cexVal)
# lines(cobsxy501$x, cobsxy501$fitted, type = 'l', col='cyan')
# lines(cobsxy502$x, cobsxy502$fitted, type = 'l', col='magenta')
rug((10**bcobsxy50$knots)/24)
# legend("topleft", lty = 1,
# col= c("red"), text.col = "black",
# legend=c("trend fit"), bty="n", cex=1.5, pt.cex = 1
# )
text(0.08, 15, paste0(sprintf("FAP = %s", formatC(fapBLS, format = "e", digits = 0))), cex=1.9, adj=0)
plot(10**(tcobsxy50$x)/24, ntoutput[[1]], type = 'l', main="Standardized TCF periodogram", log='x', xlab='Period (days) [log scale]', ylab='Power', cex.main=cexVal, cex.lab=cexVal, cex.axis=cexVal)
# lines(cobsxy501$x, cobsxy501$fitted, type = 'l', col='cyan')
# lines(cobsxy502$x, cobsxy502$fitted, type = 'l', col='magenta')
rug((10**tcobsxy50$knots)/24)
# legend("topleft", lty = 1,
# col= c("red"), text.col = "black",
# legend=c("trend fit"), bty="n", cex=1.5, pt.cex = 1
# )
text(0.08, 30, paste0(sprintf("FAP = %s", formatC(fapTCF, format = "e", digits = 0))), cex=1.9, adj=0)
###############################################################################################################
# Plot histogram of standardized periodograms. Shows log-frequency on y-axis in histogram for better visualization.
bhist.data = hist(nboutput[[1]], breaks=50, plot = FALSE)
# bSkewnessBefore <- skewness(boutput$spec)
# bKurtosisBefore <- kurtosis(boutput$spec)
thist.data = hist(ntoutput[[1]], breaks=50, plot = FALSE)
# Compute skewness and kurtosis of the original and standardized histograms.
### Refer https://brownmath.com/stat/shape.htm for more information ###
### Note: R does NOT compute the "excess kurtosis".
# The kurtosis is calculated as follows:
# ```
# n <- length(x)
# n * sum((x - mean(x))^4)/(sum((x - mean(x))^2)^2)
# ``` Taken from https://stackoverflow.com/a/21484052
# tSkewnessBefore <- skewness(toutput$outpow)
plot(bhist.data$count, type='h', log='y', main=sprintf('Standardized BLS periodogram histogram'), cex=cexVal, cex.main=cexVal, cex.lab=cexVal, cex.axis=cexVal, xaxt="n", lwd=10, lend=2, col='grey61', xlab='Power', ylab='Count')
axis(1, at=1:length(bhist.data$mids), labels=sprintf(bhist.data$mids, fmt="%.1e"), cex.axis=cexVal)
plot(thist.data$count, type='h', log='y', main=sprintf('Standardized TCF periodogram histogram'), cex=cexVal, cex.main=cexVal, cex.lab=cexVal, cex.axis=cexVal, xaxt="n", lwd=10, lend=2, col='grey61', xlab='Power', ylab='Count')
axis(1, at=1:length(thist.data$mids), labels=sprintf(thist.data$mids, fmt="%.1e"), cex.axis=cexVal)
# tKurtosisBefore <- kurtosis(toutput$outpow)
# dev.print(png, 'depth_change_gaussian_0.008.png')
dev.off()
}
###### 1. MDD for Gaussian case (465 seed value, period=2days, dur=2hrs):
# 0.006836735% for BLS and 0.009591837 for TCF
# MDD for Autoregressive case (544 seed value, period=2days, dur=2hrs):
# 0.02336735 for BLS and 0.02612245 for TCF
###### Text coordinates used:
# depth_change_gaussian_0.006.png (BLS, TCF): [adj=1]
# For period, etc: (22, 1.67e-5), (22, 43)
# For FAP: (22, 6), (22, 9.5)
# depth_change_gaussian_0.02.png: [adj=0]
# For period, etc: (0.08, 3.8e-5), (0.08, 153)
# For FAP: (0.08, 15), (0.08, 30)
# depth_change_ar_0.023.png: (BLS, TCF): (0.08, 4.6e-5), (0.08, 86); For FAP:
# depth_change_ar_0.04.png: (BLS, TCF):
# For period, etc: (0.08, 7.2e-5), (0.08, 210) -- both adj=0
# For FAP: (22, 9), (22, 39)
# Data
# 0.02% FAP_BLS = , FAP_TCF =
# 0.006836735%: FAP_BLS = , FAP_TCF =
########### Showing results on real light curves ###########
blsAndTCFDepthChangeReal <- function(
table, noiseType=1, ntransits=10, res=2, ofac=2, useOptimalFreqSampling=TRUE,
L=300, R=300, applyGPRforBLS=TRUE
) {
period <- depth <- duration <- noiseType <- ntransits <- ar <- ma <- order <- gaussStd <- NULL
significanceMode <- 'max' # Since for real light curves, passing `expected_peak` is not possible.
res <- 2
K <- ofac
rtBLS <- c()
rtTCF <- c()
table_BLS <- table[!is.na(table$Flux),]
resultBLS <- evd(y=table_BLS$Flux, t=table_BLS$times, algo="BLS", FAPSNR_mode=0, lctype="real", applyGPRforBLS=TRUE, noiseType=noiseType, L=L, R=R, res=res, ntransits=ntransits, gaussStd=gaussStd, seedValue=seedValue, useStandardization=TRUE, mode='detrend_normalize')
fapBLS <- resultBLS[1]
perResultsBLS <- resultBLS[2:4]
resultBLS <- evd(y=table_BLS$Flux, t=table_BLS$times, algo="BLS", FAPSNR_mode=1, lctype="real", applyGPRforBLS=TRUE, noiseType=noiseType, L=L, R=R, res=res, ntransits=ntransits, gaussStd=gaussStd, seedValue=seedValue, useStandardization=TRUE, mode='detrend_normalize')
snrBLS <- 1 / resultBLS[1]
rtBLS <- c(rtBLS, c(fapBLS, snrBLS, perResultsBLS))
resultTCF <- evd(y=table$Flux, t=table$times, algo="TCF", FAPSNR_mode=0, lctype="real", noiseType=noiseType, L=L, R=R, res=res, ntransits=ntransits, gaussStd=gaussStd, seedValue=seedValue, useStandardization=TRUE, mode='detrend_normalize')
fapTCF <- resultTCF[1]
perResultsTCF <- resultTCF[2:4]
resultTCF <- evd(y=table$Flux, t=table$times, algo="TCF", FAPSNR_mode=1, lctype="real", noiseType=noiseType, L=L, R=R, res=res, ntransits=ntransits, gaussStd=gaussStd, seedValue=seedValue, useStandardization=TRUE, mode='detrend_normalize')
snrTCF <- 1 / resultTCF[1]
rtTCF <- c(rtTCF, c(fapTCF, snrTCF, perResultsTCF))
y_BLS <- table_BLS$Flux
t_BLS <- table_BLS$times
y <- table$Flux
t <- table$times
# Create a frequency grid.
# Note: Optimal frequency sampling is NOT used for real light curves since the period is unknown.
bfreqGrid <- getFreqGridToTest(t_BLS, period, duration, res=res, ofac=ofac, algo=algo, lctype="real")
if (any(is.na(bfreqGrid))) {
stop("Atleast one frequency in the frequency grid is NaN!")
}
stopifnot(exprs={
all(bfreqGrid <= res / 2) # No frequency must be greater than the Nyquist frequency.
length(bfreqGrid) >= K * L # K*L is ideally going to be less than N, otherwise the bootstrap has no benefit in terms of compuation time.
length(bfreqGrid) / (K * L) <= length(t_BLS) / 2 # This condition is mentioned in https://ui.adsabs.harvard.edu/abs/2012ada..confE..16S.
})
print(sprintf("Max frequency: %f, Min frequency: %f", max(bfreqGrid), min(bfreqGrid)))
tfreqGrid <- getFreqGridToTest(t, period, duration, res=res, ofac=ofac, algo=algo, lctype="real")
if (any(is.na(bfreqGrid))) {
stop("Atleast one frequency in the frequency grid is NaN!")
}
stopifnot(exprs={
all(tfreqGrid <= res / 2) # No frequency must be greater than the Nyquist frequency.
length(tfreqGrid) >= K * L # K*L is ideally going to be less than N, otherwise the bootstrap has no benefit in terms of compuation time.
length(tfreqGrid) / (K * L) <= length(t) / 2 # This condition is mentioned in https://ui.adsabs.harvard.edu/abs/2012ada..confE..16S.
})
print(sprintf("Max frequency: %f, Min frequency: %f", max(tfreqGrid), min(tfreqGrid)))
# Get periodograms
if (isTRUE(noiseType == 2) | applyGPRforBLS) {
y <- getGPRResid(t, y) # Run Gaussian Processes Regression on light curve if autoregressive noise is present.
}
boutput <- bls(y_BLS, t_BLS, bls.plot = FALSE, per.min=min(1/bfreqGrid), per.max=max(1/bfreqGrid), nper=length(bfreqGrid))
fstep <- (max(tfreqGrid) - min(tfreqGrid)) / length(tfreqGrid)
freqs <- seq(from = min(tfreqGrid), by = fstep, length.out = length(tfreqGrid))
tperiodsToTry <- 1 / freqs
# Empirical observation: In reality, applying ARMA when Gaussian noise is present will give another Gaussian, so is not that helpful.
# However, for some reason, it was found to be important to keep ARMA irrespective of the noise to get expected results.
# Hence we apply ARMA even if Gaussian noise is present.
tresidTCF <- getResidForTCF(y)
toutput <- tcf(tresidTCF, p.try = tperiodsToTry * res, print.output = TRUE)
# Note that if NaN's are present in the light curve, then the BLS and TCF frequencies will not be the same.
# Since all the four real TESS curves have missing values, BLS and TCF frequencies will be different.
# Hence, it doesn't make sense to to check the below condition.
# stopifnot(exprs={
# identical(tfreqGrid, bfreqGrid)
# })
# Normalized periodograms
# Standardize periodograms
nboutput <- standardizeAPeriodogram(
boutput,
periodsToTry=NULL, # This argument is only needed when algo="TCF" and not needed for algo="BLS".
algo="BLS",
mode='detrend_normalize', # Other option is 'detrend' in which case only detrending is performed, no normalization using scatter is performed.
scatterWindowLength=length(boutput$periodsTested)/10
)
bcobsxy50 <- nboutput[[2]]
ntoutput <- standardizeAPeriodogram(
toutput,
periodsToTry=tperiodsToTry, # This argument is only needed when algo="TCF" and not needed for algo="BLS".
algo="TCF",
mode='detrend_normalize', # Other option is 'detrend' in which case only detrending is performed, no normalization using scatter is performed.
scatterWindowLength=length(tperiodsToTry)/10
)
tcobsxy50 <- ntoutput[[2]]
# Plotting.
png(filename="real_4.png", width = 430, height = 320, units='mm', res = 300)
par(mar=c(5,6,4,2), cex=15)
cexVal <- 2.0
layout(matrix(c(1,1,1,1,2,2, 3,3,3,4,4,4, 5,5,5,6,6,6, 7,7,7,8,8,8, 9,9,9,10,10,10), nrow=5, ncol=6, byrow=TRUE))
# layout(mat = mat1,
# heights = c(1, 1, 1, 1), # Heights of the two rows
# widths = c(1.5, 2, 2)
# ) # Widths of the two columns
bpergram <- boutput$spec
tpergram <- toutput$outpow
plot(t/24, y, type='l', main=sprintf("DTARPS 103 = TIC 89020549"), cex.main=cexVal, cex.lab=cexVal, cex.axis=cexVal, xlab='Time (days)', ylab='Flux')
acfEstimate <- acf(y, plot = FALSE, na.action = na.pass)
lJStats <- Box.test(y, lag = 1, type = "Ljung") # We want to see autocorrelation with each lag, hence pass lag = 1.
plot(acfEstimate, main="", cex.main=cexVal, cex.lab=cexVal, cex.axis=cexVal, xlim=c(1, 20), ylim=c(-0.2, +0.5))
text(10, 0.36, sprintf("P(Ljung-Box) = %.2f, ACF(1) = %.2f\n", lJStats[3], acfEstimate$acf[[2]]), cex=1.9)
# plot(acfEstimate, main=sprintf("P(Ljung-Box) = %.2f, ACF(1) = %.2f", lJStats[3], acfEstimate$acf[[2]]), cex.main=cexVal, cex.lab=cexVal, cex.axis=cexVal, cex=cexVal, xlim=c(1, 20), ylim=(-0.2, +0.5))
# ROW 2 #######################################################################################################
plot((10**bcobsxy50$x)/24, bpergram, type = 'l', main="BLS periodogram", log='x', xlab='Period (days) [log scale]', ylab='Power', cex.main=cexVal, cex.lab=cexVal, cex.axis=cexVal)
lines((10**bcobsxy50$x)/24, bcobsxy50$fitted, type = 'l', col='red', lwd=3.0)
# lines(cobsxy501$x, cobsxy501$fitted, type = 'l', col='cyan')
# lines(cobsxy502$x, cobsxy502$fitted, type = 'l', col='magenta')
rug((10**bcobsxy50$knots)/24)
# legend("topleft", lty = 1,
# col= c("red"), text.col = "black",
# legend=c("trend fit"), bty="n", cex=1.5, pt.cex = 1
# )
text(2/24, 1.62e-4, paste0(sprintf("Period = %.5f days, Depth = %.1f\nSNR = %.1f", perResultsBLS[1]/24, perResultsBLS[2]*1e6, calculateSNR(boutput$periodsTested, bpergram))), cex=1.9, adj=0)
plot(10**(tcobsxy50$x)/24, tpergram, type = 'l', main="TCF periodogram", log='x', xlab='Period (days) [log scale]', ylab='Power', cex.main=cexVal, cex.lab=cexVal, cex.axis=cexVal)
lines((10**tcobsxy50$x)/24, tcobsxy50$fitted, type = 'l', col='red', lwd=3.0)
# lines(cobsxy501$x, cobsxy501$fitted, type = 'l', col='cyan')
# lines(cobsxy502$x, cobsxy502$fitted, type = 'l', col='magenta')
rug((10**tcobsxy50$knots)/24)
# legend("topleft", lty = 1,
# col= c("red"), text.col = "black",
# legend=c("trend fit"), bty="n", cex=1.5, pt.cex = 1
# )
text(2/24, 107, paste0(sprintf("Period = %.5f days, Depth = %.1f\nSNR = %.1f", perResultsTCF[1]/24, perResultsTCF[2]*1e6, calculateSNR(tperiodsToTry * res, tpergram))), cex=1.9, adj=0)
###############################################################################################################
# print(calculateSNR(tperiodsToTry * res, tpergram))
# print(calculateSNR(boutput$periodsTested, bpergram))
# Row 3 ##############################################################################################################
# Plot histogram of original periodograms. Shows log-frequency on y-axis in histogram for better visualization.
bhist.data = hist(boutput$spec, breaks=50, plot = FALSE)
# bSkewnessBefore <- skewness(boutput$spec)
# bKurtosisBefore <- kurtosis(boutput$spec)
thist.data = hist(toutput$outpow, breaks=50, plot = FALSE)
# Compute skewness and kurtosis of the original and standardized histograms.
### Refer https://brownmath.com/stat/shape.htm for more information ###
### Note: R does NOT compute the "excess kurtosis".
# The kurtosis is calculated as follows:
# ```
# n <- length(x)
# n * sum((x - mean(x))^4)/(sum((x - mean(x))^2)^2)
# ``` Taken from https://stackoverflow.com/a/21484052
# tSkewnessBefore <- skewness(toutput$outpow)
plot(bhist.data$count, type='h', log='y', main=sprintf('BLS periodogram histogram'), cex=cexVal, cex.main=cexVal, cex.lab=cexVal, cex.axis=cexVal, xaxt="n", lwd=10, lend=2, col='grey61', xlab='Power', ylab='Count')
axis(1, at=1:length(bhist.data$mids), labels=sprintf(bhist.data$mids, fmt="%.1e"), cex.axis=cexVal)
plot(thist.data$count, type='h', log='y', main=sprintf('TCF periodogram histogram'), cex=cexVal, cex.main=cexVal, cex.lab=cexVal, cex.axis=cexVal, xaxt="n", lwd=10, lend=2, col='grey61', xlab='Power', ylab='Count')
axis(1, at=1:length(thist.data$mids), labels=sprintf(thist.data$mids, fmt="%.1e"), cex.axis=cexVal)
# tKurtosisBefore <- kurtosis(toutput$outpow)
###############################################################################################################
# Row 4 ##############################################################################################################
plot((10**bcobsxy50$x)/24, nboutput[[1]], type = 'l', main="Standardized BLS periodogram", log='x', xlab='Period (days) [log scale]', ylab='Power', cex.main=cexVal, cex.lab=cexVal, cex.axis=cexVal)
# lines(cobsxy501$x, cobsxy501$fitted, type = 'l', col='cyan')
# lines(cobsxy502$x, cobsxy502$fitted, type = 'l', col='magenta')
rug((10**bcobsxy50$knots)/24)
# legend("topleft", lty = 1,
# col= c("red"), text.col = "black",
# legend=c("trend fit"), bty="n", cex=1.5, pt.cex = 1
# )
text(22, 16, paste0(sprintf("FAP = %s", formatC(fapBLS, format = "e", digits = 0))), cex=1.9, adj=1)
plot(10**(tcobsxy50$x)/24, ntoutput[[1]], type = 'l', main="Standardized TCF periodogram", log='x', xlab='Period (days) [log scale]', ylab='Power', cex.main=cexVal, cex.lab=cexVal, cex.axis=cexVal)
# lines(cobsxy501$x, cobsxy501$fitted, type = 'l', col='cyan')
# lines(cobsxy502$x, cobsxy502$fitted, type = 'l', col='magenta')
rug((10**tcobsxy50$knots)/24)
# legend("topleft", lty = 1,
# col= c("red"), text.col = "black",
# legend=c("trend fit"), bty="n", cex=1.5, pt.cex = 1
# )
text(22, 19.5, paste0(sprintf("FAP = %s", formatC(fapTCF, format = "e", digits = 0))), cex=1.9, adj=1)
###############################################################################################################
# Plot histogram of standardized periodograms. Shows log-frequency on y-axis in histogram for better visualization.
bhist.data = hist(nboutput[[1]], breaks=50, plot = FALSE)
# bSkewnessBefore <- skewness(boutput$spec)
# bKurtosisBefore <- kurtosis(boutput$spec)
thist.data = hist(ntoutput[[1]], breaks=50, plot = FALSE)
# Compute skewness and kurtosis of the original and standardized histograms.
### Refer https://brownmath.com/stat/shape.htm for more information ###
### Note: R does NOT compute the "excess kurtosis".
# The kurtosis is calculated as follows:
# ```
# n <- length(x)
# n * sum((x - mean(x))^4)/(sum((x - mean(x))^2)^2)
# ``` Taken from https://stackoverflow.com/a/21484052
# tSkewnessBefore <- skewness(toutput$outpow)
plot(bhist.data$count, type='h', log='y', main=sprintf('Standardized BLS periodogram histogram'), cex=cexVal, cex.main=cexVal, cex.lab=cexVal, cex.axis=cexVal, xaxt="n", lwd=10, lend=2, col='grey61', xlab='Power', ylab='Count')
axis(1, at=1:length(bhist.data$mids), labels=sprintf(bhist.data$mids, fmt="%.1e"), cex.axis=cexVal)
plot(thist.data$count, type='h', log='y', main=sprintf('Standardized TCF periodogram histogram'), cex=cexVal, cex.main=cexVal, cex.lab=cexVal, cex.axis=cexVal, xaxt="n", lwd=10, lend=2, col='grey61', xlab='Power', ylab='Count')
axis(1, at=1:length(thist.data$mids), labels=sprintf(thist.data$mids, fmt="%.1e"), cex.axis=cexVal)
# tKurtosisBefore <- kurtosis(toutput$outpow)
# dev.print(png, 'depth_change_gaussian_0.008.png')
dev.off()
}
# Coordinates
# real_1.png: 2/24, 4.5e-4; 2/24, 123 ;; 22, 7; 22, 15.5
# real_2.png: 4/24, 4.15e-5; 2/24, 123 ;; 22, 14.5; 22, 29
# real_3.png: 35/24, 1.4e-4; 35/24, 240 ;;
# real_4.png: 2/24, 1.62e-4; 2/24, 107 ;; 22, 16; 22, 19.5
# showFitOverlayed <- function(
# table
# ) {
# # TODO: For BLS, I think we first remove rows with Na flux values and only then run GPR, so try doing that here.
# gp <- gausspr(table$times, table$Flux)
# predicted_y <- predict(gp, table$times)
# max.p = 5
# max.q = 5
# max.d = 0
# ARIMA.fit = auto.arima(diff(table$Flux), stepwise=FALSE, approximation=FALSE, seasonal=FALSE, max.p=max.p, max.q=max.q, max.d=max.d, d=0)
# # print(ARIMA.fit)
# png(filename="gpr_fit.png", width = 420, height = 150, units='mm', res = 300)
# par(mar=c(5,6,4,2), cex=15)
# cexVal <- 1.7
# # mat1 <- matrix(c(
# # 1, 1, 1, 1, 2, 2,
# # 3, 3, 3, 3, 4, 4
# # ), nrow = 2, ncol = 6, byrow = TRUE
# # )
# # layout(mat1)
# layout(matrix(c(
# 1, 1, 1, 1, 2, 2,
# 3, 3, 3, 3, 4, 4
# ), ncol = 6, nrow=2, byrow=TRUE))
# ################# CODE FOR GPR ################
# par(mar=c(0,6,4,2))
# plot(table$times/24, table$Flux, col='black', type='l', main="", cex.main=cexVal, cex.lab=cexVal, cex.axis=cexVal, ylab="flux", xlab="", xaxt="n")
# lines(table$times/24, predicted_y, col='red', lwd=1.0)
# text(24, 1.0012, "Gaussian Processes Regression fit", cex=cexVal, adj=1)
# acfEstimate <- acf(table$Flux, plot = FALSE, na.action = na.pass)
# lJStats <- Box.test(y, lag = 1, type = "Ljung") # We want to see autocorrelation with each lag, hence pass lag = 1.
# plot(acfEstimate, main="", cex.main=cexVal, cex.lab=cexVal, cex.axis=cexVal, xaxt="n", yaxt="n", xlim=c(1, 20), ylim=c(-0.2, +0.5))
# text(15, 0.8, sprintf("P(Ljung-Box) = %.2f, ACF(1) = %.2f\n", lJStats[3], acfEstimate$acf[[2]]), cex=1.5)
# axis(2, at=c(-0.2, 0.0, 0.2, 0.4, 0.6, 0.8, 1.0), cex.axis=cexVal)
# par(mar=c(5,6,0,2))
# plot(table$times/24, table$Flux-predicted_y, col='black', type='l', main="", cex.main=cexVal, cex.lab=cexVal, cex.axis=cexVal, ylab="Residual flux", xlab="Time (days)", yaxt="n")
# text(24, 0.00135, "Gaussian Processes Regression residuals", cex=cexVal, adj=1)
# axis(2, at=c(-0.001, 0.000, 0.001), cex.axis=cexVal)
# acfEstimate <- acf(table$Flux - predicted_y, plot = FALSE, na.action = na.pass)
# lJStats <- Box.test(y, lag = 1, type = "Ljung") # We want to see autocorrelation with each lag, hence pass lag = 1.
# plot(acfEstimate, main="", cex.main=cexVal, cex.lab=cexVal, cex.axis=cexVal, yaxt="n", xlim=c(1, 20), ylim=c(-0.2, +0.5))
# text(15, 0.8, sprintf("P(Ljung-Box) = %.2f, ACF(1) = %.2f\n", lJStats[3], acfEstimate$acf[[2]]), cex=1.5)
# axis(2, at=c(-0.2, 0.0, 0.2, 0.4, 0.6, 0.8, 1.0), cex.axis=cexVal)
# ###############################################
# ################ CODE FOR ARIMA ###############
# # par(mar=c(0,6,4,2))
# # plot(head(table$times/24, -1), diff(table$Flux), col='black', type='l', main="", cex.main=cexVal, cex.lab=cexVal, cex.axis=cexVal, ylab="Differenced flux", xlab="", xaxt="n")
# # lines(head(table$times/24, -1), fitted(ARIMA.fit), col='red', lwd=1.0)
# # text(17, 0.0015, paste0("ARIMA(", ARIMA.fit$arma[[1]], ",1,", ARIMA.fit$arma[[2]], ") fit"), cex=cexVal, adj=1)
# # acfEstimate <- acf(diff(table$Flux), plot = FALSE, na.action = na.pass)
# # lJStats <- Box.test(y, lag = 1, type = "Ljung") # We want to see autocorrelation with each lag, hence pass lag = 1.
# # plot(acfEstimate, main="", cex.main=cexVal, cex.lab=cexVal, cex.axis=cexVal, xaxt="n", yaxt="n", xlim=c(1, 20), ylim=c(-0.2, +0.5))
# # text(15, 0.8, sprintf("P(Ljung-Box) = %.2f, ACF(1) = %.2f\n", lJStats[3], acfEstimate$acf[[2]]), cex=1.5)
# # axis(2, at=c(-0.2, 0.0, 0.2, 0.4, 0.6, 0.8, 1.0), cex.axis=cexVal)
# # par(mar=c(5,6,0,2))
# # plot(head(table$times/24, -1), diff(table$Flux)-fitted(ARIMA.fit), col='black', type='l', main="", cex.main=cexVal, cex.lab=cexVal, cex.axis=cexVal, ylab="Residual flux", xlab="Time (days)", yaxt="n")
# # text(17, 0.00125, "ARIMA residuals", cex=cexVal, adj=1)
# # axis(2, at=c(-0.001, 0.000, 0.001), cex.axis=cexVal)
# # acfEstimate <- acf(residuals(ARIMA.fit), plot = FALSE, na.action = na.pass)
# # lJStats <- Box.test(y, lag = 1, type = "Ljung") # We want to see autocorrelation with each lag, hence pass lag = 1.
# # plot(acfEstimate, main="", cex.main=cexVal, cex.lab=cexVal, cex.axis=cexVal, yaxt="n", xlim=c(1, 20), ylim=c(-0.2, +0.5))
# # text(15, 0.8, sprintf("P(Ljung-Box) = %.2f, ACF(1) = %.2f\n", lJStats[3], acfEstimate$acf[[2]]), cex=1.5)
# # axis(2, at=c(-0.2, 0.0, 0.2, 0.4, 0.6, 0.8, 1.0), cex.axis=cexVal)
# ###############################################
# dev.off()
# }
centerPieceFigure <- function(
period=2, depth=0.0265, noiseType=2, duration=2, ntransits=10, res=2, ofac=2, useOptimalFreqSampling=FALSE, lctype="sim",
applyGPRforBLS=TRUE, gaussStd=1e-4, seedValue=465, L=300, R=300
) {
# Generate light curve using the parameters.
yt <- getLightCurve(period, depth, duration, noiseType=noiseType, ntransits=ntransits, res=res, gaussStd=gaussStd, seedValue=seedValue)
y <- unlist(yt[1])
t <- unlist(yt[2])
noiseStd <- unlist(yt[3])
noiseIQR <- unlist(yt[4])
# Special case (TCF fails if absolutely no noise -- so add a very small amount of noise just to prevent any errors).
if (noiseType == 0) {
y <- y + 10^-10 * rnorm(length(y))
}
# Create frequency grid.
bfreqGrid <- getFreqGridToTest(t, period, duration, res=res, ofac=ofac, useOptimalFreqSampling=useOptimalFreqSampling, algo="BLS")
tfreqGrid <- getFreqGridToTest(t, period, duration, res=res, ofac=ofac, useOptimalFreqSampling=useOptimalFreqSampling, algo="TCF")
boutput <- bls(if (noiseType == 2 | applyGPRforBLS) getGPRResid(t, y) else y, t, bls.plot = FALSE, per.min=min(1/bfreqGrid), per.max=max(1/bfreqGrid), nper=length(bfreqGrid))
bperResults <- c(boutput$per, boutput$depth, boutput$dur)
tfstep <- (max(tfreqGrid) - min(tfreqGrid)) / length(tfreqGrid)
tfreqs <- seq(from = min(tfreqGrid), by = tfstep, length.out = length(tfreqGrid))
tperiodsToTry <- 1 / tfreqs
tresidTCF <- getResidForTCF(y)
toutput <- tcf(tresidTCF, p.try = tperiodsToTry * res, print.output = TRUE)
tpowmax.loc = which.max(toutput$outpow)
tperResults <- c(toutput$inper[tpowmax.loc]/res, toutput$outdepth[tpowmax.loc], toutput$outdur[tpowmax.loc]/res)
# output$inper = output$inper / 2
# (1) Remove trend in periodogram
# TODO: Is constraint='increase' really needed??
blambdaTrend <- 1
bcobsxy50 <- cobs(boutput$periodsTested, boutput$spec, ic='BIC', tau=0.5, lambda=blambdaTrend, constraint="increase") # If tau = 0.5 and lambda = 0 => Median regression fit.
bcobsxy501 <- cobs(boutput$periodsTested, boutput$spec, ic='BIC', tau=0.9, lambda=blambdaTrend)
bcobsxy502 <- cobs(boutput$periodsTested, boutput$spec, ic='BIC', tau=0.99, lambda=blambdaTrend)
tlambdaTrend <- 1
tcobsxy50 <- cobs(tperiodsToTry, toutput$outpow, ic='BIC', tau=0.5, lambda=tlambdaTrend, constraint="increase")
tcobsxy501 <- cobs(tperiodsToTry, toutput$outpow, ic='BIC', tau=0.9, lambda=tlambdaTrend)
tcobsxy502 <- cobs(tperiodsToTry, toutput$outpow, ic='BIC', tau=0.99, lambda=tlambdaTrend)
bperiodogramTrendRemoved <- bcobsxy50$resid
tperiodogramTrendRemoved <- tcobsxy50$resid
# (2) Remove local scatter in periodogram
scatterWindowLength <- length(tfreqGrid) / 10
bScatter <- computeScatter(bperiodogramTrendRemoved, windowLength=scatterWindowLength)
tScatter <- computeScatter(tperiodogramTrendRemoved, windowLength=scatterWindowLength)
# print("Scatter")
blambdaScatter <- 1
bcobsScatter <- cobs(boutput$periodsTested, bScatter, ic='BIC', tau=0.5, lambda=blambdaScatter)
# cobss50 <- cobs(output$periodsTested, periodogramTrendRemoved, ic='BIC', tau=0.5, lambda=lambdaTrend, constraint="increase") # If tau = 0.5 and lambda = 0 => Median regression fit.
# cobss501 <- cobs(output$periodsTested, periodogramTrendRemoved, ic='BIC', tau=0.9, lambda=lambdaTrend, constraint="increase")
# cobss502 <- cobs(output$periodsTested, periodogramTrendRemoved, ic='BIC', tau=0.99, lambda=lambdaTrend)
tlambdaScatter <- 1
tcobsScatter <- cobs(tperiodsToTry, tScatter, ic='BIC', tau=0.5, lambda=tlambdaScatter)
bnormalizedPeriodogram <- bperiodogramTrendRemoved / bcobsScatter$fitted
tnormalizedPeriodogram <- tperiodogramTrendRemoved / tcobsScatter$fitted
# Call extreme value analysis code.
resultBLS <- evd(period, depth, duration, noiseType=noiseType, algo='BLS', ofac=ofac, L=L, R=R, res=res, ntransits=ntransits, gaussStd=gaussStd, FAPSNR_mode=0, seedValue=seedValue)
resultTCF <- evd(period, depth, duration, noiseType=noiseType, algo='TCF', ofac=ofac, L=L, R=R, res=res, ntransits=ntransits, gaussStd=gaussStd, FAPSNR_mode=0, seedValue=seedValue)
fapBLS <- resultBLS[1]
fapTCF <- resultTCF[1]
bpergram <- boutput$spec
tpergram <- toutput$outpow
gp <- gausspr(t, y)
predicted_y <- predict(gp, t)
max.p = 5
max.q = 5
max.d = 0
ARIMA.fit = auto.arima(diff(y), stepwise=FALSE, approximation=FALSE, seasonal=FALSE, max.p=max.p, max.q=max.q, max.d=max.d, d=0) #leave d as 0.
cexVal <-1.5
layout(matrix(c(
1, 1, 1, 2, 2, 2,
3, 3, 3, 4, 4, 4
), ncol = 6, nrow=2, byrow=TRUE))
plot(t, y, type='l')
lines(t, predicted_y, col='red')
plot(diff(y), col='black', type='l')
lines(fitted(ARIMA.fit), col='red')
plot(bcobsxy50$x/24, bpergram, type = 'l', main="BLS periodogram", log='x', xlab='Period (days) [log scale]', ylab='Power', cex.main=cexVal, cex.lab=cexVal, cex.axis=cexVal)
lines(bcobsxy50$x/24, bcobsxy50$fitted, type = 'l', col='red', lwd=3.0)
# lines(cobsxy501$x, cobsxy501$fitted, type = 'l', col='cyan')
# lines(cobsxy502$x, cobsxy502$fitted, type = 'l', col='magenta')
rug(bcobsxy50$knots/24)
# legend("topleft", lty = 1,
# col= c("red"), text.col = "black",
# legend=c("trend fit"), bty="n", cex=1.5, pt.cex = 1
# )
text(2/24, 1.62e-4, paste0(sprintf("SNR = %.1f, FAP = %.1e", calculateSNR(boutput$periodsTested, bpergram), fapBLS), "%"), cex=1.8, adj=0)
plot(tcobsxy50$x/24, tpergram, type = 'l', main="TCF periodogram", log='x', xlab='Period (days) [log scale]', ylab='Power', cex.main=cexVal, cex.lab=cexVal, cex.axis=cexVal)
lines(tcobsxy50$x/24, tcobsxy50$fitted, type = 'l', col='red', lwd=3.0)
# lines(cobsxy501$x, cobsxy501$fitted, type = 'l', col='cyan')
# lines(cobsxy502$x, cobsxy502$fitted, type = 'l', col='magenta')
rug(tcobsxy50$knots/24)
# legend("topleft", lty = 1,
# col= c("red"), text.col = "black",
# legend=c("trend fit"), bty="n", cex=1.5, pt.cex = 1
# )
text(2/24, 107, paste0(sprintf("SNR = %.1f, FAP = %.1e", calculateSNR(tperiodsToTry * res, tpergram), fapTCF), "%"), cex=1.8, adj=0)
blsFalsePeakAInd <- which(rev(bpergram) > 3e-5)[7]
blsFalsePeakBInd <- head(which(bpergram > 4e-5), n=1)
x <- bcobsxy50$x/24
print(sprintf("BLS false peak A at period = %f days with power = %f", rev(x)[blsFalsePeakAInd], rev(bpergram)[blsFalsePeakAInd]))
print(sprintf("BLS false peak B at period = %f days with power = %f", x[blsFalsePeakBInd], bpergram[blsFalsePeakBInd]))
}