From c6195eb2a347a038e8a824492d225a5648cb5cec Mon Sep 17 00:00:00 2001 From: milesmedina <44986194+milesmedina@users.noreply.github.com> Date: Wed, 10 Jul 2024 14:57:03 -0400 Subject: [PATCH] Pyro SSA --- R/ssa_pyro_otb-ce.R | 168 ++++++++++++++++++++++++++++++++++++ R/ssa_pyro_otb-cw.R | 169 +++++++++++++++++++++++++++++++++++++ R/ssa_pyro_otb-ne.R | 169 +++++++++++++++++++++++++++++++++++++ R/ssa_pyro_otb-nw.R | 168 ++++++++++++++++++++++++++++++++++++ R/ssa_pyro_otb-se.R | 169 +++++++++++++++++++++++++++++++++++++ R/ssa_pyro_otb-sw.R | 168 ++++++++++++++++++++++++++++++++++++ R/ssa_pyro_otb.R | 169 +++++++++++++++++++++++++++++++++++++ R/ssa_pyro_plots.R | 66 +++++++++++++++ data/ssa_pyro_otb.RData | Bin 0 -> 3709 bytes data/ssa_pyro_otb_ce.RData | Bin 0 -> 3584 bytes data/ssa_pyro_otb_cw.RData | Bin 0 -> 3621 bytes data/ssa_pyro_otb_ne.RData | Bin 0 -> 3508 bytes data/ssa_pyro_otb_nw.RData | Bin 0 -> 3689 bytes data/ssa_pyro_otb_se.RData | Bin 0 -> 3388 bytes data/ssa_pyro_otb_sw.RData | Bin 0 -> 3536 bytes figs/ssa_pyro_plots.png | Bin 0 -> 394840 bytes 16 files changed, 1246 insertions(+) create mode 100644 R/ssa_pyro_otb-ce.R create mode 100644 R/ssa_pyro_otb-cw.R create mode 100644 R/ssa_pyro_otb-ne.R create mode 100644 R/ssa_pyro_otb-nw.R create mode 100644 R/ssa_pyro_otb-se.R create mode 100644 R/ssa_pyro_otb-sw.R create mode 100644 R/ssa_pyro_otb.R create mode 100644 R/ssa_pyro_plots.R create mode 100644 data/ssa_pyro_otb.RData create mode 100644 data/ssa_pyro_otb_ce.RData create mode 100644 data/ssa_pyro_otb_cw.RData create mode 100644 data/ssa_pyro_otb_ne.RData create mode 100644 data/ssa_pyro_otb_nw.RData create mode 100644 data/ssa_pyro_otb_se.RData create mode 100644 data/ssa_pyro_otb_sw.RData create mode 100644 figs/ssa_pyro_plots.png diff --git a/R/ssa_pyro_otb-ce.R b/R/ssa_pyro_otb-ce.R new file mode 100644 index 0000000..ef459b3 --- /dev/null +++ b/R/ssa_pyro_otb-ce.R @@ -0,0 +1,168 @@ +# OTB Pyrodinium signal processing with SSA +# +rm(list=ls(all=TRUE)) + +# Load libraries +if(!require(Rssa)) { install.packages('Rssa') }; library(Rssa) +if(!require(lubridate)) { install.packages('lubridate') }; library(lubridate) +if(!require(dplyr)) { install.packages('dplyr') }; library(dplyr) + +# Load & process data +load( "../data/Pyro.Rdata") +# Aggregate to monthly timeframe +pyro2 <- pyro[ which(pyro$yr>=2012 & pyro$subsegment=="CE") , + c("date","pyro") ] +pyro2$pyro[ which(is.na(pyro2$pyro)) ] <- 0 # NAs indicate samples with zero cells +pyro2$month <- pyro2$date |> floor_date('month') +pyro2 <- pyro2 |> group_by(month) |> + summarise( pyro = max(pyro) ) |> as.data.frame() +pyro2$logcells <- log10( pyro2$pyro + 1 ) +# Create time series +pyrodat <- data.frame( month = seq.Date( min(pyro2$month), + max(pyro2$month), 'month' ) ) +pyrodat <- left_join( pyrodat, + pyro2[,c('month','logcells')], 'month' ) +pyrodat$logcells[ which(is.na(pyrodat$logcells)) ] <- 0 +# Plot time series +plot( logcells ~ month, data = pyrodat, las = 1, + type = 'l', lwd = 2, col = rgb(0,0,0,0.6), + main = "Pyro ts", xlab = '', ylab = 'Pyro (log10 cells/L)' ) +abline( h = axTicks(2), col = rgb(0,0,0,0.1) ) +abline( v = seq.Date( min(pyrodat$month), + max(pyrodat$month)+60, 'year' ), + col = rgb(0,0,0,0.1) ) +points( logcells ~ month, data = pyrodat, pch = 21, lwd = 2, cex = 0.5, + col = rgb(0,0,0,0.6), bg = rgb(1,1,1,1) ) + +# Plot frequencies +# select column +colnames( pyrodat ) +var <- 'logcells' +x <- pyrodat[,var] |> na.omit() +x <- x - mean(x) +# Fourier transform +spec <- spectrum( x, method = 'pgram', plot = FALSE ) +df <- data.frame( power = spec$spec, period = 1/spec$freq ) +df <- df[ order( df$period ), ] +# plot time series +par(mfrow=c(2,1)) +plot( x, type = 'l', col = rgb(0,0,0,0.5), lwd = 3, + las = 1, xlab = 'time', ylab = 'x', + main = paste0( "Time series (",var,")" ), + cex.lab = 1.3, cex.axis = 1.3, cex.main = 1.3 ) +points( x, col = rgb(0,0,0,1), pch = 16, cex = 0.8 ) +abline( v = axTicks(1), col = rgb(0,0,0,0.1)) +abline( h = axTicks(2), col = rgb(0,0,0,0.1)) +# plot periodogram +plot( power ~ period, data = df, + type = 'l', lwd = 3, col = rgb(0,0,0,0.5), + main = 'Periodogram', las = 1, bty = "L", + cex.lab = 1.3, cex.axis = 1.3, cex.main = 1.3 ) +points( power ~ period, data = df, pch = 16, cex = 0.8 ) +abline( v = axTicks(1), col = rgb(0,0,0,0.1)) +abline( h = axTicks(2), col = rgb(0,0,0,0.1)) +df <- df[ order( df$power, decreasing = TRUE ), ] +text( x = df$period[1:2], y = df$power[1:2], + labels = round(df$period[1:2],2), pos = 4, font = 2 ) +# print spectrum +df |> head(10) + + +# SSA decomposition +## +# Set window length +length( x ) +win <- 72 +# Decompose +obj <- ssa( x, L = win, neig = win, + kind = 'toeplitz-ssa' ) +# Eigentriple plots +# Singular values +par(mfrow=c(1,1)) +obj$sigma |> plot( main = "Singular values", + xlab = 'eigentriple', ylab = 'singular value' ) +obj$sigma |> lines() +abline( v = axTicks(1), col = rgb(0,0,0,0.1)) +abline( h = axTicks(2), col = rgb(0,0,0,0.1)) +# Eigenvectors +obj |> plot( type = 'vectors', numvectors = 20 ) +obj |> plot( type = 'paired', numvectors = 20 ) +# W-correlation matrix +obj |> plot( type = 'wcor' ) +wcor(obj,groups = 1:20) |> plot() + + +# SSA grouping +## +# Specify signal component groups +grp <- list( c(1,2), c(3,4), c(5,6,9,10), c(7,8) ) + +# SSA reconstruction +## +# Add a residuals (noise) group +grp[[ length(grp)+1 ]] <- which( !(1:win %in% unlist(grp)) ) +# Reconstruct grouped components +recon <- obj |> reconstruct( groups = grp ) +# W-correlation matrix +wcor.recon <- wcor( obj, groups = grp ) +wcor.recon |> plot() +wcor.recon +# Compute variance explained by each component +eigenvals <- obj$sigma^2 +varexp <- lapply( grp, function(x) sum( eigenvals[x] ) * 100 / sum(eigenvals) ) + +# Plot reconstructed components +par(mfrow=c(3,2)) +ylims <- range(unlist(recon)) +for( i in 1:length(recon) ){ + if( i < length(grp) ){ + # Plot signal components + plot( recon[[i]], type = 'l', ylim = ylims, las = 1, + main = paste0("Group ",paste(grp[[i]],collapse=", "), + " (",round(varexp[[i]],2),"%)"), + xlab = '', ylab = '' + ) + abline( v = axTicks(1), col = rgb(0,0,0,0.1)) + abline( h = axTicks(2), col = rgb(0,0,0,0.1)) + } else { + # Plot noise + plot( recon[[i]], type = 'l', col = rgb(0.1,0.2,1,0.8), + ylim = ylims, las = 1, + main = paste0("Noise"," (",round(varexp[[i]],2),"%)"), + xlab = '', ylab = '' + ) + abline( v = axTicks(1), col = rgb(0,0,0,0.1)) + abline( h = axTicks(2), col = rgb(0,0,0,0.1)) + } +} # // end i + +# Reconstruct signal and noise +signal <- do.call( cbind, recon[ 1:(length(recon)-1) ] ) |> rowSums() +sigstrength <- varexp[1:(length(varexp)-1)] |> unlist() |> sum() +noise <- recon[[ length(recon) ]] + +# Plot signal with noise +par(mfrow=c(2,1)) +ylims2 <- range( x, signal, noise ) +plot( x, type = 'l', ylim = ylims2, las = 1, + main = paste0("Signal (",round(sigstrength,2),"%)"), + xlab = "", + lwd = 2, col = rgb(0,0,0,0.6) ) +lines( signal, lwd = 4, col = rgb(1,0.2,0.1,0.8) ) +abline( v = axTicks(1), col = rgb(0,0,0,0.1)) +abline( h = axTicks(2), col = rgb(0,0,0,0.1)) +plot( noise, type = 'l', ylim = ylims2, las = 1, + main = "Noise", xlab = "time", + col = rgb(0.1,0.2,1,0.8) ) +abline( v = axTicks(1), col = rgb(0,0,0,0.1)) +abline( h = axTicks(2), col = rgb(0,0,0,0.1)) + +# Export ts, signal, noise +ssa_pyro_otb_ce <- list( dat = data.frame( month = pyrodat$month, + ts = pyrodat$logcells, + signal = signal + mean(pyrodat$logcells), + noise = noise + mean(pyrodat$logcells) ), + grp = grp, + sigstrength = sigstrength +) +save( ssa_pyro_otb_ce, file = "../data/ssa_pyro_otb_ce.RData" ) diff --git a/R/ssa_pyro_otb-cw.R b/R/ssa_pyro_otb-cw.R new file mode 100644 index 0000000..31693fa --- /dev/null +++ b/R/ssa_pyro_otb-cw.R @@ -0,0 +1,169 @@ +# OTB Pyrodinium signal processing with SSA +# +rm(list=ls(all=TRUE)) + +# Load libraries +if(!require(Rssa)) { install.packages('Rssa') }; library(Rssa) +if(!require(lubridate)) { install.packages('lubridate') }; library(lubridate) +if(!require(dplyr)) { install.packages('dplyr') }; library(dplyr) + +# Load & process data +load( "../data/Pyro.Rdata") +# Aggregate to monthly timeframe +pyro2 <- pyro[ which(pyro$yr>=2012 & pyro$subsegment=="CW") , + c("date","pyro") ] +pyro2$pyro[ which(is.na(pyro2$pyro)) ] <- 0 # NAs indicate samples with zero cells +pyro2$month <- pyro2$date |> floor_date('month') +pyro2 <- pyro2 |> group_by(month) |> + summarise( pyro = max(pyro) ) |> as.data.frame() +pyro2$logcells <- log10( pyro2$pyro + 1 ) +# Create time series +pyrodat <- data.frame( month = seq.Date( min(pyro2$month), + max(pyro2$month), 'month' ) ) +pyrodat <- left_join( pyrodat, + pyro2[,c('month','logcells')], 'month' ) +pyrodat$logcells[ which(is.na(pyrodat$logcells)) ] <- 0 +# Plot time series +plot( logcells ~ month, data = pyrodat, las = 1, + type = 'l', lwd = 2, col = rgb(0,0,0,0.6), + main = "Pyro ts", xlab = '', ylab = 'Pyro (log10 cells/L)' ) +abline( h = axTicks(2), col = rgb(0,0,0,0.1) ) +abline( v = seq.Date( min(pyrodat$month), + max(pyrodat$month)+60, 'year' ), + col = rgb(0,0,0,0.1) ) +points( logcells ~ month, data = pyrodat, pch = 21, lwd = 2, cex = 0.5, + col = rgb(0,0,0,0.6), bg = rgb(1,1,1,1) ) + +# Plot frequencies +# select column +colnames( pyrodat ) +var <- 'logcells' +x <- pyrodat[,var] |> na.omit() +x <- x - mean(x) +# Fourier transform +spec <- spectrum( x, method = 'pgram', plot = FALSE ) +df <- data.frame( power = spec$spec, period = 1/spec$freq ) +df <- df[ order( df$period ), ] +# plot time series +par(mfrow=c(2,1)) +plot( x, type = 'l', col = rgb(0,0,0,0.5), lwd = 3, + las = 1, xlab = 'time', ylab = 'x', + main = paste0( "Time series (",var,")" ), + cex.lab = 1.3, cex.axis = 1.3, cex.main = 1.3 ) +points( x, col = rgb(0,0,0,1), pch = 16, cex = 0.8 ) +abline( v = axTicks(1), col = rgb(0,0,0,0.1)) +abline( h = axTicks(2), col = rgb(0,0,0,0.1)) +# plot periodogram +plot( power ~ period, data = df, + type = 'l', lwd = 3, col = rgb(0,0,0,0.5), + main = 'Periodogram', las = 1, bty = "L", + cex.lab = 1.3, cex.axis = 1.3, cex.main = 1.3 ) +points( power ~ period, data = df, pch = 16, cex = 0.8 ) +abline( v = axTicks(1), col = rgb(0,0,0,0.1)) +abline( h = axTicks(2), col = rgb(0,0,0,0.1)) +df <- df[ order( df$power, decreasing = TRUE ), ] +text( x = df$period[1:2], y = df$power[1:2], + labels = round(df$period[1:2],2), pos = 4, font = 2 ) +# print spectrum +df |> head(10) + + +# SSA decomposition +## +# Set window length +length( x ) +win <- 72 +# Decompose +obj <- ssa( x, L = win, neig = win, + kind = 'toeplitz-ssa' ) +# Eigentriple plots +# Singular values +par(mfrow=c(1,1)) +obj$sigma |> plot( main = "Singular values", + xlab = 'eigentriple', ylab = 'singular value' ) +obj$sigma |> lines() +abline( v = axTicks(1), col = rgb(0,0,0,0.1)) +abline( h = axTicks(2), col = rgb(0,0,0,0.1)) +# Eigenvectors +obj |> plot( type = 'vectors', numvectors = 20 ) +obj |> plot( type = 'paired', numvectors = 20 ) +# W-correlation matrix +obj |> plot( type = 'wcor' ) +wcor(obj,groups = 1:20) |> plot() + + +# SSA grouping +## +# Specify signal component groups +grp <- list( c(1,2), c(3,4), c(5,7), c(6,8) ) + +# SSA reconstruction +## +# Add a residuals (noise) group +grp[[ length(grp)+1 ]] <- which( !(1:win %in% unlist(grp)) ) +# Reconstruct grouped components +recon <- obj |> reconstruct( groups = grp ) +# W-correlation matrix +wcor.recon <- wcor( obj, groups = grp ) +wcor.recon |> plot() +wcor.recon +# Compute variance explained by each component +eigenvals <- obj$sigma^2 +varexp <- lapply( grp, function(x) sum( eigenvals[x] ) * 100 / sum(eigenvals) ) + +# Plot reconstructed components +par(mfrow=c(3,2)) +ylims <- range(unlist(recon)) +for( i in 1:length(recon) ){ + if( i < length(grp) ){ + # Plot signal components + plot( recon[[i]], type = 'l', ylim = ylims, las = 1, + main = paste0("Group ",paste(grp[[i]],collapse=", "), + " (",round(varexp[[i]],2),"%)"), + xlab = '', ylab = '' + ) + abline( v = axTicks(1), col = rgb(0,0,0,0.1)) + abline( h = axTicks(2), col = rgb(0,0,0,0.1)) + } else { + # Plot noise + plot( recon[[i]], type = 'l', col = rgb(0.1,0.2,1,0.8), + ylim = ylims, las = 1, + main = paste0("Noise"," (",round(varexp[[i]],2),"%)"), + xlab = '', ylab = '' + ) + abline( v = axTicks(1), col = rgb(0,0,0,0.1)) + abline( h = axTicks(2), col = rgb(0,0,0,0.1)) + } +} # // end i + +# Reconstruct signal and noise +signal <- do.call( cbind, recon[ 1:(length(recon)-1) ] ) |> rowSums() +sigstrength <- varexp[1:(length(varexp)-1)] |> unlist() |> sum() +noise <- recon[[ length(recon) ]] + +# Plot signal with noise +par(mfrow=c(2,1)) +ylims2 <- range( x, signal, noise ) +plot( x, type = 'l', ylim = ylims2, las = 1, + main = paste0("Signal (",round(sigstrength,2),"%)"), + xlab = "", + lwd = 2, col = rgb(0,0,0,0.6) ) +lines( signal, lwd = 4, col = rgb(1,0.2,0.1,0.8) ) +abline( v = axTicks(1), col = rgb(0,0,0,0.1)) +abline( h = axTicks(2), col = rgb(0,0,0,0.1)) +plot( noise, type = 'l', ylim = ylims2, las = 1, + main = "Noise", xlab = "time", + col = rgb(0.1,0.2,1,0.8) ) +abline( v = axTicks(1), col = rgb(0,0,0,0.1)) +abline( h = axTicks(2), col = rgb(0,0,0,0.1)) + + +# Export ts, signal, noise +ssa_pyro_otb_cw <- list( dat = data.frame( month = pyrodat$month, + ts = pyrodat$logcells, + signal = signal + mean(pyrodat$logcells), + noise = noise + mean(pyrodat$logcells) ), + grp = grp, + sigstrength = sigstrength +) +save( ssa_pyro_otb_cw, file = "../data/ssa_pyro_otb_cw.RData" ) \ No newline at end of file diff --git a/R/ssa_pyro_otb-ne.R b/R/ssa_pyro_otb-ne.R new file mode 100644 index 0000000..3f1e815 --- /dev/null +++ b/R/ssa_pyro_otb-ne.R @@ -0,0 +1,169 @@ +# OTB Pyrodinium signal processing with SSA +# +rm(list=ls(all=TRUE)) + +# Load libraries +if(!require(Rssa)) { install.packages('Rssa') }; library(Rssa) +if(!require(lubridate)) { install.packages('lubridate') }; library(lubridate) +if(!require(dplyr)) { install.packages('dplyr') }; library(dplyr) + +# Load & process data +load( "../data/Pyro.Rdata") +# Aggregate to monthly timeframe +pyro2 <- pyro[ which(pyro$yr>=2012 & pyro$subsegment=="NE") , + c("date","pyro") ] +pyro2$pyro[ which(is.na(pyro2$pyro)) ] <- 0 # NAs indicate samples with zero cells +pyro2$month <- pyro2$date |> floor_date('month') +pyro2 <- pyro2 |> group_by(month) |> + summarise( pyro = max(pyro) ) |> as.data.frame() +pyro2$logcells <- log10( pyro2$pyro + 1 ) +# Create time series +pyrodat <- data.frame( month = seq.Date( min(pyro2$month), + max(pyro2$month), 'month' ) ) +pyrodat <- left_join( pyrodat, + pyro2[,c('month','logcells')], 'month' ) +pyrodat$logcells[ which(is.na(pyrodat$logcells)) ] <- 0 +# Plot time series +plot( logcells ~ month, data = pyrodat, las = 1, + type = 'l', lwd = 2, col = rgb(0,0,0,0.6), + main = "Pyro ts", xlab = '', ylab = 'Pyro (log10 cells/L)' ) +abline( h = axTicks(2), col = rgb(0,0,0,0.1) ) +abline( v = seq.Date( min(pyrodat$month), + max(pyrodat$month)+60, 'year' ), + col = rgb(0,0,0,0.1) ) +points( logcells ~ month, data = pyrodat, pch = 21, lwd = 2, cex = 0.5, + col = rgb(0,0,0,0.6), bg = rgb(1,1,1,1) ) + +# Plot frequencies +# select column +colnames( pyrodat ) +var <- 'logcells' +x <- pyrodat[,var] |> na.omit() +x <- x - mean(x) +# Fourier transform +spec <- spectrum( x, method = 'pgram', plot = FALSE ) +df <- data.frame( power = spec$spec, period = 1/spec$freq ) +df <- df[ order( df$period ), ] +# plot time series +par(mfrow=c(2,1)) +plot( x, type = 'l', col = rgb(0,0,0,0.5), lwd = 3, + las = 1, xlab = 'time', ylab = 'x', + main = paste0( "Time series (",var,")" ), + cex.lab = 1.3, cex.axis = 1.3, cex.main = 1.3 ) +points( x, col = rgb(0,0,0,1), pch = 16, cex = 0.8 ) +abline( v = axTicks(1), col = rgb(0,0,0,0.1)) +abline( h = axTicks(2), col = rgb(0,0,0,0.1)) +# plot periodogram +plot( power ~ period, data = df, + type = 'l', lwd = 3, col = rgb(0,0,0,0.5), + main = 'Periodogram', las = 1, bty = "L", + cex.lab = 1.3, cex.axis = 1.3, cex.main = 1.3 ) +points( power ~ period, data = df, pch = 16, cex = 0.8 ) +abline( v = axTicks(1), col = rgb(0,0,0,0.1)) +abline( h = axTicks(2), col = rgb(0,0,0,0.1)) +df <- df[ order( df$power, decreasing = TRUE ), ] +text( x = df$period[1:2], y = df$power[1:2], + labels = round(df$period[1:2],2), pos = 4, font = 2 ) +# print spectrum +df |> head(10) + + +# SSA decomposition +## +# Set window length +length( x ) +win <- 72 +# Decompose +obj <- ssa( x, L = win, neig = win, + kind = 'toeplitz-ssa' ) +# Eigentriple plots +# Singular values +par(mfrow=c(1,1)) +obj$sigma |> plot( main = "Singular values", + xlab = 'eigentriple', ylab = 'singular value' ) +obj$sigma |> lines() +abline( v = axTicks(1), col = rgb(0,0,0,0.1)) +abline( h = axTicks(2), col = rgb(0,0,0,0.1)) +# Eigenvectors +obj |> plot( type = 'vectors', numvectors = 20 ) +obj |> plot( type = 'paired', numvectors = 20 ) +# W-correlation matrix +obj |> plot( type = 'wcor' ) +wcor(obj,groups = 1:20) |> plot() + + +# SSA grouping +## +# Specify signal component groups +grp <- list( c(1,2), c(3,4), c(7,8), c(9,10) ) + +# SSA reconstruction +## +# Add a residuals (noise) group +grp[[ length(grp)+1 ]] <- which( !(1:win %in% unlist(grp)) ) +# Reconstruct grouped components +recon <- obj |> reconstruct( groups = grp ) +# W-correlation matrix +wcor.recon <- wcor( obj, groups = grp ) +wcor.recon |> plot() +wcor.recon +# Compute variance explained by each component +eigenvals <- obj$sigma^2 +varexp <- lapply( grp, function(x) sum( eigenvals[x] ) * 100 / sum(eigenvals) ) + +# Plot reconstructed components +par(mfrow=c(3,2)) +ylims <- range(unlist(recon)) +for( i in 1:length(recon) ){ + if( i < length(grp) ){ + # Plot signal components + plot( recon[[i]], type = 'l', ylim = ylims, las = 1, + main = paste0("Group ",paste(grp[[i]],collapse=", "), + " (",round(varexp[[i]],2),"%)"), + xlab = '', ylab = '' + ) + abline( v = axTicks(1), col = rgb(0,0,0,0.1)) + abline( h = axTicks(2), col = rgb(0,0,0,0.1)) + } else { + # Plot noise + plot( recon[[i]], type = 'l', col = rgb(0.1,0.2,1,0.8), + ylim = ylims, las = 1, + main = paste0("Noise"," (",round(varexp[[i]],2),"%)"), + xlab = '', ylab = '' + ) + abline( v = axTicks(1), col = rgb(0,0,0,0.1)) + abline( h = axTicks(2), col = rgb(0,0,0,0.1)) + } +} # // end i + +# Reconstruct signal and noise +signal <- do.call( cbind, recon[ 1:(length(recon)-1) ] ) |> rowSums() +sigstrength <- varexp[1:(length(varexp)-1)] |> unlist() |> sum() +noise <- recon[[ length(recon) ]] + +# Plot signal with noise +par(mfrow=c(2,1)) +ylims2 <- range( x, signal, noise ) +plot( x, type = 'l', ylim = ylims2, las = 1, + main = paste0("Signal (",round(sigstrength,2),"%)"), + xlab = "", + lwd = 2, col = rgb(0,0,0,0.6) ) +lines( signal, lwd = 4, col = rgb(1,0.2,0.1,0.8) ) +abline( v = axTicks(1), col = rgb(0,0,0,0.1)) +abline( h = axTicks(2), col = rgb(0,0,0,0.1)) +plot( noise, type = 'l', ylim = ylims2, las = 1, + main = "Noise", xlab = "time", + col = rgb(0.1,0.2,1,0.8) ) +abline( v = axTicks(1), col = rgb(0,0,0,0.1)) +abline( h = axTicks(2), col = rgb(0,0,0,0.1)) + + +# Export ts, signal, noise +ssa_pyro_otb_ne <- list( dat = data.frame( month = pyrodat$month, + ts = pyrodat$logcells, + signal = signal + mean(pyrodat$logcells), + noise = noise + mean(pyrodat$logcells) ), + grp = grp, + sigstrength = sigstrength +) +save( ssa_pyro_otb_ne, file = "../data/ssa_pyro_otb_ne.RData" ) \ No newline at end of file diff --git a/R/ssa_pyro_otb-nw.R b/R/ssa_pyro_otb-nw.R new file mode 100644 index 0000000..ff0facf --- /dev/null +++ b/R/ssa_pyro_otb-nw.R @@ -0,0 +1,168 @@ +# OTB Pyrodinium signal processing with SSA +# +rm(list=ls(all=TRUE)) + +# Load libraries +if(!require(Rssa)) { install.packages('Rssa') }; library(Rssa) +if(!require(lubridate)) { install.packages('lubridate') }; library(lubridate) +if(!require(dplyr)) { install.packages('dplyr') }; library(dplyr) + +# Load & process data +load( "../data/Pyro.Rdata") +# Aggregate to monthly timeframe +pyro2 <- pyro[ which(pyro$yr>=2012 & pyro$subsegment=="NW") , + c("date","pyro") ] +pyro2$pyro[ which(is.na(pyro2$pyro)) ] <- 0 # NAs indicate samples with zero cells +pyro2$month <- pyro2$date |> floor_date('month') +pyro2 <- pyro2 |> group_by(month) |> + summarise( pyro = max(pyro) ) |> as.data.frame() +pyro2$logcells <- log10( pyro2$pyro + 1 ) +# Create time series +pyrodat <- data.frame( month = seq.Date( min(pyro2$month), + max(pyro2$month), 'month' ) ) +pyrodat <- left_join( pyrodat, + pyro2[,c('month','logcells')], 'month' ) +pyrodat$logcells[ which(is.na(pyrodat$logcells)) ] <- 0 +# Plot time series +plot( logcells ~ month, data = pyrodat, las = 1, + type = 'l', lwd = 2, col = rgb(0,0,0,0.6), + main = "Pyro ts", xlab = '', ylab = 'Pyro (log10 cells/L)' ) +abline( h = axTicks(2), col = rgb(0,0,0,0.1) ) +abline( v = seq.Date( min(pyrodat$month), + max(pyrodat$month)+60, 'year' ), + col = rgb(0,0,0,0.1) ) +points( logcells ~ month, data = pyrodat, pch = 21, lwd = 2, cex = 0.5, + col = rgb(0,0,0,0.6), bg = rgb(1,1,1,1) ) + +# Plot frequencies +# select column +colnames( pyrodat ) +var <- 'logcells' +x <- pyrodat[,var] |> na.omit() +x <- x - mean(x) +# Fourier transform +spec <- spectrum( x, method = 'pgram', plot = FALSE ) +df <- data.frame( power = spec$spec, period = 1/spec$freq ) +df <- df[ order( df$period ), ] +# plot time series +par(mfrow=c(2,1)) +plot( x, type = 'l', col = rgb(0,0,0,0.5), lwd = 3, + las = 1, xlab = 'time', ylab = 'x', + main = paste0( "Time series (",var,")" ), + cex.lab = 1.3, cex.axis = 1.3, cex.main = 1.3 ) +points( x, col = rgb(0,0,0,1), pch = 16, cex = 0.8 ) +abline( v = axTicks(1), col = rgb(0,0,0,0.1)) +abline( h = axTicks(2), col = rgb(0,0,0,0.1)) +# plot periodogram +plot( power ~ period, data = df, + type = 'l', lwd = 3, col = rgb(0,0,0,0.5), + main = 'Periodogram', las = 1, bty = "L", + cex.lab = 1.3, cex.axis = 1.3, cex.main = 1.3 ) +points( power ~ period, data = df, pch = 16, cex = 0.8 ) +abline( v = axTicks(1), col = rgb(0,0,0,0.1)) +abline( h = axTicks(2), col = rgb(0,0,0,0.1)) +df <- df[ order( df$power, decreasing = TRUE ), ] +text( x = df$period[1:2], y = df$power[1:2], + labels = round(df$period[1:2],2), pos = 4, font = 2 ) +# print spectrum +df |> head(10) + + +# SSA decomposition +## +# Set window length +length( x ) +win <- 72 +# Decompose +obj <- ssa( x, L = win, neig = win, + kind = 'toeplitz-ssa' ) +# Eigentriple plots +# Singular values +par(mfrow=c(1,1)) +obj$sigma |> plot( main = "Singular values", + xlab = 'eigentriple', ylab = 'singular value' ) +obj$sigma |> lines() +abline( v = axTicks(1), col = rgb(0,0,0,0.1)) +abline( h = axTicks(2), col = rgb(0,0,0,0.1)) +# Eigenvectors +obj |> plot( type = 'vectors', numvectors = 20 ) +obj |> plot( type = 'paired', numvectors = 20 ) +# W-correlation matrix +obj |> plot( type = 'wcor' ) +wcor(obj,groups = 1:20) |> plot() + + +# SSA grouping +## +# Specify signal component groups +grp <- list( c(1,2), c(3,4,5) ) + +# SSA reconstruction +## +# Add a residuals (noise) group +grp[[ length(grp)+1 ]] <- which( !(1:win %in% unlist(grp)) ) +# Reconstruct grouped components +recon <- obj |> reconstruct( groups = grp ) +# W-correlation matrix +wcor.recon <- wcor( obj, groups = grp ) +wcor.recon |> plot() +wcor.recon +# Compute variance explained by each component +eigenvals <- obj$sigma^2 +varexp <- lapply( grp, function(x) sum( eigenvals[x] ) * 100 / sum(eigenvals) ) + +# Plot reconstructed components +par(mfrow=c(3,2)) +ylims <- range(unlist(recon)) +for( i in 1:length(recon) ){ + if( i < length(grp) ){ + # Plot signal components + plot( recon[[i]], type = 'l', ylim = ylims, las = 1, + main = paste0("Group ",paste(grp[[i]],collapse=", "), + " (",round(varexp[[i]],2),"%)"), + xlab = '', ylab = '' + ) + abline( v = axTicks(1), col = rgb(0,0,0,0.1)) + abline( h = axTicks(2), col = rgb(0,0,0,0.1)) + } else { + # Plot noise + plot( recon[[i]], type = 'l', col = rgb(0.1,0.2,1,0.8), + ylim = ylims, las = 1, + main = paste0("Noise"," (",round(varexp[[i]],2),"%)"), + xlab = '', ylab = '' + ) + abline( v = axTicks(1), col = rgb(0,0,0,0.1)) + abline( h = axTicks(2), col = rgb(0,0,0,0.1)) + } +} # // end i + +# Reconstruct signal and noise +signal <- do.call( cbind, recon[ 1:(length(recon)-1) ] ) |> rowSums() +sigstrength <- varexp[1:(length(varexp)-1)] |> unlist() |> sum() +noise <- recon[[ length(recon) ]] + +# Plot signal with noise +par(mfrow=c(2,1)) +ylims2 <- range( x, signal, noise ) +plot( x, type = 'l', ylim = ylims2, las = 1, + main = paste0("Signal (",round(sigstrength,2),"%)"), + xlab = "", + lwd = 2, col = rgb(0,0,0,0.6) ) +lines( signal, lwd = 4, col = rgb(1,0.2,0.1,0.8) ) +abline( v = axTicks(1), col = rgb(0,0,0,0.1)) +abline( h = axTicks(2), col = rgb(0,0,0,0.1)) +plot( noise, type = 'l', ylim = ylims2, las = 1, + main = "Noise", xlab = "time", + col = rgb(0.1,0.2,1,0.8) ) +abline( v = axTicks(1), col = rgb(0,0,0,0.1)) +abline( h = axTicks(2), col = rgb(0,0,0,0.1)) + +# Export ts, signal, noise +ssa_pyro_otb_nw <- list( dat = data.frame( month = pyrodat$month, + ts = pyrodat$logcells, + signal = signal + mean(pyrodat$logcells), + noise = noise + mean(pyrodat$logcells) ), + grp = grp, + sigstrength = sigstrength +) +save( ssa_pyro_otb_nw, file = "../data/ssa_pyro_otb_nw.RData" ) \ No newline at end of file diff --git a/R/ssa_pyro_otb-se.R b/R/ssa_pyro_otb-se.R new file mode 100644 index 0000000..cc7119b --- /dev/null +++ b/R/ssa_pyro_otb-se.R @@ -0,0 +1,169 @@ +# OTB Pyrodinium signal processing with SSA +# +rm(list=ls(all=TRUE)) + +# Load libraries +if(!require(Rssa)) { install.packages('Rssa') }; library(Rssa) +if(!require(lubridate)) { install.packages('lubridate') }; library(lubridate) +if(!require(dplyr)) { install.packages('dplyr') }; library(dplyr) + +# Load & process data +load( "../data/Pyro.Rdata") +# Aggregate to monthly timeframe +pyro2 <- pyro[ which(pyro$yr>=2012 & pyro$subsegment=="SE") , + c("date","pyro") ] +pyro2$pyro[ which(is.na(pyro2$pyro)) ] <- 0 # NAs indicate samples with zero cells +pyro2$month <- pyro2$date |> floor_date('month') +pyro2 <- pyro2 |> group_by(month) |> + summarise( pyro = max(pyro) ) |> as.data.frame() +pyro2$logcells <- log10( pyro2$pyro + 1 ) +# Create time series +pyrodat <- data.frame( month = seq.Date( min(pyro2$month), + max(pyro2$month), 'month' ) ) +pyrodat <- left_join( pyrodat, + pyro2[,c('month','logcells')], 'month' ) +pyrodat$logcells[ which(is.na(pyrodat$logcells)) ] <- 0 +# Plot time series +plot( logcells ~ month, data = pyrodat, las = 1, + type = 'l', lwd = 2, col = rgb(0,0,0,0.6), + main = "Pyro ts", xlab = '', ylab = 'Pyro (log10 cells/L)' ) +abline( h = axTicks(2), col = rgb(0,0,0,0.1) ) +abline( v = seq.Date( min(pyrodat$month), + max(pyrodat$month)+60, 'year' ), + col = rgb(0,0,0,0.1) ) +points( logcells ~ month, data = pyrodat, pch = 21, lwd = 2, cex = 0.5, + col = rgb(0,0,0,0.6), bg = rgb(1,1,1,1) ) + +# Plot frequencies +# select column +colnames( pyrodat ) +var <- 'logcells' +x <- pyrodat[,var] |> na.omit() +x <- x - mean(x) +# Fourier transform +spec <- spectrum( x, method = 'pgram', plot = FALSE ) +df <- data.frame( power = spec$spec, period = 1/spec$freq ) +df <- df[ order( df$period ), ] +# plot time series +par(mfrow=c(2,1)) +plot( x, type = 'l', col = rgb(0,0,0,0.5), lwd = 3, + las = 1, xlab = 'time', ylab = 'x', + main = paste0( "Time series (",var,")" ), + cex.lab = 1.3, cex.axis = 1.3, cex.main = 1.3 ) +points( x, col = rgb(0,0,0,1), pch = 16, cex = 0.8 ) +abline( v = axTicks(1), col = rgb(0,0,0,0.1)) +abline( h = axTicks(2), col = rgb(0,0,0,0.1)) +# plot periodogram +plot( power ~ period, data = df, + type = 'l', lwd = 3, col = rgb(0,0,0,0.5), + main = 'Periodogram', las = 1, bty = "L", + cex.lab = 1.3, cex.axis = 1.3, cex.main = 1.3 ) +points( power ~ period, data = df, pch = 16, cex = 0.8 ) +abline( v = axTicks(1), col = rgb(0,0,0,0.1)) +abline( h = axTicks(2), col = rgb(0,0,0,0.1)) +df <- df[ order( df$power, decreasing = TRUE ), ] +text( x = df$period[1:2], y = df$power[1:2], + labels = round(df$period[1:2],2), pos = 4, font = 2 ) +# print spectrum +df |> head(10) + + +# SSA decomposition +## +# Set window length +length( x ) +win <- 72 +# Decompose +obj <- ssa( x, L = win, neig = win, + kind = 'toeplitz-ssa' ) +# Eigentriple plots +# Singular values +par(mfrow=c(1,1)) +obj$sigma |> plot( main = "Singular values", + xlab = 'eigentriple', ylab = 'singular value' ) +obj$sigma |> lines() +abline( v = axTicks(1), col = rgb(0,0,0,0.1)) +abline( h = axTicks(2), col = rgb(0,0,0,0.1)) +# Eigenvectors +obj |> plot( type = 'vectors', numvectors = 20 ) +obj |> plot( type = 'paired', numvectors = 20 ) +# W-correlation matrix +obj |> plot( type = 'wcor' ) +wcor(obj,groups = 1:20) |> plot() + + +# SSA grouping +## +# Specify signal component groups +grp <- list( c(1,2), c(3,4), c(5,6), c(7,8) ) + +# SSA reconstruction +## +# Add a residuals (noise) group +grp[[ length(grp)+1 ]] <- which( !(1:win %in% unlist(grp)) ) +# Reconstruct grouped components +recon <- obj |> reconstruct( groups = grp ) +# W-correlation matrix +wcor.recon <- wcor( obj, groups = grp ) +wcor.recon |> plot() +wcor.recon +# Compute variance explained by each component +eigenvals <- obj$sigma^2 +varexp <- lapply( grp, function(x) sum( eigenvals[x] ) * 100 / sum(eigenvals) ) + +# Plot reconstructed components +par(mfrow=c(3,2)) +ylims <- range(unlist(recon)) +for( i in 1:length(recon) ){ + if( i < length(grp) ){ + # Plot signal components + plot( recon[[i]], type = 'l', ylim = ylims, las = 1, + main = paste0("Group ",paste(grp[[i]],collapse=", "), + " (",round(varexp[[i]],2),"%)"), + xlab = '', ylab = '' + ) + abline( v = axTicks(1), col = rgb(0,0,0,0.1)) + abline( h = axTicks(2), col = rgb(0,0,0,0.1)) + } else { + # Plot noise + plot( recon[[i]], type = 'l', col = rgb(0.1,0.2,1,0.8), + ylim = ylims, las = 1, + main = paste0("Noise"," (",round(varexp[[i]],2),"%)"), + xlab = '', ylab = '' + ) + abline( v = axTicks(1), col = rgb(0,0,0,0.1)) + abline( h = axTicks(2), col = rgb(0,0,0,0.1)) + } +} # // end i + +# Reconstruct signal and noise +signal <- do.call( cbind, recon[ 1:(length(recon)-1) ] ) |> rowSums() +sigstrength <- varexp[1:(length(varexp)-1)] |> unlist() |> sum() +noise <- recon[[ length(recon) ]] + +# Plot signal with noise +par(mfrow=c(2,1)) +ylims2 <- range( x, signal, noise ) +plot( x, type = 'l', ylim = ylims2, las = 1, + main = paste0("Signal (",round(sigstrength,2),"%)"), + xlab = "", + lwd = 2, col = rgb(0,0,0,0.6) ) +lines( signal, lwd = 4, col = rgb(1,0.2,0.1,0.8) ) +abline( v = axTicks(1), col = rgb(0,0,0,0.1)) +abline( h = axTicks(2), col = rgb(0,0,0,0.1)) +plot( noise, type = 'l', ylim = ylims2, las = 1, + main = "Noise", xlab = "time", + col = rgb(0.1,0.2,1,0.8) ) +abline( v = axTicks(1), col = rgb(0,0,0,0.1)) +abline( h = axTicks(2), col = rgb(0,0,0,0.1)) + + +# Export ts, signal, noise +ssa_pyro_otb_se <- list( dat = data.frame( month = pyrodat$month, + ts = pyrodat$logcells, + signal = signal + mean(pyrodat$logcells), + noise = noise + mean(pyrodat$logcells) ), + grp = grp, + sigstrength = sigstrength + ) +save( ssa_pyro_otb_se, file = "../data/ssa_pyro_otb_se.RData" ) diff --git a/R/ssa_pyro_otb-sw.R b/R/ssa_pyro_otb-sw.R new file mode 100644 index 0000000..3e31d9f --- /dev/null +++ b/R/ssa_pyro_otb-sw.R @@ -0,0 +1,168 @@ +# OTB Pyrodinium signal processing with SSA +# +rm(list=ls(all=TRUE)) + +# Load libraries +if(!require(Rssa)) { install.packages('Rssa') }; library(Rssa) +if(!require(lubridate)) { install.packages('lubridate') }; library(lubridate) +if(!require(dplyr)) { install.packages('dplyr') }; library(dplyr) + +# Load & process data +load( "../data/Pyro.Rdata") +# Aggregate to monthly timeframe +pyro2 <- pyro[ which(pyro$yr>=2012 & pyro$subsegment=="SW") , + c("date","pyro") ] +pyro2$pyro[ which(is.na(pyro2$pyro)) ] <- 0 # NAs indicate samples with zero cells +pyro2$month <- pyro2$date |> floor_date('month') +pyro2 <- pyro2 |> group_by(month) |> + summarise( pyro = max(pyro) ) |> as.data.frame() +pyro2$logcells <- log10( pyro2$pyro + 1 ) +# Create time series +pyrodat <- data.frame( month = seq.Date( min(pyro2$month), + max(pyro2$month), 'month' ) ) +pyrodat <- left_join( pyrodat, + pyro2[,c('month','logcells')], 'month' ) +pyrodat$logcells[ which(is.na(pyrodat$logcells)) ] <- 0 +# Plot time series +plot( logcells ~ month, data = pyrodat, las = 1, + type = 'l', lwd = 2, col = rgb(0,0,0,0.6), + main = "Pyro ts", xlab = '', ylab = 'Pyro (log10 cells/L)' ) +abline( h = axTicks(2), col = rgb(0,0,0,0.1) ) +abline( v = seq.Date( min(pyrodat$month), + max(pyrodat$month)+60, 'year' ), + col = rgb(0,0,0,0.1) ) +points( logcells ~ month, data = pyrodat, pch = 21, lwd = 2, cex = 0.5, + col = rgb(0,0,0,0.6), bg = rgb(1,1,1,1) ) + +# Plot frequencies +# select column +colnames( pyrodat ) +var <- 'logcells' +x <- pyrodat[,var] |> na.omit() +x <- x - mean(x) +# Fourier transform +spec <- spectrum( x, method = 'pgram', plot = FALSE ) +df <- data.frame( power = spec$spec, period = 1/spec$freq ) +df <- df[ order( df$period ), ] +# plot time series +par(mfrow=c(2,1)) +plot( x, type = 'l', col = rgb(0,0,0,0.5), lwd = 3, + las = 1, xlab = 'time', ylab = 'x', + main = paste0( "Time series (",var,")" ), + cex.lab = 1.3, cex.axis = 1.3, cex.main = 1.3 ) +points( x, col = rgb(0,0,0,1), pch = 16, cex = 0.8 ) +abline( v = axTicks(1), col = rgb(0,0,0,0.1)) +abline( h = axTicks(2), col = rgb(0,0,0,0.1)) +# plot periodogram +plot( power ~ period, data = df, + type = 'l', lwd = 3, col = rgb(0,0,0,0.5), + main = 'Periodogram', las = 1, bty = "L", + cex.lab = 1.3, cex.axis = 1.3, cex.main = 1.3 ) +points( power ~ period, data = df, pch = 16, cex = 0.8 ) +abline( v = axTicks(1), col = rgb(0,0,0,0.1)) +abline( h = axTicks(2), col = rgb(0,0,0,0.1)) +df <- df[ order( df$power, decreasing = TRUE ), ] +text( x = df$period[1:2], y = df$power[1:2], + labels = round(df$period[1:2],2), pos = 4, font = 2 ) +# print spectrum +df |> head(10) + + +# SSA decomposition +## +# Set window length +length( x ) +win <- 72 +# Decompose +obj <- ssa( x, L = win, neig = win, + kind = 'toeplitz-ssa' ) +# Eigentriple plots +# Singular values +par(mfrow=c(1,1)) +obj$sigma |> plot( main = "Singular values", + xlab = 'eigentriple', ylab = 'singular value' ) +obj$sigma |> lines() +abline( v = axTicks(1), col = rgb(0,0,0,0.1)) +abline( h = axTicks(2), col = rgb(0,0,0,0.1)) +# Eigenvectors +obj |> plot( type = 'vectors', numvectors = 20 ) +obj |> plot( type = 'paired', numvectors = 20 ) +# W-correlation matrix +obj |> plot( type = 'wcor' ) +wcor(obj,groups = 1:20) |> plot() + + +# SSA grouping +## +# Specify signal component groups +grp <- list( c(1,2), c(3,4), c(5,6,7,8) ) + +# SSA reconstruction +## +# Add a residuals (noise) group +grp[[ length(grp)+1 ]] <- which( !(1:win %in% unlist(grp)) ) +# Reconstruct grouped components +recon <- obj |> reconstruct( groups = grp ) +# W-correlation matrix +wcor.recon <- wcor( obj, groups = grp ) +wcor.recon |> plot() +wcor.recon +# Compute variance explained by each component +eigenvals <- obj$sigma^2 +varexp <- lapply( grp, function(x) sum( eigenvals[x] ) * 100 / sum(eigenvals) ) + +# Plot reconstructed components +par(mfrow=c(3,2)) +ylims <- range(unlist(recon)) +for( i in 1:length(recon) ){ + if( i < length(grp) ){ + # Plot signal components + plot( recon[[i]], type = 'l', ylim = ylims, las = 1, + main = paste0("Group ",paste(grp[[i]],collapse=", "), + " (",round(varexp[[i]],2),"%)"), + xlab = '', ylab = '' + ) + abline( v = axTicks(1), col = rgb(0,0,0,0.1)) + abline( h = axTicks(2), col = rgb(0,0,0,0.1)) + } else { + # Plot noise + plot( recon[[i]], type = 'l', col = rgb(0.1,0.2,1,0.8), + ylim = ylims, las = 1, + main = paste0("Noise"," (",round(varexp[[i]],2),"%)"), + xlab = '', ylab = '' + ) + abline( v = axTicks(1), col = rgb(0,0,0,0.1)) + abline( h = axTicks(2), col = rgb(0,0,0,0.1)) + } +} # // end i + +# Reconstruct signal and noise +signal <- do.call( cbind, recon[ 1:(length(recon)-1) ] ) |> rowSums() +sigstrength <- varexp[1:(length(varexp)-1)] |> unlist() |> sum() +noise <- recon[[ length(recon) ]] + +# Plot signal with noise +par(mfrow=c(2,1)) +ylims2 <- range( x, signal, noise ) +plot( x, type = 'l', ylim = ylims2, las = 1, + main = paste0("Signal (",round(sigstrength,2),"%)"), + xlab = "", + lwd = 2, col = rgb(0,0,0,0.6) ) +lines( signal, lwd = 4, col = rgb(1,0.2,0.1,0.8) ) +abline( v = axTicks(1), col = rgb(0,0,0,0.1)) +abline( h = axTicks(2), col = rgb(0,0,0,0.1)) +plot( noise, type = 'l', ylim = ylims2, las = 1, + main = "Noise", xlab = "time", + col = rgb(0.1,0.2,1,0.8) ) +abline( v = axTicks(1), col = rgb(0,0,0,0.1)) +abline( h = axTicks(2), col = rgb(0,0,0,0.1)) + +# Export ts, signal, noise +ssa_pyro_otb_sw <- list( dat = data.frame( month = pyrodat$month, + ts = pyrodat$logcells, + signal = signal + mean(pyrodat$logcells), + noise = noise + mean(pyrodat$logcells) ), + grp = grp, + sigstrength = sigstrength +) +save( ssa_pyro_otb_sw, file = "../data/ssa_pyro_otb_sw.RData" ) \ No newline at end of file diff --git a/R/ssa_pyro_otb.R b/R/ssa_pyro_otb.R new file mode 100644 index 0000000..f83fde4 --- /dev/null +++ b/R/ssa_pyro_otb.R @@ -0,0 +1,169 @@ +# OTB Pyrodinium signal processing with SSA +# +rm(list=ls(all=TRUE)) + +# Load libraries +if(!require(Rssa)) { install.packages('Rssa') }; library(Rssa) +if(!require(lubridate)) { install.packages('lubridate') }; library(lubridate) +if(!require(dplyr)) { install.packages('dplyr') }; library(dplyr) + +# Load & process data +load( "../data/Pyro.Rdata") + # Aggregate to monthly timeframe + pyro2 <- pyro[ which(pyro$yr>=2012) , c("date","pyro") ] + pyro2$pyro[ which(is.na(pyro2$pyro)) ] <- 0 # NAs indicate samples with zero cells + pyro2$month <- pyro2$date |> floor_date('month') + pyro2 <- pyro2 |> group_by(month) |> + summarise( pyro = max(pyro) ) |> as.data.frame() + pyro2$logcells <- log10( pyro2$pyro + 1 ) + # Create time series + pyrodat <- data.frame( month = seq.Date( min(pyro2$month), + max(pyro2$month), 'month' ) ) + pyrodat <- left_join( pyrodat, + pyro2[,c('month','logcells')], 'month' ) + pyrodat$logcells[ which(is.na(pyrodat$logcells)) ] <- 0 + # Plot time series + plot( logcells ~ month, data = pyrodat, las = 1, + type = 'l', lwd = 2, col = rgb(0,0,0,0.6), + main = "Pyro ts", xlab = '', ylab = 'Pyro (log10 cells/L)' ) + abline( h = axTicks(2), col = rgb(0,0,0,0.1) ) + abline( v = seq.Date( min(pyrodat$month), + max(pyrodat$month)+60, 'year' ), + col = rgb(0,0,0,0.1) ) + points( logcells ~ month, data = pyrodat, pch = 21, lwd = 2, cex = 0.5, + col = rgb(0,0,0,0.6), bg = rgb(1,1,1,1) ) + +# Plot frequencies + # select column + colnames( pyrodat ) + var <- 'logcells' + x <- pyrodat[,var] |> na.omit() + x <- x - mean(x) + # Fourier transform + spec <- spectrum( x, method = 'pgram', plot = FALSE ) + df <- data.frame( power = spec$spec, period = 1/spec$freq ) + df <- df[ order( df$period ), ] + # plot time series + par(mfrow=c(2,1)) + plot( x, type = 'l', col = rgb(0,0,0,0.5), lwd = 3, + las = 1, xlab = 'time', ylab = 'x', + main = paste0( "Time series (",var,")" ), + cex.lab = 1.3, cex.axis = 1.3, cex.main = 1.3 ) + points( x, col = rgb(0,0,0,1), pch = 16, cex = 0.8 ) + abline( v = axTicks(1), col = rgb(0,0,0,0.1)) + abline( h = axTicks(2), col = rgb(0,0,0,0.1)) + # plot periodogram + plot( power ~ period, data = df, + type = 'l', lwd = 3, col = rgb(0,0,0,0.5), + main = 'Periodogram', las = 1, bty = "L", + cex.lab = 1.3, cex.axis = 1.3, cex.main = 1.3 ) + points( power ~ period, data = df, pch = 16, cex = 0.8 ) + abline( v = axTicks(1), col = rgb(0,0,0,0.1)) + abline( h = axTicks(2), col = rgb(0,0,0,0.1)) + df <- df[ order( df$power, decreasing = TRUE ), ] + text( x = df$period[1:2], y = df$power[1:2], + labels = round(df$period[1:2],2), pos = 4, font = 2 ) + # print spectrum + df |> head(10) + + +# SSA decomposition +## + # Set window length + length( x ) + win <- 72 + # Decompose + obj <- ssa( x, L = win, neig = win, + kind = 'toeplitz-ssa' ) + # Eigentriple plots + # Singular values + par(mfrow=c(1,1)) + obj$sigma |> plot( main = "Singular values", + xlab = 'eigentriple', ylab = 'singular value' ) + obj$sigma |> lines() + abline( v = axTicks(1), col = rgb(0,0,0,0.1)) + abline( h = axTicks(2), col = rgb(0,0,0,0.1)) + # Eigenvectors + obj |> plot( type = 'vectors', numvectors = 20 ) + obj |> plot( type = 'paired', numvectors = 20 ) + # W-correlation matrix + obj |> plot( type = 'wcor' ) + wcor(obj,groups = 1:20) |> plot() + + +# SSA grouping +## + # Specify signal component groups + grp <- list( c(1,2), c(3,4,8,10), c(5,6,7,9) ) + + # SSA reconstruction + ## + # Add a residuals (noise) group + grp[[ length(grp)+1 ]] <- which( !(1:win %in% unlist(grp)) ) + # Reconstruct grouped components + recon <- obj |> reconstruct( groups = grp ) + # W-correlation matrix + wcor.recon <- wcor( obj, groups = grp ) + wcor.recon |> plot() + wcor.recon + # Compute variance explained by each component + eigenvals <- obj$sigma^2 + varexp <- lapply( grp, function(x) sum( eigenvals[x] ) * 100 / sum(eigenvals) ) + +# Plot reconstructed components + par(mfrow=c(3,2)) + ylims <- range(unlist(recon)) + for( i in 1:length(recon) ){ + if( i < length(grp) ){ + # Plot signal components + plot( recon[[i]], type = 'l', ylim = ylims, las = 1, + main = paste0("Group ",paste(grp[[i]],collapse=", "), + " (",round(varexp[[i]],2),"%)"), + xlab = '', ylab = '' + ) + abline( v = axTicks(1), col = rgb(0,0,0,0.1)) + abline( h = axTicks(2), col = rgb(0,0,0,0.1)) + } else { + # Plot noise + plot( recon[[i]], type = 'l', col = rgb(0.1,0.2,1,0.8), + ylim = ylims, las = 1, + main = paste0("Noise"," (",round(varexp[[i]],2),"%)"), + xlab = '', ylab = '' + ) + abline( v = axTicks(1), col = rgb(0,0,0,0.1)) + abline( h = axTicks(2), col = rgb(0,0,0,0.1)) + } + } # // end i + +# Reconstruct signal and noise + signal <- do.call( cbind, recon[ 1:(length(recon)-1) ] ) |> rowSums() + sigstrength <- varexp[1:(length(varexp)-1)] |> unlist() |> sum() + noise <- recon[[ length(recon) ]] + +# Plot signal with noise + par(mfrow=c(2,1)) + ylims2 <- range( x, signal, noise ) + plot( x, type = 'l', ylim = ylims2, las = 1, + main = paste0("Signal (",round(sigstrength,2),"%)"), + xlab = "", + lwd = 2, col = rgb(0,0,0,0.6) ) + lines( signal, lwd = 4, col = rgb(1,0.2,0.1,0.8) ) + abline( v = axTicks(1), col = rgb(0,0,0,0.1)) + abline( h = axTicks(2), col = rgb(0,0,0,0.1)) + plot( noise, type = 'l', ylim = ylims2, las = 1, + main = "Noise", xlab = "time", + col = rgb(0.1,0.2,1,0.8) ) + abline( v = axTicks(1), col = rgb(0,0,0,0.1)) + abline( h = axTicks(2), col = rgb(0,0,0,0.1)) + + +# Export ts, signal, noise + ssa_pyro_otb <- list( dat = data.frame( month = pyrodat$month, + ts = pyrodat$logcells, + signal = signal + mean(pyrodat$logcells), + noise = noise + mean(pyrodat$logcells) ), + grp = grp, + sigstrength = sigstrength + ) + save( ssa_pyro_otb, file = "../data/ssa_pyro_otb.RData" ) + \ No newline at end of file diff --git a/R/ssa_pyro_plots.R b/R/ssa_pyro_plots.R new file mode 100644 index 0000000..d79b2fb --- /dev/null +++ b/R/ssa_pyro_plots.R @@ -0,0 +1,66 @@ +# OTB Pyrodinium signal processing with SSA +# +rm(list=ls(all=TRUE)) + +# Load libraries +if(!require(lubridate)) { install.packages('lubridate') }; library(lubridate) +if(!require(dplyr)) { install.packages('dplyr') }; library(dplyr) + +# Load SSA outputs +load( "../data/ssa_pyro_otb.RData" ) +load( "../data/ssa_pyro_otb_nw.RData" ) +load( "../data/ssa_pyro_otb_ne.RData" ) +load( "../data/ssa_pyro_otb_cw.RData" ) +load( "../data/ssa_pyro_otb_ce.RData" ) +load( "../data/ssa_pyro_otb_sw.RData" ) +load( "../data/ssa_pyro_otb_se.RData" ) + +# Plot signals and noise +obj <- ls()[ c(1,5,4,3,2,7,6) ] +objlab <- c( "OTB segment", + "OTB, NW subsegment", "OTB, NE subsegment", + "OTB, CW subsegment", "OTB, CE subsegment", + "OTB, SW subsegment", "OTB, SE subsegment" ) +png( "../figs/ssa_pyro_plots.png", height = 9, width = 7, units = 'in', res = 500 ) +par( mfrow=c(7,1), mar=c(1,5,2,1), oma=c(2,0,0,0) ) +for( i in 1:length( obj ) ){ + + this <- eval( parse(text=obj[i]) ) + + plot( ts ~ month, dat = this$dat, + type = 'l', ylim = c(0,7), las = 1, + xlab = "", ylab = "", yaxt = 'n', xaxt = 'n', + lwd = 2, col = rgb(0,0,0,0.6) ) + mtext( paste0( "(",letters[i], ") ", objlab[i]," (signal strength: ", + round(this$sigstrength,2), "%)" ), + side = 3, line = 0, + font = 2, cex = 1.1, adj = 0 ) + date.seq <- seq.Date( min(this$dat$month), max(this$dat$month)+365, 'year' ) + if( i==length(obj) ){ + axis( 1, at = date.seq, labels = year(date.seq), cex.axis = 1.3 ) + } else { + axis( 1, at = date.seq, labels = rep("",length(date.seq)) ) + } + if( i==4 ){ + mtext( "Monthly maximum Pyro abundance (cells/L)", + side = 2, line = 3, cex = 1.1 ) + } + axis( 2, at = c(0,2,4,6), las = 1, cex.axis = 1.2, + labels = c( 0, expression(10^2), + expression(10^4), + expression(10^6) ) ) + lines( signal ~ month, dat = this$dat, + lwd = 4, col = rgb(1,0.2,0.1,0.8) ) + abline( v = date.seq, col = rgb(0,0,0,0.1)) 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