auxfunc.R 37.7 KB
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#
# Time Course Inspector: Shiny app for plotting time series data
# Author: Maciej Dobrzynski
#
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# Auxilary functions & definitions of global constants
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#


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library(ggplot2)
library(RColorBrewer)
library(gplots) # for heatmap.2
library(grid) # for modifying grob
library(Hmisc) # for CI calculation
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# Global parameters ----
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# if true, additional output printed to R console
DEB = T

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# font sizes in pts for plots in the manuscript
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# PLOTFONTBASE = 8
# PLOTFONTAXISTEXT = 8
# PLOTFONTAXISTITLE = 8
# PLOTFONTFACETSTRIP = 10
# PLOTFONTLEGEND = 8

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# font sizes in pts for screen display
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PLOTFONTBASE = 16
PLOTFONTAXISTEXT = 16
PLOTFONTAXISTITLE = 16
PLOTFONTFACETSTRIP = 20
PLOTFONTLEGEND = 16

# height (in pixels) of ribbon and single traj. plots
PLOTRIBBONHEIGHT = 500 # in pixels
PLOTTRAJHEIGHT = 500 # in pixels
PLOTPSDHEIGHT = 500 # in pixels
PLOTBOXHEIGHT = 500 # in pixels
PLOTSCATTERHEIGHT = 500 # in pixels
PLOTWIDTH = 85 # in percent
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# default number of facets in plots
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PLOTNFACETDEFAULT = 3
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# internal column names
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COLRT   = 'time'
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COLY    = 'y'
COLID   = 'id'
COLIDUNI = 'trackObjectsLabelUni'
COLGR   = 'group'
COLIN   = 'mid.in'
COLOBJN = 'obj.num'
COLPOSX = 'pos.x'
COLPOSY = 'pos.y'
COLIDX = 'IDX'
COLIDXDIFF = 'IDXdiff'
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COLCL = 'cl'
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# file names
FCSVOUTLIERS = 'outliers.csv'
FCSVTCCLEAN  = 'tCoursesSelected_clean.csv'
FPDFTCMEAN   = "tCoursesMeans.pdf"
FPDFTCSINGLE = "tCourses.pdf"
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FPDFTCPSD    = 'tCoursesPsd.pdf'
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FPDFBOXAUC   = 'boxplotAUC.pdf'
FPDFBOXTP    = 'boxplotTP.pdf'
FPDFSCATTER  = 'scatter.pdf'

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# Colour definitions ----
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rhg_cols <- c(
  "#771C19",
  "#AA3929",
  "#E25033",
  "#F27314",
  "#F8A31B",
  "#E2C59F",
  "#B6C5CC",
  "#8E9CA3",
  "#556670",
  "#000000"
)

md_cols <- c(
  "#FFFFFF",
  "#F8A31B",
  "#F27314",
  "#E25033",
  "#AA3929",
  "#FFFFCC",
  "#C2E699",
  "#78C679",
  "#238443"
)

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# list of palettes for the heatmap
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l.col.pal = list(
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  "Spectral" = 'Spectral',
  "Red-Yellow-Green" = 'RdYlGn',
  "Red-Yellow-Blue" = 'RdYlBu',
  "Greys" = "Greys",
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  "Reds" = "Reds",
  "Oranges" = "Oranges",
  "Greens" = "Greens",
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  "Blues" = "Blues"
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)

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# list of palettes for the dendrogram
l.col.pal.dend = list(
  "Rainbow" = 'rainbow_hcl',
  "Sequential" = 'sequential_hcl',
  "Heat" = 'heat_hcl',
  "Terrain" = 'terrain_hcl',
  "Diverge HCL" = 'diverge_hcl',
  "Diverge HSV" = 'diverge_hsv'
)

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# list of palettes for the dendrogram
l.col.pal.dend.2 = list(
  "Colorblind 10" = 'Color Blind',
  "Tableau 10" = 'Tableau 10',
  "Tableau 20" = 'Tableau 20',
  "Classic 10" = "Classic 10",
  "Classic 20" = "Classic 20",
  "Traffic 9" = 'Traffic',
  "Seattle Grays 5" = 'Seattle Grays'
)

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# Help text ----
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helpText.server = c(
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  alDataFormat =  paste0("<p>Switch between long and wide formats of input data. ",
                           "TCI accepts CSV or compressed CSV files (gz or bz2).</p>",
                           "<p><b>Long format</b> - a row is a single data point and consecutive time series are arranged vertically. ",
                           "Data file should contain at least 3 columns separated with a comma:</p>",
                           "<li>Identifier of a time series</li>",
                           "<li>Time points</li>",
                           "<li>A time-varying variable</li>",
                           "<br>",
                           "<p><b>Wide format</b> - a row is a time series with columns as time points.",
                           "At least 3 columns shuold be present:</p>",
                           "<li>First two columns in wide format should contain grouping and track IDs</li>",
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                           "<li>A column with a time point. Headers of columns with time points need to be numeric</li>"),
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  inDataGen1 =   paste0("Generate 3 groups with 20 random synthetic time series. ",
                        "Every time series contains 101 time points. ",
                        "Track IDs are unique across entire dataset."),
  chBtrajRem =   paste0("Load CSV file with a column of track IDs for removal. ",
                        "IDs should correspond to those used for plotting."),
  chBstim =      paste0("Load CSV file with stimulation pattern. Should contain 5 columns: ",
                        "grouping, start and end time points of stimulation, start and end of y-position, dummy column with ID."),
  chBtrajInter = paste0("Interpolate missing measurements indicated with NAs in the data file. ",
                        "In addition, interpolate a row that is completely missing from the data. ",
                        "The interval of the time column must be provided to know which rows are missing."),
  chBtrackUni =  paste0("If the track ID in the uploaded dataset is unique only within a group (e.g. an experimental condition), ",
                        "make it unique by prepending other columns to the track ID (typically a grouping column)."), 
  chBgroup    = "Select columns to group data according to treatment, condition, etc.",
  inSelMath   = "Select math operation to perform on a single or two measurement columns,",
  chBtimeTrim = "Trim time for further processing.",
  chBnorm     = "Divide measurements by the mean/median or calculate z-score with respect to selected time span.",
  rBnormMeth  = "Fold-change or z-score with respect to selected time span.",
  slNormRtMinMax = "Normalise with respect to this time span.",
  chBnormRobust  = "Calculate fold-change and z-score using the median and Median Absolute Deviation, instead of the mean and standard deviation.",
  chBnormGroup   = "Normalise to mean/median of selected time calculated globally, per group, or for individual time series.",
  downloadDataClean = "Download all time series after modifications in this panel.",
  alertNAsPresent            = "NAs present in the measurement column. Consider interpolation.",
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  alertWideMissesNumericTime = "Non-numeric headers of time columns. Data in wide format should have numeric column headers corresponding to time points.",
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  alertWideTooFewColumns     = "Insufficient columns. Data in wide format should contain at least 3 columns: grouping, track ID, and a single time point."
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)

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# Functions for data processing ----
#' Calculate the mean and CI around time series
#'
#' @param in.dt Data table in long format
#' @param in.col.meas Name of the column with the measurement
#' @param in.col.by Column names for grouping (default NULL - no grouping). Typically, you want to use at least a column with time.
#' @param in.type Choice of normal approximation or boot-strapping
#' @param ... Other params passed to smean.cl.normal and smean.cl.boot; these include \code{conf.int} for the confidence level, \code{B} for the number of boot-strapping iterations.
#'
#' @return Datatable with columns: Mean, lower and upper CI, and grouping columns if provided.
#' @export
#' @import data.table
#' @import Hmisc
#'
#' @examples
#'
#'
#' # generate synthetic time series; 100 time points long, with 10 randomly placed NAs
#' dt.tmp = genTraj(100, 10, 6, 3, in.addna = 10)
#'
#' # calculate single stats from all time points
#' calcTrajCI(dt.tmp, 'objCyto_Intensity_MeanIntensity_imErkCor')
#'
#' # calculate the mean and CI along the time course
#' calcTrajCI(dt.tmp, 'objCyto_Intensity_MeanIntensity_imErkCor', 'Metadata_RealTime')
LOCcalcTrajCI = function(in.dt, in.col.meas, in.col.by = NULL, in.type = c('normal', 'boot'), ...) {
  in.type = match.arg(in.type)
  
  if (in.type %like% 'normal')
    loc.dt = in.dt[, as.list(smean.cl.normal(get(in.col.meas), ...)), by = in.col.by] else
      loc.dt = in.dt[, as.list(smean.cl.boot(get(in.col.meas), ...)), by = in.col.by]
    
    return(loc.dt)
}

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#' Calculate standard error of the mean
#'
#' @param x Vector
#' @param na.rm Remove NAs; default = FALSE
#'
#' @return A scalar with the result
#' @export
#'
#' @examples
LOCstderr = function(x, na.rm=FALSE) {
  if (na.rm) 
    x = na.omit(x)
  
  return(sqrt(var(x)/length(x)))
}

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#' Calculate the power spectrum density for time-series
#'
#' @param in.dt Data table in long format
#' @param in.col.meas Name of the column with the measurement
#' @param in.col.id Name of the column with the unique series identifier
#' @param in.col.by Column names for grouping (default NULL - no grouping). PSD of individual trajectories will be averaged within a group.
#' @param in.method Name of the method for PSD estimation, must be one of c("pgram", "ar"). Default to "pgram*.
#' @param in.return.period Wheter to return densities though periods (1/frequencies) instead of frequencies.
#' @param ... Other paramters to pass to stats::spectrum()
#'
#' @return Datatable with columns: (frequency or period), spec (the density) and grouping column
#' @export
#' @import data.table
#'
#' @examples
LOCcalcPSD <- function(in.dt,
                    in.col.meas,
                    in.col.id,
                    in.col.by,
                    in.method = "pgram",
                    in.return.period = TRUE,
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                    in.time.btwPoints = 1,
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                    ...){
  require(data.table)
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  # Method "ar" returns $spec as matrix whereas "pgram" returns a vector, custom function to homogenze output format
  mySpectrum <- function(x, ...){
    args_spec <- list(x=x, plot=FALSE)
    inargs <- list(...)
    args_spec[names(inargs)] <- inargs
    out <- do.call(spectrum, args_spec)
    out$spec <- as.vector(out$spec)
    return(out)
  }
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  if(!in.method %in% c("pgram", "ar")){
    stop('Method should be one of: c("pgram", "ar"')
  }
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  dt_spec <-  in.dt[, (mySpectrum(get(in.col.meas), plot = FALSE, method = in.method)[c("freq", "spec")]), by = in.col.id]
  dt_group <- in.dt[, .SD[1, get(in.col.by)], by = in.col.id]
  setnames(dt_group, "V1", in.col.by)
  dt_spec <- merge(dt_spec, dt_group, by = in.col.id)
  dt_agg <- dt_spec[, .(spec = mean(spec)), by = c(in.col.by, "freq")]
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  if(in.return.period){
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    dt_agg[, period := 1/freq]
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    dt_agg[, freq := NULL]
    # Adjust period unit to go from frame unit  to time unit
    dt_agg[, period := period * in.time.btwPoints]
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  } else {
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    dt_agg[, freq := freq * (1/in.time.btwPoints)]
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    setnames(dt_agg, "freq", "frequency")
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  }
  return(dt_agg)
}


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#' Generate synthetic CellProfiler output with single-cell time series
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#'
#' @param in.ntpts Number of time points (default 60)
#' @param in.ntracks Number of tracks per FOV (default 10)
#' @param in.nfov Number of FOV (default 6)
#' @param in.nwells Number of wells (default 1)
#' @param in.addna Number of NAs to add randomly in the data (default NULL)
#'
#' @return Data table with the follwoing columns: Metadata_Site, Metadata_Well, Metadata_RealTime, objCyto_Intensity_MeanIntensity_imErkCor (normal distributed),
#' objNuc_Intensity_MeanIntensity_imErkCor (normal distributed), objNuc_Location_X and objNuc_Location_Y (uniform ditributed), TrackLabel
#' @export
#' @import data.table

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LOCgenTraj <- function(in.ntpts = 60, in.ntracks = 10, in.nfov = 6, in.nwells = 1, in.addna = NULL, in.addout = NULL) {
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  x.rand.1 = c(rnorm(in.ntpts * in.ntracks * in.nfov * 1/3, 0.5, 0.1), rnorm(in.ntpts * in.ntracks * in.nfov * 1/3,   1, 0.2), rnorm(in.ntpts * in.ntracks * in.nfov * 1/3,  2, 0.5))
  x.rand.2 = c(rnorm(in.ntpts * in.ntracks * in.nfov * 1/3, 0.25, 0.1), rnorm(in.ntpts * in.ntracks * in.nfov * 1/3, 0.5, 0.2),  rnorm(in.ntpts * in.ntracks * in.nfov * 1/3, 1, 0.2))
  
  # add NA's for testing
  if (!is.null(in.addna)) {
    locTabLen = length(x.rand.1)
    x.rand.1[round(runif(in.addna) * locTabLen)] = NA
    x.rand.2[round(runif(in.addna) * locTabLen)] = NA
  }
  
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  # add outliers for testing
  if (!is.null(in.addout)) {
    locTabLen = length(x.rand.1)
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    x.rand.1[round(runif(in.addout) * locTabLen)] = 5
    x.rand.2[round(runif(in.addout) * locTabLen)] = 5
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  }
  
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  x.arg = rep(seq(1, in.ntpts), in.ntracks * in.nfov)
  
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  dt.nuc = data.table(well = rep(LETTERS[1:in.nwells], each = in.ntpts * in.nfov * in.ntracks / in.nwells),
                      group = rep(1:in.nfov, each = in.ntpts * in.ntracks),
                      time = x.arg,
                      y1 = x.rand.1,
                      y2  = x.rand.2,
                      posx = runif(in.ntpts * in.ntracks * in.nfov, min = 0, max = 1),
                      posy = runif(in.ntpts * in.ntracks * in.nfov, min = 0, max = 1),
                      id = rep(1:(in.ntracks*in.nfov), each = in.ntpts))
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  return(dt.nuc)
}

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LOCgenTraj2 <- function(n_perGroup = 20, sd_noise = 0.01, sampleFreq = 0.2, endTime = 50)
{
  # Function definition ----------------------------------
  sim_expodecay_lagged_stim <-
    function (n,
              noise,
              interval.stim = 5,
              lambda = 0.2,
              freq = 0.2,
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              end = 40)
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    {
      require(data.table)
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      tvec <- seq(0, end, by = freq)
      stim_time <- seq(interval.stim, end, interval.stim)
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      stim_time_matrix <-
        matrix(stim_time, nrow = length(stim_time),
               ncol = n)
      noise_matrix <- abs(replicate(n, rnorm(
        n = length(stim_time),
        mean = 0,
        sd = noise
      )))
      stim_time_matrix <- stim_time_matrix + noise_matrix
      trajs <- matrix(0, nrow = length(tvec), ncol = n)
      for (col in 1:ncol(stim_time_matrix)) {
        for (row in 1:nrow(stim_time_matrix)) {
          index <- which(tvec >= stim_time_matrix[row, col])[1]
          trajs[index, col] <- 1
        }
      }
      decrease_factor <- exp(-lambda * freq)
      for (col in 1:ncol(trajs)) {
        for (row in 2:nrow(trajs)) {
          if (trajs[row, col] != 1) {
            trajs[row, col] <- trajs[row - 1, col] * decrease_factor
          }
        }
      }
      trajs <- as.data.table(trajs)
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      trajs <- cbind(seq(0, end, by = freq), trajs)
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      colnames(trajs)[1] <- "Time"
      trajs <- melt(trajs, id.vars = "Time")
      return(trajs)
    }
  
  
  # Dataset creation -----------------------------------------------
  dt1 <-
    sim_expodecay_lagged_stim(
      n = n_perGroup,
      noise = 0.75,
      interval.stim = 10,
      lambda = 0.4,
      freq = sampleFreq,
      end = endTime
    )
  dt2 <-
    sim_expodecay_lagged_stim(
      n = n_perGroup,
      noise = 0.75,
      interval.stim = 10,
      lambda = 0.1,
      freq = sampleFreq,
      end = endTime
    )
  dt3 <-
    sim_expodecay_lagged_stim(
      n = n_perGroup,
      noise = 0.75,
      interval.stim = 10,
      lambda = 0.4,
      freq = sampleFreq,
      end = endTime
    )
  dt3[, value := value / 3]
  
  dt1[, Group := "fastDecay"]
  dt2[, Group := "slowDecay"]
  dt3[, Group := "lowAmplitude"]
  
  dt <- rbindlist(list(dt1, dt2, dt3))
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  dt[, ID := sprintf("%s_%02d", Group, as.integer(gsub('[A-Z]', '', variable)))]
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  dt[, variable := NULL]
  dt[, Group := as.factor(Group)]
  
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  dt[, value := value + runif(1, -0.1, 0.1), by = .(Group, ID)]
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  noise_vec <- rnorm(n = nrow(dt), mean = 0, sd = sd_noise)
  dt[, value := value + noise_vec]
  
  setnames(dt, "value", "Meas")
  setcolorder(dt, c("Group", "ID", "Time", "Meas"))
  
  return(dt)
}

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#' Normalize Trajectory
#'
#' Returns original dt with an additional column with normalized quantity.
#' The column to be normalised is given by 'in.meas.col'.
#' The name of additional column is the same as in.meas.col but with ".norm" suffix added.
#' Normalisation is based on part of the trajectory;
#' this is defined by in.rt.min and max, and the column with time in.rt.col.#'
#'
#' @param in.dt Data table in long format
#' @param in.meas.col String with the column name to normalize
#' @param in.rt.col String with the colum name holding time
#' @param in.rt.min Lower bound for time period used for normalization
#' @param in.rt.max Upper bound for time period used for normalization
#' @param in.by.cols String vector with 'by' columns to calculate normalization per group; if NULL, no grouping is done
#' @param in.robust Whether robust measures should be used (median instead of mean, mad instead of sd); default TRUE
#' @param in.type Type of normalization: z.score or mean (i.e. fold change w.r.t. mean); default 'z-score'
#'
#' @return Returns original dt with an additional column with normalized quantity.
#' @export
#' @import data.table

LOCnormTraj = function(in.dt,
                    in.meas.col,
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                    in.rt.col = COLRT,
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                    in.rt.min = 10,
                    in.rt.max = 20,
                    in.by.cols = NULL,
                    in.robust = TRUE,
                    in.type = 'z.score') {
  loc.dt <-
    copy(in.dt) # copy so as not to alter original dt object w intermediate assignments
  
  if (is.null(in.by.cols)) {
    if (in.robust)
      loc.dt.pre.aggr = loc.dt[get(in.rt.col) >= in.rt.min &
                                 get(in.rt.col) <= in.rt.max, .(meas.md = median(get(in.meas.col), na.rm = TRUE),
                                                                meas.mad = mad(get(in.meas.col), na.rm = TRUE))]
    else
      loc.dt.pre.aggr = loc.dt[get(in.rt.col) >= in.rt.min &
                                 get(in.rt.col) <= in.rt.max, .(meas.md = mean(get(in.meas.col), na.rm = TRUE),
                                                                meas.mad = sd(get(in.meas.col), na.rm = TRUE))]
    
    loc.dt = cbind(loc.dt, loc.dt.pre.aggr)
  }  else {
    if (in.robust)
      loc.dt.pre.aggr = loc.dt[get(in.rt.col) >= in.rt.min &
                                 get(in.rt.col) <= in.rt.max, .(meas.md = median(get(in.meas.col), na.rm = TRUE),
                                                                meas.mad = mad(get(in.meas.col), na.rm = TRUE)), by = in.by.cols]
    else
      loc.dt.pre.aggr = loc.dt[get(in.rt.col) >= in.rt.min &
                                 get(in.rt.col) <= in.rt.max, .(meas.md = mean(get(in.meas.col), na.rm = TRUE),
                                                                meas.mad = sd(get(in.meas.col), na.rm = TRUE)), by = in.by.cols]
    
    loc.dt = merge(loc.dt, loc.dt.pre.aggr, by = in.by.cols)
  }
  
  
  if (in.type == 'z.score') {
    loc.dt[, meas.norm := (get(in.meas.col) - meas.md) / meas.mad]
  } else {
    loc.dt[, meas.norm := (get(in.meas.col) / meas.md)]
  }
  
  setnames(loc.dt, 'meas.norm', paste0(in.meas.col, '.norm'))
  
  loc.dt[, c('meas.md', 'meas.mad') := NULL]
  return(loc.dt)
}


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# Clustering ----
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# Return a dt with cell IDs and corresponding cluster assignments depending on dendrogram cut (in.k)
# This one works wth dist & hclust pair
# For sparse hierarchical clustering use getDataClSpar
# Arguments:
# in.dend  - dendrogram; usually output from as.dendrogram(hclust(distance_matrix))
# in.k - level at which dendrogram should be cut

getDataCl = function(in.dend, in.k) {
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  cat(file = stderr(), 'getDataCl \n')
  
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  loc.clAssign = dendextend::cutree(in.dend, in.k, order_clusters_as_data = TRUE, )
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  #print(loc.m)
  
  # The result of cutree containes named vector with names being cell id's
  # THIS WON'T WORK with sparse hierarchical clustering because there, the dendrogram doesn't have original id's
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  loc.dt.clAssign = as.data.table(loc.clAssign, keep.rownames = T)
  setnames(loc.dt.clAssign, c(COLID, COLCL))
  
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  #cat('===============\ndataCl:\n')
  #print(loc.dt.cl)
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  return(loc.dt.clAssign)
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}

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# Return a dt with cell IDs and corresponding cluster assignments depending on dendrogram cut (in.k)
# This one works with sparse hierarchical clustering!
# Arguments:
# in.dend  - dendrogram; usually output from as.dendrogram(hclust(distance_matrix))
# in.k - level at which dendrogram should be cut
# in.id - vector of cell id's

getDataClSpar = function(in.dend, in.k, in.id) {
  cat(file = stderr(), 'getDataClSpar \n')
  
  loc.m = dendextend::cutree(in.dend, in.k, order_clusters_as_data = TRUE)
  #print(loc.m)
  
  # The result of cutree containes named vector with names being cell id's
  # THIS WON'T WORK with sparse hierarchical clustering because there, the dendrogram doesn't have original id's
  loc.dt.cl = data.table(id = in.id,
                         cl = loc.m)
  
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  #cat('===============\ndataCl:\n')
  #print(loc.dt.cl)
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  return(loc.dt.cl)
}



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# prepares a table with cluster numbers in 1st column and colour assignments in 2nd column
# the number of rows is determined by dendrogram cut
getClCol <- function(in.dend, in.k) {
  
  loc.col_labels <- get_leaves_branches_col(in.dend)
  loc.col_labels <- loc.col_labels[order(order.dendrogram(in.dend))]
  
  return(unique(
    data.table(cl.no = dendextend::cutree(in.dend, k = in.k, order_clusters_as_data = TRUE),
               cl.col = loc.col_labels)))
}

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# Cluster validation ----

#Customize factoextra functions to accept dissimilarity matrix from start. Otherwise can't use distance functions that are not in base R, like DTW.

# Inherit and adapt hcut function to take input from UI, used for fviz_clust 
LOChcut <- function(x, k = 2, isdiss = inherits(x, "dist"), hc_func = "hclust", hc_method = "average", hc_metric = "euclidean"){
  if(!inherits(x, "dist")){stop("x must be a distance matrix")}
  return(factoextra::hcut(x = x, k = k, isdiss = TRUE, hc_func = hc_func, hc_method = hc_method, hc_metric = hc_metric))
}

# Modified from factoextra::fviz_nbclust
# Allow (actually enforce) x to be a distance matrix; no GAP statistics for compatibility
LOCnbclust <- function (x, FUNcluster = LOChcut, method = c("silhouette", "wss"), k.max = 10, verbose = FALSE, 
          barfill = "steelblue", barcolor = "steelblue", linecolor = "steelblue", 
          print.summary = TRUE, ...) 
{
  set.seed(123)
  if (k.max < 2) 
    stop("k.max must bet > = 2")
  method = match.arg(method)
  if (!inherits(x, c("dist")))
    stop("x should be an object of class dist")
  else if (is.null(FUNcluster)) 
    stop("The argument FUNcluster is required. ", "Possible values are kmeans, pam, hcut, clara, ...")
  else if (method %in% c("silhouette", "wss")) {
    diss <- x  # x IS ENFORCED TO BE A DISSIMILARITY MATRIX
    v <- rep(0, k.max)
    if (method == "silhouette") {
      for (i in 2:k.max) {
        clust <- FUNcluster(x, i, ...)
        v[i] <- factoextra:::.get_ave_sil_width(diss, clust$cluster)
      }
    }
    else if (method == "wss") {
      for (i in 1:k.max) {
        clust <- FUNcluster(x, i, ...)
        v[i] <- factoextra:::.get_withinSS(diss, clust$cluster)
      }
    }
    df <- data.frame(clusters = as.factor(1:k.max), y = v)
    ylab <- "Total Within Sum of Square"
    if (method == "silhouette") 
      ylab <- "Average silhouette width"
    p <- ggpubr::ggline(df, x = "clusters", y = "y", group = 1, 
                        color = linecolor, ylab = ylab, xlab = "Number of clusters k", 
                        main = "Optimal number of clusters")
    if (method == "silhouette") 
      p <- p + geom_vline(xintercept = which.max(v), linetype = 2, 
                          color = linecolor)
    return(p)
  }
}

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# Custom plotting functions ----
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#' Custom ggPlot theme based on theme_bw
#'
#' @param in.font.base
#' @param in.font.axis.text
#' @param in.font.axis.title
#' @param in.font.strip
#' @param in.font.legend
#'
#' @return
#' @export
#'
#' @examples
#'
LOCggplotTheme = function(in.font.base = 12,
                       in.font.axis.text = 12,
                       in.font.axis.title = 12,
                       in.font.strip = 14,
                       in.font.legend = 12) {
  loc.theme =
    theme_bw(base_size = in.font.base, base_family = "Helvetica") +
    theme(
      panel.spacing = unit(1, "lines"),
      panel.grid.minor = element_blank(),
      panel.grid.major = element_blank(),
      panel.border = element_blank(),
      axis.line = element_line(color = "black", size = 0.25),
      axis.text = element_text(size = in.font.axis.text),
      axis.title = element_text(size = in.font.axis.title),
      strip.text = element_text(size = in.font.strip, face = "bold"),
      strip.background = element_blank(),
      legend.key = element_blank(),
      legend.text = element_text(size = in.font.legend),
      legend.key.height = unit(1, "lines"),
      legend.key.width = unit(2, "lines"))
  
  return(loc.theme)
}

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# Build Function to Return Element Text Object
# From: https://stackoverflow.com/a/36979201/1898713
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LOCrotatedAxisElementText = function(angle, position='x', size = 12){
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  angle     = angle[1]; 
  position  = position[1]
  positions = list(x=0, y=90, top=180, right=270)
  if(!position %in% names(positions))
    stop(sprintf("'position' must be one of [%s]",paste(names(positions),collapse=", ")), call.=FALSE)
  if(!is.numeric(angle))
    stop("'angle' must be numeric",call.=FALSE)
  rads = (-angle - positions[[ position ]])*pi/180
  hjust = round((1 - sin(rads)))/2
  vjust = round((1 + cos(rads)))/2
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  element_text(size = size, angle = angle, vjust = vjust, hjust = hjust)
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}

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# Plot individual time series
LOCplotTraj = function(dt.arg, # input data table
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                        x.arg,  # string with column name for x-axis
                        y.arg, # string with column name for y-axis
                        group.arg, # string with column name for grouping time series (typicaly cell ID)
                        facet.arg, # string with column name for facetting
                        facet.ncol.arg = 2, # default number of facet columns
                        facet.color.arg = NULL, # vector with list of colours for adding colours to facet names (currently a horizontal line on top of the facet is drawn)
                        line.col.arg = NULL, # string with column name for colouring time series (typically when individual time series are selected in UI)
                        xlab.arg = NULL, # string with x-axis label
                        ylab.arg = NULL, # string with y-axis label
                        plotlab.arg = NULL, # string with plot label
                        dt.stim.arg = NULL, # plotting additional dataset; typically to indicate stimulations (not fully implemented yet, not tested!)
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                        x.stim.arg = c('tstart', 'tend'), # column names in stimulation dt with x and xend parameters
                        y.stim.arg = c('ystart', 'yend'), # column names in stimulation dt with y and yend parameters
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                        tfreq.arg = 1, # unused
                        xlim.arg = NULL, # limits of x-axis; for visualisation only, not trimmimng data
                        ylim.arg = NULL, # limits of y-axis; for visualisation only, not trimmimng data
                        stim.bar.width.arg = 0.5, # width of the stimulation line; plotted under time series
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                        aux.label1 = NULL, # 1st point label; used for interactive plotting; displayed in the tooltip; typically used to display values of column holding x & y coordinates
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                        aux.label2 = NULL,
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                        aux.label3 = NULL,
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                        stat.arg = c('', 'mean', 'CI', 'SE')) {
  
  # match arguments for stat plotting
  loc.stat = match.arg(stat.arg, several.ok = TRUE)

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  # aux.label12 are required for plotting XY positions in the tooltip of the interactive (plotly) graph
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  p.tmp = ggplot(dt.arg,
                 aes_string(x = x.arg,
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                            y = y.arg,
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                            group = group.arg,
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                            label = group.arg))
  #,
  #                          label  = aux.label1,
  #                          label2 = aux.label2,
  #                          label3 = aux.label3))
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  if (is.null(line.col.arg)) {
    p.tmp = p.tmp +
      geom_line(alpha = 0.25, 
                              size = 0.25)
  }
  else {
    p.tmp = p.tmp + 
      geom_line(aes_string(colour = line.col.arg), 
                              alpha = 0.5, 
                              size = 0.5) +
      scale_color_manual(name = '', 
                         values =c("FALSE" = rhg_cols[7], "TRUE" = rhg_cols[3], "SELECTED" = 'green', "NOT SEL" = rhg_cols[7]))
  }
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  # this is temporary solution for adding colour according to cluster number
  # use only when plotting traj from clustering!
  # a horizontal line is added at the top of data
  if (!is.null(facet.color.arg)) {

    loc.y.max = max(dt.arg[, c(y.arg), with = FALSE])
    loc.dt.cl = data.table(xx = 1:length(facet.color.arg), yy = loc.y.max)
    setnames(loc.dt.cl, 'xx', facet.arg)
    
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    # adjust facet.color.arg to plot
    
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    p.tmp = p.tmp +
      geom_hline(data = loc.dt.cl, colour = facet.color.arg, yintercept = loc.y.max, size = 4) +
      scale_colour_manual(values = facet.color.arg,
                          name = '')
  }
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  if ('mean' %in% loc.stat)
    p.tmp = p.tmp + 
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    stat_summary(
      aes_string(y = y.arg, group = 1),
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      fun.y = mean, 
      na.rm = T,
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      colour = 'red',
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      linetype = 'solid',
      size = 1,
      geom = "line",
      group = 1
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    )

  if ('CI' %in% loc.stat)
    p.tmp = p.tmp + 
    stat_summary(
      aes_string(y = y.arg, group = 1),
      fun.data = mean_cl_normal,
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      na.rm = T,
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      colour = 'red',
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      alpha = 0.25,
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      geom = "ribbon",
      group = 1
    )
  
  if ('SE' %in% loc.stat)
    p.tmp = p.tmp + 
    stat_summary(
      aes_string(y = y.arg, group = 1),
      fun.data = mean_se,
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      na.rm = T,
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      colour = 'red',
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      alpha = 0.25,
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      geom = "ribbon",
      group = 1
    )
  
  
  
  p.tmp = p.tmp + 
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    facet_wrap(as.formula(paste("~", facet.arg)),
               ncol = facet.ncol.arg,
               scales = "free_x")
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  # plot stimulation bars underneath time series
  # dt.stim.arg is read separately and should contain 4 columns with
  # xy positions of beginning and end of the bar
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  if(!is.null(dt.stim.arg)) {
    p.tmp = p.tmp + geom_segment(data = dt.stim.arg,
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                                 aes_string(x = x.stim.arg[1],
                                            xend = x.stim.arg[2],
                                            y = y.stim.arg[1],
                                            yend = y.stim.arg[2],
                                            group = 'group'),
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                                 colour = rhg_cols[[3]],
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                                 size = stim.bar.width.arg) 
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  }
  
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  p.tmp = p.tmp + coord_cartesian(xlim = xlim.arg, ylim = ylim.arg)
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  p.tmp = p.tmp + 
    xlab(paste0(xlab.arg, "\n")) +
    ylab(paste0("\n", ylab.arg)) +
    ggtitle(plotlab.arg) +
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    LOCggplotTheme(in.font.base = PLOTFONTBASE, 
                   in.font.axis.text = PLOTFONTAXISTEXT, 
                   in.font.axis.title = PLOTFONTAXISTITLE, 
                   in.font.strip = PLOTFONTFACETSTRIP, 
                   in.font.legend = PLOTFONTLEGEND) + 
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    theme(legend.position = "top")
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  return(p.tmp)
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}

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# Plot average time series with CI together in one facet
LOCplotTrajRibbon = function(dt.arg, # input data table
                          x.arg, # string with column name for x-axis
                          y.arg, # string with column name for y-axis
                          group.arg = NULL, # string with column name for grouping time series (here, it's a column corresponding to grouping by condition)
                          col.arg = NULL, # colour pallette for individual time series
                          dt.stim.arg = NULL, # data table with stimulation pattern
                          x.stim.arg = c('tstart', 'tend'), # column names in stimulation dt with x and xend parameters
                          y.stim.arg = c('ystart', 'yend'), # column names in stimulation dt with y and yend parameters
                          stim.bar.width.arg = 0.5,
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                          xlim.arg = NULL, # limits of x-axis; for visualisation only, not trimmimng data
                          ylim.arg = NULL, # limits of y-axis; for visualisation only, not trimmimng data
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                          ribbon.lohi.arg = c('Lower', 'Upper'), # column names containing lower and upper bound for plotting the ribbon, e.g. for CI; set to NULL to avoid plotting the ribbon
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                          ribbon.fill.arg = 'grey50',
                          ribbon.alpha.arg = 0.5,
                          xlab.arg = NULL,
                          ylab.arg = NULL,
                          plotlab.arg = NULL) {
  
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  p.tmp = ggplot(dt.arg, aes_string(x = x.arg, group = group.arg))
  
  if (!is.null(ribbon.lohi.arg))
    p.tmp = p.tmp + 
      geom_ribbon(aes_string(ymin = ribbon.lohi.arg[1], ymax = ribbon.lohi.arg[2]),
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                fill = ribbon.fill.arg,
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                alpha = ribbon.alpha.arg)
  
  p.tmp = p.tmp + geom_line(aes_string(y = y.arg, colour = group.arg))
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  # plot stimulation bars underneath time series
  # dt.stim.arg is read separately and should contain 4 columns with
  # xy positions of beginning and end of the bar
  if(!is.null(dt.stim.arg)) {
    p.tmp = p.tmp + geom_segment(data = dt.stim.arg,
                                 aes_string(x = x.stim.arg[1],
                                     xend = x.stim.arg[2],
                                     y = y.stim.arg[1],
                                     yend = y.stim.arg[2]),
                                 colour = rhg_cols[[3]],
                                 size = stim.bar.width.arg,
                                 group = 1) 
  }

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  p.tmp = p.tmp + coord_cartesian(xlim = xlim.arg, ylim = ylim.arg)
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  if (is.null(col.arg)) {
    p.tmp = p.tmp +
      scale_color_discrete(name = '')
  } else {
    p.tmp = p.tmp +
      scale_colour_manual(values = col.arg, name = '')
  }
  
  if (!is.null(plotlab.arg))
    p.tmp = p.tmp + ggtitle(plotlab.arg)
  
  p.tmp = p.tmp +
    xlab(xlab.arg) +
    ylab(ylab.arg)
  
  return(p.tmp)
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}

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# Plot average power spectrum density per facet
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LOCplotPSD <- function(dt.arg, # input data table
                    x.arg, # string with column name for x-axis
                    y.arg, # string with column name for y-axis
                    group.arg=NULL, # string with column name for grouping time series (here, it's a column corresponding to grouping by condition)
                    xlab.arg = x.arg,
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                    ylab.arg = y.arg,
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                    facet.color.arg = NULL){
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  require(ggplot2)
  if(length(setdiff(c(x.arg, y.arg, group.arg), colnames(dt.arg))) > 0){
    stop(paste("Missing columns in dt.arg: ", setdiff(c(x.arg, y.arg, group.arg), colnames(dt.arg))))
  }
  p.tmp <- ggplot(dt.arg, aes_string(x=x.arg, y=y.arg)) +
    geom_line() +
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    geom_rug(sides="b", alpha = 1, color = "lightblue") +
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    facet_wrap(group.arg) +
    labs(x = xlab.arg, y = ylab.arg)
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  if (!is.null(facet.color.arg)) {
    
    loc.y.max = max(dt.arg[, c(y.arg), with = FALSE])
    loc.dt.cl = data.table(xx = 1:length(facet.color.arg), yy = loc.y.max)
    setnames(loc.dt.cl, 'xx', group.arg)
    
    # adjust facet.color.arg to plot
    
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    p.tmp = p.tmp +
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      geom_hline(data = loc.dt.cl, colour = facet.color.arg, yintercept = loc.y.max, size = 4) +
      scale_colour_manual(values = facet.color.arg,
                          name = '')
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  }
  
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  return(p.tmp)
}
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#' Plot a scatter plot with an optional linear regression
#'
#' @param dt.arg input of data.table with 2 columns with x and y coordinates
#' @param facet.arg 
#' @param facet.ncol.arg 
#' @param xlab.arg 
#' @param ylab.arg 
#' @param plotlab.arg 
#' @param alpha.arg 
#' @param trend.arg 
#' @param ci.arg 

LOCggplotScat = function(dt.arg, 
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                        facet.arg = NULL,
                        facet.ncol.arg = 2,
                        xlab.arg = NULL,
                        ylab.arg = NULL,
                        plotlab.arg = NULL,
                        alpha.arg = 1,
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                        trend.arg = T,
                        ci.arg = 0.95) {
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  p.tmp = ggplot(dt.arg, aes(x = x, y = y, label = id)) +
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    geom_point(alpha = alpha.arg)

  if (trend.arg) {
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    p.tmp = p.tmp +
      stat_smooth(
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        method = "lm",
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        fullrange = FALSE,
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        level = ci.arg,
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        colour = 'blue'
      )
  }
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  if (!is.null(facet.arg)) {
    p.tmp = p.tmp +
      facet_wrap(as.formula(paste("~", facet.arg)),
                 ncol = facet.ncol.arg)
    
  }
  
  if (!is.null(xlab.arg))
    p.tmp = p.tmp +
      xlab(paste0(xlab.arg, "\n"))
  
  if (!is.null(ylab.arg))
    p.tmp = p.tmp +
      ylab(paste0("\n", ylab.arg))
  
  if (!is.null(plotlab.arg))
    p.tmp = p.tmp +
      ggtitle(paste0(plotlab.arg, "\n"))
  
  p.tmp = p.tmp +
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    LOCggplotTheme(in.font.base = PLOTFONTBASE, 
                   in.font.axis.text = PLOTFONTAXISTEXT, 
                   in.font.axis.title = PLOTFONTAXISTITLE, 
                   in.font.strip = PLOTFONTFACETSTRIP, 
                   in.font.legend = PLOTFONTLEGEND) + 
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    theme(legend.position = "none")

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  return(p.tmp)
}
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LOCplotHeatmap <- function(data.arg,
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                          dend.arg,
                          palette.arg,
                          palette.rev.arg = TRUE,
                          dend.show.arg = TRUE,
                          key.show.arg = TRUE,
                          margin.x.arg = 5,
                          margin.y.arg = 20,
                          nacol.arg = 0.5,
                          colCol.arg = NULL,
                          labCol.arg = NULL,
                          font.row.arg = 1,
                          font.col.arg = 1,
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                          breaks.arg = NULL,
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                          title.arg = 'Clustering') {
  
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  loc.n.colbreaks = 99
  
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  if (palette.rev.arg)
    my_palette <-
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    rev(colorRampPalette(brewer.pal(9, palette.arg))(n = loc.n.colbreaks))
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  else
    my_palette <-
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    colorRampPalette(brewer.pal(9, palette.arg))(n = loc.n.colbreaks)
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  col_labels <- get_leaves_branches_col(dend.arg)
  col_labels <- col_labels[order(order.dendrogram(dend.arg))]
  
  if (dend.show.arg) {
    assign("var.tmp.1", dend.arg)
    var.tmp.2 = "row"
  } else {
    assign("var.tmp.1", FALSE)
    var.tmp.2 = "none"
  }
  
  loc.p = heatmap.2(
    data.arg,
    Colv = "NA",
    Rowv = var.tmp.1,
    srtCol = 90,
    dendrogram = var.tmp.2,
    trace = "none",
    key = key.show.arg,
    margins = c(margin.x.arg, margin.y.arg),
    col = my_palette,
    na.col = grey(nacol.arg),
    denscol = "black",
    density.info = "density",
    RowSideColors = col_labels,
    colRow = col_labels,
    colCol = colCol.arg,
    labCol = labCol.arg,
    #      sepcolor = grey(input$inPlotHierGridColor),
    #      colsep = 1:ncol(loc.dm),
    #      rowsep = 1:nrow(loc.dm),
    cexRow = font.row.arg,
    cexCol = font.col.arg,
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    main = title.arg,
    symbreaks = FALSE,
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    symkey = FALSE,
    breaks = if (is.null(breaks.arg)) NULL else seq(breaks.arg[1], breaks.arg[2], length.out = loc.n.colbreaks+1)
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  )
  
  return(loc.p)
}