Last updated: 2018-12-04

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Set up environment

Load the ggplot2 and cowplot packages, and the functions definining the mean and variances used to simulate the data.

library(ggplot2)
library(cowplot)
source("../code/signals.R")

Generate the ground-truth signals

Here, n specifies the length of the signals.

n = 1024
t = 1:n/n

Some code.

mu.s = spike.f(t)

More code.

pos = c(0.1, 0.13, 0.15, 0.23, 0.25, 0.4, 0.44, 0.65, 0.76, 0.78, 0.81)
hgt = 2.97/5 * c(4, 5, 3, 4, 5, 4.2, 2.1, 4.3, 3.1, 5.1, 4.2)
wth = c(0.005, 0.005, 0.006, 0.01, 0.01, 0.03, 0.01, 0.01, 0.005, 0.008, 0.005)
mu.b = rep(0, n)
for (j in 1:length(pos))
  mu.b = mu.b + hgt[j]/((1 + (abs(t - pos[j])/wth[j]))^4)

mu.dop     = dop.f(t)
mu.dop     = 3/(max(mu.dop) - min(mu.dop)) * (mu.dop - min(mu.dop))
mu.dop.var = 10 * dop.f(t)
mu.dop.var = mu.dop.var - min(mu.dop.var)

sig = ((2 * t + 0.5) * (t <= 0.15)) +
      ((-12 * (t - 0.15) + 0.8) * (t > 0.15 & t <= 0.2)) +
      0.2 * (t > 0.2 & t <= 0.5) + 
      ((6 * (t - 0.5) + 0.2) * (t > 0.5 & t <= 0.6)) +
      ((-10 * (t - 0.6) + 0.8) * (t > 0.6 & t <= 0.65)) +
      ((-0.5 * (t - 0.65) + 0.3) * (t > 0.65 & t <= 0.85)) +
      ((2 * (t - 0.85) + 0.2) * (t > 0.85))
mu.ang = 3/5 * ((5/(max(sig) - min(sig))) * sig - 1.6) - 0.0419569

heavi = 4 * sin(4 * pi * t) - sign(t - 0.3) - sign(0.72 - t)
mu.hs = heavi/sqrt(var(heavi)) * 1 * 2.99/3.366185
mu.hs = mu.hs - min(mu.hs)

pos    = c(0.1, 0.13, 0.15, 0.23, 0.25, 0.4, 0.44, 0.65, 0.76, 0.78, 0.81)
hgt    = 2.88/5 * c(4, (-5), 3, (-4), 5, (-4.2), 2.1, 4.3, (-3.1), 2.1, (-4.2))
mu.blk = rep(0, n)
for (j in 1:length(pos))
  mu.blk = mu.blk + (1 + sign(t - pos[j])) * (hgt[j]/2)

mu.cblk = mu.blk
mu.cblk[mu.cblk < 0] = 0

Define the Blip mean function.

mu.blip = (0.32 + 0.6 * t +
           0.3 * exp(-100 * (t - 0.3)^2)) * (t >= 0 & t <= 0.8) +
  (-0.28 + 0.6 * t + 0.3 * exp(-100 * (t - 1.3)^2)) * (t > 0.8 & t <= 1)

Define the Corner mean function.

mu.cor = 623.87 * t^3 * (1 - 2 * t) * (t >= 0 & t <= 0.5) +
         187.161 * (0.125 - t^3) * t^4 * (t > 0.5 & t <= 0.8) +
         3708.470441 * (t - 1)^3 * (t > 0.8 & t <= 1)
mu.cor = (0.6/(max(mu.cor) - min(mu.cor))) * mu.cor
mu.cor = mu.cor - min(mu.cor) + 0.2

Define the rest of the mean functions.

mu.sp   = (1 + mu.s)/5
mu.bump = (1 + mu.b)/5
mu.blk  = 0.2 + 0.6 * (mu.blk - min(mu.blk))/max(mu.blk - min(mu.blk))
mu.ang  = (1 + mu.ang)/5
mu.dop  = (1 + mu.dop)/5

Define the variance functions.

var1 = rep(1, n)
var2 = (1e-02 + 4 * (exp(-550 * (t - 0.2)^2) +
                     exp(-200 * (t - 0.5)^2) +
                     exp(-950 * (t - 0.8)^2)))
var3 = (1e-02 + 2 * mu.dop.var)
var4 = 1e-02 + mu.b
var5 = 1e-02 + 1 * (mu.cblk - min(mu.cblk))/max(mu.cblk)
var1 = var1/2
var2 = var2/max(var2)
var3 = var3/max(var3)
var4 = var4/max(var4)
var5 = var5/max(var5)

Plot the signal means

These plots show each of the mean functions used to generate the simulated data sets.

plot_grid(qplot(t,mu.sp,  geom="line",xlab="",ylab="",main="Spikes (sp)"),
          qplot(t,mu.bump,geom="line",xlab="",ylab="",main="Bumps (bump)"),
          qplot(t,mu.blk, geom="line",xlab="",ylab="",main="Blocks (blk)"),
          qplot(t,mu.ang, geom="line",xlab="",ylab="",main="Angles (ang)"),
          qplot(t,mu.dop, geom="line",xlab="",ylab="",main="Doppler (dop)"),
          qplot(t,mu.blip,geom="line",xlab="",ylab="",main="Blip (blip)"),
          qplot(t,mu.cor, geom="line",xlab="",ylab="",main="Corner (cor)"),
          nrow = 4,ncol = 2)

Expand here to see past versions of plot-mean-functions-1.png:
Version Author Date
dc4c6cd Peter Carbonetto 2018-12-04

Plot the signal variances

These are rescaled in the simulations to achieve the desired signal-to-noise ratios (see the paper for a more detailed explanation).

plot(t,var1,xlab = "",ylab = "",ylim = c(0,1),type = "l",
     main = "Constant variance function")

plot(t,var2,xlab = "",ylab = "",type = "l",
     main = "Triple exponential variance function")

plot(t,var3,xlab = "",ylab = "",type = "l",main = "Doppler variance function")

plot(t,var4,xlab = "",ylab = "",type = "l",main = "Bumps variance function")

plot(t,var5,xlab = "",ylab = "",type = "l",main = "Clipped variance function")

Session information

sessionInfo()
R version 3.4.3 (2017-11-30)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS High Sierra 10.13.6

Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/3.4/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.4/Resources/lib/libRlapack.dylib

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] cowplot_0.9.3 ggplot2_3.1.0

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.0        compiler_3.4.3    pillar_1.2.1     
 [4] git2r_0.23.0      plyr_1.8.4        workflowr_1.1.1  
 [7] bindr_0.1.1       R.methodsS3_1.7.1 R.utils_2.6.0    
[10] tools_3.4.3       digest_0.6.17     evaluate_0.11    
[13] tibble_1.4.2      gtable_0.2.0      pkgconfig_2.0.2  
[16] rlang_0.2.2       yaml_2.2.0        bindrcpp_0.2.2   
[19] withr_2.1.2       stringr_1.3.1     dplyr_0.7.6      
[22] knitr_1.20        rprojroot_1.3-2   grid_3.4.3       
[25] tidyselect_0.2.4  glue_1.3.0        R6_2.2.2         
[28] rmarkdown_1.10    purrr_0.2.5       magrittr_1.5     
[31] whisker_0.3-2     backports_1.1.2   scales_0.5.0     
[34] htmltools_0.3.6   assertthat_0.2.0  colorspace_1.4-0 
[37] labeling_0.3      stringi_1.2.4     lazyeval_0.2.1   
[40] munsell_0.4.3     R.oo_1.21.0      

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