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style="text-align:left;"> File </th> <th style="text-align:left;"> Version </th> <th style="text-align:left;"> Author </th> <th style="text-align:left;"> Date </th> <th style="text-align:left;"> Message </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;"> html </td> <td style="text-align:left;"> <a href="https://cdn.rawgit.com/stephenslab/smash-paper/68974658940fa7afefe44c5919341d238cd34c0f/docs/gaussian_signals.html" target="_blank">6897465</a> </td> <td style="text-align:left;"> Peter Carbonetto </td> <td style="text-align:left;"> 2018-12-04 </td> <td style="text-align:left;"> Added gaussian_signals page to the home. </td> </tr> <tr> <td style="text-align:left;"> Rmd </td> <td style="text-align:left;"> <a href="https://github.com/stephenslab/smash-paper/blob/7ebd8995d3f61172745319d65f50fa212d87951f/analysis/gaussian_signals.Rmd" target="_blank">7ebd899</a> </td> <td style="text-align:left;"> Peter Carbonetto </td> <td style="text-align:left;"> 2018-12-04 </td> <td style="text-align:left;"> wflow_publish(c(“gaussian_signals.Rmd”, “index.Rmd”)) </td> </tr> <tr> <td style="text-align:left;"> html </td> <td style="text-align:left;"> <a href="https://cdn.rawgit.com/stephenslab/smash-paper/f35239b78220e9622e1130586e0d6cf4356875a0/docs/gaussian_signals.html" target="_blank">f35239b</a> </td> <td style="text-align:left;"> Peter Carbonetto </td> <td style="text-align:left;"> 2018-12-04 </td> <td style="text-align:left;"> Completed the gaussian_signals page. </td> </tr> <tr> <td style="text-align:left;"> Rmd </td> <td style="text-align:left;"> <a href="https://github.com/stephenslab/smash-paper/blob/53df81d0f5e6f1bef34e7adc0722aa840ff39250/analysis/gaussian_signals.Rmd" target="_blank">53df81d</a> </td> <td style="text-align:left;"> Peter Carbonetto </td> <td style="text-align:left;"> 2018-12-04 </td> <td style="text-align:left;"> wflow_publish(“gaussian_signals.Rmd”) </td> </tr> <tr> <td style="text-align:left;"> html </td> <td style="text-align:left;"> <a href="https://cdn.rawgit.com/stephenslab/smash-paper/abc74e5dfa683eba26cee0d09abfebbdf053413c/docs/gaussian_signals.html" target="_blank">abc74e5</a> </td> <td style="text-align:left;"> Peter Carbonetto </td> <td style="text-align:left;"> 2018-12-04 </td> <td style="text-align:left;"> Added plots for for variance signals. </td> </tr> <tr> <td style="text-align:left;"> Rmd </td> <td style="text-align:left;"> <a href="https://github.com/stephenslab/smash-paper/blob/c8957e03b3aa0fd8555e4493ef05a64d40b76038/analysis/gaussian_signals.Rmd" target="_blank">c8957e0</a> </td> <td style="text-align:left;"> Peter Carbonetto </td> <td style="text-align:left;"> 2018-12-04 </td> <td style="text-align:left;"> wflow_publish(“gaussian_signals.Rmd”) </td> </tr> <tr> <td style="text-align:left;"> html </td> <td style="text-align:left;"> <a href="https://cdn.rawgit.com/stephenslab/smash-paper/1fe523e244f7a10f4d4f375c0a997d437d5e1a17/docs/gaussian_signals.html" target="_blank">1fe523e</a> </td> <td style="text-align:left;"> Peter Carbonetto </td> <td style="text-align:left;"> 2018-12-04 </td> <td style="text-align:left;"> Adjusted the plots of the mean functions. </td> </tr> <tr> <td style="text-align:left;"> Rmd </td> <td style="text-align:left;"> <a href="https://github.com/stephenslab/smash-paper/blob/1bddd73584b6de79f1a59d83a9dba1a137742a5d/analysis/gaussian_signals.Rmd" target="_blank">1bddd73</a> </td> <td style="text-align:left;"> Peter Carbonetto </td> <td style="text-align:left;"> 2018-12-04 </td> <td style="text-align:left;"> wflow_publish(“gaussian_signals.Rmd”) </td> </tr> <tr> <td style="text-align:left;"> html </td> <td style="text-align:left;"> <a href="https://cdn.rawgit.com/stephenslab/smash-paper/dc4c6cdeab52ee2f5a43f313c91fe24a4dff89bb/docs/gaussian_signals.html" target="_blank">dc4c6cd</a> </td> <td style="text-align:left;"> Peter Carbonetto </td> <td style="text-align:left;"> 2018-12-04 </td> <td style="text-align:left;"> I now have plots of all the mean functions in gaussian_signals.Rmd. </td> </tr> <tr> <td style="text-align:left;"> Rmd </td> <td style="text-align:left;"> <a href="https://github.com/stephenslab/smash-paper/blob/a8b97227a8d490082a4cef04d0c8c5b8339f1d3b/analysis/gaussian_signals.Rmd" target="_blank">a8b9722</a> </td> <td style="text-align:left;"> Peter Carbonetto </td> <td style="text-align:left;"> 2018-12-04 </td> <td style="text-align:left;"> wflow_publish(“gaussian_signals.Rmd”) </td> </tr> <tr> <td style="text-align:left;"> Rmd </td> <td style="text-align:left;"> <a href="https://github.com/stephenslab/smash-paper/blob/2ab6ac046a1ccf4297eb4285cad8e2209204975c/analysis/gaussian_signals.Rmd" target="_blank">2ab6ac0</a> </td> <td style="text-align:left;"> Peter Carbonetto </td> <td style="text-align:left;"> 2018-12-04 </td> <td style="text-align:left;"> wflow_publish(“gaussian_signals.Rmd”) </td> </tr> <tr> <td style="text-align:left;"> Rmd </td> <td style="text-align:left;"> <a href="https://github.com/stephenslab/smash-paper/blob/ee71f272006352b6848a91f35c5d3b97923f1852/analysis/gaussian_signals.Rmd" target="_blank">ee71f27</a> </td> <td style="text-align:left;"> Peter Carbonetto </td> <td style="text-align:left;"> 2018-12-04 </td> <td style="text-align:left;"> Made a few small adjustments to the text in the “gaussianmeanest” analysis. </td> </tr> </tbody> </table> </ul> <p></details></p> <hr /> <div id="set-up-environment" class="section level2"> <h2>Set up environment</h2> <p>Load the ggplot2 and cowplot packages, and the functions definining the mean and variances used to simulate the data.</p> <pre class="r"><code>library(ggplot2) library(cowplot) source("../code/signals.R")</code></pre> </div> <div id="generate-the-ground-truth-signals" class="section level2"> <h2>Generate the ground-truth signals</h2> <p>Here, <code>n</code> specifies the length of the signals.</p> <pre class="r"><code>n = 1024 t = 1:n/n</code></pre> <p>Define the Spikes mean function.</p> <pre class="r"><code>mu.s = spike.f(t)</code></pre> <p>Define the Bumps variance function.</p> <pre class="r"><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)</code></pre> <p>Define the Doppler mean function.</p> <pre class="r"><code>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)</code></pre> <p>Define the Angle mean function.</p> <pre class="r"><code>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</code></pre> <p>Define the Block mean and variance functions.</p> <pre class="r"><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 = 2.88/5 * 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</code></pre> <p>Define the Blip mean function.</p> <pre class="r"><code>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)</code></pre> <p>Define the Corner mean function.</p> <pre class="r"><code>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</code></pre> <p>Define the rest of the mean functions.</p> <pre class="r"><code>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</code></pre> <p>Define the variance functions.</p> <pre class="r"><code>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)</code></pre> </div> <div id="plot-the-signal-means" class="section level2"> <h2>Plot the signal means</h2> <p>These plots show each of the mean functions used in generating the Gaussian data sets.</p> <pre class="r"><code>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)</code></pre> <p><img src="figure/gaussian_signals.Rmd/plot-mean-functions-1.png" width="576" style="display: block; margin: auto;" /></p> <details> <summary><em>Expand here to see past versions of plot-mean-functions-1.png:</em></summary> <table style="border-collapse:separate; border-spacing:5px;"> <thead> <tr> <th style="text-align:left;"> Version </th> <th style="text-align:left;"> Author </th> <th style="text-align:left;"> Date </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;"> <a href="https://github.com/stephenslab/smash-paper/blob/1fe523e244f7a10f4d4f375c0a997d437d5e1a17/docs/figure/gaussian_signals.Rmd/plot-mean-functions-1.png" target="_blank">1fe523e</a> </td> <td style="text-align:left;"> Peter Carbonetto </td> <td style="text-align:left;"> 2018-12-04 </td> </tr> <tr> <td style="text-align:left;"> <a href="https://github.com/stephenslab/smash-paper/blob/dc4c6cdeab52ee2f5a43f313c91fe24a4dff89bb/docs/figure/gaussian_signals.Rmd/plot-mean-functions-1.png" target="_blank">dc4c6cd</a> </td> <td style="text-align:left;"> Peter Carbonetto </td> <td style="text-align:left;"> 2018-12-04 </td> </tr> </tbody> </table> <p></details></p> </div> <div id="plot-the-signal-variances" class="section level2"> <h2>Plot the signal variances</h2> <p>These plots show the variance functions used in generating the Gaussian data sets. In practice, these functions are rescaled in the simulations to achieve the desired signal-to-noise ratios (see the paper for a more detailed explanation).</p> <pre class="r"><code>plot_grid( qplot(t,var1,geom="line",xlab="",ylab="",main="Constant variance (v1)"), qplot(t,var2,geom="line",xlab="",ylab="",main="Triple exponential (v2)"), qplot(t,var3,geom="line",xlab="",ylab="",main="Doppler (v3)"), qplot(t,var4,geom="line",xlab="",ylab="",main="Bumps (v4)"), qplot(t,var5,geom="line",xlab="",ylab="",main="Clipped (v5)"), nrow = 3,ncol = 2)</code></pre> <p><img src="figure/gaussian_signals.Rmd/plot-variance-functions-1.png" width="576" style="display: block; margin: auto;" /></p> <details> <summary><em>Expand here to see past versions of plot-variance-functions-1.png:</em></summary> <table style="border-collapse:separate; border-spacing:5px;"> <thead> <tr> <th style="text-align:left;"> Version </th> <th style="text-align:left;"> Author </th> <th style="text-align:left;"> Date </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;"> <a href="https://github.com/stephenslab/smash-paper/blob/abc74e5dfa683eba26cee0d09abfebbdf053413c/docs/figure/gaussian_signals.Rmd/plot-variance-functions-1.png" target="_blank">abc74e5</a> </td> <td style="text-align:left;"> Peter Carbonetto </td> <td style="text-align:left;"> 2018-12-04 </td> </tr> </tbody> </table> <p></details></p> </div> <div id="session-information" class="section level2"> <h2>Session information</h2> <pre class="r"><code>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</code></pre> </div> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { availableFonts: ["TeX"] } }); </script> <!-- Adjust MathJax settings so that all math formulae are shown using TeX fonts only; see http://docs.mathjax.org/en/latest/configuration.html. 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