Last updated: 2018-10-21

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    rmd 7b6b664 Lei Sun 2018-10-21 wflow_publish(c(“analysis/cash_paper_fig_gd.rmd”,

Introduction

Plotting the standard Gaussian and its standardized derivatives.

source("../code/gdash_lik.R")
Loading required package: EQL
Loading required package: ttutils
Loading required package: SQUAREM
Loading required package: REBayes
Loading required package: Matrix
Loading required package: CVXR

Attaching package: 'CVXR'
The following object is masked from 'package:stats':

    power
Loading required package: PolynomF
Warning: package 'PolynomF' was built under R version 3.4.4
Loading required package: Rmosek
Loading required package: ashr

Attaching package: 'ashr'
The following object is masked from 'package:CVXR':

    get_np
plotx <- seq(-10, 10, length = 1000)
gd.ord <- 10
hermite = Hermite(gd.ord)
gd0.std = dnorm(plotx)
matrix_lik_plot = cbind(gd0.std)
for (i in 1 : gd.ord) {
  gd.std = (-1)^i * hermite[[i]](plotx) * gd0.std / sqrt(factorial(i))
  matrix_lik_plot = cbind(matrix_lik_plot, gd.std)
}
method.col <- scales::hue_pal()(gd.ord)
setEPS()
postscript("../output/paper/GD.eps", height = 4.5, width = 15)
#pdf("../output/paper/GD.pdf", height = 4.5, width = 15)

par(mfrow = c(1, 2))
par(mar = c(3, 6.5, 1, 1.5))
plot(plotx, gd0.std, type = "l", xlim = c(-5, 5), ylim = range(matrix_lik_plot), xlab = "", ylab = '', main = '', bty = 'n', lwd = 2)
title(ylab = latex2exp::TeX('$\\frac{1}{\\sqrt{\\textit{l}!}}\\varphi^{(\\textit{l})}(\\cdot)$'), line = 2.5, cex.lab = 1.5)
for (i in 1 : 4) {
  lines(plotx, matrix_lik_plot[, (i + 1)], col = method.col[i], lty = i + 1, lwd = 2)
}
legend("topright", col = c(1, method.col[1 : 4]), lty = 1 : 5, lwd = 2, bty = "n", cex = 1.5,
       c(latex2exp::TeX('$\\varphi$'), 
         latex2exp::TeX('$\\textit{l} = 1$'), 
         latex2exp::TeX('$\\textit{l} = 2$'), 
         latex2exp::TeX('$\\textit{l} = 3$'), 
         latex2exp::TeX('$\\textit{l} = 4$')
       ))

plot(plotx, gd0.std, type = "l", xlim = c(-5, 5), ylim = range(matrix_lik_plot), xlab = "", ylab = '', main = '', bty = 'n', lwd = 2)
title(ylab = latex2exp::TeX('$\\frac{1}{\\sqrt{\\textit{l}!}}\\varphi^{(\\textit{l})}(\\cdot)$'), line = 2.5, font = 1, cex.lab = 1.5)
for (i in 7 : 10) {
  lines(plotx, matrix_lik_plot[, (i + 1)], col = method.col[i], lty = i + 1, lwd = 2)
}
legend("topright", col = c(1, method.col[7 : 10]), lty = c(1, 8 : 11), lwd = 2, bty = "n", cex = 1.5,
       c(latex2exp::TeX('$\\varphi$'), 
         latex2exp::TeX('$\\textit{l} = 7$'), 
         latex2exp::TeX('$\\textit{l} = 8$'), 
         latex2exp::TeX('$\\textit{l} = 9$'), 
         latex2exp::TeX('$\\textit{l} = 10$')
       ))

dev.off()
quartz_off_screen 
                2

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] ashr_2.2-3        Rmosek_8.0.69     PolynomF_1.0-2    CVXR_0.99        
[5] REBayes_1.2       Matrix_1.2-12     SQUAREM_2017.10-1 EQL_1.0-0        
[9] ttutils_1.0-1    

loaded via a namespace (and not attached):
 [1] latex2exp_0.4.0   gmp_0.5-13.2      Rcpp_0.12.18     
 [4] plyr_1.8.4        compiler_3.4.3    git2r_0.21.0     
 [7] workflowr_1.1.1   R.methodsS3_1.7.1 R.utils_2.7.0    
[10] iterators_1.0.9   tools_3.4.3       digest_0.6.15    
[13] bit_1.1-12        evaluate_0.10.1   lattice_0.20-35  
[16] foreach_1.4.4     yaml_2.1.18       parallel_3.4.3   
[19] Rmpfr_0.7-1       ECOSolveR_0.4     stringr_1.3.0    
[22] knitr_1.20        rprojroot_1.3-2   bit64_0.9-7      
[25] grid_3.4.3        R6_2.2.2          rmarkdown_1.9    
[28] magrittr_1.5      whisker_0.3-2     scales_0.5.0     
[31] MASS_7.3-50       backports_1.1.2   codetools_0.2-15 
[34] htmltools_0.3.6   scs_1.1-1         colorspace_1.3-2 
[37] stringi_1.1.6     munsell_0.4.3     pscl_1.5.2       
[40] doParallel_1.0.11 truncnorm_1.0-7   R.oo_1.22.0

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