diff options
Diffstat (limited to 'report/figures/results')
56 files changed, 3087 insertions, 0 deletions
diff --git a/report/figures/results/1000_max.txt b/report/figures/results/1000_max.txt new file mode 100644 index 0000000..9ba19c3 --- /dev/null +++ b/report/figures/results/1000_max.txt @@ -0,0 +1,70 @@ + -8.00000000e+00 6.44968312e-04 + -7.79710145e+00 1.10565996e-03 + -7.59420290e+00 6.44968312e-04 + -7.39130435e+00 1.19779829e-03 + -7.18840580e+00 1.19779829e-03 + -6.98550725e+00 1.47421329e-03 + -6.78260870e+00 1.19779829e-03 + -6.57971014e+00 1.19779829e-03 + -6.37681159e+00 8.29244973e-04 + -6.17391304e+00 1.19779829e-03 + -5.97101449e+00 2.02704327e-03 + -5.76811594e+00 2.11918160e-03 + -5.56521739e+00 2.21131993e-03 + -5.36231884e+00 4.33050153e-03 + -5.15942029e+00 5.15974650e-03 + -4.95652174e+00 6.35754479e-03 + -4.75362319e+00 9.95093968e-03 + -4.55072464e+00 1.48342712e-02 + -4.34782609e+00 1.67691761e-02 + -4.14492754e+00 2.56144558e-02 + -3.94202899e+00 3.45518739e-02 + -3.73913043e+00 4.94782834e-02 + -3.53623188e+00 6.09034364e-02 + -3.33333333e+00 7.73961975e-02 + 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--git a/report/figures/results/1500_max.txt b/report/figures/results/1500_max.txt new file mode 100644 index 0000000..1072246 --- /dev/null +++ b/report/figures/results/1500_max.txt @@ -0,0 +1,70 @@ + -8.00000000e+00 7.50734414e-04 + -7.79710145e+00 4.69209009e-04 + -7.59420290e+00 1.12610162e-03 + -7.39130435e+00 9.38418018e-05 + -7.18840580e+00 4.69209009e-04 + -6.98550725e+00 1.31378522e-03 + -6.78260870e+00 1.12610162e-03 + -6.57971014e+00 1.12610162e-03 + -6.37681159e+00 1.68915243e-03 + -6.17391304e+00 2.43988685e-03 + -5.97101449e+00 1.68915243e-03 + -5.76811594e+00 3.94135567e-03 + -5.56521739e+00 4.31672288e-03 + -5.36231884e+00 4.78593189e-03 + -5.15942029e+00 7.69502774e-03 + -4.95652174e+00 1.18240670e-02 + -4.75362319e+00 1.55777391e-02 + -4.55072464e+00 2.05513546e-02 + -4.34782609e+00 2.95601676e-02 + -4.14492754e+00 3.92258731e-02 + -3.94202899e+00 4.69209009e-02 + -3.73913043e+00 6.47508432e-02 + -3.53623188e+00 7.07567185e-02 + -3.33333333e+00 9.43110108e-02 + 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--git a/report/figures/results/500_max.txt b/report/figures/results/500_max.txt new file mode 100644 index 0000000..2f6476b --- /dev/null +++ b/report/figures/results/500_max.txt @@ -0,0 +1,70 @@ + -8.00000000e+00 6.28392408e-04 + -7.79710145e+00 9.87473784e-04 + -7.59420290e+00 1.34655516e-03 + -7.39130435e+00 1.34655516e-03 + -7.18840580e+00 9.87473784e-04 + -6.98550725e+00 7.18162752e-04 + -6.78260870e+00 9.87473784e-04 + -6.57971014e+00 1.34655516e-03 + -6.37681159e+00 1.43632550e-03 + -6.17391304e+00 9.87473784e-04 + -5.97101449e+00 1.34655516e-03 + -5.76811594e+00 1.07724413e-03 + -5.56521739e+00 1.79540688e-03 + -5.36231884e+00 1.61586619e-03 + -5.15942029e+00 2.33402895e-03 + -4.95652174e+00 3.41127307e-03 + -4.75362319e+00 4.30897651e-03 + -4.55072464e+00 7.18162752e-03 + -4.34782609e+00 9.96450819e-03 + -4.14492754e+00 1.41837144e-02 + -3.94202899e+00 2.12755715e-02 + -3.73913043e+00 3.07912280e-02 + -3.53623188e+00 4.56033348e-02 + -3.33333333e+00 6.48141884e-02 + 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b/report/figures/results/pdf_stats.m new file mode 100644 index 0000000..dde2b25 --- /dev/null +++ b/report/figures/results/pdf_stats.m @@ -0,0 +1,21 @@ +function [skew, kurtosis] = pdf_stats(x,p) + + % Define some useful bits + dx = x(2) - x(1); + + % The expected value (From LibreTexts 4.1) + E = @(x) sum(x .* p) * dx; + + % First moment (mean) (From LibreTexts 4.3) + mu = E(x); + + % Second moment (variance) (From LibreTexts 4.3) + sigma = sqrt(E((x - mu).^2)); + + % Third moment (skewness) (From LibreTexts 4.4) + skew = E(((x - mu)/sigma).^3); + + % Fourth moment (excess kurtosis) (From LibreTexts 4.4) + kurtosis = E(((x - mu)/sigma).^4) - 3; + +end diff --git a/report/figures/results/plot.gnu b/report/figures/results/plot.gnu new file mode 100644 index 0000000..53517b3 --- /dev/null +++ b/report/figures/results/plot.gnu @@ -0,0 +1,104 @@ +#set term x11 persist +set term cairolatex pdf size 6in,6in +set output "size_pts.tex" +set linetype 1 lc rgb '#E41A1C' # red +set linetype 2 lc rgb '#377EB8' # blue +set linetype 3 lc rgb '#4DAF4A' # green + +set key samplen 2 +set grid +set xlabel "x" +set ylabel "p(x)" + +set style fill transparent solid 0.5 border -1 + +set multiplot layout 3,2 + +set title "$N$=1750, $L$=128, $S$=$-$0.169, $K$=0.139" +plot 'N1750_L128.txt' using 1:2 with boxes lt 2 notitle, \ + '../tracy-widom-approx/tracy_widom_normal.txt' using 1:2 with lines lt 1 lw 5 notitle + +set title "$N$=500, $L$=128, $S$=0.227, $K$=0.753" +plot 'N500_L128.txt' using 1:2 with boxes lt 2 notitle, \ + '../tracy-widom-approx/tracy_widom_normal.txt' using 1:2 with lines lt 1 lw 5 notitle + +set title "$N$=1750, $L$=2048, $S$=$-$0.044, $K$=0.065" +plot 'N1750_L2048.txt' using 1:2 with boxes lt 2 notitle, \ + '../tracy-widom-approx/tracy_widom_normal.txt' using 1:2 with lines lt 1 lw 5 notitle + +set title "$N$=500, $L$=2048, $S$=0.187, $K$=0.204" +plot 'N500_L2048.txt' using 1:2 with boxes lt 2 notitle, \ + '../tracy-widom-approx/tracy_widom_normal.txt' using 1:2 with lines lt 1 lw 5 notitle + +set title "$N$=1750, $L$=4096, $S$=$-$0.045, $K$=0.072" +plot 'N1750_L4096.txt' using 1:2 with boxes lt 2 notitle, \ + '../tracy-widom-approx/tracy_widom_normal.txt' using 1:2 with lines lt 1 lw 5 notitle + +set title "$N$=500, $L$=4096, $S$=0.140, $K$=0.218" +plot 'N500_L4096.txt' using 1:2 with boxes lt 2 notitle, \ + '../tracy-widom-approx/tracy_widom_normal.txt' using 1:2 with lines lt 1 lw 5 notitle + +unset multiplot + +set terminal cairolatex pdf size 6in,3in +set output "single.tex" +unset title +set lmargin at screen 0.15 +set rmargin at screen 0.85 + +plot 'N1750_L4096.txt' using 1:2 with boxes title '$N=1750,\, L=4096$' lt 2, \ + '../tracy-widom-approx/tracy_widom_normal.txt' using 1:2 with lines title 'TW\textsubscript{1}' lt 1, \ + '../tracy-widom-approx/tracy_widom_normal.txt' using 1:3 with lines title 'N(0,1)' dt 2 lt 3 + + +set terminal cairolatex pdf size 6in, 6in +set output "maxcomp.tex" +#set term x11 persist +set multiplot layout 3,2 + +unset lmargin +unset rmargin + +set title "$N$=500" +plot '500_max.txt' using 1:2 with boxes notitle lt 3, \ + '../tracy-widom-approx/tracy_widom_normal.txt' using 1:2 with lines lt 1 lw 5 notitle +set title "$N$=750" +plot '750_max.txt' using 1:2 with boxes notitle lt 3, \ + '../tracy-widom-approx/tracy_widom_normal.txt' using 1:2 with lines lt 1 lw 5 notitle +set title "$N$=1000" +plot '1000_max.txt' using 1:2 with boxes notitle lt 3, \ + '../tracy-widom-approx/tracy_widom_normal.txt' using 1:2 with lines lt 1 lw 5 notitle +set title "$N$=1250" +plot '1250_max.txt' using 1:2 with boxes notitle lt 3, \ + '../tracy-widom-approx/tracy_widom_normal.txt' using 1:2 with lines lt 1 lw 5 notitle +set title "$N$=1500" +plot '1500_max.txt' using 1:2 with boxes notitle lt 3, \ + '../tracy-widom-approx/tracy_widom_normal.txt' using 1:2 with lines lt 1 lw 5 notitle +set title "$N$=1750" +plot '1750_max.txt' using 1:2 with boxes notitle lt 3, \ + '../tracy-widom-approx/tracy_widom_normal.txt' using 1:2 with lines lt 1 lw 5 notitle + +unset multiplot + +#set term x11 persist +set terminal cairolatex pdf size 6in,3in +set output "parameters.tex" +unset title +set lmargin at screen 0.15 +set rmargin at screen 0.85 + +set arrow from 400,0.2935 to 1800,0.2935 nohead lt 1 dt 3 lw 8 +set arrow from 400,0.1292 to 1800,0.1292 nohead lt 2 dt 3 lw 8 + +set xlabel "$N$" +set ylabel "Skewness/Excess Kurtosis" + +set y2tics +set ytics nomirror +set y2label "Error [\\%]" +set key outside top center horizontal + +plot 'props.txt' using 1:2 with linespoints lt 1 pt 7 ps 0.4 title "Skewness" axes x1y1, \ + 'props.txt' using 1:(($2-0.2935)/(0.2935)*100) with lines lt 1 dt 2 axes x1y2 title "Skewness Error", \ + 'props.txt' using 1:3 with linespoints lt 2 pt 7 ps 0.4 title "Excess Kurtosis" axes x1y1, \ + 'props.txt' using 1:(($3-0.1292)/(0.1292)*100) with lines lt 2 dt 2 axes x1y2 title "Excess Kurtosis Error" diff --git a/report/figures/results/plot_results.m b/report/figures/results/plot_results.m new file mode 100644 index 0000000..f6c1713 --- /dev/null +++ b/report/figures/results/plot_results.m @@ -0,0 +1,104 @@ +close all; +clear; clc; + +% Get all results files +files = dir("../../../results/*.out"); +tw = load("../tracy-widom-approx/tracy_widom_normal.txt"); +x = tw(:,1); +tw1 = tw(:,2); +nrm = tw(:,3); + +N_list = [] + +%% Make a histogram for every results file + +for f = 1:length(files) + + % Get filename + filename = files(f).name; + + % Extract N and L + tokens = regexp(filename,'eigs_(\d+)_(\d+)\.out', 'tokens'); + N = str2double(tokens{1}{1}); + N_list = [N_list, N]; + L = str2double(tokens{1}{2}); + + % Import actual data + data = load(strcat("../../../results/",filename)); + % And clip to just the eigenvalues + data = data(:,2); + + % Remove outliers + data_clean = data(data > sqrt(N)); + + % Scale and such + s_data = (data_clean - 2*sqrt(N))*N^(1/6); + + % Plot them + figure(f); + title([num2str(N)," matrix size, ",num2str(L)," data points"]) + hold on + [counts, bins] = hist(s_data(s_data > -6), linspace(-6,4,40)); + bin_width = bins(2)-bins(1); + pdf = counts/(sum(counts) * bin_width); + bar(bins, pdf); + plot(x,tw1); + A = [bins', pdf'] + save("-ascii",["N",num2str(N),"_L",num2str(L),".txt"],"A") +end + +%% Plot largest sample size for each matrix size N + +skews = []; +kurts = []; +i = 0; +% Plot totals +for n = unique(N_list) + i = i + 1; + + % Plot all histogram values for this N + n_files = dir(strcat("../../../results/eigs_",num2str(n),"_*.out")); + n_vals = []; + SSE = []; + + % Get cumulative values + for f = 1:length(n_files) + filename = n_files(f).name; + data = load(strcat("../../../results/",filename)); + data = data(:,2); + data_clean = data(data > sqrt(n)); + s_data = (data_clean -2*sqrt(n)) * n^(1/6); + n_vals = [n_vals, s_data']; + end + + % Plot a histogram showing the Gaussian, TW1, and sampled distribution + figure(n) + title(num2str(length(n_vals))) + hold on + + % Generate the histogram + [counts, bins] = hist(n_vals(n_vals > -8), linspace(-8,6,70)); + bin_width = bins(2)-bins(1); + pdf = counts/(sum(counts) * bin_width); + + % And plot it + bar(bins,pdf) + plot(bins, pdf); + plot(x,nrm,'--') + plot(x,tw1); + + % Save the histogram to file + A = [bins', pdf'] + save("-ascii",[num2str(n),"_max.txt"], "A") + + % Calculate some statistics + [skews(i),kurts(i)]=pdf_stats(bins,pdf); +end + +figure(n+1) +plot(unique(N_list),skews) +hold on +plot(unique(N_list),kurts) +set(gca, "xtick", unique(N_list)) +A = [unique(N_list)', skews', kurts'] +save -ascii props.txt A diff --git a/report/figures/results/props.txt b/report/figures/results/props.txt new file mode 100644 index 0000000..9c9dc45 --- /dev/null +++ b/report/figures/results/props.txt @@ -0,0 +1,6 @@ + 5.00000000e+02 -8.99346072e-03 8.58814716e-01 + 7.50000000e+02 -5.74508029e-02 7.66588276e-01 + 1.00000000e+03 -9.21968249e-02 6.92386742e-01 + 1.25000000e+03 -1.18510028e-01 6.61642693e-01 + 1.50000000e+03 -1.18784301e-01 4.56704146e-01 + 1.75000000e+03 -1.47054483e-01 4.22739414e-01 diff --git a/report/figures/results/single.pdf b/report/figures/results/single.pdf Binary files differnew file mode 100644 index 0000000..8e3e557 --- /dev/null +++ b/report/figures/results/single.pdf diff --git a/report/figures/results/single.tex b/report/figures/results/single.tex new file mode 100644 index 0000000..e6b85f9 --- /dev/null +++ b/report/figures/results/single.tex @@ -0,0 +1,130 @@ +% GNUPLOT: LaTeX picture with Postscript +\begingroup + \makeatletter + \providecommand\color[2][]{% + \GenericError{(gnuplot) \space\space\space\@spaces}{% + Package color not loaded in conjunction with + terminal option `colourtext'% + }{See the gnuplot documentation for explanation.% + }{Either use 'blacktext' in gnuplot or load the package + color.sty in LaTeX.}% + \renewcommand\color[2][]{}% + }% + \providecommand\includegraphics[2][]{% + \GenericError{(gnuplot) \space\space\space\@spaces}{% + Package graphicx or graphics not loaded% + }{See the gnuplot documentation for explanation.% + }{The gnuplot epslatex terminal needs graphicx.sty or graphics.sty.}% + \renewcommand\includegraphics[2][]{}% + }% + \providecommand\rotatebox[2]{#2}% + \@ifundefined{ifGPcolor}{% + \newif\ifGPcolor + \GPcolortrue + }{}% + \@ifundefined{ifGPblacktext}{% + \newif\ifGPblacktext + \GPblacktexttrue + }{}% + % define a \g@addto@macro without @ in the name: + \let\gplgaddtomacro\g@addto@macro + % define empty templates for all commands taking text: + \gdef\gplbacktext{}% + \gdef\gplfronttext{}% + \makeatother + \ifGPblacktext + % no textcolor at all + \def\colorrgb#1{}% + \def\colorgray#1{}% + \else + % gray or color? + \ifGPcolor + \def\colorrgb#1{\color[rgb]{#1}}% + \def\colorgray#1{\color[gray]{#1}}% + \expandafter\def\csname LTw\endcsname{\color{white}}% + \expandafter\def\csname LTb\endcsname{\color{black}}% + \expandafter\def\csname LTa\endcsname{\color{black}}% + \expandafter\def\csname 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`colourtext'% + }{See the gnuplot documentation for explanation.% + }{Either use 'blacktext' in gnuplot or load the package + color.sty in LaTeX.}% + \renewcommand\color[2][]{}% + }% + \providecommand\includegraphics[2][]{% + \GenericError{(gnuplot) \space\space\space\@spaces}{% + Package graphicx or graphics not loaded% + }{See the gnuplot documentation for explanation.% + }{The gnuplot epslatex terminal needs graphicx.sty or graphics.sty.}% + \renewcommand\includegraphics[2][]{}% + }% + \providecommand\rotatebox[2]{#2}% + \@ifundefined{ifGPcolor}{% + \newif\ifGPcolor + \GPcolortrue + }{}% + \@ifundefined{ifGPblacktext}{% + \newif\ifGPblacktext + \GPblacktexttrue + }{}% + % define a \g@addto@macro without @ in the name: + \let\gplgaddtomacro\g@addto@macro + % define empty templates for all commands taking text: + \gdef\gplbacktext{}% + \gdef\gplfronttext{}% + \makeatother + \ifGPblacktext + % no textcolor at all + \def\colorrgb#1{}% + \def\colorgray#1{}% + \else + % gray or color? + 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\put(7675,450){\makebox(0,0){\strut{}$2$}}% + \csname LTb\endcsname%% + \put(8283,450){\makebox(0,0){\strut{}$4$}}% + }% + \gplgaddtomacro\gplfronttext{% + \csname LTb\endcsname%% + \put(4496,1457){\rotatebox{-270.00}{\makebox(0,0){\strut{}p(x)}}}% + \csname LTb\endcsname%% + \put(6763,143){\makebox(0,0){\strut{}x}}% + \csname LTb\endcsname%% + \put(6763,2566){\makebox(0,0){\strut{}$N$=500, $L$=4096, $S$=0.140, $K$=0.218}}% + }% + \gplbacktext + \put(0,0){\includegraphics[width={432.00bp},height={432.00bp}]{size_pts}}% + \gplfronttext + \end{picture}% +\endgroup diff --git a/report/figures/results/sk_tester.m b/report/figures/results/sk_tester.m new file mode 100644 index 0000000..c396934 --- /dev/null +++ b/report/figures/results/sk_tester.m @@ -0,0 +1,14 @@ +close all; +clear; clc; + +N = [1750, 500]; +L = [128, 2048, 4096]; + +for n = N + for l = L + % Read the data + data = load(["N",num2str(n),"_L",num2str(l),".txt"]); + [skew, kurt] = pdf_stats(data(:,1),data(:,2)); + fprintf("N=%i, L=%i: skew=%f, kurt=%f\n",n,l,skew,kurt) + end +end diff --git a/report/figures/results/tracywidom_appx.m b/report/figures/results/tracywidom_appx.m new file mode 100644 index 0000000..bbab815 --- /dev/null +++ b/report/figures/results/tracywidom_appx.m @@ -0,0 +1,38 @@ +function [pdftwappx, cdftwappx] = tracywidom_appx(x, i) +% +% +% [pdftwappx, cdftwappx]=tracywidom_appx(x, i) +% +% SHIFTED GAMMA APPROXIMATION FOR THE TRACY-WIDOM LAWS, by M. Chiani, 2012 +% +% TW ~ Gamma[k,theta]-alpha +% +% [pdf,cdf]=tracywidom_appx(x,2) gives the approximated pdf(x) and CDF(x) of the TW2 +% +% [pdf,cdf]=tracywidom_appx(x,i) for i=1,2,4 gives TW1, TW2, TW4 +% +% see paper M.Chiani, "Distribution of the largest eigenvalue for real +% Wishart and Gaussian random matrices and a simple approximation for the +% Tracy-Widom distribution", submitted 2012, ArXiv +% +kappx = [46.44604884387787, 79.6594870666346, 0, 146.0206131050228]; % K, THETA, ALPHA +thetaappx = [0.18605402228279347, 0.10103655775856243, 0, 0.05954454047933292]; +alphaappx = [9.848007781128567, 9.819607173436484, 0, 11.00161520109004]; +cdftwappx = cdfgamma(x+alphaappx(i), thetaappx(i), kappx(i)); % Chiani's appx: Tracy-Widom as a shifted Gamma +pdftwappx = pdfgamma(x+alphaappx(i), thetaappx(i), kappx(i)); % Chiani's appx: Tracy-Widom as a shifted Gamma +end +function [pdfgamma]=pdfgamma(x, ta, ka) % Utility: PDF of a Gamma + if(x > 0) + pdfgamma=1/(gamma(ka)*ta^ka) * x.^(ka - 1) .* exp(-x/ta); + else + pdfgamma=0 ; + end +end +function[cdfgamma]=cdfgamma(x, ta, ka) % Utility: CDF of a Gamma + if(x > 0) + cdfgamma=gammainc(x/ta,ka); + else + cdfgamma=0; + end + +end |