用 Matlab 计算并画出大量数据的CDF

     这篇 blog 将展示用 matlab 计算并画出大量数据的 CDF （累计分布函数）的两种方法。第一种是我自己于2012年写的，后来用的过程中发现有缺陷；后来2014年写另一篇paper时，搜寻到第二种简易又高效的方法。这里我给出它们各自的用例，包括画图用的数据与脚本，以及效果图。For your reference.

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     Section A. 第一种方法

     今天(2012-10-17)有一些数据需要处理，这些数据好不容易从文件中剥离了出来，然后自己写了一个function，计算并控制 plot 这些数据的 CDF 图。因为第一种方法用到的例子的数据文件太大，就没有贴上来。如果有想亲自试验一下这个过程的同学，请参照下文中第二个方法中的完整用例。

% ----------------------- 自实现 CDF 计算 function:  funcCDF.m

% para@1: CNT_pnts, the number of points to denote the CDF;% para@2: Range_low, the lower bound of variable;% para@3: Range_up, the upper bound of variable;% para@4 : arr_Vals, array of the values to be processed.function [x, CDF_Vals] = funcCDF(CNT_pnts, Range_low, Range_up, arr_Vals)data = sort( arr_Vals' ); % T', horizon arrays of T.N = length(data);stepLen = (Range_up-Range_low)/CNT_pnts;Counter = zeros(1,CNT_pnts);for i = 1:1:Nfor j = 1:1:CNT_pntsif ( data(1,i) <= (Range_low + j*stepLen) )Counter(1,j) = Counter(1,j) + 1;endendendCDF = Counter(1,:)./N;CDF_Vals = CDF(1,:)';x = (Range_low+stepLen):stepLen:Range_up;% ---- end of func.

% --------------------- 2 use cases：

CNT_pnts = 100;deadline_N500r1 = 550;deadline_N500r3 = 270;deadline_N500r5 = 240;PntVal_N500Tau100r1 = textread('N500Tau100r1.tr','%*s %*s %*s %*s %*s %*s %*s %*s %*s %*s %*s %.2f');[x_r1,cdf_r1] = funcCDF(CNT_pnts, 0, deadline_N500r1, PntVal_N500Tau100r1);plot(x_r1, cdf_r1, 'ob')hold onPntVal_N500Tau100r3 = textread('N500Tau100r3.tr','%*s %*s %*s %*s %*s %*s %*s %*s %*s %*s %*s %.2f');[x_r3,cdf_r3] = funcCDF(CNT_pnts, 0, deadline_N500r3, PntVal_N500Tau100r3);plot(x_r3, cdf_r3, 'or')hold onPntVal_N500Tau100r5 = textread('N500Tau100r5.tr','%*s %*s %*s %*s %*s %*s %*s %*s %*s %*s %*s %.2f');[x_r5,cdf_r5] = funcCDF(CNT_pnts, 0, deadline_N500r5, PntVal_N500Tau100r5);plot(x_r5, cdf_r5, 'oc')grid

% --------------------- 3 效果图：

Fig.1 CDF_N200r3--Tau-60-80-100-100Pnts

Fig.2 CDF_N500Tau100--r-1-3-5-100Pnts

      当把参数 CNT_pnts = 100; 调为 CNT_pnts = 50; 后，显示在图中的点就会减少一半，shows as follow:

Fig.3 CDF_N500Tau100--r-1-3-5-50Pnts

Davy_H （2012-10-17）

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    Section B. 第二种方法

    今天(2014-10-15) 回过头来看这篇blog，前边贴的图太丑，而且其实第一种方法有不完美的地方，即数据少的时候，曲线有时不会从原点开始画。后来寻到更好的方法来画 CDF 图，为了对得起2000+的访问量，所以，今日我决定花些时间，把更好的例子分享出来。

    废话不多说：1）效果图；2）部分数据文件；3）画图的脚本。

1) ------------------ 

2) ------------------ _Trace_file.tr

-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 134-C_FillUp 35-Cost_OPT 77-CNT_STimes 24-Thresh 0-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 113-C_FillUp 75-Cost_OPT 43-CNT_STimes 36-Thresh 0-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 115-C_FillUp 88-Cost_OPT 26-CNT_STimes 36-Thresh 0-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 84-C_FillUp 38-Cost_OPT 44-CNT_STimes 28-Thresh 0-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 100-C_FillUp 73-Cost_OPT 35-CNT_STimes 30-Thresh 0-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 104-C_FillUp 54-Cost_OPT 38-CNT_STimes 36-Thresh 0-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 88-C_FillUp 48-Cost_OPT 41-CNT_STimes 30-Thresh 0-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 140-C_FillUp 63-Cost_OPT 80-CNT_STimes 21-Thresh 0.01-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 134-C_FillUp 90-Cost_OPT 55-CNT_STimes 16-Thresh 0.01-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 131-C_FillUp 76-Cost_OPT 62-CNT_STimes 15-Thresh 0.01-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 100-C_FillUp 59-Cost_OPT 53-CNT_STimes 17-Thresh 0.01-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 118-C_FillUp 77-Cost_OPT 46-CNT_STimes 9-Thresh 0.01-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 118-C_FillUp 90-Cost_OPT 67-CNT_STimes 15-Thresh 0.01-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 151-C_FillUp 30-Cost_OPT 123-CNT_STimes 4-Thresh 0.05-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 83-C_FillUp 59-Cost_OPT 20-CNT_STimes 5-Thresh 0.05-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 124-C_FillUp 105-Cost_OPT 2-CNT_STimes 5-Thresh 0.05-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 140-C_FillUp 88-Cost_OPT 91-CNT_STimes 4-Thresh 0.05-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 107-C_FillUp 88-Cost_OPT 17-CNT_STimes 3-Thresh 0.05-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 177-C_FillUp 77-Cost_OPT 77-CNT_STimes 2-Thresh 0.05-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 133-C_FillUp 90-Cost_OPT 27-CNT_STimes 2-Thresh 0.05-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 140-C_FillUp 110-Cost_OPT 32-CNT_STimes 1-Thresh 0.1-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 115-C_FillUp 97-Cost_OPT 33-CNT_STimes 1-Thresh 0.1-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 130-C_FillUp 96-Cost_OPT 46-CNT_STimes 2-Thresh 0.1-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 148-C_FillUp 109-Cost_OPT 66-CNT_STimes 1-Thresh 0.1-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 144-C_FillUp 105-Cost_OPT 48-CNT_STimes 1-Thresh 0.1-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 137-C_FillUp 96-Cost_OPT 58-CNT_STimes 2-Thresh 0.1-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 116-C_FillUp 91-Cost_OPT 52-CNT_STimes 1-Thresh 0.1-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 117-C_FillUp 97-Cost_OPT 31-CNT_STimes 1-Thresh 0.1-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 149-C_FillUp 96-Cost_OPT 48-CNT_STimes 3-Thresh 0.2-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 127-C_FillUp 106-Cost_OPT 32-CNT_STimes 2-Thresh 0.2-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 108-C_FillUp 87-Cost_OPT 36-CNT_STimes 2-Thresh 0.2-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 134-C_FillUp 105-Cost_OPT 25-CNT_STimes 2-Thresh 0.2-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 140-C_FillUp 79-Cost_OPT 37-CNT_STimes 1-Thresh 0.2-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 158-C_FillUp 107-Cost_OPT 48-CNT_STimes 2-Thresh 0.2-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 142-C_FillUp 99-Cost_OPT 37-CNT_STimes 1-Thresh 0.2-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 114-C_FillUp 92-Cost_OPT 41-CNT_STimes 1-Thresh 0.2-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 158-C_FillUp 64-Cost_OPT 103-CNT_STimes 2-Thresh 0.3-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 151-C_FillUp 108-Cost_OPT 45-CNT_STimes 1-Thresh 0.3-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 115-C_FillUp 74-Cost_OPT 43-CNT_STimes 2-Thresh 0.3-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 147-C_FillUp 110-Cost_OPT 47-CNT_STimes 1-Thresh 0.3-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 154-C_FillUp 67-Cost_OPT 114-CNT_STimes 2-Thresh 0.3-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 152-C_FillUp 92-Cost_OPT 68-CNT_STimes 1-Thresh 0.3-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 132-C_FillUp 74-Cost_OPT 42-CNT_STimes 2-Thresh 0.3-T 60-K 10-N_HC 30-N_S 30-C_DFLOWA 111-C_FillUp 83-Cost_OPT 29-CNT_STimes 1-Thresh 0.3

3) ------------------ Codes:

clear;% --------------- A. Read the Data.X_ = textread('_Trace_file.tr','%*s%*s %*s%*s %*s%*s %*s%*s %*s%*s %*s%*s %*s%*s %*s%*s %*s%f');CNT_resolve_times = textread('_Trace_file.tr','%*s%*s %*s%*s %*s%*s %*s%*s %*s%*s %*s%*s %*s%*s %*s%d %*s%*s' );% --------------- B. Count the the Costs.% --------- X_items is the "-Threshold"X_items =[0.0,0.01,0.05,0.1,0.2,0.3];CNT_X = length(X_items);% --------- Define the range_x of the x_coordinate in the figure.step = 1;range_end = 50;range_x = 0:step:range_end;figure% ---------- Format of figure:TextFontSize=18;LegendFontSize = 16;set(0,'DefaultAxesFontName','Times',...'DefaultLineLineWidth',2,...'DefaultLineMarkerSize',8);set(gca,'FontName','Times New Roman','FontSize',TextFontSize);set(gcf,'Units','inches','Position',[0 0 6.0 4.0]);% ---------- Format of figure:~% ------ Plot linesfor i = 1:1:CNT_XVal_item = X_items(i);idx_it_Lazy = find( X_ == Val_item );% --- 1 CNT_STimesCNT_Re_times_its = [];CNT_Re_times_its = CNT_resolve_times( idx_it_Lazy );% --- 2 Plot CDF of CNT_Resloving_times, i.e., the "CNT_STimes" in the trace file.if (i==1) linePoint_type = '-sk'; step = 5; range_x = 0:step:range_end;elseif (i==2) linePoint_type = '-^r';elseif (i==3) linePoint_type = '-+b'; step = 1; range_x = 0:step:range_end;elseif (i==4) linePoint_type = '-c';  step = 1; range_x = 0:step:range_end;elseif (i==5) linePoint_type = '--g'; step = 1; range_x = 0:step:range_end;elseif (i==6) linePoint_type = '-.m'; step = 1; range_x = 0:step:range_end;end%%% ====== Critical Code of CDF-Ploting :h_rtl = hist( CNT_Re_times_its, range_x );pr_approx_cdf = cumsum(h_rtl) / ( sum(h_rtl) );%%% ====== Critical Code of CDF-Ploting :~handler = plot( range_x, pr_approx_cdf, linePoint_type );if(i==4) h4 = handler;elseif(i==5) h5 = handler;elseif(i==6) h6 = handler;endhold onend% --------- Set the other formats of the figure :grid offaxis([0 range_end 0 1.0])ylabel('CDF')xlabel('Resolving times')% --------- Plot the multi-legends :hg1=legend('{\it \chi_0}=0', '{\it \chi_0}=0.01', '{\it \chi_0}=0.05',  0);set(hg1,'FontSize',LegendFontSize);ah1 = axes('position',get(gca,'position'), 'visible','off');  hg2 = legend(ah1, [h4,h5,h6],  '{\it \chi_0}=0.10','{\it \chi_0}=0.20','{\it \chi_0}=0.30',  0);set(hg2,'FontSize',LegendFontSize);% --------- Plot the multi-legends :~% --------- Set the other formats of the figure :~

    关键代码处，我已经做了注释，此处再强调一下：

    1. 画 CDF 的2句关键代码，其中的3个 functions 请自己查询。

    %%% ====== Critical operation of CDF-Ploting :
    h_rtl = hist ( CNT_Re_times_its, range_x );
    pr_approx_cdf = cumsum(h_rtl) / ( sum(h_rtl) );
    %%% ====== Critical operation of CDF-Ploting :~

  

    2. for 循环中的那一段 if else 语句，是为了设置各条曲线的点线型( linePoint type ) 与 各条线上的取样点的密度。  

    3. 此外，从这个脚本里，也可以额外获取画多个图例 (plot multiple legends) 的方法。

Davy_H (2014-10-15)

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