用 Matlab 計算並畫出大量數據的CDF

   這篇 blog 將展示用 matlab 計算並畫出大量數據的 CDF （累計分佈函數）的兩種方法。第一種是我自己於2012年寫的，後來用的過程中發現有缺陷；後來2014年寫另一篇paper時，搜尋到第二種簡易又高效的方法。這裏我給出它們各自的用例，包括畫圖用的數據與腳本，以及效果圖。For your reference.

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     Section A. 第一種方法

     今天(2012-10-17)有一些數據需要處理，這些數據好不容易從文件中剝離了出來，然後自己寫了一個function，計算並控制 plot 這些數據的 CDF 圖。因爲第一種方法用到的例子的數據文件太大，就沒有貼上來。如果有想親自試驗一下這個過程的同學，請參照下文中第二個方法中的完整用例。

% ----------------------- 自實現 CDF 計算 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:N
    for j = 1:1:CNT_pnts
        if ( data(1,i) <= (Range_low + j*stepLen) )
            Counter(1,j) = Counter(1,j) + 1;
        end
    end
end
CDF = 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 on

PntVal_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 on

PntVal_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 效果圖：

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

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

      當把參數 CNT_pnts = 100; 調爲 CNT_pnts = 50; 後，顯示在圖中的點就會減少一半，shows as follow:

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

Davy_H （2012-10-17）

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    Section B. 第二種方法

    今天(2014-10-15) 回過頭來看這篇blog，前邊貼的圖太醜，而且其實第一種方法有不完美的地方，即數據少的時候，曲線有時不會從原點開始畫。後來尋到更好的方法來畫 CDF 圖，爲了對得起2000+的訪問量，所以，今日我決定花些時間，把更好的例子分享出來。

    廢話不多說：1）效果圖；2）部分數據文件；3）畫圖的腳本。

1) ------------------ 

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 lines
for i = 1:1:CNT_X
    Val_item = X_items(i);
    idx_it_Lazy = find( X_ == Val_item );

    % --- 1 CNT_STimes
    CNT_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;
    end
    hold on
end

% --------- Set the other formats of the figure :
    grid off
    axis([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 :~

    關鍵代碼處，我已經做了註釋，此處再強調一下：

    1. 畫 CDF 的2句關鍵代碼，其中的3個 functions 請自己查詢。

    %%% ====== 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 循環中的那一段 if else 語句，是爲了設置各條曲線的點線型( linePoint type ) 與 各條線上的取樣點的密度。  

    3. 此外，從這個腳本里，也可以額外獲取畫多個圖例 (plot multiple legends) 的方法。

y = evrnd(0,3,100,1);

cdfplot(y);

hold on;

x = -20:0.1:10;

f = evcdf(x,0,3);

plot(x,f,'m');

legend('Empirical','Theoretical','Location','NW')