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SERA Toolbox1 and Toolbox2 standalone versions

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This commit is contained in:
Konstantinos Leptokaropoulos
2019-07-05 10:31:31 +02:00
parent 6f5c52a565
commit 758751a7b0
71 changed files with 54733 additions and 3 deletions
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22
Magnitude_Complexity_TOOLBOX_D23_2/ADTestMagnitudes_VERSION_2/ADTestMag_Plot.m Normal file
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function ADTestMag_Plot(M,mmin,P,EPS,MTdistribution)
clf
EPS2=0.1;
xa=min(M):EPS2:max(M);xa1=[min(mmin) max(mmin)];
subplot(2,1,1);plot(mmin,P,'ro-','MarkerSize',12,'LineWidth',1,'MarkerFaceColor',[0.33 0.66 0.99]);
hold on;plot([min(M)-EPS max(M)],[0.05 0.05],'k--','Linewidth',2);xlim([min(M)-EPS max(M)]);
ylabel('p-value','FontSize',16);legend('p-value','0.05 line','Location','best');
if strcmp(MTdistribution,'exp');title('AD Test for Exponential Distribution','FontSize',16)
elseif strcmp(MTdistribution,'weibul');title('AD Test for Weibull Distribution','FontSize',16)
end
subplot(2,1,2);histogram(M,numel(xa),'FaceColor',[0.7 0.7 0.8]);set(gca,'YScale','log');hold on
xlim([min(M)-EPS max(M)]);xlabel('Data','FontSize',16);ylabel('N','FontSize',16);
title('Event Counts','FontSize',16)
cd Outputs_ADTestMag\;saveas(gcf,'ADTestMag_output.jpg');cd ../
end

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Magnitude_Complexity_TOOLBOX_D23_2/ADTestMagnitudes_VERSION_2/ADTestMag_V2_8.m Normal file
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% FUNCTION: ADTestMag
% VERSION: [Wrapper Standalone Version] V2.8
% COMPATIBLE with Matlab version 2017b or later
% TOOLBOX: "Magnitude Complexity Toolbox" within SERA Project
% DOCUMENT: "READ_ME_App_2A_v2_Description_ADTestMag.docx"
% --------------------------------------------------------------------------------------------------------
% Test performed for the distribution of a given dataset (time-series)
% the distributions to be tested are Exponential and Weibull
% ------------------------------------------------------------------------------------------------------
% OVERVIEW: This Application is a Matlab function which performs the
% Anderson-Darling (AD) test for testing the null hypothesis whether a given
% set of magnitudes, follows the Exponential or Weibull distribution. Please
% check also to the "ADTestMag_wrapper" and "ADTestMag_Plot" scripts
% for a specific application (scenario) and plotting results.
% -----------------------------------------------------------------------------------------------------
% AUTHORS: K. Leptokaropoulos, and P. Urban
% last updated: 01/2019, within SERA PROJECT, EU Horizon 2020 R&I
% programme under grant agreement No.730900
% CURRENT VERSION: v2.8 **** [Wrapper Standalone Version]
% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
% PLEASE refer to the accompanying document:
% "READ_ME_App_2A_v2_Description_ADTestMag.docx"
% for description of the Application and its requirements.
% ------------------------------------------------------------------------------------------------------
% DESCRIPTION:
% This function performs the Anderson-Darling test (e.g. Anderson & Darling,
% 1954; Marsaglia & Marsaglia, 2004) for testing the Null Hypothesis, H0, that
% a given set of magnitudes, follows the exponential or the weibull distribution
% This is accomplished as a function on minimum magnitude, therefore, multiple
% results are produced (iteration process). The corresponing p-values for the H0
% is the main output of the program. Before applying the AD test, the magnitude
% values are randomized within their round-off interval, following the formula
% introduced by Lasocki and Papadimitriou, 2006.
% -----------------------------------------------------------------------------------------------------
% ITERATION PROCESS:
% The AD test is perform with an iteration process for a variety of magnitude
% ranges. First the funstion is executed for magnitudes M, with Mmin<M<M1
% where M1 is the higher Magnitude in the selected Catalog. Then, the process
% is repeated for Mmin+EPS<M<M1, then for Mmin+2*EPS<M<M1, etc till
% Mmax<M<M1. Please see INPUT section for reference to the symbols.
% -----------------------------------------------------------------------------------------------------
% INPUT: The function takes as input any matlab vector (input parameter "M").
% The input data can be uploaded by the use of "ADTestMag_wrapper"
% script, from an ASCII file (e.g. *.txt). Such file should contain a vector
% (raw or column) of the Data that the User wishes to process. The User
% is afterwards requested to enter values for some additional parameters.
% Input Parameters Overview:
% --- M: Time-Series (e.g. Magnitude) vector, read i.e. from an ASCII
% file.
% --- EPS: Round-off interval, i.e. minimum non-zero difference of
% the input data. It also corresponds to step for calculations
% (AD test iterations process)
% --- MTdistribution: The User is requested to define the selected
% parameter distribution for which the null hypothesis is to be
% tested. Possible values: 'exp' for 'Exponential' and 'weibul' for
% 'Weibull' distribution.
% --- Mmin: Corresponds to the minumum input vector value (e.g.
% magnitude) for which the AD test is performed (cut-off value).
% For the magnitude case, it is recommended (yet, not restricted)
% to be equal to the catalog completeness threshold, Mc (if known).
% --- Mmax: Corresponds to the maximum input vector value (e.g.
% magnitude) to be considered as minimum thresohold for the
% AD test to be performed. The maximum value is the one for
% which the number of events with M>=Mmax is greater than
% 4 (i. e. the minimum possible sample for ADTestMag function
% exectution). The function automatically finds this value when the
% User sets a higher one.
% --- trials: Number of randomization realizations (trials) perfomed
% in order to diminish the influence of magnitude randomization
% on the resulting p-value. Recommended value: 100.
% ------------------------------------------------------------------------------------------------------
% OUTPUT:
% --- Output Report with parameters used and results
% ('Output_ADTestMag.txt file')
% --- Output Parameters:
% * P - The average of the p-values obtained by the defined
% number of trials performed (also exists within the
% output structure 'pval')
% * S - The corresponding standard deviation of the
% p-values obtained by the defined number of trials
% * pval - Structure with the vectors of p-values obtained by the
% defined number of trials for each minimum magnitude.
% The structure also contais parameters 'P' and 'mmin'.
% [NOTE: histograms of such p-values indicate that their
% distribution is not normal, neither even symmetric
% for a large number of cases]
% * mmin - vector with the minimum magnitudes to which
% the aforementioned output parameters correspond
% (also exists within the output structure 'pval')
% * NN - vector with number of events corresponding to
% each mmin value.
% * bval - b-value corresponding to each set defined by the
% aforementioned mmin values
% --- Output Figures:
% ____ [after running the auxiliary "ADTestMag_Plot" script] _____
% - Figure with average p-value (P parameter) as a function of
% mmin, together with a histogram of the events count per
% magnitude bin. The 0.05 significance level is plotted as well
% -------------------------------------------------------------------------------------------------------
% REFERENCES:
% -- Lasocki S. and E. E, Papadimitriou (2006), "Magnitude distribution
% complexity revealed in seismicity from Greece", J. Geophys. Res.,
% 111, B11309, doi:10.1029/2005JB003794.
% -- Anderson T. W., and D. A. Darling, (1954), "A test of goodness of fit",
% J. Amer. Stat. Assoc., 49, 765-769.
% -- Marsaglia, G., and J. Marsaglia (2004), "Evaluating the Anderson-Darling
% distribution", J. Stat. Soft., 9, 1-5.
% ------------------------------------------------------------------------------------------------------
% LICENSE
% This is free software: you can redistribute it and/or modify it under
% the terms of the GNU General Public License as published by the
% Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful, but
% WITHOUT ANY WARRANTY; without even the implied warranty
% of MERCHANTABILITY or FITNESS FOR A PARTICULAR
% PURPOSE. See the GNU General Public License for more details.
% ----------------------------------------------------------------------------------
function [pval,mmin,NN,P,S,bval]=ADTestMag_V2_8(M,EPS,MTdistribution,Mmin,Mmax,trials)
mkdir Outputs_ADTestMag
% Constrain mangitude limits within data range
if Mmin<min(M);Mmin=min(M);end
if Mmax>max(M);Mmax=max(M);end
% INPUT PARAMETERS ARE SPECIFIED AS FUNCTION ARGUMENTS
M=round(M/EPS)*EPS;
Mmin=floor(Mmin/EPS)*EPS;MMax=ceil(max(M)/EPS)*EPS;
Rp=round(-log10(EPS));
mags=Mmin:EPS:MMax;mags=round(mags/EPS)*EPS;
N=find(abs(mags-Mmax)<EPS/2);
% magnitude distribution to be tested
if strcmp(MTdistribution,'exp')==1;MTdist='Exponential';
elseif strcmp(MTdistribution,'weibul')==1;MTdist='Weibull';
end
% Anderson-Darling Test for exponentiality
% Loop for different magnitudes
for j=1:N
mmin(j)=Mmin+(j-1)*EPS;%mmin=round(mmin/EPS)*EPS;
m=M(M>=mmin(j)-EPS/2); % numel(m)
if numel(m)<4;warning(['insufficient events number for M>',num2str(mmin(j)-EPS)]);
N=j-1;mmin=mmin(1:N);Merr=1;break
else
Merr=0;cou=0;
for i=1:trials
[beta]=beta_AK_UT_Mbin(mmin(j),m,Rp);
[m_corr]=korekta(m,mmin(j),EPS,beta);
Mag=m_corr-min(m)+EPS/2;
[h1 p1]=adtest(Mag,'Distribution',MTdistribution);
h(i)=h1;p(i,j)=p1;
if p1<=0.0005+eps;cou=cou+1;else, cou=0;end
if cou==2;p(i:trials,j)=0.0005;break;end
end
end
NN(j)=numel(m);bval(j)=beta/log(10);sb(j)=bval(j)/sqrt(NN(j));
P(j)=mean(p(:,j));
S(j)=std(p(:,j)); % p-values are not normally distributed!!
clear b
end
% creating results for the report
for j=1:N
pval(j).p=p(:,j);
pval(j).mmin=mmin(j);
pval(j).P=P(j);
end
for i=1:length(P);
if P(i)<0.05;h_decision{i,1}='rejected';
else h_decision{i,1}='not_rejected';
end
end
%h_decision=h_decision';
RES=[mmin' NN' bval' P' S']
%SAVE OUTPUTS
cd Outputs_ADTestMag
SaveOuts(EPS,Mmin,Mmax,trials,RES,h_decision,MTdist,Merr)
%saveas(gcf,'Exponentiality_Output.jpg')
%print(gcf,'Exponentiality_Output.jpeg','-djpeg','-r300')
cd ../
end
%% ******************************************************************
% *************************** FUNCTIONS ***************************
% ****-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-****
%% --------------------------------------------------------------------------------------
function [beta]=beta_AK_UT_Mbin(Mmin,m,Rp)
%
% m - magnitude vector
% Mmin - completeness magitude threshold
% beta - beta value. b(G-R)=beta/log(10)
% Rp - Rounding precision, (1 - one decimal, 2 - two decimals, etc)
beta=1/(mean(m)-(Mmin-0.5*10^(-Rp)));
end
%% --------------------------------------------------------------------------------------
% % Magnitude randomization
%
function [m_corr]=korekta(m,Mmin,EPS,beta)
%
% m - magnitude vector
% Mmin - completeness magitude threshold
% beta - beta value. b(G-R)=beta/log(10)
% EPS - magnitude round-off interval
%
% m_corr - randomized magnitude vector
%
F1=1-exp(-beta*(m-Mmin-0.5*EPS));
F2=1-exp(-beta*(m-Mmin+0.5*EPS));
u=rand(size(m));
w=u.*(F2-F1)+F1;
m_corr=Mmin-log(1-w)./beta;
end
%% --------------------------------------------------------------------------------------------------------
% --------------------------------------- SAVE OUTPUTS in the report file ---------------------------------------
% Save Outputs
function SaveOuts(EPS,Mmin,Mmax,trials,RES,h_decision,MTdist,Merr)
% ---- Save *.txt file with Parameters Report ----
%cd Outputs/
fid=fopen('REPORT_ADTestMag.txt','w');
fprintf(fid,['PARAMETERS & RESULTS from DISTRIBUTION TESTING (created on ', datestr(now),')\n']);
fprintf(fid,'------------------------------------------------------------------------------------\n');
fprintf(fid,['<Round-off interval >: ', num2str(EPS),'\n']);
fprintf(fid,['<Data Distribution tested >: ', MTdist,'\n']);
fprintf(fid,['<Data Range for Analysis >: ', num2str(Mmin), ' to ', num2str(Mmax),'\n']);
fprintf(fid,['<Number of randomization trials >: ', num2str(trials),'\n']);
fprintf(fid,'------------------------------------------------------------------------------------\n');
fprintf(fid,['Mmin N b-value mean(p) std(p) Decision for H0 \n']);
fprintf(fid,[' from ',num2str(trials),' trials (0.05 significance)\n']);
for j=1:size(RES,1);
fprintf(fid,['%5.2f %6d %5.3f %5.4f %5.3f %s \n'],RES(j,:),h_decision{j});
end
if Merr==1;fprintf(fid,['insufficient events number for M>',num2str(RES(j,1))]);end
fclose(fid);
%saveas()
% Save Output Structure
% prompt={'\fontsize{12} Please enter output file name:'};
% name='Extract Output Structure';
% numlines=1;
% defaultanswer={'Tdata.mat'};
% opts.Interpreter='tex';
% answer=inputdlg(prompt,name,numlines,defaultanswer,opts);
% save(char(answer),'Tdata')
% cd ../
end

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Magnitude_Complexity_TOOLBOX_D23_2/ADTestMagnitudes_VERSION_2/ADTestMag_wrapper.m Normal file
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% This is a Wrapper Script for Performing the Anderson-Darling Test for testing
% the hypothesis that a given time-series (e.g. magnitude) follows the exponential
% or weibull distribution. The Matlab function "ADTestMag_v2_*.m" is executed for
% this purpose.The description of the function can be found in the comments within
% 'ADTestMag_V2_*.m' code. Here, the input data and parameters (i.e. arguments
% of the Function) are defined by the User. Please modify parameters in the script
% accordingly, the lines that can be modified are followed by a comment "- PLEASE SET".
% PLEASE REFER ALSO TO APPLCATION DOCUMENTATION:
% "READ_ME_App_2B_v2_Description_MM_MB.docx"
clc;clear
% STEP 1. DATA Upload:
cd Sample_Data % PLEASE Specify data directory path
vector=dlmread('test_vector.txt'); % PLEASE SET data (magnitude) vector input file
cd ../
% STEP 2. Minimum Vector Value Selection:
Mmin=0.0; % PLEASE SET
% STEP 3. Maximum Vector Value Selection:
Mmax=5.0; % PLEASE SET
% STEP 4. Parameter Round-off Interval:
EPS=0.1; % PLEASE SET
% STEP 5. Define number of Trials:
trials=100; % PLEASE SET (interger)
% STEP 6. Distribution Selection:
MTdistribution='exp'; % PLEASE SET ('exp' or 'weibul')
% STEP 7. RUN Function ['ADTestMag']
[pval, mmin, NN ,P ,S, bval]=ADTestMag_V2_8(vector,EPS,MTdistribution,Mmin,Mmax,trials);
% STEP 8. Optional: plotting results %PLEASE Comment next line to deactivate plotting
ADTestMag_Plot(vector,mmin,P,EPS,MTdistribution)

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Magnitude_Complexity_TOOLBOX_D23_2/ADTestMagnitudes_VERSION_2/Sample_Data/test_vector.txt Normal file
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1.7
0.8
1.8
1.5
1.7
0.8
1.7
2.1
0.9
1.3
1.1
1.9
2.3
1.7
1.9
1.4
1.5
1.6
1.5
2.7
2.9
1.3
1.2
0.9
2.7
1.4
1.2
1.4
1.7
1.5
1.4
1.5
2.4
2.7
1.7
2.1
1.0
1.7
2.3
1.3
1.7
1.2
1.8
1.5
1.7
1.1
1.6
1.3
1.1
1.3
1.2
1.1
2.1
0.9
1.5
1.5
0.9
2.1
1.5
2.0
3.4
2.7
2.1
1.8
2.1
1.4
2.6
0.8
1.5
4.1
1.7
2.0
2.1
1.7
2.1
2.0
1.7
2.2
1.7
2.1
2.2
1.5
3.6
2.0
1.5
1.5
2.0
1.8
1.3
1.5
2.8
1.3
1.5
1.9
1.5
2.4
1.6
0.5
1.8
1.4
1.6
1.5
2.2
1.4
1.5
1.9
2.5
3.2
2.9
1.0
1.4
1.8
2.0
2.2
1.4
1.6
1.8
2.0
1.3
2.8
1.4
1.3
1.1
1.8
1.6
1.1
0.8
1.4
1.0
1.7
1.3
1.5
1.7
3.2
1.9
1.6
2.1
1.6
1.7
1.9
1.6
2.6
1.2
2.3
2.1
2.1
1.8
1.4
1.1
1.9
3.3
1.4
1.6
1.8
1.7
2.4
1.6
1.7
2.2
2.9
2.7
1.3
2.2
1.4
1.9
1.6
1.4
2.0
1.5
1.5
2.1
1.8
3.3
1.5
1.3
1.9
1.3
1.9
3.8
1.7
1.2
2.2
1.7
1.6
2.3
1.6
1.8
2.7
1.5
1.4
1.5
1.6
1.3
1.6
1.1
2.0
1.8
0.8
2.5
1.7
1.9
1.8
3.2
1.1
1.9
2.9
1.1
1.7
1.8
1.6
1.6
1.9
1.4
1.6
1.5
1.7
1.6
1.8
1.3
1.4
0.6
1.4
1.2
1.8
1.7
1.6
1.3
1.6
1.5
2.4
2.0
2.1
2.5
1.8
1.4
2.0
1.1
1.4
2.5
1.5
1.9
1.9
1.6
1.2
1.3
2.8
2.8
2.7
2.4
2.6
2.3
1.0
1.6
1.3
2.0
0.8
1.7
0.7
1.1
1.2
0.6
1.1
0.9
3.1
0.9
1.0
2.0
1.6
1.1
1.0
1.2
2.3
1.5
2.2
1.2
1.6
2.6
1.4
1.3
1.9
1.6
2.2
1.7
2.0
2.4
1.3
1.6
1.8
1.7
1.7
2.1
2.2
2.3
1.8
2.3
1.7
1.4
1.6
2.5
1.3
1.1
1.4
3.0
1.2
1.7
1.7
1.8
2.2
1.7
2.1
2.9
1.8
1.8
2.1
1.7
1.2
2.3
1.2
1.5
1.7
1.8
1.4
1.5
2.7
2.4
1.6
1.9
2.2
1.6
1.6
1.9
1.7
1.8
1.8
2.0
1.0
1.2
1.3
1.6
2.9
1.5
1.3
1.4
1.3
1.7
1.8
1.9
1.9
3.7
1.5
2.0
1.6
1.6
1.5
2.5
4.2
1.6
3.6
1.9
1.8
2.0
1.8
3.0
2.4
1.2
1.5
2.8
2.8
1.7
1.8
2.3
1.5
1.5
1.9
1.9
1.8
1.2
1.2
1.3
2.1
2.0
1.8
1.7
1.6
1.9
1.9
2.0
1.7
1.8
1.2
2.1
0.8
2.2
1.9
1.6
1.0
2.1
2.3
1.6
1.2
1.9
1.7
2.3
1.8
3.3
1.7
2.5
2.0
1.2
1.5
2.5
1.8
2.7
1.2
3.4
1.6
2.4
1.6
2.2
0.6
2.0
1.9
1.6
2.4
1.4
1.3
1.1
2.3
0.5
0.7
0.8
1.8
1.5
1.0
2.3
1.7
0.5
1.8
2.7
2.5
1.5
2.1
5.8
1.5
1.1
1.5
2.4
2.2
1.2
1.9
1.0
2.0
1.2
1.1
1.5
1.9
0.5
2.5
1.6
1.4
1.9
2.5
1.3
2.1
1.6
1.6
1.3
1.7
1.5
2.1
1.6
1.5
3.2
1.2
2.6
1.4
1.3
1.6
1.7
1.4
1.6
1.8
1.5
1.9
0.9
2.6
1.6
1.8
2.1
1.6
1.2
0.8
1.6
1.2
0.7
1.1
3.1
2.4
2.1
2.2
3.0
1.6
1.8
1.5
3.2
1.1
1.4
1.9
1.2
1.9
1.4
2.4
1.8
1.3
1.8
2.3
1.9
1.9
1.5
1.2
1.6
1.5
2.4
1.9
1.5
1.8
1.7
1.8
2.2
1.5
1.6
2.3
1.8
2.7
1.7
2.0
3.0
1.8
2.1
1.5
1.0
1.9
1.7
2.6
2.7
2.0
1.5
1.9
1.7
2.1
1.7
1.3
1.6
2.9
3.1
1.7
2.4
1.3
2.0
2.0
1.7
4.6
2.6
1.5
2.0
1.3
1.4
1.8
1.4
1.3
1.9
1.4
1.7
1.5
1.7
0.9
1.9
1.3
1.2
1.4
1.4
1.3
1.1
1.3
2.1
1.5
1.9
1.9
4.6
1.1
1.0
1.7
1.2
1.7
0.6
1.3
1.7
1.8
1.9
1.6
1.6
1.7
1.8
2.2
1.7
1.4
1.1
1.1
1.5
1.7
1.8
1.3
1.1
1.7
1.6
0.9
1.8
1.8
1.2
1.3
1.6
0.8
1.4
2.2
1.8
1.5
1.9
2.0
1.7
1.6
1.0
0.8
1.5
2.1
1.4
2.7
1.5
1.1
1.2
1.7
2.2
2.1
1.6
1.2
1.6
1.8
1.1
2.3
1.2
1.6
1.4
1.7
1.6
1.0
1.5
1.8
2.0
1.5
3.0
1.7
2.0
1.7
2.4
2.7
1.5
1.3
2.2
3.3
1.4
2.1
2.0
1.7
1.4
2.1
1.7
2.3
1.2
1.7
1.5
1.7
1.7
2.3
1.8
1.5
2.7
2.3
3.0
2.4
2.4
2.9
1.7
1.5
1.0
2.5
1.7
1.9
2.0
1.8
1.4
2.1
1.6
2.3
1.7
2.3
2.7
1.8
1.4
1.6
1.7
1.2
2.5
1.5
1.9
1.4
1.9
1.5
1.9
1.4
1.7
1.5
1.5
1.6
2.1
1.7
2.3
1.0
1.5
1.5
1.4
0.9
2.8
1.6
2.1
1.8
1.7
2.3
1.8
2.0
1.3
2.1
2.0
0.5
1.2
1.2
2.2
2.2
0.8
1.2
1.8
1.0
1.9
2.0
1.7
1.9
2.5
1.1
2.2
1.1
1.4
1.4
1.7
2.1
1.4
2.0
1.9
1.7
2.5
1.2
0.9
1.2
2.2
2.9
2.5
2.0
2.1
2.0
1.8
2.0
2.1
2.0
1.5
1.5
2.7
1.8
2.6
1.4
1.9
2.6
1.5
2.1
1.6
2.2
2.0
1.5
2.1
1.8
1.9
2.0
1.8
0.9
2.0
4.6
3.6
1.6
1.4
1.3
2.0
2.9
1.3
2.3
1.7
1.5
3.1
1.8
1.4
1.7
2.9
1.9
1.2
3.0
1.7
2.5
1.3
4.2
1.4
1.6
2.2
2.2
1.5
1.6
1.7
1.7
1.3
2.1
3.1
2.6
1.6
1.5
1.7
1.0
1.0
1.9
1.4
1.2
0.9
2.2
1.6
1.4
2.2
2.2
1.2
1.5
1.2
1.9
1.3
2.1
0.9
1.2
1.3
1.5
1.5
2.4
2.4
2.3
1.9
2.0
2.2
0.8
1.8
1.9
1.1
1.2
1.5
3.4
1.6
1.5
1.4
0.9
1.7
1.5