SERA Toolbox1 and Toolbox2 standalone versions
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Magnitude_Complexity_TOOLBOX_D23_2/!Read_me.txt
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Magnitude_Complexity_TOOLBOX_D23_2/!Read_me.txt
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Welcome to the Magnitude Complexity Toolbox!
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VERSION_1 is a Interactive Standalone mode.
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VERSION_2 is a Function Standalone mode.
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please refer to the "READ_ME******.docx" file in each directory for further
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instructions on the step-by-step implementation of the applications as well
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as for data requirements and general tips.
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ENJOY!
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% FUNCTION: ADTestMag
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% VERSION: [Interactive Hybrid Standalone Version] V1.8
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% COMPATIBLE with Matlab version 2017b or later
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% TOOLBOX: "Magnitude Complexity Toolbox" within SERA Project
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% DOCUMENT: "READ_ME_App_2A_v1_Description_ADTestMag.docx"
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% -----------------------------------------------------------------------------------------------------------------------
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%% EXAMPLE TO RUN:
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% x=exprnd(log10(exp(1)),1000,1);
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% [pval mmin NN P S bval]=ADTestMag_V1_8(x,0.1,'exp',0.5,2.0,200) % for Interactivity OFF
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% [pval mmin NN P S bval ]=ADTestMag_V1_8(x); % for Interactivity ON
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%% ------------------------------------------------------------------------------------------------------------------------
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% Test for Exponential/Weibull distribution of a time-series (e.g. Magnitudes)
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% -----------------------------------------------------------------------------------------------------------------------
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% INPUT DATA:THE CURRENT VERSION USES AS INPUT A MAGNITUDE VECTOR
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% (Appropriate for standalone use - function mode)
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% -----------------------------------------------------------------------------------------------------------------------
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% OVERVIEW: THE FUNCTION performs the Anderson-Darling test for testing whether
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% a given set of observations (e.g. magnitudes), follows the exponential, or the
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% Weibull distribution
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% -----------------------------------------------------------------------------------------------------------------------
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% AUTHORS: K. Leptokaropoulos, and P. Urban
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% last updated: 03/2019, within SERA PROJECT, EU Horizon 2020 R&I
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% programme under grant agreement No.730900
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% CURRENT VERSION: v1.8 **** [INTERACTIVE HYBRID STANDALONE VERSION!!]
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% ----- THIS IS a dual-mode version: If all input arguments are set, then the
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% ----- Application operates as a function. However, if only the input vector
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% ----- is introduced, the application switch to interactive mode.
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%% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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% PLEASE refer to the accompanying document:
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% "READ_ME_App_2A_v1_Description_ADTestMag.docx"
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% for description of the Application and its requirements.
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%% -----------------------------------------------------------------------------------------------------------------------
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% DESCRIPTION:
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% THE FUNCTION performs the Anderson-Darling test for testing the Null Hypothesis, H0,
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% that a given dataset (e.g. magnitudes), has been drawn from the exponential or Weibull distribution
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%(e.g. Marsaglia and % Marsaglia, 2004). This is performed as a function on minimum magnitude, such that
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% multiple results are produced. The significance of the the H0 (p-value) is the main
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% output of the program. Before applying the AD test the magnitudes are randomized
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% within their round-off interval, by the formula introduced by Lasocki & Papadimitriou,
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% 2006.
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% % -----------------------------------------------------------------------------------------------------------------------
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%
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%CALLING SEQUENCE
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% [pval mmin NN P S bval ]=ADTestMag_V1_8(vector,EPS,MTdistribution,Mmin,Mmax,trials)
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%
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% INPUT PARAMETERS:
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% -- 'vector': A sample data (e.g. Magnitude) Vector. The program
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% takes as input any matlab vector. The input data can
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% be uploaded by the User from an ASCII file (e. g. the
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% file "test_vector.txt" file, located within the directory
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% "Sample_Data").Such file should contain a vector (row
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% or column) of the Data the User wishes to process. The
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% User is afterwards requested to enter parameters values:
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%
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% - EPS: Round-off interval, i.e. minimum non-zero difference of the
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% input data. It also corresponds to step for calculations (AD
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% test iterations process). Default value is calculated from the
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% given dataset. It is recommended to use 0.1 (or 0.01) for
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% magnitude vectors
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% - MTdistribution: Distribution to be tested. Possible values:
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% 'exp' for the Exponential, 'weibul' for the Weibull distribution
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% - Mmin: Corresponds to the minumum 'vector' value for which
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% the AD test is performed (cut-off value). If 'vector' consists of magnitudes
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% it is recommended (yet, not restricted) to set Mmin equal to the
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% catalog completeness threshold, Mc (if known).
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% - Mmax: The test is carried out succesively for 'vector' values >= [Mmin, Mmin+EPS, Mmin+2EPS,..,Mmax]
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% The default MMax is the 'vector' value for which the number of
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% 'vector' values >=Mmax is greater than 4 (minimum possible
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% sample for AD test function execution)
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% - trials: Number of randomization realizations (trials) perfomed in
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% order to diminish the influence of randomization on the
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% resulting p-value. Default is 100.
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% The User may also use the calling sequence [pval mmin NN P S bval ]=ADTestMag_V1_8(vector)
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% In such a case they are requested interactivelly to provide the rest of input
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% parameters.
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% -----------------------------------------------------------------------------------------------------------------------
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% OUTPUT:
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%
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% - Output Parameters:
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% * pval - Structure with 3 fields:
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% p - vector of test p-values obtained in successive trials,
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% mmin - Minimum value of 'vector' used in the test,
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% P - the average of p-values
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% [NOTE: histograms of such p-values indicate that
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% their distribution is not normal, neither even symmetric
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% for a large number of cases]
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%
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% * P - vector of the average of the p-values obtained when testing for
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% the consecutive mmin values
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% * S - vector of the standard deviation of the
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% p-values obtained when testing for the consecutive mmin values
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% * mmin - vector with minimum values of 'vector' used in the consecutive tests
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% * NN - vector with the number of 'vector' values >= each mmin value.
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% * bval - the Gutenberg-Richter b-value for 'vector' values >= each mmin value.
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% This parameter has a meaning only when 'vector' consists of magnitudes.
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%
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% - Output:
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% RES - a five column matrix. Col 1 - mmin values,
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% Col 2 - NN values, Col 3 - b values, Col 4 - P
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% values, Col 5 - S values
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% mmin, NN, P, S as defined above
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%
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% - Output Figures:
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% Figure with the average p-value (P parameter) as a function of
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% mmin, together with histogram of events count in bin=EPS.
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% The 0.05 significance level is plotted as well
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% -----------------------------------------------------------------------------------------------------------------------
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% REFERENCES:
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% -- Lasocki S. and E. E, Papadimitriou (2006), "Magnitude distribution
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% complexity revealed in seismicity from Greece", J. Geophys. Res.,
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% 111, B11309, doi:10.1029/2005JB003794.
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% -- Marsaglia, G., and J. Marsaglia (2004), "Evaluating the Anderson-Darling
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% distribution", J. Stat. Soft., 1-5.
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% -----------------------------------------------------------------------------------------------------------------------
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% LICENSE
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% This is free software: you can redistribute it and/or modify it under
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% the terms of the GNU General Public License as published by the Free
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% Software Foundation, either version 3 of the License, or
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% (at your option) any later version.
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%
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% This program is distributed in the hope that it will be useful,
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
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% See the GNU General Public License for more details.
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% -----------------------------------------------------------------------------------------------------------------------
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%% EXAMPLE TO RUN:
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% x=exprnd(log10(exp(1)),1000,1);
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% [pval mmin NN P S bval]=ADTestMag_V1_8(x,0.1,'exp',0.5,2.0,200) % for Interactivity OFF
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% [pval mmin NN P S bval ]=ADTestMag_V1_8(x); % for Interactivity ON
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%% ------------------------------------------------------------------------------------------------------------------------
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function [pval, mmin, NN, P, S, bval ]=ADTestMag_V1_8(vector,EPS,MTdistribution,Mmin,Mmax,trials)
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mkdir Outputs_ADTestMag
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if nargin==1
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%DEFINE INPUT PARAMETERS MANUALLY: NARGIN==1
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% Select Mc and filter parameters for M>=Mc
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[MM,Mmin,EPS,MTdistribution]=FiltMcVector(vector);
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if Mmin<min(MM);Mmin=min(MM);end
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% ROUND MAGNITUDES to the selected EPS
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M=round(MM/EPS)*EPS;
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Mmin=floor(Mmin/EPS)*EPS;MMax=ceil(max(M)/EPS)*EPS;
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Rp=round(-log10(EPS));
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trials=dialog1('number of trials',{'100'})
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% define number of classes for calculation,
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% up to the M where a minimum of N=5 occurs
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mags=Mmin:EPS:MMax;mags=round(mags/EPS)*EPS;
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%%Alternative way to estimate counts of events
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hi=histc(M,mags-eps/2); % Check the rounding
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H=flipud(cumsum(flipud(hi)));
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N1=numel(H(H>=4));
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Mmax=dialog1(['Maximum value for calculations ',num2str(Mmin),'\leqM\leq', num2str(mags(N1)),')'],{num2str(mags(N1))})
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N=find(abs(mags-Mmax)<EPS/2);
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tic;
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elseif nargin>1
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% INPUT PARAMETERS ARE SPECIFIED AS FUNCTION ARGUMENTS
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M=round(vector/EPS)*EPS;
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Mmin=floor(Mmin/EPS)*EPS;MMax=ceil(max(M)/EPS)*EPS;
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Rp=round(-log10(EPS));if Mmax>max(M);Mmax=max(M);end
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mags=Mmin:EPS:MMax;mags=round(mags/EPS)*EPS;
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N1=find(abs(mags-Mmax)<EPS/2);
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hi=histc(M,mags-eps/2); % Check the rounding
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H=flipud(cumsum(flipud(hi)));
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N2=numel(H(H>=4));
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N=min(N1,N2);
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end
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% magnitude distribution to be tested
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if strcmp(MTdistribution,'exp')==1;MTdist='Exponential';
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elseif strcmp(MTdistribution,'weibul')==1;MTdist='Weibull';
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end
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% Anderson-Darling Test for exponentiality
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% Loop for different maggnitudes
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for j=1:N
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mmin(j)=Mmin+(j-1)*EPS;%mmin=round(mmin/EPS)*EPS;
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m=M(M>=mmin(j)-EPS/2);
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cou=0;
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for i=1:trials
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[beta]=beta_AK_UT_Mbin(mmin(j),m,Rp);
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[m_corr]=korekta(m,mmin(j),EPS,beta);
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Mag=m_corr-min(m)+EPS/2;
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[h1, p1]=adtest(Mag,'Distribution',MTdistribution);
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h(i)=h1;p(i,j)=p1;
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if p1<=0.0005+eps;cou=cou+1;else, cou=0;end
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if cou==2;p(i:trials,j)=0.0005;break;end
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end
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%j
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NN(j)=numel(m);bval(j)=beta/log(10);sb(j)=bval(j)/sqrt(NN(j));
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P(j)=mean(p(:,j));
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S(j)=std(p(:,j)); % p-values are not normally distributed!!
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clear b
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end
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%mean(p),std(p)
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%subplot(2,1,1);hist(h);xlim([-1 2]);subplot(2,1,2);histogram(p,0:0.05:1.0);
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%hold on;plot([mean(p) mean(p)],[0 200],'r--','LineWidth',2);
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%PLOTTING
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EPS2=0.1;
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xa=min(M):EPS2:max(M);xa1=[min(mmin) max(mmin)];
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subplot(2,1,1);plot(mmin,P,'ro-','MarkerSize',12,'LineWidth',1,'MarkerFaceColor',[0.33 0.66 0.99]);
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hold on;plot([min(M)-EPS max(M)],[0.05 0.05],'k--','Linewidth',2);xlim([min(M)-EPS max(M)]);
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ylabel('p-value','FontSize',16);
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if strcmp(MTdistribution,'exp')==1;title('AD Test for Exponentiality','FontSize',16);
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elseif strcmp(MTdistribution,'weibul')==1;title('AD Test for Weibull Distribution','FontSize',16);
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end
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subplot(2,1,2);histogram(M,numel(xa),'FaceColor',[0.7 0.7 0.8]);set(gca,'YScale','log');hold on
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xlim([min(M)-EPS max(M)]);xlabel('Data','FontSize',16);ylabel('N','FontSize',16);
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for j=1:N
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pval(j).p=p(:,j);
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pval(j).mmin=mmin(j);
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pval(j).P=P(j);
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end
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for i=1:length(P);
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if P(i)<0.05;h_decision{i,1}='rejected';
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else h_decision{i,1}='not_rejected';
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end
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end
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%h_decision=h_decision';
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RES=[mmin' NN' bval' P' S']
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%SAVE OUTPUTS
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cd Outputs_ADTestMag
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SaveOuts(EPS,Mmin,Mmax,trials,RES,h_decision,MTdist)
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%saveas(gcf,'Exponentiality_Output.jpg')
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print(gcf,'ADTestMag_Output.jpeg','-djpeg','-r300')
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cd ../
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end
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%% ******************************************************************
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% *************************** FUNCTIONS ***************************
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% ****-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-****
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%% Select Mc and filter parameters for M>=Mc
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% [OK!!!!!!!!!!!!!!]
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function [Cmag,Mc,EPS,MTdist]=FiltMcVector(vector)
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Cmag=vector;
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sm=sort(Cmag); sm1=sm(2:length(sm))-sm(1:length(sm)-1); EPS1=min(sm1(sm1>0));clc
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if EPS1<0.01;warning('Data round-off interval is too small, please consider setting a higher value (e.g. 0.1)');end
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EPS=dialog1('Data round-off interval',{num2str(EPS1)});
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ar=min(Cmag):0.1:max(Cmag);
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fig_Mc=figure;histogram(Cmag,length(ar));set(gca,'YScale','log')
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title('Please Select Data Cutoff','FontSize',14);xlabel('M','FontSize',14),ylabel('Log_1_0N','FontSize',14)
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% Select events above Mc
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[Mc,N]=ginput(1);Mc=floor(Mc/EPS)*EPS,close(fig_Mc);
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%Cmag=Cmag(Cmag>=Mc);
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% select magnitude distribution to be tested
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[MTd,ok]=listdlg('PromptString','Select field:',...
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'ListString',{'Exponential','Weibul'},'SelectionMode','single')
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if MTd==1;MTdist='exp';else; MTdist='weibul';end
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end
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%% --------------------------------------------------------------------------------------
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function [ou]=dialog1(name,defaultanswer)
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prompt=['\fontsize{12} Please enter ',name, ':'];
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prompt={prompt};
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numlines=1; opts.Interpreter='tex';
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ou=inputdlg(prompt,'Parameter Setting',numlines,defaultanswer,opts);ou=str2double(ou{1});
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end
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%% --------------------------------------------------------------------------------------
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function [beta]=beta_AK_UT_Mbin(Mmin,m,Rp)
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%
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% m - magnitude vector
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% Mmin - completeness magitude threshold
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% beta - beta value. b(G-R)=beta/log(10)
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% Rp - Rounding precision, (1 - one decimal, 2 - two decimals, etc)
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beta=1/(mean(m)-(Mmin-0.5*10^(-Rp)));
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end
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%% --------------------------------------------------------------------------------------
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% Magnitude randomization
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%
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function [m_corr]=korekta(m,Mmin,EPS,beta)
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%
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% m - magnitude vector
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% Mmin - completeness magitude threshold
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% beta - beta value. b(G-R)=beta/log(10)
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% EPS - magnitude round-off interval
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%
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% m_corr - randomized magnitude vector
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%
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F1=1-exp(-beta*(m-Mmin-0.5*EPS));
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F2=1-exp(-beta*(m-Mmin+0.5*EPS));
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u=rand(size(m));
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w=u.*(F2-F1)+F1;
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m_corr=Mmin-log(1-w)./beta;
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end
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%% --------------------------------------------------------------------------------------------------------
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% --------------------------------------- SAVE OUTPUTS in the report file ---------------------------------------
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% Save Outputs
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function SaveOuts(EPS,Mmin,Mmax,trials,RES,h_decision,MTdist)
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% ---- Save *.txt file with Parameters Report ----
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%cd Outputs/
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fid=fopen('REPORT_ADTestMag.txt','w');
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fprintf(fid,['PARAMETERS & RESULTS from DISTRIBUTION TESTING (created on ', datestr(now),')\n']);
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fprintf(fid,'------------------------------------------------------------------------------------\n');
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fprintf(fid,['<Round-off interval >: ', num2str(EPS),'\n']);
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fprintf(fid,['<Data Distribution tested >: ', MTdist,'\n']);
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fprintf(fid,['<Data Range for Analysis >: ', num2str(Mmin), ' to ', num2str(Mmax),'\n']);
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fprintf(fid,['<Number of randomization trials >: ', num2str(trials),'\n']);
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fprintf(fid,'------------------------------------------------------------------------------------\n');
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fprintf(fid,['Mmin N b-value mean(p) std(p) Decision for H0 \n']);
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fprintf(fid,[' from ',num2str(trials),' trials (0.05 significance)\n']);
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for j=1:size(RES,1);
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fprintf(fid,['%5.2f %6d %5.3f %5.4f %5.3f %s \n'],RES(j,:),h_decision{j});
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end
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fclose(fid);
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||||
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||||
%saveas()
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||||
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||||
% Save Output Structure
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||||
% prompt={'\fontsize{12} Please enter output file name:'};
|
||||
% name='Extract Output Structure';
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||||
% numlines=1;
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% defaultanswer={'Tdata.mat'};
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||||
% opts.Interpreter='tex';
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||||
% answer=inputdlg(prompt,name,numlines,defaultanswer,opts);
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||||
% save(char(answer),'Tdata')
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||||
% cd ../
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||||
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||||
end
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||||
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||||
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Binary file not shown.
@@ -0,0 +1,880 @@
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1.7
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0.8
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1.8
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1.5
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1.7
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0.8
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1.7
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2.1
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0.9
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1.3
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1.1
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1.9
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2.3
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1.7
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1.9
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1.4
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1.5
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1.6
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1.5
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2.7
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2.9
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1.3
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1.2
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0.9
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2.7
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1.4
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1.2
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1.4
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1.7
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1.5
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1.4
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1.5
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||||
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
|
||||
@@ -0,0 +1,22 @@
|
||||
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
|
||||
|
||||
|
||||
|
||||
@@ -0,0 +1,266 @@
|
||||
% 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
|
||||
|
||||
|
||||
|
||||
|
||||
@@ -0,0 +1,39 @@
|
||||
% 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)
|
||||
|
||||
|
||||
|
||||
Binary file not shown.
@@ -0,0 +1,880 @@
|
||||
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
|
||||
@@ -0,0 +1,701 @@
|
||||
% FUNCTION: MM_MB
|
||||
% VERSION: [Interactive Hybrid Standalone Version] V1.8
|
||||
% COMPATIBLE with Matlab version 2017b or later
|
||||
% TOOLBOX: "Magnitude Complexity Toolbox" within SERA Project
|
||||
% DOCUMENT: "READ_ME_App_2B_v1_Description_MM_MB.docx"
|
||||
%--------------------------------------------------------------------------------------------------------------
|
||||
%% EXAMPLE TO RUN:
|
||||
% x=exprnd(log10(exp(1)),1000,1);
|
||||
% [n,bval,Rmodes,hcrit_modes,Rbumps,hcrit_bumps,gau,gau_b,poch,poch2,zer1,zer2,x1,x2]...
|
||||
% =MM_MB_V1_8(x,0.2,500,500,0.01,0.001,'Efron','Silverman') % for Interactivity OFF
|
||||
% [n,bval,Rmodes,hcrit_modes,Rbumps,hcrit_bumps,gau,gau_b,poch,poch2,zer1,zer2,x1,x2]...
|
||||
% =MM_MB_V1_8(x); % for Interactivity ON
|
||||
%% ----------------------------------------------------------------------------------------------------------
|
||||
% Test performed for Magnitude Distribution of a given dataset checking
|
||||
% whether PDF demonstrates multi-modes/ multi-bumps
|
||||
% --------------------------------------------------------------------------------------------------------
|
||||
% INPUT: THE CURRENT VERSION USES AS INPUT ANY MAGNITUDE VECTOR
|
||||
% (Appropriate for standalone use - function mode)
|
||||
% --------------------------------------------------------------------------------------------------------
|
||||
% OVERVIEW: This Application is a Matlab function which performs testing
|
||||
% of hypotheses of 1) multimodality and 2) existence of multi-bumps in a given
|
||||
% magnitude distribution.
|
||||
% --------------------------------------------------------------------------------------------------------
|
||||
% AUTHORS: K. Leptokaropoulos and P. Urban,
|
||||
% last updated: 03/2019, within SERA PROJECT, EU Horizon 2020 R&I
|
||||
% programme under grant agreement No.730900
|
||||
% CURRENT VERSION: v1.8 **** [INTERACTIVE HYBRID STANDALONE VERSION!!]
|
||||
% ----- THIS IS a dual-mode version: If all input arguments are set, then the
|
||||
% ----- Application operates as a function. However, if only the input vector
|
||||
% ----- is introduced, the application switch to interactive mode.
|
||||
% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
|
||||
% PLEASE refer to the accompanying document:
|
||||
% "READ_ME_App_2B_v1_Description_MM_MB.docx"
|
||||
% for a description of the Application and its requirements.
|
||||
% --------------------------------------------------------------------------------------------------------
|
||||
% DESCRIPTION:
|
||||
% The function studies the magniutude distribution complexity by means of the
|
||||
% Mulitmodality Test (Silverman, 1986; Efron and Tibshirani, 1993). Two null
|
||||
% hypotheses (H0s) are tested:
|
||||
% H01 - multimodality: The magnitude PDF is unimodal
|
||||
% H02 - multi-bump: The magnitude PDF has one bump to the right of the
|
||||
% mode.
|
||||
% A mode is a local maximum of probability density and a bump is an interval
|
||||
% [a,b] such that the probability density is concave over [a,b] but not over any
|
||||
% larger interval (Silverman, 1986). The importance of modes and bumps relies
|
||||
% on the fact that multiple occurrences of these features in a PDF indicate, for
|
||||
% most standard densities, a mixing of components (e.g. Cox, 1966).
|
||||
% --------------------------------------------------------------------------------------------------------
|
||||
% INPUT: If the User Provides only the magnitude vector as input, then the
|
||||
% function enables a GUI allowing the User to interactivelly set the rest
|
||||
% of the input parameters by the User. Otherwise the User has to define
|
||||
% the 7 input parameters in addition to the input magnitude vector.
|
||||
% PLEASE REFER TO "MM_MB.doc" FOR A COMPREHENSIVE
|
||||
% PARAMETER DESCRIPTION
|
||||
% Input Parameters Overview:
|
||||
% --- M: A Time-Series (e.g. Magnitude) Vector. The program
|
||||
% takes as input any matlab vector. The input data can be
|
||||
% uploaded by the User from an ASCII file (e.g. the file
|
||||
% "test_vector.txt", located in the "Sample_Data"). Such file
|
||||
% should contain a vector (raw or column) of the Data the
|
||||
% User wishes to process. The User is afterwards requested
|
||||
% to enter parameters values:
|
||||
% --- Mc: Corresponds to the catalog completeness threshold.
|
||||
% --- m: number of points to divide magnitude sample, default 100,
|
||||
% recommended 100-1000.
|
||||
% % INPUTS for MODE and BUMP HUNTING
|
||||
% - n_boot: Number of bootstrap iterations for both MM and MB
|
||||
% (default: 100)
|
||||
% - delta_h: Smoothing parameter step for successive trials in defining
|
||||
% the critical h for MM and MB process (h-critical accuracy)
|
||||
% (default: 0.001)
|
||||
% - h : initial value of the smoothing factor to apply in defining the
|
||||
% critical h for the MM testing process (default:0.01)
|
||||
% - MMmeth: Method for multimodality Testing. Possible values:
|
||||
% 'Efron', 'Silverman'
|
||||
% - MBmeth: Method for multibumps Testing. Possible values:
|
||||
% 'Silverman', 'Efron'
|
||||
% NOTE: The initial value for MB process is taken equal to the
|
||||
% critical value defined in the MM process minus its
|
||||
% accuracy (i.e. hcrit_Modes-delta_h, see OUTPUT below)
|
||||
% ---------------------------------------------------------------------------------------------------------
|
||||
% OUTPUT:
|
||||
% - Output Report with data and parameters used
|
||||
% ('Output_MM_MB.txt file')
|
||||
% - Output Parameters:
|
||||
% % DOUBLES:
|
||||
% * n - Number of observations used
|
||||
% * bval- b-value of the G-R law
|
||||
% * Rmodes - The estimated significance of null hypothesis (H01)
|
||||
% * hcrit_modes - estimated critical smoothness parameter for MM test
|
||||
% * Rbumps - The estimated significance of null hypothesis (H02)
|
||||
% * hcrit_bumps - estimated critical smoothness parameter for MB test
|
||||
% * zer1 - point where 1st derivative is zero (extremum)
|
||||
% * zer2 - point(s) where 2nd derivative is zero (inflection points)
|
||||
% [NOTE: zer2 can be a vector]
|
||||
% % VECTORS:
|
||||
% * gau: Data vector PDF estimated for h critical from Multimodality
|
||||
% * gau_b: Data vector PDF estimated for h critical from Multibumps
|
||||
% * poch: 1st derivative of Data vector PDF for h critical from Multibumps
|
||||
% * poch2: 2nd derivative of Data vector PDF for h critical from Multibumps
|
||||
% * x1,x2: minimum and maximum Data points after randomization
|
||||
% (parameters needed for plotting)
|
||||
% - Output Figures:
|
||||
%
|
||||
% ---------------------------------------------------------------------------------------------------------
|
||||
% REFERENCES:
|
||||
% -- Cox, D. R., (1966), Notes on the analysis of mixed frequency distributions.
|
||||
% Br. J. Math. Stat. Psychol. 19, 39-47, doi.org/10.1111/j.2044-8317.1966.tb00353.x.
|
||||
% -- Efron, B., and Tibshirani R.J. (1993) An Introduction to the Bootstrap,
|
||||
% CRC Press, Boca Raton, Fla.
|
||||
% -- Lasocki S. and E. E, Papadimitriou (2006), "Magnitude distribution
|
||||
% complexity revealed in seismicity from Greece", J. Geophys. Res.,
|
||||
% 111, B11309, doi:10.1029/2005JB003794.
|
||||
% -- Silverman, B. W., (1986), Density estimation for statistics and data analysis,
|
||||
% CRC press, Boa Raton, Fla.
|
||||
% ---------------------------------------------------------------------------------------------------------
|
||||
% 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.
|
||||
% ---------------------------------------------------------------------------------------------------------
|
||||
%% EXAMPLE TO RUN:
|
||||
% x=exprnd(log10(exp(1)),1000,1);
|
||||
% [n,bval,Rmodes,hcrit_modes,Rbumps,hcrit_bumps,gau,gau_b,poch,poch2,zer1,zer2,x1,x2]...
|
||||
% =MM_MB_V1_8(x,0.2,500,500,0.01,0.001,'Efron','Silverman') % for Interactivity OFF
|
||||
% [n,bval,Rmodes,hcrit_modes,Rbumps,hcrit_bumps,gau,gau_b,poch,poch2,zer1,zer2,x1,x2]...
|
||||
% =MM_MB_V1_8(x); % for Interactivity ON
|
||||
%% ----------------------------------------------------------------------------------------------------------
|
||||
|
||||
function [n,bval,Rmodes,hcrit_modes,Rbumps,hcrit_bumps,gau,gau_b,poch,poch2,zer1,zer2,x1,x2]...
|
||||
=MM_MB_V1_8(M,Mc,m,n_boot,h,delta_h,MMmeth,MBmeth)
|
||||
|
||||
mkdir Outputs_MM_MB
|
||||
|
||||
% define round-off interval and select data above Mc
|
||||
sm=sort(M);dm=sm(2:length(sm))-sm(1:length(sm)-1);
|
||||
dm=dm(dm>0);eps_M=min(dm);
|
||||
|
||||
%% --------------------------------------- INTERACTIVE MODE ----------------------------------------
|
||||
if nargin==1
|
||||
|
||||
[Mi,Mmin]=FiltMcVector(M,eps_M);
|
||||
M=Mi(Mi>=Mmin-eps_M/2);
|
||||
|
||||
m=dialog1('number of points to divide sample',{'100'});
|
||||
|
||||
Rp=round(-log10(eps_M)); %% check the RP parameter
|
||||
[beta]=beta_AK_UT_Mbin (Mmin,M,Rp) ;
|
||||
|
||||
% Randomize magnitude
|
||||
m_corr(:,1) = korekta(M,Mmin,eps_M,beta);
|
||||
|
||||
% SETTING PARAMETERS
|
||||
n=length(m_corr);
|
||||
x1=floor(min(m_corr)*10)/10; %nieco mniej ni<EFBFBD> min(m) zaokr<EFBFBD>glone do jednej dziesi<EFBFBD>tej
|
||||
x2=ceil(max(m_corr)*10)/10; %nieco wi<EFBFBD>cej ni<EFBFBD> max(m) zaokr<EFBFBD>glone do jednej dziesi<EFBFBD>tej
|
||||
|
||||
|
||||
% MULTIMODALITY TESTING
|
||||
% Give number of bootstrap attempts and h values
|
||||
[n_boot,delta_h,h]=dialog2('Multimodality',{'100','0.001','0.01'});
|
||||
n_boot1=n_boot;
|
||||
%delta_h=0.1;%input('czynnik wygladzajacy '); %0.1
|
||||
%h=0.01; %0.001
|
||||
[hcrit,gau]=critical_smoothing(m_corr,n,delta_h,x1,x2,m,h);
|
||||
hcrit;
|
||||
|
||||
% Select Method of Multimodality testing 'Silverman' or 'Efron'
|
||||
clc;
|
||||
disp('Please Select Method for Multimodality Testing: ');
|
||||
disp('(1 - for Efron, 2 - for Silverman)');
|
||||
MM=input(' ');
|
||||
|
||||
% ---------testing plot-----------
|
||||
plot(1:m,gau);title('Data density for critical smoothing factor (h_c_r_i_t)');
|
||||
|
||||
disp('press any key ...')
|
||||
pause
|
||||
close all
|
||||
% ---------testing plot-----------
|
||||
|
||||
% Run Multimodality testing
|
||||
switch MM
|
||||
case 1
|
||||
[R] = test_multimodality_e (m_corr,n,x1,x2,m,hcrit,n_boot1);
|
||||
case 2
|
||||
[R] = test_multimodality (m_corr,n,x1,x2,m,hcrit,n_boot1);
|
||||
end
|
||||
|
||||
% ------------------------------------------------------------------------
|
||||
% [zer1]=zera_1st(m_corr,n,x1,x2,m,hcrit-delta_h);
|
||||
% ------------------------------------------------------------------------
|
||||
|
||||
% BUMP HUNTING
|
||||
% Give number of bootstrap attempts and h values
|
||||
[n_boot,delta_h,h]=dialog2('Multibumps',{'100','0.001',num2str(hcrit)});
|
||||
n_boot2=n_boot;
|
||||
%delta_h=0.1;
|
||||
|
||||
[hcrit_bumps,gau_b,poch,poch2]=critical_smoothing_bumps(m_corr,n,delta_h,x1,x2,m,hcrit-delta_h);
|
||||
hcrit_bumps;
|
||||
|
||||
|
||||
% Select Method for testing the bump size 'Silverman' or 'Efron'
|
||||
disp(' ');disp(' ');disp(' ');
|
||||
disp('Please Select Method for Bump Testing: ');
|
||||
disp('(1 - for Silverman, 2 - for Efron)');
|
||||
BM=input(' ');
|
||||
|
||||
% Run Bump hunting
|
||||
switch BM
|
||||
case 1
|
||||
[Rb] = bump_hunt (m_corr,n,x1,x2,m,hcrit_bumps,n_boot2);
|
||||
case 2
|
||||
[Rb] = bump_hunt_e (m_corr,n,x1,x2,m,hcrit_bumps,n_boot2);
|
||||
end
|
||||
|
||||
|
||||
%% -------------------------------------- FUNCTION MODE ----------------------------------------
|
||||
|
||||
elseif nargin>1
|
||||
% INPUT PARAMETERS ARE SPECIFIED AS FUNCTION ARGUMENTS
|
||||
MM=M;Mmin=Mc;M=M(M>=Mmin-eps_M/2);
|
||||
m;n_boot;h;delta_h;MMmeth;MBmeth;
|
||||
|
||||
|
||||
Rp=round(-log10(eps_M)); %% check the RP parameter
|
||||
[beta]=beta_AK_UT_Mbin (Mmin,M,Rp); % beta value
|
||||
|
||||
% Randomize magnitude
|
||||
m_corr(:,1) = korekta(M,Mmin,eps_M,beta);
|
||||
|
||||
% SETTING PARAMETERS
|
||||
n=length(m_corr);
|
||||
x1=floor(min(m_corr)*10)/10; %nieco mniej ni<EFBFBD> min(m) zaokr<EFBFBD>glone do jednej dziesi<EFBFBD>tej
|
||||
x2=ceil(max(m_corr)*10)/10; %nieco wi<EFBFBD>cej ni<EFBFBD> max(m) zaokr<EFBFBD>glone do jednej dziesi<EFBFBD>tej
|
||||
|
||||
% MULTIMODALITY TESTING
|
||||
|
||||
[hcrit,gau]=critical_smoothing(m_corr,n,delta_h,x1,x2,m,h);
|
||||
|
||||
switch MMmeth
|
||||
case 'Efron'
|
||||
[R] = test_multimodality_e (m_corr,n,x1,x2,m,hcrit,n_boot);
|
||||
case 'Silverman'
|
||||
[R] = test_multimodality (m_corr,n,x1,x2,m,hcrit,n_boot);
|
||||
end
|
||||
|
||||
% BUMP HUNTING
|
||||
|
||||
[hcrit_bumps,gau_b,poch,poch2]=critical_smoothing_bumps(m_corr,n,delta_h,x1,x2,m,hcrit-delta_h);
|
||||
|
||||
switch MBmeth
|
||||
case 'Silverman'
|
||||
[Rb] = bump_hunt (m_corr,n,x1,x2,m,hcrit_bumps,n_boot);
|
||||
case 'Efron'
|
||||
[Rb] = bump_hunt_e (m_corr,n,x1,x2,m,hcrit_bumps,n_boot);
|
||||
end
|
||||
|
||||
end
|
||||
|
||||
|
||||
bval=beta/log(10);
|
||||
% Display the Results:
|
||||
re=table(n, bval, R,hcrit,Rb,hcrit_bumps)
|
||||
|
||||
disp(['Significance of Ho(1) that input data distribution is unimodal is: ', num2str(R)])
|
||||
disp(['Significance of Ho(2) that input data distribution has no more '])
|
||||
disp(['than one bumps to the right of the global maximum is: ', num2str(Rb)])
|
||||
|
||||
[zer1]=zera_1st(m_corr,n,x1,x2,m,hcrit_bumps-delta_h); % use the same h in both cases???
|
||||
[zer2]=zera_2nd(m_corr,n,x1,x2,m,hcrit_bumps-delta_h);
|
||||
|
||||
|
||||
|
||||
%% -------------------------- PLOTTING AND SAVING RESULTS ----------------------------
|
||||
% ----- plotting magnitude density and its derivatives ------
|
||||
xp=linspace(x1,x2,m);
|
||||
%st=range([x1 x2])/(m-1);xp=x1:st:x2;
|
||||
figure('rend','painters','pos',[800 100 600 900]);hold on
|
||||
subplot(3,1,1);
|
||||
plot(xp,gau_b,'LineWidth',2);hold on;
|
||||
for i=1:length(zer1)
|
||||
Le1=plot([zer1(i) zer1(i)],[0 10],'k--','LineWidth',1);
|
||||
end
|
||||
for i=1:length(zer2)
|
||||
Le2=plot([zer2(i) zer2(i)],[0 10],'r--','LineWidth',1);
|
||||
end
|
||||
xlim([min(M)-0.1 max(M)+0.1]);ylim([0 max(gau_b)+0.01])
|
||||
title(['Data density for h_c_r_i_t ';' (critical smoothing factor) '],'FontSize',14);%axis square
|
||||
legend([Le1,Le2],{'extremum','Inflection Point(s)'});ylabel('PDF','FontSize',14)
|
||||
subplot(3,1,2);
|
||||
plot(xp,poch,'LineWidth',2);ylabel('1^s^t derivative','FontSize',14);hold on;%axis square;
|
||||
plot([xp(1) xp(length(xp))],[0 0],'--','LineWidth',1)
|
||||
for i=1:length(zer1)
|
||||
plot([zer1(i) zer1(i)],[min(poch)-0.01 max(poch)+0.01],'k--','LineWidth',1)
|
||||
end
|
||||
for i=1:length(zer2)
|
||||
plot([zer2(i) zer2(i)],[min(poch)-0.01 max(poch)+0.01],'r--','LineWidth',1)
|
||||
end
|
||||
xlim([min(M)-0.1 max(M)+0.1]);ylim([min(poch)-0.01 max(poch)+0.01])
|
||||
subplot(3,1,3);
|
||||
plot(xp,poch2,'LineWidth',2);ylabel('2^n^d derivative','FontSize',14);%axis square
|
||||
hold on; plot([xp(1) xp(length(xp))],[0 0],'--','LineWidth',1)
|
||||
for i=1:length(zer1)
|
||||
plot([zer1(i) zer1(i)],[min(poch2)-0.01 max(poch2)+0.01],'k--','LineWidth',1)
|
||||
end
|
||||
for i=1:length(zer2)
|
||||
plot([zer2(i) zer2(i)],[min(poch2)-0.01 max(poch2)+0.01],'r--','LineWidth',1)
|
||||
end
|
||||
xlim([min(M)-0.1 max(M)+0.1]);ylim([min(poch2)-0.01 max(poch2)+0.01])
|
||||
xlabel('Data','FontSize',14);
|
||||
|
||||
% Save Outputs
|
||||
cd Outputs_MM_MB
|
||||
Rmodes=R;Rbumps=Rb;hcrit_modes=hcrit;
|
||||
SaveOuts(eps_M,Mmin,m,n_boot,n_boot,n,bval,Rmodes,hcrit_modes,Rbumps,hcrit_bumps)
|
||||
saveas(gcf,'Multimodality_Output.jpg')
|
||||
cd ../
|
||||
|
||||
|
||||
%% ******************************************************************
|
||||
% *************************** FUNCTIONS ***************************
|
||||
% ****-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-****
|
||||
%% Select Mc and filter parameters for M>=Mc
|
||||
|
||||
function [Cmag,Mc]=FiltMcVector(magnitude_vector,EPS1)
|
||||
Cmag=magnitude_vector;
|
||||
|
||||
%sm=sort(Cmag); sm1=sm(2:length(sm))-sm(1:length(sm)-1); EPS1=min(sm1(sm1>0));
|
||||
%EPS=dialog1('magnitude round-off interval',{num2str(EPS1)});
|
||||
|
||||
ar=min(Cmag):0.1:max(Cmag);
|
||||
fig_Mc=figure;histogram(Cmag,length(ar));set(gca,'YScale','log')
|
||||
title('Please Select Data Cutoff','FontSize',14);xlabel('M','FontSize',14),ylabel('Log_1_0N','FontSize',14)
|
||||
% Select events above Mc
|
||||
[Mc,N]=ginput(1);Mc=floor(Mc/EPS1)*EPS1,close(fig_Mc);
|
||||
|
||||
%Cmag=Cmag(Cmag>=Mc);
|
||||
|
||||
end
|
||||
%% --------------------------------------------------------------------------------------
|
||||
%% --------------------------------------------------------------------------------------
|
||||
% finds a field defined by a certain (string) name
|
||||
function [id] = findfield( catalog,field )
|
||||
id=0;
|
||||
j=1;
|
||||
while j <= size(catalog,2) && id==0
|
||||
if (strcmp(catalog(j).field,field)==1)
|
||||
id=j;
|
||||
end
|
||||
j=j+1;
|
||||
end
|
||||
end
|
||||
%% --------------------------------------------------------------------------------------
|
||||
function [ou]=dialog1(name,defaultanswer)
|
||||
|
||||
prompt=['\fontsize{12} Please enter ',name, ':'];
|
||||
prompt={prompt};
|
||||
numlines=1; opts.Interpreter='tex';
|
||||
ou=inputdlg(prompt,'Parameter Setting',numlines,defaultanswer,opts);ou=str2num(ou{1});
|
||||
|
||||
end
|
||||
|
||||
%% --------------------------------------------------------------------------------------
|
||||
|
||||
function [ou1, ou2, ou3]=dialog2(titl,defaultanswer)
|
||||
|
||||
prompt={'\fontsize{12} Please enter number of bootstrap iterations:','\fontsize{12} Please enter \Deltah (h_c_r_i_t accuracy):','\fontsize{12} Please enter h (smoothing factor):'};
|
||||
name=['Parameters for ',titl, ':'];
|
||||
numlines=1;
|
||||
opts.Interpreter='tex';
|
||||
answer=inputdlg(prompt,name,numlines,defaultanswer,opts);
|
||||
ou1=answer(1);ou2=answer(2);ou3=answer(3);
|
||||
ou1=str2num(ou1{1});ou2=str2num(ou2{1});ou3=str2num(ou3{1});
|
||||
|
||||
end
|
||||
|
||||
%% --------------------------------------------------------------------------------------
|
||||
%
|
||||
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
|
||||
%% --------------------------------------------------------------------------------------
|
||||
% Finding critical smoothing parameter value for which the non parametric
|
||||
% PDF demonstrates one mode in the selected interval
|
||||
%
|
||||
function [hcrit,gau]=critical_smoothing(mm,n,delta_h,x1,x2,m,h)
|
||||
%
|
||||
|
||||
x=sort(mm);
|
||||
p=2.0;
|
||||
c=sqrt(2*pi);
|
||||
%x1=input('Lower limit ');
|
||||
%x2=input('Upper limit ');
|
||||
%m=input('No. of points ');
|
||||
y=linspace(x1,x2,m);
|
||||
%h=input('Initial smoothing factor ');
|
||||
while p>1
|
||||
for i=1:m,
|
||||
poch(i)=-sum((y(i)-x).*exp(-0.5*((y(i)-x)./h).^2));
|
||||
end
|
||||
p=0;
|
||||
for i=2:m,
|
||||
if poch(i-1)*poch(i)<0
|
||||
p=p+1;
|
||||
end
|
||||
end
|
||||
h=h+delta_h;
|
||||
end
|
||||
hcrit=h-delta_h;
|
||||
for i=1:m,
|
||||
gau(i)=sum(exp(-0.5*((y(i)-x)./hcrit).^2))/c/n/hcrit;
|
||||
end
|
||||
end
|
||||
%% --------------------------------------------------------------------------------------
|
||||
% "SMOOTHED BOOTSTRAP"
|
||||
%
|
||||
function [R]=test_multimodality(m,n,x1,x2,n_point,h_crit,mm)
|
||||
%
|
||||
|
||||
x=sort(m);
|
||||
c=sqrt(2*pi);
|
||||
%x1=input('Lower limit ');
|
||||
%x2=input('Upper limit ');
|
||||
%m=input('No. of points ');
|
||||
y=linspace(x1,x2,n_point);
|
||||
%h_crit=input('Critical smoothing factor ');
|
||||
%mm=input('No of trials ');
|
||||
no_wielom=0;
|
||||
for j=1:mm,
|
||||
ind=unidrnd(n,n,1);
|
||||
eps=normrnd(0,1,n,1);
|
||||
z=x(ind)+h_crit.*eps;
|
||||
z=sort(z);
|
||||
poch(1)=-sum((y(1)-z).*exp(-0.5*((y(1)-z)./h_crit).^2));
|
||||
p=0;
|
||||
for i=2:n_point,
|
||||
poch(i)=-sum((y(i)-z).*exp(-0.5*((y(i)-z)./h_crit).^2));
|
||||
if poch(i-1)*poch(i)<0
|
||||
p=p+1;
|
||||
end
|
||||
end
|
||||
if p>1
|
||||
no_wielom=no_wielom+1;
|
||||
end
|
||||
end
|
||||
R=no_wielom/mm;
|
||||
end
|
||||
%% --------------------------------------------------------------------------------------
|
||||
% "SMOOTHED BOOTSTRAP"
|
||||
% EFRON
|
||||
%
|
||||
function [R]=test_multimodality_e(m,n,x1,x2,n_point,h_crit,mm)
|
||||
%
|
||||
x=sort(m);
|
||||
s2=sqrt(1+h_crit^2/var(x));
|
||||
c=sqrt(2*pi);
|
||||
%x1=input('Lower limit ');
|
||||
%x2=input('Upper limit ');
|
||||
%m=input('No. of points ');
|
||||
y=linspace(x1,x2,n_point);
|
||||
%h_crit=input('Critical smoothing factor ');
|
||||
%mm=input('No of trials ');
|
||||
no_wielom=0;
|
||||
for j=1:mm,
|
||||
ind=unidrnd(n,n,1);
|
||||
eps=normrnd(0,1,n,1);
|
||||
me=mean(x(ind));
|
||||
z=me+(x(ind)-me+h_crit.*eps)./s2;
|
||||
z=sort(z);
|
||||
poch(1)=-sum((y(1)-z).*exp(-0.5*((y(1)-z)./h_crit).^2));
|
||||
p=0;
|
||||
for i=2:n_point,
|
||||
poch(i)=-sum((y(i)-z).*exp(-0.5*((y(i)-z)./h_crit).^2));
|
||||
if poch(i-1)*poch(i)<0
|
||||
p=p+1;
|
||||
end
|
||||
end
|
||||
if p>1
|
||||
no_wielom=no_wielom+1;
|
||||
end
|
||||
end
|
||||
R=no_wielom/mm;
|
||||
end
|
||||
%% --------------------------------------------------------------------------------------
|
||||
% Finding critical smoothing parameter value for which the non parametric
|
||||
% PDF demonstrates one bump in the selected interval
|
||||
%
|
||||
function [hcrit,gau,poch,poch2]=critical_smoothing_bumps(mm,n,delta_h,x1,x2,m,h)
|
||||
%
|
||||
|
||||
x=sort(mm);
|
||||
p=2.0;
|
||||
c=sqrt(2*pi);
|
||||
%x1=input('Lower limit ');
|
||||
%x2=input('Upper limit ');
|
||||
%m=input('No. of points ');
|
||||
y=linspace(x1,x2,m);
|
||||
%h=input('Initial smoothing factor ');
|
||||
while p>1
|
||||
for i=1:m,
|
||||
% poch(i)=-sum((y(i)-x).*exp(-0.5*((y(i)-x)./h).^2));
|
||||
poch2(i)=sum((((y(i)-x)./h).^2-1).*exp(-0.5*((y(i)-x)./h).^2));
|
||||
end
|
||||
p=0;
|
||||
for i=2:m,
|
||||
if poch2(i-1)*poch2(i)<0
|
||||
p=p+1;
|
||||
end
|
||||
end
|
||||
h=h+delta_h;
|
||||
end
|
||||
hcrit=h-delta_h;
|
||||
for i=1:m,
|
||||
gau(i)=sum(exp(-0.5*((y(i)-x)/hcrit).^2))/c/n/hcrit;
|
||||
poch(i)=-sum((y(i)-x).*exp(-0.5*((y(i)-x)./hcrit).^2));
|
||||
poch2(i)=sum((((y(i)-x)./hcrit).^2-1).*exp(-0.5*((y(i)-x)./hcrit).^2));
|
||||
end
|
||||
end
|
||||
%% --------------------------------------------------------------------------------------
|
||||
% "SMOOTHED BOOTSTRAP"
|
||||
%
|
||||
function [R]=bump_hunt(m,n,x1,x2,n_point,h_crit,mm)
|
||||
%
|
||||
x=sort(m);
|
||||
c=sqrt(2*pi);
|
||||
%x1=input('Lower limit ');
|
||||
%x2=input('Upper limit ');
|
||||
%m=input('No. of points ');
|
||||
y=linspace(x1,x2,n_point);
|
||||
%h_crit=input('Critical smoothing factor ');
|
||||
%mm=input('No of trials ');
|
||||
no_bump=0;
|
||||
for j=1:mm,
|
||||
ind=unidrnd(n,n,1);
|
||||
eps=normrnd(0,1,n,1);
|
||||
z=x(ind)+h_crit.*eps;
|
||||
z=sort(z);
|
||||
% poch(1)=-sum((y(1)-z).*exp(-0.5*((y(1)-z)./h_crit).^2));
|
||||
poch2(1)=sum((((y(1)-z)./h_crit).^2-1).*exp(-0.5*((y(1)-z)./h_crit).^2));
|
||||
p=0;
|
||||
for i=2:n_point,
|
||||
% poch(i)=-sum((y(i)-z).*exp(-0.5*((y(i)-z)./h_crit).^2));
|
||||
poch2(i)=sum((((y(i)-z)./h_crit).^2-1).*exp(-0.5*((y(i)-z)./h_crit).^2));
|
||||
if poch2(i-1)*poch2(i)<0
|
||||
p=p+1;
|
||||
end
|
||||
end
|
||||
if p>1
|
||||
no_bump=no_bump+1;
|
||||
end
|
||||
end
|
||||
R=no_bump/mm;
|
||||
end
|
||||
%% --------------------------------------------------------------------------------------
|
||||
% "SMOOTHED BOOTSTRAP"
|
||||
% EFRON
|
||||
%
|
||||
function [R]=bump_hunt_e(m,n,x1,x2,n_point,h_crit,mm)
|
||||
%
|
||||
x=sort(m);
|
||||
s2=sqrt(1+h_crit^2/var(x));
|
||||
c=sqrt(2*pi);
|
||||
%x1=input('Lower limit ');
|
||||
%x2=input('Upper limit ');
|
||||
%m=input('No. of points ');
|
||||
y=linspace(x1,x2,n_point);
|
||||
%h_crit=input('Critical smoothing factor ');
|
||||
%mm=input('No of trials ');
|
||||
no_bump=0;
|
||||
for j=1:mm,
|
||||
ind=unidrnd(n,n,1);
|
||||
eps=normrnd(0,1,n,1);
|
||||
me=mean(x(ind));
|
||||
z=me+(x(ind)-me+h_crit.*eps)./s2;
|
||||
z=sort(z);
|
||||
% poch(1)=-sum((y(1)-z).*exp(-0.5*((y(1)-z)./h_crit).^2));
|
||||
poch2(1)=sum((((y(1)-z)./h_crit).^2-1).*exp(-0.5*((y(1)-z)./h_crit).^2));
|
||||
p=0;
|
||||
for i=2:n_point,
|
||||
% poch(i)=-sum((y(i)-z).*exp(-0.5*((y(i)-z)./h_crit).^2));
|
||||
poch2(i)=sum((((y(i)-z)./h_crit).^2-1).*exp(-0.5*((y(i)-z)./h_crit).^2));
|
||||
if poch2(i-1)*poch2(i)<0
|
||||
p=p+1;
|
||||
end
|
||||
end
|
||||
if p>1
|
||||
no_bump=no_bump+1;
|
||||
end
|
||||
end
|
||||
R=no_bump/mm;
|
||||
end
|
||||
|
||||
%% --------------------------------------------------------------------------------------
|
||||
% Determination of PDF first derivative zeros estimates in the selected interval
|
||||
%
|
||||
function [zer1]=zera_1st(mm,n,x1,x2,m,h)
|
||||
%
|
||||
|
||||
x=sort(mm);
|
||||
c=sqrt(2*pi);
|
||||
y=linspace(x1,x2,m);
|
||||
for i=1:m,
|
||||
poch(i)=-sum((y(i)-x).*exp(-0.5*((y(i)-x)./h).^2));
|
||||
end
|
||||
p=0;
|
||||
for i=2:m,
|
||||
if poch(i-1)*poch(i)<0
|
||||
p=p+1;
|
||||
zer1(p)=(y(i)+y(i-1))/2; %K 23JAN2019
|
||||
end
|
||||
end
|
||||
|
||||
end
|
||||
%% --------------------------------------------------------------------------------------
|
||||
% Determination of PDF second derivative zeros in the selected interval
|
||||
%
|
||||
|
||||
function [zer2]=zera_2nd(mm,n,x1,x2,m,h)
|
||||
%
|
||||
x=sort(mm);
|
||||
c=sqrt(2*pi);
|
||||
y=linspace(x1,x2,m);
|
||||
for i=1:m,
|
||||
poch2(i)=sum((((y(i)-x)./h).^2-1).*exp(-0.5*((y(i)-x)./h).^2));
|
||||
end
|
||||
p1=0;
|
||||
for i=2:m,
|
||||
if poch2(i-1)*poch2(i)<0
|
||||
p1=p1+1;
|
||||
zer2(p1)=(y(i)+y(i-1))/2; %K 23JAN2019
|
||||
end
|
||||
end
|
||||
|
||||
end
|
||||
|
||||
%% --------------------------------------------------------------------------------------------------------
|
||||
% --------------------------------------- SAVE OUTPUTS in the report file ---------------------------------------
|
||||
% Save Outputs
|
||||
function SaveOuts(EPS,Mmin,m,n_boot1,n_boot2,n,bval,Rmodes,hcrit_modes,Rbumps,hcrit_bumps)
|
||||
% ---- Save *.txt file with Parameters Report ----
|
||||
%cd Outputs/
|
||||
fid=fopen('REPORT_Multimodality.txt','w');
|
||||
fprintf(fid,['RESULTS from MULTIMODALITY/MULTIBUMP TESTING (created on ', datestr(now),')\n']);
|
||||
fprintf(fid,'------------------------------------------------------------------------------\n');
|
||||
fprintf(fid,['<Round-off interval >: ', num2str(EPS),'\n']);
|
||||
fprintf(fid,['<Number of points to divide the sample >: ', num2str(m),'\n']);
|
||||
fprintf(fid,['<Completeness Threshold >: ', num2str(Mmin),'\n']);
|
||||
fprintf(fid,['<Number of events used >: ', num2str(n),'\n']);
|
||||
fprintf(fid,['<Gutenberg-Richter b-value >: ', num2str(bval,'%5.3f'),'\n']);
|
||||
fprintf(fid,['<Number of bootstrap iterations (multimodality) >: ', num2str(n_boot1),'\n']);
|
||||
fprintf(fid,['<Number of bootstrap iterations (multibumps) >: ', num2str(n_boot2),'\n']);
|
||||
fprintf(fid,'------------------------------------------------------------------------------\n');
|
||||
fprintf(fid,['<Critical Smoothing Parameter,h (for modes) >: ', num2str(hcrit_modes,'%6.4f'),'\n']);
|
||||
fprintf(fid,['<Critical Smoothing Parameter,h (for bumps) >: ', num2str(hcrit_bumps,'%6.4f'),'\n']);
|
||||
fprintf(fid,['<Significance of H01 that input data PDF is unimodal >: ', num2str(Rmodes,'%4.3f'),'\n']);
|
||||
fprintf(fid,['<Significance of H02 that input data PDF has no more \n']);
|
||||
fprintf(fid,[' than one bump to the right of the global maximum >: ', num2str(Rbumps,'%4.3f'),'\n']);
|
||||
|
||||
|
||||
|
||||
fclose(fid);
|
||||
|
||||
end
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
end
|
||||
Binary file not shown.
@@ -0,0 +1,880 @@
|
||||
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
|
||||
@@ -0,0 +1,45 @@
|
||||
|
||||
function MM_MB_Plot(M,Mc,x1,x2,m,zer1,zer2,gau_b,poch,poch2)
|
||||
M=M(M>=Mc);
|
||||
|
||||
% ----- plotting magnitude density and its derivatives ------
|
||||
xp=linspace(x1,x2,m)';
|
||||
%st=range([x1 x2])/(m-1);xp=x1:st:x2;
|
||||
figure('rend','painters','pos',[800 100 600 900]);hold on
|
||||
subplot(3,1,1);
|
||||
plot(xp,gau_b,'LineWidth',2);hold on;
|
||||
for i=1:length(zer1)
|
||||
Le1=plot([zer1(i) zer1(i)],[0 10],'k--','LineWidth',1);
|
||||
end
|
||||
for i=1:length(zer2)
|
||||
Le2=plot([zer2(i) zer2(i)],[0 10],'r--','LineWidth',1);
|
||||
end
|
||||
xlim([min(M)-0.1 max(M)+0.1]);ylim([0 max(gau_b)+0.01])
|
||||
title(['Data density for h_c_r_i_t ';' (critical smoothing factor) '],'FontSize',14);%axis square
|
||||
legend([Le1,Le2],{'extremum','Inflection Point(s)'});ylabel('PDF','FontSize',14)
|
||||
subplot(3,1,2);
|
||||
plot(xp,poch,'LineWidth',2);ylabel('1^s^t derivative','FontSize',14);hold on;%axis square;
|
||||
plot([xp(1) xp(length(xp))],[0 0],'--','LineWidth',1)
|
||||
for i=1:length(zer1)
|
||||
plot([zer1(i) zer1(i)],[min(poch)-0.01 max(poch)+0.01],'k--','LineWidth',1)
|
||||
end
|
||||
for i=1:length(zer2)
|
||||
plot([zer2(i) zer2(i)],[min(poch)-0.01 max(poch)+0.01],'r--','LineWidth',1)
|
||||
end
|
||||
xlim([min(M)-0.1 max(M)+0.1]);ylim([min(poch)-0.01 max(poch)+0.01])
|
||||
subplot(3,1,3);
|
||||
plot(xp,poch2,'LineWidth',2);ylabel('2^n^d derivative','FontSize',14);%axis square
|
||||
hold on; plot([xp(1) xp(length(xp))],[0 0],'--','LineWidth',1)
|
||||
for i=1:length(zer1)
|
||||
plot([zer1(i) zer1(i)],[min(poch2)-0.01 max(poch2)+0.01],'k--','LineWidth',1)
|
||||
end
|
||||
for i=1:length(zer2)
|
||||
plot([zer2(i) zer2(i)],[min(poch2)-0.01 max(poch2)+0.01],'r--','LineWidth',1)
|
||||
end
|
||||
xlim([min(M)-0.1 max(M)+0.1]);ylim([min(poch2)-0.01 max(poch2)+0.01])
|
||||
xlabel('Data','FontSize',14);
|
||||
|
||||
cd Outputs_MM_MB\;saveas(gcf,'Mulitimodality_output.jpg');cd ../
|
||||
|
||||
end
|
||||
|
||||
@@ -0,0 +1,489 @@
|
||||
% FUNCTION: MM_MB
|
||||
% VERSION: [Wrapper Standalone Version] V2.8
|
||||
% COMPATIBLE with Matlab version 2017b or later
|
||||
% TOOLBOX: "Magnitude Complexity Toolbox" within SERA Project
|
||||
% DOCUMENT: "READ_ME_App_2B_v2_Description_MM_MB.docx"
|
||||
% --------------------------------------------------------------------------------------------------------
|
||||
% Test performed for the Distribution of a given dataset (time-series)
|
||||
% checking whether PDF demonstrates multi-modes/ multi-bumps
|
||||
% --------------------------------------------------------------------------------------------------------
|
||||
% OVERVIEW: This Application is a Matlab function which performs testing
|
||||
% of hypotheses of 1) multimodality and 2) existence of multi-bumps in a given
|
||||
% magnitude distribution. Please check also the accompanying auxiliary scripts
|
||||
% 'MM_MB_wrapper' and 'MM_MB_Plot' for a specific application (scenario)
|
||||
% and plotting results.
|
||||
% --------------------------------------------------------------------------------------------------------
|
||||
% AUTHORS: K. Leptokaropoulos and P. Urban
|
||||
% last updated: 03/2019, 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_2B_v2_Description_MM_MB.docx"
|
||||
% for description of the Application and its requirements.
|
||||
% --------------------------------------------------------------------------------------------------------
|
||||
% DESCRIPTION:
|
||||
% The function studies the magniutude distribution complexity by means of the
|
||||
% Mulitmodality Test (Silverman, 1986; Efron and Tibshirani, 1993). Two null
|
||||
% hypotheses (H0s) are tested:
|
||||
% H01 - multimodality: The magnitude PDF is unimodal
|
||||
% H02 - multi-bump: The magnitude PDF has one bump to the right of the
|
||||
% mode.
|
||||
% A mode is a local maximum of probability density and a bump is an interval
|
||||
% [a,b] such that the probability density is concave over [a,b] but not over any
|
||||
% larger interval (Silverman, 1986). The importance of modes and bumps relies
|
||||
% on the fact that multiple occurrences of these features in a PDF indicate, for
|
||||
% most standard densities, a mixing of components (e.g. Cox, 1966).
|
||||
% --------------------------------------------------------------------------------------------------------
|
||||
% 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.
|
||||
% --- Mc: Corresponds to the input data completeness threshold.
|
||||
% --- m: number of points to divide the data sample, default 100,
|
||||
% recommended 100-1000.
|
||||
% % INPUTS for MODE and BUMP HUNTING
|
||||
% - n_boot: Number of bootstrap iterations for both MM and MB
|
||||
% (default: 100)
|
||||
% - delta_h: Smoothing parameter step for successive trials in defining
|
||||
% the critical h for MM and MB process (h-critical accuracy)
|
||||
% (default: 0.001)
|
||||
% - h : initial value of the smoothing factor to apply in defining the
|
||||
% critical h for the MM testing process (default:0.01)
|
||||
% - MMmeth: Method for multimodality Testing. Possible values:
|
||||
% 'Efron', 'Silverman'
|
||||
% - MBmeth: Method for multibumps Testing. Possible values:
|
||||
% 'Silverman', 'Efron'
|
||||
% NOTE: The initial value for MB process is taken equal to the
|
||||
% critical value defined in the MM process minus its
|
||||
% accuracy (i.e. hcrit_Modes-delta_h, see OUTPUT below)
|
||||
% ---------------------------------------------------------------------------------------------------------
|
||||
% OUTPUT:
|
||||
% - Output Report with data and parameters used
|
||||
% ('Output_MM_MB.txt file')
|
||||
% - Output Parameters:
|
||||
% % DOUBLES:
|
||||
% * n - Number of observations used
|
||||
% * bval- b-value of the G-R law
|
||||
% * Rmodes - The estimated significance of null hypothesis (H01)
|
||||
% * hcrit_modes - estimated critical smoothness parameter for MM test
|
||||
% * Rbumps - The estimated significance of null hypothesis (H02)
|
||||
% * hcrit_bumps - estimated critical smoothness parameter for MB test
|
||||
% * zer1 - point where 1st derivative is zero (extremum)
|
||||
% * zer2 - point(s) where 2nd derivative is zero (inflection points)
|
||||
% [NOTE: zer2 can be a vector]
|
||||
% % VECTORS:
|
||||
% * gau: Data vector PDF estimated for h critical from Multimodality
|
||||
% * gau_b: Data vector PDF estimated for h critical from Multibumps
|
||||
% * poch: 1st derivative of Data vector PDF for h critical from Multibumps
|
||||
% * poch2: 2nd derivative of Data vector PDF for h critical from Multibumps
|
||||
% * x1,x2: minimum and maximum data points after randomization
|
||||
% (parameters needed for plotting)
|
||||
% - Output Figures: Please refer to the Auxiliary Function: "MM_MB_Plot"
|
||||
%
|
||||
% ---------------------------------------------------------------------------------------------------------
|
||||
% REFERENCES:
|
||||
% -- Cox, D. R., (1966), Notes on the analysis of mixed frequency distributions.
|
||||
% Br. J. Math. Stat. Psychol. 19, 39-47, doi.org/10.1111/j.2044-8317.1966.tb00353.x.
|
||||
% -- Efron, B., and Tibshirani R.J. (1993) An Introduction to the Bootstrap,
|
||||
% CRC Press, Boca Raton, Fla.
|
||||
% -- Lasocki S. and E. E, Papadimitriou (2006), "Magnitude distribution
|
||||
% complexity revealed in seismicity from Greece", J. Geophys. Res.,
|
||||
% 111, B11309, doi:10.1029/2005JB003794.
|
||||
% -- Silverman, B. W., (1986), Density estimation for statistics and data analysis,
|
||||
% CRC press, Boa Raton, Fla.
|
||||
% ---------------------------------------------------------------------------------------------------------
|
||||
% 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 [n,bval,Rmodes,hcrit_modes,Rbumps,hcrit_bumps,gau,gau_b,poch,poch2,zer1,zer2,x1,x2]...
|
||||
=MM_MB_V2_8(M,Mc,m,n_boot,h,delta_h,MMmeth,MBmeth)
|
||||
tic
|
||||
mkdir Outputs_MM_MB
|
||||
% define round-off interval and select data above Mc
|
||||
sm=sort(M);dm=sm(2:length(sm))-sm(1:length(sm)-1);
|
||||
dm=dm(dm>0);eps=min(dm);
|
||||
M=M(M>=Mc);
|
||||
|
||||
% calculate beta
|
||||
Rp=round(-log10(eps)); %% check the RP parameter
|
||||
[beta]=beta_AK_UT_Mbin (Mc,M,Rp);
|
||||
|
||||
% Randomize magnitude
|
||||
m_corr(:,1) = korekta(M,Mc,eps,beta);
|
||||
|
||||
% SETTING PARAMETERS
|
||||
n=length(m_corr);
|
||||
x1=min(m_corr)-0.001; %a bit lower than Mmin
|
||||
x2=max(m_corr)+0.001; %a bit higher than Mmax
|
||||
|
||||
|
||||
|
||||
% MULTIMODALITY TESTING
|
||||
[hcrit_modes,gau]=critical_smoothing(m_corr,n,delta_h,x1,x2,m,h);
|
||||
|
||||
% Run Multimodality testing
|
||||
switch MMmeth
|
||||
case 'Efron'
|
||||
[Rmodes] = test_multimodality_e (m_corr,n,x1,x2,m,hcrit_modes,n_boot);
|
||||
case 'Silverman'
|
||||
[Rmodes] = test_multimodality (m_corr,n,x1,x2,m,hcrit_modes,n_boot);
|
||||
end
|
||||
|
||||
% ------------------------------------------------------------------------
|
||||
% [zer1]=zera_1st(m_corr,n,x1,x2,m,hcrit-delta_h);
|
||||
% ------------------------------------------------------------------------
|
||||
|
||||
% BUMP HUNTING
|
||||
[hcrit_bumps,gau_b,poch,poch2]=critical_smoothing_bumps(m_corr,n,delta_h,x1,x2,m,hcrit_modes-delta_h);
|
||||
|
||||
% Run Bump hunting
|
||||
switch MBmeth
|
||||
case 'Silverman'
|
||||
[Rbumps] = bump_hunt (m_corr,n,x1,x2,m,hcrit_bumps,n_boot);
|
||||
case 'Efron'
|
||||
[Rbumps] = bump_hunt_e (m_corr,n,x1,x2,m,hcrit_bumps,n_boot);
|
||||
end
|
||||
|
||||
bval=beta/log(10);
|
||||
% Display and Save the Results:
|
||||
re=table(n,bval,Rmodes,hcrit_modes,Rbumps,hcrit_bumps)
|
||||
|
||||
[zer1]=zera_1st(m_corr,n,x1,x2,m,hcrit_bumps-delta_h); % use the same h in both cases
|
||||
[zer2]=zera_2nd(m_corr,n,x1,x2,m,hcrit_bumps-delta_h);
|
||||
|
||||
|
||||
toc
|
||||
|
||||
% Save Outputs
|
||||
cd Outputs_MM_MB\
|
||||
SaveOuts(eps,Mc,m,n_boot,n_boot,n,bval,Rmodes,hcrit_modes,Rbumps,hcrit_bumps)
|
||||
cd ../
|
||||
end
|
||||
|
||||
% ----- plotting magnitude density and its derivatives ------
|
||||
% ****************************************************
|
||||
|
||||
%% ******************************************************************
|
||||
% *************************** 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
|
||||
%% --------------------------------------------------------------------------------------
|
||||
% Finding critical smoothing parameter value for which the non parametric
|
||||
% PDF demonstrates one mode in the selected interval
|
||||
%
|
||||
function [hcrit,gau]=critical_smoothing(mm,n,delta_h,x1,x2,m,h)
|
||||
%
|
||||
x=sort(mm);
|
||||
p=2.0;
|
||||
c=sqrt(2*pi);
|
||||
%x1=input('Lower limit ');
|
||||
%x2=input('Upper limit ');
|
||||
%m=input('No. of points ');
|
||||
y=linspace(x1,x2,m);
|
||||
%h=input('Initial smoothing factor ');
|
||||
while p>1
|
||||
for i=1:m,
|
||||
poch(i)=-sum((y(i)-x).*exp(-0.5*((y(i)-x)./h).^2));
|
||||
end
|
||||
p=0;
|
||||
for i=2:m,
|
||||
if poch(i-1)*poch(i)<0
|
||||
p=p+1;
|
||||
end
|
||||
end
|
||||
h=h+delta_h;
|
||||
end
|
||||
hcrit=h-delta_h;
|
||||
for i=1:m,
|
||||
gau(i)=sum(exp(-0.5*((y(i)-x)./hcrit).^2))/c/n/hcrit;
|
||||
end
|
||||
end
|
||||
%% --------------------------------------------------------------------------------------
|
||||
% "SMOOTHED BOOTSTRAP"
|
||||
%
|
||||
function [R]=test_multimodality(m,n,x1,x2,n_point,h_crit,mm)
|
||||
%
|
||||
x=sort(m);
|
||||
c=sqrt(2*pi);
|
||||
%x1=input('Lower limit ');
|
||||
%x2=input('Upper limit ');
|
||||
%m=input('No. of points ');
|
||||
y=linspace(x1,x2,n_point);
|
||||
%h_crit=input('Critical smoothing factor ');
|
||||
%mm=input('No of trials ');
|
||||
no_wielom=0;
|
||||
for j=1:mm,
|
||||
ind=unidrnd(n,n,1);
|
||||
eps=normrnd(0,1,n,1);
|
||||
z=x(ind)+h_crit.*eps;
|
||||
z=sort(z);
|
||||
poch(1)=-sum((y(1)-z).*exp(-0.5*((y(1)-z)./h_crit).^2));
|
||||
p=0;
|
||||
for i=2:n_point,
|
||||
poch(i)=-sum((y(i)-z).*exp(-0.5*((y(i)-z)./h_crit).^2));
|
||||
if poch(i-1)*poch(i)<0
|
||||
p=p+1;
|
||||
end
|
||||
end
|
||||
if p>1
|
||||
no_wielom=no_wielom+1;
|
||||
end
|
||||
end
|
||||
R=no_wielom/mm;
|
||||
end
|
||||
%% --------------------------------------------------------------------------------------
|
||||
% "SMOOTHED BOOTSTRAP"
|
||||
% EFRON
|
||||
%
|
||||
function [R]=test_multimodality_e(m,n,x1,x2,n_point,h_crit,mm)
|
||||
%
|
||||
x=sort(m);
|
||||
s2=sqrt(1+h_crit^2/var(x));
|
||||
c=sqrt(2*pi);
|
||||
%x1=input('Lower limit ');
|
||||
%x2=input('Upper limit ');
|
||||
%m=input('No. of points ');
|
||||
y=linspace(x1,x2,n_point);
|
||||
%h_crit=input('Critical smoothing factor ');
|
||||
%mm=input('No of trials ');
|
||||
no_wielom=0;
|
||||
for j=1:mm,
|
||||
ind=unidrnd(n,n,1);
|
||||
eps=normrnd(0,1,n,1);
|
||||
me=mean(x(ind));
|
||||
z=me+(x(ind)-me+h_crit.*eps)./s2;
|
||||
z=sort(z);
|
||||
poch(1)=-sum((y(1)-z).*exp(-0.5*((y(1)-z)./h_crit).^2));
|
||||
p=0;
|
||||
for i=2:n_point,
|
||||
poch(i)=-sum((y(i)-z).*exp(-0.5*((y(i)-z)./h_crit).^2));
|
||||
if poch(i-1)*poch(i)<0
|
||||
p=p+1;
|
||||
end
|
||||
end
|
||||
if p>1
|
||||
no_wielom=no_wielom+1;
|
||||
end
|
||||
end
|
||||
R=no_wielom/mm;
|
||||
end
|
||||
%% --------------------------------------------------------------------------------------
|
||||
% Finding critical smoothing parameter value for which the non parametric
|
||||
% PDF demonstrates one bump in the selected interval
|
||||
%
|
||||
function [hcrit,gau,poch,poch2]=critical_smoothing_bumps(mm,n,delta_h,x1,x2,m,h)
|
||||
%
|
||||
x=sort(mm);
|
||||
p=2.0;
|
||||
c=sqrt(2*pi);
|
||||
%x1=input('Lower limit ');
|
||||
%x2=input('Upper limit ');
|
||||
%m=input('No. of points ');
|
||||
y=linspace(x1,x2,m);
|
||||
%h=input('Initial smoothing factor ');
|
||||
while p>1
|
||||
for i=1:m,
|
||||
% poch(i)=-sum((y(i)-x).*exp(-0.5*((y(i)-x)./h).^2));
|
||||
poch2(i)=sum((((y(i)-x)./h).^2-1).*exp(-0.5*((y(i)-x)./h).^2));
|
||||
end
|
||||
p=0;
|
||||
for i=2:m,
|
||||
if poch2(i-1)*poch2(i)<0
|
||||
p=p+1;
|
||||
end
|
||||
end
|
||||
h=h+delta_h;
|
||||
end
|
||||
hcrit=h-delta_h;
|
||||
for i=1:m,
|
||||
gau(i)=sum(exp(-0.5*((y(i)-x)/hcrit).^2))/c/n/hcrit;
|
||||
poch(i)=-sum((y(i)-x).*exp(-0.5*((y(i)-x)./hcrit).^2));
|
||||
poch2(i)=sum((((y(i)-x)./hcrit).^2-1).*exp(-0.5*((y(i)-x)./hcrit).^2));
|
||||
end
|
||||
end
|
||||
%% --------------------------------------------------------------------------------------
|
||||
% "SMOOTHED BOOTSTRAP"
|
||||
%
|
||||
function [R]=bump_hunt(m,n,x1,x2,n_point,h_crit,mm)
|
||||
%
|
||||
x=sort(m);
|
||||
c=sqrt(2*pi);
|
||||
%x1=input('Lower limit ');
|
||||
%x2=input('Upper limit ');
|
||||
%m=input('No. of points ');
|
||||
y=linspace(x1,x2,n_point);
|
||||
%h_crit=input('Critical smoothing factor ');
|
||||
%mm=input('No of trials ');
|
||||
no_bump=0;
|
||||
for j=1:mm,
|
||||
ind=unidrnd(n,n,1);
|
||||
eps=normrnd(0,1,n,1);
|
||||
z=x(ind)+h_crit.*eps;
|
||||
z=sort(z);
|
||||
% poch(1)=-sum((y(1)-z).*exp(-0.5*((y(1)-z)./h_crit).^2));
|
||||
poch2(1)=sum((((y(1)-z)./h_crit).^2-1).*exp(-0.5*((y(1)-z)./h_crit).^2));
|
||||
p=0;
|
||||
for i=2:n_point,
|
||||
% poch(i)=-sum((y(i)-z).*exp(-0.5*((y(i)-z)./h_crit).^2));
|
||||
poch2(i)=sum((((y(i)-z)./h_crit).^2-1).*exp(-0.5*((y(i)-z)./h_crit).^2));
|
||||
if poch2(i-1)*poch2(i)<0
|
||||
p=p+1;
|
||||
end
|
||||
end
|
||||
if p>1
|
||||
no_bump=no_bump+1;
|
||||
end
|
||||
end
|
||||
R=no_bump/mm;
|
||||
end
|
||||
%% --------------------------------------------------------------------------------------
|
||||
% "SMOOTHED BOOTSTRAP"
|
||||
% EFRON
|
||||
%
|
||||
function [R]=bump_hunt_e(m,n,x1,x2,n_point,h_crit,mm)
|
||||
%
|
||||
x=sort(m);
|
||||
s2=sqrt(1+h_crit^2/var(x));
|
||||
c=sqrt(2*pi);
|
||||
%x1=input('Lower limit ');
|
||||
%x2=input('Upper limit ');
|
||||
%m=input('No. of points ');
|
||||
y=linspace(x1,x2,n_point);
|
||||
%h_crit=input('Critical smoothing factor ');
|
||||
%mm=input('No of trials ');
|
||||
no_bump=0;
|
||||
for j=1:mm,
|
||||
ind=unidrnd(n,n,1);
|
||||
eps=normrnd(0,1,n,1);
|
||||
me=mean(x(ind));
|
||||
z=me+(x(ind)-me+h_crit.*eps)./s2;
|
||||
z=sort(z);
|
||||
% poch(1)=-sum((y(1)-z).*exp(-0.5*((y(1)-z)./h_crit).^2));
|
||||
poch2(1)=sum((((y(1)-z)./h_crit).^2-1).*exp(-0.5*((y(1)-z)./h_crit).^2));
|
||||
p=0;
|
||||
for i=2:n_point,
|
||||
% poch(i)=-sum((y(i)-z).*exp(-0.5*((y(i)-z)./h_crit).^2));
|
||||
poch2(i)=sum((((y(i)-z)./h_crit).^2-1).*exp(-0.5*((y(i)-z)./h_crit).^2));
|
||||
if poch2(i-1)*poch2(i)<0
|
||||
p=p+1;
|
||||
end
|
||||
end
|
||||
if p>1
|
||||
no_bump=no_bump+1;
|
||||
end
|
||||
end
|
||||
R=no_bump/mm;
|
||||
end
|
||||
|
||||
%% --------------------------------------------------------------------------------------
|
||||
% Determination of PDF first derivative zeros estimates in the selected interval
|
||||
%
|
||||
function [zer1]=zera_1st(mm,n,x1,x2,m,h)
|
||||
%
|
||||
x=sort(mm);
|
||||
c=sqrt(2*pi);
|
||||
y=linspace(x1,x2,m);
|
||||
for i=1:m,
|
||||
poch(i)=-sum((y(i)-x).*exp(-0.5*((y(i)-x)./h).^2));
|
||||
end
|
||||
p=0;
|
||||
for i=2:m,
|
||||
if poch(i-1)*poch(i)<0
|
||||
p=p+1;
|
||||
zer1(p)=(y(i)+y(i-1))/2; %K 23JAN2019
|
||||
end
|
||||
end
|
||||
|
||||
end
|
||||
%% --------------------------------------------------------------------------------------
|
||||
% Determination of PDF second derivative zeros estimates in the selected interval
|
||||
%
|
||||
|
||||
function [zer2]=zera_2nd(mm,n,x1,x2,m,h)
|
||||
%
|
||||
x=sort(mm);
|
||||
c=sqrt(2*pi);
|
||||
y=linspace(x1,x2,m);
|
||||
for i=1:m,
|
||||
poch2(i)=sum((((y(i)-x)./h).^2-1).*exp(-0.5*((y(i)-x)./h).^2));
|
||||
end
|
||||
p1=0;
|
||||
for i=2:m,
|
||||
if poch2(i-1)*poch2(i)<0
|
||||
p1=p1+1;
|
||||
zer2(p1)=(y(i)+y(i-1))/2; %K 23JAN2019
|
||||
end
|
||||
end
|
||||
|
||||
end
|
||||
%% --------------------------------------------------------------------------------------------------------
|
||||
% --------------------------------------- SAVE OUTPUTS in the report file ---------------------------------------
|
||||
% Save Outputs
|
||||
function SaveOuts(EPS,Mmin,m,n_boot1,n_boot2,n,bval,Rmodes,hcrit_modes,Rbumps,hcrit_bumps)
|
||||
% ---- Save *.txt file with Parameters Report ----
|
||||
%cd Outputs/
|
||||
fid=fopen('REPORT_Multimodality.txt','w');
|
||||
fprintf(fid,['RESULTS from MULTIMODALITY/MULTIBUMP TESTING (created on ', datestr(now),')\n']);
|
||||
fprintf(fid,'------------------------------------------------------------------------------\n');
|
||||
fprintf(fid,['<Data Round-off interval >: ', num2str(EPS),'\n']);
|
||||
fprintf(fid,['<Number of points to divide the sample >: ', num2str(m),'\n']);
|
||||
fprintf(fid,['<Completeness Threshold >: ', num2str(Mmin),'\n']);
|
||||
fprintf(fid,['<Number of events used >: ', num2str(n),'\n']);
|
||||
fprintf(fid,['<Gutenberg-Richter b-value >: ', num2str(bval,'%5.3f'),'\n']);
|
||||
fprintf(fid,['<Number of bootstrap iterations (multimodality) >: ', num2str(n_boot1),'\n']);
|
||||
fprintf(fid,['<Number of bootstrap iterations (multibumps) >: ', num2str(n_boot2),'\n']);
|
||||
fprintf(fid,'------------------------------------------------------------------------------\n');
|
||||
fprintf(fid,['<Critical Smoothing Parameter,h (for modes) >: ', num2str(hcrit_modes,'%6.4f'),'\n']);
|
||||
fprintf(fid,['<Critical Smoothing Parameter,h (for bumps) >: ', num2str(hcrit_bumps,'%6.4f'),'\n']);
|
||||
fprintf(fid,['<p-value of H01 that input data PDF is unimodal >: ', num2str(Rmodes,'%4.3f'),'\n']);
|
||||
fprintf(fid,['<p-value of H02 that input data PDF has no more than \n']);
|
||||
fprintf(fid,[' one bump to the right of the global maximum >: ', num2str(Rbumps,'%4.3f'),'\n']);
|
||||
|
||||
|
||||
|
||||
fclose(fid);
|
||||
|
||||
end
|
||||
@@ -0,0 +1,46 @@
|
||||
% This is a Wrapper Script for performing a test for the existence of multi-modes
|
||||
% and multi-bumps in a given (magnitude) time-series. The function MM_MB is
|
||||
% executed for this purpose. The description of the fuction can be found in
|
||||
% comments within "MM_MB_V2_*.m" code. Here, the input data and the
|
||||
% parameters (i.e. the function's arguments) are defined by the User. Please
|
||||
% modify the 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
|
||||
M=dlmread('test_vector.txt'); % PLEASE SET data (magnitude) vector input file
|
||||
cd ../
|
||||
|
||||
% STEP 2. Completeness Threshold Selection:
|
||||
Mc=1.5; % PLEASE SET
|
||||
|
||||
% STEP 3. Number of points:
|
||||
m=100; % PLEASE SET
|
||||
|
||||
% STEP 4. Bootstrap Iterations:
|
||||
n_boot=100; % PLEASE SET
|
||||
|
||||
% STEP 5. Initial h:
|
||||
h=0.01; % PLEASE SET
|
||||
|
||||
% STEP 6. h step (dh):
|
||||
delta_h=0.001; % PLEASE SET
|
||||
|
||||
% STEP 7. Method for MM testing:
|
||||
MMmeth='Efron'; % PLEASE SET
|
||||
|
||||
% STEP 8. Method for MB testing:
|
||||
MBmeth='Silverman'; % PLEASE SET
|
||||
|
||||
% STEP 9. RUN Function ['MM_MB']
|
||||
[n,bval,Rmodes,hcrit_modes,Rbumps,hcrit_bumps,gau,gau_b,poch,poch2,zer1,zer2,x1,x2]=...
|
||||
MM_MB_V2_8(M,Mc,m,n_boot,h,delta_h,MMmeth,MBmeth);
|
||||
|
||||
% STEP 10. Optional, Plotting % PLEASE Comment the next line to deactivate visualization
|
||||
MM_MB_Plot(M,Mc,x1,x2,m,zer1,zer2,gau_b,poch,poch2);
|
||||
|
||||
|
||||
|
||||
Binary file not shown.
@@ -0,0 +1,880 @@
|
||||
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
|
||||
Reference in New Issue
Block a user