Matlab tips (16) consistency verification of matrix eigenvector eigenvalue solution -- analytic hierarchy process

Preface

MATLAB Learning about image processing is very friendly , You can start from scratch , There are many encapsulated functions that can be called directly for basic image processing , This series of articles is mainly to introduce some of you in MATLAB Some concept functions are commonly used in routine demonstration ！

The eigenvalues and eigenvectors of the matrix are solved , According to the maximum eigenvalue and the corresponding eigenvector , The feature vector of criterion layer and the maximum feature root of criterion layer are obtained , Then calculate the consistency inspection parameters , If the threshold is satisfied, the consistency verification is satisfied , If the threshold is not met, it needs to be re scored .

The example encountered when searching for data , Here to share ,MATLAB Version is MATLAB2015b.

One . MATLAB Simulation

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% function ： Consistency verification of eigenvalue solution of matrix eigenvector -- Analytic hierarchy process example 
% Environmental Science ：Win7,Matlab2015b
%Modi: C.S
% Time ：2022-06-24
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%  Clear environment variables 
clear all
clc

tic
A=[1	1/5	 1	1/5	 1/6   1/6
5	1	 5	1/2	 1/2   1/2
2	1/5	 1  1/4	 1/6   1/4
5	1/2	 4	1	 1/2   1/2
6	2	 6	2	 1	   1
6	2	 4	2	 1	   1]

[n,n]=size(A);
[V,D]=eig(A);% Get the eigenvector and eigenvalue 
            % Find the maximum eigenvalue and its corresponding eigenvector 
tempNum=D(1,1);
pos=1;
for h=1:n
    if D(h,h)>tempNum
        tempNum=D(h,h);
        pos=h;
    end
end    
w=abs(V(:,pos));
w=w/sum(w);
t=D(pos,pos);
disp(' Criterion layer eigenvector w=');disp(w);disp(' Maximum characteristic root of criterion layer t=');disp(t);
         % The following is the consistency test 
CI=(t-n)/(n-1);RI=[0 0 0.58 0.89 1.12 1.26 1.36 1.41 1.46 1.49 1.52 1.54 1.56 1.58 1.59 1.60 1.61 1.615 1.62 1.63];
CR=CI/RI(n);
if CR<0.10
    disp(' The consistency of this matrix is acceptable !');
    disp('CI=');disp(CI);
    disp('CR=');disp(CR);
else
    disp(' Consistency verification of this matrix failed , Please re rate !');
end
toc

Two . Simulation results

A =

    1.0000    0.2000    1.0000    0.2000    0.1667    0.1667
    5.0000    1.0000    5.0000    0.5000    0.5000    0.5000
    2.0000    0.2000    1.0000    0.2500    0.1667    0.2500
    5.0000    0.5000    4.0000    1.0000    0.5000    0.5000
    6.0000    2.0000    6.0000    2.0000    1.0000    1.0000
    6.0000    2.0000    4.0000    2.0000    1.0000    1.0000

 Criterion layer eigenvector w=
    0.0425
    0.1677
    0.0546
    0.1580
    0.2976
    0.2797

 Maximum characteristic root of criterion layer t=
    6.0846

 The consistency of this matrix is acceptable !
CI=
    0.0169

CR=
    0.0134

 Time has passed  0.007250  second .

3、 ... and . Summary

Examples of consistency verification , It may be used later , Take a note here . Learn one every day MATLAB Little knowledge , Let's learn and make progress together ！