├── quadrant.m
├── quadrantwieghted.m
└── QuadScanalphawieghtedFull.m


/quadrant.m:
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 1 | function qq=quadrant(rr)
 2 | 
 3 | %This function is to calculate the density quadrant scan curve from a recurrence matrix rr
 4 | 
 5 | [dx,dy]=size(rr);
 6 | 
 7 | if dx~=dy,
 8 |     disp('matrix not square');
 9 | end;
10 | 
11 | hand=waitbar(0,'quadrant');
12 | 
13 | for i=1:dx
14 |     pp=rr(1:i,1:i);  %points at the first quadrant
15 |     ff=rr((i+1):dx,(i+1):dx);  %points at the third quadrant
16 |     pf=rr(1:i,(i+1):dx);   %points at the second quadrant
17 |     fp=rr((i+1):dx,1:i);    % points at the fourth quadrant
18 |     qs=(sum(pp(:))+sum(ff(:))) /(i^2+(dx-i)^2);
19 |     qs=qs / (qs + (sum(pf(:))+sum(fp(:)))/(i*(dx-i)*2));
20 |     qq(i)=qs;
21 |     waitbar(i/dx,hand);
22 | 
23 | end;
24 | close(hand);
25 | 


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/quadrantwieghted.m:
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 1 | function qq=quadrantwieghted(rr)
 2 | 
 3 | %This function is to calculate the weighted quadrand scan from a recurrence matrix rr
 4 | 
 5 | [dx,dy]=size(rr);
 6 | 
 7 | if dx~=dy,
 8 |     disp('matrix not square');
 9 | end;
10 | 
11 | hand=waitbar(0,'quadrant');
12 | qq(1)=0.5;
13 | qq(dx)=0.5;
14 | for i=2:dx-1
15 |     wieghtp=0.5*(1-tanh(((1:i-1)-200)/50));  %the 200 and 50 are parameters and should be changed according to your application
16 |     wieghtp=wieghtp(end:-1:1);
17 |     wieghtf=0.5*(1-tanh(((1:dx-i)-200)/50)); %the 200 and 50 are parameters and should be changed according to your application
18 |     wieghtpp=wieghtp'*wieghtp;
19 |     wieghtpp=wieghtpp./wieghtpp(end,end);
20 |     wieghtff=wieghtf'*wieghtf;
21 |     wieghtff=wieghtff./wieghtff(1,1);
22 |     wieghtpf=wieghtp'*wieghtf;
23 |     wieghtpf=wieghtpf./wieghtpf(end,1);
24 |     wieghtfp=wieghtf'*wieghtp;
25 |     wieghtfp=wieghtfp./wieghtfp(1,end);
26 |     pp=rr(1:(i-1),1:(i-1)).*wieghtpp;
27 |     ff=rr((i+1):dx,(i+1):dx).*wieghtff;
28 |     pf=rr(1:(i-1),(i+1):dx).*wieghtpf;
29 |     fp=rr((i+1):dx,1:(i-1)).*wieghtfp;
30 |     qs=sum(pp(:))+sum(ff(:));
31 |     qs=qs / (qs + (sum(pf(:))+sum(fp(:))));
32 |     qq(i)=qs;
33 |     waitbar(i/dx,hand);
34 | 
35 | end;
36 | close(hand);
37 | 


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/QuadScanalphawieghtedFull.m:
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 1 | function [Dist,RM,QS]=QuadScanalphawieghtedFull(X,alpha)
 2 | 
 3 | %This function is to apply Recurrence plot and Quardant Scan analysis for
 4 | %transitions or boundaries detection. 
 5 | %X is the input data, X could be multivariate input where columns
 6 | %are the variables
 7 | %alpha is the threshold, it is for the recurrence analysis
 8 | %Dist is the distance (norm) matrix, RM is the recurrence matrix, QS is the quadrant scan curve
 9 | %If you use this code please read and cite our paper "Fast Automatic Detection of Geological Boundaries from Multivariate Log Data Using Recurrence
10 | %Journal: Computers and Geosciences"
11 | 
12 | X=bsxfun(@rdivide,X,sum(X)); %normalisation (importnat when we have multi-variable input)
13 | 
14 | N = size(X,1);
15 | 
16 | Dist=zeros(N);
17 | 
18 | %%%% Norm Matrix %%%%
19 | for i=1:N
20 |     
21 |     x0=i;
22 |     for j=i:N
23 |         y0=j;
24 |         % Calculate the euclidean distance
25 |         distance = norm(X(i,:)-X(j,:));
26 |         % Store the minimum distance between the two points
27 |         Dist(x0,y0) = distance;
28 |         Dist(y0,x0) = distance;        
29 |     end
30 | end
31 | 
32 | 
33 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%Ploting the Distance (Norm) Matrix)%%%%%
34 | 
35 |     figure('Position',[100 100 550 400]);
36 |     imagesc(Dist);
37 |     colorbar;
38 |     axis image;    
39 |     xlabel('Depth Index','FontSize',10,'FontWeight','bold');
40 |     ylabel('Depth Index','FontSize',10,'FontWeight','bold');
41 |     title('Norm Matrix','FontSize',10,'FontWeight','bold');
42 |     get(gcf,'CurrentAxes');
43 |     set(gca,'YDir','normal')
44 |     set(gca,'LineWidth',2,'FontSize',10,'FontWeight','bold');
45 | 
46 | 
47 | %%%%% Define threshold %%%%
48 | threshold=alpha*(mean(Dist(:))+3*std(Dist(:)));
49 | 
50 | %%%%% Recurrence plot matrix %%%%
51 | RM=zeros(size(Dist,1),size(Dist,2));
52 | for i=1:size(Dist,1)       
53 |     for j=i+1:size(Dist,1)
54 |         if Dist(i,j) <= threshold
55 |             RM(i,j)=1;
56 |             RM(j,i)=1;
57 |         end
58 |     end
59 | end
60 | RM = RM +eye(size(Dist,1));
61 | 
62 | %%%% Ploting the recurrence plot %%%
63 |     figure('Position',[100 100 550 400]);
64 |     imagesc(RM);
65 |     axis image;    
66 |     xlabel('Depth','FontSize',10,'FontWeight','bold');
67 |     ylabel('Depth','FontSize',10,'FontWeight','bold');
68 |     title('Recurrence Plot','FontSize',10,'FontWeight','bold');
69 |     get(gcf,'CurrentAxes');
70 |     set(gca,'YDir','normal')
71 |     set(gca,'LineWidth',2,'FontSize',10,'FontWeight','bold');
72 | 
73 | %%%% Quadrant Scan: Two options: %%%%
74 | % (1) Density QS 
75 |  QS=quadrant(RM);   % Density Quadrant Scan: import Function "quadrant"
76 | 
77 | % (2) Weighted QS
78 | % QS=quadrantwieghted(RM); %Weighted Quadrant Scan: import Function "quadrantwieghted"
79 | 
80 | %%%% Ploting the quadrant scan %%%%
81 | figure('Position',[100 100 550 400]);
82 | plot(QS)
83 | 


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