How can I use a loop to maximize correlation of multiple graphs?

I have data that is made up of a (mostly) horizontal line, a sloped line, and another horizontal line, as shown below. I am trying to get a best fit for each section and have tried to do this using the correlation coefficient. What I would like to do is create a loop that will determine the best location (j and k variables) to get the length of sections that result in the best fit for the sloped section.

Many of the things I have tried don't work because the correlation is dependent on the values of j and k, making the solution iterative rather than something that could be solved using fminsearch or similar solvers.

Thank you for any help!

function CrackLocationFIT 

file = 'FileName.xlsx'

T = readtable(file, 'Sheet', 'Sheet Name'); %import table from excel

[a,~]=size(T); %determine size of imported table

n = a;
increment = 13; %number of lines to skip when reading excel files

xdata = 0:199; %number of data points

for i = 15:increment:n
    A = xlsread(file, 'Sheet Name', strcat('C',num2str(i),':GT',num2str(i))); %read y-coordinates from the excel sheet
    scatter(xdata,A,'k', '.') %plot scatter for data set
   
    j = 25;
    k = 140;
    
    sec1 = 0:(j-1);
    sec2 = j:(k-1);
    sec3 = k:199;
    
    P1 = mean(A(:,1:j));
    P2 = polyfit(sec2,A(:,(j+1):(k)),1);
    P3 = mean(A(:,(k+1):200));
     
    yfit1 = repmat(P1(1),1,length(sec1));
    yfit2 = P2(1)*sec2+P2(2);
    yfit3 = repmat(P3(1),1,length(sec3));
        
    c1 = corrcoef(yfit1,A(:,1:j));
    c2 = corrcoef(yfit2,A(:,(j+1):(k)));
    c3 = corrcoef(yfit3,A(:,(k+1):200));

    plot(sec1,yfit1,'-r') %plot data for data set 1
    plot(sec2,yfit2,'-r') %plot data for data set 2
    plot(sec3,yfit3,'-r') %plot data for data set 3

    xlabel('Location Along Perpendicular Line')
    xlim([0 199]) %set x limit for uniform plot
    ylabel('Y Displacement [in,]')
    title(graphtitle)
    hold on
    
end

hold off

end

Answer 1

[Stijn Haenen]

Maybe something like this can help you:

clear
Y_data=[ones(1,40)*-6,-6:-2/20:-8,ones(1,140)*-8]; %just an example
for x1=1:197
    for x2=x1+2:199
        hor_section_1=ones(x1,1)*mean(Y_data(1:x1)); %first horizontal section
        hor_section_2=ones(200-x2,1)*mean(Y_data(200-x2:200)); %second horizontal section
        slope=hor_section_1(1):(hor_section_2(1)-hor_section_1(1))/(x2-x1):hor_section_2(1); %slanting line inbetween
        line=[hor_section_1(:)',slope(:)', hor_section_2(:)'];

        corr0(x1,x2)=sum(Y_data.*line)/sqrt(sum(Y_data.^2)*sum(line.^2)); 
    end
end
[a,b]=find(corr0==max(corr0(:)));

[Mary Juno]

That worked! Thank you so much!