Find minimum value out of a 3D contour plot

Hi!

I plotted a contour graph and I want to find its minimum value i.e. without using a thinner mesh. However, I do not know what is the best way to get its minimum value as much accurate as possible. I do not know if an interpolation or fit is the best way to do that or if exists a better option. What I exactly want are the values of a and c for which M is minimum.

a=[SUMMARY(1,1) SUMMARY(10,1) SUMMARY(19,1) SUMMARY(28,1) SUMMARY(37,1) SUMMARY(46,1) SUMMARY(55,1) SUMMARY(64,1) SUMMARY(73,1)];
c=[SUMMARY(1,2) SUMMARY(2,2) SUMMARY(3,2) SUMMARY(4,2) SUMMARY(5,2) SUMMARY(6,2) SUMMARY(7,2) SUMMARY(8,2) SUMMARY(9,2)];
[x,y]=meshgrid(a,c);

M=zeros(9,9);
for i=1:length(SUMMARY)
    if i<=9
    M(1,i)=SUMMARY(i,5); 
    elseif i>9 && i<=18
    M(2,i-9)=SUMMARY(i,5); 
    elseif i>18 && i<=27
    M(3,i-18)=SUMMARY(i,5); 
    elseif i>27 && i<=36
    M(4,i-27)=SUMMARY(i,5);  
    elseif i>36 && i<=45
    M(5,i-36)=SUMMARY(i,5); 
    elseif i>45 && i<=54
    M(6,i-45)=SUMMARY(i,5); 
    elseif i>54 && i<=63
    M(7,i-54)=SUMMARY(i,5);    
    elseif i>63 && i<=72
    M(8,i-63)=SUMMARY(i,5); 
    elseif i>72 && i<=81
    M(9,i-72)=SUMMARY(i,5); 
    end
end
contourf(x,y,M)
xlabel('a (\AA)','Interpreter','Latex','FontSize',14,'FontWeight','bold');
ylabel('c (\AA)','Interpreter','Latex','FontSize',14,'FontWeight','bold');

Regard

[Adam Danz]

Attaching a mat file with experimental_data_1 and experimental_data_2 data would give us a full picture of what's going on in that contour plot.

[Miguel Cardoso]

I added the full code and attached my experimental data.

Answer 1

[Adam Danz]

Below is a simplification of your code.

load('SUMMARY.mat')
a = SUMMARY([1 10 19 28 37 46 55 64 73],1).'; % Simpler
c = SUMMARY(1:9,2).';                         % Simpler
[x,y]=meshgrid(a,c);

M = reshape(SUMMARY(:,5),size(x)).'; % This produces the same thing as your for-loop.
 
contourf(x,y,M); 
xlabel('a (\AA)','Interpreter','Latex','FontSize',14,'FontWeight','bold');
ylabel('c (\AA)','Interpreter','Latex','FontSize',14,'FontWeight','bold');

axis equal; % added
colorbar    % added

To find the (x,y) coordinate of the minimum z-value within your data,

[~, minIdx] = min(M(:)); 
[row,col] = ind2sub(size(M),minIdx); 
xMin = x(row,col); 
yMin = y(row,col); 

% Plot this coordinate
hold on 
plot(xMin, yMin, 'rx')

[Update] To interpolate and find minimum, (plot shown below)

% same as above
load('SUMMARY.mat')
a = SUMMARY([1 10 19 28 37 46 55 64 73],1).'; 
c = SUMMARY(1:9,2).'; 
[x,y]=meshgrid(a,c);
M = reshape(SUMMARY(:,5),size(x)).';
contourf(x,y,M,20); 

% interpolate using cubic convolution (1000 points)
[xq,yq]=meshgrid(linspace(min(a),max(a),1000), linspace(min(c),max(c),1000));
Mq = interp2(x,y,M,xq,yq,'cubic');

% Same as above but acting on interpolated data
% Find min
[~, minIdx] = min(Mq(:)); 
[row,col] = ind2sub(size(Mq),minIdx); 
xMin = xq(row,col); 
yMin = yq(row,col); 
% Mark min  on plot
hold on 
plot(xMin, yMin, 'rx', 'MarkerSize', 12)

[Miguel Cardoso]

Thank you Adam Danz.

[Adam Danz]

You may also want to in create the number of contour lines using the levels input: contourf(___,levels)

contourf(x,y,M,20); 

Also, to see all of your data points on top of the contour,

hold on
plot(x(:),y(:),'m.')

[Miguel Cardoso]

It is possible to interpolate this region and get a point outside of my dataset? I do not know if I should use an interpolation or a fit.

[Adam Danz]

Yes! I've updated my answer to show how.