Accurately obtaining the value of a variable at the requested points

Dear all

I am attaching a data set, where the first and second columns represent spatial coordinates (x,y) in two-dimensional space, while the third column shows the value of a given magnitude at the aforementioned set of (x,y) points. I was wondering which could be the best option in a scenario inside a for loop, where the (x,y) variables change at each step, to obtain an accurate value for the aforementioned variable defined in the third column of the attached file, even if for that combination of (x,y) coordinates the value of the variable is not present a priori. Would be something like

griddata(file(:,1),file(:,2),file(:,3),x,y,"cubic");

a quick and accurate approach?

[Ayush Modi]

Hi Richard,

Your data is gridded. It is better to go with griddedInterpolant method.

Refer the following MathWorks documentation for more information on griddedInterpolant function:

https://www.mathworks.com/help/matlab/ref/griddedinterpolant.html

To learn more about different interpolation methods in griddedInterpolant function, refer the following section:

https://www.mathworks.com/help/matlab/ref/griddedinterpolant.html#bvh2cy0-Method:~:text=Sample%20values%0Aarray-,Method%20%E2%80%94%20Interpolation%20method,-%27linear%27%20(default

Note - You can optimize your code, by using vectorization to make a single call to the function instead of making multiple calls from inside a for loop.

Refer to the following MathWorks documentation to know more about vectorization:

https://www.mathworks.com/help/matlab/matlab_prog/vectorization.html

Answer 1

[Divyam]

Hi @Richard Wood,

Interpolation can be used in this scenario to figure out the unknown values. To run either 'griddata' or 'griddedInterpolant' there must be enough data entries for each grid dimension which is not the case in the data you provided. In scenarios like these, you can either use the 'reshape' function to reshape your data or use 'scatteredInterpolant' for scattered interpolation.

%% Preprocessing the data to get unique values for x and y
T = readtable('file.txt','Delimiter',' ');
arr = table2array(T);
[r,c] = size(arr);
% This loop can be edited to get unique values for (x,y) pair
for i=1:200
    x(i) = arr(2*i+200*i-1,1);
    y(i) = arr(2*i+200*i-1,2);
    mag(i) = arr(2*i+200*i-1,3);
end

%% Using scattered interpolation
F = scatteredInterpolant(x',y',mag');
xq = linspace(-100,-50,100);
yq = linspace(-100,-50,100);
magOut = F(xq,yq);

%% Plotting 3-D Data
plot3(x,y,mag,'.',xq,yq,magOut,'o');
grid on
title('Linear Interpolation');
xlabel('x'), ylabel('y'), zlabel('Values');
legend('Sample data','Interpolated query data','Location','Best');

For more information regarding 'scatteredInterpolant' you can refer to the following documentation: https://www.mathworks.com/help/matlab/ref/scatteredinterpolant.html