multiple integration with non uniform spacing
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I need help to find an area intergeral of the attached file(av_val_1) with 10 columns.
where 1st column = R , second column = C, Fifth column = F(R,C).
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
R= avg_val_1(:,1);%first columsn = r axis
C = avg_val_1(:,2);%second column = c axis
F = avg_val_1(:,5);%fifth column = F(r,c)
I = trapz(C,trapz(R,F,2)); %area integeral of the total area. This line is wrong.
And
q = integral2(F(r,c),Rmin,Rmax,Cmin,Cmax) %area integeral of the particular area portion. This line is wrong. please see attached figure for reference
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Accepted Answer
Ameer Hamza
on 26 Apr 2020
Edited: Ameer Hamza
on 26 Apr 2020
You first need to convert the data into a grid before applying the trapz twice
x = load('avg_val_1.txt');
R = x(:,1);
C = x(:,2);
F = x(:,5);
r = linspace(min(R), max(R), 1000);
c = linspace(min(C), max(C), 1000);
[Rg, Cg] = meshgrid(r, c);
Fg = griddata(R, C, F, Rg, Cg);
result = trapz(c, trapz(r, Fg, 2));
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More Answers (3)
MS
on 26 Apr 2020
Edited: Ameer Hamza
on 26 Apr 2020
13 Comments
Ameer Hamza
on 26 Apr 2020
Sorry, I don't have much expertise in multivariate calculus.
Isn't this just two independent integrals. You can do it like this.
trapz(r,u) + trapz(c,v)
Ameer Hamza
on 27 Apr 2020
For simple integrals, you don't need to use geiddata. You can do something like this
%%%%%%%%%%%%%%%%
for i=1:numel(avg_mat)
writematrix(avg_mat{i}, ['avg_val_' num2str(i)]);
R = avg_mat{i}(:,1);
C = avg_mat{i}(:,2);
u = avg_mat{i}(:,3);
v = avg_mat{i}(:,4);
line_integeral(i)= trapz(R,u) + trapz(C,v)
% fseg = interp2(Rg,Cg,Fg,rcseg(:,1),rcseg(:,2)); %%this line is wrong, The number of input coordinate arrays does not equal the number of dimensions (NDIMS) of these arrays%%%%
% d = cumsum([0;sqrt(sum(diff(rcseg).^2,2))]);
% line_integeral(i) = trapz(d,fseg)
end
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