I want to integrate a symbolic matrix numerically. How can I do it??
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syms x y
A= [1 x^2+y^2;x-y x^2+y^2];
I want to numerically integrate all elements of A for x limits (0-10) and ylimits (0-15) .
Thanks for your time and help..
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Walter Roberson
il 28 Apr 2023
Use nested vpaintegral() calls. The inner call will execute first and figure out that it cannot integrate because there is an additional free variable, so it will return a vpaintegral() data form. The outer vpaintegral will recognize the vpaintegral data form from the inner and will be able to proceed with the 2d integration.
2 Commenti
Walter Roberson
il 28 Apr 2023
syms x y
A= [1 x^2+y^2;x-y x^2+y^2];
result = vpaintegral(vpaintegral(A, x, 0, 10), y, 0, 15)
Più risposte (2)
Paul
il 28 Apr 2023
I don't think there's a function for numerically integrating an arrayvalued function of two variables. Here's a loop approach to integrating each element of A individually using integral2
syms x y
A = [1 x^2+y^2;x-y x^2+y^2];
for ii = 1:2,
for jj = 1:2
Afun = matlabFunction(A(ii,jj),'vars',{'x' 'y'});
% add 0*x to ensure proper dimension when integrating A(1,1)
result(ii,jj) = integral2(@(x,y) Afun(x,y)+0*x,0,10,0,15);
end
end
format short e
result
2 Commenti
Paul
il 29 Apr 2023
syms x y
A = [1 x^2+y^2;x-y x^2+y^2];
tic
for kk = 1:100
result = nan(2,2);
for ii = 1:2,
for jj = 1:2
Afun = matlabFunction(A(ii,jj),'vars',{'x' 'y'});
% add 0*x to ensure proper dimension when integrating A(1,1)
result(ii,jj) = integral2(@(x,y) Afun(x,y)+0*x,0,10,0,15);
end
end
end
toc
tic
for kk = 1:100
result = vpaintegral(vpaintegral(A, x, 0, 10), y, 0, 15);
end
toc
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