I want to integrate a symbolic matrix numerically. How can I do it??
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clear all
clc
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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채택된 답변
Walter Roberson
2023년 4월 28일
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.
댓글 수: 2
Walter Roberson
2023년 4월 28일
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)
추가 답변 (2개)
Paul
2023년 4월 28일
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
댓글 수: 2
Paul
2023년 4월 29일
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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