Integrating the eigenvalues of a matrix...

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w 2012-1-15

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/26140-integrating-the-eigenvalues-of-a-matrix

Hi people,

The simplified version of problem is the following.

I have a complicated matrix function f(x,y). The integrand of my problem is a function of the eigen system of f(x,y). Suppose

[s,t]=eig(f(x,y));

The integrand is, for example, g(x,y)=2*s(1,2)*t(1,1), so the integration goes as

dblquad(g,-1,1,-1,1)

which cannot be carried out.

The problem is that, the quad routine converts x and y into an array of values, which are the sampling points of the routine. The command [s,t]=eig(f(x,y)) cannot be carried out, as x and y are now arrays, and the matrix function f(x,y) are no longer well defined.

So how should I proceed? Thank you a lot.

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w 2012-1-15

I tried to express the integrand using the command

integrnd1=@(xp,yp)arrayfun(@(x,y)2*s*t,xp,yp);

When xp and yp are arrays of the same size, integrnd1(xp,yp) manages to yield the correct results.

However, when I tried to integrate it, the following message appears:

??? Error using ==> arrayfun

All of the input arguments must be of the same size and shape.

Previous inputs had size 13 in dimension 2. Input #3 has size 1.

Not sure what it means...

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Answer 1

w 2012-1-16

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/26140-integrating-the-eigenvalues-of-a-matrix#answer_34205

It turns out that all I had to do was, instead of using dblquad, to integrate x and y separately. The command integrnd1=@(xp,yp)arrayfun(@(x,y)2*s*t,xp,yp); should be separated into two parts, too: one for x, the other for y.