NIntegrate fails to work...

• To: mathgroup at smc.vnet.net
• Subject: [mg122740] NIntegrate fails to work...
• From: GQ Wang <gqwang1984 at gmail.com>
• Date: Wed, 9 Nov 2011 06:24:22 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

```Hi guys,

I came across this problem in my calculation:

I have G(x, y), which is a very complicated matrix function of x and
y. The integrand of my problem, denoted by f(G(x, y)), is a function
of the eigenvalues and eigenvectors of G(x, y), and so naturally is a
function of x and y.

G(x, y) is formally so complicated that it's impractical to be
diagonalized symbolically on the level of variables x and y. When I
indeed tried this symbolic calculation, I get the error message

Eigenvectors::eivec0: Unable to find all eigenvectors. >>

and get the zero vector as the result.

So I thought numerical integration should be the way to go. The
procedure in my mind goes like this: write down G(x, y) numerically
for each (x0, y0) point which appeared in the numerical integration,
diagonalize the numerical matrix, calculate the eigenvectors and
eigenvalues, and then calculate f(G(x0, y0)). In this way, at least in
principle, the numerical integration could be performed.
The code goes like
G[x_, y_]:=...
f[x_,y_]:=...
NIntegrate[f[x, y],{x, xmin, xmax}, {y, ymin, ymax}]

But it did not work out. The reason probably is, I suspect (based on
the same error message that I received), that mathematica evaluates
the integrand at each (x0, y0) point using something like
f(G(x, y))/{x->x0, y->y0},
which requires the explicit form of the integrand f(G(x, y)), which,
as I have mentioned, mathematica fails to calculate symbolically.

So, my question is, how should I proceed... It seemed such an innocent
problem.

Thanks a lot guys.

Cheers,
GQ

```

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