expm() products NaN as answer.

I have the matrix

 A=1.0 e 04*
    1.3371   0.0000      0      0
    0.0130  -0.0000      0      0
    0.0000        0 -0.0001 0.0001
    0.0000        0 -0.0001 0.0001

Only 0 is a real 0 and 0.0000 is because the number is too small to show at such a scale. The expm(A) gives NaN as ans. I thought it is because of the matrix is badly scaled. But it works fine for expm(-A). So, where the problem is and how can I get the right ans?

Answer 1

[Matt J]

It is badly scaled. Try

 >> expm(A/1e4) %finite result, better scaled

Now try computing expm(A) in the following equivalent way,

 >> expm(A/1e4)*exp(1e4) %the desired computation, but non-finite result

The fact that exp(1e4)=Inf ruins everything.