[SciPy-user] Inverse of complex matrix
Michael McNeil Forbes
mforbes@physics.ubc...
Sat Nov 10 01:59:43 CST 2007
Hi Roger,
Your matrix is extremely singular. The singular values are:
>>> U,d,V = linalg.svd(R)
>>> d
array([1.41944451e+01, 1.23913727e+01, 9.46227279e+00,
2.81247753e-04, 1.11035378e-14, 1.02548448e-14,
8.22627497e-15, 6.74668324e-15, 5.51882714e-15,
4.78886237e-15, 2.82020737e-15, 7.14721524e-16])
Thus, the matrix is really il-conditioned (the ratio of the largest
to smallest singular value is of the order of the machine precision.
It is essentially singular, and only has 4 linearly independent
columns). Thus, it is not surprising that the round-off errors are
significant.
You can't reasonably expect to invert a matrix when the ratio of the
singular values is of order the machine precision.
Michael.
On 9 Nov 2007, at 10:16 PM, Roger Herikstad wrote:
> Dear scipy users,
> I am trying to invert a 12 by 12 complex matrix R using
> scipy.linalg.inv(), but the round-off errors seem a bit too big. If
> I do scipy.dot(Ri,R), the first row of the resulting matrix looks
> like this:
>
> array([ 0.953125 +0.j , 0.06542969+0.01171875j,
> 0.08154297+0.15234375j, -0.078125 -0.09375j ,
> 0.19140625-0.0859375j , 0.08203125+0.140625j ,
> -0.08398438+0.0078125j , -0.02539062-0.03125j ,
> -0.06738281+0.015625j , -0.04736328+0.15820312j,
> -0.09057617+0.02832031j, 0.109375 -0.0625j ])
>
>
> Is this normal? Inverting a 2x2 matrix produces the expected
> result. I've attached a pickle of my matrix. Thanks!
>
> ~ Roger
> <matrix.pck>
>
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