> > sage: numpy.linalg.inv(a)
> >
> > array([[ 2.25125019e+15, -4.50250038e+15, 2.25125019e+15],
> > [ -4.50250038e+15, 9.00500077e+15, -4.50250038e+15],
> > [ 2.25125019e+15, -4.50250038e+15, 2.25125019e+15]])
>
> I get this:
> sage: scipy.linalg.inv(a)
>
> array([[ -4.50359963e+15, 9.00719925e+15, -4.50359963e+15],
> [ 9.00719925e+15, -1.80143985e+16, 9.00719925e+15],
> [ -4.50359963e+15, 9.00719925e+15, -4.50359963e+15]])
Some notes:
Scipy uses numpy as its backend
The numerical noise problem is probably something deeper, because it
doesn't affect only the results of inv(), but others as well, like when
trying to get the autovalues matrix after obtaining the eigenvectors
matrix. In Ipython:
In [34]: from pylab import *
In [35]: k = array([[1,2,4],[4,7,5],[8,7,9]],dtype='float64')
In [36]: lambdas, P = eig(k)
In [37]: dot(P.T,dot(k,P))
Out[37]:
array([[ 16.47731777, 0.48505536, -0.12297265],
[ -4.20177431, -1.90215152, 0.03248141],
[ -0.8356282 , -0.02547992, 2.42483375]])
In [38]: lambdas
Out[38]: array([ 16.47731777, -1.90215152, 2.42483375])
One can see the main diagonal fits the autovalues right, but the other
elements should be zero, when one of them gets to a significant value
(-4 is even greater in modulus than two of the autovalues)
Ronan
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