[Numpy-discussion] Inversion of near singular matrices.
akabaila at pcug.org.au
Sat Jan 29 06:40:05 EST 2011
I am interested in determining if a matrix is singular or
"nearly singular" - very ill conditioned. The problem occurs in
structural engineering applications.
My OS is kubuntu 10.10 (32 bit)
numpy and numpy.linalg binaries from ubuntu repositories.
The attached tar ball has a little CLI script that generates
singular or near singular matrices (because of the inevitable
roundoffs) for matrices with elements from sequence 1, 2, 3, 4
The dimension of matrix nn can be passed as command line
parameter via sys.argv . If argv does not exist, the 5x5
default matrix is used.
for nn = 3 and 4 numpy does not raise an exception
for nn = 5 it does raise an exception
for nn = 6, 7 np not raises exception
for nn = 8 np does raise exception
for nn = 9 np does not raise exception
for higher nn values np mostly raises the exception, but for nn
= 23 and nn=120 it does NOT raise the exception.
It is worht noting that in practical problems of engineering
analyisis the ill conditioned matrix is not "exact" - there
always are approximations and roundoff errors.
So my question is: how can one reliably detect singularity (or
near singularity) and raise an exception?
Many thanks for your attention,
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