On 11/3/10 3:30 PM, David Joyner wrote:
Hi:
Sage seems to be reporting eigenvalues incorrectly. Can this bug been
reported before?
It's well known that serious numerical issues come up when doing
eigenvalues of CC or RR matrices. That's why the warning is printed
that you see below.
Try using CDF, which ends up using numpy:
sage: M = matrix(CDF,[ [ 1476226, 1476226, 1476224, 1476225, 1476224 ],
[ 1476226, 1476224, 1476225, 1476224, 1476226 ],
[ 1476224, 1476225, 1476224, 1476226, 1476226 ],
[ 1476225, 1476224, 1476226, 1476226, 1476224 ],
[ 1476224, 1476226, 1476226, 1476224, 1476225 ] ])
sage: M.eigenvalues()
[7381125.0, 2.23606797746 - 4.42419210147e-31*I, 2.23606797737 +
4.42417798985e-31*I, -2.23606797751 + 1.92201810023e-11*I,
-2.23606797751 - 1.92199318576e-11*I]
Sometime, we'll hopefully have an ALGLIB interface that will fix this
for CC.
Maybe we should add a note to the warning printed out below to try using
CDF instead of CC, and RDF instead of RR.
Jason
sage: M = matrix(QQ,[ [ 1476226, 1476226, 1476224, 1476225, 1476224 ],
....: [ 1476226, 1476224, 1476225, 1476224, 1476226 ],
....: [ 1476224, 1476225, 1476224, 1476226, 1476226 ],
....: [ 1476225, 1476224, 1476226, 1476226, 1476224 ],
....: [ 1476224, 1476226, 1476226, 1476224, 1476225 ] ])
sage: M.eigenvalues()
[7381125, -2.236067977499790?, 2.236067977499790?,
-2.236067977499790?, 2.236067977499790?]
sage: M = matrix(CC,[ [ 1476226, 1476226, 1476224, 1476225, 1476224 ],
[ 1476226, 1476224, 1476225, 1476224, 1476226 ],
[ 1476224, 1476225, 1476224, 1476226, 1476226 ],
[ 1476225, 1476224, 1476226, 1476226, 1476224 ],
[ 1476224, 1476226, 1476226, 1476224, 1476225 ] ])
sage: M.eigenvalues()
.../sage-4.6/local/bin/sage-ipython:1: UserWarning: Using generic
algorithm for an inexact ring, which will probably give incorrect
results due to numerical precision issues.
#!/usr/bin/env python
[7.38112500000000e6 - 5.79188112676979e-48*I, 373.809799796897 +
373.812578248468*I, 373.809799796897 - 373.812578248468*I,
-373.809799797006 + 373.793647358285*I, -373.809799797006 -
373.793647358285*I]
- David Joyner
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