Linear algebra over RR is generic and, in many cases, really bad so
far. Use RDF or even scipy unless you really need arbitrary
precision. (If the RDF interface is inconsistent, fix it and send a
patch :-)
- Robert
On Aug 1, 2007, at 6:28 AM, Robert Miller wrote:
>
> Hi everyone,
>
> I have a symmetric square matrix of real numbers, and I wish to
> compute the (necessarily) real eigenvalues of this matrix.
>
> sage: version()
> 'SAGE Version 2.7.2, Release Date: 2007-07-28'
>
> sage: M = random_matrix(RDF, 4, 4)
> sage: M += M.transpose()
>
> Now M is such a matrix. My first instinct was to try 'eigenspaces':
>
> sage: M.eigenspaces()
> Exception (click to the left for traceback):
> ...
> NotImplementedError
>
> So I then tried using RR instead of RDF, and often I was getting
> variables in the eigenvalues. The example is no longer symmetric, and
> I suspect this might be why:
>
> sage: M = random_matrix(RR, 4, 4)
> sage: M.eigenspaces()
> [
> (-0.687210648633541, []),
> (0.251596873005605, []),
> (1.00000000000000*a2, [])
> ]
>
> Wouldn't it be better to return the complex eigenvalues?
>
> When I went back to RDF, I was surprised by the function eigen, which
> seems to be doing exactly what I want:
>
> sage: M = random_matrix(RDF, 4, 4)
> sage: M += M.transpose()
> sage: M.eigen()
> ([2.83698656526, 1.12513535857, -1.92195925813, -0.781971696103],
> [ -0.685785481323 0.676886167426 -0.249484727275
> -0.0963367054158]
> [ 0.171856298084 -0.00520796932156 -0.108449572475
> -0.97912051357]
> [ 0.704671991219 0.683316875186 -0.135215217363
> 0.135026952387]
> [ 0.0600089260487 -0.273634868922 -0.952739684321
> 0.117515876478])
>
> However, the output is a little confusing-- I'm guessing either the
> columns or rows of the matrix are the eigenvectors. So I check the
> documentation (this is on sagenb.org):
>
> sage: M.eigen?
> Traceback (most recent call last):
> File "<stdin>", line 1, in <module>
> File "/home/server2/nb1/sage_notebook/worksheets/rlmill/0/code/
> 50.py", line 4, in <module>
> print _support_.docstring("M.eigen", globals())
> File "/usr/local/sage-2.6/local/lib/python2.5/site-packages/sage/
> server/support.py", line 142, in docstring
> s += 'Definition: %s\n'%sageinspect.sage_getdef(obj, obj_name)
> File "/usr/local/sage-2.6/local/lib/python2.5/site-packages/sage/
> misc/sageinspect.py", line 267, in sage_getdef
> spec = sage_getargspec(obj)
> File "/usr/local/sage-2.6/local/lib/python2.5/site-packages/sage/
> misc/sageinspect.py", line 252, in sage_getargspec
> args, varargs, varkw = inspect.getargs(func_obj.func_code)
> UnboundLocalError: local variable 'func_obj' referenced before
> assignment
>
> I have absolutely no idea what to make of this.
>
> -R Miller
>
>
>
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