Here is the full traceback.
sage: M = random_matrix(RDF, 4, 4)
sage: M.eigenspaces()
---------------------------------------------------------------------------
<type 'exceptions.NotImplementedError'> Traceback (most recent call
last)
/Volumes/HOME/robert/sage-2.7.2/<ipython console> in <module>()
/Volumes/HOME/robert/sage-2.7.2/matrix2.pyx in
matrix2.Matrix.eigenspaces()
/Volumes/HOME/robert/sage-2.7.2/matrix2.pyx in matrix2.Matrix.fcp()
/Volumes/HOME/robert/sage-2.7.2/polynomial_element.pyx in
polynomial_element.Polynomial.factor()
<type 'exceptions.NotImplementedError'>:
What is happening is that polynomial_element.Polynomial.factor doesn't
know what to do with the RDF ring. It checks whether the ring is real,
but only does this for RR, not RDF:
elif is_RealField(R):
n = pari.set_real_precision(int(3.5*R.prec()) + 1)
G = list(self._pari_('x').factor())
is_RealField(RDF) is False. So it makes it to the end of factor(),
where it says:
if G is None:
raise NotImplementedError
So the real problem is that polynomials over RDF don't know how to be
factored:
sage: R = PolynomialRing(RDF, 'x')
sage: f = R('x^2')
sage: f.factor()
---------------------------------------------------------------------------
<type 'exceptions.NotImplementedError'> Traceback (most recent call
last)
/Volumes/HOME/robert/sage-2.7.2/<ipython console> in <module>()
/Volumes/HOME/robert/sage-2.7.2/polynomial_element.pyx in
polynomial_element.Polynomial.factor()
<type 'exceptions.NotImplementedError'>:
On Aug 3, 3:03 pm, Joshua Kantor <[EMAIL PROTECTED]> wrote:
> The eigen routine uses numpy. If you do
> p,e=m.eigen()
>
> then p is an array of eigenvalues and e is a matrix whose columns are
> eigenvectors.
> The documentation works fine in my local install not sure why it fails
> on sage.math
>
> Josh
>
> On Aug 3, 2:43 pm, Robert Bradshaw <[EMAIL PROTECTED]>
> wrote:
>
> > 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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