On Mar 16, 6:14 am, jpc pedrocruzave...@gmail.com wrote:
like matlab fzero command, the numerical answer of the
equation is $x \approx 0$ because of the change of sign of
$1/x \in [-1,1]$.
This is not really a complete description of Matlab's behavior
in this situation. If you simply define f(x) = 1/x and apply
fzero, without requesting any additional information, you get:
f = @(x) 1/x;
fzero(f,-1,1)
ans =
-2.6773e-16
However, you can ask Matlab to provide more information via:
[x,fval,exitflag,output] = fzero(f,-1,1);
Now, fval is a huge number and output.message indicates that
the function might be singular. Similarly, Mathematica
yields a numerical zero but issues a warning.
Now, you can find that Sage uses SciPy's implementation
of Brent's algorithm when tackling this problem by typing
find_root?? and SciPy provides similar functionality as
Matlab, in this case. What I find particularly puzzling,
though, is that scipy.opitimize.brentq, raises an error
for this problem, at least when applied to the interval
[-1.0, 1.0]. On the other hand, brentq runs without
reporting a complaint when applied to the interval
[1.0, pi]. See below.
Mark McClure
from scipy.optimize import brentq
def f(x): return 1/x
[x,info] = brentq(f, -1.0, pi, full_output=True)
[x,info.converged]
[-1.155868814851219e-12, True]
brentq(f, -1.0, 1.0, full_output=True)
Traceback (most recent call last):
File stdin, line 1, in module
File /Users/markmcclure/.sage/sage_notebook/worksheets/admin/31/
code/16.py, line 9, in module
[a,b] = brentq(f, -_sage_const_1p0 , _sage_const_1p0 ,
full_output=True)
File /Applications/Sage.app/Contents/Resources/sage/local/lib/
python2.5/site-packages/SQLAlchemy-0.4.6-py2.5.egg/, line 1, in
module
File /Applications/Sage.app/Contents/Resources/sage/local/lib/
python2.5/site-packages/scipy/optimize/zeros.py, line 223, in brentq
r = _zeros._brentq(f,a,b,xtol,maxiter,args,full_output,disp)
File /Users/markmcclure/.sage/sage_notebook/worksheets/admin/31/
code/16.py, line 8, in f
def f(x): return _sage_const_1 /x
File element.pyx, line 1201, in
sage.structure.element.RingElement.__div__ (sage/structure/element.c:
9116)
File coerce.pyx, line 672, in
sage.structure.coerce.CoercionModel_cache_maps.bin_op (sage/structure/
coerce.c:5437)
ZeroDivisionError: float division
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