If I try this with mpmath 0.16 (the version we currently have in sympy in the
latest git master), I get:
In [22]: print 'subs: ', mpmath.findroot(lambda xi: p.subs(x, xi), 1.0)
subs:
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
/Users/aaronmeurer/Documents/python/sympy/sympy/<ipython console> in <module>()
/Users/aaronmeurer/Documents/python/sympy/sympy/sympy/mpmath/calculus/optimization.pyc
in findroot(ctx, f, x0, solver, tol, verbose, verify, **kwargs)
968 '(%g > %g)\n'
969 'Try another starting point or tweak
arguments.'
--> 970 % (norm(f(*xl))**2, tol))
971 return x
972 finally:
ValueError: Could not find root within given tolerance. (6.67917e-33 >
1.71057e-49)
Try another starting point or tweak arguments.
Another option for Poly is eval. I get this:
In [37]: print 'eval: ', mpmath.findroot(lambda xi: p.eval(x, xi), 1.0)
eval: 0.774596669241483377035853079956479922166584341
In [38]: print 'exact: ', mpmath.sqrt(mpmath.mpf('3.0')/mpmath.mpf('5.0'))
exact: 0.774596669241483377035853079956479922166584341
In [39]: print 'lambda:', mpmath.findroot(lambda x: 5.0*x**3/2.0 - 3.0*x/2.0,
1.0)
lambda: 0.774596669241483377035853079956479922166584341
So I'd say there is some kind of bug with subs.
Aaron Meurer
On May 26, 2011, at 8:21 PM, Matthew Emmett wrote:
> Hi everyone,
>
> I am having trouble combining mpmath's findroot function with sympy.
> Here is a short example of what I am trying to accomplish:
>
> import sympy
> import mpmath
>
> mpmath.mp.dps = 45
>
> x = sympy.var('x')
> p = (5.0/2.0*x**3 - 3.0/2.0*x).as_poly()
>
> print 'subs: ', mpmath.findroot(lambda xi: p.subs(x, xi), 1.0)
> print 'lambda:', mpmath.findroot(lambda x: 5.0*x**3/2.0 - 3.0*x/2.0,
> 1.0)
> print 'exact: ', mpmath.sqrt(mpmath.mpf('3.0')/mpmath.mpf('5.0'))
>
>
> The output is:
>
> subs: 0.77459666924148342341315597798728447146706553
> lambda: 0.774596669241483377035853079956479922166584341
> exact: 0.774596669241483377035853079956479922166584341
>
>
> That is, when using mpmath.findroot, substituting into a SymPy
> polynomial does not produce the same result as using a lambda form
> with a handwritten version of the polynomial. Is there a way to the
> SymPy subs method to work as expected?
>
> Thanks,
> Matt
>
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