[SciPy-user] fsolve with sparse matrices
Jan Wicijowski
janislaw@o2...
Sat Apr 18 08:45:13 CDT 2009
Dnia 17-04-2009 o 18:28:14 Pauli Virtanen <pav@iki.fi> napisał(a):
> If you write a sparse trust-region Newton algorithm in Python, I'm sure
> there's a place in Scipy for it :)
In my work I immediately picked ready solution of scipy.optimize.fsolve,
and didn't look at simpler methods. Fortran hybrj algorithm works
blazingly fast for my problem, and I expect simpler methods to converge
much slower. Although it may be a reasonable trade-off with sparse
matrices.
> The easier way would be just to implement a Newton method combined with
> line search:
>
> x = x0
> maxiter = 100
> abs_tolerance = 1e-8
> for k in xrange(maxiter):
> J = jacobian(x)
> r = residual(x)
> d = -sparse.linalg.spsolve(J, r) # or, iterative
>
> r_norm = norm(r)
>
> # check convergence
> if r_norm < abs_tolerance:
> break
>
> # naive line search, could consider using
> # scipy.optimize.line_search instead
> for alpha in [1, 0.5, 0.1, 0.01]:
> x2 = x + alpha*d
> r2 = residual(x2)
> if norm(r2) < r_norm:
> break
> x = x2
> else:
> raise RuntimeError("Didn't converge")
>
> It's very naive, but if your problem is easy enough, it works.
Cool, it looks nice and self-explanatory. I'll try it ASAP.
If the results for my problem won't satisfy me, expect to see hybrj
algorithm ported to python in two weeks or so ;)
Thanks for your help - you've pointed out many important facts for my work.
Regards,
Jan Wicijowski
--
Jan Wicijowski
a29jaGFtIEp1bGnqIEcu
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