Algorithms as objects?
Diez B. Roggisch
deets at nospam.web.de
Fri Aug 28 10:14:59 CEST 2009
Kreso schrieb:
> I am writing an application that essentially calculates set of numbers,
> say N1, N2, ..., where they can be calculated by several different
> algorithms. (One should be able to choose the algorithm at run time.)
> In each algorithm one starts from a set of functions, say f1, f2, ...,
> which are then transformed into some other functions g1(f1, f2, ..),
> g2(f1, f2, ...), ... , then maybe transformed once more and result is
> obtained by evaluating final functions.
> I can naturally think about this as a collection of transformation
> blocks, which have functions as input and output, and which can be
> put together to get the final results. However, I am not sure
> how to program this, especially since one cannot subclass function
> type. To be clear let me give simplified example of what is needed:
>
> f(x) has unknown shape, so one would like to try, say
>
> f1(x) = ax - b x**2 or f2(x) = a sin(b*x),
>
> where a and b are variable parameters.
>
> Then, one would like to create, with known k(x,y), function g(x)
> in one of two ways:
>
> g1(x) = k(x, x)*f(x) or g2(x) = integrate(k(x, y) * f(y), y=0..1),
>
> and finally evaluate N=g(1) as result. In this simple example
> there are 4 different algorithms for f(x) -> g(x) -> N, and one
> should be able to simply choose between them, e.g. by calling
> N(g1, f2, (a,b)).
>
> In practice algorithm is not necessary so linear, but is
> generally tree-lika:
>
> (a,b) -> f1(x) --->g1(x)---+
> |--> h(x) --> N
> (c,d) ---+--> g2(x)--------+
> |
> f2(x) --+
>
>
> It would be nice to have some class of function-objects,
> that f1(x), .., g1(x), ... could be members/instances of so that common
> operations on these functions could be possible (checking
> that they satisfy some necessary properties, plotting them, ...),
> and then second "class" of transformations/methods operating on
> these objects.
> I seem to be confused by the fact that I would like to somehow treat
> algorithms as objects (so that one can experiment with different
> algorithm systems) but I don't have clear picture how to do it.
> I am just brainstorming for ideas. Any advice is welcome.
>
Sound like simple function combinators to me. Like this:
import inspect
def combine(f, g):
if len(inspect.getargspec(g)[0]) > 1:
def h(*args):
return g(*f(*args))
return h
else:
def h(*args):
return g(f(*args))
return h
def a(x):
return 10 + x
def b(x):
return x ** 2
print combine(a, b)(20)
def c(x):
return x, x * 2
def d(x, y):
return x + y
print combine(c, d)(10)
But to be honest - I don't think you win much with this whole thing.
Spelling out the function-calls the way they are made is in the end as
efficient and clear as it can get. And for *real* algorithms, you need
non-strict constructs, control-structures and the like, and in the end
of the day, you create a programming language on top of a programming
language.
Diez
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