Hi all
I've (at least) two ways of plotting a function.
The first one is the classic :
f=(x**2).function(x)
Q=plot(f,x,-1,1)
I've an other one :
==================================
class CallFunction(object):
def __init__(self,f):
self.f=f
def __call__(self,x):
return self.f(x)
P=plot(CallFunction(f),x,-1,1)
=================================
The latter has the advantage to accept any "function" in the sense of
anything that takes a x and return a number.
My question in the following : is it normal that the second one is
*much* slower than the first one ?
In the following real live example, the second method takes several
minutes against a couple of seconds for the first :
#! /usr/bin/sage -python
# -*- coding: utf8 -*-
from sage.all import *
from scipy import stats
class Density(object):
def __init__(self,law,K,h,Npoints=300):
self.Npoints=Npoints
X=law.rvs(size=self.Npoints)
self.N=Npoints
self.hn=h(self.Npoints)
self.K=K
self.X=X
def __call__(self,x):
return (1/(self.Npoints*self.hn))*sum( [self.K((Xi-x)/self.hn )
for Xi in self.X ] )
def fast_density(law,K,h,Npoints=300):
hn=h(Npoints)
X=law.rvs(size=Npoints)
f = (1/(Npoints*hn))*sum( [ K( (Xi-x)/hn ) for Xi in X ] )
return f.function(x)
var('n')
K1=((1/sqrt(2*pi))*exp(-x**2/2)).function(x)
h=(n**(-0.2)).function(n)
law=stats.norm
a=-5
b=5
f=fast_density(law,K1,h)
P=plot(f,x,a,b) # couple of seconds
print "P is done ..."
g=Density(law,K1,h)
Q=plot(g,x,a,b) # Minutes !
print "Q is done ...
For the record, the plotted functions is an approximation of the density
function of a sequence of points.
Of course, in that precise example, I don't need the __call__()
technique because everything is "function". In my "even more real live",
however the function K is not analytic and has to be created by
def K(x):
... blabla
The difference between the two techniques are some hundreds of calls to
Density.__call__(x) instead of f(x)
Any idea how to make the computation faster ?
Thanks
Laurent
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