Hi,
I have a short piece of code where the use of an index array "feels
right", but incurs a severe performance penalty: It's about an order
of magnitude slower than all other operations with arrays of that
size.
It comes up in a piece of code which is doing a large number of "on
the fly" histograms via
hist[i,j] += 1
where i is an array with the bin index to be incremented and j is
simply enumerating the histograms. I attach a full short sample code
below which shows how it's being used in context, and corresponding
timeit output from the critical code section.
Questions:
- Is this a matter of principle, or due to an inefficient
implementation?
- Is there an equivalent way of doing it which is fast?
Regards,
Marcel
=================================================================
#! /usr/bin/env python
# Plot the bifurcation diagram of the logistic map
from pylab import *
Nx = 800
Ny = 600
I = 50000
rmin = 2.5
rmax = 4.0
ymin = 0.0
ymax = 1.0
rr = linspace (rmin, rmax, Nx)
x = 0.5*ones(rr.shape)
hist = zeros((Ny+1,Nx), dtype=int)
j = arange(Nx)
dy = ymax/Ny
def f(x):
return rr*x*(1.0-x)
for n in xrange(1000):
x = f(x)
for n in xrange(I):
x = f(x)
i = array(x/dy, dtype=int)
hist[i,j] += 1
figure()
imshow(hist,
cmap='binary',
origin='lower',
interpolation='nearest',
extent=(rmin,rmax,ymin,ymax),
norm=matplotlib.colors.LogNorm())
xlabel ('$r$')
ylabel ('$x$')
title('Attractor of the logistic map $x_{n+1} = r \, x_n (1-x_n)$')
show()
====================================================================
In [4]: timeit y=f(x)
10000 loops, best of 3: 19.4 us per loop
In [5]: timeit i = array(x/dy, dtype=int)
10000 loops, best of 3: 22 us per loop
In [6]: timeit img[i,j] += 1
10000 loops, best of 3: 119 us per loop
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