The document discusses different methods for optimizing Python code for plotting the bifurcation diagram of the logistic map, including PyPy, C extensions, and Cython. PyPy can speed up Python code without changes but does not support matplotlib. C extensions can provide large speedups but require writing C code. Cython allows generating C code from Python-like code and provides speed gains with less effort than C extensions. The document demonstrates using Cython to optimize the logistic map bifurcation diagram code.

1. Making of:
The logistic map
bifurcation diagram
BradMartsberger

2. What is this talk about?
Makingaprettypicture
Squeezingperformance outof python
PyPy, Cython, C extensions
With atoyphysics model(chaos!)

3. Fun with fractals

4. Cool, but...
Where did that come from?
Can you show me some python already?

5. The logistic map
Map avalue, x, from [0, 1] to [0, 1] accordingto:
r *x *(1 -x)
Let's play...
x=0.25
r=2.5
forjinrange(limit):
print"x:",x
x=r*x*(1-x)

6. What do we need to make that
sweet graph?
Python
Matplotlib
Patience ... lots of patience

7. Simplified version
bif_diag=[[0.0]*height]*width
forkinrange(width):
#histogramofhowfrequentlyeachpixelisvisited.
h=logmap_histogram(r,x_len,x1,x2,height)
#Normalizethehistogramtogofrom0to1.
h=divide_list(h,1.0*max(h))
#stickitinupsidedowntotheimage
bif_diag[k-1]=h[::-1]
plot_bif_diag(bif_diag,plt,cm,(x1,x2),(r_lower,r_upper))

8. Inner loop
deflogmap_histogram(r,x_len,x1,x2,height):
result=[0]*height
dx=1.0*(x2-x1)/(height-1)
transient=500
x=0.25
forkinxrange(transient):
x=x*r*(1-x)
forkinxrange(x_len):
x=x*r*(1-x)
incr=int((x-x1)/dx)
ifincr>=0andincr<M:
result[incr]+=1
returnresult

9. Matplotlib bit
defplot_bif_diag(bif_diag,plt,cm,xlim,rlim):
width,height,=len(bif_diag),len(bif_diag[1])
to_plot=[[1-pixforpixincol]forcolinbif_diag]
to_plot=map(list,zip(*to_plot))
plt.imshow(to_plot,cm.gray,clim=(0.7,1))
font={'family':'serif','size':24}
plt.xlabel('r',fontdict=font)
plt.ylabel('x*',fontdict=font)
plt.xticks(linspace(1,N,9),['%.2g'%rforrinlinspace(rlim[0],rlim[1],9)])
plt.yticks(linspace(1,M-1,5),['%.2g'%xforxinlinspace(xlim[1],xlim[0],5)]
ax=plt.gca()
ax.set_position([80./(width+100.),80./(height+100.),width/(width+100.),
plt.gcf().canvas.manager.window.geometry("{0}x{1}+30+30".format(width+100,height+
plt.show()

10. Let's run this
thing already...

11. That was a little disappointing
Nothorrible, buttoo slow to do some coolstuff.

12. Options for doing better
0. Quitusingpython
1. PyPy
2. C extension
3. Cython
4. There are others (numpywith numexpr)

13. PyPy
Straightfrom pypy.org:
Fast, compliantalternative implementation of the Python
language (2.7.6 and 3.2.3) with severaladvantages:
Speed, due to Just-In-Time compiler
Takes less memory
Supports anumber of third partylibraries:
ctypes, django, sqlalchemy, twisted, etc.
Does notrequire anychange to your code!
Unfortunately, matplotlib is notsupported.
Numpyis partiallysupported.

14. C extensions
Write functions in C thatare callable from python
Pass python objects as arguments thatmustbe converted to C
values
Returns apython object, e.g., alist
Compiled and fast
Do this atleastonce

15. Let's have a look
staticPyObject*logmap_attractor_histogram(PyObject*self,PyObject*args){
doubler1,r2,x,x1,x2;
intxxlen,rrlen,M;
inttransient=500;//Shorttransientforeachr.
if(!PyArg_ParseTuple(args,"ddiiddi",&r1,&r2,&rrlen,&xxlen,&x1,&x2,&M)){
returnNULL;
}
//Storeourhistograminanintarray,copyittoapythonlistandreturn
//thelistasaPyObject*
intarray[M];
PyObject*list=PyList_New(M);
//Initializearraytoallzeros
intj,k;
for(j=0;j<M;++j){
array[j]=0;
}
doubler,dr,dx;
intincr;
//Settheamountwewillsteptogetfromr1tor2inrrlen-1steps
dr=0;
if(rrlen>1){dr=(r2-r1)/(rrlen-1);}
//Histogrambinsize
dx=(x2-x1)/(M-1);
//loopoverr(perhapschangetofor(r=r1;r<=r2;r+=dr))

16. Compiling to an importable module
Create asetup.pyfile, e.g:
fromdistutils.coreimportsetup,Extension
setup(name='logmap',version='1.0',
ext_modules=[Extension('logmap',['logmapmodule.c'])])
Then installit
>>>pythonsetup.pyinstall
And itcan be imported and called
importlogmap
h= logmap.attractor_histogram(...)

17. Let's see it already...

18. Cython
Directlyfrom cython.org:
Static compiler for python
Makes writingC extensions for python as easyas writing
python
Generates C code from your python code
Has the potentialto deliver the speed gains thatwe getfrom aC
extension with less hassle

19. How to make it work
Create setup.pyfile:
Build like this:
Then you can importfrom
logistic_map_bifurcation_diagram_cython
fromdistutils.coreimportsetup
fromCython.Buildimportcythonize
setup(
name='logmap_cython',
ext_modules=cythonize("logistic_map_bifurcation_diagram_cython.pyx"),
)
%>pythonsetup.pybuild_ext--in_place

20. Making cython faster
Cython's code generation is helped byprovidingithints in the
form of type declarations
deflogmap_histogram(floatr1,floatr2,intrrlen,intxxlen,floatx1,floatx2,intM)
result=[0]*M
cdeffloatdx
dx=1.0*(x2-x1)/(M-1)
transient=500
cdeffloatx
cdeffloatr
cdeffloatk
forrinlinspace(r1,r2,rrlen):
x=0.25
forkinrange(transient):
x=x*r*(1-x)
forkinrange(xxlen):
x=x*r*(1-x)
incr=int((x-x1)/dx)
ifincr>=0andincr<M:
result[incr]+=1
returnresult

21. Questions...Comments, etc.