# [Doesn’t work anymore, sorry, might fix that one day…] Customize your IPython notebook with CSS

In the coming IPython 1.0 (available on their github) you will be able to change the style of your notebook using a custom CSS file. Here are three attempts, which I will describe in details:

## Creating a IPython profile

Credit and many thanks for this part go to Matthias Bussonier for his thorough explanatory blog on the subject.

Creating a profile is easy, you just type this line in a terminal:

ipython profile create yourprofilename


Note that you can send commands to the terminal from within your IPython notebook by writing %%bash in the first line of a code cell:

%%bash
ipython profile create yourprofilename


This has created a folder named profile_yourprofilename in your IPython folder. If you don’t know where this folder is, just type in a terminal

ipython locate


You have now a new profile ! In the future, to launch IPython with this new profile, use the command

ipython notebook --profile yourprofilename


To later rename a profile, go to your .ipython folder, rename the folder “profile_name” into “profile_newname”, then run

ipython profile create newname


For the moment your profile is identical to the default profile. Now go in your profile folder, and create a subfolder profile_yourprofile/static/css/. In this /css folder we will put CSS files and pictures to tune the appearance of the notebook. Start by creating a file custom.css, we will see how to fill it in the next sections. I just learned enough CSS to make the themes, so I am not really in control here. Comments and suggestions are welcome 🙂

# Theme 1: A Clean Notebook

My favorite 🙂 . Here is the content of my custom.css . I just hope that the structure and class names of IPynb html pages will not change too much in the future

/* file custom.css for the theme CleanNotebook */
div#notebook { /* centers the page content */
}

div.cell { /* Tunes the space between cells */
margin-top:1em;
margin-bottom:1em;
}

div.text_cell_render h1 { /* Main titles bigger, centered */
font-size: 2.2em;
line-height:1.4em;
text-align:center;
}

div.text_cell_render h2 { /*  Parts names nearer from text */
margin-bottom: -0.4em;
}

div.text_cell_render { /* Customize text cells */
font-family: 'Times New Roman';
font-size:1.5em;
line-height:1.4em;
}

#notebook li { /* More space between bullet points */
margin-top:0.8em;
}

div.cell.code_cell {  /* Areat containing both code and output */
background-color:#F1F0FF; /* light blue */
border-radius: 10px; /* rounded borders = friendlier */
}


### Bonus: Motivational Penguin

I am really fond of the motivational penguin from chibird.com (thanks Jacqueline !!!).

If you want the motivational penguin to cheer you up on the side of your screen while you are coding, put the GIF file in the /css folder and add these few lines to the code above:

#notebook_panel {
background : url('motivational_penguin.gif') no-repeat left center ;
}


# Theme 2: Zen of IPython

For this theme you will need to place each of these pictures in your CSS folder (I made all of them from Public Domain pictures from Wikimedia Commons and I put all of them in the Public Domain, where they belong).

The css code is surely far from optimized.

div#notebook {
}

div#ipython-main-app {
background: url('Shotei.jpeg') no-repeat top left;
}

body {
background : url('paper.jpeg') ;
}

div.cell {
margin-top:20px;
margin-bottom:20px;
}

h1 {
text-align:center;
}

div#notebook li {
margin-bottom:20px;
}

p,li,h1 {
line-height:120%;
}

p,ul {
}

.text_cell_render{
font-family: 'Palatino','Arial';
font-size:1.8em;
}

.text_cell h1 {
font-size: 2.2em;
text-align:center;
line-height:120%;
}

.text_cell h2 {
font-size: 1.8em;
margin-bottom:0;
}

div.input_area {
background: url('mountain_paper.png') ;
overflow:auto;
}

div.CodeMirror {
background: url('mountain.jpeg') repeat-y top right;
background-size: 20%;
font-size: 1.3em;
}

div.CodeMirror-scroll {
}

.output_wrapper{
background-image: url('sky.jpeg');
}

div.output {
background: url('cherryFlower.jpeg') repeat-y right;
background-size: 25%;
}

div.prompt.input_prompt{
display:none;
}

div.code_cell {
background: #e6ddce;
font-size:14px;}



# Theme 3: Gameboy

For this one you will need the buttons:

.prompt {display:none;}

div.cell.code_cell {
max-width: 800px;
background-color:white;
background:url('buttons.jpeg') no-repeat center bottom;
background-size:80%;
border-color: black;
}

div.output_wrapper {
margin-left:0px;
}

div.input_area, .output_stdout  {
margin-left:110px;
border-style:solid;
max-width:600px;
background-color: #626e02;
border-color: #656e7f;
border-width: 20px;

}

div.output_stdout {
border-top: none;
margin-top:-26px;
}
div.CodeMirror-scroll {
}

div.CodeMirror, div.output_stdout pre {
font-size: 1.6em;
font-family:"G.B.BOOT";
}

.cm-s-ipython { color: black; }
.cm-s-ipython span.cm-keyword {color: black;}
.cm-s-ipython span.cm-number {color: black;}
.cm-s-ipython span.cm-operator {color:black;}
.cm-s-ipython span.cm-meta {color: black;}
.cm-s-ipython span.cm-comment {color: black;}
.cm-s-ipython span.cm-string {color: black;}
.cm-s-ipython span.cm-error {color: black;}
.cm-s-ipython span.cm-builtin {color: black;}
.cm-s-ipython span.cm-variable {color: black;}


# Delay differential equations in Python

I wrote a very simple and user-friendly method, that I called ddeint, to solve delay differential equations (DDEs) in Python, using the ODE solving capabilities of the Python package Scipy. As usual the code is available at the end of the post :).

## Example 1 : Sine

I start with an example whose exact solution is known so that I can check that the algorithm works as expected. We consider the following equation:

$y(t) = sin(t) \ \ \ for\ \ \ t < 0$

$y'(t) = y(t-3\pi/2) \ \ \ for\ \ \ t \geq 0$

The trick here is that $sin(t-3\pi/2) = cos(t)=sin'(t)$ so the exact solution of this equation is actually the sine function.

from pylab import *

model = lambda Y,t : Y(t - 3*pi/2) # Model
tt = linspace(0,50,10000) # Time start, end, and number of points/steps
g=sin # Expression of Y(t) before the integration interval
yy = ddeint(model,g,tt) # Solving

# PLOTTING
fig,ax=subplots(1)
ax.plot(tt,yy,c='r',label="$y(t)$")
ax.plot(tt,sin(tt),c='b',label="$sin(t)$")
ax.set_ylim(ymax=2) # make room for the legend
ax.legend()
show()


The resulting plot compares our solution (red) with the exact solution (blue). See how our result eventually detaches itself from the actual solution as a consequence of many successive approximations ? As DDEs tend to create chaotic behaviors, you can expect the error to explode very fast. As I am no DDE expert, I would recommend checking for convergence in all cases, i.e. increasing the time resolution and see how it affects the result. Keep in mind that the past values of Y(t) are computed by interpolating the values of Y found at the previous integration points, so the more points you ask for, the more precise your result.

## Example 2 : Delayed negative feedback

You can select the parameters of your model at integration time, like in Scipy’s ODE and odeint. As an example, imagine a product with degradation rate r, and whose production rate is negatively linked to the quantity of this same product at the time (t-d):

$y(t) = 0 \ \ \ for\ \ \ t < 0$

$y'(t) = \dfrac{1}{1+(\dfrac{y(t-d)}{K})^2} -ry(t) \ \ \ for\ \ \ t \geq 0$

We have three parameters that we can choose freely. For K = 0.1, d = 5, r = 1, we obtain oscillations !

from pylab import *

# MODEL, WITH UNKNOWN PARAMETERS
model = lambda Y,t,k,d,r :  1/(1+(Y(t-d)/k)**2) - r*Y(t)

# HISTORY
g = lambda t:0

# SOLVING
tt = linspace(0,50,10000)
yy = ddeint(model,g,tt,fargs=( 0.1 , 5 , 1 )) # K = 0.1, d = 5, r = 1

# PLOTTING
fig,ax=subplots(1)
ax.plot(tt,yy,lw=2)
show()


## Example 3 : Lotka-Volterra system with delay

The variable Y can be a vector, which means that you can solve DDE systems of several variables. Here is a version of the famous Lotka-Volterra two-variables system, where we introduce some delay d. For d=0 we find the solution of a classical Lotka-Volterra system, and for d non-nul, the system undergoes an important amplification:

$\big(x(t), y(t)\big) = (1,2) \ \ \ for\ \ t < 0, \ \ else$

$x'(t) = 0.5x(t)\big(1-y(t-d)\big)\\ y'(t) = -0.5y(t)\big(1-x(t-d)\big)$

from pylab import *

def model(Y,t,d):
x,y = Y(t)
xd,yd = Y(t-d)
return array([0.5*x*(1-yd), -0.5*y*(1-xd)])

g = lambda t : array([1,2])
tt = linspace(2,30,20000)
fig,ax=subplots(1)

for d in [0, 0.2]:
yy = ddeint(model,g,tt,fargs=(d,))
# WE PLOT X AGAINST Y
ax.plot(yy[:,0],yy[:,1],lw=2,label='delay = %.01f'%d)

ax.legend()
show()


## Example 4 : A DDE with varying delay

This time the delay depends on the value of Y(t) !

$y(t) = 1,\ \ \ t \leq 0$

$y'(t) = - y\big(t-3\cos(y(t))^2 \big),\ \ \ t > 0$

from pylab import *
model = lambda Y,t:  -Y(t-3*cos(Y(t))**2)
tt = linspace(0,30,2000)
yy = ddeint(model, lambda t:1, tt)
fig,ax=subplots(1)
ax.plot(tt,yy,lw=2)
show()


## Code

### Explanations

The code is written on top of Scipy’s ‘ode’ (ordinary differential equation) class, which accepts differential equations under the form

model(Y,t) = ” expression of Y'(t) ”

where $Y$, and the output $Y'$, must be Numpy arrays (i.e. vectors).

For our needs, we need the input $Y$ to be a function of time, more precisely a function that can compute $Y(t)$ at any past or present $t$ using the values of $Y$ already computed. We also need $Y(t)$ to return the value of some function $g(t)$ if t is inferior to some time $tc$ that marks the start of the integration.

To this end, I first implemented a class (ddeVar) of variables/functions which can be called at any time $t$: for $t<latex t_c$, it will return the value of $g(t)$, and for $t>tc$, it will look for two already computed values $Y_a$ and $Y_b$ at times $t_a, from which it will deduce $Y(t)$ using a linear interpolation. Scipy offers many other kinds of interpolation, but these will be slower and won't support vectors for $Y$.

Such variables need to be updated every time a new value of $Y(t)$ is computed, so I created a class 'dde' that inherits from Scipy's 'ode' class but overwrites its integration method so that our special function $Y$ is updated after each integration step. Since 'ode' would feed the model with a vector Y (a Numpy array to be precise), which we don't want, we give to the integrator an interface function that takes a Numpy array Y as an argument, but immediately dumps it and calls the model with our special ddeVar variable Y (I hope that was clear 🙂 ).

### Ok, here you are for the code

You will find the code and all the examples as an IPython notebook HERE (if you are a scientific pythonist and you don’t know about the IPython notebook, you are really missing something !). Just change the extension to .ipynb to be able to open it. In case you just asked for the code:

# REQUIRES PACKAGES Numpy AND Scipy INSTALLED
import numpy as np
import scipy.integrate
import scipy.interpolate

class ddeVar:
""" special function-like variables for the integration of DDEs """

def __init__(self,g,tc=0):
""" g(t) = expression of Y(t) for t<tc """

self.g = g
self.tc= tc
# We must fill the interpolator with 2 points minimum
self.itpr = scipy.interpolate.interp1d(
np.array([tc-1,tc]), # X
np.array([self.g(tc),self.g(tc)]).T, # Y
kind='linear', bounds_error=False,
fill_value = self.g(tc))

def update(self,t,Y):
""" Add one new (ti,yi) to the interpolator """

self.itpr.x = np.hstack([self.itpr.x, [t]])
Y2 = Y if (Y.size==1) else np.array([Y]).T
self.itpr.y = np.hstack([self.itpr.y, Y2])
self.itpr.fill_value = Y

def __call__(self,t=0):
""" Y(t) will return the instance's value at time t """

return (self.g(t) if (t<=self.tc) else self.itpr(t))

class dde(scipy.integrate.ode):
""" Overwrites a few functions of scipy.integrate.ode"""

def __init__(self,f,jac=None):

def f2(t,y,args):
return f(self.Y,t,*args)
scipy.integrate.ode.__init__(self,f2,jac)
self.set_f_params(None)

def integrate(self, t, step=0, relax=0):

scipy.integrate.ode.integrate(self,t,step,relax)
self.Y.update(self.t,self.y)
return self.y

def set_initial_value(self,Y):

self.Y = Y #!!! Y will be modified during integration
scipy.integrate.ode.set_initial_value(self, Y(Y.tc), Y.tc)

def ddeint(func,g,tt,fargs=None):
""" similar to scipy.integrate.odeint. Solves the DDE system
defined by func at the times tt with 'history function' g
and potential additional arguments for the model, fargs
"""

dde_ = dde(func)
dde_.set_initial_value(ddeVar(g,tt[0]))
dde_.set_f_params(fargs if fargs else [])
return np.array([g(tt[0])]+[dde_.integrate(dde_.t + dt)
for dt in np.diff(tt)])


## Other implementations

If you need a faster or more reliable implementation, have a look at the packages pyDDE and pydelay, which seem both very serious but are less friendly in their syntax.

# Typing keyboard + python = Musical instrument !

In this post I will show you how to do this :

I am not the first to do that, but most people who play their computer on Youtube use either very expensive programs, or programs that won’t run on your computer, or not-so-efficient programs with not-that-much possibilities of extension, or cheap programs with a big lag between pressing the key and actually hearing the note.

So here is a very small Python script which will run fine even on a basic netbook. If you are not familiar with Python, you should take online courses , it is really worth it 🙂 !
If you are faminiliar with Python, then you are welcome to improve the code on its Github page.

## Transforming your keyboard into a mixtable

My original idea was to transform my computer keyboard into a mixtable, to make something like in this very awesome video:

So my first move was to make a program that would take a configuration file my_configuration.cf containing this:

 q, dog.wav w, cat.wav e, tarzan.wav r, scream.mp3 

And then if you hit q you would hear a dog from the dog.wav soundfile, if you hit w you’d hear a cat, etc…
This is pretty easy to do with Python’s pygame package. Here is my code (inspired by similar stuff from the package Mingus):


import pygame as pg
import csv
import time

SAMPLE_WIDTH = 16
FPS = 44100
N_CHANNELS = 2
BUFFER = 2**9

def minimix(config_file,mode = 'instrument'):
"""
Opens an interface that lets you press the keys of your keyboard
to plays the related soundfiles as sepcified in the provided
configuration file.

Args:
config_file (str):  A file associating keyboard keys with
file names. Each line must be of the form
key , filename.

mode (str) :
instrument -- causes autorepeat of samples as long
as the key is pressed.
sustain -- causes autorepeat of the samples until its
key is pressed again.
player -- striking the key causes the sound to play once.

Returns:
a list of the (time,events).
"""

repeat = 0 if (mode is 'player') else (-1)

pg.mixer.pre_init(FPS,-SAMPLE_WIDTH,N_CHANNELS,BUFFER)
pg.init()
screen = pg.display.set_mode((640,480))

key2sound = {}
key2file = {}

for key, soundfile in config:

key,soundfile = key.strip(' '),soundfile.strip(' ')

if key is not '#':

key2file[key] = soundfile
key2sound[key] = pg.mixer.Sound(soundfile)

events_list = []
currently_playing = {k : False for k in key2sound.iterkeys()}

##### MAIN LOOP

while True:

event =  pg.event.wait()

if event.type in (pg.KEYDOWN,pg.KEYUP):
key = pg.key.name(event.key)

if key in key2sound:

if event.type == pg.KEYDOWN:

if (mode == 'sustain') and currently_playing[key]:

currently_playing[key] = False

else:

key2sound[key].play(repeat)
currently_playing[key] = True

events_list.append((time.time(),key2file[key]))

elif event.type == pg.KEYUP and (mode == 'instrument'):

key2sound[key].stop()
currently_playing[key] = False

events_list.append((time.time(),key2file[key]))

elif event.key == pg.K_ESCAPE:

break

pg.quit()

return events_list


## Transforming your keyboard into a musical instrument

If instead of using various noises like cat and dog you use different notes from the same instrument, then you turned your computer into some kind of piano. The problem is that a set of soundfiles with all the notes of an instrument is difficult to find on the internet, so I wrote a script that makes as many notes as you want from just one sound by shifting its pitch up or down. It uses the audio processing program Soundstretch that you will need to install first :

import os

def shift_wav(wavfile,output,shifts,verbose=False):
"""
Makes new sounds by shifting the pitch of a sound.
Requires soundstrech installed.

Args:
wavfile : Name of the file containing the original sound
output: name to use as a prefix for the output files and for
the output folder name
shifts (list of int): specifies of how many half-tones the pitch
shifts should be. For instance [-2,-1,1,2] will produce
4 files containing the sound 2 half-tones lower, one
halftone lower, one halftone higher and two halftones
higher.
"""

folder = os.path.dirname(output)

if not os.path.exists(folder):

os.makedirs(folder)

for i,s in enumerate(shifts):

outputfile = '%s%02d.wav'%(output,i)

command = 'soundstretch %s %s -pitch=%d'%(wavfile,outputfile,s)
if verbose:
print command
os.system(command)


## Going further

There is so much one could do to improve the program.

On the musical side, for instance, finding configurations of the keyboard that are particularly ergonomic. In the video above I used this configuration:

I called it typewriter because it enables you to play very fast things while moving your hands a minimum (the video is a bad example :P) . But maybe there is better to find !

Also, one could start listing every cool piece of music that can be played on a typing keyboard. I use 46 keys ( almost 4 octaves !), that makes a lot of possibilities !

On the programming side, there is a lot of little things I can think of, like automatizing scale changes, introducing nuances, designing nice interfaces (why not a guitar-hero-like game where you would actually be playing music on a playback ?), writing a script that would take some sheet music (in a nice format, like ABC, MIDI, lylipond) and return the list of the keys you should strike to play it.

I actually wrote a lot more code, for instance to make it easier to write configuration files, for sound processing, etc., but since it is not strictly necessary I am not reporting it here (I’ll certainly put a working version on GitHub, or such, some day).

## Philosophy of the musical keyboard

Your typing keyboard is a real instrument. Of course it is not its primary use, but our voice’s primary purpose was not to sing, either. Now do the math : how many people out there have a piano at home ? And how many have a computer ? That gives you an idea of how many people would like to play the piano, cannot, but could play their computers instead.

So promoting computer-keyboardism is ultimately about bringing music to the masses. It is about providing everyone with an instrument that you can practice at home, in the train, at work, and that will be familiar to anyone everywhere in the world.

There is more : how many of you, pianist readers, have started the piano for seduction purposes ? (yeah, sure, me neither…) But public places with a piano on which you could show off your mad skills are getting pretty rare, aren’t they ? Especially since most bars have traded their good old piano for a TV. But think about all these places with a computer at hand ! Yep, time for you to develop a talent that will be useful in real life !

So practice, get good, be one of the first composers for tomorrow’s instrument, impress your friends and spread the good news ! If you are still reading me after so much gibberish , then do not hesitate : you just proved how little you value your free time, you are the right person for the task !

# Finding a subnetwork with a given topology in E. Coli

A few weeks ago I posted about how easy it was, using Python’s Networkx module and the RegulonDB database, to get and navigate through the genetic network of E. Coli. I didn’t mention at the time that you can also find all the subnetworks of E. Coli sharing a given topology with just a few lines of code:

import networkx.algorithms.isomorphism as iso
def find_pattern(graph,pattern,sign_sensitive = True):

if sign_sensitive:
edge_match = lambda e1,e2 : (e1['sign']==e2['sign'])
else:
edge_match = None
matcher = iso.DiGraphMatcher(graph,pattern,edge_match=edge_match)
return list(matcher.subgraph_isomorphisms())


## Feedforward loops in E. coli

As an example, let us have a look at the feedforward loops in E. coli. A feedforward loop can be described as a gene having an action on another gene, both directly and through the intermediary of another gene, like in the following sketch, where the arrows can represent activations or repressions

A feedforward !

If you want to print all the feedforward loops in E. coli’s network (as represented by RegulonDB), try this :

import networkx as nx
feedforward = nx.DiGraph()
ffwd_in_ecoli = find_pattern(ECN,feedforward,sign_sensitive=False)
for subgraph in ffwd_in_ecoli:
print subgraph


This prints each feedforward loop with the respective roles of the different genes (A,I, or C). As you can see there are 63 feedforward loops in regulonDB’s network, which is many. Let us now get sign-specific :

import itertools as itt
labels = []
frequencies = []
for signs in itt.product(('+','-'),repeat = 3):

ffwd = nx.DiGraph()
('I','B',{'sign':signs[1]}),
('A','B',{'sign':signs[2]})])
frequency = len(list(find_pattern(ECN,ffwd,True)))
frequencies.append(frequency)
labels.append(" ".join(signs))

frequencies = array([float(f) for f in frequencies])/sum(frequencies)
fig,ax = subplots(1, figsize=(5,5))
title('feedforward loops in E. coli, \n by signs of A->I,I->B,A->B')
show()


Relative frequencies of the different feedforward loops in E. coli

I’m not the first one to do such reasearch, but that won’t prevent me from commenting 🙂 The most frequent pattern can be seen as a double repression : gene A represses gene B, and, as an additional punishment, also represses the activator I of B. Such feedforwards are called coherent, as the two actions of the gene A have the same effect on the gene B. The second most frequent feedforward is incoherent: gene A activates gene B while activating a repressor of B, which seems a little foolish, but can be a way of creating bumps of activity (B is awaken just a few minutes before its repressor puts it down again).

## A word of caution

Note that the algorithm didn’t find any feedforward loop with activations only (+++), while some have been reported in the literature. The same way, I couldn’t find any mutual interaction between two genes (A has an action on B and B has an action on A). So if you are going to use regulonDB’s network of interactions for reasearch purposes, always have in mind :

• The database is INCOMPLETE, meaning that you can use it (carefully) to deduce the existence of stuff, but not to prove the absence of something. In particular, many gene interactions that occur through the intermediary of metabolites are omited ! For instance, the gene cyaA produces the cyclic AMP that is necessary to activate the genes regulated by crp. However only crp appears as a regulator of these genes.
• In the context of synthetic biology, the few genes added to the bacteria are often supposed to work independently of the rest of the bacteria (some biologists say that they are orthogonal to the rest of the system). Thus, if you design a feedforward loop, it will be a feedforward loop and nothing else. But keep in mind that when the pattern-matching algorithm finds a feedforward loop in E. coli’s networks, each gene of the triangle could also be under the influence of many other, and maybe the behavior of the circuit is not what could be inferred by looking only at these three genes.
• The algorithm consider isomorphism between subnetworks, which implies that it won’t mind if the subnetwork is under the influence of external genes, but it will mind if the subnetwork has auto-regulations that do not appear on the provided pattern. For instance, fis regulates crp and vice-versa, but this won’t be reported if you simply look for the pattern $A\leftrightarrow B$ because, in addition, fis and crp regulate themselves !

# Extract data from graph pictures with Python

If you want to transform a picture of a graph into exploitable data (which is very useful in science if you want to exploit a figure from an article without bothering the authors), here is a minimalistic interface written in python with the following features:

• Data extraction from picture files or from a picture in the clipboard.
• Data extraction from rotated graphs or graphs shown with (moderate) perspective.
• Advanced interface (left-click to select a point, right-click to deselect).
• Stores the points’ coordinates in a python variable and in the clipboard (for use in another application).

You can launch the interface with

points = pic2data()


This will either start a session using the picture from the clipboard, or , if there is none, wait for the clipboard to contain a picture. Alternatively you can use a picture from a file with

points = pic2data('graph.jpeg')


You will then be asked you to place the origin of the graph, as well as the coordinates of this origin (in case it it not (0,0)), and one reference point for each axis X and Y (i.e. points of these axis whose coordinates you know). Then you can select/deselect as many points of the curve as you want, and exit with the middle button.The list of selected points [(x1,y1),(x2,y2),…] is returned.

By default the program will consider that the graph is rectangular and parralel to the edges of the pictures (wich I will call straight in what follows). This will typically be the case for a graph from a scientific article. As a consequence the algorithm will automatically replace the reference point you chose for the X axis in order to put it at the same height as the origin, and it will replace the reference point for Y exactly above the origin. However if the graph on the picture is not straight, like in a photo, use the argument straight=False.

As an example, let us take a photo with a graph, like this one.

Fig. 1: Young Frederic Chopin disguised as Mozart.

As the graph is not straight we will use

points = pic2data('mozart.jpeg', straight = False)


Which gets you to that:

After placing the points and getting their coordinates one can redraw the plot with

from pylab import *
figure()
x,y = zip(*points)
plot(x,y,'o')
show()


And voilà !

Here is the code. Happy curving !

from urlparse import urlparse

import pygtk
import gtk
import tkSimpleDialog

import matplotlib.image as mpimg
import matplotlib.pyplot as plt

import numpy as np

def tellme(s):
print s
plt.title(s,fontsize=16)
plt.draw()

def pic2data(source='clipboard',straight=True):
""" GUI to get data from a XY graph image. Either provide the graph
as a path to an image in 'source' or copy it to the clipboard.
"""

##### GET THE IMAGE

clipboard = gtk.clipboard_get()

if source=='clipboard':

# This chunk tries the text content of the clipboard
# and empties it if it is not a file path

print "Waiting for an image in the clipboard..."
while not ( clipboard.wait_is_uris_available()
or clipboard.wait_is_image_available()):
pass

if clipboard.wait_is_uris_available(): # it's a path to a file !

source = clipboard.wait_for_uris()[0]
source = urlparse(source).path
return pic2data(source)

image = clipboard.wait_for_image().get_pixels_array()
origin = 'upper'

else: # source is a path to a file !

origin = 'lower'

###### DISPLAY THE IMAGE

plt.ion() # interactive mode !
fig, ax = plt.subplots(1)
imgplot = ax.imshow(image, origin=origin)
fig.canvas.draw()
plt.draw()

##### PROMPT THE AXES

def promptPoint(text=None):

if text is not None: tellme(text)
return  np.array(plt.ginput(1,timeout=-1)[0])

initialvalue=initialvalue)

origin = promptPoint('Place the origin')

Xref =  promptPoint('Place the X reference')

Yref =  promptPoint('Place the Y reference')

if straight :

Xref[1] = origin[1]
Yref[0] = origin[0]

##### PROMPT THE POINTS

selected_points = []

print "Right-click or press 's' to select"
print "Left-click or press 'del' to deselect"
print "Middle-click or press 'Enter' to confirm"
print "Note that the keyboard may not work."

selected_points = plt.ginput(-1,timeout=-1)

##### RETURN THE POINTS COORDINATES

#~ selected_points.sort() # sorts the points in increasing x order

# compute the coordinates of the points in the user-defined system

OXref = Xref - origin
OYref = Yref - origin
xScale =  (Xref_value - origin_value[0]) / np.linalg.norm(OXref)
yScale =  (Yref_value - origin_value[1]) / np.linalg.norm(OYref)

ux = OXref / np.linalg.norm(OXref)
uy = OYref / np.linalg.norm(OYref)

result = [(ux.dot(pt - origin) * xScale + origin_value[0],
uy.dot(pt - origin) * yScale + origin_value[1])
for pt in selected_points ]

# copy the result to the clipboard

clipboard.set_text('[' + '\n'.join([str(p) for p in result]) + ']')

clipboard.store() # makes the data available to other applications

plt.ioff()

return result


# Animate your 3D plots with Python’s Matplotlib

When you have a complicated 3D plot to show in a video or slideshow, it can be nice to animate it:

I obtained this surface with

import matplotlib.pyplot as plt
from matplotlib import cm
from mpl_toolkits.mplot3d import axes3d

fig = plt.figure()
X, Y, Z = axes3d.get_test_data(0.05)
s = ax.plot_surface(X, Y, Z, cmap=cm.jet)
plt.axis('off') # remove axes for visual appeal


To animate it I created the function rotanimate that you can use like that:

import numpy as np
angles = np.linspace(0,360,21)[:-1] # A list of 20 angles between 0 and 360

# create an animated gif (20ms between frames)
rotanimate(ax, angles,'movie.gif',delay=20)

# create a movie with 10 frames per seconds and 'quality' 2000
rotanimate(ax, angles,'movie.mp4',fps=10,bitrate=2000)

# create an ogv movie
rotanimate(ax, angles, 'movie.ogv',fps=10)


Here is the source-code:

import matplotlib.pyplot as plt
from matplotlib import cm
from mpl_toolkits.mplot3d import axes3d
import os, sys
import numpy as np

##### TO CREATE A SERIES OF PICTURES

def make_views(ax,angles,elevation=None, width=4, height = 3,
prefix='tmprot_',**kwargs):
"""
Makes jpeg pictures of the given 3d ax, with different angles.
Args:
ax (3D axis): te ax
angles (list): the list of angles (in degree) under which to
take the picture.
width,height (float): size, in inches, of the output images.
prefix (str): prefix for the files created.

Returns: the list of files created (for later removal)
"""

files = []
ax.figure.set_size_inches(width,height)

for i,angle in enumerate(angles):

ax.view_init(elev = elevation, azim=angle)
fname = '%s%03d.jpeg'%(prefix,i)
ax.figure.savefig(fname)
files.append(fname)

return files

##### TO TRANSFORM THE SERIES OF PICTURE INTO AN ANIMATION

def make_movie(files,output, fps=10,bitrate=1800,**kwargs):
"""
Uses mencoder, produces a .mp4/.ogv/... movie from a list of
picture files.
"""

output_name, output_ext = os.path.splitext(output)
command = { '.mp4' : 'mencoder "mf://%s" -mf fps=%d -o %s.mp4 -ovc lavc\
-lavcopts vcodec=msmpeg4v2:vbitrate=%d'
%(",".join(files),fps,output_name,bitrate)}

command['.ogv'] = command['.mp4'] + '; ffmpeg -i %s.mp4 -r %d %s'%(output_name,fps,output)

print command[output_ext]
output_ext = os.path.splitext(output)[1]
os.system(command[output_ext])

def make_gif(files,output,delay=100, repeat=True,**kwargs):
"""
Uses imageMagick to produce an animated .gif from a list of
picture files.
"""

loop = -1 if repeat else 0
os.system('convert -delay %d -loop %d %s %s'
%(delay,loop," ".join(files),output))

def make_strip(files,output,**kwargs):
"""
Uses imageMagick to produce a .jpeg strip from a list of
picture files.
"""

os.system('montage -tile 1x -geometry +0+0 %s %s'%(" ".join(files),output))

##### MAIN FUNCTION

def rotanimate(ax, angles, output, **kwargs):
"""
Produces an animation (.mp4,.ogv,.gif,.jpeg,.png) from a 3D plot on
a 3D ax

Args:
ax (3D axis): the ax containing the plot of interest
angles (list): the list of angles (in degree) under which to
show the plot.
output : name of the output file. The extension determines the
kind of animation used.
**kwargs:
- width : in inches
- heigth: in inches
- framerate : frames per second
- delay : delay between frames in milliseconds
- repeat : True or False (.gif only)
"""

output_ext = os.path.splitext(output)[1]

files = make_views(ax,angles, **kwargs)

D = { '.mp4' : make_movie,
'.ogv' : make_movie,
'.gif': make_gif ,
'.jpeg': make_strip,
'.png':make_strip}

D[output_ext](files,output,**kwargs)

for f in files:
os.remove(f)

##### EXAMPLE

if __name__ == '__main__':

fig = plt.figure()
X, Y, Z = axes3d.get_test_data(0.05)
s = ax.plot_surface(X, Y, Z, cmap=cm.jet)
plt.axis('off') # remove axes for visual appeal

angles = np.linspace(0,360,21)[:-1] # Take 20 angles between 0 and 360

# create an animated gif (20ms between frames)
rotanimate(ax, angles,'movie.gif',delay=20)

# create a movie with 10 frames per seconds and 'quality' 2000
rotanimate(ax, angles,'movie.mp4',fps=10,bitrate=2000)

# create an ogv movie
rotanimate(ax, angles, 'movie.ogv',fps=10)


# Sound up your Python !

Long simulations and optimisations are a plea to the modern modelist. Worst of all are the programs of average length (say, 5 to 15 minutes) that do not let you the time to start anything else during the runs, and have you lose your day before you know it. I wrote a few Python functions to ease the pain. The first is called ring() and produces… a ring (like an egg timer ! but if you have office-mates you may use a more neutral sound like somenone coughing, or scratching, etc…). You can use it like this:

def myLongFunction():
for i in range(100000):
print "I'm the world's most useless function !"

myLongFunction();ring()


In case you want your function to always ring at the end, you can also use my decorator @ringatend when you define the function :

@ringatend
def myLongFunction():
for i in range(100000):
print "I'm the world's most useless function !"

myLongFunction() # will ring at the end, no need to call 'ring()'


Now, if you really want to make your colleagues jealous (or crazy) you can ask Python to play some music in the background while the function runs, with my decorator @inmusic

@inmusic
def myLongFunction():
.................

myLongFunction() # will play music during the function's run !


Believe me, simulations look way shorter with on some Beny Hill (but they are actually slower 🙂 )

You can also combine the decorators to get a function that will play some music, and ring at the end:

@ringatend
@inmusic
def myLongFunction():


Here is the code for all that. You will need to install Pygame to play the sounds. I have also included some functions to splash popups: popup and @popupatend:

rom Tkinter import *
import tkMessageBox
import time
import pygame

# RING

def ring(sound='./cough.wav'):

pygame.mixer.init()
sound = pygame.mixer.Sound(sound=)
sound.play()
time.sleep(sound.get_length())
pygame.mixer.quit()

def ringatend(target):
""" a decorator to make your functions rings when they are done """

def f(*args,**kwargs):

result = target(*args,**kwargs)
ring()
return result

return f

# IN MUSIC !

def inmusic(target):
""" a decorator to play your functions in music """

def f(*args,**kwargs):

pygame.mixer.init()
sound = pygame.mixer.Sound('./music.wav')
sound.play()
result = target(*args,**kwargs)
sound.stop()
pygame.mixer.quit()
return result

return f

# POPUPS

def popup(txt='Finished'):
root = Tk()
tkMessageBox.showinfo('Finished!',txt)
root.destroy()
root.mainloop()

def popupatend(target):

def f(*args,**kwargs):

# Run the function
result = target(*args,**kwargs)

# Make a pretty text
fname = target.func_name
pretty_args = ','.join([str(a) for a in args])
pretty_kwargs = ','.join(['%s=%s'%(str(k),str(v))
for k,v in kwargs.iteritems()])
descr ='%s(%s,%s)'%(fname,pretty_args, pretty_kwargs)
descr = descr[:100] # in case it really is too long

# popup description
popup(txt='%s done !'%(descr))

return result

return f

### EXAMPLES

@ringatend
@inmusic
def myLongFunction():
for i in range(100000):
print "I'm the world's most useless function !"

myLongFunction()

@popupatend
def myLongFunction():
for i in range(100000):
print "I'm the most useless function !"

myLongFunction()


If you want to go further with the decorators, here are versions of the decorators with options that let you choose the sound or music you want to be played.



def ringatend2(soundFile):
""" a decorator generator using a specified soundfile """

def decorator(target):
""" a decorator using the specified soundfile """

def f(*args,**kwargs):

result = target(*args,**kwargs)
ring(soundFile)
return result

return f

return decorator

def inmusic2(soundFile):
""" a decorator generator using a specified soundfile """

def decorator(target):
""" a decorator to play your functions in music """

def f(*args,**kwargs):

pygame.mixer.init()
sound = pygame.mixer.Sound(soundFile)
sound.play()
result = target(*args,**kwargs)
sound.stop()
pygame.mixer.quit()
return result

return f

return decorator

### EXAMPLES

@ringatend2('./tarzan.wav')
@inmusic2('./diesIrae.wav')
def myLongFunction():
for i in range(10000):
print "The world's most useless function !"