Command Summary

You can get more information on the commands below from the following websites:

Quick Tour

Command Module Description
python NA Command entered at the system command line to start Python
ipython NA Command entered at the system command line to start IPython
print('some text') built-in Python print command
* + = / built-in Multiplication, addition, subtraction, and division
** built-in x**y is x to the power y
exit() built-in Exits Python
from modulename import * built-in Imports all of the code in modulename into an interactive Python session
import modulename as mn built-in Imports all of the code in modulename into an interactive Python session. Attributes, functions, and methods in modulename are referenced using mn. notation. For example to reference the function func(), in your code use mn.func().
linspace(start,stop,num=n) pylab (numpy) Creates an evenly spaced array of n elements from start to stop
x,y,z=loadtxt(filename,usecols=(0,2,5),unpack=True) pylab (numpy) Loads data from a text file. filename is the name of the text file.
usecols specifies which columns to read, with 0 being the first.
unpack=True transposes the returned array, so that the data may be unpacked using x,y,z = loadtxt(...)
len(x) built-in Returns the length or number of elements in the array x.
plot(x,y,'bo') pylab (matplotlib.pyplot) Plot x and y using blue circle markers (bo)
xlabel('axis label') pylab (matplotlib.pyplot) Add a label to the x axis of a plot
ylabel('axis label') pylab (matplotlib.pyplot) Add a label to the y axis of a plot
title('plot title') pylab (matplotlib.pyplot) Add a title to a plot
show() pylab (matplotlib.pyplot) Displays all plots in figure windows in non-interactive mode.
fitpar=polyfit(x,y,deg) pylab (numpy) Fit a polynomial of degree deg (i.e. if deg = 2, y(x) = a2 x2 + a1 x + a0, then fitpar = a2, a1, a0)
sin(x) pylab (numpy) Returns the sine of x (x in radians)
x can be a single number or an array
log10(x) pylab (numpy) Returns the base 10 log of x
x can be a single number or an array
sqrt(x) pylab (numpy) Returns the square root of x
x can be a single number or an array

Python Programming Essentials

if statement syntax 

if (conditional statement):
	block of code
elif (conditional statement):
	block of code
else (conditional statement):
	block of code

while statement syntax 

while condition:
	block of code

for statement syntax 

for element in sequence:
	block of code

Function definition syntax 

def function name(arguments):
	function code
	return function outputs
Command Module Description
type(object) built-in Returns the object type
array( [2,3,4] ) pylab (numpy) Creates a numpy array from a python list
linspace(start, stop, num=n) pylab (numpy) Creates an evenly spaced numpy array of n elements from start to stop
logspace(a, b, num=n) pylab (numpy) Creates an array of n numbers logarithmically spaced from 10a to 10b
zeros(n) pylab (numpy) Creates a array of n zeros
ones(n) pylab (numpy) Creates a array of n ones.
rand(n) pylab (numpy) Creates an array of n random numbers in the interval 0 to 1
print("string with format specifiers" % (variables)) built-in Formatted print
mystr = input("prompt text") built-in Writes "prompt text" to the screen. It reads a line from input, converts it to a string and returns it to mystr.
range(start, stop, step) built-in Creates a list of integers from start to stop-1, step specifies the increment, start and step are optional arguments.
import module_name built-in Imports all modules_name objects, module_name objects are referenced as module_name.object_name
import module_name as myname built-in Imports module_name objects under the name myname, objects referenced as myname.object_name
from module_name import * built-in Imports all objects in module_name using the wild card symbol
from module_name import objectA,objectB built-in Imports objectA and objectB from module_name

Finding Roots of Equations

Command Module Description
figure(num) pylab (matplotlib) Creates a new figure window or makes the figure num active. The num parameter is an integer that specifies the number of the figure window.
clf() pylab (matplotlib) Clears the current figure.
fsolve(func, x_est) scipy.optimize Returns the root of the equation defined by func(x)=0 given the starting estimate x_est.

Numerical Integration

Command Module Description
value,error = quad(func,a,b,args=(func_params)) scipy.integrate Integrate func from a to b. Extra arguments are passed using the optional args parameter. The limits of integration can be set to ±∞ infinity using inf or -inf.
value,error = dblquad(func,a,b,gfun,hfun,args=(func_params)) scipy.integrate Computes the double integral. Note that gfun and hfun are the limits of integration for the inner integral and must be functions not numerical values.
value,error = tplquad(func,a,b,gfun,hfun,qfun,rfun,args=(func_params)) scipy.integrate Computes the triple integral. Works like dblquad(). Except that qfun and rfun are the inner-most limits of integration.
trapz(yd,xd) pylab (numpy) Computes the integral of a function given at discrete points xd and yd using the trapezoidal rule. NOTE the inverted order of the arguments of trapz(yd,xd).

Ordinary Differential Equations I

Command Module Description
x = append(x,z) pylab
(numpy) 		Appends the array z to the array x.

Ordinary Differential Equations II

Command Module Description
X = odeint(f_func,X0,t) scipy.integrate Solves a system of first-order ODEs defined by the function f_func(state,time) given the initial conditions X0 at the times specified by the array t. It returns the two-dimensional array X. The first argument of X specifies the time point. The second specifies the component of the state vector.
subplot(nRow, nCol, plotNum) pylab (matplotlib.pyplot) Makes an array of plots on the same page, where nRow specifies the number of plots per row, nCol specifies the number of columns, and plotNum specifies where the next plot should be placed. Numbering starts at the upper-left corner.
axis('equal') pylab (matplotlib.pyplot) Forces the plot to have same scaling on x and y axes.
axis([xmin, xmax, ymin, ymax]) pylab (matplotlib.pyplot) Sets the minimums and maximums for the x and y axes.

For more information on the new plotting commands see the 2D Plotting tutorial or the matplotlib website.

Data Fitting

Command Module Description
af,cov= curve_fit(func,x,y,sigma=yerr,p0=ag) scipy.optimize Does a non-linear least squares fit to the function func() using data in x and y with uncertainty sigma and initial guess parameters p0. Returns best fit parameters and covariance matrix.
prob=chi2.cdf(chisqr,dof) scipy.stats Computes the probability of getting a χ2 in the range 0 to chisqr, where dof is the number of degrees of freedom.
errorbar(x,y,yerr=sigma,fmt='bo') pylab (matplotlib.pyplot) Plots data with errorbars given in yerr. fmt specifies the plot symbol, the default is fmt='-'.

Monte Carlo Simulations

Command Module Description
rand(d0, d1, ..., dn) numpy.random Creates an array of the given shape and populates it with random samples from a uniform distribution over [0, 1).
randn(d0, d1, ..., dn) numpy.random Creates an array of the given shape and populates it with random numbers sampled from a univariate "normal" (Gaussian) distribution of mean 0 and variance 1.