Introduction¶
SciPy is a collection of mathematical algorithms and convenience functions built on the Numpy extension of Python. It adds significant power to the interactive Python session by providing the user with high-level commands and classes for manipulating and visualizing data. With SciPy an interactive Python session becomes a data-processing and system-prototyping environment rivaling systems such as MATLAB, IDL, Octave, R-Lab, and SciLab.
The additional benefit of basing SciPy on Python is that this also makes a powerful programming language available for use in developing sophisticated programs and specialized applications. Scientific applications using SciPy benefit from the development of additional modules in numerous niches of the software landscape by developers across the world. Everything from parallel programming to web and data-base subroutines and classes have been made available to the Python programmer. All of this power is available in addition to the mathematical libraries in SciPy.
This tutorial will acquaint the first-time user of SciPy with some of its most important features. It assumes that the user has already installed the SciPy package. Some general Python facility is also assumed, such as could be acquired by working through the Python distribution’s Tutorial. For further introductory help the user is directed to the Numpy documentation.
For brevity and convenience, we will often assume that the main packages (numpy, scipy, and matplotlib) have been imported as:
>>> import numpy as np
>>> import matplotlib as mpl
>>> import matplotlib.pyplot as plt
These are the import conventions that our community has adopted after discussion on public mailing lists. You will see these conventions used throughout NumPy and SciPy source code and documentation. While we obviously don’t require you to follow these conventions in your own code, it is highly recommended.
SciPy Organization¶
SciPy is organized into subpackages covering different scientific computing domains. These are summarized in the following table:
| Subpackage | Description |
|---|---|
cluster |
Clustering algorithms |
constants |
Physical and mathematical constants |
fftpack |
Fast Fourier Transform routines |
integrate |
Integration and ordinary differential equation solvers |
interpolate |
Interpolation and smoothing splines |
io |
Input and Output |
linalg |
Linear algebra |
ndimage |
N-dimensional image processing |
odr |
Orthogonal distance regression |
optimize |
Optimization and root-finding routines |
signal |
Signal processing |
sparse |
Sparse matrices and associated routines |
spatial |
Spatial data structures and algorithms |
special |
Special functions |
stats |
Statistical distributions and functions |
Scipy sub-packages need to be imported separately, for example:
>>> from scipy import linalg, optimize
Because of their ubiquitousness, some of the functions in these
subpackages are also made available in the scipy namespace to ease
their use in interactive sessions and programs. In addition, many
basic array functions from numpy are also available at the
top-level of the scipy package. Before looking at the
sub-packages individually, we will first look at some of these common
functions.
Finding Documentation¶
SciPy and NumPy have documentation versions in both HTML and PDF format available at https://docs.scipy.org/, that cover nearly all available functionality. However, this documentation is still work-in-progress and some parts may be incomplete or sparse. As we are a volunteer organization and depend on the community for growth, your participation - everything from providing feedback to improving the documentation and code - is welcome and actively encouraged.
Python’s documentation strings are used in SciPy for on-line
documentation. There are two methods for reading them and
getting help. One is Python’s command help in the pydoc
module. Entering this command with no arguments (i.e. >>> help )
launches an interactive help session that allows searching through the
keywords and modules available to all of Python. Secondly, running the command
help(obj) with an object as the argument displays that object’s calling
signature, and documentation string.
The pydoc method of help is sophisticated but uses a pager to display
the text. Sometimes this can interfere with the terminal you are
running the interactive session within. A numpy/scipy-specific help system
is also available under the command numpy.info. The signature and
documentation string for the object passed to the help command are
printed to standard output (or to a writeable object passed as the
third argument). The second keyword argument of numpy.info defines
the maximum width of the line for printing. If a module is passed as
the argument to help then a list of the functions and classes defined
in that module is printed. For example:
>>> np.info(optimize.fmin)
fmin(func, x0, args=(), xtol=0.0001, ftol=0.0001, maxiter=None, maxfun=None,
full_output=0, disp=1, retall=0, callback=None)
Minimize a function using the downhill simplex algorithm.
Parameters
----------
func : callable func(x,*args)
The objective function to be minimized.
x0 : ndarray
Initial guess.
args : tuple
Extra arguments passed to func, i.e. ``f(x,*args)``.
callback : callable
Called after each iteration, as callback(xk), where xk is the
current parameter vector.
Returns
-------
xopt : ndarray
Parameter that minimizes function.
fopt : float
Value of function at minimum: ``fopt = func(xopt)``.
iter : int
Number of iterations performed.
funcalls : int
Number of function calls made.
warnflag : int
1 : Maximum number of function evaluations made.
2 : Maximum number of iterations reached.
allvecs : list
Solution at each iteration.
Other parameters
----------------
xtol : float
Relative error in xopt acceptable for convergence.
ftol : number
Relative error in func(xopt) acceptable for convergence.
maxiter : int
Maximum number of iterations to perform.
maxfun : number
Maximum number of function evaluations to make.
full_output : bool
Set to True if fopt and warnflag outputs are desired.
disp : bool
Set to True to print convergence messages.
retall : bool
Set to True to return list of solutions at each iteration.
Notes
-----
Uses a Nelder-Mead simplex algorithm to find the minimum of function of
one or more variables.
Another useful command is source. When given a function
written in Python as an argument, it prints out a listing of the
source code for that function. This can be helpful in learning about
an algorithm or understanding exactly what a function is doing with
its arguments. Also don’t forget about the Python command dir
which can be used to look at the namespace of a module or package.