SciPy Tutorial

Basic functions

# 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.