• When you need more advanced mathematical functions, where do you look?


  • Understand that SciPy exists and what kinds of things it has.

  • Understand the importance of using external libraries and how to use them.

  • Understand the purpose of wrapping existing C/Fortran code.

  • Non-objective: know details of everything (or anything) in SciPy.

See also

SciPy is a library that builds on top of NumPy. It contains a lot of interfaces to battle-tested numerical routines written in Fortran or C, as well as python implementations of many common algorithms.

What’s in SciPy?

Briefly, it contains functionality for

  • Special functions (Bessel, Gamma, etc.)

  • Numerical integration

  • Optimization

  • Interpolation

  • Fast Fourier Transform (FFT)

  • Signal processing

  • Linear algebra (more complete than in NumPy)

  • Sparse matrices

  • Statistics

  • More I/O routine, e.g. Matrix Market format for sparse matrices, MATLAB files (.mat), etc.

Many (most?) of these are not written specifically for SciPy, but use the best available open source C or Fortran libraries. Thus, you get the best of Python and the best of compiled languages.

Most functions are documented ridiculously well from a scientific standpoint: you aren’t just using some unknown function, but have a full scientific description and citation to the method and implementation.

Exercises: use SciPy

These exercises do not exist because you might need these functions someday. They are because you will need to read documentation and understand documentation of an an external library eventually.

1: Numerical integration


Do the following exercise or read the documentation and understand the relevant functions of SciPy:

Define a function of one variable and using scipy.integrate.quad calculate the integral of your function in the interval [0.0, 4.0]. Then vary the interval and also modify the function and check whether scipy can integrate it.

2: Sparse matrices


Do the following exercise or read the documentation and understand the relevant functions of SciPy:

Use the SciPy sparse matrix functionality to create a random sparse matrix with a probability of non-zero elements of 0.05 and size 10000 x 10000. The use the SciPy sparse linear algebra support to calculate the matrix-vector product of the sparse matrix you just created and a random vector. Use the %timeit macro to measure how long it takes. Does the optional format argument when you create the sparse matrix make a difference?

Then, compare to how long it takes if you’d instead first convert the sparse matrix to a normal NumPy dense array, and use the NumPy dot method to calculate the matrix-vector product.

Can you figure out a quick rule of thumb when it’s worth using a sparse matrix representation vs. a dense representation?

See also


  • When you need advance math or scientific functions, let’s just admit it: you do a web search first.

  • But when you see something in SciPy come up, you know your solutions are in good hands.