Chapter 5. Advanced Computing with SciPy, Numba, and NumbaPro

In this chapter, the user will learn how to use SciPy to perform scientific computations. The Numba package will then be introduced as a way to accelerate computations. Finally, the NumbaPro capabilities of parallel execution in the GPU will be presented.

In this chapter, we will cover the following topics:

• Overview of SciPy

• Advanced mathematical algorithms with SciPy

• Accelerating computations with Numba and NumbaPro

Before running the examples in this chapter, load pylab by running the following command in a computing cell:

%pylab inline

Overview of SciPy

SciPy is an extensive library for applied mathematics and scientific computation. The following is the complete list of all the modules available in the library:

Module	Functionality
cluster	Clustering algorithms
constants	Physical and mathematical constants
fftpack	Fast Fourier Transform
integrate	Integration and ordinary differential equations
interpolate	Interpolation and splines
io	Input and output
linalg	Linear algebra
ndimage	Image processing
odr	Orthogonal distance regression
optimize	Optimization and root-finding
signal	Signal processing
sparse	Sparse matrices
spatial	Spatial data structures
special	Special functions
stats	Statistical distributions
weave	C/C++ integration

The standard way to import SciPy modules in scripts is using the following command line:

from scipy import signal

Then, individual functions can be called with the usual module reference syntax, as follows:

signal.correlate(…)...

Advanced mathematical algorithms with SciPy

In this section, we will cover some of the algorithms available in SciPy. Each of the following subsections features a representative example from a significant area of applied science. The examples are chosen so as not to require extensive domain knowledge but still be realistic. These are the topics and examples that we present:

• Solving equations and finding optimal values: We will study a market model that requires the solution of a nonlinear system and a facility location problem requiring a nonstandard optimization.

• Calculus and differential equations: We will present a volume calculation that uses integral calculus, and Newton's canon, a thought experiment proposed by Isaac Newton, which we will model using a system of differential equations. Finally, we will present a three-dimensional system, the famous Lorenz equations, which is an early example displaying chaotic behavior.

Solving equations and finding optimal values

To illustrate this...

Accelerating computations with Numba and NumbaPro

In this section, we will discuss Numba and NumbaPro, two very exciting libraries to accelerate the NumPy code. Numba and NumbaPro were created by Continuum Analytics, the same company that produces the Anaconda distribution. Numba is part of the standard Anaconda distribution, but NumbaPro is a commercial product that must be purchased separately as part of the Accelerate package. However, NumbaPro can be downloaded for a free trial period.

These libraries are unique in that they allow the acceleration of code with the addition of a few lines of code. As the first example, let's consider the following lines of code to multiply two matrices:

def matrix_multiply(A, B):
    m, n = A.shape
    n, r = B.shape
    C = zeros((m, r), float64)
    for i in range(m):
        for j in range(r):
            acc = 0
            for k in range(n):
                acc += A[i, k] * B[k, j]
            C[i, j] = acc
    return C

The preceding code uses the...

Summary

In this chapter, we covered the use of advanced mathematical algorithms in SciPy, including solving equations and finding optimal values, integration, and differential equations. The chapter concluded with a discussion on using parallelization in the GPU to accelerate computations.

Advanced mathematical algorithms with SciPy

In this section, we will cover some of the algorithms available in SciPy. Each of the following subsections features a representative example from a significant area of applied science. The examples are chosen so as not to require extensive domain knowledge but still be realistic. These are the topics and examples that we present:

• Solving equations and finding optimal values: We will study a market model that requires the solution of a nonlinear system and a facility location problem requiring a nonstandard optimization.

• Calculus and differential equations: We will present a volume calculation that uses integral calculus, and Newton's canon, a thought experiment proposed by Isaac Newton, which we will model using a system of differential equations. Finally, we will present a three-dimensional system, the famous Lorenz equations, which is an early example displaying chaotic behavior.

Solving equations and finding optimal values

To illustrate this...

Accelerating computations with Numba and NumbaPro

In this section, we will discuss Numba and NumbaPro, two very exciting libraries to accelerate the NumPy code. Numba and NumbaPro were created by Continuum Analytics, the same company that produces the Anaconda distribution. Numba is part of the standard Anaconda distribution, but NumbaPro is a commercial product that must be purchased separately as part of the Accelerate package. However, NumbaPro can be downloaded for a free trial period.

These libraries are unique in that they allow the acceleration of code with the addition of a few lines of code. As the first example, let's consider the following lines of code to multiply two matrices:

def matrix_multiply(A, B):
    m, n = A.shape
    n, r = B.shape
    C = zeros((m, r), float64)
    for i in range(m):
        for j in range(r):
            acc = 0
            for k in range(n):
                acc += A[i, k] * B[k, j]
            C[i, j] = acc
    return C

The preceding code uses the...

Summary

In this chapter, we covered the use of advanced mathematical algorithms in SciPy, including solving equations and finding optimal values, integration, and differential equations. The chapter concluded with a discussion on using parallelization in the GPU to accelerate computations.