Book Image

Learning SciPy for Numerical and Scientific Computing

By : Francisco J. Blanco-Silva
Book Image

Learning SciPy for Numerical and Scientific Computing

By: Francisco J. Blanco-Silva

Overview of this book

<p>It's essential to incorporate workflow data and code from various sources in order to create fast and effective algorithms to solve complex problems in science and engineering. Data is coming at us faster, dirtier, and at an ever increasing rate. There is no need to employ difficult-to-maintain code, or expensive mathematical engines to solve your numerical computations anymore. SciPy guarantees fast, accurate, and easy-to-code solutions to your numerical and scientific computing applications.<br /><br />"Learning SciPy for Numerical and Scientific Computing" unveils secrets to some of the most critical mathematical and scientific computing problems and will play an instrumental role in supporting your research. The book will teach you how to quickly and efficiently use different modules and routines from the SciPy library to cover the vast scope of numerical mathematics with its simplistic practical approach that's easy to follow.<br /><br />The book starts with a brief description of the SciPy libraries, showing practical demonstrations for acquiring and installing them on your system. This is followed by the second chapter which is a fun and fast-paced primer to array creation, manipulation, and problem-solving based on these techniques.<br /><br />The rest of the chapters describe the use of all different modules and routines from the SciPy libraries, through the scope of different branches of numerical mathematics. Each big field is represented: numerical analysis, linear algebra, statistics, signal processing, and computational geometry. And for each of these fields all possibilities are illustrated with clear syntax, and plenty of examples. The book then presents combinations of all these techniques to the solution of research problems in real-life scenarios for different sciences or engineering — from image compression, biological classification of species, control theory, design of wings, to structural analysis of oxides.</p>
Table of Contents (15 chapters)

Optimization


The field of optimization deals with finding extreme values of functions or their roots. We have seen the power of optimization already in the curve-fitting arena, but it does not stop here. There are applications to virtually every single branch of engineering, and robust algorithms to perform these tasks are a must in every scientist toolbox.

The curve_fit routine is actually syntactic sugar for the general algorithm that performs least-squares minimization – leastsq, with the imposing syntax:

leastsq(func, x0, args=(), Dfun=None, full_output=0,
        col_deriv=0, ftol=1.49012e-8, xtol=1.49012e-8,
        gtol=0.0, maxfev=0, epsfcn=0.0, factor=100, diag=None):

For instance, the curve_fit routine could have been called with a leastsq call instead:

leastsq(error_function,p0,argx=(x,y))

Here, error_function is equal to lambda p,x,y: target_function(x,p[0],p[1],p[2])-y. Most of the optimization routines in SciPy can be accessed from either native Python code, or as wraps of Fortran...