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)

Matrix methods


Besides inheriting all the array methods, matrices enjoy four extra attributes – T for transpose, H for conjugate transpose, I for inverse, and A to cast as ndarray.

>>> A = numpy.matrix("1+1j, 2-1j; 3-1j, 4+1j")
>>> print A.T; print A.H
[[ 1.+1.j  3.-1.j]
 [ 2.-1.j  4.+1.j]]
[[ 1.-1.j  3.+1.j]
 [ 2.+1.j  4.-1.j]]

Operations between matrices

We have briefly covered the most basic operation between two matrices, the matrix product. For any other kind of product we resort to the basic utilities in the NumPy libraries – dot product for arrays or vectors (dot, vdot), inner and outer products of two arrays (inner, outer), tensor dot product along specified axes (tensordot), or the Kronecker product of two arrays (kron).

Let's see an example on creation of orthonormal bases.

Create an orthonormal basis of the nine-dimensional real space from an orthonormal basis of the three-dimensional real space.

For example, we choose the orthonormal basis formed by the vectors...