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)

Ordinary differential equations


As with integration, SciPy has some extremely accurate general-purpose solvers for systems of ordinary differential equations of first order.

For the case of real-valued functions we have basically two flavors – ode (with options passed with the set_integrator method) and odeint (simpler interface). The syntax of ode is as follows:

ode(f,jac=None)

The first parameter, f, is the function to be integrated, and the second parameter, jac, refers to the matrix of partial derivatives with respect to the dependent variables (the Jacobian). This creates an ode object, with different methods to indicate the algorithm to solve the system (set_integrator), the initial conditions (set_initial_value), and different parameters to be sent to the function or its Jacobian.

The options for integration algorithm are 'vode' for real-valued variable coefficient ODE solver, with fixed-leading-coefficient implementation (it provides Adam's method for non-stiff problems, and BDF for...