Book Image

GNU Octave Beginner's Guide

By : Jesper Schmidt Hansen
Book Image

GNU Octave Beginner's Guide

By: Jesper Schmidt Hansen

Overview of this book

Today, scientific computing and data analysis play an integral part in most scientific disciplines ranging from mathematics and biology to imaging processing and finance. With GNU Octave you have a highly flexible tool that can solve a vast number of such different problems as complex statistical analysis and dynamical system studies.The GNU Octave Beginner's Guide gives you an introduction that enables you to solve and analyze complicated numerical problems. The book is based on numerous concrete examples and at the end of each chapter you will find exercises to test your knowledge. It's easy to learn GNU Octave, with the GNU Octave Beginner's Guide to hand.Using real-world examples the GNU Octave Beginner's Guide will take you through the most important aspects of GNU Octave. This practical guide takes you from the basics where you are introduced to the interpreter to a more advanced level where you will learn how to build your own specialized and highly optimized GNU Octave toolbox package. The book starts by introducing you to work variables like vectors and matrices, demonstrating how to perform simple arithmetic operations on these objects before explaining how to use some of the simple functionality that comes with GNU Octave, including plotting. It then goes on to show you how to write new functionality into GNU Octave and how to make a toolbox package to solve your specific problem. Finally, it demonstrates how to optimize your code and link GNU Octave with C and C++ code enabling you to solve even the most computationally demanding tasks. After reading GNU Octave Beginner's Guide you will be able to use and tailor GNU Octave to solve most numerical problems and perform complicated data analysis with ease.
Table of Contents (15 chapters)
GNU Octave
Credits
About the Author
About the Reviewers
www.PacktPub.com
Preface

Time for action - using lsode for numerical integration


  1. 1. Since we have an autonomous system, we can simply use the function given in Code Listing 5.5 as input to lsode. First,we specify the time vector array to contain 200 elements equally spaced from 0 to 50 as well as the initial condition:

octave:26>global_b = 1; t = linespace(0,50,200); init = [0.4 0.2];
  1. 2. Next we call lsode to obtain a numerical solution to the Sel'kov model:

octave:27> x = lsode("selkov", init, t);
  1. 3. Now, the output variable x contains the solutions to x1 and x2 in a column-wise manner, meaning column one is the solution for x1 and column two for x2. We can then plot the columns versus the time vector array, for example:

2See http://www.netlib.org/alliant/ode/prog/lsode.f

octave:28> plot(t, x(:,1), "-r", "linewidth", 5, t, x(:,2), "-b", "linewidth", 5);
  1. 4. The result (or something close to it, depending on your plotting program) is shown in the left-hand side window in the figure below.

    If we repeat Commands...