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Introduction to Numerical Recipes in C
R. Sureshkumar and Gregory J. McRae
Department of Chemical EngineeringMassachusetts Institute of Technology
Cambridge, MA 02139
Table of Contents
[ 10.001 Home Page | MIT Home Page ]
What are Numerical Recipes in C?
Numerical Recipes in C is a collection (or a library) of C functions written by Press et al. (1992) which can be used for standard numerical applications. These applications include solution of systems of linear equations, matrix manipulations, evaluation of functions, solution of non-linear algebraic equations, solution of differential and integral equations and statistical analysis. The book by Press et al. has a listing and a short description of each one of the C functions.
The motivation in using libraries such as Numerical Recipes in C is the following. As a result of modeling a process/system of our interest, we typically arrive at a mathematical description of the process or system. If we can break up the mathematical problem into a set of standard mathematical problems whose numerical solution can be obtained through the use of functions available in libraries, we can save the substantial time and effort which go into the coding and debugging. Typically, for standard applications, the scientific computing libraries are robust enough to allow for their use in design/research work.
This document describes how to find the Numerical Recipes in C routines on Athena, how to compile them, and then link them into your own codes for use in solving practical problems.
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Where are the sources files on Athena?
The source files for Numerical Recipes in C are located in an Athena locker. The following sequence of commands show you how to:
- Attach the NRC recipes locker to your account
- Change directory to the source files for NRC
- List the contents of the directory
- Display the C code for the Gauss Jordan program
(Please note that the characters 'athena%' signifies the Athena prompt.)
A partial listing of the routines from the command ls * is As a specific example the file gaussj.c provides a C function for solving systems of linear algebra problems of the form A x = b using Gauss-Jordan reduction with pivoting. Further details of the use of the algorithm itself and a listing can be seen in Chapter 2, p. 36 of Press et al. (1992). The first few lines of the file obtained with more gaussj.c is: gaussj.cPress et al.more gaussj.c
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How do we use Numerical Recipes in C on Athena?
In order to use a NRC function we need to write a driver program. A driver program is typically one in which we read the relevant data for the problems (in this case, matrix a, number of equations n, the number of right hand side vectors m, and the r.h.s. data for each right hand side in a matrix of dimension n*m), call the appropriate Numerical Recipes in C function (in this case gaussj) and do any post processing and printing of the results. In this case, the function gaussj can be called by reference, and if you refer to book, Press et al. (1992) you will find that after the call to the function, the matrix a has the inverse of the original (input) matrix and b contains the solution vectors.
Note: You may choose to get the source code and modify it, but the driver program route is more elegant, prone to less difficulties in debugging and more systematic, in my opinion. The next section of this document contains secveral examples of the use of driver programs.
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