Difference between revisions of "LinAlgebraPacks"

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From http://en.wikipedia.org/wiki/System_of_linear_equations:
 
From http://en.wikipedia.org/wiki/System_of_linear_equations:
 +
 +
For example, consider the following system:
 +
:<math>\begin{alignat}{7}
 +
x &&\; + \;&& 3y &&\; - \;&& 2z &&\; = \;&& 5 & \\
 +
3x &&\; + \;&& 5y &&\; + \;&& 6z &&\; = \;&& 7 & \\
 +
2x &&\; + \;&& 4y &&\; + \;&& 3z &&\; = \;&& 8 &
 +
\end{alignat}</math>
  
 
The following computation shows Gauss-Jordan elimination applied to the matrix above:
 
The following computation shows Gauss-Jordan elimination applied to the matrix above:

Revision as of 15:39, 27 January 2011

Packages for Linear Algebra: Solving your system of equations using (optimised, bug-free) code that someone else has already written!


Introduction

svn co https://svn.ggy.bris.ac.uk/subversion-open/num-methods1 ./num-methods1

From http://en.wikipedia.org/wiki/System_of_linear_equations:

For example, consider the following system:

[math]\displaystyle{ \begin{alignat}{7} x &&\; + \;&& 3y &&\; - \;&& 2z &&\; = \;&& 5 & \\ 3x &&\; + \;&& 5y &&\; + \;&& 6z &&\; = \;&& 7 & \\ 2x &&\; + \;&& 4y &&\; + \;&& 3z &&\; = \;&& 8 & \end{alignat} }[/math]

The following computation shows Gauss-Jordan elimination applied to the matrix above:

[math]\displaystyle{ \left[\begin{array}{rrr|r} 1 & 3 & -2 & 5 \\ 3 & 5 & 6 & 7 \\ 2 & 4 & 3 & 8 \end{array}\right] }[/math][math]\displaystyle{ \sim \left[\begin{array}{rrr|r} 1 & 3 & -2 & 5 \\ 0 & -4 & 12 & -8 \\ 2 & 4 & 3 & 8 \end{array}\right] }[/math][math]\displaystyle{ \sim \left[\begin{array}{rrr|r} 1 & 3 & -2 & 5 \\ 0 & -4 & 12 & -8 \\ 0 & -2 & 7 & -2 \end{array}\right] }[/math][math]\displaystyle{ \sim \left[\begin{array}{rrr|r} 1 & 3 & -2 & 5 \\ 0 & 1 & -3 & 2 \\ 0 & -2 & 7 & -2 \end{array}\right] }[/math][math]\displaystyle{ \sim \left[\begin{array}{rrr|r} 1 & 3 & -2 & 5 \\ 0 & 1 & -3 & 2 \\ 0 & 0 & 1 & 2 \end{array}\right] }[/math][math]\displaystyle{ \sim \left[\begin{array}{rrr|r} 1 & 3 & -2 & 5 \\ 0 & 1 & 0 & 8 \\ 0 & 0 & 1 & 2 \end{array}\right] }[/math][math]\displaystyle{ \sim \left[\begin{array}{rrr|r} 1 & 3 & 0 & 9 \\ 0 & 1 & 0 & 8 \\ 0 & 0 & 1 & 2 \end{array}\right] }[/math][math]\displaystyle{ \sim \left[\begin{array}{rrr|r} 1 & 0 & 0 & -15 \\ 0 & 1 & 0 & 8 \\ 0 & 0 & 1 & 2 \end{array}\right]. }[/math]

To solve this using LAPACK:

cd num-methods1/examples/example1
make
./dgesv-example.exe