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