Difference between revisions of "LinAlgebraPacks"

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m (Protected "LinAlgebraPacks" ([edit=sysop] (indefinite) [move=sysop] (indefinite)))
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=Introduction=
 
=Introduction=
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</pre>
 
</pre>
  
http://en.wikipedia.org/wiki/System_of_linear_equations
+
From http://en.wikipedia.org/wiki/System_of_linear_equations:
 +
 
 +
The following computation shows Gauss-Jordan elimination applied to the matrix above:
 +
:<math>\left[\begin{array}{rrr|r}
 +
1 & 3 & -2 & 5 \\
 +
3 & 5 & 6 & 7 \\
 +
2 & 4 & 3 & 8
 +
\end{array}\right]</math><math>\sim
 +
\left[\begin{array}{rrr|r}
 +
1 & 3 & -2 & 5 \\
 +
0 & -4 & 12 & -8 \\
 +
2 & 4 & 3 & 8
 +
\end{array}\right]</math><math>\sim
 +
\left[\begin{array}{rrr|r}
 +
1 & 3 & -2 & 5 \\
 +
0 & -4 & 12 & -8 \\
 +
0 & -2 & 7 & -2
 +
\end{array}\right]</math><math>\sim
 +
\left[\begin{array}{rrr|r}
 +
1 & 3 & -2 & 5 \\
 +
0 & 1 & -3 & 2 \\
 +
0 & -2 & 7 & -2
 +
\end{array}\right]</math><math>\sim
 +
\left[\begin{array}{rrr|r}
 +
1 & 3 & -2 & 5 \\
 +
0 & 1 & -3 & 2 \\
 +
0 & 0 & 1 & 2
 +
\end{array}\right]</math><math>\sim
 +
\left[\begin{array}{rrr|r}
 +
1 & 3 & -2 & 5 \\
 +
0 & 1 & 0 & 8 \\
 +
0 & 0 & 1 & 2
 +
\end{array}\right]</math><math>\sim
 +
\left[\begin{array}{rrr|r}
 +
1 & 3 & 0 & 9 \\
 +
0 & 1 & 0 & 8 \\
 +
0 & 0 & 1 & 2
 +
\end{array}\right]</math><math>\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:
  
 
<pre>
 
<pre>

Revision as of 15:36, 27 January 2011

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:

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