LU Decomposition, linear equations

The algorithm goes as follows

• Set up the matrix $\bf A$ and the vector $\bf w$ with their correct dimensions. This determines the dimensionality of the unknown vector $\bf x$.
• Then LU decompose the matrix $\bf A$ through a call to the function ludcmp(double a, int n, int indx, double &d). This functions returns the LU decomposed matrix $\bf A$, its determinant and the vector indx which keeps track of the number of interchanges of rows. If the determinant is zero, the solution is malconditioned.
• Thereafter you call the function lubksb(double a, int n, int indx, double w) which uses the LU decomposed matrix $\bf A$ and the vector $\bf w$ and returns $\bf x$ in the same place as $\bf w$. Upon exit the original content in $\bf w$ is destroyed. If you wish to keep this information, you should make a backup of it in your calling function.

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