# Manipulations of determinants¶

Warning

This library is stable, but documentation is currently being written and needs a serious rereading and cleaning

The purpose of this little class is to regroup standard block manipulations on determinant, used in several algorithms.

Given a function $$F(x,y)$$, and two sets of values $$x_i,y_i \ 0\leq i < N$$, we can define the $$N\times N$$ square matrix

$M_{i,j} = F(x_i,y_j)$

When adding/removing a line and column (i.e. a value of x, y), $$M^{-1}$$ and $$det M$$ can be fast updated using standard block matrix computations. This class implements these general operations. It contains:

• Datas:
• $$M^{-1}$$ and $$det M$$
• a vector containing $$x_i,y_i \ 0\leq i \leq N$$
• Methods to quickly update $$M^{-1}$$ and $$\det M$$ when one:
• adds/removes a line and a column (i.e. adding or removing one x and one y)
• adds/removes two lines and two columns (i.e. adding or removing two x and two y)
• changes a line/colum, etc…