Partial Pivot LU decomposition for matrix inversion

[beomki-yeo]

This PR is motivated by the poor precision of the cofactor method of cmath plugin: The single precision result of the cofactor method is quite different from the double precision one.

Following values is the determinant of 6x6 matrix that appears during the kalman filtering

• eigen-eigen float: 0.00000000004306401069

• eigen-eigen double: 0.00000000004306355415

• array-cmath float with cofactor: 0.00000000004327766964 (BAD)

• array-cmath double with cofactor: 0.00000000004306355415

• array-cmath float with partial pivot LU decomposition: 0.00000000004306400722

• array-cmath double with partial pivot LU decomposition: 0.00000000004306355415

It is obvious that LU decomposition gives more reliable result with single precision.

[beomki-yeo]

Clients will not be expected to use types like algebra::determinant::partial_pivot_lud directly, right?

Right. They should not be exposed to clients in general. In case users want to call the decomposed matrix thru algebra::cmath::matrix::decomposition::lud, it will be problematic because SMatrix doesn't seem to have LU decompose function.

But I don't think we have a specific use case for that.