Inverse of a Matrix: Efficient Code (timewise)

[sgsawant]

I need to find the inverse of a matrix which contains floating point numbers. Can anyone share an efficient (w.r.t. time) code?

[Marc G]

Bing

[OReubens]

http://people.richland.edu/james/lec.../inverses.html
http://www.wikihow.com/Inverse-a-3X3-Matrix
http://mathworld.wolfram.com/MatrixInverse.html
http://www.mathwords.com/i/inverse_of_a_matrix.htm

For small matrixes, efficiency is a bit of a moot issue since there's very little you can do to optimise things. You can typically get the best results by hardcoding a function for a specific matrix size not using any loops. This will quickly become unwieldy as your matrix size increases. But for 2x2, 3x3 and 4x4 it's definately worth the effort. I would expect a performance oriented 3D lib to have such hardcoded matrix calculations since they typically only have to deal with 1 size matrix.

For large matrixes, there are a number of systems that have varying degrees of performance over the raw calculation.

[Lindley]

Usually the fastest approach involves some form of matrix decomposition. LU, SVD, or Cholesky decompositions are common.

As noted, these are probably overkill for small matrices.

[sgsawant]

I was aiming for a range of 24X24.

I found a file through Google:
http://users.erols.com/mdinolfo/matrix.htm

He's shown an example with 200x200. In that regard I have a naive question to ask:

If I include a header file, but delete all but a single function out of that header file, will my .exe be as large as it would have been if I had used the entire header file? In both cases I am using the same function, but in the first case I am removing the extra baggage. Does the compiler understand and reduce the compiled code?

[Lindley]

Compilers are usually pretty good about trimming unused code, especially in a non-DLL context. However, unless you're working on an embedded platform, exe size should be fairly low down your list of priorities IMO.