Re: Implementation of mldivide?

[Jordi Gutiérrez Hermoso]

On 26 July 2011 03:33, CdeMills <address@hidden> wrote:

> I compute the derivative of some vector like this: from an input
> data vector y, I first compute a vector Z. From the values of Z I
> compute L, whose columns are function of elements Zi. Then I compute

> B = L\y

> Now I'm trying to compute dB/dZ. To this end, I assume that the
> analytical form of B is

> B=inv(L.'*L)*L.'*y

> I obtain a formulation implying B, L, y, and dL/dZ. When I try to
> validate this by simulations, i.e. introducing noise on y, having Z,
> L, and B varying with noise, I can validate most of the components
> of dBdZ, but not all. So I'm wondering: how is mldivide implemented
> analytically ? In which source file is its code ?

I'm not sure what you mean by "analytically". The formula you wrote
down for the inverse of L is certainly not used by the backslash
operator. Ignoring that word, the answer is a little complicated,
because the implementation of the backslash operator is spread out
over several source files depending on the inputs. You may find these
answers from the manual more illuminating:

     
http://www.gnu.org/software/octave/doc/interpreter/Techniques-Used-for-Linear-Algebra.html#Techniques-Used-for-Linear-Algebra
     
http://www.gnu.org/software/octave/doc/interpreter/Sparse-Linear-Algebra.html#Sparse-Linear-Algebra

HTH,
- Jordi G. H.