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From Gilles <gil...@harfang.homelinux.org>
Subject Re: [math] refactoring least squares
Date Mon, 24 Feb 2014 18:23:25 GMT
On Mon, 24 Feb 2014 11:49:26 -0500, Evan Ward wrote:
> I've looked into improving performance further, but it seems any 
> further
> improvements will need big API changes for memory management.
>
> Currently using Gauss-Newton with Cholesky (or LU) requires 4 matrix
> allocations _each_ evaluation. The objective function initially
> allocates the Jacobian matrix. Then the weights are applied through
> matrix multiplication, allocating a new matrix. Computing the normal
> equations allocates a new matrix to hold the result, and finally the
> decomposition allocates it's own matrix as a copy. With QR there are 
> 3
> matrix allocations each model function evaluation, since there is no
> need to compute the normal equations, but the third allocation+copy 
> is
> larger. Some empirical sampling data I've collected with the 
> jvisualvm
> tool indicates that matrix allocation and copying takes 30% to 80% of
> the execution time, depending on the dimension of the Jacobian.
>
> One way to improve performance would be to provide pre-allocated 
> space
> for the Jacobian and reuse it for each evaluation.

Do you have actual data to back this statement?

> The
> LeastSquaresProblem interface would then be:
>
> void evaluate(RealVector point, RealVector resultResiduals, 
> RealVector
> resultJacobian);
>
> I'm interested in hearing your ideas on other approaches to solve 
> this
> issue. Or even if this is an issue worth solving.

Not before we can be sure that in-place modification (rather than
reallocation) always provides a performance benefit.


Best Regards,
Gilles

> Evan


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