2011/6/6 Márton Danóczy<marton78@xxxxxxxxx>:

Hi all,
I'm trying to optimize the evaluation of a squared loss function and
its gradient. That is, I'd like to calculate
L = 0.5 ||Ax-b||^2
dL/dx = A'(Ax-b)
where A has more columns than rows, i.e. A'A would be huge and caching
it would be infeasible.
Right now, i have the following routine:
Scalar objfunc(const Matrix<Scalar, Dynamic, 1>& x, Matrix<Scalar,
Dynamic, 1>& g)
{
e.noalias() = A * x - b;
g.noalias() = A.adjoint() * e;
return Scalar(0.5) * e.squaredNorm();
}
where /e/ is pre-allocated as a class member. When hand coding this,
instead of storing /e/, I would calculate it component-wise and
accumulate its squared norm along the way, thus avoiding iterating
twice. Is there a clever way to accomplish this with Eigen?

If A is of size n*n, then just reading it is n^2 memory accesses,
while you trick would be saving only n memory accesses (since e is a
vector of size n), so I'd say it's going to be negligible unless n is
very small. Also, by computing e coefficient-wise, you lose the
benefit of Eigen's cache-friendly matrix-vector product
implementation, which is important for large n.