sparse matrices could allow sparsity-invariant changes to the elements

[Didou09]

Fast element-wise update to a sparse matrix without changing sparsity structure

• Some algorithms (e.g.: least_squares()) require call a user-defined sparse matrix at every iteration. It happens that, for each iteration, although the matrix is different, its sparsity structure remains constant (i.e.: changing the values of the non-zero floats inside without touching the zeros).
• Currently, unless I am mistaken, we're forced to re-instanciate the whole matrix at every iteration (which slows down the calling algorithm, like least_square(), which can have a lot of iterations).
• A more efficient way would be to instanciate the matrix before calling the algorithm, and updating only the non-zero values inside at every iteration, like we could do with a dense numpy array.

Describe the solution you'd like

• A set_items() method to allow for such element-wise changes with constant sparsity would be very welcome, and since the sparsity is constant, it should be possible to make it quite fast and efficient.
• I guess this method would have to be sparse-format specific:
  • would allow for row-wise changes for csr_matrix
  • would allow for column-wise changes for csc_matrix
  • ....
• An optional indices array could be provided to specify which elements in the row / column would be changed (by defaut assume all non-zero elements are changed ?)

Describe alternatives you've considered

• Alternatively, we could use a different sparse format better at assigning (e.g.: lil_matrix) and perform conversion to csr_matrix (because least_squares is best used with csr_matrix format). But it means there would be a sparse format conversion at every iteration, which would be an unnecessary cpu time usage.

[perimosocordiae]

The current way that we allow users to make efficient sparsity-preserving updates is by allowing access to the .data member array. It's a power user feature that comes with some caveats, but it's very fast and very flexible.

I'm not so familiar with the least squares usage, but I suspect we could improve it using this technique.

[Didou09]

Thanks @perimosocordiae, I didn't know I could access the data attribute, I'll try it and come back here if I see something constructive to propose in relation with least_square