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Currently we refer to the parameter_axis as the first dimension, but the DPP/cvxpylayers papers puts it as the last (third) dimension. We need to adjust to avoid further confusions. This will also lead consistency for the row and col axis.

In terms of implementation, only the NumPy backend requires major changes. The other ones will probably only involve updating some docstrings.

My goal is to create additional unit-tests that have little to no boilerplate (ie: repeated code sections, duplicate instantiations). This will be helpful when adding unit-tests for the numpy backend.

This will allow all functions from the PythonCanonBackend class to be used freely (ie: transpose, upper_tri, etc.)

Prompted from a discussion with Riley on inability of targeting a certain type of DGP canonicalization. I will open an issue on the official repository soon.

select_rows and apply_all have just been completed today.

here is a list of functions that can now be completed easily (apply_all):

• promote
• hstack
• neg
• sum_entries
• diag_vec

For select_rows we have the following:

• index
• vstack
• transpose
• upper_tri
• diag_mat

In order to finalise the numpy backend, we must complete the implementation for the following 10 methods.
Some of them are very similar, so we should be able to finish a couple at a time. (ex: kron_r and kron_l, r_mul, etc.)

• parametrised_mul
• rmul
• parametrised_rmul
• mul_elementwise
• mul_elementwise_param
• div
• trace
• conv
• kron_r
• kron_l

currently, there are some unit-tests that do not make use of the fixtures I have created last time. For example, in test_parametrized_mul, we are still hardcoding ScipyTensorView as we are passing "hardcoded parameters to it". This should be changed to allow seamless testing for all backends.

multiply is the most important function that is reused in other functionalities. for example, all of kron, parametrised_mul, conv make use of multiply.

This could help avoid flattening the constant then reshaping it back

I will need to build upon an "official" documentation section of the backend. This can include description of the linear operations and how they are performed, along with detailed walkthrough of some simple examples.

Link to helpful resource: https://www.cvxpy.org/contributing/index.html#solver-interfaces
Link to example for Clarabel (by Paul Goulart): cvxpy#1888
Link to python-interface: https://github.com/oxfordcontrol/cosmo-python (also need to email the author for pip addition potentially)
Let's first inquire the developers if this would still be a desired addition before continuing further.
We also will need to deal with some minor issues with python-julia's interface.

set the foundation for the stacked-slices --> pygraphBLAS.
import equivalent graph algorithms to common linear algebra operations (mul, kronecker, reshaping, etc.)

perhaps under doc/source/api_reference?

using LaTeX and potential Jupyter book.

This issue can be closed once all the secondary details of the PR have been checked off the lists

We need to follow the example that was done for testing param_sum_elem.
The one where we used clever kron to perform what was needed.