ENH - More efficient B.dot and B.T.dot in Cox datafit

[Badr-MOUFAD]

In Cox datafit, It is possible to perform the operations evolving the matrix B in linear time and without having to form explicitly the matrix.

Up to a sorting permutation of tm, the matrix B has a block triangular structure involving matrices with coordinates equal to 1.
Hence applying B to a vector (slightly) resembles performing a cumulative sum on the coordinates of v.

Advantage

• reduce the memory footprint of Cox datafit from O(n²) --> O(n) as we no longer store B
• Evaluate gradient and Hessian in O(n) instead of O(n²)

Benchmarks

A link to benchmark results to showcase the timing improvements compared to the main branch.

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Riding "la trottinette 🛴 à la @agramfort"

[Badr-MOUFAD]

Need to merge #167 beforehand

[Badr-MOUFAD]

The test fails because the gradient and Hessian disagree with scipy check_grad at atol=1e-3.
I'm not that familiar with truncation and roundoff errors to blame numerical errors for that.

However, I pushed a debug_script that checks independently the matrix-vector operations. It reveals that both operations are the same (difference of 1e-11).

@mathurinm, any clues?

[mathurinm]

nice!