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Really looks good to me. I did the time benchmark as suggested and I'm getting same time factors.

One remark a bit uncorrelated to this PR, I had a look into the _fast_chi_square function of cobaya which, in most of the time, fall down to camb.mathutils.chi_squared (in case camb is installed) but in case camb is not installed the default way to compute $\chi^2$ is https://github.com/CobayaSampler/cobaya/blob/master/cobaya/likelihoods/base_classes/DataSetLikelihood.py#L27 Regarding time benchmark, we noticed sometimes ago that dot product was slightly slower than @ product introduced in python 3.5. So we might save few microseconds in case someone use mflike (or any likelihood relying to _fast_chi_square) without camb installed.

Interesting, I had assumed they mapped to identical code. If I do this in jupyter (for n=9000) if anything the .dot form seems to be faster for me

timeit v @ cov @ v
%timeit cov.dot(v).dot(v)
%timeit v @ cov @ v
%timeit cov.dot(v).dot(v)

11.4 ms ± 222 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)
10.4 ms ± 63.7 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)
11.2 ms ± 154 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)
10.6 ms ± 196 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)

CAMB's gets the extra factor of 2 from symmetry.

I also thought they map to the same piece of code. In your test, the cov matrix is very sparse (so the purpose of this PR). If you do the test on the same 9000x9000 matrix with random numbers, then the @ is much faster than dot. I'm not sure I understand the difference between dot and matmul which corresponds to the @ implementation https://numpy.org/doc/stable/reference/generated/numpy.matmul.html#numpy.matmul

odd, I see the same with random numbers and matmul or @ (Maybe it changed in numpy 2 or depends on threading?)