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michaelweylandt avatar michaelweylandt commented on May 28, 2024

As discussed in the review of PR #11, our current UFL implementation is a bit wasteful memory wise and might be easier to speed up using "vector" style calculations rather than matrix multiplies.

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Banana1530 avatar Banana1530 commented on May 28, 2024

Just to be clear, the ADMM or AMA does not involve matrix multiplication of those triangular matrices. I would suggest we first transform the weight matrix provided by users to a vector on the R side.

  • Comparison of the two algorithms.
    Judging from theoretic time complexity, as dimension grows, DP is faster (O(n)). But considering the nature of path algorithm, I observe that when lambda is relatively small (fewer knots encountered before the algorithm terminated), path algorithm is advantageous for length < 1000.

  • Improvement of the heap implementation.
    In the sift-up and sift-down operation I use a simple swap function. Actually extra copying can be avoided. For example, in a chain a -> b -> c -> d, to sift a to the right most, we can first store a somewhere else, and then move b, c and d to the left sequentially, then plug a into the slot where d was. What we are doing in the code is swap ab, then ac, then ad.

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