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There won't be any parallel loops generated by default with this setup as there is no outer dense loop to parallelize over. Perhaps if you made a different format {Dense, Sparse, Sparse, Sparse} you would see parallel loops generated.
I'm using the taco C++ API (built with OpenMP ON) to compute the contraction between two sparse tensors using this code:
And I found the printed code is not omp parallel in the loop. However, I test the spmv computation and it is generated with omp parallel.
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