Faster MTTKRP

[dahong67]

The current MTTKRP implementation (used for ALS) is simple but inefficient.

A significant part of the cost can come from forming the tensor matricization on this line:

GCPDecompositions.jl/src/gcp-opt.jl

Lines 183 to 184 in 6a796a5

	# Matricized tensor (in mode n)
	Xn = reshape(permutedims(X, [n; setdiff(1:N, n)]), size(X, n), :)

Can be seen by profiling in VS Code as follows:

X = randn(100,200,300);
@profview gcp(X, 10)

Note that time spent in permutedims accounts for a significant part of gcp.

We should implement the more efficient MTTKRP described in Section III-B of this paper: https://ieeexplore.ieee.org/document/6544287

Just focus on a single mode for now - we'll save the MTTKRPS (MTTKRP sequence) for #17.

Make sure to give them credit in the docstring!

[dahong67]

Re-running the above profile with the new implementation indicates that the bottlenecks are now:

• Khatri-Rao - lots of opportunity to improve Faster Khatri-Rao product #34
• computing the norm of the tensor - also lots of opportunity to improve

For this simple test case, the main Khatri-Rao costs came from the n==1 and n==N MTTKRP's. Makes sense since those Khatri-Rao products are larger.