Replacement of a matmul + use of merge

[jvdp1]

As discussed, to be tested on different datasets

[milancurcic]

Some quick and dirty timing timings of examples/dense_mnist. This is on AMD Ryzen 5 5500U (lower end mobile CPU):

GFortran 11

• fpm profile debug:
  • main: ~35 s
  • jvdp1:optim: ~20s
• fpm profile release, -fno-frontend-optim:
  • main: ~25 s
  • jvdp1:optim: ~9s
• fpm profile release:
  • main: ~8 s, does not converge (bad result!)
  • jvdp1:optim: ~6 s, converges (good result!)

ifort classic 2021.10

• profile release:
  • main: ~8.2 s
  • jvdp1:optim: ~5.3 s

The overall training speed up is very nice, but the best part is that this PR also fixes the erroneous behavior with GFortran in release mode which previously required -fno-frontend-optimize.

@jvdp1 is this PR still a draft or can we mark it as "Ready for review"?

[jvdp1]

Thank you @milancurcic for testing the changes. It is actually ready.

[milancurcic]

Excellent, I'll go ahead and merge it then. Thank you!