Htydjtk

Sorry that this is quite a specific question but I need to diagonalise large matrices for the problem I'm trying to solve and can't for the life of me work out what's going on:

I was expecting that diagonalising these would be much quicker on my desktop than laptop, however there seems to be very little performance difference and in fact my more powerful desktop - every aspect of the system is significantly superior to my laptop - is about 15% slower.

The simplest code that produces the difference is:

AbsoluteTiming[Eigensystem[Table[RandomReal[{0, 1}], {i, 10000}, {j, 10000}],-10, Method -> "Arnoldi"];]

This takes on average about 64 seconds on my desktop but around 58 secs on my laptop. For the specific task I'm trying to solve that difference actually seems larger too.

Any idea what's going on and if there's anyway to solve it? I've read that Mathematica can be a slower on AMD chips than Intel but I seem to get faster performance in almost every task on my desktop than on my laptop... apart from this specific one.

Full specs:

Desktop: AMD Ryzen 5 2600 3.4 GHz 6-core (3.7 GHz Boost),
32 GB 3000 MT/s (2x16 GB) RAM, Intel EVO 970(R 3500, W 2200)

Laptop (Surface Book 1): Intel i5-6300U 2.4 GHz Dual Core (3.0 GHz Boost),
8 GB 1866 MT/s (2x4 GB) RAM, SSD (R 1500, W 600)

Edit:
I notice that the CPU usage in Task Manager is slightly different - running at around 60-65% for the laptop but at 50% for the desktop. Is there perhaps a different implementation of Arnoldi for Intel that can take advantage of multiple cores?

Here are some possible explanations that came to my mind. But after further thinking, none of those should really apply to OP's situation. However, I leave this for documentation reasons.

• Probably Mathematica uses a non-parallelized implementation of
  Anoldi's method. In single-core performance, these processors are not
  that much different:
  https://cpu.userbenchmark.com/Compare/Intel-Core-i5-6300U-vs-AMD-Ryzen-5-2600/m27864vs3955. But thinking of it: By Haswell Quad Core executes this Eigensystem at 400 % CPU speed (that's macOS' way of telling me that it runs on all cores without hyperthreading) and it only takes about 29 seconds...




• Mathematica uses the Intel MKL for many numerical tasks and these libraries are best optimized for - guess what - Intel CPUs. Thinking of it, this is probably not the case for Arnoldi's method; I heard once that Mathematica uses ARPACK...




• Arnoldi's method uses mostly matrix-vector multiplications. Those are usually far from operating at peak floating point performance in case of sparse arrays because they are somewhat memory bound (nearly random access of memory is required). For dense matrices however, these are usually highly optimized. So this is probably also not the reason for the Ryzen not profiting from its peak performance... -- unless the BLAS that Mathematica uses on your system is really shabby.