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I'm pretty sure that this is due to bias correction that generally takes place when you have MSE. You can read about the formula for bias correction that is used in the references they provided in ?sae::meanSFH. In one of the articles, they provided a case study where the average MSE is negative. (I found this in Molina et al., 2009. They identify the bias correction in a few places, but it's very clear on pp. 452-453.)

You can visualize the errors and see how very close they are to zero.

I believe using -AllMatches on Select-String should sort out the need to find all matches per line, another alternative could be to use [regex]::Matches(..) to find all appearances of the matched pattern.

Regarding the need to sort alphabetically the characters, I would personally use:

Q : " Writing to a file parallely while processing in a loop in python ... "

A :
Frankly speaking, the file-I/O is not your performance-related enemy.

_{"With all due respect to the colleagues, Python (since ever) used GIL-lock to avoid any level of concurrent execution ( actually re-SERIAL-ising the code-execution flow into dancing among any amount of threads, lending about 100 [ms] of code-interpretation time to one-AFTER-another-AFTER-another, thus only increasing the interpreter's overhead times ( and devastating all pre-fetches into CPU-core caches on each turn ... paying the full mem-I/O costs on each next re-fetch(es) ). So threading is ANTI-pattern in python (except, I may accept, for network-(long)-transport latency masking ) – user3666197 44 mins ago "}

Given about the 65k files, listed in CSV, ought get processed ASAP, the performance-tuned orchestration is the goal, file-I/O being just a negligible ( and by-design well latency-maskable ) part thereof _{( which does not mean, we can't screw it even more ( if trying to organise it in another performance-devastating ANTI-pattern ), can we? )}

Tip #1 : avoid & resist to use any low-hanging fruit SLOCs if The Performance is the goal

If the code starts with a cheapest-ever iterator-clause,
be it a mock-up for aRow in aCsvDataSET: ...
or the real-code for i in range( len( queries ) ): ... - these (besides being known for ages to be awfully slow part of the python code-interpretation capabilites, the second one being even an iterator-on-range()-iterator in Py3 and even a silent RAM-killer in Py2 ecosystem for any larger sized ranges) look nice in "structured-programming" evangelisation, as they form a syntax-compliant separation of a deeper-level part of the code, yet it does so at an awfully high costs impacts due to repetitively paid overhead-costs accumulation. A finally injected need to "coordinate" unordered concurrent file-I/O operations, not necessary in principle at all, if done smart, are one such example of adverse performance impacts if such a trivial SLOC's ( and similarly poor design decisions' ) are being used.

Better way?

• a ) avoid the top-level (slow & overhead-expensive) looping
• b ) "split" the 65k-parameter space into not much more blocks than how many memory-I/O-channels are present on your physical device ( the scoring process, I can guess from the posted text, is memory-I/O intensive, as some model has to go through all the texts for scoring to happen )
• c ) spawn n_jobs-many process workers, that will joblib.Parallel( n_jobs = ... )( delayed( <_scoring_fun_> )( block_start, block_end, ...<_params_>... ) ) and run the scoring_fun(...) for such distributed block-part of the 65k-long parameter space.
• d ) having computed the scores and related outputs, each worker-process can and shall file-I/O its own results in its private, exclusively owned, conflicts-prevented output file
• e ) having finished all partial block-parts' processing, the main-Python process can just join the already ( just-[CONCURRENTLY] created, smoothly & non-blocking-ly O/S-buffered / interleaved-flow, real-hardware-deposited ) stored outputs, if such a need is ...,
  and
  finito - we are done ( knowing there is no faster way to compute the same block-of-tasks, that are principally embarrasingly independent, besides the need to orchestrate them collision-free with minimised-add-on-costs).

If interested in tweaking a real-system End-to-End processing-performance,
start with lstopo-map
next verify the number of physical memory-I/O-channels
and
may a bit experiment with Python joblib.Parallel()-process instantiation, under-subscribing or over-subscribing the n_jobs a bit lower or a bit above the number of physical memory-I/O-channels. If the actual processing has some, hidden to us, maskable latencies, there might be chances to spawn more n_jobs-workers, until the End-to-End processing performance keeps steadily growing, until a system-noise hides any such further performance-tweaking effects

A Bonus part - why un-managed sources of latency kill The Performance

We could use cur_group_id()

That's related to some unexpected issue related to the use of --nomultiline or IRB.conf[:USE_MULTILINE] = false inside .irbrc file.

Similar issue with the hack

To avoid that issue, you can just skip using --nomultiline option, when launching your rails console.

Yes, data misalignment could explain your 2x slowdown for small arrays that fit in L1d. You'd hope that with every other load/store being a cache-line split, it might only slow down by a factor of 1.5x, not 2, if a split load or store cost 2 accesses to L1d instead of 1.

But it has extra effects like replays of uops dependent on the load result that apparently account for the rest of the problem, either making out-of-order exec less able to overlap work and hide latency, or directly running into bottlenecks like "split registers".

ld_blocks.no_sr counts number of times cache-line split loads are temporarily blocked because all resources for handling the split accesses are in use.

When a load execution unit detects that the load splits across a cache line, it has to save the first part somewhere (apparently in a "split register") and then access the 2nd cache line. On Intel SnB-family CPUs like yours, this 2nd access doesn't require the RS to dispatch the load uop to the port again; the load execution unit just does it a few cycles later. (But presumably can't accept another load in the same cycle as that 2nd access.)

• https://chat.stackoverflow.com/transcript/message/48426108#48426108 - uops waiting for the result of a cache-split load will get replayed.
• Are load ops deallocated from the RS when they dispatch, complete or some other time? But the load itself can leave the RS earlier.
• How can I accurately benchmark unaligned access speed on x86_64? general stuff on split load penalties.

The extra latency of split loads, and also the potential replays of uops waiting for those loads results, is another factor, but those are also fairly direct consequences of misaligned loads. Lots of counts for ld_blocks.no_sr tells you that the CPU actually ran out of split registers and could otherwise be doing more work, but had to stall because of the unaligned load itself, not just other effects.

You could also look for the front-end stalling due to the ROB or RS being full, if you want to investigate the details, but not being able to execute split loads will make that happen more. So probably all the back-end stalling is a consequence of the unaligned loads (and maybe stores if commit from store buffer to L1d is also a bottleneck.)

On a 100KB I reproduce the issue: 1075ns vs 1412ns. On 1 MB I don't think I see it.

Data alignment doesn't normally make that much difference for large arrays (except with 512-bit vectors). With a cache line (2x YMM vectors) arriving less frequently, the back-end has time to work through the extra overhead of unaligned loads / stores and still keep up. HW prefetch does a good enough job that it can still max out the per-core L3 bandwidth. Seeing a smaller effect for a size that fits in L2 but not L1d (like 100kiB) is expected.

Of course, most kinds of execution bottlenecks would show similar effects, even something as simple as un-optimized code that does some extra store/reloads for each vector of array data. So this alone doesn't prove that it was misalignment causing the slowdowns for small sizes that do fit in L1d, like your 10 KiB. But that's clearly the most sensible conclusion.

Code alignment or other front-end bottlenecks seem not to be the problem; most of your uops are coming from the DSB, according to idq.dsb_uops. (A significant number aren't, but not a big percentage difference between slow vs. fast.)

How can I mitigate the impact of the Intel jcc erratum on gcc? can be important on Skylake-derived microarchitectures like yours; it's even possible that's why your idq.dsb_uops isn't closer to your uops_issued.any.

One option to achieve your desired result would be via the ggnewscale package which allows for multiple scales and legends for the same aesthetic.

1. Put your colors into a named vector which assign a color to each of your Genus
2. Make a list of Filums with associated Genuss. To this end I make use of dplyr::distinct and split.

I think it would be safer to match the color within the data frame and then map via scale_identity. I feel this gives you a better control of your mapping - and you will also be able to better debug mismatches. This allows also easily for different groups to be present or not.

Consider below approach