D Mir: standard deviation speed

[tastyminerals]

On Wednesday, 15 July 2020 at 07:51:31 UTC, 9il wrote:
> On Wednesday, 15 July 2020 at 07:34:59 UTC, tastyminerals wrote:
>> On Wednesday, 15 July 2020 at 06:57:21 UTC, 9il wrote:
>>> On Wednesday, 15 July 2020 at 06:55:51 UTC, 9il wrote:
>>>> On Wednesday, 15 July 2020 at 06:00:46 UTC, tastyminerals 
>>>> wrote:
>>>>> On Wednesday, 15 July 2020 at 02:08:48 UTC, 9il wrote:
>>>>>> [...]
>>>>>
>>>>> Good to know. So, it's fine to use it with sum!"fast" but 
>>>>> better avoid it for general purposes.
>>>>
>>>> They both are more precise by default.
>>>
>>> This was a reply to the other your post in the thread, sorry. 
>>> Mir algorithms are more precise by default then the 
>>> algorithms you have provided.
>>
>> Right. Is this why standardDeviation is significantly slower?
>
> Yes. It allows you to pick a summation option, you can try 
> others then default in benchmarks.

Indeed, I played around with VarianceAlgo and Summation options, 
and they impact the end result a lot.

ans = matrix.flattened.standardDeviation!(VarianceAlgo.naive, 
Summation.appropriate);
std of [300, 300] matrix 0.375903
std of [60, 60] matrix 0.0156448
std of [600, 600] matrix 1.54429
std of [800, 800] matrix 3.03954

ans = matrix.flattened.standardDeviation!(VarianceAlgo.online, 
Summation.appropriate);
std of [300, 300] matrix 1.12404
std of [60, 60] matrix 0.041968
std of [600, 600] matrix 5.01617
std of [800, 800] matrix 8.64363


The Summation.fast behaves strange though. I wonder what happened 
here?

ans = matrix.flattened.standardDeviation!(VarianceAlgo.naive, 
Summation.fast);
std of [300, 300] matrix 1e-06
std of [60, 60] matrix 9e-07
std of [600, 600] matrix 1.2e-06
std of [800, 800] matrix 9e-07

ans = matrix.flattened.standardDeviation!(VarianceAlgo.online, 
Summation.fast);
std of [300, 300] matrix 9e-07
std of [60, 60] matrix 9e-07
std of [600, 600] matrix 1.1e-06
std of [800, 800] matrix 1e-06