arm_var_f32.c : Variance computation does not use common algorithm

[etiennedemontalivet]

File Path: CMSIS_5/CMSIS/DSP/Source/StatisticsFunctions/arm_var_f32.c

I have just tested the ouptut of _arm_varf32. As detailed in the doc, it uses the algorithm : Result = sum(element - meanOfElements)^2) / numElement - 1 Should'nt it be instead : Result = sum(element - meanOfElements)^2) / numElement Same for the standard deviation ?

[etiennedemontalivet]

I would propose to compute variance and standard deviation always using numElement instead of numElement - 1 Attached are associated patches for variance and standard deviation, only for f32 format.

arm_std_f32_patch.txt arm_var_f32_patch.txt

[christophe0606]

@etiennedemontalivet We have plan to rework those functions because they are not using the best algorithms in term of numerical stability.

The numElement - 1 is normal otherwise the estimator of the variance is biased.

You can look at the "Two-pass algorithm" here https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance

Now the bias is not the only important factor for an estimator. So, this function may not match all the needs.

[etiennedemontalivet]

Thanks for pointing that out.