[BUG] getPeaks gives error when calculating 1st polynomial order

[Freymaurer]

Describe the bug
When using the FSharp.Stats.Signal.PeakDetection.SecondDerivative.getPeaks function for the 1st polynomial order in combination with the second derivative, it results in an "System.IndexOutOfRangeException: Index was outside the bounds of the array." - error.

To Reproduce
Steps to reproduce the behavior:

I looked into the code and tried to narrow the origin of the error down and found it was the fault of the
Signal.Filtering.savitzky_golay function used for calculating the second derivative and for data smoothing.

open FSharp.Stats

///a = height of the gaussians peak, b = mean of gaussian distri, c = sigma of gaussian distribution,
///x = window on x -axis
let gaussianFunctionForY height mean sigma x =  height*(exp( -((x-mean) ** 2.) / (2.*(sigma ** 2.)) ))


let XX = [|0. .. 0.1 .. 100.|]
let gaussianYY = XX |> Array.map (fun x -> gaussianFunctionForY 50. 30. 0.3 x)

getPeaks 0. 1 5 XX gaussianYY  ///error seen above

let smoothedData = 
    Signal.Filtering.savitzky_golay 5 1 0 1 gaussianYY
    |> Array.ofSeq        ///no error, works as intended

Signal.Filtering.savitzky_golay 5 1 2 1 smoothedData  ///error seen above

Signal.Filtering.savitzky_golay 5 1 2 1 gaussianYY  ///error seen above

Signal.Filtering.savitzky_golay 5 1 1 1 gaussianYY //no error

Signal.Filtering.savitzky_golay 5 2 2 1 gaussianYY //no error

Apparently, the savitzky_golay function gives an error at the following line, but i am not 100% sure if i read the debugger correctly.

let m = (Algebra.LinearAlgebraManaged.pseudoInvers b).Row(deriv) * ((float(rate)**float(deriv)) * SpecialFunctions.Factorial.factorial(deriv))

Expected behavior
Should smooth data, while trying to fit the data to first order polynomials on second derivative.

OS and framework information (please complete the following information):

• OS: Windows 10 professional
• OS Version 1809
• .NET Core SDK 2.2.104
• .NET Framework 4.7.2 SDK

Additional context
I am using the FSharp.Stats developer branch

[bvenn]

The reason for the error is, that the pseudoinvers matrix b has just 2 rows and by setting the derivative to 2 you aim to access the non existing row number 3.

let deriv =2
let m = (Algebra.LinearAlgebraManaged.pseudoInvers b).Row(deriv) * ((float(rate)**float(deriv)) * SpecialFunctions.Factorial.factorial(deriv))

Explanation of this behaviour:
A first order polynomial takes the form f(x)=ax+b. The first derivative is f'(x)=a and consequently the second derivative is f''(x)=0, and therefore cannot be accessed.
I do not think that it is a good idea (and invalid), to use the savitzky golay filter with these parameters.

[bvenn]

closed by a3c5a6d