Peak finding benchmarks

Peaks.jl functions can be very fast, but some features (wider window widths, support for missing, etc) come at a performance penalty. Below, 3 example peak finding functions^[1] and Images.findlocalmaxima are benchmarked against argmaxima and simplemaxima from Peaks.jl. (Only maxima type functions are benchmarked below, but similar results can be found for equivalent minima finding functions.)

One important difference between the Peaks.jl functions (argmaxima, simplemaxima, etc) and Images.findlocalmaxima or the example functions is that only Peaks.jl functions recognize plateaus. Depending on the type and origins of your data (quantized data, such as data sampled from physical measurements using ADC's, has a higher likelihood of plateaus), recognizing plateaus may or may not be an important/relevant feature. As a result, Peaks.jl functions are doing more work, but are still competitive with other obvious implementations.

The data generation for the above benchmark was a sine function with a peak every 5 elements; similar results are observed for more sparsely spaced peaks. However, that benchmark may not accurately reflect real-world performance when peaks are spaced more variably^[2].

When benchmarking against randomly sampled data, we see roughly the same performance characteristics, now presented relative to the speed of simplemaxima (higher is slower):

The large difference in speed between simplemaxima and other functions is due to the use of SIMD code for suitable input arrays and element types; see the docstring for its limitations compared to argmaxima.

Benchmarked functions:

function naivemaxima(x)
   pks = Int[]
   i = firstindex(x) + 1
   for i in firstindex(x)+1:lastindex(x)-1
       if x[i+1] < x[i] > x[i-1]
           push!(pks, i)
       end
   end
   return pks
end

function diffmaxima(x)
    dx = diff(x)
    return findall((diff(dx) .< 0) .& (dx[begin:end-1] .> 0) .& (dx[begin+1:end] .< 0)) .+ firstindex(x)
end

function viewsmaxima(x)
    x1 = @view x[begin:end - 2]
    x2 = @view x[begin+1:end - 1]
    x3 = @view x[begin+2:end]
    return axes(x,1)[2:end-1][x1 .< x2 .> x3]
end