Differential Equations and Parameter Estimation

General Usage
22

Chris: based on the idea of a student, I extended his idea to the following utility function for zero order spline with constant step length in the abscissa:

function zero_spline(x,dx,y)
    if x < 0
        return y[1]
    elseif x >= length(y)*dx
        return y[end]
    else
        return y[trunc(Int,x/dx)+1]
    end
end

I’ve run some simple benchmarks based on a vector pair xd, yd each of length(xd) = 10_001:

julia> y = ZeroSpline(yd,xd)
julia> x = range(0,8000*60,length=10^4)
julia> @benchmark y.(x)
BenchmarkTools.Trial: 
  memory estimate:  78.27 KiB
  allocs estimate:  3
  --------------
  minimum time:     202.679 ms (0.00% GC)
  median time:      228.310 ms (0.00% GC)
  mean time:        225.889 ms (0.00% GC)
  maximum time:     245.988 ms (0.00% GC)
  --------------
  samples:          23
  evals/sample:     1

If I instead use my utility function, I find:

julia> y1 = (x) -> zero_spline(x,60,xd)
julia> @benchmark y1.(x)
BenchmarkTools.Trial: 
  memory estimate:  539.33 KiB
  allocs estimate:  29497
  --------------
  minimum time:     809.201 μs (0.00% GC)
  median time:      1.401 ms (0.00% GC)
  mean time:        1.498 ms (3.67% GC)
  maximum time:     6.355 ms (38.53% GC)
  --------------
  samples:          3327
  evals/sample:     1

OK… the ZeroSpline instantiator uses ca. 7 times less memory, but “my” utility function is 150 times faster. If I remove the “safeguards” which allows for extrapolation, my code is a little bit faster, but not much.

Questions

  1. Is there a version of ZeroSpline for the case of constant abscissa step size?
  2. Would a ZeroSpline instantiator with constant abscissa step size be as fast as “my” utility function?
  3. Is there a way to reduce the memory usage of my utility function?

Of course, I realize that the DataInterpolations package is much more fancy than my simple utility function.

23

It would be nice to just add this in. I think what would do it is just a specialization of findfirst for when t is an AbstractRange. Just add a branch and ZeroSpline should get the speed increase you see from the utility function. Sounds like a good PR :slight_smile: