Suppose, I have a nonlinear map, like this:
m1 = Compile[{{n, _Real}, {k2, _Real}, {k3, _Real}, {x, _Real, 1}},
{x[[1]] Cos[2. \[Pi] (0.663 + n)] + 10. x[[2]] Sin[2. \[Pi] (0.663 + n)],
x[[2]] Cos[2. \[Pi] (0.663 + n)] - 0.1 x[[1]] Sin[2. \[Pi] (0.663 + n)] -
k2 (x[[1]] Cos[2. \[Pi] (0.663 + n)] + 10. x[[2]] Sin[2. \[Pi] (0.663 + n)])^2 -
k3 (x[[1]] Cos[2. \[Pi] (0.663 + n)] + 10. x[[2]] Sin[2. \[Pi] (0.663 + n)])^3},
CompilationTarget -> "C", RuntimeAttributes -> {Listable}, Parallelization -> True]
I turned On["Packing"].
Just after evaluation I see warnings from MMA about "Unpackung array with dimensions {21}", then other "dimensions", then "Unpacking array with dimensions {1} in call to Flatten", etc. What does this mean?
I use this m1 inside FoldList. The problem is that this FoldList function has great memory consumption. So I decided it might be related to using unpacked arrays and used On["Packing"] to check.
The main function is:
data = RandomVariate[BinormalDistribution[{Sqrt[10^-5 10.], Sqrt[10^-5/10.]}, 0], 100000];
With[{n = 0.004, k2 = 0.25, k3 = -1., t = 10000, nt = 1000},
Block[{mo = Transpose[{PadLeft[Range[0., n, n/t], t + nt + 1, 0.],
PadRight[Range[0., k2, k2/nt], t + nt + 1, k2],
PadRight[Range[0., k3, k3/nt], t + nt + 1, k3]}], rp},
rp = Reap[
FoldList[(Sow[Count[UnitStep[(#[[;; , 1]] - 0.05)], 1]];
m1[#2[[1]], #2[[2]], #2[[3]],
Pick[#, UnitStep[(#[[;; , 1]] - 0.05) (#[[;; , 1]] + 0.05)], 0]]) &, data, mo]][[2, 1]]]]
Running this function also gives warnings about unpacking. I'm not sure unpacking affects memory consumption, but my main goal is to optimize this function in terms of time and memory. Now what I see in Windows task manager is ~10GB memory of MMA when this function finished.
ADD
OK, more simple question. Why this does not unpack:
Compile[{{x,_Real}},{{Cos@x, Sin@x},{-x^2,x}}]
and this one displays warning about unpacking:
Compile[{{x,_Real}},{{Cos@x, Sin@x},{-Sin@x,Cos@x}}].
I do not understand, for me these two Compile are the same, what is the difference?
InputForm for the first example gives clean code, but for the second one it contains
Function[{x}, Block[{Compile`$10}, Compile`$10 = Cos[x]; {{Compile`$10, x},
{-Sin[x], Compile`$10}}]], Evaluate
Why Cos[x] is inside Block and Function, why not Sin[x] as well?
