options - How to find out which method Mathematica selected?

There are commands like NonlinearModelFit[] or NDSolve[] that have the option Method it typically defaults to Automatic. How can you check after the evaluation of the command which method Mathematica picked?

Answer

I think you can actually see (most of) what Mathematica is doing by using Trace[..., TraceInternal -> True].

For example,

Select[Flatten[
  Trace[NDSolve[y'[x] == x && y[0] == 0, y, {x, 0, 6}], 
   TraceInternal -> True]], ! FreeQ[#, Method | NDSolve`MethodData] &]

shows the DE was evaluated using NDSolve`LSODA and Newton's method. (I think)

And

Select[Flatten[
  Trace[NDSolve[{Derivative[1][x][t]^2 + x[t]^2 == 1, x[0] == 1/2}, 
    x, {t, 0, 10 Pi}, SolveDelayed -> True], 
   TraceInternal -> True]], ! FreeQ[#, Method | NDSolve`MethodData] &]

used NDSolve`IDA.

As an aside, here's something I just learnt from Trott's Mathematica guidebook for numerics, to see all of the methods and suboptions for NDSolve

{#, First /@ #2} & @@@ 
 Select[{#, Options[#]} & /@ (ToExpression /@ 
   DeleteCases[Names["NDSolve`*"],(* PDE method only *) "NDSolve`MethodOfLines"]), 
   (Last[#] =!= {}) &]

Comments

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plotting - Mathematica: 3D plot based on combined 2D graphs

I have several sigmoidal fits to 3 different datasets, with mean fit predictions plus the 95% confidence limits (not symmetrical around the mean) and the actual data. I would now like to show these different 2D plots projected in 3D as in but then using proper perspective. In the link here they give some solutions to combine the plots using isometric perspective, but I would like to use proper 3 point perspective. Any thoughts? Also any way to show the mean points per time point for each series plus or minus the standard error on the mean would be cool too, either using points+vertical bars, or using spheres plus tubes. Below are some test data and the fit function I am using. Note that I am working on a logit(proportion) scale and that the final vertical scale is Log10(percentage). (* some test data *) data = Table[Null, {i, 4}]; data[[1]] = {{1, -5.8}, {2, -5.4}, {3, -0.8}, {4, -0.2}, {5, 4.6}, {1, -6.4}, {2, -5.6}, {3, -0.7}, {4, 0.04}, {5, 1.0}, {1, -6.8}, {2, -4.7}, {3, -1.

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