nested MapThread

Question

I am trying to repair a list of supposedly monotonically and smoothly ascending numbers, like a CDF. An example would be like

aa={1,2,3,4,5,100,200,300,400,500,30,31,32,33,34,35};
bb=Differences[aa]

The objective is to scale up the first five elements to synch up with the sixth which is 100, and then to scale down the first ten elements to bring the first ten elements of the revised list to line up with the remaining six elements.

I have tried the following

MapThread[If[#1>90||#1<-10,MapThread[ReplacePart[aa,#2*Position[bb,#1+1]/Position[bb,#1]]&,{aa[[1;;Position[bb,#2]]]}]&,{bb}]

Apparently, #1 for the first MapThread and #2 for the second MapThread were not executed as intended. Any suggestions or corrections will be much appreciated.

Answer 1

You can use a combination of Split + Fold + Rescale as follows:

split = Split[aa, .5 < #2/# < 3 &]

{{1, 2, 3, 4, 5}, {100, 200, 300, 400, 500}, {30, 31, 32, 33, 34, 35}}

cc = N @ Fold[Join[Rescale[#, {First@#, Last@#}, First /@ {#, #2}], #2] &, split]

{1., 2.43838, 3.87675, 5.31513, 6.75351, 6.75351, 12.5651, 18.3768, 24.1884,
 30., 30., 31., 32., 33., 34., 35.}

ListPlot[{aa, cc}, PlotRange -> All, Joined -> {False, True}]

Use FoldList to see all steps:

N@FoldList[Join[Rescale[#, {First@#, Last@#}, First /@ {#, #2}], #2] &, split] // Column