# TakeWhile for nested list

I have a nested list of time and position for multiple particles over multiple time steps. I want to cut all the time steps off (for each particle) after which the $z$ coordinate goes above a certain value $zmax$.

So far I've been using the TakeWhile function but that only returns the $z$ values, not the entire list.

Is there a way to get around this?

The structure of the list is

{
{{t1(0), x1(0), z1(0)}, ..., {t1(n), x1(n), z1(n)}},
{{t2(0), x2(0), z2(0)}, ..., {t2(n), x2(n), z2(n)}},
{{}, ...,                    {tn(n), xn(n), zn(n)}}
}


where the number after the letter is the particle number, and the one in brackets is the time step. If that helps!

For 2 particle example:

Data = {{{0,0,0},{1,10,10},{2,20,20}},{{0,0,0},{1,15,15},{2,30,30}}}.


Setting the zmax to be 20 for example. Code used:

TakeWhile[Data[[1, All, 3]], # < 40 &]


Which gives: {0,10}. This is only for the first particle, so I presume I'd use some sort of iterative process to do it for all, but I mostly want the output to be {{0,0,0},{1,10,10}} so that every field is displayed.

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• Can you give example data, and code showing how you tried to use TakeWhile[]? – J. M. is away Nov 3 '15 at 16:29
• Did you try something like Map[Function[particle, TakeWhile[particle, Last[#] < zmax &]], yournestedlist] (alternatively TakeWhile[#, Last[#] < zmax &] & /@ yournestedlist)? – მამუკა ჯიბლაძე Nov 3 '15 at 16:41
• For 2 particle example: Data = {{{0,0,0},{1,10,10},{2,20,20}},{{0,0,0},{1,15,15},{2,30,30}}}. Setting the zmax to be 20 for example. Code used: TakeWhile[Data[[1, All, 3]], # < 40 &] gives: {0,10}. This is only for the first partile, so I presume I'd use some sort of iterative process to do it for all, but I mostly want the output to be {{0,0,0},{1,10,10}} so that every field is displayed. – jj364 Nov 3 '15 at 16:43
• Edit the question with your example. A better example should show what you expect when a particle in the middle of the row goes out of bounds. (OR perhaps the particles are known to be ordered so they always terminate right to left??) – george2079 Nov 3 '15 at 17:18

I used the latter suggestion from @მამუკა ჯიბლაძე's comment:

Did you try something like Map[Function[particle, TakeWhile[particle, Last[#] < zmax &]], yournestedlist] (alternatively TakeWhile[#, Last[#] < zmax &] & /@ yournestedlist)

TakeWhile[#, Last[#] < zmax &] & /@ Data


Although I used the general form for the choice of element (so I could constrain it by x or z) so my actual line was:

TakeWhile[#, #[[3]] < zmax &] & /@ Data


This approach gave me the new list for all the particles and desired time steps. Thank you for your help!