# Using Select function based on data range

I am using Select to take values from a multidimensional list based on a previously calculated range.

The list is of time and position of a particle over time steps done for multiple particles. The structure of the list meansqdCut is

meansqdCut = {{{t10,x10},{t11,x11}},{{t20,x20}{t21,x21}},..,{{tn0,xn0},{tn1,xn1}}}


Where t10 is first particle, 0th time step. So for example (2 time steps)

meansqdCut = {{{0,0},{1,5}},{{0,0},{1,8}},...,{{0,0},{1,6}}}


I have previously plotted the data and I'm using the first maximum of position as the upper limit of the range. Using

peaks = FindPeaks[meansqdCut[[#, All, 2]]] & /@ Range [1, upper]


finds the position of the maxima and I'm using the first maximum to specify the higher extent of the range. I want to take all elements of the list for each particle up to a point where the x value is greater than the maximum specified by peaks.Then using the select function:

meansqdCutMax =
Select[meansqdCut[[#]], 0 <= #[[1]] <= peaks[[#, 1, 1]] &] & /@
Range [1, 10]


Where Range[1,10] means performing this operation on particles 1 to 10. Each particle will have a different range of elements I want to select.

This gives me multiple errors saying that "The expression {0.943462,0.} cannot be used as a part specification" and I'm not sure why this arises.

If I replace the upper limit of the range with a number so

meansqdCutMax =
Select[meansqdCut[[#]], 0 <= #[[1]] <= 100 &] & /@
Range [1, 10]


then I get the desired output. So I'm presuming it is a problem with the # in the upper limit.

• What is upper? Is it Length@meansqdCut? What is the structure of meansqdCut? Is it { {pos of particle 1 at time t0, pos of particle 2 at time t0}, {pos of particle 1 at time t1, pos of particle 2 at time t1}, ...}? Are you using FindPeaks to find which of the second elements is greater? What are you Selecting for? Point is: It's a little unclear what you're trying to do. – march Nov 10 '15 at 18:22
• Hi, sorry, it is a bit unclear, I'll edit my question and make it clearer. – jj364 Nov 10 '15 at 19:03
• I have removed the 'upper' and changed it to 10. This specifies which particles I want to perform this operation on. – jj364 Nov 10 '15 at 19:13
• I'm guessing that in peaks[[#, 1, 1]], the # is supposed to be the Slot for the outer function that is being Mapped over Range[1, 10], but since it is insede the test function for Select, you are feeding elements of meansqdCut[[#]] to it. How about this instead: Cases[meansqdCut[[#]], a_ /; 0 <= a[[1]] <= peaks[[#, 1]]] & /@ Range[1, 10] – march Nov 10 '15 at 19:20
• I think it would be beneficial to add a more complicated example of meansqdCut, one where meansqdCutMax actually produces something different than just the original list, because we might be able to come up with something a little cleaner. – march Nov 10 '15 at 19:22

I've managed to get this working using one of the suggestions by @march
I'm guessing that in peaks[[#, 1, 1]], the # is supposed to be the Slot for the outer function that is being Mapped over Range[1, 10], but since it is insede [sic] the test function for Select, you are feeding elements of meansqdCut[[#]] to it. How about this instead: Cases[meansqdCut[[#]], a_ /; 0 <= a[[1]] <= peaks[[#, 1]]] & /@ Range[1, 10]march
meansqdCutMax = Cases[meansqdCut[[#]], a_ /; 0 <= a[[1]] <= peaks[[#, 1, 1]]] & /@ Range[1, upper];

Which solved the problem with the use of Slots for the Select and the Mapping.