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This question already has an answer here:

I have a list of X values and Y values separately, and also together with:

data=Transpose[{X,Y}]

This data is from a chromatogram, and I want to extract the retention time tR (X) that corresponds to the highest value of absorbance (Y). I normally perform an interpolation with

f=Interpolation[data];
tR=x/.Last[FindMaximum[f[x],{x,1}]];

For some reason this approach is not working with a recent chromatogram, and I wanted to extract the X value that corresponds to the maximum Y value directly from the two lists like this:

Position[Y,Max[Y]]

This gives me the position in the vector where I can find the X value I want. If I input the value manually I get the X value I am looking for:

X[[9970]]

So far so good. However, if I try to assign Position[Y,Max[Y]] to a variable (for automation, since I have a program that does all the data extraction and plotting for me), I cannot get the X value:

ymaxposition=Position[Y,Max[Y]];
tR=X[[ymaxposition]]

Part::pspec: Part specification {{9970}} is neither a machine-sized integer nor a list of machine-sized integers. >>

This isn't working either:

Position[Y,Max[Y]]
tR=X[[%]]

Any help will be very welcome.

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marked as duplicate by Mr.Wizard Jun 27 '15 at 9:20

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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    $\begingroup$ X[[ymaxposition[[1,1]]]] $\endgroup$ – Kuba Jun 10 '14 at 9:35
  • $\begingroup$ What Kuba said. And I assume there will not be more than one maximum in Y? Else you'll want to be sure to handle that appropriately. $\endgroup$ – ciao Jun 10 '14 at 9:38
  • $\begingroup$ @Kuba. Perfect. Thank you. $\endgroup$ – PMG870505 Jun 10 '14 at 10:30
  • $\begingroup$ Position provides the result in a format that is suitable for use with Extract. Braces are used to indicate the depth/level of the results. $\endgroup$ – Sjoerd C. de Vries Jun 10 '14 at 14:16
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Why don't you pick the X value directly from data? something like this:

Sort[data, #1[[2]] > #2[[2]] &][[1, 1]]
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  • $\begingroup$ Excellent. Thank you. Also X[[ymaxposition[[1,1]]]] worked $\endgroup$ – PMG870505 Jun 10 '14 at 10:31
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Try this:

Y={1,3,4,1,2,3,5,5,2};
X=Y-1;
data=Transpose[{X,Y}];
Select[data,#[[2]]==Max[Y]&][[All, 1]]

or shorter

Pick[X, Y, Max[Y]]
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