# Extract X value from corresponding Y value from a List or Transpose [duplicate]

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.

• X[[ymaxposition[[1,1]]]] – Kuba Jun 10 '14 at 9:35
• 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. – ciao Jun 10 '14 at 9:38
• @Kuba. Perfect. Thank you. – PMG870505 Jun 10 '14 at 10:30
• 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. – Sjoerd C. de Vries Jun 10 '14 at 14:16

Why don't you pick the X value directly from data? something like this:

Sort[data, #1[[2]] > #2[[2]] &][[1, 1]]

• Excellent. Thank you. Also X[[ymaxposition[[1,1]]]] worked – PMG870505 Jun 10 '14 at 10:31

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]]