Changing the unknown variable in a matlab line

I have the following line in matlab:

y=sum(bin(xout>xout(1) & xout < -lim));

In the above line, Iam computing the value 'y' from known row-vectors 'bin' , 'xout', and known value 'lim'

How can I write the above equation, if I want to compute the value 'lim' if the value 'y' and row-vectors 'bin', 'xout' are now known.

%%---- Following scenario ---%% PICTURE ADDED

http://i45.tinypic.com/2a50njo.png

Please help

[Image Analyst]

Now known, or not known or unknown?

[Azzi Abdelmalek]

what is the lengtht of bin and xout, are they big?

[zozo]

@ImageAnalyst: NOW known(already known). Find lim given y, bin, xout.

@Azzi: bin(1x200) and xout(1x6000).

[Andrei Bobrov]

xout was sorted?

[zozo]

no..its random

[Azzi Abdelmalek]

do you mean bin(1x6000) and xout(1x200)? because with bin(1x200) and xout(1x6000).

y=sum(bin(xout>xout(1) & xout < -lim));

don't work

Answer 1

[Azzi Abdelmalek]

Example: run this to find y

 bin=rand(20,1);xout=rand(20,1);lim=-0.5;
 y=sum(bin(xout>xout(1) & xout < -lim));

then run this to find lim

 lim=[];
 for k=1:length(xout);
     if sum(bin(xout>xout(1) & xout < xout(k)))==y;
         lim=[lim -xout(k)]
     end
 end
 lim=max(lim)

note: you will notice that lim is not exactly the same as the first. and if lim contains many values, you choose the bigest (-lim will be the smaller)

[zozo]

@azzi: It is returning an empty variable 'lim'. It works for ur example(but not for all values)

*note: I have added a picture in my question, please have a look*

[Azzi Abdelmalek]

if y is given by

y=sum(bin(xout>xout(1) & xout < -lim));

lim can't be empty, unless you impose y. in this case, it's possible that lim will be empty

[zozo]

I changed:

if sum(bin(xout>xout(1) & xout < xout(k)))==y;

to

if sum(bin(xout>xout(1) & xout < xout(k)))<=y;

and now it works! Thanks Azzi

Answer 2

[Image Analyst]

How about (untested)

% Get area as function of xout.
cumulativeSum = cumsum(bin);

% For a given area, called desiredArea, 
% find the index where the cumulative sum first exceeds that area.
lim = find(cumulativeSum >= desiredArea, 1, 'first');

% lim was the index.  Now find the xout value at that index:
xOutValue = xout(lim);

[zozo]

thanku @image analyst