# Finding indices when the curve stops decreasing

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Hi,

I have a curve I like to find the maximum and then find the indices under the peak for which it stops decreasing on each sides.

How can I do this?

I can find the maximum by

max(y)

but how can I determine once the curve stops decreasing? The curve is a bit noisy.

I guess I could maybe use;

diff(y)

but how do I estimate the tolerance for which

diff(y) > some tolerance.

The noise level s kind of big and varies from curve to curve. The one I am looking at now goes from 1500 to -1500 at baseline. I would determine the tolerance automatically if possible.

##### 0 Comments

### Answers (3)

Matt Tearle
on 20 Oct 2014

Otherwise, you might want to try some kind of smoothing before looking for the max:

>> nwindow = 5;

>> ySmooth = conv(y,ones(nwindow,1)/nwindow,'same');

Then look for where the difference goes through zero (and the second difference is negative). You can use the diff function to do finite difference derivatives by providing the x values as well as the y.

##### 0 Comments

SK
on 20 Oct 2014

Suppose the maximum was at index im. Then take:

dyrgt = diff( y(im : end) );

dylft = diff( y(im : -1 : 1) );

irgt = im + find(dyrgt >= 0, 1) - 1;

ilft = im - find(dylft >= 0, 1) + 1;

##### 3 Comments

SK
on 21 Oct 2014

I did the following with your data sets:

data_s = smooth(data, 20);

plot(data_s);

[~, im] = max(data_s);

dyrgt = diff( data_s(im : end) );

dylft = diff( data_s(im : -1 : 1) );

irgt = im + find(dyrgt >= 0, 1) - 1;

ilft = im - find(dylft >= 0, 1) + 1;

hold on

plot(ilft, 1, '*r');

plot(irgt, 1, '*r');

% ____

data2_s = smooth(data2, 20);

[~, im] = max(data2_s);

dyrgt = diff( data2_s(im : end) );

dylft = diff( data2_s(im : -1 : 1) );

irgt = im + find(dyrgt >= 0, 1) - 1;

ilft = im - find(dylft >= 0, 1) + 1;

close all

plot(data2_s);

hold on

plot(ilft, 1, '*r');

plot(irgt, 1, '*r');

It appears to give the correct points, unless you want the small hump on the left of the peak in data2 to be treated as noise.

SK
on 20 Oct 2014

Edited: SK
on 20 Oct 2014

##### 2 Comments

SK
on 21 Oct 2014

I shouldn't have opened my mouth.

Can you assume that your data is essentially VV shaped? Meaning there is basically only one "real" peak and it falls off on both sides and then possibly rises again somewhat at the sides. Then you have an ansatz for your function shape ie: piecewise continuous with four linear pieces. You can then use nlinfit() with a custom model function. Read the docs for nlinfit(). Perhaps you can also use the fit() function with fittype as 'linearinterp'.

The advantage of picewise linear is that it is the 'roughest' approximation so it should cover all those bumps and jaggies and give you the "one true solution" for the troughs (but it probably wont give the exact minima). For example in your data2, you could leave it to take care of that hump on the left - it will decide whether it is significant or not.

On the other hand you could use a smooth approximation (cubic splines say) to approximate the curve, but the problem with smooth curves is that they may follow the shape of your data too closely so there may still be some ambiguity about points where the troughs are.

Anyway, you'll have to think about this, depending on the exact problem you want to solve and the amount of time you have on your hands.

Sorry, but I'm not sure I can be of more help.

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