Isolate the linear segment of data/graph

I am trying to create a script where I plot data and I need to find the slope of the most linear segment of the data/graph. Any ideas on how I can do that for a script whose data will vary for each trial.

[Adam Danz]

Are you refering to the vertical line at x=0?

Define "most linear". What segment is most linear in this plot below?

plot(round(sin(-4:.05:4)))
axis padded

[Luis Martin Romero]

When I say "most linear" I mean the initial segment that appears to be vertical but in reality just has a tiny slope. After the value "60" on the y-axis you can see how the line changes from "linear" to more parabolic, that's what I mean by "most linear". I'd like to find the range of points that have a constant slope.

Thanks

[Adam Danz]

I'd compute the slope using gradient as Star Strider recommended. If you plot the results you'll see a relatively straight line at some high value and will be precipitously fall off at the point where the original data starts to call off. To quantitatively determine the endpoint of the 'straight' line, you could take the 2nd derivative (gradient of the gradient) to locate the first spike that crosses a threhold you set.

Answer 1

[Star Strider]

One reasonably straightforward way to determine the slope of a curve is to use the gradient function.

For example, the gradient of the hyperbolic tangent function:

x = linspace(-4, 4, 500);
f = tanh(x);
dfdx = gradient(f) ./ gradient(x);

figure
plot(x, f)
hold on
plot(x, dfdx)
hold off
grid
legend('Function','Derivative', 'Location','best')

Then use the gradient result to determine what parts of the curve have the characteristics you’re interested in.

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