How to plot the derivative from experimental data
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Hi I have a number of points (experimental data) plotted as an x-y plot. I want to generate the derivative of y w.r.t x from this plot. Is there a function in MATLAB which can do this ?
TIA
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Star Strider
2014-5-19
编辑：Star Strider
2019-3-25
Not a specific MATLAB function, but it’s easy:
dydx = diff(y(:))./diff(x(:));
If you want dydx to be the same length as x and y (so you can plot it against x), ‘zero-pad’ the first value with eps:
dydx = diff([eps; y(:)])./diff([eps; x(:)]);
Both produce a column vector, so you may have to transpose it if x is a row vector in order to plot it with the others.
UPDATE — (24 Mar 2019 00:30)
A much more accurate approach would be:
dydx = gradient(y(:)) ./ gradient(x(:));
5 个评论
Star Strider
2014-5-19
编辑：Star Strider
2014-5-19
My pleasure!
eps is essentially machine precision, usually on the order of 1E-15 or so. I use it to avoid NaN and Inf values (in some situations) and avoid crashes.
You can also use zero-padding (replacing eps with 0 in this example), but that doesn’t always work successfully, especially if you’re dividing vectors.
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EDIT — ‘Why should the differential of y and x be column vectors ?’
‘Both produce a column vector, so you may have to transpose it if x is a row vector in order to plot it with the others.’
I created them that way to make the eps-padding (or zero-padding) code easier to write. Either transpose it, or add these lines:
if diff(size(x)) > 0
dydx = dydx';
end
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(The sincerest form of appreciation here on MATLAB Answers is to Accept the answer that most closely solves your problem.)
Konuralp Bayrak
2020-2-19
what exactly is the difference between diff and gradient apart from the fact that gradiet assumes that experimental y values match up to evenly spaced x values. I am using both and get completely different results.
Star Strider
2022-1-1
Assuming vector arguments, the diff function takes the differences between successive elements of the vector, so the outputt is one element shorter than the arguments. The gradient function uses a central difference approximation of the derivative (except at the ends, where it calculates a simple difference) so the output has the same number of elements as the argument.
See the documentation on both for details.
.
Shiva Vikram Bhagavatula
2023-9-15
The function sampling may be poor at some or all points if completely different results are obtained for diff and gradient. For example,let the derivative be calculated at point 2 in a set of three points (p1,p2,p3). Assuming the spacing along the independent variable axis is dx, diff produces (p2-p1)/dx . Gradient produces (p3-p1)/(2dx). For them to be equal, the condition is (p3+p1)/2=p2,i.e; all three points are collinear( lie on the same straight line). The difference between gradient and diff would be a measure of the deviation of the points from the collinear fit.
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Abhinendra Singh
2017-11-27
0 个投票
Hello, Can any one of you please post a working example of the above problem?
I appreciate the help!
3 个评论
Sajib Biswas Shuvo
2021-7-3
x = 0:0.1:10;
y = sin(x);
plot(x, gradient(y)./gradient(x));
hold on;
plot(x,y);
legend('dy/dx', 'y');
hold off;
Shahlan Ahmad
2022-1-1
good work
Um, only one call to gradient needed.
x = 0:0.1:10;
y = sin(x);
plot(x, gradient(y,x));
When gradient is called with TWO arguments, it assumes you have passed in x also as the second argument. Now it computes a derivative estimate at each point. A simple finite difference scheme is used.
help gradient
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