How to plot the derivative from experimental data

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

Answer 1

[Star Strider]

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(:));

See the documentation section on the gradient (link) function for details.

[Sreedhar]

Thank you. BTW, if x and y are row vectors and you write dydx as

dydx = diff([eps y(:)])./diff([eps x(:)]); an error is generated

??? Error using ==> horzcat CAT arguments dimensions are not consistent.

Why should the differential of y and x be column vectors ?

TIA

[Star Strider]

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.

-----

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

-----

(The sincerest form of appreciation here on MATLAB Answers is to Accept the answer that most closely solves your problem.)

[Konuralp Bayrak]

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]

@Konuralp Bayrak —

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]

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.

Answer 2

[Abhinendra Singh]

Hello, Can any one of you please post a working example of the above problem?

I appreciate the help!

[Sajib Biswas Shuvo]

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]

good work

[John D'Errico]

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

 GRADIENT Approximate gradient.
    [FX,FY] = GRADIENT(F) returns the numerical gradient of the matrix F.
    FX corresponds to dF/dx, the differences in x (horizontal) direction.
    FY corresponds to dF/dy, the differences in y (vertical) direction.
    The spacing between points in each direction is assumed to be one.
    When F is a vector, DF = GRADIENT(F) is the 1-D gradient.
 
    [FX,FY] = GRADIENT(F,H), where H is a scalar, uses H as the constant
    spacing between points in each direction.
 
    [FX,FY] = GRADIENT(F,HX,HY), when F is 2-D, uses the spacing specified
    by HX and HY. HX and HY can either be scalars to specify the spacing
    between coordinates or vectors to specify the coordinates of the
    points. If HX and HY are vectors, their lengths must match the
    corresponding dimension of F.
 
    [FX,FY,FZ] = GRADIENT(F), when F is a 3-D array, returns the numerical
    gradient of F. FZ corresponds to dF/dz, the differences in the z
    direction. GRADIENT(F,H), where H is a scalar, uses H as the constant
    spacing between points in each direction.
 
    [FX,FY,FZ] = GRADIENT(F,HX,HY,HZ) uses the spacing given by HX, HY, HZ.
 
    [FX,FY,FZ,...] = GRADIENT(F,...) extends similarly when F is N-D and
    must be invoked with N outputs and either 2 or N+1 inputs.
 
    Note: The first output FX is always the gradient along the first
    dimension of F, going across columns.  The second output FY is always
    the gradient along the second dimension of F, going across rows.  For
    the third output FZ and the outputs that follow, the Nth output is the
    gradient along the Nth dimension of F.
 
    Examples:
        x = -2:.2:2; y = (-1:.15:1).';
        z = x .* exp(-x.^2 - y.^2);
        [px,py] = gradient(z,.2,.2);
        contour(x,y,z), hold on
        quiver(x,y,px,py), hold off
 
    Class support for input F:
       float: double, single
 
    See also DIFF, DEL2.

    Documentation for gradient
       doc gradient

    Other functions named gradient

       gpuArray/gradient    sym/gradient