diff vs. gradient

Why does:

diffpressure = gradient(pressure)./gradient(density);

and

diffpressure = diff(pressure)./diff(density);

give drastically different results? The derivative using each method are completely different. See attached figure

Answer 1

[Matt J]

gradient uses central differences while diff(x) uses right-hand differences x(i+1)-x(i).

[Benjamin]

Look at my attached figure, should they really be that different?

[Matt J]

I don't see why not, but on the other hand the picture isn't all that informative. You should provide the input data in a .mat file.

[Benjamin]

Check file now. It shows the original function, and the derivative using diff and derivative using grad. Surely, the derivative is not that sensitive to the method. I have hundreds of points on the curve.

[Matt J]

I see no change in the attachment.

[Benjamin]

Sorry, check now

[Matt J]

You have only plotted one of the original functions. We cannot tell if this is density or pressure and without both we also cannot gain any insight into the ratio of their gradients.

Once again, the most helpful thing would be to attach your numeric data in a .mat file.

[Matt J]

My preliminary guess would be that the gradient of density is tending toward zero, where the ratio calculation gradient(pressure)./gradient(density) becomes numerically unstable.

[Benjamin]

The y-axis is pressure, x-axis is density. Ok, I'll try and attach, but quick question: If I have x values and yvalues, how would I differentiate y wrt to x? do I do diff(y)/diff(x) or just do diff(y) and plot it as plot(x,diff(y))

[Benjamin]

Perhaps the better question is, if I have numerical X and Y data, what way should I differentiate y with respect to x?

[Benjamin]

Do you think diff(y) / diff(x) is the way to go here?

[Star Strider]

Yes!

[Matt J]

If the X-data are not equi-spaced, use diff().