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From: "Adrian " <adrianb_remove_this@uga.edu>
Newsgroups: comp.soft-sys.matlab
Subject: Problems with Logs and the gradient function
Date: Thu, 12 Aug 2010 21:14:05 +0000 (UTC)
Organization: University of Georgia
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I am trying to understand the gradient function in Matlab. As I understand it, 

gradient(y)

for y a vector, will calculate the gradient of y assuming a unit interval between the points. In other words, it will calculate dy/dx assuming dx=1 for all points in the series. 

This works as expected if I have 

x = 1:20;
y = x.^2;
dydx = 2*x;

disp([dydx; gradient(y)]);

in which case dydx and gradient(y) produce the same vales (except at the end points which is to be expected). 

Now let's take the same function but have the x values geometrically spaced

n = 1:10;
x = 2.^(n-1);
y = x.^2;

If I use the gradient function, it will still assume a unit spacing of x between the data points. 

My question is: why isn't gradient(y) = dy/dlog2(x)?

log2(x) is equally spaced with unit interval but the gradient function is producting something different. In this case, dy/dlog2(x) = 2*log(2)*x.*x but this is not equal to the values produced by gradient(y). However, the ratio between the two is constant (except at the endpoints)

(dy/dlog2(x))./gradient(y) = 0.73936

I'm obviously missing something somewhere, can someone help me out here?

Thanks,

Adrian