gradient() fuction for bi-dimensional array returns first in y direction and then in x

Seems the return of gradient() function, for a two dimensional array, is changed compared to matlab. The biggest problem is it’s not documented.

See, in MATLAB:

x = [1,2,3; 4,5,6];
[gx, gy] = gradient(x)

gx =
     1     1     1
     1     1     1

gy =
     3     3     3
     3     3     3

Now, in NumPy:

x = np.array([[1,2,3], [4,5,6]])
[gx, gy] = np.gradient(x)

gx
array([[ 3.,  3.,  3.],
       [ 3.,  3.,  3.]])

gy
array([[ 1.,  1.,  1.],
       [ 1.,  1.,  1.]])

As we can see, the return of gradient() at NumPy is not in x direction and later in y. It is in y direction and then x. In my opinion that is ok this change. However, when you are trying to port a large code from matlab to python, like me, this behavior can be a pain. Also, the return is not well explained at docs, since there is only shown the gradient with a one-dimensional array.

[rcatwood]

Sorry but I still find the documentation that I can find, ambiguous. What does it mean to say ‘axis=0 is rows’ ? does that mean that the value of the coordinate, 0, changes as you move along a row or changes as you move across a row? likewise what is the gradient 'in the columns direction? is it dU/dx0 or dU/dx1 ?

It doesn’t make sense to me or agree with what I obtain . Here is a 2-dimensional dataset. xyplane [[ 0. 6. 12. 18. 24. 30.] [ 1. 7. 13. 19. 25. 31.] [ 2. 8. 14. 20. 26. 32.] [ 3. 9. 15. 21. 27. 33.] [ 4. 10. 16. 22. 28. 34.] [ 5. 11. 17. 23. 29. 35.]]

Clearly the gradient ‘in rows’ is 6 everywhere.

So if grad=numpy.gradient(xyplane) and it says that grad[0] is the gradient ‘in rows’ then it should be 6 everywhere. however it is 1, which is the gradient ‘in columns’. grad[0] [[ 1. 1. 1. 1. 1. 1.] [ 1. 1. 1. 1. 1. 1.] [ 1. 1. 1. 1. 1. 1.] [ 1. 1. 1. 1. 1. 1.] [ 1. 1. 1. 1. 1. 1.] [ 1. 1. 1. 1. 1. 1.]] grad[1] [[ 6. 6. 6. 6. 6. 6.] [ 6. 6. 6. 6. 6. 6.] [ 6. 6. 6. 6. 6. 6.] [ 6. 6. 6. 6. 6. 6.] [ 6. 6. 6. 6. 6. 6.] [ 6. 6. 6. 6. 6. 6.]]

Could someone clarify in terms of mathematical symbols e.g. partial derivative of value with respect to coordinate zero , coordinate 1, etc. ? Dispense with mentioning ‘row’ and ‘column’ because the screen output is rather arbitrary?

[eric-wieser]

This problem is one only of documentation. The docs were improved, but it sounds like not by enough.

In your example, the problem is actually that meshgrid behaves inconsistently with gradient. Perhaps the gradient docstrinng should call that out as a common mistake in the examples section.

meshgrid(indexing='ij') would fix that example.