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pythonarraysnumpygradient

Numpy gradient of 2D array

I have a 2D array sinusoidal pattern and want to plot both the x and y gradient of that function. I have a 2D array image_data:

def get_image(params):
    # do some maths on params
    return(image)

params = (a, b, c)
image_data = get_image(params)

I use numpy.gradient to get the gradients:

gradients = numpy.gradient(image_data)
x_grad = gradients[0]
y_grad = gradients[1]

Plotting all three looks like:

gradients

This pattern is not at 45 degrees. I'd expect x and y gradients to be different. In my mind x_gradient[i][j] should be the gradient of image_data[i][j] with respect to the indexes either side and y_gradient[i][j] the gradient with respect to indexes above and below. Because the pattern is angled slightly, in image_data the gradient changes at different rates.

Am I misinterpreting my data or not understanding numpy.gradient output?

Solution

  • I'm not sure why you think the gradients should be different. But the gradient shapes for the given function should have the same shape with different levels. Let's do it analytically:

    partial derivatives

    So you can see they both have the same shape. Add the color levels and you'll see the difference.