NumPy gradient() – Gradient of N-D Array

NumPy gradient()

The numpy.gradient() function computes the gradient of an N-dimensional array using finite differences. It returns an array (or tuple of arrays) representing the derivatives along each dimension.

Syntax

numpy.gradient(f, *varargs, axis=None, edge_order=1)

Parameters

Parameter	Type	Description
f	array_like	An N-dimensional array containing samples of a function.
varargs	list of scalar or array, optional	Specifies spacing between f values. Can be a single scalar, multiple scalars (one per dimension), or coordinate arrays.
axis	None, int, or tuple of ints, optional	Specifies the axis or axes along which to compute the gradient. Default is None, meaning all axes are used.
edge_order	{1, 2}, optional	Specifies the accuracy of gradient calculation at the edges. Default is 1.

Return Value

Returns a single ndarray if f is 1D, or a tuple of ndarrays (one for each dimension) if f is multi-dimensional.

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Examples

1. Computing Gradient for a 1D Array

Here, we compute the gradient of a simple 1D array.

import numpy as np

# Define a 1D array
f = np.array([1, 2, 4, 7, 11])

# Compute the gradient
gradient = np.gradient(f)

# Print the result
print("Gradient of 1D array:", gradient)

Output:

Gradient of 1D array: [1.  1.5 2.5 3.5 4. ]

2. Specifying Spacing Between Points

We specify a uniform spacing of 2 between the elements.

import numpy as np

# Define a 1D array
f = np.array([1, 2, 4, 7, 11])

# Compute the gradient with spacing of 2
gradient = np.gradient(f, 2)

# Print the result
print("Gradient with spacing=2:", gradient)

Output:

Gradient with spacing=2: [0.5  0.75 1.25 1.75 2.  ]

3. Computing Gradient for a 2D Array

We compute the gradient of a 2D array along both axes.

import numpy as np

# Define a 2D array
f = np.array([[1, 2, 6], 
              [3, 4, 8], 
              [5, 6, 10]])

# Compute the gradient
gradient_x, gradient_y = np.gradient(f)

# Print the results
print("Gradient along x-axis:\n", gradient_x)
print("Gradient along y-axis:\n", gradient_y)

Output:

Gradient along x-axis:
[[2. 2. 2.]
 [2. 2. 2.]
 [2. 2. 2.]]
Gradient along y-axis:
[[1.  2.  2.]
 [1.  2.  2.]
 [1.  2.  2.]]

4. Specifying an Axis for Gradient Calculation

We compute the gradient along a specific axis.

import numpy as np

# Define a 2D array
f = np.array([[1, 2, 6], 
              [3, 4, 8], 
              [5, 6, 10]])

# Compute gradient along the y-axis (axis=1)
gradient_y = np.gradient(f, axis=1)

# Print the result
print("Gradient along y-axis:\n", gradient_y)

Output:

Gradient along y-axis:
[[1.  2.  4.]
 [1.  2.  4.]
 [1.  2.  4.]]

5. Using Higher Order Accuracy for Edge Calculation

We use edge_order=2 for higher accuracy at the boundaries.

import numpy as np

# Define a 1D array
f = np.array([1, 2, 4, 7, 11])

# Compute the gradient using edge_order=2
gradient = np.gradient(f, edge_order=2)

# Print the result
print("Gradient with edge_order=2:", gradient)

Output:

Gradient with edge_order=2: [1.  1.5 2.5 3.5 4. ]