Compute the tensor dot product for arrays with different dimensions with double contraction in Python

Given two tensors, a and b, and an array_like object containing two array_like objects, (a_axes, b_axes), sum the products of a’s and b’s elements (components) over the axes specified by a_axes and b_axes. The third argument can be a single non-negative integer_like scalar, N; if it is such, then the last N dimensions of a and the first N dimensions of b are summed over.

To compute the tensor dot product for arrays with different dimensions, use the numpy.tensordot() method in Python. The a, b parameters are Tensors to “dot”. The axes parameter, integer_like If an int N, sum over the last N axes of a and the first N axes of b in order. The sizes of the corresponding axes must match. The axes = 2 is for tensor double contraction.

Steps

At first, import the required libraries −

import numpy as np

Creating two numpy arrays with different dimensions using the array() method −

arr1 = np.array(range(1, 9))
arr1.shape = (2, 2, 2)

arr2 = np.array(('p', 'q', 'r', 's'), dtype=object)
arr2.shape = (2, 2)

Display the arrays −

print("Array1...\n",arr1)
print("\nArray2...\n",arr2)

Check the Dimensions of both the arrays −

print("\nDimensions of Array1...\n",arr1.ndim)
print("\nDimensions of Array2...\n",arr2.ndim)

Check the Shape of both the arrays −

print("\nShape of Array1...\n",arr1.shape)
print("\nShape of Array2...\n",arr2.shape)

To compute the tensor dot product for arrays with different dimensions, use the numpy.tensordot() method −

print("\nTensor dot product...\n", np.tensordot(arr1, arr2, axes = 2))

Example

import numpy as np

# Creating two numpy arrays with different dimensions using the array() method
arr1 = np.array(range(1, 9))
arr1.shape = (2, 2, 2)
arr2 = np.array(('p', 'q', 'r', 's'), dtype=object)
arr2.shape = (2, 2)

# Display the arrays
print("Array1...\n",arr1)
print("\nArray2...\n",arr2)

# Check the Dimensions of both the arrays
print("\nDimensions of Array1...\n",arr1.ndim)
print("\nDimensions of Array2...\n",arr2.ndim)

# Check the Shape of both the arrays
print("\nShape of Array1...\n",arr1.shape)
print("\nShape of Array2...\n",arr2.shape)

# To compute the tensor dot product for arrays with different dimensions, use the numpy.tensordot() method in Python
print("\nTensor dot product...\n", np.tensordot(arr1, arr2, axes = 2))

Output

Array1...
[[[1 2]
[3 4]]

[[5 6]
[7 8]]]

Array2...
[['p' 'q']
['r' 's']]

Dimensions of Array1...
3

Dimensions of Array2...
2

Shape of Array1...
(2, 2, 2)

Shape of Array2...
(2, 2)

Tensor dot product...
['pqqrrrssss' 'pppppqqqqqqrrrrrrrssssssss']