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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']
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