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Get the inverse of a Four-Dimensional array in Python

To compute the inverse of a Four-Dimensional array, use the numpy.linalg.tensorinv() method in Python. The result is an inverse for a relative to the tensordot operation tensordot(a, b, ind), i. e., up to floating-point accuracy, tensordot(tensorinv(a), a, ind) is the “identity” tensor for the tensordot operation.

The method returns a’s tensordot inverse, shape a.shape[ind:] + a.shape[:ind]. The 1st parameter is a, the Tensor to ‘invert’. Its shape must be ‘square’, i. e., prod(a.shape[:ind]) == prod(a.shape[ind:]). The 2nd parameter is ind, the number of first indices that are involved in the inverse sum. Must be a positive integer, default is 2.

Steps

At first, import the required libraries-

import numpy as np
from numpy.linalg import inv

Create an array. The numpy.eye() returns a 2-D array with ones on the diagonal and zeros elsewhere −

arr = np.eye(4*6)

Changing the shape of the array created above −

arr.shape = (4, 6, 8, 3)

Display the array −

print("Our Array...\n",arr)

Check the Dimensions −

print("\nDimensions of our Array...\n",arr.ndim)

Get the Datatype −

print("\nDatatype of our Array object...\n",arr.dtype)

Get the Shape −

print("\nShape of our Array object...\n",arr.shape)

To compute the inverse of a Four-Dimensional array, use the numpy.linalg.tensorinv() method in Python −

print("\nResult...\n",np.linalg.tensorinv(arr))

Example

import numpy as np
from numpy.linalg import inv

# Create an array

# The numpy.eye() returns a 2-D array with ones on the diagonal and zeros elsewhere
arr = np.eye(4*6)

# Changing the shape of the array created above
arr.shape = (4, 6, 8, 3)

# Display the array
print("Our Array...\n",arr)

# Check the Dimensions
print("\nDimensions of our Array...\n",arr.ndim)

# Get the Datatype
print("\nDatatype of our Array object...\n",arr.dtype)

# Get the Shape
print("\nShape of our Array object...\n",arr.shape)

# To compute the inverse of a Four-Dimensional array, use the numpy.linalg.tensorinv() method in Python.
print("\nResult...\n",np.linalg.tensorinv(arr))

Output

Our Array...
   [[[[1. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]]

   [[0. 1. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]]

   [[0. 0. 1.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]]

   [[0. 0. 0.]
   [1. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]]

   [[0. 0. 0.]
   [0. 1. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]]

   [[0. 0. 0.]
   [0. 0. 1.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]]]


   [[[0. 0. 0.]
   [0. 0. 0.]
   [1. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]]

   [[0. 0. 0.]
   [0. 0. 0.]
   [0. 1. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]]

   [[0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 1.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]]

   [[0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [1. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]]

   [[0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 1. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]]

   [[0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]]]


   [[[0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [1. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]]

   [[0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 1. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]]

   [[0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 1.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]]

   [[0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [1. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]]

   [[0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 1. 0.]
   [0. 0. 0.]
   [0. 0. 0.]]

   [[0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 1.]
   [0. 0. 0.]
   [0. 0. 0.]]]


   [[[0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [1. 0. 0.]
   [0. 0. 0.]]

   [[0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 1. 0.]
   [0. 0. 0.]]

   [[0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 1.]
   [0. 0. 0.]]

   [[0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [1. 0. 0.]]

   [[0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 1. 0.]]

   [[0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 0.]
   [0. 0. 1.]]]]

Dimensions of our Array...
4

Datatype of our Array object...
float64

Shape of our Array object...
(4, 6, 8, 3)

Result...
   [[[[1. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]]

   [[0. 1. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]]

   [[0. 0. 1. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]]]


   [[[0. 0. 0. 1. 0. 0.]
   [0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]]

   [[0. 0. 0. 0. 1. 0.]
   [0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]]

   [[0. 0. 0. 0. 0. 1.]
   [0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]]]


   [[[0. 0. 0. 0. 0. 0.]
   [1. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]]

   [[0. 0. 0. 0. 0. 0.]
   [0. 1. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]]

   [[0. 0. 0. 0. 0. 0.]
   [0. 0. 1. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]]]


   [[[0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 1. 0. 0.]
   [0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]]

   [[0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 1. 0.]
   [0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]]

   [[0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 1.]
   [0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]]]


   [[[0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]
   [1. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]]

   [[0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]
   [0. 1. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]]

   [[0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]
   [0. 0. 1. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]]]


   [[[0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 1. 0. 0.]
   [0. 0. 0. 0. 0. 0.]]

   [[0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 1. 0.]
   [0. 0. 0. 0. 0. 0.]]

   [[0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 1.]
   [0. 0. 0. 0. 0. 0.]]]


   [[[0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]
   [1. 0. 0. 0. 0. 0.]]

   [[0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]
   [0. 1. 0. 0. 0. 0.]]

   [[0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]
   [0. 0. 1. 0. 0. 0.]]]


   [[[0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 1. 0. 0.]]

   [[0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 1. 0.]]

   [[0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 0.]
   [0. 0. 0. 0. 0. 1.]]]]