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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.]]]]
Updated on: 25-Feb-2022
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