Compute the square root of complex inputs with scimath in Python

In this article, we will cover how to compute the square root of complex inputs with scimath in Python using NumPy.

Example

Input: [-1 -2]
Output: [0.+1.j  0.+1.41421356j]
Explanation: Square root of complex input.

NumPy.emath.sqrt method

The np.emath.sqrt() method from the NumPy library calculates the square root of complex inputs. A complex value is returned for negative input elements unlike numpy.sqrt. which returns NaN.

Syntax: np.emath.sqrt()

Parameters:

• x: array like object. input array.

Return: out: scalar or ndarray.

Example 1:

If the array contains negative input values, complex numbers are returned in the output, and the shape, datatype, and dimensions of the array can be found by .shape , .dtype, and .ndim attributes.

Python3

import numpy as np

# Creating an array
array = np.array([-1, -2])
print(array)

# shape of the array is
print("Shape of the array is : ",array.shape)

# dimension of the array
print("The dimension of the array is : ",array.ndim)

# Datatype of the array
print("Datatype of our Array is : ",array.dtype)

# computing the square root of negative inputs
print(np.emath.sqrt(array))

Output:

[-1 -2]
Shape of the array is :  (2,)
The dimension of the array is :  1
Datatype of our Array is :  int64
[0.+1.j  0.+1.41421356j]

Time complexity: O(n), where n is the number of elements in the array.
Auxiliary space: O(n), as we are creating a new array of the same size as the input array to store the square roots of the negative inputs.

Example 2:

In this example, the NumPy package is imported. A 2-d complex array is created using NumPy.array() method and np.emath.sqrt()  is used to compute the square root of complex inputs. The shape, datatype, and dimensions of the array can be found by .shape , .dtype, and .ndim attributes.

Python3

import numpy as np

# Creating an array
array = np.array([complex(1,2),complex(3,5)])
print(array)

# shape of the array is
print("Shape of the array is : ",array.shape)

# dimension of the array
print("The dimension of the array is : ",array.ndim)

# Datatype of the array
print("Datatype of our Array is : ",array.dtype)

# computing the square root of complex inputs
print(np.emath.sqrt(array))

Output:

[1.+2.j 3.+5.j]
Shape of the array is :  (2,)
The dimension of the array is :  1
Datatype of our Array is :  complex128
[1.27201965+0.78615138j 2.10130339+1.18973776j]

Time complexity: O(n), where n is the number of elements in the array.
Auxiliary space: O(n), where n is the number of elements in the array.