numpy.arctanh in Python()

numpy.arctanh() : This mathematical function helps user to calculate inverse hyperbolic tangent, element-wise for all arr.

Syntax : numpy.arctanh(arr, /, out=None, *, where=True, casting=’same_kind’, order=’K’, dtype=None, ufunc ‘arctanh’)
Parameters :

arr : array_like
Input array.
out : [ndarray, optional] A location into which the result is stored.
  -> If provided, it must have a shape that the inputs broadcast to.
  -> If not provided or None, a freshly-allocated array is returned.
where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
**kwargs :Allows to pass keyword variable length of argument to a function. Used when we want to handle named argument in a function.

Return : An array with inverse hyperbolic tangent of arr
for all arr i.e. array elements.

Note :

2pi Radians = 360 degrees
The convention is to return the angle of arr whose imaginary part lies in [-pi/2, pi/2].

Code #1 : Working

# Python program explaining
# arctanh() function

import numpy as np

in_array = [0.2, 0.11, 0.5, 0.99]
print ("Input array : \n", in_array)

arctanh_Values = np.arctanh(in_array)
print ("\nInverse hyperbolic tangent values of input array : \n", arctanh_Values)

Output :

Input array : 
 [0.2, 0.11, 0.5, 0.99]

Inverse hyperbolic tangent values of input array : 
 [ 0.20273255  0.11044692  0.54930614  2.64665241]

Code #2 : Graphical representation

# Python program showing
# Graphical representation
# of arctanh() function % matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
in_array = np.linspace(0.1, 0.99, 25)
out_array1 = np.tan(in_array)
out_array2 = np.arctanh(in_array)

print("in_array : ", in_array)
print("\nout_array with tan : ", out_array1)
print("\nout_array with arctanh : ", out_array2)
# blue for numpy.tanh()
# red for numpy.arctanh()
plt.plot(in_array, out_array1,
            color = 'blue', marker = ".")

plt.plot(in_array, out_array2,
            color = 'red', marker = "+")

plt.title("blue : numpy.tan() \nred : numpy.arctanh()")
plt.xlabel("X")
plt.ylabel("Y")

Output :

in_array :  [ 0.1         0.13708333  0.17416667  0.21125     0.24833333  0.28541667
  0.3225      0.35958333  0.39666667  0.43375     0.47083333  0.50791667
  0.545       0.58208333  0.61916667  0.65625     0.69333333  0.73041667
  0.7675      0.80458333  0.84166667  0.87875     0.91583333  0.95291667
  0.99      ]

out_array with tan :  [ 0.10033467  0.13794852  0.17594936  0.21444958  0.25356734  0.29342809
  0.33416626  0.37592723  0.41886955  0.46316761  0.5090147   0.55662672
  0.60624669  0.65815012  0.7126517   0.77011355  0.83095552  0.89566817
  0.96482941  1.03912577  1.11938038  1.20658966  1.30197266  1.40703805
  1.52367674]

out_array with arctanh :  [ 0.10033535  0.13795183  0.17596049  0.21447937  0.25363582  0.29356929
  0.33443481  0.37640728  0.41968694  0.4645065   0.51114049  0.5599181
  0.61124089  0.66560789  0.72365253  0.78619832  0.85434644  0.92961997
  1.01421559  1.11147549  1.22686186  1.37025371  1.5625545   1.86258009
  2.64665241]