numpy.arccosh() in Python

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

Syntax :

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

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 cosine 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, pi] and the real part in [0, inf].

Code #1 : Working

# Python program explaining
# arccosh() function

import numpy as np

in_array = [2, 1, 10, 100]
print ("Input array : \n", in_array)

arccosh_Values = np.arccosh(in_array)
print ("\nInverse hyperbolic Cosine values : \n", arccosh_Values)

Output :

Input array : 
 [2, 1, 10, 100]

Inverse hyperbolic Cosine values : 
 [ 1.3169579   0.          2.99322285  5.29829237]

Code #2 : Graphical representation

# Python program showing
# Graphical representation
# of arccosh() function
%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
in_array = np.linspace(1, np.pi, 18)
out_array1 = np.cos(in_array)
out_array2 = np.arccosh(in_array)

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

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

plt.title("blue : numpy.cos() \nred : numpy.arccosh()")
plt.xlabel("X")
plt.ylabel("Y")

Output :

in_array :  [ 1.          1.12597604  1.25195208  1.37792812  1.50390415  1.62988019
  1.75585623  1.88183227  2.00780831  2.13378435  2.25976038  2.38573642
  2.51171246  2.6376885   2.76366454  2.88964058  3.01561662  3.14159265]

out_array with cos :  [ 0.54030231  0.43029566  0.31346927  0.19167471  0.0668423  -0.0590495
 -0.18400541 -0.30604504 -0.42323415 -0.53371544 -0.63573787 -0.72768451
 -0.80809809 -0.87570413 -0.92943115 -0.96842762 -0.99207551 -1.        ]

out_array with arccosh :  [ 0.          0.49682282  0.69574433  0.84411504  0.96590748  1.07053332
  1.16287802  1.24587516  1.32145434  1.39096696  1.45540398  1.51551804
  1.57189678  1.62500948  1.67523791  1.7228975   1.76825238  1.81152627]

)