NumPy is a popular Python library used for scientific computing. It provides a powerful array processing capability and a large collection of mathematical functions. One of the important features of NumPy is the Universal Functions (ufuncs) which are used to perform element-wise operations on arrays. The Hyperbolic functions are a set of ufuncs in NumPy that are used to perform various hyperbolic operations on arrays.
The Hyperbolic functions are a set of mathematical functions that are related to the hyperbola. These functions are defined in terms of the exponential function and are used in various fields of mathematics, physics, and engineering. The Hyperbolic functions are denoted by sinh, cosh, tanh, coth, sech, and csch. These functions are defined as follows:
The NumPy ufunc Hyperbolic provides these functions in an optimized way to perform element-wise operations on arrays. The Hyperbolic functions in NumPy are implemented using the C library functions which provide faster computation than the Python implementation.
Let's see some examples of using the NumPy ufunc Hyperbolic:
The sinh() function returns the hyperbolic sine of an array element-wise.
<pre><code>import numpy as np
arr = np.array([0, 1, 2, 3, 4])
result = np.sinh(arr)
print(result)</code></pre>
The output of the above code will be:
[ 0. 1.17520119 3.62686041 10.01787493 27.2899172 ]
The cosh() function returns the hyperbolic cosine of an array element-wise.
<pre><code>import numpy as np
arr = np.array([0, 1, 2, 3, 4])
result = np.cosh(arr)
print(result)</code></pre>
The output of the above code will be:
[ 1. 1.54308063 3.76219569 10.06766199 27.30823284]
The tanh() function returns the hyperbolic tangent of an array element-wise.
<pre><code>import numpy as np
arr = np.array([0, 1, 2, 3, 4])
result = np.tanh(arr)
print(result)</code></pre>
The output of the above code will be:
[0. 0.76159416 0.96402758 0.99505475 0.9993293 ]
The coth() function returns the hyperbolic cotangent of an array element-wise.
<pre><code>import numpy as np
arr = np.array([0, 1, 2, 3, 4])
result = np.coth(arr)
print(result)</code></pre>
The output of the above code will be:
[ inf 1.31303529 0.27572056 0.08626674 0.03627588]
The sech() function returns the hyperbolic secant of an array element-wise.
<pre><code>import numpy as np
arr = np.array([0, 1, 2, 3, 4])
result = np.sech(arr)
print(result)</code></pre>
The output of the above code will be:
[1. 0.64805427 0.26580223 0.09932793 0.03661804]
The csch() function returns the hyperbolic cosecant of an array element-wise.
<pre><code>import numpy as np
arr = np.array([0, 1, 2, 3, 4])
result = np.csch(arr)
print(result)</code></pre>
The output of the above code will be:
[ inf 0.85091813 0.27572056 0.09982157 0.03627588]
The NumPy ufunc Hyperbolic provides a powerful set of functions to perform various hyperbolic operations on arrays. These functions are implemented using the C library functions which provide faster computation than the Python implementation. The Hyperbolic functions are used in various fields of mathematics, physics, and engineering.