NumPy arcsinh() – Inverse Hyperbolic Sine

NumPy arcsinh()

The numpy.arcsinh() function computes the inverse hyperbolic sine (also known as the area hyperbolic sine) of each element in an input array.

Syntax

numpy.arcsinh(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True)

Parameters

Parameter	Type	Description
x	array_like	Input array containing values for which the inverse hyperbolic sine is computed.
out	ndarray, None, or tuple of ndarray and None, optional	Optional output array where the result is stored. If None, a new array is created.
where	array_like, optional	Boolean mask specifying which elements to compute. Elements where where=False retain their original value.
casting	str, optional	Defines the casting behavior when computing the function.
order	str, optional	Memory layout order of the output array.
dtype	data-type, optional	Defines the data type of the output array.
subok	bool, optional	Determines if subclasses of ndarray are preserved in the output.

Return Value

Returns an array with the inverse hyperbolic sine values of the input elements. If the input is a scalar, a scalar is returned.

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Examples

1. Computing arcsinh of a Single Value

Here, we compute the inverse hyperbolic sine of a single value.

import numpy as np

# Define a single value
value = 1.0

# Compute the inverse hyperbolic sine of the value
result = np.arcsinh(value)

# Print the result
print("arcsinh(1.0):", result)

Output:

arcsinh(1.0): 0.881373587019543

2. Computing arcsinh for an Array of Values

We compute the inverse hyperbolic sine for an array of values.

import numpy as np

# Define an array of values
values = np.array([-2, -1, 0, 1, 2])

# Compute the inverse hyperbolic sine for each value
arcsinh_values = np.arcsinh(values)

# Print the results
print("Input values:", values)
print("arcsinh values:", arcsinh_values)

Output:

Input values: [-2 -1  0  1  2]
arcsinh values: [-1.44363548 -0.88137359  0.          0.88137359  1.44363548]

3. Using the out Parameter

Using an output array to store results instead of creating a new array.

import numpy as np

# Define an array of values
values = np.array([-1, 0, 1])

# Create an output array with the same shape
output_array = np.ndarray(values.shape)

# Compute inverse hyperbolic sine and store the result in output_array
np.arcsinh(values, out=output_array)

# Print the results
print("Computed arcsinh values:", output_array)

Output:

Computed arcsinh values: [-0.88137359  0.          0.88137359]

4. Using the where Parameter

Using a condition to compute the inverse hyperbolic sine only for selected elements.

import numpy as np

# Define an array of values
values = np.array([-2, -1, 0, 1, 2])

# Define a mask (compute arcsinh only where mask is True)
mask = np.array([True, False, True, False, True])

# Compute inverse hyperbolic sine where mask is True
result = np.arcsinh(values, where=mask)

# Print the results
print("Computed arcsinh values with mask:", result)

Output:

Computed arcsinh values with mask: [-1.44363548e+000  0.00000000e+000  0.00000000e+000  4.95242130e+223
  1.44363548e+000]

The arcsinh values are computed only for elements where mask=True. The other values remain unchanged.