NumPy hypot() – Hypotenuse Function

NumPy hypot()

The numpy.hypot() function computes the hypotenuse of a right triangle given its two perpendicular sides. It is equivalent to calculating sqrt(x1**2 + x2**2) element-wise.

Syntax

numpy.hypot(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True)

Parameters

Parameter	Type	Description
x1, x2	array_like	Legs of the right triangle(s). If x1 and x2 have different shapes, they must be broadcastable.
out	ndarray, None, or tuple of ndarray and None, optional	Optional output array to store results. If None, a new array is created.
where	array_like, optional	Boolean mask specifying where to compute the hypotenuse. Elements where where=False retain their original value.
casting	str, optional	Specifies casting behavior during computation.
order	str, optional	Specifies memory layout order of the output array.
dtype	data-type, optional	Specifies 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 containing the hypotenuse values computed element-wise. If both x1 and x2 are scalars, a scalar is returned.

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Examples

1. Computing the Hypotenuse of a Right Triangle

Computing the hypotenuse of a right triangle with given side lengths.

import numpy as np

# Define the lengths of the two perpendicular sides
x1 = 3
x2 = 4

# Compute the hypotenuse
hypotenuse = np.hypot(x1, x2)

# Print the result
print("Hypotenuse length:", hypotenuse)

Output:

Hypotenuse length: 5.0

2. Computing Hypotenuse for Arrays

Computing the hypotenuse for multiple sets of right triangle sides using arrays.

import numpy as np

# Define arrays of perpendicular side lengths
x1 = np.array([3, 6, 8])
x2 = np.array([4, 8, 15])

# Compute hypotenuse for each pair of sides
hypotenuse_values = np.hypot(x1, x2)

# Print the results
print("Side 1:", x1)
print("Side 2:", x2)
print("Hypotenuse:", hypotenuse_values)

Output:

Side 1: [3 6 8]
Side 2: [ 4  8 15]
Hypotenuse: [ 5. 10. 17.]

3. Using the out Parameter

Using an output array to store the hypotenuse values instead of creating a new array.

import numpy as np

# Define arrays of perpendicular sides
x1 = np.array([5, 12, 9])
x2 = np.array([12, 5, 40])

# Create an output array with the same shape
output_array = np.ndarray(shape=[1, 3])

# Compute hypotenuse and store in output_array
np.hypot(x1, x2, out=output_array)

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

Output:

Computed hypotenuse values: [13. 13. 41.]

4. Using the where Parameter

Using a condition to compute the hypotenuse only for selected elements.

import numpy as np

# Define arrays of perpendicular sides
x1 = np.array([3, 5, 9, 12])
x2 = np.array([4, 12, 40, 5])

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

# Compute hypotenuse values where mask is True
result = np.hypot(x1, x2, where=mask)

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

Output:

Computed hypotenuse values with mask: [ 5.  0. 41.  0.]

The hypotenuse values are computed only for elements where mask=True.