NumPy arctan2() Function

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The NumPy arctan2() function is used to compute the inverse tangent of two arrays (y, x) element-wise.

It returns the angle (in radians) between the positive x-axis and the point (x, y) on the plane, calculated as arctan(y / x), but with appropriate handling of the signs of both arguments to determine the correct quadrant of the result.

This function is particularly useful for calculating the angle from the origin to a point (x, y).

• Domain: The function accepts two input arrays or scalars representing the y and x values. Both inputs can be scalars, arrays, or a combination thereof. The domain is all real numbers.
• Range: The output values lie in the range [-, ], as the angle can be positive or negative depending on the quadrant.

Syntax

Following is the syntax of the NumPy arctan2() function −

numpy.arctan2(y, x, /, out=None, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

Parameters

This function accepts the following parameters −

• y: The y-coordinate or array of y-values. This parameter represents the vertical distance from the origin to the point (x, y).
• x: The x-coordinate or array of x-values. This parameter represents the horizontal distance from the origin to the point (x, y).
• out (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 (optional): This condition is broadcast over the input. At locations where the condition is True, the result will be computed. Otherwise, the result will retain its original value.
• casting (optional): Controls what kind of data casting may occur. Defaults to 'same_kind'.
• order (optional): Controls the memory layout order of the result. 'C' means C-order, 'F' means Fortran-order, 'A' means 'F' if inputs are all F, 'C' otherwise, 'K' means match the layout of the inputs as closely as possible.
• dtype (optional): The type of the returned array and of the accumulator in which the elements are processed. The dtype of y and x is used by default unless dtype is specified.
• subok (optional): If True, then sub-classes will be passed-through, otherwise the returned array will be forced to be a base-class array.

Return Value

This function returns an array where each element is the arctangent (inverse tangent) of the corresponding pair of elements (y, x) in the input arrays, in radians. The angle is calculated based on the signs of both the x and y values to determine the correct quadrant.

Example: Basic Usage of arctan2() Function

In the following example, we use the arctan2() function to compute the arctangent of pairs of values (y, x) in two 1-dimensional arrays −

import numpy as np

# Creating two 1-dimensional arrays for y and x
y = np.array([1, 1, -1, -1])
x = np.array([1, -1, 1, -1])

# Applying arctan2 to each pair (y, x)
result = np.arctan2(y, x)
print(result)

The output obtained will be −

[ 0.78539816  2.35619449 -0.78539816 -2.35619449]

Example: Arctangent of Arrays with Different Shapes

In this example, we calculate the arctangent for arrays of different shapes. NumPy will broadcast the arrays to have compatible shapes before performing the operation −

import numpy as np

# Creating 1-dimensional arrays for y and x
y = np.array([1, 2, 3])
x = np.array([4, 5, 6])

# Applying arctan2 to each pair (y, x)
result = np.arctan2(y, x)
print(result)

This will produce the following result −

[0.24497866 0.38050638 0.46364761]

Example: Arctangent with Scalars

In this example, we calculate the arctangent of a pair of scalar values (y, x) −

import numpy as np

# Scalar values for y and x
y = 1
x = 1

# Applying arctan2 to the scalar values
result = np.arctan2(y, x)
print(result)

The output obtained is −

0.7853981633974483

Example: Arctangent for Negative Values

In this example, we calculate the arctangent for pairs of negative values for y and x. The function returns angles corresponding to the correct quadrant based on the signs of both y and x −

import numpy as np

# Negative values for y and x
y = np.array([-1, -1, 1, 1])
x = np.array([-1, 1, -1, 1])

# Applying arctan2 to each pair (y, x)
result = np.arctan2(y, x)
print(result)

This will produce the following result −

[-2.35619449 -0.78539816  2.35619449  0.78539816]