Polar coordinates describe the position of a point in terms of its distance from the origin and the angle it makes with the positive x-axis. Polar coordinates can simplify certain calculations, such as integration over a circular region and, can be used to represent geographical locations, such as latitude and longitude. NumPy provides a simple and efficient way to perform this conversion on arrays of data. In this guide, we will walk through the steps to convert an array of Cartesian coordinates to polar coordinates.
1. Using "hypot()" and "arctan2()" functions:
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hypot()is a NumPy function that calculates the hypotenuse (Euclidean norm) of a right-angled triangle. It takes two arguments, and returns the square root of the sum of their squares, which is equivalent to the length of the hypotenuse of a right-angled triangle. -
NumPy’s
arctan2()function that returns the angle in radians between the positive x-axis and the point (y, x). It takes two arguments, and returns an array of the same shape containing the angle values.
let’s see the example given below to gain better understanding:
We first import the NumPy library and assign it the alias np. Here, we use the np.hypot() to compute the magnitude of each Cartesian coordinate (i.e., the distance from the origin), and then use np.arctan2() to compute the angle in radians. We then stack these two arrays horizontally using np.column_stack() to create a new NumPy array of polar coordinates.
2. Using "linalg.norm()" function:
The linalg.norm() function is used to compute the norm of a vector or a matrix. The norm is a measure of the size or length of a vector, and it is often used in linear algebra and other mathematical applications.
let’s see the example given below:
We first import the NumPy library and assign it the alias np. We use the np.linalg.norm() function to compute the Euclidean norm (i.e., magnitude or length) of each row of the Cartesian coordinates matrix. We specify axis=1 to compute the norm along each row instead of the entire matrix. We then stack these two arrays horizontally using np.column_stack() to create a new NumPy array of polar coordinates.
3. Using "sqrt()" function :
The numpy.sqrt() function is a mathematical function provided by the NumPy library to calculates the square root of each element in an array.
We first import the NumPy library and assign it the alias np. We use np.sqrt() and np.arctan2() functions to compute the polar coordinates r and theta , respectively. Finally, we stack these two arrays horizontally using np.column_stack() to create a new Numpy array of polar coordinates.