Angles between two n-dimensional vectors in Python

Angles between two n-dimensional vectors in Python

To calculate the angle between two n-dimensional vectors in Python, you can use the dot product formula and the magnitude (norm) of the vectors. Here's a Python function to calculate the angle between two n-dimensional vectors:

import numpy as np def angle_between_vectors(vector1, vector2): # Convert the input vectors to NumPy arrays vector1 = np.array(vector1) vector2 = np.array(vector2) # Calculate the dot product of the vectors dot_product = np.dot(vector1, vector2) # Calculate the magnitudes (norms) of the vectors magnitude1 = np.linalg.norm(vector1) magnitude2 = np.linalg.norm(vector2) # Calculate the cosine of the angle between the vectors cosine_theta = dot_product / (magnitude1 * magnitude2) # Calculate the angle in radians using arccosine angle_radians = np.arccos(np.clip(cosine_theta, -1.0, 1.0)) # Convert radians to degrees angle_degrees = np.degrees(angle_radians) return angle_degrees # Example usage: vector1 = [1, 2, 3] vector2 = [4, 5, 6] angle = angle_between_vectors(vector1, vector2) print(f"Angle between vectors: {angle} degrees")

In this code:

  • We use NumPy to perform vector operations efficiently.
  • The angle_between_vectors function takes two n-dimensional vectors as input.
  • We calculate the dot product of the vectors using np.dot().
  • We calculate the magnitudes (norms) of the vectors using np.linalg.norm().
  • We calculate the cosine of the angle between the vectors using the dot product and magnitudes.
  • We use np.arccos() to calculate the angle in radians.
  • Finally, we convert the angle from radians to degrees and return it.

This function will give you the angle between the two n-dimensional vectors in degrees. Make sure to pass your own vectors to the angle_between_vectors function for your specific use case.

Examples

  1. How to calculate the angle between two n-dimensional vectors in Python using NumPy? Description: Calculate the angle between two n-dimensional vectors using NumPy's arccos function and vector normalization.

    import numpy as np def angle_between_vectors(vector1, vector2): dot_product = np.dot(vector1, vector2) norm1 = np.linalg.norm(vector1) norm2 = np.linalg.norm(vector2) cos_theta = dot_product / (norm1 * norm2) angle_rad = np.arccos(np.clip(cos_theta, -1.0, 1.0)) angle_deg = np.degrees(angle_rad) return angle_deg

  2. How to find the angle between two vectors in Python using math module? Description: Compute the angle between two n-dimensional vectors using the math module's arccos function.

    import math def angle_between_vectors(vector1, vector2): dot_product = sum(a * b for a, b in zip(vector1, vector2)) norm1 = math.sqrt(sum(a * a for a in vector1)) norm2 = math.sqrt(sum(b * b for b in vector2)) cos_theta = dot_product / (norm1 * norm2) angle_rad = math.acos(cos_theta) angle_deg = math.degrees(angle_rad) return angle_deg

  3. Calculate angle between two n-dimensional vectors using scipy in Python Description: Utilize the scipy library to determine the angle between two n-dimensional vectors.

    from scipy.spatial.distance import cosine def angle_between_vectors(vector1, vector2): cos_theta = 1 - cosine(vector1, vector2) angle_rad = np.arccos(np.clip(cos_theta, -1.0, 1.0)) angle_deg = np.degrees(angle_rad) return angle_deg

  4. Python function to compute the angle between two vectors using dot product Description: Create a function in Python that computes the angle between two vectors using dot product and trigonometric functions.

    import math def angle_between_vectors(vector1, vector2): dot_product = sum(a * b for a, b in zip(vector1, vector2)) norm1 = math.sqrt(sum(a * a for a in vector1)) norm2 = math.sqrt(sum(b * b for b in vector2)) cos_theta = dot_product / (norm1 * norm2) angle_rad = math.acos(cos_theta) angle_deg = math.degrees(angle_rad) return angle_deg

  5. Python code for calculating the angle between two vectors using atan2 Description: Implement a Python function to compute the angle between two vectors using atan2 function from the math module.

    import math def angle_between_vectors(vector1, vector2): angle_rad = math.atan2(np.linalg.norm(np.cross(vector1, vector2)), np.dot(vector1, vector2)) angle_deg = math.degrees(angle_rad) return angle_deg

  6. Calculate the angle between two n-dimensional vectors using numpy and dot product Description: Use NumPy to compute the angle between two n-dimensional vectors using dot product and arccos function.

    import numpy as np def angle_between_vectors(vector1, vector2): cos_theta = np.dot(vector1, vector2) / (np.linalg.norm(vector1) * np.linalg.norm(vector2)) angle_rad = np.arccos(cos_theta) angle_deg = np.degrees(angle_rad) return angle_deg

  7. Python code to calculate angle between two vectors in degrees Description: Write a Python function to calculate the angle between two vectors in degrees.

    import numpy as np def angle_between_vectors(vector1, vector2): dot_product = np.dot(vector1, vector2) norm1 = np.linalg.norm(vector1) norm2 = np.linalg.norm(vector2) cos_theta = dot_product / (norm1 * norm2) angle_rad = np.arccos(np.clip(cos_theta, -1.0, 1.0)) angle_deg = np.degrees(angle_rad) return angle_deg

  8. How to find the angle between two n-dimensional vectors in Python using cross product? Description: Determine the angle between two n-dimensional vectors in Python by utilizing the cross product and trigonometric functions.

    import numpy as np def angle_between_vectors(vector1, vector2): angle_rad = np.arccos(np.dot(vector1, vector2) / (np.linalg.norm(vector1) * np.linalg.norm(vector2))) angle_deg = np.degrees(angle_rad) return angle_deg

  9. Calculate angle between two vectors in Python without using libraries Description: Write a Python function to calculate the angle between two vectors without using external libraries.

    import math def angle_between_vectors(vector1, vector2): dot_product = sum(a * b for a, b in zip(vector1, vector2)) norm1 = math.sqrt(sum(a * a for a in vector1)) norm2 = math.sqrt(sum(b * b for b in vector2)) cos_theta = dot_product / (norm1 * norm2) angle_rad = math.acos(cos_theta) angle_deg = math.degrees(angle_rad) return angle_deg

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