TODO15 Create the CosineSimilarity by following the below instructions: Define the class CosineSimilarity using the class keyword. Define the init() method which takes in three arguments self, x, and z and saves them as class variables. These two arguments will be the vectors in which the cosine similarity will be computed. Define a method called compute_angle() that takes in no arguments other than self (remember self is a required argument for methods). Within the compute_angle() method compute the angle between two vectors and return the answer in degrees. Use the following equation to compute the angle between two vector. $$ \theta = \text{arccos}(\frac{\mathbf{x} \cdot \mathbf{z}}{||\mathbf{x}||_2 ||\mathbf{z}||_2}) $$ Hint 1: Recall from the quiz that $\cdot$ represents the dot product and $||\cdot||_2$ represents the L2 norm $$ ||\mathbf{x}||_2 = \sqrt{x_1^2 + x_2^2 + ... + x_n^2} = \sqrt{\mathbf{x} \cdot \mathbf{x}} $$ where a vector dotted with itself is the same as squaring the vector. Hint 2: Use np.sqrt() to compute the square root and np.arccos() to compute arccos. Hint 3: The output of np.arccos() is in radians! Be sure to use np.degrees() to convert your output into degrees. If you don't do this you will fail the test. Hint 4: Due to rounding errors your answer should be close to ~180 degrees. # TODO 15.1 x = np.array([1, 1]) z = np.array([-2, -2]) cosin_sim = CosineSimilarity(x, z) angle = cosin_sim.compute_angle() print(f"angle output: {angle}") todo_check([ (np.isclose(angle,180.0),'The value of the angle is not approximately 180 degrees! Make sure you converted from radians to degrees.') ])

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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TODO15

Create the CosineSimilarity by following the below instructions:
1. Define the class CosineSimilarity using the class keyword.
2. Define the __init__() method which takes in three arguments self, x, and z and saves them as class variables. These two arguments will be the vectors in which the cosine similarity will be computed.
3. Define a method called compute_angle() that takes in no arguments other than self (remember self is a required argument for methods).
4. Within the compute_angle() method compute the angle between two vectors and return the answer in degrees. Use the following equation to compute the angle between two vector. $$ \theta = \text{arccos}(\frac{\mathbf{x} \cdot \mathbf{z}}{||\mathbf{x}||_2 ||\mathbf{z}||_2}) $$
  1. Hint 1: Recall from the quiz that $\cdot$ represents the dot product and $||\cdot||_2$ represents the L2 norm $$ ||\mathbf{x}||_2 = \sqrt{x_1^2 + x_2^2 + ... + x_n^2} = \sqrt{\mathbf{x} \cdot \mathbf{x}} $$ where a vector dotted with itself is the same as squaring the vector.
  2. Hint 2: Use np.sqrt() to compute the square root and np.arccos() to compute arccos.
  3. Hint 3: The output of np.arccos() is in radians! Be sure to use np.degrees() to convert your output into degrees. If you don't do this you will fail the test.
  4. Hint 4: Due to rounding errors your answer should be close to ~180 degrees.

# TODO 15.1

x = np.array([1, 1])

z = np.array([-2, -2])

cosin_sim = CosineSimilarity(x, z)

angle = cosin_sim.compute_angle()

print(f"angle output: {angle}")

todo_check([

(np.isclose(angle,180.0),'The value of the angle is not approximately 180 degrees! Make sure you converted from radians to degrees.')

])

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