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Write a Python function mat_to_prob(R) that returns the matrix P= (P₁, P2, ..., Pm) where Pi is the i-th row of matrix P , and Pi is the probability vector obtained from R; using the formulation in Question 1. In other words, convert each row of the input matrix into a probability vector. Sample inputs and outputs: • Input: np.array([[4, 6], [3.5, 9.1]); Output: [[0.11920292 0.88079708] [0.00368424 0.99631576]] • Input: np. array([[2, 3.1, 5], [10, 3.7, 12], [4, 5.5, 0]])) Output: [[4.15115123e-02 1.24707475e-01 8.33781013e-01] [1.19176835e-01 2.18844992e-04 8.80604320e-01] [1.81818026e-01 8.14851861e-01 3.33011331e-03]] Hint: use numpy.sum with an appropriate axis and keepdims settings. You should also check broadcasting in numpy. Question 2b In fact, the function above is called the softmax function, and scipy has an implementation for it. First, read the API at: https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.softmax.html. Then write code to apply this version of the softmax function on the sample matrices above and print out the results. # The function has been imported for you from scipy.special import softmax # Write your code here, remember to print out the result

Write a Python function mat_to_prob(R) that returns the matrix P= (P₁, P2, ..., Pm) where Pi is the i-th row of matrix P , and Pi is the probability vector obtained from R; using the formulation in Question 1. In other words, convert each row of the input matrix into a probability vector. Sample inputs and outputs: • Input: np.array([[4, 6], [3.5, 9.1]); Output: [[0.11920292 0.88079708] [0.00368424 0.99631576]] • Input: np. array([[2, 3.1, 5], [10, 3.7, 12], [4, 5.5, 0]])) Output: [[4.15115123e-02 1.24707475e-01 8.33781013e-01] [1.19176835e-01 2.18844992e-04 8.80604320e-01] [1.81818026e-01 8.14851861e-01 3.33011331e-03]] Hint: use numpy.sum with an appropriate axis and keepdims settings. You should also check broadcasting in numpy. Question 2b In fact, the function above is called the softmax function, and scipy has an implementation for it. First, read the API at: https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.softmax.html. Then write code to apply this version of the softmax function on the sample matrices above and print out the results. # The function has been imported for you from scipy.special import softmax # Write your code here, remember to print out the result

Database System Concepts
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
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Write a Python function mat_to_prob (R) that returns the matrix P = (P₁, P2, ..., Pm) where Pi is the i-th row of matrix P , and Pi is the probability vector obtained from R; using the formulation in Question 1. In other words, convert each row of the input matrix into a probability vector. Sample inputs and outputs: • Input: np.array([[4, 6], [3.5, 9.11) Output: [[0.11920292 0.88079708] [0.00368424 0.99631576]] • Input: np.array([[2, 3.1, 5], [10, 3.7, 12], [4, 5.5, 0]])) Output: [[4.15115123e-02 1.24707475e-01 8.33781013e-01] [1.19176835e-01 2.18844992e-04 8.80604320e-01] [1.81818026e-01 8.14851861e-01 3.33011331e-03]] Hint: use numpy.sum with an appropriate axis and keepdims settings. You should also check broadcasting in numpy. Question 2b In fact, the function above is called the softmax function, and scipy has an implementation for it. First, read the API at: https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.softmax.html. Then write code to apply this version of the softmax function on the sample matrices above and print out the results. # The function has been imported for you from scipy.special import softmax # Write your code here, remember to print out the result
Transcribed Image Text:Write a Python function mat_to_prob (R) that returns the matrix P = (P₁, P2, ..., Pm) where Pi is the i-th row of matrix P , and Pi is the probability vector obtained from R; using the formulation in Question 1. In other words, convert each row of the input matrix into a probability vector. Sample inputs and outputs: • Input: np.array([[4, 6], [3.5, 9.11) Output: [[0.11920292 0.88079708] [0.00368424 0.99631576]] • Input: np.array([[2, 3.1, 5], [10, 3.7, 12], [4, 5.5, 0]])) Output: [[4.15115123e-02 1.24707475e-01 8.33781013e-01] [1.19176835e-01 2.18844992e-04 8.80604320e-01] [1.81818026e-01 8.14851861e-01 3.33011331e-03]] Hint: use numpy.sum with an appropriate axis and keepdims settings. You should also check broadcasting in numpy. Question 2b In fact, the function above is called the softmax function, and scipy has an implementation for it. First, read the API at: https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.softmax.html. Then write code to apply this version of the softmax function on the sample matrices above and print out the results. # The function has been imported for you from scipy.special import softmax # Write your code here, remember to print out the result
Expert Solution
Step 1: Algorithm :

Algorithm: mat_to_prob(R)

Input: 
  - R: A 2D numpy array representing the input matrix.

Output:
  - P: A 2D numpy array where each row is a probability vector.

Step 1: Import the required libraries.
   - Import numpy as np
   - From scipy.special, import softmax

Step 2: Define the function mat_to_prob(R) as follows:

   2.1: Calculate P using softmax function:
        - P = softmax(R, axis=1)

   2.2: Return P as the result.

Step 3: End of the function.

Sample Inputs and Outputs:
   - Call mat_to_prob with sample input matrices.
   - Print the resulting probability matrices.

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