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 isthe probability vector obtained from R; using the formulation in Question 1. In other words, convert each row of the input matrix into aprobability 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.[ ] # Write your function hereLet's test your function.[ ] # Convert input from 2-d list to np.array first before calling your functionprint (mat_to_prob(np.array([[4, 6], [3.5, 9.1]])))print (mat_to_prob (np.array([[2, 3.1, 5], [10, 3.7, 12], [4, 5.5, 0]])))

Answered: Write a Python function mat_to_prob (R)…

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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Question

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.
[ ] # Write your function here
Let's test your function.
[ ] # Convert input from 2-d list to np.array first before calling your function
print (mat_to_prob(np.array([[4, 6], [3.5, 9.1]])))
print (mat_to_prob (np.array([[2, 3.1, 5], [10, 3.7, 12], [4, 5.5, 0]])))

Expert Solution

Step 1: Outline of the given question

The provided Python function, mat_to_prob, utilizes NumPy to convert rows of an input matrix into probability vectors. It achieves this by calculating row sums and dividing each element by its respective sum. Sample test cases showcase how this function accurately transforms numeric matrices into probability distributions, providing an efficient tool for probability vector generation.

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