Given a vector of real numbers r = (r1, V2, . . ., rn). We can convert this vector into a probability vectorP = (P1, P2, . . ., Pn) using the formulation: p; = e¹¹/(Σï-₁ e¹¹), for all i.Write a Python function vec_to_prob(r) that takes the vector r as input and returns the vector p. Both r and p willbe numpy arrays. You can assume r is non-empty.Sample inputs and outputs:Input: np.array([4, 6]), output: [0.11920292 0.88079708]• Input: np.array([3.4, 6.2, 7.1, 9.8]), output: [0.00151576 0.02492606 0.06130823 0.91224995]Hint: use numpy.sum[ ] # Write your function hereLet's test your function.[ ] # Convert input from list to np.array first before calling your function to avoid errorsprint (vec_to_prob(np.array([4, 6])))print (vec_to_prob (np. array ( [3.4, 6.2, 7.1, 9.8])))print (vec_to_prob (np.array([3, 5.5, 0])))

Answered: Given a vector of real numbers r = (r₁,…

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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Given a vector of real numbers r = (r1, V2, . . ., rn). We can convert this vector into a probability vector
P = (P1, P2, . . ., Pn) using the formulation: p; = e¹¹/(Σï-₁ e¹¹), for all i.
Write a Python function vec_to_prob(r) that takes the vector r as input and returns the vector p. Both r and p will
be numpy arrays. You can assume r is non-empty.
Sample inputs and outputs:
Input: np.array([4, 6]), output: [0.11920292 0.88079708]
• Input: np.array([3.4, 6.2, 7.1, 9.8]), output: [0.00151576 0.02492606 0.06130823 0.91224995]
Hint: use numpy.sum
[ ] # Write your function here
Let's test your function.
[ ] # Convert input from list to np.array first before calling your function to avoid errors
print (vec_to_prob(np.array([4, 6])))
print (vec_to_prob (np. array ( [3.4, 6.2, 7.1, 9.8])))
print (vec_to_prob (np.array([3, 5.5, 0])))

Expert Solution

Step 1: Algorithm :

Algorithm: Convert Vector to Probability Vector

Input:
- r: A numpy array of real numbers

Output:
- p: A numpy array representing the probability vector

Steps:
1. Calculate exp_r = e^r for each element in the input array r.
2. Compute the sum of all elements in exp_r using numpy.sum() and store it in a variable sum_exp_r.
3. Create an empty numpy array p with the same shape as r.
4. For each element in exp_r at index i:
- Calculate p[i] = exp_r[i] / sum_exp_r.
5. Return the probability vector p as the output.

End of Algorithm

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