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 function that gets an array of ints of length n, and a number k, and returns the longest subsequence of consecutive k’s in the array. For example - On input ([1, 1, 3, 3, 3, 1, 5, 1], 1), the function returns 3 - On input ([1, 3, 3, 2, 3, 3, 3, 3], 3), the function returns 4 - On input ([3, 5, 2, 5, 2, 5, 5], 3), the function returns 2 - On input ([1, 2, 3, 3, 3, 3], 5), the function returns 0 // returns the length of the longest subsequence // of consecutive k’s in the array int longest_seq(const int* ar, int n, int k);   test for the function: void test_q1() { inta1[] = {1, 1, 3, 3, 3, 1, 5, 1}; if (longest_seq(a1, 8, 1) == 2) printf("Q1-1 ok\n"); else printf("Q1-1 ERROR\n"); inta2[] = {1,3,3,2,3,3,3,3}; if (longest_seq(a2, 8, 3) == 4) printf("Q1-2 ok\n"); else printf("Q1-2 ERROR\n"); }

Given an array of integers, find the maximum sum of a contiguous subarray. Write a function called maxSubarraySum that takes an array of integers as input and returns the maximum sum of a contiguous subarray. Example: Input: [1, -3, 2, 1, -1] Output: 3 Explanation: The subarray with the maximum sum is [2, 1], and the sum is 3. You need to implement the maxSubarraySum function. You can use any programming language of your choice.

Develop a function that finds the starting index of the longest subsequence of values that is strictly increasing. For example, given the array {12, 3, 7, 5, 9, 8, 1, 4, 6}, the function would return 6, since the subsequence {1, 4, 6} is the longest that is strictly increasing. Develop a function that takes a string and a single character, then returns a list of the indexes in the string where the character occurs. For example, given the string “bookkeeper” and ‘e’, the function would return {5, 6, 8} since ‘e’ occurs at those positions. Return an empty list if the character does not appear in the string even once.  Develop a function that takes two lists of integers and returns a list containing any value that appears in both parameter lists.

Using Matlab Write a function that takes one input: A matrix with m rows and n columns. It should return one output: The product of all of the odd numbers inside of that matrix. Recall that rem(n,2) will return 1 when n is odd and 0 when n is even.

In python, how do you generate a distance matrix H where in each entry hij, the distance between row i and row j are stored, distance is computed by the inner product <x,y>C := xTCy, where the matrix C is a 3x3 matrix: [3 1 6  1 2 1  6 1 27].  The dataset is a 26x5 matrix and I need to find the distance using the above inner product between each row - I should end up with a 26x26 distance matrix H, where each diagonal entry (i=j) is 0.

By the "n queens problem" we mean the problem of placing n queens on an nXn “chessboard" in such a way that no queen can capture any other on the next move. In class we solved the "8 queens" problem. Write a function that inputs an integer n and returns the number of solutions to the “n queens" problem. Your function should use the one dimensional representation for the board, the algorithm we discussed in class, and no gotos. Test your function with a main program that prompts the user for an integer n. The main program then calls the function n times, once for each number from 1 – n, and then prints the number of solutions to each of these problems, one on a line. For example, if you enter n=5 your program should output: 1. There are 2. There are 3. There are 4. There are solutions to the 1 queens problem. solutions to the 2 queens problem. solutions to the 3 queens problem. solutions to the 4 queens problem. solutions to the 5 queens problem. 5. There are Now, since each time…

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