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

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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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,…
Write a program that inputs a matrix and displays the trans- pose of that matrix. A transpose of a matrix is obtained by converting all the rows of a given matrix into columns and vice versa.
IN PYTHON! Given an n×n matrix A and n×1 right-hand side b, write a function that carries out q iterations of the Gauss elimination outer loop (without pivoting), where q is an integer between 1 and n, and returns the resulting augmented matrix with all below-diagonal elements transformed to zero in the left-most q columns. ##The code format given below may help # def gaussq (A, b, q): '''Apply Gauss elimination (without pivoting) to first q columns of a given linear system Inputs: A, coefficient matrix, size n by n b, vector of constants, n by 1 q, number of columns to apply Gauss elimination to, an integer between 1 and n Output: Aa, augmented matrix with all below-diagonal elements transformed to zero in the left-most q columns, n by n+1 #to check the work
In Python, generate a random matrix A with 100 entries each of which is an independent numberpseudo-randomly drawn (uniformly) from the interval (0, 1). Let B = A + AT . Use Python to calculatethe diagonal matrix D with the same eigenvalues as B. Then use the QR method to block-diagonalize Bover R. Do at least 100 steps of the QR switching. You should end up with a matrix E which is differentthan D. Answer the question of why.
Given a vector of real numbers r = (r1, r2, ..., rm). We can standardize the vector using the formulation: vi = "im, where m ri-m is the mean of the vector r, and s is the standard deviation of r. The vector v = (v1, v2, ..., Un) will be the scaled vector. Write a Python function scale_vec (r) that takes the vector r as input and returns the scaled vector v. Sample inputs and outputs: ● Input: np.array([1, 3, 5]), output: [-1.22474487 0. 1.22474487] • Input: np. array([3.3, 1.2, -2.7, -0.6]), output: [1.35457092 0.40637128 -1.35457092 -0.40637128] Hint: Use numpy.mean and numpy.std with default parameters. # Write your function here. Let's test your function. [ ] import numpy as np print (scale_vec (np.array([1, 3, 5]))) print (scale_vec (np.array([3.3, 1.2, -2.7, -0.6])))
A matrix's trace is equal to its trace transposed. The diag method of Numpy may be used to extract the elements along the diagonal of a square matrix. Retrieving data from diagonals above or below the primary diagonal is possible using the optional parameter k. The call trace, just like in Python programming, may be used to get a matrix's trace.
Create a MATLAB function that selects a random element from a list of values in a vector. Using the built-in function 'randi'. Example: For input options = [3, 2, 5], the output for this function should be able to choose one of the three numbers, with an equal chance of choosing each (20% chance each). chosen_value = select_random_option([3, 2, 5]) value = 3 chosen_value = select_random_option([3, 2, 5]) value = 5 chosen_value = select_random_option([3, 2, 5]) value = 2
This assignment is to a analyze a random experiment. Assume that you have to toss a fair coin (50% probability for each head and tail) N times, where N→ 00, When head comes up, you will be rewarded (gain) RM1, while if tail comes up, you will be penalized (loss) RM1. Write a function function sum_return coin_toss (N) that returns a row vector sum_return of length N+1. Each column i represents gained sum from i-1 number of coin tosses, i.e. sum_return (1) =0. To solve this problem, you will need both a for statement and the rand function. Try out several (minimum of 2) tries a value of N of 1000, 10000, 100000, 1000000 and plot the results. The x-axis must show the values from 0 to N. The y-axis should be limited to the maximum gain and minimum loss during each experiment. Note that as N is large, plotting N points will take a long time. Find a way on how this can be made faster.
Please follow the following code format and not coping other codes cuz it doesn't work THANK YOU!IN PYTHON: Given an n×n matrix A and n×1 right-hand side b, write a function that carries out q iterations of the Gauss elimination outer loop (without pivoting), where q is an integer between 1 and n, and returns the resulting augmented matrix with all below-diagonal elements transformed to zero in the left-most q columns. the code format:
Write a Python function that takes in three parameters - an adjacency matrix of a simple directed graph, a start node, and an end node; and returns "True" if there is a way to get from the start node to the end node using the provided edges. You can use this file as a starter code: path.py ↓ For example: Using the same graph given above. Consider your function with the same adjacency matrix given above as input and: If the start node is 1 and the end node is 4 then your function should return True. If the start node is 2 and the end node is 4 then your function should return False. Input: This function will have three parameters. First is an adjacency matrix in the form of a list of lists (as given above). Then the start_node and the end_node will be integers. Note that python indexing starts from 0 and not from 1, so the naming of the nodes will also follow the python convention and start from 0 instead of 1. Output: Boolean value: True or False.
4x1+4x2+6x3+9x4=03x1+3x5=26x2+5x4+7x5=-46x1+8x4+2x5=54x5+7x2+6x3+8x1=-10Represent the set of equations in a matrix equation, Ax=b, where A is a square matrix and x and b are column vectors. Write the line of code to define matrix A for this problem matlab/octave language
The moment (torque) of a force is given by M =F-d-sin(0), where M is the moment, F is the force, and d is the distance between line of action of the force to the pivot, and 0 is the angle between the force and the arm. Both Fand d can be any row vectors. Use F = [50 75 90 120] and d = [3 5 8] in your work to compute the moments M. Given 0 = 45°. Show your Matlab commands. You don't need to calculate the moments.