Python function
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- A robot moves in a 2D lattice. The robot can only move north (N), south (S), east (E), and west (W) by a certain number of steps. Assume that the robot always starts at (0,0), and that the x axis is oriented east, while the y axis is oriented north. Write a Python function that, given a set of moves, calculates the final position of the robot. For example, if the set of moves provided as input is: N 2 E 4 S 1 W 3 then the final position of the robot is (1,1). The integer that follows a move is always positive. Follow this code skeleton: def robot_move (moves): X = 0 y = 0 # your code here return (x,y) The moves are provided as an array of tuples. The array can have any number of moves in any order. The example above is passed as input as follows: [('N',2), ('E',4), ('S',1), ('W',3)]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])))Apply Python Programming to this problem:With a rotated conic as such: Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0, write a function classifyconic(x) which has a purpose to classify if the given parameter of a conic is elliptic, hyperbolic or parabolic. The given parameter is x = [A, B, C, D, E, F].Note: A parabolic rotated conic has a discriminant D = B^2 - 4AC that is equal to zero. An elliptical rotated conic has a discriminant less than zero. A hyperbolic rotated conic has a discriminant greater than zero.Consider these questions:What type of rotated conics are these equations?1. x^2 - 3xy - 2y^2 + 8x + 6y + F1 = 02. x^2 + 2xy + y^2 + 2x + 4y + F2 = 03. x^2 + 3xy + 4y^2 + 3x + 5y + F3 = 0
- IN PYTHON A tridiagonal matrix is one where the only nonzero elements are the ones on the main diagonal and the ones immediately above and below it.Write a function that solves a linear system whose coefficient matrix is tridiag- onal. In this case, Gauss elimination can be made much more efficient because most elements are already zero and don't need to be modified or added. As an example, consider a linear system Ax = b with 100,000 unknowns and the same number of equations. The coefficient matrix A is tridiagonal, with all elements on the main diagonal equal to 3 and all elements on the diagonals above and below it equal to 1. The vector of constant terms b contains all ones, except that the first and last elements are zero. You can use td to find that x1= −0.10557. The following code format should help: def td(l, m, u, b): '''Solve a linear system Ax = b where A is tridiagonal Inputs: l, lower diagonal of A, n-1 vector m, main diagonal of A, n vector u,…Program in python There is function F. Give an integer n (n ≥ 2), consider the prime factorization n=PI¹1 P2¹2 Prr Let g=gcd(k₁, k2.... kr) and m, = k₁/g The function F is defined as: F(n) = P11 P22- Pr Now, we have to summing up the value of this function for the first N natural numbers, we have w to evaluate the following expression for a given value of N. F(2) + F(3)+...+F(N). As the above sum can be extremely large Example if F(125)=5, thus the answer for this is by five more than for the previous one.Write a python code that implements the Forward Euler method to solve thedifferential equation. The slope function depends on the unknown solution y(t). Define your slope function so that the model parameters, b, PM, h areinput variables in your function definition. Complete your code by writing a loop that calculates the solution foreach time point and can plot your final approximate solution.
- Program in python .There is function F. Give an integer n (n ≥ 2), consider the prime factorization n=p₁¹₁ p2²2- Pr Let g = gcd(k₁, k2.... k) and m₁ = k/g. The function F is defined as: F(n) = P11 P22 Pr r Now, we have to summing up the value of this function for the first N natural numbers, we have w to evaluate the following expression for a given value of N: F(2) + F(3) + ... + F(N).As the above sum can be extremely large Example if F(125) = 5, thus the answer for this is by five more than for the previous one.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.Given A = {1,2,3} and B={u,v}, determine. a. A X B b. B X B
- Given a function f_prime(), which represents the derivative of some loss function, learning rate Ir = 0.01, and maximum number of iterations max_iter = 1000, write the for loop that represents gradient descent updates to variable w. Assume that initial w has been initialized and that an implementation of f_prime() has been defined somewhere else. Write your code in python.Computer Science Prove that the set M = {x ∈ R: x 2 = 2a3 b , a ∈ N, b ∈ N} is countably infinite. Your solution should either give a bijective function f : N → M or give pseudo-code of a program that prints all the values of such a function, in the following format (in this case you don’t have to define f explicitly, but need to also show the first five lines of output): 0: element of M 1: another element of M 2: yet another element of MDevelop a program that creates a plot of the function f(x)= sin(1/(x+E)) for x in the unit interval, where E>0 is a given input parameter. Use n+1 nodes in the plot.