R code for gradient descent backtrack line search with varying step size. The objective function is f(x1,x2) = (10x1^2+x2^2)/2.
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R code for gradient descent backtrack line search with varying step size. The objective function is f(x1,x2) = (10x1^2+x2^2)/2.
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- Write down the algorithm for linear search.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 workWrite a function that diagonally orders numbers in a n x n matrix, depending on which of the four corners you originate from: upper-left ( u1 ), upper-right (ur), lower-left (11), lower-right (1r). Examples diagonalize(3, "ul") [0, 1, 2], [1, 2, 3], [2, 3, 4] (Ctrl) - [
- In pythion with numpy I have code in a for loop that creates a vecor of 12 elements:x = 1 2 3 4 5 6 7 8 9 10 11 12 The loop iterates 10 times. The second iteration generates a new vector x = 12 11 10 9 8 7 6 5 4 3 2 1 etc. At the end of the loop I need to have a 12 X 10 matrix x x x x x x x x x x x x x x x x x x x xx x x x x x x x x x x x x x x x x x x xx x x x x x x x x x x x x x x x x x x xx x x x x x x x x x x x x x x x x x x xx x x x x x x x x x x x x x x x x x x xx x x x x x x x x x x x x x x x x x x x I cannot figure out how to createa matrix where it takes the output and uses the output as rowList all the steps performed by Linear Search for the input L = 1,3,5,7,9,11,13 and x = 5.Q1. Design a generic matrix multiplier. Here ‘generic’ means the design should work for anymatrix multiplication X∙Y = Z, where the matrices X, Y, and Z are of sizes a×b, b×c, and a×crespectively. Now, pick a, b, c from the last three digits of your roll number. ( If any of the digitsis 0, take 3 instead of it; if two digits are 0s, then take 3 for the first 0, and 5 for the second 0)For Example, if the last three digits are 123 then a = 1, b = 2, and c = 3; if the last three digitsare 204 then a = 2, b = 3, c = 4; f the last three digits are 100 then a = 1, b = 3, c = 5.
- Given a vector x=[12 3 4 5 . ], take the square of each element and sum them up. What should be the dimension of the vector x so that the squared sum (as above) is as close as possible to 1000 but not more than 1000? ....Please debug the following trenchTranveral javascript function. The function should return true if the node's value is less than -5 and false if equal to or greater than -5. function findNeighbors(node, matrix) { const neighbors = []; const [row, col] = node; const currNum = matrix[row][col]; // Check top if (matrix[row - 1] && Math.abs(matrix[row - 1][col] < - 5)) { neighbors.push([row - 1, col]); } // Check bottom if (matrix[row + 1] && Math.abs(matrix[row + 1][col] < - 5)) { neighbors.push([row + 1, col]); } // Check left if (matrix[row][col - 1] && Math.abs(matrix[row][col - 1] < - 5)) { neighbors.push([row, col - 1]); } // Check right if (matrix[row][col + 1] && Math.abs(matrix[row][col + 1] < - 5)) { neighbors.push([row, col + 1]); } // Return neighbors return neighbors; // Only consider N, S, E, W nodes } function trenchTraversal(node, matrix, visited) { const [row, col] = node; let stack = [node] visited.add(node.toString())…1. [20 points] [MID] The subset21 problem is stated as follows. Given a set of N positive integers X elements of P is equal to 21. For example, if N=5 and the set X = {12, 17, 3, 24, 6}, the set P = {12, 3, 6} is a valid solution for the subset21 problem in this example. {x1, x2, ..., xm}. Find a subset P of the set X such that the sum of the Formulate the subset21 problem as a Genetic or Evolutionary Algorithm optimization. You may use binary representation, OR any representation that you think is more appropriate. you should specify: • A fitness function. Give 3 examples of individuals and their fitness values if are solving the above example (i.e. X you {12, 17, 3, 24, 6}). • A set of mutation and/or crossover and/or repair operators. Intelligent operators that are suitable for this particular domain will earn more credit. • A termination criterion for the evolutionary optimization which insures that you terminate with a valid solution for the subset21 problem if possible without…
- The vector x ∈ R N has L different entries. For example, L = 4 for x = [3,4,4,5,3,1,5,3]T . One can express x as x = S u, where u ∈ R L satisfies (u)i < (u)j if i < j and S is a matrix that contains only zeros and ones. Write the function repeated_entries, which takes x as input and returns S and u.The following javascript functions should determine if a given matrix includes a trench by comparing each node and its neighbors to determine if there a trench. A trench has a length of three or more nodes, each node in the trench must be deeper than -5 and trenches may not branch into (any form of) a "T" shape. A node with more than two neighbors will result in branching "T" shape.def weighted_mse_grad(w, X, y, V):"""Calculate gradient of the weight MSE loss in the given point w Parameters----------w: array_likeCurrent point, in which we want to evaluate gradient (vector with k+1 elements)X: array_likeDesign matrix with N rows and k+1 columnsy: array_likeVector with N observations of the target variableV: array_likeDiagonal matrix N x N, with the weightsReturns----------out: ndarrayvector of gradient, k+1"""# your code here # TEST weighted_mse_grad()w = np.zeros(5)X = np.random.randn(10, 5)y = np.ones(10)V = np.diag(np.ones(10)) L_grad = weighted_mse_grad(w, X, y, V)assert(L_grad.shape == (5,)) w = np.zeros(5)X = np.eye(5)y = np.ones(5)V = np.diag(np.ones(5))L_grad = weighted_mse_grad(w, X, y, V)assert(L_grad.shape == (5,)), 'The shape of the output on the test case is wrong'assert(np.allclose(5 * L_grad,- y * 2)), 'The values of the output on the test case is wrong'