Linear algebra for ML

Quiz 1

 

from elice_utils import EliceUtils

import numpy as np

from numpy import array

from scipy.linalg import svd

elice_utils = EliceUtils()

def main():

    M=array([[1,0,0,0,2],[0,0,3,0,0],[0,0,0,0,0],[0,4,0,0,0]])

   

    # Task 1: Compute SVD

    '''svd 관련 설명은 https://docs.scipy.org/doc/scipy/reference/generated/scipy.linalg.svd.html'''

    U, S, VT = svd(M)

   

    # Task 2: Print out the shapes of these SVDs

   

    print(U.shape, S.shape, VT.shape)

   

    return U,S,VT

   

if __name__ == "__main__":

    main()

 

Quiz 2

from elice_utils import EliceUtils

import numpy as np

elice_utils = EliceUtils()

def main():

   

    # Task 1: Compute the pseudo_inv function without using any built-in pinv library

   

    #TODO

    A = np.array([[1, -3, 1],[-2, -1, -3], [-1, 1, 5], [0, 1, 1]])

    # what should b yield?

    #TODO

    b = np.array([1, 5, -7, -3])

   

    pinA = pseudo_inv(A)

   

    # Task 2: Find the solution to the equation by solving the problem in Ax=b manner.

   

    x = solve_linear(A,b)

    # c) Rearrange the system of equations in the format By = 0 then find the optimal value of y

    #TODO

    B = np.array([[1, -3, 1],[-2, -1, -3], [-1, 1, 5], [0, 1, 1]])

    optimal_y = solve_non_linear(B)

    #elice_utils.send_image('elice.png')

    #elice_utils.send_file('data/input.txt')

def pseudo_inv(A):

    #TODO

    A_transpose = np.transpose(A)

    A_midinv = np.dot(A_transpose, A)

    A_pinv = np.dot(np.linalg.inv(A_midinv), A_transpose)

    return A_pinv

   

def solve_linear(A,b):

    #TODO

    x = np.dot(pseudo_inv(A), b)

    return x

   

def solve_non_linear(B):

    #TODO

    U, S, VT = np.linalg.svd(B)

    y = VT[-1] '''V의 마지막 행이 optimal solution'''

    y /= y[-1] '''정규화'''

    return y

if __name__ == "__main__":

    main()