Question

Question 1: using python

Given a matrix, please write a python script to calculate the singular value decomposition (SVD).

Answer 1

The calculate SVD, following packages should be installed with in PYTHON:

1. numpy
2. scipy

numpy is to define array (matrix).

scipy to calculate SVD.

Steps:

1. define a matrix/array
2. output the matrix
3. use svd() method from scipy which takes matrix/array as input and returns the value of U, s and VT
4. output the calculated SVD

CODE (PLEASE REFER THE SCREENSHOTS FOR CODE INDENTATION):

'''
Given a matrix, please write a python script to calculate the singular
value decomposition (SVD)

The pre-requisite for program is numpy and scipy module

'''
# import array from numpy
from numpy import array

# import svd from scipy.linalg
from scipy.linalg import svd

# input matrix
matrix = array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])

print ("Input matrix = ")
print(matrix)

# calculate SVD using scipy svd() method.
# it returns U , s and VT
U, s, VT = svd(matrix)

# print the SVD
print("\nU =")
print (U)
print ("\ns =")
print(s)
print("\nVT =")
print(VT)

OUTPUT: