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25.2: Code Review

Last updated

Sep 17, 2022
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- 25.1: Orthogonal and Orthonormal
- 25.3: Gram-Schmidt

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In the next in-class assignment, we are going to avoid some of the more advanced libraries (i.e. no numpy or scipy or sympy) to try to get a better understanding about what is going on in the math. The following code implements some common linear algebra functions:

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#Standard Python Libraries only
import math
import copy

#Standard Python Libraries only
import math
import copy

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def dot(u,v):
    '''Calculate the dot product between vectors u and v'''
    temp = 0;
    for i in range(len(u)):
        temp += u[i]*v[i]
    return temp

def dot(u,v):
    '''Calculate the dot product between vectors u and v'''
    temp = 0;
    for i in range(len(u)):
        temp += u[i]*v[i]
    return temp

Do This

Write a quick test to compare the output of the above dot function with the numpy dot function.

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# Put your test code here

# Put your test code here

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def multiply(m1,m2):
    '''Calculate the matrix multiplication between m1 and m2 represented as list-of-list.'''
    n = len(m1)
    d = len(m2)
    m = len(m2[0])
    
    if len(m1[0]) != d:
        print("ERROR - inner dimentions not equal")
    
    #make zero matrix
    result = [[0 for j in range(m)] for i in range(n)]
#    print(result)
    for i in range(0,n):
        for j in range(0,m):
            for k in range(0,d):
                #print(i,j,k)
                #print('result', result[i][j])
                #print('m1', m1[i][k])
                #print('m2', m2[k][j])
                result[i][j] = result[i][j] + m1[i][k] * m2[k][j]
    return result

def multiply(m1,m2):
    '''Calculate the matrix multiplication between m1 and m2 represented as list-of-list.'''
    n = len(m1)
    d = len(m2)
    m = len(m2[0])
    
    if len(m1[0]) != d:
        print("ERROR - inner dimentions not equal")
    
    #make zero matrix
    result = [[0 for j in range(m)] for i in range(n)]
#    print(result)
    for i in range(0,n):
        for j in range(0,m):
            for k in range(0,d):
                #print(i,j,k)
                #print('result', result[i][j])
                #print('m1', m1[i][k])
                #print('m2', m2[k][j])
                result[i][j] = result[i][j] + m1[i][k] * m2[k][j]
    return result

Do This

Write a quick test to compare the output of the above multiply function with the numpy multiply function.

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# Put your test code here

# Put your test code here

Question

What is the big-O complexity of the above multiply function?

Question

Line 11 in the provided multiply code initializes a matrix of the size of the output matrix as a list of lists with zeros. What is the big-O complexity of line 11?

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def norm(u):
    '''Calculate the norm of vector u'''
    nm = 0
    for i in range(len(u)):
        nm += u[i]*u[i]
    return math.sqrt(nm)

def norm(u):
    '''Calculate the norm of vector u'''
    nm = 0
    for i in range(len(u)):
        nm += u[i]*u[i]
    return math.sqrt(nm)

Do This

Write a quick test to compare the outputs of the above norm function with the numpy norm function.

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#Put your test code here

#Put your test code here

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def transpose(A):
    '''Calculate the transpose of matrix A represented as list of lists'''
    n = len(A)
    m = len(A[0])
    AT = list()
    for j in range(0,m):    
        temp = list()
        for i in range(0,n):
            temp.append(A[i][j])
        AT.append(temp)
    return AT

def transpose(A):
    '''Calculate the transpose of matrix A represented as list of lists'''
    n = len(A)
    m = len(A[0])
    AT = list()
    for j in range(0,m):    
        temp = list()
        for i in range(0,n):
            temp.append(A[i][j])
        AT.append(temp)
    return AT

Do This

Write a quick test to compare the output of the above transpose function with the numpy transpose function.

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# Put your test code here

# Put your test code here

Question

What is the big-O complexity of the above transpose function?

Question

Explain any differences in results between the provided functions and their numpy counterparts.

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Do This

Question

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