## Instructions

**Objective**

Write a python homework program to implement bug fixing.

## Requirements and Specifications

**Source Code**

```
from types import TracebackType
import numpy as np
'''
QUESTION 1
'''
def prod(S):
prod = 1
for x in S:
prod = prod*x
return prod
'''
QUESTION 2
'''
for k in range(len(exacts)):
if abs(exacts[k] - approx[k])/approx[k] < 0.001:
print(f"Test case {k}: pass")
else:
print(f"Test case {k}: fail")
'''
QUESTION 3
'''
# No question 3
'''
QUESTION 4
'''
def stats(sample):
sample_min = min(sample)
sample_max = max(sample)
sample_mean = sum(sample)/len(sample)
sample_variance = sum([s**2 for s in sample])/len(sample) - sample_mean**2
return (sample_min, sample_max, sample_mean, sample_variance)
def faststats(sample):
N = len(sample)
sample_min = 1E+99
sample_max = -1E+99
sum_of_x = 0
sum_of_xx = 0
for x in sample:
if x < sample_min:
sample_min = x
if x > sample_max:
sample_max = x
sum_of_x += x
sum_of_xx += x**2
sample_mean = sum_of_x/N
sample_variance = sum_of_xx/N - sample_mean**2
return (sample_min, sample_max, sample_mean, sample_variance)
print(stats(sample))
print(faststats(sample))
'''
QUESTION 5
'''
midpts = (x[:-1] + x[1:])/2
'''
QUESTION 6
'''
def trace(A):
assert A.shape[0] == A.shape[1], "Matrix is not square"
return sum([A[i][i] for i in range(A.shape[0])])
'''
QUESTION 7
'''
sorted_sample = np.sort(sample)
N = len(sample)
if N%2 > 0:
sample_median = sorted_sample[int(N/2)]
else:
sample_median = 0.5*(sorted_sample[int(N/2)]+ sorted_sample[int(N/2)+1])
'''
QUESTION 8
'''
positions = np.loadtxt('output-run-2965.dat', delimiter=',')
x = positions[:,0]
y = positions[:,1]
z = positions[:,2]
# Get number of points
N = positions.shape[0]
dists = np.zeros((N,N))
# Compute
for i in range(N):
for j in range(N):
if i != j:
p1 = np.array([x[i], y[i], z[i]])
p2 = np.array([x[j], y[j], z[j]])
distance = np.linalg.norm(p1-p2) # Euclidean distance
dists[i,j] = distance
'''
QUESTION 9
'''
def expectation(dice):
Y = get_value(dice)
P = get_probability(dice)
assert all(P >= 0) and all(P <= 1) and (sum(P) == 1)
return sum(P*Y)
'''
QUESTION 10
'''
R2 = R1.copy() # The bug occurs here. If you use R2 = R1, when changing R2 will also change R1
# So the correct way is using the function copy()
for r in R2:
r[0] = -r[0]
r[1] = -r[1]
dR = np.zeros(R1.shape[0])
for k in range(R1.shape[0]):
dR[k] = np.sqrt(np.sum((R1[k,:] - R2[k,:])**2))
'''
QUESTION 11???
'''
most_emitters = 0
# We need to pre-allocate the variable winner
winner = -1
for k in range(len(galaxies)):
if len(galaxies[k]) > 0 and galaxies[k].count('x') > most_emitters:
winner = k
most_emitters = galaxies[k].count('x')
if winner != -1:
print(f"galaxy {winner} has the most x-ray emitters; {most_emitters} of them")
else:
print("There is no galaxy with 'x's in it")
```

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