Construction of 21 by 21 total games matrix in python

Question

I have 8 by 8 matrix for possible game scores during a set of tennis, for example 6,0 6,1 0,6 1,6 tiebreaks represented like 7,6 and 6,7. Assuming matrices for 2nd and 3rd set are the same, construct 21 by 21 matrix of possible game scores for the full match. 8 by 8 matrix is just called matrix.

Answer 1

We have an 8 by 8 matrix that shows possible scores for a set of tennis games. We need to create a 21 by 21 matrix that shows all possible scores for a full match of three sets.

1. 8 by 8 Matrix: This matrix shows the possible scores for one set. For example, if the matrix at (6, 0) has a 1, it means a set can end with a score of 6-0.
2. 21 by 21 Matrix: This matrix will show the possible scores for the entire match, considering three sets. The reason it's 21 by 21 is because the maximum score sum for three sets is 6+6+6=18, but we consider up to 20 for edge cases.
3. Combining Sets: We combine the scores from three sets to get the total score for the match and update the 21 by 21 matrix.

Code:

import numpy as np

# Define the 8x8 matrix with example scores

# Let's assume 1 means the score is possible, and 0 means it's not

matrix = np.array([

[1, 1, 0, 0, 0, 0, 0, 0],

[1, 1, 1, 0, 0, 0, 0, 0],

[0, 1, 1, 1, 0, 0, 0, 0],

[0, 0, 1, 1, 1, 0, 0, 0],

[0, 0, 0, 1, 1, 1, 0, 0],

[0, 0, 0, 0, 1, 1, 1, 0],

[0, 0, 0, 0, 0, 1, 1, 1],

[0, 0, 0, 0, 0, 0, 1, 1]

])

# Initialize the 21x21 matrix with zeros

full_match_matrix = np.zeros((21, 21), dtype=int)

# Go through all possible combinations of scores for three sets

for i1 in range(8):

for j1 in range(8):

if matrix[i1, j1] == 0:

continue # Skip impossible scores

for i2 in range(8):

for j2 in range(8):

if matrix[i2, j2] == 0:

continue # Skip impossible scores

for i3 in range(8):

for j3 in range(8):

if matrix[i3, j3] == 0:

continue # Skip impossible scores

# Sum the scores of the three sets

total_i = i1 + i2 + i3

total_j = j1 + j2 + j3

# Update the 21x21 matrix

full_match_matrix[total_i, total_j] += 1

# Display the result

print(full_match_matrix)

How it Works:

1. Define the 8x8 Matrix: We create an example matrix where 1 means the score is possible and 0 means it's not.
2. Initialize the 21x21 Matrix: We start with a 21 by 21 matrix filled with zeros.
3. Nested Loops to Combine Scores: We use three nested loops to go through every possible combination of scores for three sets. If the combination is possible (i.e., the value in the matrix is 1), we add the scores for the three sets and update the corresponding cell in the 21 by 21 matrix.
4. Display the Result: Finally, we print the 21 by 21 matrix.