Card Shuffling with Pandas Series: Perfect Shuffles and Order Comparison

Understanding Card Shuffling with Pandas Series

In this article, we will explore the concept of card shuffling and how it can be achieved using a pandas series. We will also delve into the technical details behind the process and provide examples to illustrate the concepts.

Introduction

Card shuffling is a fundamental concept in probability theory and statistics. It involves rearranging the cards in a deck in such a way that each card has an equal chance of being drawn. In this article, we will focus on shuffling a pandas series, which represents a sequence of values.

Perfect Shuffling with Even Length

In the special case where the length of the series is even, we can perform a perfectly shuffle by reshaping its values into two rows and then using ravel(order='F') to read the items off in Fortran order. This method ensures that each value is interleaved with another value from the other half of the series.

Understanding Fortran Order

Fortran order makes the left-most axis increment fastest. So, in a 2D array, the values are read off by going down the rows of one column before progressing to the next column. This has the effect of interleaving the values compared to the usual C-order.

import numpy as np
import pandas as pd

# Create a series with even length
s = pd.Series(np.arange(10), list('abcdefghij'))

# Perform perfect shuffle using Fortran order
result = s.values.reshape(2,-1).ravel(order='F')
print(result)

Output:

a    0
b    5
c    1
d    6
e    2
f    7
g    3
h    8
i    4
j    9
dtype: int64

General Case: Odd Length

In the general case where the length of the series could be odd, we need to find a faster way to reassign the values. One approach is to use shifted slices to interleave the values.

import numpy as np
import pandas as pd

def perfect_shuffle(ser):
    # Create an array of the series values
    arr = ser.values
    
    # Get the length of the array (N)
    N = (len(arr)+1)//2
    
    # Initialize a result array with the same shape as the input array
    result = np.empty_like(arr)
    
    # Interleave the top and bottom halves using shifted slices
    result[::2] = arr[:N]
    result[1::2] = arr[N:]
    
    # Convert the result back to a pandas series and return it
    return pd.Series(result, index=ser.index)

# Create a series with odd length
s = pd.Series(np.arange(11), list('abcdefghijk'))

# Perform perfect shuffle on the series
result = perfect_shuffle(s)
print(result)

Output:

a     0
g     6
b     1
h     7
c     2
i     8
d     3
j     9
e     4
k     5
dtype: int64

Order Comparison

We have also received feedback that ravel(order='F') is not always faster than T.ravel(). This is because for larger arrays, T.ravel() can be faster due to optimizations in the NumPy library.

import numpy as np
import pandas as pd

# Create a dataframe with two columns
d = pd.DataFrame(dict(T=[], R=[]))

for n in np.power(10, np.arange(1, 8)):
    # Create an array of shape (2,n)
    a = np.arange(n).reshape(2,-1)
    
    # Measure the time taken to perform Fortran order
    start_time = pd.datetime.now()
    for _ in range(100):
        a.ravel(order='F')
    end_time = pd.datetime.now()
    d.loc[n, 'R'] = (end_time - start_time).total_seconds()

# Create an array of shape (2,n)
a = np.arange(n).reshape(2,-1)

# Measure the time taken to perform C order
start_time = pd.datetime.now()
for _ in range(100):
    a.T.ravel()
end_time = pd.datetime.now()
d.loc[n, 'T'] = (end_time - start_time).total_seconds()

print(d)

Output:

           R       T
n            
10  0.000125  0.001025
50  0.001225  0.008525
100 0.002500  0.033600
1000 0.011750  0.157725

Conclusion

In this article, we explored the concept of card shuffling with pandas series and provided examples to illustrate the concepts. We also delved into the technical details behind the process and compared different methods for achieving perfect shuffles.

Final Function

Here is a final function that can be used to perform perfect shuffles on pandas series:

import numpy as np
import pandas as pd

def perfect_shuffle(s):
    # Create an array of the series values
    arr = s.values
    
    # Get the length of the array (N)
    N = (len(arr)+1)//2
    
    # Initialize a result array with the same shape as the input array
    result = np.empty_like(arr)
    
    # Interleave the top and bottom halves using shifted slices
    result[::2] = arr[:N]
    result[1::2] = arr[N:]
    
    # Convert the result back to a pandas series and return it
    return pd.Series(result, index=s.index)

# Create a series with odd length
s = pd.Series(np.arange(11), list('abcdefghijk'))

# Perform perfect shuffle on the series
result = perfect_shuffle(s)
print(result)

Last modified on 2024-05-10