solving math equation for data loading problem-CodePudding

I'm having a dataframe df_N with n observations. I'd want to write a code that would create new dataframe df_M with records from df_N. The number of observations in df_M ( ie m observations ) is several orders greater that the number of observations on df_N. The number of observations on df_M can be represented in by the following formula.

m = (n*(2^x)) n^y z

Note that the first part of the equation is the series n, n2, n4, n*8. ie n times 2^x

Note that all values are integers.

For example if n = 8 and m = 82 the values of the formula would be 82= (8*(2^3) 8^2 2 = 8*8 16 2 = 64 16 2 = 82 values of x = 3 , y = 2 and z = 2

Also note that always (n*(2^x)) > n^y > z . This constraint will restrict the number of solutions for the equation.

Is there a way of solving this equation on python and finding the values of x y and z, given n and m?

Once the value of x y and z are determined, I'd be able to write a code to create additional records for each of the segment of the equation and combiming them to a single dataframe df_M

CodePudding user response：

Assuming that you also want to maximize n*y over z, m and n are positive and other numbers should be non-negative:

x = m.bit_length() - 1
m -= 2**x
y = m//n
z = m - y*n

CodePudding user response：

where x is a positive integer representing the number of times the observations in df_N will be replicated in df_M.

Here is an example of how the code could look like:

# Import necessary libraries
import pandas as pd

# Set the number of replications
x = 5

# Create the dataframe df_N
df_N = pd.DataFrame({'ID': [1, 2, 3], 'Name': ['John', 'Jane', 'Bob'], 'Age': [20, 30, 25]})

# Create an empty dataframe df_M
df_M = pd.DataFrame()

# Loop through the observations in df_N and append them to df_M
for i in range(x):
    df_M = df_M.append(df_N)

# View the resulting dataframe
print(df_M)

This code will create a new dataframe df_M with x times the number of observations in df_N. In the example above, df_M will have 15 observations, since x is set to 5.

CodePudding user response：

Assuming that you also want to maximize n*y over z, m and n are positive and other numbers should be non-negative:

x = m.bit_length() - 1
m -= 2**x
y = m//n
z = m - y*n