求助：按指定递推公式批量计算DataFrame各列值（附示例）

The Problem Breakdown #

You need to compute updated values for each column in a pandas DataFrame using this chain of recursive formulas:

• For every row:
  • New B = A + (1 - A) × Original B
  • New C = Updated B + (1 - Updated B) × Original C
  • New D = Updated C + (1 - Updated C) × Original D
• This pattern needs to apply to all 11 columns in your actual dataset (the 4-column example is just for testing).

Sample Data #

Original Input

Expected Output

Solution Code #

Here's a clean, scalable way to implement this logic that works for any number of columns:

import pandas as pd

# Initialize your original DataFrame
df = pd.DataFrame({
    'A': [0.2, 0.4, 0.8, 0.3],
    'B': [0.4, 0.5, 0.1, 0.4],
    'C': [0.8, 0.6, 0.5, 0.1],
    'D': [0.5, 0.2, 0.4, 0.8]
})

# Create a copy to preserve the original data (always a good practice!)
df_updated = df.copy()

# Loop through columns starting from the second one (since A stays as-is)
for col_pos in range(1, df_updated.shape[1]):
    # Get the already-updated values from the previous column
    prev_updated_col = df_updated.iloc[:, col_pos - 1]
    # Get the original values from the current column (don't use the updated copy here!)
    original_curr_col = df.iloc[:, col_pos]
    
    # Apply your recursive formula
    df_updated.iloc[:, col_pos] = prev_updated_col + (1 - prev_updated_col) * original_curr_col

# Print the result to verify
print(df_updated)

How This Works #

1. Data Setup: We start by defining your sample DataFrame. For your 11-column dataset, just add the additional columns to this initial setup.
2. Preserve Original Data: Making a copy of the original DataFrame ensures we don't overwrite raw data, which is crucial for debugging or validating results.
3. Column Iteration: We loop through each column starting from index 1 (the second column, B). For each column:
   • We grab the updated values from the prior column (e.g., when calculating C, we use the already-updated B values)
   • We use the original values from the current column (using the original df instead of df_updated prevents accidental overwriting mid-calculation)
4. Formula Application: We compute the new values using your specified recursive logic, updating each column in sequence.

Verification #

Let's spot-check the first row to confirm:

• Updated B: 0.2 + (1 - 0.2) * 0.4 = 0.2 + 0.32 = 0.52 ✔️
• Updated C: 0.52 + (1 - 0.52) * 0.8 = 0.52 + 0.384 = 0.904 ✔️
• Updated D: 0.904 + (1 - 0.904) * 0.5 = 0.904 + 0.048 = 0.952 ✔️

This matches your expected output exactly, and the code will handle all 11 columns automatically without any extra changes.

内容的提问来源于stack exchange，提问作者bradon Mc