解决NumPy元组排序标量转换错误及特征向量载荷输出问题

Hey there, let's tackle your two issues one by one:

一、Fixing the TypeError When Sorting Eigenvalue-Eigenvector Pairs #

The error TypeError: only length-1 arrays can be converted to Python scalars pops up because of how np.linalg.eig returns eigenvectors: eig_vecs is a matrix where each column corresponds to an eigenvector, not each row. When you use zip(eig_vals, eig_vecs), you're pairing each scalar eigenvalue with a row from eig_vecs (not the matching eigenvector column), creating tuples of (scalar, 1D array). Converting this list to a numpy array fails because numpy can't treat those 1D arrays as scalars to build a regular array.

Here's the corrected code to properly pair and sort your eigenvalues and eigenvectors:

# Generate list of (eigenvalue, eigenvector) tuples correctly
# Transpose eig_vecs so each row is an eigenvector matching the index of eig_vals
eig_pairs = list(zip(eig_vals, eig_vecs.T))

# Sort the pairs in descending order of eigenvalues
eig_pairs.sort(key=lambda x: x[0], reverse=True)

# Optional: Convert back to numpy array if needed (use dtype=object to handle mixed types)
eig_pairs = np.array(eig_pairs, dtype=object)

After this, your loop to print sorted eigenvalues will work as expected.

二、Exporting Loadings (or Scores) to a File #

First, let's clarify two common terms to ensure we're aligned:

• Variable Loadings: The weight of each original feature on each principal component (calculated as eigenvectors multiplied by the square root of their corresponding eigenvalues).
• Sample Scores: The projection of each data point onto the principal components (calculated by multiplying standardized data with the eigenvector matrix).

1. Export Variable Loadings #

# Calculate variable loadings: eigenvectors * sqrt(eigenvalues)
loadings = eig_vecs * np.sqrt(eig_vals)

# Convert to DataFrame for readability (use original feature names as index)
loadings_df = pd.DataFrame(
    loadings,
    columns=[f'PC{i+1}' for i in range(len(eig_vals))],
    index=df_to_save.columns
)

# Save to CSV file
loadings_df.to_csv('variable_loadings.csv', index=True)

2. Export Sample Principal Component Scores #

# Calculate sample scores: standardized data @ eigenvector matrix
scores = X_std @ eig_vecs

# Convert to DataFrame (retain original index if needed)
scores_df = pd.DataFrame(
    scores,
    columns=[f'PC{i+1}' for i in range(len(eig_vals))]
)
scores_df.index = df_to_save.index  # Match original data's index

# Save to CSV file
scores_df.to_csv('sample_scores.csv', index=True)

If you want to use the sorted eigenvalues/eigenvectors (from the first part of the solution) for loadings/scores, extract them from the sorted eig_pairs first:

# Extract sorted eigenvalues and eigenvectors
sorted_eig_vals = np.array([pair[0] for pair in eig_pairs])
sorted_eig_vecs = np.array([pair[1] for pair in eig_pairs]).T  # Transpose back to column matrix

# Calculate sorted loadings and scores
sorted_loadings = sorted_eig_vecs * np.sqrt(sorted_eig_vals)
sorted_scores = X_std @ sorted_eig_vecs

内容的提问来源于stack exchange，提问作者James Danowski