Project: 033_Combatting_Dimensional_Collapse_in_LLM_Pre-Trainin | Function: cal_egin (iclr)

system: You are an expert Python programmer implementing algorithms from scientific papers.
Complete the masked function based on the algorithm description.
Follow Python best practices and maintain consistent code style.
Return **only** the complete Python function code.

user: Complete this Python function:

**DESCRIPTION:** Function to calculate dominance scores using eigenvalue analysis to quantify dimensional collapse in the feature space

**KEY TERMS:** {
  "eigenvalue": "λ_i eigenvalues",
  "ratio": "dominance score",
  "topk_egin": "top k eigenvalues"
}

**CONTEXT CODE:** import numpy as np
import torch

def off_diagonal(x):
    n, m = x.shape
    assert n == m
    return x.flatten()[:-1].view(n - 1, n + 1)[:, 1:].flatten()

def cal_egin(feat_mat):

    raise NotImplementedError("Function implementation has been masked for testing")

if __name__ == "__main__":
    yourpath=""  # selected feature path
    batch_size=128  # number of samples used for calculating dominance score
    feat_dim=768 # dimension of feature
    selected_feature = torch.tensor(np.memmap(yourpath, dtype='float32', mode='r', shape=(batch_size,feat_dim)))

    dominance_score=cal_egin(selected_feature)
    print("dominance_score:",dominance_score)


Complete the function implementation replacing "raise NotImplementedError".