code: def rank_correction(measure, N, rank=1, dtype=torch.float):
      """Return low-rank matrix L such that A + L is normal."""
      if measure == "legs":
          assert rank >= 1
          P = torch.sqrt(0.5 + torch.arange(N, dtype=dtype)).unsqueeze(
              0
          )  # (1 N)
      elif measure == "legt":
          assert rank >= 2
          P = torch.sqrt(1 + 2 * torch.arange(N, dtype=dtype))  # (N)
          P0 = P.clone()
          P0[0::2] = 0.0
          P1 = P.clone()
          P1[1::2] = 0.0
          P = torch.stack([P0, P1], dim=0)  # (2 N)
          P *= 2 ** (
              -0.5
          )  # Halve the rank correct just like the original matrix was halved
      elif measure in ["fourier", "fout"]:
          P = torch.zeros(N)
          P[0::2] = 2**0.5
          P[0] = 1
          P = P.unsqueeze(0)
      elif measure in ["fourier_diag", "foud", "legsd"]:
          P = torch.zeros(1, N, dtype=dtype)
      else:
          raise NotImplementedError
  
      d = P.size(0)
      if rank > d:
          P = torch.cat(
              [P, torch.zeros(rank - d, N, dtype=dtype)], dim=0
          )  # (rank N)
      return P
  
imports: import logging
  import math
  import os
  from functools import wraps
  from typing import Any, Callable, Optional
  import numpy
  import opt_einsum
  import torch
  import torch.nn
  import torch.nn.functional
  from einops import rearrange, repeat
  from espnet2.asr.state_spaces.components import Activation, DropoutNd, LinearActivation
label_desc: Use image node_id 7 for calling a global function with example usage: rank_correction(measure, N, rank, dtype) and returns: P