code: def transform_to_match_coherence(
      signal: npt.NDArray,
      desired_coherence: npt.NDArray,
      method: str = "cholesky",
      ref_channel: int = 0,
      corrcoef_threshold: float = 0.2,
  ) -> npt.NDArray:
      """Transform the input multichannel signal to match the desired coherence.
  
      Note: It's assumed that channels are independent.
  
      Args:
          signal: independent noise signals with shape (num_samples, num_channels)
          desired_coherence: desired coherence with shape (num_subbands, num_channels, num_channels)
          method: decomposition method used to construct the transformation matrix
          ref_channel: reference channel for power normalization of the input signal
          corrcoef_threshold: used to detect input signals with high correlation between channels
  
      Returns:
          Signal with coherence approximately matching the desired coherence, shape (num_samples, num_channels)
  
      References:
          E.A.P. Habets, I. Cohen and S. Gannot, 'Generating nonstationary multisensor
          signals under a spatial coherence constraint', Journal of the Acoustical Society
          of America, Vol. 124, Issue 5, pp. 2911-2917, Nov. 2008.
      """
      num_channels = signal.shape[1]
      num_subbands = desired_coherence.shape[0]
      assert desired_coherence.shape[1] == num_channels
      assert desired_coherence.shape[2] == num_channels
  
      fft_length = 2 * (num_subbands - 1)
  
      # remove DC component
      signal = signal - np.mean(signal, axis=0)
  
      # channels needs to have equal power, so normalize with the ref mic
      signal_power = np.mean(np.abs(signal) ** 2, axis=0)
      signal = (
          signal
          * np.sqrt(signal_power[ref_channel])
          / np.sqrt(signal_power)
      )
  
      # input channels should be uncorrelated
      # here, we just check for high correlation coefficients between channels to detect ill-constructed inputs
      corrcoef_matrix = np.corrcoef(signal.transpose())
      # mask the diagonal elements
      np.fill_diagonal(corrcoef_matrix, 0.0)
      if np.any(np.abs(corrcoef_matrix) > corrcoef_threshold):
          raise RuntimeError(
              f"Input channels are correlated above the threshold {corrcoef_threshold}. Max abs off-diagonal element of the coefficient matrix: {np.abs(corrcoef_matrix).max()}."
          )
  
      # analysis transform
      S = librosa.stft(signal.transpose(), n_fft=fft_length)
      # (channel, subband, frame) -> (subband, frame, channel)
      S = S.transpose(1, 2, 0)
  
      # generate output signal for each subband
      X = np.zeros_like(S)
  
      # factorize the desired coherence (skip the DC component)
      if method == "cholesky":
          L = np.linalg.cholesky(desired_coherence[1:])
          A = L.swapaxes(1, 2)
      elif method == "evd":
          w, V = np.linalg.eig(desired_coherence[1:])
          # scale eigenvectors
          A = np.sqrt(w)[:, None, :] * V
          # prepare transform matrix
          A = A.swapaxes(1, 2)
      else:
          raise ValueError(f"Unknown method {method}")
  
      # transform vectors at each time step:
      #   x_t = A^T * s_t
      # or in matrix notation: X = S * A
      X[1:, ...] = np.matmul(S[1:, ...], A)
  
      # synthesis transform
      # transpose X from (subband, frame, channel) to (channel, subband, frame)
      x = librosa.istft(X.transpose(2, 0, 1), length=len(signal))
      # (channel, sample) -> (sample, channel)
      x = x.transpose()
  
      return x
  
imports: import math
  from typing import Iterable, Optional, Union
  import librosa
  import numpy
  import numpy.typing
  import scipy
  import soundfile
  import torch
  from scipy.spatial.distance import pdist, squareform
  from nemo.utils import logging
label_desc: Use image node_id 7 for calling a global function with example usage: transform_to_match_coherence(signal, desired_coherence, method, ref_channel, corrcoef_threshold) and returns: x