code: def inv(x):
      """Inverse Hermitian Matrix.
  
      This method finds the inverse of a complex Hermitian matrix
      represented by its upper triangular part. The result will have
      the following format: (*, C, C, 2).
  
      Arguments
      ---------
      x : tensor
          An input matrix to work with. The tensor must have the
          following format: (*, 2, C+P)
  
      Example
      -------
      >>> import torch
      >>>
      >>> from speechbrain.dataio.dataio import read_audio
      >>> from speechbrain.processing.features import STFT
      >>> from speechbrain.processing.multi_mic import Covariance
      >>> from speechbrain.processing.decomposition import inv
      >>>
      >>> xs_speech = read_audio(
      ...    'tests/samples/multi-mic/speech_-0.82918_0.55279_-0.082918.flac'
      ... )
      >>> xs_noise = read_audio('tests/samples/multi-mic/noise_0.70225_-0.70225_0.11704.flac')
      >>> xs = xs_speech + 0.05 * xs_noise
      >>> xs = xs.unsqueeze(0).float()
      >>>
      >>> stft = STFT(sample_rate=16000)
      >>> cov = Covariance()
      >>>
      >>> Xs = stft(xs)
      >>> XXs = cov(Xs)
      >>> XXs_inv = inv(XXs)
      """
  
      # Dimensions
      d = x.dim()
      p = x.shape[-1]
      n_channels = int(round(((1 + 8 * p) ** 0.5 - 1) / 2))
  
      # Output matrix
      ash = f(pos_def(x))
      ash_inv = torch.inverse(ash)
      as_inv = finv(ash_inv)
  
      indices = torch.triu_indices(n_channels, n_channels)
  
      x_inv = torch.zeros(
          x.shape[slice(0, d - 2)] + (n_channels, n_channels, 2),
          dtype=x.dtype,
          device=x.device,
      )
  
      x_inv[..., indices[1], indices[0], 0] = as_inv[..., 0, :]
      x_inv[..., indices[1], indices[0], 1] = -1 * as_inv[..., 1, :]
      x_inv[..., indices[0], indices[1], 0] = as_inv[..., 0, :]
      x_inv[..., indices[0], indices[1], 1] = as_inv[..., 1, :]
  
      return x_inv
  
file_path: speechbrain/speechbrain/processing/decomposition.py
imports: import torch
label_desc: Use image node_id 8 for calling a global function with example usage: inv(x) and returns: x_inv