text: import librosa
  import numpy as np
  import torch
  import torch.nn.functional as F
  
  
  def _stft(y, hop_size, win_size, fft_size):
      return librosa.stft(y=y, n_fft=fft_size, hop_length=hop_size, win_length=win_size, pad_mode='constant')
  
  
  def _istft(y, hop_size, win_size):
      return librosa.istft(y, hop_length=hop_size, win_length=win_size)
  
  
  def griffin_lim(S, hop_size, win_size, fft_size, angles=None, n_iters=30):
      angles = np.exp(2j * np.pi * np.random.rand(*S.shape)) if angles is None else angles
      S_complex = np.abs(S).astype(np.complex)
      y = _istft(S_complex * angles, hop_size, win_size)
      for i in range(n_iters):
          angles = np.exp(1j * np.angle(_stft(y, hop_size, win_size, fft_size)))
          y = _istft(S_complex * angles, hop_size, win_size)
      return y
  
  
  def istft(amp, ang, hop_size, win_size, fft_size, pad=False, window=None):
      spec = amp * torch.exp(1j * ang)
      spec_r = spec.real
      spec_i = spec.imag
      spec = torch.stack([spec_r, spec_i], -1)
      if window is None:
          window = torch.hann_window(win_size).to(amp.device)
      if pad:
          spec = F.pad(spec, [0, 0, 0, 1], mode='reflect')
      wav = torch.istft(spec, fft_size, hop_size, win_size)
      return wav
  
  
  def griffin_lim_torch(S, hop_size, win_size, fft_size, angles=None, n_iters=30):
      """
  
      Examples:
      >>> x_stft = librosa.stft(wav, n_fft=fft_size, hop_length=hop_size, win_length=win_length, pad_mode="constant")
      >>> x_stft = x_stft[None, ...]
      >>> amp = np.abs(x_stft)
      >>> angle_init = np.exp(2j * np.pi * np.random.rand(*x_stft.shape))
      >>> amp = torch.FloatTensor(amp)
      >>> wav = griffin_lim_torch(amp, angle_init, hparams)
  
      :param amp: [B, n_fft, T]
      :param ang: [B, n_fft, T]
      :return: [B, T_wav]
      """
      angles = torch.exp(2j * np.pi * torch.rand(*S.shape)) if angles is None else angles
      window = torch.hann_window(win_size).to(S.device)
      y = istft(S, angles, hop_size, win_size, fft_size, window=window)
      for i in range(n_iters):
          x_stft = torch.stft(y, fft_size, hop_size, win_size, window)
          x_stft = x_stft[..., 0] + 1j * x_stft[..., 1]
          angles = torch.angle(x_stft)
          y = istft(S, angles, hop_size, win_size, fft_size, window=window)
      return y
  
  
  # Conversions
  _mel_basis = None
  _inv_mel_basis = None
  
  
  def _build_mel_basis(audio_sample_rate, fft_size, audio_num_mel_bins, fmin, fmax):
      assert fmax <= audio_sample_rate // 2
      return librosa.filters.mel(audio_sample_rate, fft_size, n_mels=audio_num_mel_bins, fmin=fmin, fmax=fmax)
  
  
  def _linear_to_mel(spectogram, audio_sample_rate, fft_size, audio_num_mel_bins, fmin, fmax):
      global _mel_basis
      if _mel_basis is None:
          _mel_basis = _build_mel_basis(audio_sample_rate, fft_size, audio_num_mel_bins, fmin, fmax)
      return np.dot(_mel_basis, spectogram)
  
  
  def _mel_to_linear(mel_spectrogram, audio_sample_rate, fft_size, audio_num_mel_bins, fmin, fmax):
      global _inv_mel_basis
      if _inv_mel_basis is None:
          _inv_mel_basis = np.linalg.pinv(_build_mel_basis(audio_sample_rate, fft_size, audio_num_mel_bins, fmin, fmax))
      return np.maximum(1e-10, np.dot(_inv_mel_basis, mel_spectrogram))
  