code: def griffinlim(
      S: np.ndarray,
      *,
      n_iter: int = 32,
      hop_length: Optional[int] = None,
      win_length: Optional[int] = None,
      n_fft: Optional[int] = None,
      window: _WindowSpec = "hann",
      center: bool = True,
      dtype: Optional[DTypeLike] = None,
      length: Optional[int] = None,
      pad_mode: _PadModeSTFT = "constant",
      momentum: float = 0.99,
      init: Optional[str] = "random",
      random_state: Optional[
          Union[int, np.random.RandomState, np.random.Generator]
      ] = None,
  ) -> np.ndarray:
      """Approximate magnitude spectrogram inversion using the "fast" Griffin-Lim algorithm.
  
      Given a short-time Fourier transform magnitude matrix (``S``), the algorithm randomly
      initializes phase estimates, and then alternates forward- and inverse-STFT
      operations. [#]_
  
      Note that this assumes reconstruction of a real-valued time-domain signal, and
      that ``S`` contains only the non-negative frequencies (as computed by
      `stft`).
  
      The "fast" GL method [#]_ uses a momentum parameter to accelerate convergence.
  
      .. [#] D. W. Griffin and J. S. Lim,
          "Signal estimation from modified short-time Fourier transform,"
          IEEE Trans. ASSP, vol.32, no.2, pp.236–243, Apr. 1984.
  
      .. [#] Perraudin, N., Balazs, P., & Søndergaard, P. L.
          "A fast Griffin-Lim algorithm,"
          IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (pp. 1-4),
          Oct. 2013.
  
      Parameters
      ----------
      S : np.ndarray [shape=(..., n_fft // 2 + 1, t), non-negative]
          An array of short-time Fourier transform magnitudes as produced by
          `stft`.
  
      n_iter : int > 0
          The number of iterations to run
  
      hop_length : None or int > 0
          The hop length of the STFT.  If not provided, it will default to ``n_fft // 4``
  
      win_length : None or int > 0
          The window length of the STFT.  By default, it will equal ``n_fft``
  
      n_fft : None or int > 0
          The number of samples per frame.
          By default, this will be inferred from the shape of ``S`` as an even number.
          However, if an odd frame length was used, you can explicitly set ``n_fft``.
  
      window : string, tuple, number, function, or np.ndarray [shape=(n_fft,)]
          A window specification as supported by `stft` or `istft`
  
      center : boolean
          If ``True``, the STFT is assumed to use centered frames.
          If ``False``, the STFT is assumed to use left-aligned frames.
  
      dtype : np.dtype
          Real numeric type for the time-domain signal.  Default is inferred
          to match the precision of the input spectrogram.
  
      length : None or int > 0
          If provided, the output ``y`` is zero-padded or clipped to exactly ``length``
          samples.
  
      pad_mode : string
          If ``center=True``, the padding mode to use at the edges of the signal.
          By default, STFT uses zero padding.
  
      momentum : number >= 0
          The momentum parameter for fast Griffin-Lim.
          Setting this to 0 recovers the original Griffin-Lim method [1]_.
          Values near 1 can lead to faster convergence, but above 1 may not converge.
  
      init : None or 'random' [default]
          If 'random' (the default), then phase values are initialized randomly
          according to ``random_state``.  This is recommended when the input ``S`` is
          a magnitude spectrogram with no initial phase estimates.
  
          If `None`, then the phase is initialized from ``S``.  This is useful when
          an initial guess for phase can be provided, or when you want to resume
          Griffin-Lim from a previous output.
  
      random_state : None, int, np.random.RandomState, or np.random.Generator
          If int, random_state is the seed used by the random number generator
          for phase initialization.
  
          If `np.random.RandomState` or `np.random.Generator` instance, the random number
          generator itself.
  
          If `None`, defaults to the `np.random.default_rng()` object.
  
      Returns
      -------
      y : np.ndarray [shape=(..., n)]
          time-domain signal reconstructed from ``S``
  
      See Also
      --------
      stft
      istft
      magphase
      filters.get_window
  
      Examples
      --------
      A basic STFT inverse example
  
      >>> y, sr = librosa.load(librosa.ex('trumpet'))
      >>> # Get the magnitude spectrogram
      >>> S = np.abs(librosa.stft(y))
      >>> # Invert using Griffin-Lim
      >>> y_inv = librosa.griffinlim(S)
      >>> # Invert without estimating phase
      >>> y_istft = librosa.istft(S)
  
      Wave-plot the results
  
      >>> import matplotlib.pyplot as plt
      >>> fig, ax = plt.subplots(nrows=3, sharex=True, sharey=True)
      >>> librosa.display.waveshow(y, sr=sr, color='b', ax=ax[0])
      >>> ax[0].set(title='Original', xlabel=None)
      >>> ax[0].label_outer()
      >>> librosa.display.waveshow(y_inv, sr=sr, color='g', ax=ax[1])
      >>> ax[1].set(title='Griffin-Lim reconstruction', xlabel=None)
      >>> ax[1].label_outer()
      >>> librosa.display.waveshow(y_istft, sr=sr, color='r', ax=ax[2])
      >>> ax[2].set_title('Magnitude-only istft reconstruction')
      """
      if random_state is None:
          rng = np.random.default_rng()
      elif isinstance(random_state, int):
          rng = np.random.RandomState(seed=random_state)  # type: ignore
      elif isinstance(
          random_state, (np.random.RandomState, np.random.Generator)
      ):
          rng = random_state  # type: ignore
      else:
          raise ParameterError(
              f"Unsupported random_state={random_state!r}"
          )
  
      if momentum > 1:
          warnings.warn(
              f"Griffin-Lim with momentum={momentum} > 1 can be unstable. "
              "Proceed with caution!",
              stacklevel=2,
          )
      elif momentum < 0:
          raise ParameterError(
              f"griffinlim() called with momentum={momentum} < 0"
          )
  
      # Infer n_fft from the spectrogram shape
      if n_fft is None:
          n_fft = 2 * (S.shape[-2] - 1)
  
      # Infer the dtype from S
      angles = np.empty(S.shape, dtype=util.dtype_r2c(S.dtype))
      eps = util.tiny(angles)
  
      if init == "random":
          # randomly initialize the phase
          angles[:] = util.phasor(
              (2 * np.pi * rng.random(size=S.shape))
          )
      elif init is None:
          # Initialize an all ones complex matrix
          angles[:] = 1.0
      else:
          raise ParameterError(
              f"init={init} must either None or 'random'"
          )
  
      # Place-holders for temporary data and reconstructed buffer
      rebuilt = None
      tprev = None
      inverse = None
  
      # Absorb magnitudes into angles
      angles *= S
      for _ in range(n_iter):
          # Invert with our current estimate of the phases
          inverse = istft(
              angles,
              hop_length=hop_length,
              win_length=win_length,
              n_fft=n_fft,
              window=window,
              center=center,
              dtype=dtype,
              length=length,
              out=inverse,
          )
  
          # Rebuild the spectrogram
          rebuilt = stft(
              inverse,
              n_fft=n_fft,
              hop_length=hop_length,
              win_length=win_length,
              window=window,
              center=center,
              pad_mode=pad_mode,
              out=rebuilt,
          )
  
          # Update our phase estimates
          angles[:] = rebuilt
          if tprev is not None:
              angles -= (momentum / (1 + momentum)) * tprev
          angles /= np.abs(angles) + eps
          angles *= S
          # Store
          rebuilt, tprev = tprev, rebuilt
  
      # Return the final phase estimates
      return istft(
          angles,
          hop_length=hop_length,
          win_length=win_length,
          n_fft=n_fft,
          window=window,
          center=center,
          dtype=dtype,
          length=length,
          out=inverse,
      )
  
imports: from __future__ import annotations
  import warnings
  import numpy
  import scipy
  import scipy.ndimage
  import scipy.signal
  import scipy.interpolate
  from numba import jit
  from .None import convert
  from .fft import get_fftlib
  from .audio import resample
  from .._cache import cache
  from ..None import util
  from ..util.exceptions import ParameterError
  from ..filters import get_window, semitone_filterbank
  from ..filters import window_sumsquare
  from numpy.typing import DTypeLike
  from typing import Any, Callable, Optional, Tuple, List, Union, overload
  from typing_extensions import Literal
  from .._typing import _WindowSpec, _PadMode, _PadModeSTFT, _SequenceLike, _ScalarOrSequence, _ComplexLike_co, _FloatLike_co
label_desc: Use image node_id 32 for calling a global function with example usage: griffinlim(S) and returns: istft