text: #!/usr/bin/env python
  # -*- coding: utf-8 -*-
  """
  Onset detection
  ===============
  .. autosummary::
      :toctree: generated/
  
      onset_detect
      onset_backtrack
      onset_strength
      onset_strength_multi
  """
  
  import numpy as np
  import scipy
  
  from ._cache import cache
  from . import core
  from . import util
  from .util.exceptions import ParameterError
  
  from .feature.spectral import melspectrogram
  
  __all__ = ['onset_detect',
             'onset_strength',
             'onset_strength_multi',
             'onset_backtrack']
  
  
  def onset_detect(y=None, sr=22050, onset_envelope=None, hop_length=512,
                   backtrack=False, energy=None,
                   units='frames', **kwargs):
      """Basic onset detector.  Locate note onset events by picking peaks in an
      onset strength envelope.
  
      The `peak_pick` parameters were chosen by large-scale hyper-parameter
      optimization over the dataset provided by [1]_.
  
      .. [1] https://github.com/CPJKU/onset_db
  
  
      Parameters
      ----------
      y          : np.ndarray [shape=(n,)]
          audio time series
  
      sr         : number > 0 [scalar]
          sampling rate of `y`
  
      onset_envelope     : np.ndarray [shape=(m,)]
          (optional) pre-computed onset strength envelope
  
      hop_length : int > 0 [scalar]
          hop length (in samples)
  
      units : {'frames', 'samples', 'time'}
          The units to encode detected onset events in.
          By default, 'frames' are used.
  
      backtrack : bool
          If `True`, detected onset events are backtracked to the nearest
          preceding minimum of `energy`.
  
          This is primarily useful when using onsets as slice points for segmentation.
  
      energy : np.ndarray [shape=(m,)] (optional)
          An energy function to use for backtracking detected onset events.
          If none is provided, then `onset_envelope` is used.
  
      kwargs : additional keyword arguments
          Additional parameters for peak picking.
  
          See `librosa.util.peak_pick` for details.
  
  
      Returns
      -------
  
      onsets : np.ndarray [shape=(n_onsets,)]
          estimated positions of detected onsets, in whichever units
          are specified.  By default, frame indices.
  
          .. note::
              If no onset strength could be detected, onset_detect returns
              an empty list.
  
  
      Raises
      ------
      ParameterError
          if neither `y` nor `onsets` are provided
  
          or if `units` is not one of 'frames', 'samples', or 'time'
  
      See Also
      --------
      onset_strength : compute onset strength per-frame
      onset_backtrack : backtracking onset events
      librosa.util.peak_pick : pick peaks from a time series
  
  
      Examples
      --------
      Get onset times from a signal
  
      >>> y, sr = librosa.load(librosa.util.example_audio_file(),
      ...                      offset=30, duration=2.0)
      >>> onset_frames = librosa.onset.onset_detect(y=y, sr=sr)
      >>> librosa.frames_to_time(onset_frames, sr=sr)
      array([ 0.07 ,  0.395,  0.511,  0.627,  0.766,  0.975,
              1.207,  1.324,  1.44 ,  1.788,  1.881])
  
      Or use a pre-computed onset envelope
  
      >>> o_env = librosa.onset.onset_strength(y, sr=sr)
      >>> times = librosa.frames_to_time(np.arange(len(o_env)), sr=sr)
      >>> onset_frames = librosa.onset.onset_detect(onset_envelope=o_env, sr=sr)
  
  
      >>> import matplotlib.pyplot as plt
      >>> D = np.abs(librosa.stft(y))
      >>> plt.figure()
      >>> ax1 = plt.subplot(2, 1, 1)
      >>> librosa.display.specshow(librosa.amplitude_to_db(D, ref=np.max),
      ...                          x_axis='time', y_axis='log')
      >>> plt.title('Power spectrogram')
      >>> plt.subplot(2, 1, 2, sharex=ax1)
      >>> plt.plot(times, o_env, label='Onset strength')
      >>> plt.vlines(times[onset_frames], 0, o_env.max(), color='r', alpha=0.9,
      ...            linestyle='--', label='Onsets')
      >>> plt.axis('tight')
      >>> plt.legend(frameon=True, framealpha=0.75)
  
      """
  
      # First, get the frame->beat strength profile if we don't already have one
      if onset_envelope is None:
          if y is None:
              raise ParameterError('y or onset_envelope must be provided')
  
          onset_envelope = onset_strength(y=y, sr=sr, hop_length=hop_length)
  
      # Shift onset envelope up to be non-negative
      # (a common normalization step to make the threshold more consistent)
      onset_envelope -= onset_envelope.min()
  
      # Do we have any onsets to grab?
      if not onset_envelope.any():
          return np.array([], dtype=np.int)
  
      # Normalize onset strength function to [0, 1] range
      onset_envelope /= onset_envelope.max()
  
      # These parameter settings found by large-scale search
      kwargs.setdefault('pre_max', 0.03*sr//hop_length)       # 30ms
      kwargs.setdefault('post_max', 0.00*sr//hop_length + 1)  # 0ms
      kwargs.setdefault('pre_avg', 0.10*sr//hop_length)       # 100ms
      kwargs.setdefault('post_avg', 0.10*sr//hop_length + 1)  # 100ms
      kwargs.setdefault('wait', 0.03*sr//hop_length)          # 30ms
      kwargs.setdefault('delta', 0.07)
  
      # Peak pick the onset envelope
      onsets = util.peak_pick(onset_envelope, **kwargs)
  
      # Optionally backtrack the events
      if backtrack:
          if energy is None:
              energy = onset_envelope
  
          onsets = onset_backtrack(onsets, energy)
  
      if units == 'frames':
          pass
      elif units == 'samples':
          onsets = core.frames_to_samples(onsets, hop_length=hop_length)
      elif units == 'time':
          onsets = core.frames_to_time(onsets, hop_length=hop_length, sr=sr)
      else:
          raise ParameterError('Invalid unit type: {}'.format(units))
  
      return onsets
  
  
  def onset_strength(y=None, sr=22050, S=None, lag=1, max_size=1,
                     ref=None,
                     detrend=False, center=True,
                     feature=None, aggregate=None,
                     centering=None,
                     **kwargs):
      """Compute a spectral flux onset strength envelope.
  
      Onset strength at time `t` is determined by:
  
      `mean_f max(0, S[f, t] - ref[f, t - lag])`
  
      where `ref` is `S` after local max filtering along the frequency
      axis [1]_.
  
      By default, if a time series `y` is provided, S will be the
      log-power Mel spectrogram.
  
      .. [1] Böck, Sebastian, and Gerhard Widmer.
             "Maximum filter vibrato suppression for onset detection."
             16th International Conference on Digital Audio Effects,
             Maynooth, Ireland. 2013.
  
      Parameters
      ----------
      y        : np.ndarray [shape=(n,)]
          audio time-series
  
      sr       : number > 0 [scalar]
          sampling rate of `y`
  
      S        : np.ndarray [shape=(d, m)]
          pre-computed (log-power) spectrogram
  
      lag      : int > 0
          time lag for computing differences
  
      max_size : int > 0
          size (in frequency bins) of the local max filter.
          set to `1` to disable filtering.
  
      ref : None or np.ndarray [shape=(d, m)]
          An optional pre-computed reference spectrum, of the same shape as `S`.
          If not provided, it will be computed from `S`.
          If provided, it will override any local max filtering governed by `max_size`.
  
      detrend : bool [scalar]
          Filter the onset strength to remove the DC component
  
      center : bool [scalar]
          Shift the onset function by `n_fft / (2 * hop_length)` frames
  
      feature : function
          Function for computing time-series features, eg, scaled spectrograms.
          By default, uses `librosa.feature.melspectrogram` with `fmax=11025.0`
  
      aggregate : function
          Aggregation function to use when combining onsets
          at different frequency bins.
  
          Default: `np.mean`
  
      kwargs : additional keyword arguments
          Additional parameters to `feature()`, if `S` is not provided.
  
  
      Returns
      -------
      onset_envelope   : np.ndarray [shape=(m,)]
          vector containing the onset strength envelope
  
  
      Raises
      ------
      ParameterError
          if neither `(y, sr)` nor `S` are provided
  
          or if `lag` or `max_size` are not positive integers
  
  
      See Also
      --------
      onset_detect
      onset_strength_multi
  
  
      Examples
      --------
      First, load some audio and plot the spectrogram
  
      >>> import matplotlib.pyplot as plt
      >>> y, sr = librosa.load(librosa.util.example_audio_file(),
      ...                      duration=10.0)
      >>> D = np.abs(librosa.stft(y))
      >>> times = librosa.frames_to_time(np.arange(D.shape[1]))
      >>> plt.figure()
      >>> ax1 = plt.subplot(2, 1, 1)
      >>> librosa.display.specshow(librosa.amplitude_to_db(D, ref=np.max),
      ...                          y_axis='log', x_axis='time')
      >>> plt.title('Power spectrogram')
  
      Construct a standard onset function
  
      >>> onset_env = librosa.onset.onset_strength(y=y, sr=sr)
      >>> plt.subplot(2, 1, 2, sharex=ax1)
      >>> plt.plot(times, 2 + onset_env / onset_env.max(), alpha=0.8,
      ...          label='Mean (mel)')
  
  
      Median aggregation, and custom mel options
  
      >>> onset_env = librosa.onset.onset_strength(y=y, sr=sr,
      ...                                          aggregate=np.median,
      ...                                          fmax=8000, n_mels=256)
      >>> plt.plot(times, 1 + onset_env / onset_env.max(), alpha=0.8,
      ...          label='Median (custom mel)')
  
  
      Constant-Q spectrogram instead of Mel
  
      >>> onset_env = librosa.onset.onset_strength(y=y, sr=sr,
      ...                                          feature=librosa.cqt)
      >>> plt.plot(times, onset_env / onset_env.max(), alpha=0.8,
      ...          label='Mean (CQT)')
      >>> plt.legend(frameon=True, framealpha=0.75)
      >>> plt.ylabel('Normalized strength')
      >>> plt.yticks([])
      >>> plt.axis('tight')
      >>> plt.tight_layout()
  
      """
  
      if aggregate is False:
          raise ParameterError('aggregate={} cannot be False when computing full-spectrum onset strength.')
  
      odf_all = onset_strength_multi(y=y,
                                     sr=sr,
                                     S=S,
                                     lag=lag,
                                     max_size=max_size,
                                     ref=ref,
                                     detrend=detrend,
                                     center=center,
                                     feature=feature,
                                     aggregate=aggregate,
                                     channels=None,
                                     **kwargs)
  
      return odf_all[0]
  
  
  def onset_backtrack(events, energy):
      '''Backtrack detected onset events to the nearest preceding local
      minimum of an energy function.
  
      This function can be used to roll back the timing of detected onsets
      from a detected peak amplitude to the preceding minimum.
  
      This is most useful when using onsets to determine slice points for
      segmentation, as described by [1]_.
  
      .. [1] Jehan, Tristan.
             "Creating music by listening"
             Doctoral dissertation
             Massachusetts Institute of Technology, 2005.
  
      Parameters
      ----------
      events : np.ndarray, dtype=int
          List of onset event frame indices, as computed by `onset_detect`
  
      energy : np.ndarray, shape=(m,)
          An energy function
  
      Returns
      -------
      events_backtracked : np.ndarray, shape=events.shape
          The input events matched to nearest preceding minima of `energy`.
  
      Examples
      --------
      >>> y, sr = librosa.load(librosa.util.example_audio_file(),
      ...                      offset=30, duration=2.0)
      >>> oenv = librosa.onset.onset_strength(y=y, sr=sr)
      >>> # Detect events without backtracking
      >>> onset_raw = librosa.onset.onset_detect(onset_envelope=oenv,
      ...                                        backtrack=False)
      >>> # Backtrack the events using the onset envelope
      >>> onset_bt = librosa.onset.onset_backtrack(onset_raw, oenv)
      >>> # Backtrack the events using the RMS values
      >>> rms = librosa.feature.rms(S=np.abs(librosa.stft(y=y)))
      >>> onset_bt_rms = librosa.onset.onset_backtrack(onset_raw, rms[0])
  
      >>> # Plot the results
      >>> import matplotlib.pyplot as plt
      >>> plt.figure()
      >>> plt.subplot(2,1,1)
      >>> plt.plot(oenv, label='Onset strength')
      >>> plt.vlines(onset_raw, 0, oenv.max(), label='Raw onsets')
      >>> plt.vlines(onset_bt, 0, oenv.max(), label='Backtracked', color='r')
      >>> plt.legend(frameon=True, framealpha=0.75)
      >>> plt.subplot(2,1,2)
      >>> plt.plot(rms[0], label='RMS')
      >>> plt.vlines(onset_bt_rms, 0, rms.max(), label='Backtracked (RMS)', color='r')
      >>> plt.legend(frameon=True, framealpha=0.75)
      '''
  
      # Find points where energy is non-increasing
      # all points:  energy[i] <= energy[i-1]
      # tail points: energy[i] < energy[i+1]
      minima = np.flatnonzero((energy[1:-1] <= energy[:-2]) &
                              (energy[1:-1] < energy[2:]))
  
      # Pad on a 0, just in case we have onsets with no preceding minimum
      # Shift by one to account for slicing in minima detection
      minima = util.fix_frames(1 + minima, x_min=0)
  
      # Only match going left from the detected events
      return minima[util.match_events(events, minima, right=False)]
  
  
  @cache(level=30)
  def onset_strength_multi(y=None, sr=22050, S=None, lag=1, max_size=1,
                           ref=None, detrend=False, center=True, feature=None,
                           aggregate=None, channels=None, **kwargs):
      """Compute a spectral flux onset strength envelope across multiple channels.
  
      Onset strength for channel `i` at time `t` is determined by:
  
      `mean_{f in channels[i]} max(0, S[f, t+1] - S[f, t])`
  
  
      Parameters
      ----------
      y        : np.ndarray [shape=(n,)]
          audio time-series
  
      sr       : number > 0 [scalar]
          sampling rate of `y`
  
      S        : np.ndarray [shape=(d, m)]
          pre-computed (log-power) spectrogram
  
      lag      : int > 0
          time lag for computing differences
  
      max_size : int > 0
          size (in frequency bins) of the local max filter.
          set to `1` to disable filtering.
  
      ref : None or np.ndarray [shape=(d, m)]
          An optional pre-computed reference spectrum, of the same shape as `S`.
          If not provided, it will be computed from `S`.
          If provided, it will override any local max filtering governed by `max_size`.
  
      detrend : bool [scalar]
          Filter the onset strength to remove the DC component
  
      center : bool [scalar]
          Shift the onset function by `n_fft / (2 * hop_length)` frames
  
      feature : function
          Function for computing time-series features, eg, scaled spectrograms.
          By default, uses `librosa.feature.melspectrogram` with `fmax=11025.0`
  
      aggregate : function or False
          Aggregation function to use when combining onsets
          at different frequency bins.
  
          If `False`, then no aggregation is performed.
  
          Default: `np.mean`
  
      channels : list or None
          Array of channel boundaries or slice objects.
          If `None`, then a single channel is generated to span all bands.
  
      kwargs : additional keyword arguments
          Additional parameters to `feature()`, if `S` is not provided.
  
  
      Returns
      -------
      onset_envelope   : np.ndarray [shape=(n_channels, m)]
          array containing the onset strength envelope for each specified channel
  
  
      Raises
      ------
      ParameterError
          if neither `(y, sr)` nor `S` are provided
  
  
      See Also
      --------
      onset_strength
  
      Notes
      -----
      This function caches at level 30.
  
      Examples
      --------
      First, load some audio and plot the spectrogram
  
      >>> import matplotlib.pyplot as plt
      >>> y, sr = librosa.load(librosa.util.example_audio_file(),
      ...                      duration=10.0)
      >>> D = np.abs(librosa.stft(y))
      >>> plt.figure()
      >>> plt.subplot(2, 1, 1)
      >>> librosa.display.specshow(librosa.amplitude_to_db(D, ref=np.max),
      ...                          y_axis='log')
      >>> plt.title('Power spectrogram')
  
      Construct a standard onset function over four sub-bands
  
      >>> onset_subbands = librosa.onset.onset_strength_multi(y=y, sr=sr,
      ...                                                     channels=[0, 32, 64, 96, 128])
      >>> plt.subplot(2, 1, 2)
      >>> librosa.display.specshow(onset_subbands, x_axis='time')
      >>> plt.ylabel('Sub-bands')
      >>> plt.title('Sub-band onset strength')
  
      """
  
      if feature is None:
          feature = melspectrogram
          kwargs.setdefault('fmax', 11025.0)
  
      if aggregate is None:
          aggregate = np.mean
  
      if lag < 1 or not isinstance(lag, int):
          raise ParameterError('lag must be a positive integer')
  
      if max_size < 1 or not isinstance(max_size, int):
          raise ParameterError('max_size must be a positive integer')
  
      # First, compute mel spectrogram
      if S is None:
          S = np.abs(feature(y=y, sr=sr, **kwargs))
  
          # Convert to dBs
          S = core.power_to_db(S)
  
      # Retrieve the n_fft and hop_length,
      # or default values for onsets if not provided
      n_fft = kwargs.get('n_fft', 2048)
      hop_length = kwargs.get('hop_length', 512)
  
      # Ensure that S is at least 2-d
      S = np.atleast_2d(S)
  
      # Compute the reference spectrogram.
      # Efficiency hack: skip filtering step and pass by reference
      # if max_size will produce a no-op.
      if ref is None:
          if max_size == 1:
              ref = S
          else:
              ref = scipy.ndimage.maximum_filter1d(S, max_size, axis=0)
      elif ref.shape != S.shape:
          raise ParameterError('Reference spectrum shape {} must match input spectrum {}'.format(ref.shape, S.shape))
  
      # Compute difference to the reference, spaced by lag
      onset_env = S[:, lag:] - ref[:, :-lag]
  
      # Discard negatives (decreasing amplitude)
      onset_env = np.maximum(0.0, onset_env)
  
      # Aggregate within channels
      pad = True
      if channels is None:
          channels = [slice(None)]
      else:
          pad = False
  
      if aggregate:
          onset_env = util.sync(onset_env, channels,
                                aggregate=aggregate,
                                pad=pad, axis=0)
  
      # compensate for lag
      pad_width = lag
      if center:
          # Counter-act framing effects. Shift the onsets by n_fft / hop_length
          pad_width += n_fft // (2 * hop_length)
  
      onset_env = np.pad(onset_env, ([0, 0], [int(pad_width), 0]),
                         mode='constant')
  
      # remove the DC component
      if detrend:
          onset_env = scipy.signal.lfilter([1.0, -1.0], [1.0, -0.99],
                                           onset_env, axis=-1)
  
      # Trim to match the input duration
      if center:
          onset_env = onset_env[:, :S.shape[1]]
  
      return onset_env
  