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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def validate(ref_intervals, ref_pitches, ref_velocities, est_intervals, est_pitches, est_velocities):
 """Checks that the input annotations have valid time intervals, pitches, and velocities, and throws helpful errors if not. Parameters ref_intervals : np.ndarray, shape=(n,2) Array of reference notes time intervals (onset and offset times) ref_pitches : np.ndarray, shape=(n,) Array of reference pitch values in Hertz ref_velocities : np.ndarray, shape=(n,) Array of MIDI velocities (i.e. between 0 and 127) of reference notes est_intervals : np.ndarray, shape=(m,2) Array of estimated notes time intervals (onset and offset times) est_pitches : np.ndarray, shape=(m,) Array of estimated pitch values in Hertz est_velocities : np.ndarray, shape=(m,) Array of MIDI velocities (i.e. between 0 and 127) of estimated notes """

    transcription.validate(ref_intervals, ref_pitches, est_intervals,
                           est_pitches)
    # Check that velocities have the same length as intervals/pitches
    if not ref_velocities.shape[0] == ref_pitches.shape[0]:
        raise ValueError('Reference velocities must have the same length as '
                         'pitches and intervals.')
    if not est_velocities.shape[0] == est_pitches.shape[0]:
        raise ValueError('Estimated velocities must have the same length as '
                         'pitches and intervals.')
    # Check that the velocities are positive
    if ref_velocities.size > 0 and np.min(ref_velocities) < 0:
        raise ValueError('Reference velocities must be positive.')
    if est_velocities.size > 0 and np.min(est_velocities) < 0:
        raise ValueError('Estimated velocities must be positive.')