.. currentmodule:: brian

.. index::
   pair: example usage; Sound
   pair: example usage; MiddleEar
   pair: example usage; sqrt
   pair: example usage; set_default_samplerate

.. _example-hears-tan_carney_2003_tan_carney_Fig7:

Example: tan_carney_Fig7 (hears/tan_carney_2003)
================================================

CF-dependence of compressive nonlinearity in the Tan&Carney model.
Reproduces Fig. 7 from:

Tan, Q., and L. H. Carney.
    "A Phenomenological Model for the Responses of Auditory-nerve Fibers.
    II. Nonlinear Tuning with a Frequency Glide".
    The Journal of the Acoustical Society of America 114 (2003): 2007.

::

    
    import itertools
    
    import numpy as np
    import matplotlib.pyplot as plt
    from scipy.interpolate import interp1d
    
    from brian import *
    #set_global_preferences(useweave=True)
    from brian.hears import *
    from brian.hears.filtering.tan_carney import TanCarneySignal, MiddleEar
    
    samplerate = 50*kHz
    set_default_samplerate(samplerate)
    duration = 50*ms
    
    def gen_tone(freq, level):
        ''' 
        Little helper function to generate a pure tone at frequency `freq` with
        the given `level`. The tone has a duration of 50ms and is ramped with
        two ramps of 2.5ms.
        '''
        freq = float(freq) * Hz
        level = float(level) * dB    
        return tone(freq, duration).ramp(when='both',
                                         duration=2.5*ms,
                                         inplace=False).atlevel(level)
    
    freqs = [500, 1100, 2000, 4000]
    levels = np.arange(-10, 100.1, 5)
    cf_level = list(itertools.product(freqs, levels))
    
    # steady-state
    start = 10*ms*samplerate
    end = 45*ms*samplerate
    
    # For Figure 7 we have manually adjusts the gain for different CFs -- otherwise
    # the RMS values wouldn't be identical for low CFs. Therefore, try to estimate
    # suitable gain values first using the lowest CF as a reference
    ref_tone = gen_tone(freqs[0], levels[0])
    F_out_reference = TanCarneySignal(MiddleEar(ref_tone, gain=1), freqs[0],
                                      update_interval=1).process().flatten()
    
    ref_rms = np.sqrt(np.mean((F_out_reference[start:end] -
                               np.mean(F_out_reference[start:end]))**2))
    
    gains = np.linspace(0.1, 1, 50) # for higher CFs we need lower gains
    cf_gains = list(itertools.product(freqs[1:], gains))
    tones = Sound([gen_tone(freq, levels[0]) for freq, _ in cf_gains])
    F_out_test = TanCarneySignal(MiddleEar(tones, gain=np.array([g for _, g in cf_gains])),
                                 [cf for cf,_  in cf_gains], update_interval=1).process()
    
    reshaped_Fout = F_out_test.T.reshape((len(freqs[1:]), len(gains), -1))
    rms = np.sqrt(np.mean((reshaped_Fout[:, :, start:end].T -
                           np.mean(reshaped_Fout[:, :, start:end], axis=2).T).T**2,
                           axis=2))
    
    # get the best gain for each CF using simple linear interpolation
    gain_dict = {freqs[0]: 1.} # reference gain
    for idx, freq in enumerate(freqs[1:]):
        gain_dict[freq] = interp1d(rms[idx, :], gains)(ref_rms)
    
    # now do the real test: tones at different levels for different CFs
    tones = Sound([gen_tone(freq, level) for freq, level in cf_level])
    F_out = TanCarneySignal(MiddleEar(tones,
                                      gain=np.array([gain_dict[cf] for cf, _ in cf_level])),
                            [cf for cf, _ in cf_level],
                            update_interval=1).process()
    
    reshaped_Fout = F_out.T.reshape((len(freqs), len(levels), -1))
    
    rms = np.sqrt(np.mean((reshaped_Fout[:, :, start:end].T -
                          np.mean(reshaped_Fout[:, :, start:end], axis=2).T).T**2,
                          axis=2))
    
    # This should more or less reproduce Fig. 7
    plt.plot(levels, rms.T)
    plt.legend(['%.0f Hz' % cf for cf in freqs], 0)
    plt.xlim(-20, 100)
    plt.ylim(1e-6, 1)
    plt.yscale('log')
    plt.xlabel('input signal SPL (dB)')
    plt.ylabel('rms of AC component of Fout')
    plt.show()