from __future__ import print_function

# Copyright (c) 2013, <NAME>
# All rights reserved.

import warnings

import numpy as np
from scipy.signal import decimate, lfilter, buttord, butter, \
                         BadCoefficients, lti

from undaqTools.misc.burg import arburg
from undaqTools.misc.cdf import percentile

warnings.filterwarnings('ignore',category=BadCoefficients)

class SteeringEntropyModel:
    def __init__(self, **kwds):
        """
        SteeringEntropyModel(**kwds)
        
        Steering Entropy Model as described by Boer, Rakauskas, Ward, and
        Goodrich (2005).

        Model is calibrated to the unique spectral characteristics of the
        driver. This makes it sensitive to a variety of coping strategies
        employed by drivers in response to increased workload demands.

        A model should be built for each participant. A baseline segment
        of steering angle data is needed to fit the model via the baseline
        method. This segment of data should be at least 2 minutes.
        baseline() will raise an exception if less than 1 minute of data
        is supplied.

        Parameters
        ----------
        resample_fs : float, optional
            Rate in Hz to resample input data. Default is 4. According to
            Borg et al. this rate is optimizes the senstivity of the
            entropy estimates.

        alpha : float, optional
            controls the spacing of the bins used to estimate the
            prediction errors distribution. Must be between 0-1. The
            default value is 0.2. According to Borg et al. this rate
            is optimizes the senstivity of the entropy estimates.

        M : int, optional
            Controls the number of bins used to estimate the prediction
            errors distribution. Number of bins is 2*M + 2. Default is 6
            (resulting in 14 bins). This is set to avoid having an
            excess of empty counts when the data set is small. 

        b_pe : array, optional
            AR coefficients
            (initialized when fit_baseline is called)

        pkbas : array, optional
            baseline prediction error density coefficients
            cooresponding to bins (initialized when fit_baseline is called)
            

        bin_edges : array, optional
            baseline prediction error density bin edges corresponding
            to pkbas (initialized when fit_baseline is called)

            len(bins) == len(pkbas) + 1
            

        hbas : float, optional
            baseline entropy estimate (initialized when fit_baseline is called)

        cdf : CDF, optional
            Object holding the cumulative density function data of the
            baseline prediction errors. Used to build bins.
            (initialized when fit_baseline is called)

        Example
        -------
        >>> se_model = SteeringEntropyModel()
        >>> baseline_entropy = se_model.fit_baseline(baseline_steering_data)
        >>> task_entropy = se_model.get_entropy(task_steering_data)
        
        References
        ----------
        <NAME>., <NAME>., <NAME>., and <NAME>.
            (2005). Steering Entropy Revisited.  Proceedings of the
            Third International Driving Symposium on Human Factors in
            Driver Assessment, Training and Vehicle Design.  June 27-30,
            2005.  Rockport, Maine.

        <NAME>., Behavioral entropy as an index of workload
            Proceedings of the IEA 2000 /  HFES 2000 Congress.

        <NAME>., <NAME>., <NAME>., and <NAME>.,
            Development of a steering entropy method for evaluating
            driver workload. SAE Technical Paper Series #1999-01-0892.
            Presented at the International Congress and Exposition,
            Detriot, Michigan. March 1-4, 1999.

        Notes
        -----

        Expecting data to be in degrees. It may not matter but small
        values will sometimes cause overflow errors in arburg. If you
        your steering data is in radians it might be better to convert
        it to degrees.
        
        Loosely based off of Chris' SteeringEntropy.m script in ndaqTools.
        Users familiar with ndaqTools should note that the steeringentropy
        function in ndaqTools (Chris' matlab) uses the first 60 s to find
        the AR coeffs and the second 60 s to find baseline prediction error
        distribution. This module splits the baseline data in half. This
        class applies a 5th order lowpass to 3/7 the resample_fs as
        suggested by Boer et al. before resampling. The ndaqTools algorithm
        just applies an integer factor downsample. Because of these slight
        differences entropy estimates may differ.
        """
        self.resample_fs = kwds.get('resample_fs', 4.)
        self.alpha = kwds.get('alpha', 0.2)
        self.M = kwds.get('M', 6)
        self.b_pe = kwds.get('b_pe', None)
        self.pkbas = kwds.get('pkbas', None)
        self.bin_edges = kwds.get('bin_edges', None)
        self.hbas = kwds.get('hbas', None)
        self.cdf = kwds.get('cdf', None)

    def _build_lpfilter(self, fs):
        """
        builds low-pass filter with a cutoff frequency of 3/7th the resample
        frequency. The filter should be down 40 dB at 1.5 times the cutoff
        frequency (6/7th) the resample frequency.

        Parameters
        ----------
        fs : the base sampling rate

        Returns
        -------
        b, a : array_like
            Numerator (b) and denominator (a) polynomials of the IIR filter. 
        """
        nyq = fs/2. # nyquist frequency
        cutoff = (3./7.)*self.resample_fs # cutoff freq defined by Boer
        wp = cutoff * nyq # pass edge freq (pi radians / sample)
        ws = wp*2.        # pass edge freq (pi radians / sample)
        gpass = 1.5       # The maximum loss in the passband (dB)
        gstop = 40        # The minimum attenuation in the stopband (dB)
        n, wn = buttord(wp, ws, gpass, gstop)
        #print('n =',n,'wn =',wn)
        b, a = butter(n, wn, analog=True)

        return b, a
        
    def _resample(self, x, fs):
        """
        Private method applies 5th low-pass Butterworth filter to x
        and resamples and returns x at self.resample_fs.

        Parameters
        ----------
        x : array_like
            Input data.
        fs : float
            sampling rate of x in Hz
        
        Returns
        -------
        x_resampled : np.ndarray
            low-passed and resampled copy of x
        """
        b,a = self._build_lpfilter(fs)
        return decimate(lfilter(b, a, x).real, int(fs/self.resample_fs))
        
    def fit_baseline(self, x, fs=60., _tsplot=False):
        """
        fit_baseline(self, x[, fs=60.][, _tsplot=False])

        Finds AR coefficients to build prediction errors and estimates baseline
        prediction errors distribution. Returns the baseline entropy.

        Parameters
        ----------
        x : array_like
            Input data. Should specify steering wheel angle over at least 120 s.
            x[:N/2] is used to find the AR coefficients.
            x[N/2:] is used to build the baseline prediciton error distribution.
            
        fs : float
            sampling rate of x in Hz. Default is 60 Hz. Be sure to specify fs if
            x was not sampled at 60 Hz.

        Returns
        -------
        hbas : float
            baseline entropy
        """
        
        # unpack relevant parameters
        N = len(x)
        M = self.M
        alpha = self.alpha
        resample_fs = self.resample_fs
        
        # apply LP and downsample signal
        _x = self._resample(x, fs)
        Nx = len(_x)
        
        if len(_x) < resample_fs * 60:
            raise Exception('Need at least 60 seconds of steering '
                            'data to calculate baseline\n(ideally '
                            'need ~ 120 seconds of data).')
        
        # use first half of x to find coefficients of AR model
        # using Burg's method
        #
        # sign on coeffs returned by arburg is reversed
        b_pe = arburg(_x[:Nx/2], 3)
        
        # use second half of x to calculate baseline entropy
        # use AR coefficents to build prediction errors
        PE = lfilter(b_pe, 1, _x[Nx/2:])

        # need to build bins to approximate the PE distribution
        cdf = percentile(PE) # cdf is a CDF object
        pe_alpha = 0.5*(abs(cdf.find(alpha)) + abs(cdf.find(1.-alpha)))
        bin_edges = [-10e12]+list(np.linspace(-M, M, 2*M+1)*pe_alpha)+[10e12]

        # now we can calculate the baseline entropy
        # np.histogram returns a tuple of histogram counts and bin_edges
        Pk = np.histogram(PE, bins=bin_edges)[0]/float(len(PE))
        
        # replace small values to avoid excessively high entropy
        Pk[Pk < 1e-3] = 1e-3
        
        # and the baseline entropy is
        hbas = np.sum(np.multiply(-Pk, np.log2(Pk)))

        # store the relevant information
        self.bin_edges = bin_edges
        self.b_pe = b_pe
        self.cdf = cdf
        self.pkbas = Pk
        self.hbas = hbas

        if _tsplot:
            return hbas, self._baseline_tsplot(x[N/2:], _x[Nx/2:], PE, fs)

        return hbas
        
    def get_entropy(self, x, fs=60., _pedistplot=False):
        """
        get_entropy(self, x[, fs=60.][, _pedistplot=False])

        Returns steering entropy from given data vector. Specify fs if not
        collected at 60 Hz.

        Parameters
        ----------
        x : array_like
            Input data. Should specify steering wheel angle over at least 60 s
            
        fs : float
            sampling rate of x in Hz. Default is 60 Hz.
            Be sure to specify fs if x was not sampled at 60 Hz.

        Returns
        -------
        hbas : float
            baseline entropy
        """
        bin_edges = self.bin_edges
        pkbas = self.pkbas
        b_pe = self.b_pe

        if not x: # x is empty
            return 0.
        
        if b_pe is None:
            raise Exception('must first find build baseline AR model')

        # apply LP and downsample signal
        _x = self._resample(x, fs)
        
        # Use AR coefficents to build prediction errors
        PE = lfilter(self.b_pe, 1, _x)
        
        # Calculate and entropy
        Pk = np.histogram(PE, bins=bin_edges)[0]/float(len(PE))
        Pk[Pk < 1e-3] = 1e-3
        h = np.sum(np.multiply(-Pk, np.log2(pkbas)))
        
        if _pedistplot:
            return h, self._pedistplot(Pk)
        
        return h

    def _lpfilter_bode(self):
        """
        returns bode plot of the lp filter applied before downsampling
        
        Parameters
        ----------
        None
        
        Returns
        -------
        fig : matplotlib.figure.Figure
        """

        b, a = self._build_lpfilter(60.)        
        w, mag, phase = lti(b,a).bode()

        import matplotlib.pyplot as plt        
        plt.rc('font', family='serif')
        fig = plt.figure(figsize=(6,6))
        fig.subplots_adjust(bottom=.125, top=.92, right=.95, hspace=0.1)

        xticks = [.01, .03, .1, .3, 1., 3., 10.]
        xlim = [.01, 10.]
        
        # magnitude
        ax1 = fig.add_subplot(211)
        ax1.semilogx(w, mag)
        ax1.set_xlim(xlim)
        ax1.set_xticks(xticks)
        ax1.set_xticklabels(['' for t in xticks])
        ax1.set_ylabel('Gain (db)')
##        ax1.set_title('n = %i, wn = %.6f'%(n, wn) )
        ax1.grid()

        # phase
        ax2 = fig.add_subplot(212)
        ax2.semilogx(w, phase)
        ax2.set_xlim(xlim)
        ax2.set_xticks(xticks)
        ax2.set_xticklabels(['%.3f'%t for t in xticks], rotation=30)
        ax2.set_ylabel('Phase (deg)')
        ax2.set_xlabel('Frequency (Hz)')
        ax2.grid()

        return fig

    def _baseline_tsplot(self, x, _x, PE, fs):
        """
        returns ts plot to fit_baseline so it can be
        returned indirectly to user
        
        Parameters
        ----------
        x : array_like
            unfiltered data
            
        _x : array_like
            lowpassed and downsampled data
        
        PE : array_like
            prediction errors
        
        fs : float
            base sampling rate
        
        Returns
        -------
        fig : matplotlib.figure.Figure
        """
        pe_alpha = self.bin_edges[8] - self.bin_edges[7]
        bin_edges = self.bin_edges
        
        import matplotlib.pyplot as plt        
        plt.rc('font', family='serif')
        fig = plt.figure(figsize=(12, 12*(9/16.)))
        fig.subplots_adjust(left=.07, right=.97, bottom=.03, 
                            top=.96, hspace=0.35)
        
        # unfiltered data
        ax1 = fig.add_subplot(311)
        ax1.plot(x)
        ax1.set_xlim([0, len(x)])
        ax1.set_title('Unfiltered Data')
        ax1.grid()

        # unfiltered data
        ax2 = fig.add_subplot(312)
        ax2.plot(-1*_x)
        ax2.set_xlim([0, len(_x)])
        ax2.set_title('Lowpassed and Downsampled Data')
        ax2.grid()
        
        # phase
        ax3 = fig.add_subplot(313)
        ax3.plot(PE)
        ax3.set_xlim([0, len(PE)])
        ax3.set_yticks(bin_edges[1:-1])
        ax3.set_ylim([bin_edges[2], bin_edges[-2]])
        ax3.set_yticklabels([r'%i$PE(\alpha)$'%i for i in xrange(-6,7)])
        ax3.set_title('Prediction Errors')
        ax3.grid()

        return fig

    def _pedistplot(self, Pk):
        """
        returns plot to get_entropy so it can be
        returned indirectly to user
        """
        pkbas = self.pkbas
        M = self.M
        x = np.linspace(-(M+1), (M+1), 2*(M+1))
        h = np.multiply(-Pk, np.log2(pkbas))
        
        import matplotlib.pyplot as plt        
        plt.rc('font', family='serif')
        
        fig = plt.figure(figsize=(5,5))
        fig.subplots_adjust(left=.12)
        
        ax = fig.add_subplot(111)
        ax.plot(x, pkbas, color= 'b', alpha=.3, label='baseline')
        ax.plot(x, Pk, color= 'g', alpha=.3, label='task')
        ax.plot(x, h, color='r', alpha=.8, label='entropy')
        ax.scatter(x, pkbas, color= 'b', marker='*')
        ax.scatter(x, Pk, color='g', marker='+')
        ax.legend()

        
        return fig
    
    def bode(self):
        """
        returns bode plot of AR coeffs filter

        Parameters
        ----------
        None
        
        Returns
        -------
        fig : matplotlib.figure.Figure
        
        """
        b_pe = self.b_pe
        w, mag, phase = lti(b_pe, [1,1,1,1]).bode()
        w *= (.5*np.pi)
        iend = np.searchsorted(w, self.resample_fs)

        import matplotlib.pyplot as plt        
        plt.rc('font', family='serif')        
        fig = plt.figure(figsize=(6,6))
        fig.subplots_adjust(bottom=.125, top=.95, right=.95, hspace=0.1)

        xticks = [.1, .3, 1., 3., 10.]
        xlim = [.1, 10.]
        
        # magnitude
        ax1 = fig.add_subplot(211)
        ax1.semilogx(w[:iend], mag[:iend])
        ax1.set_xlim(xlim)
        ax1.set_xticks(xticks)
        ax1.set_xticklabels(['' for t in xticks])
        ax1.set_ylabel('Gain (db)')
        ax1.set_title('AR coeffs = [%s]'%' '.join('%.3f'%c for c in b_pe))
        ax1.grid()

        # phase
        ax2 = fig.add_subplot(212)
        ax2.semilogx(w[:iend], phase[:iend])  # Bode phase plot
        ax2.set_xlim(xlim)
        ax2.set_xticks(xticks)
        ax2.set_xticklabels(['%.3f'%t for t in xticks], rotation=30)
        ax2.set_ylabel('Phase (deg)')
        ax2.set_xlabel('Frequency (Hz)')
        ax2.grid()
        
##        # Nakamura et al. (1999) Taylor series coeffs
##        wt, magt, phaset = lti([1,-2.5,2,-.5], [1,1,1,1]).bode()
##        ax1.semilogx(w[:iend], magt[:iend])
##        ax2.semilogx(w[:iend], phaset[:iend])
##        
##        fig.savefig('bode.png')
##        plt.close('all')

        return fig

    def __str__(self):
        return '\n'.join(['b_pe = %s,'%str(self.b_pe),
                          'hbas = %s,'%str(self.hbas),
                          'pkbas = %s'%str(self.pkbas)])

    def __repr__(self):
        st = ('SteeringEntropyModel(resample_fs=%s, alpha=%s, M=%s,'\
                'b_pe=%s, pkbas=%s, bin_edges=%s, hbas=%s, '\
                %(repr(self.resample_fs), repr(self.alpha), repr(self.M),
                  repr(self.b_pe), repr(self.pkbas), repr(self.bin_edges),
                  repr(self.hbas) )).replace('array(','np.array(')

        st += 'cdf=%s)'%repr(self.cdf)

        return st

from __future__ import print_function

# Copyright (c) 2013, <NAME>
# All rights reserved.

import warnings

import numpy as np
from scipy.signal import decimate, lfilter, buttord, butter, \
                         BadCoefficients, lti

from undaqTools.misc.burg import arburg
from undaqTools.misc.cdf import percentile

warnings.filterwarnings('ignore',category=BadCoefficients)

class SteeringEntropyModel:
    def __init__(self, **kwds):
        """
        SteeringEntropyModel(**kwds)
        
        Steering Entropy Model as described by Boer, Rakauskas, Ward, and
        Goodrich (2005).

        Model is calibrated to the unique spectral characteristics of the
        driver. This makes it sensitive to a variety of coping strategies
        employed by drivers in response to increased workload demands.

        A model should be built for each participant. A baseline segment
        of steering angle data is needed to fit the model via the baseline
        method. This segment of data should be at least 2 minutes.
        baseline() will raise an exception if less than 1 minute of data
        is supplied.

        Parameters
        ----------
        resample_fs : float, optional
            Rate in Hz to resample input data. Default is 4. According to
            Borg et al. this rate is optimizes the senstivity of the
            entropy estimates.

        alpha : float, optional
            controls the spacing of the bins used to estimate the
            prediction errors distribution. Must be between 0-1. The
            default value is 0.2. According to Borg et al. this rate
            is optimizes the senstivity of the entropy estimates.

        M : int, optional
            Controls the number of bins used to estimate the prediction
            errors distribution. Number of bins is 2*M + 2. Default is 6
            (resulting in 14 bins). This is set to avoid having an
            excess of empty counts when the data set is small. 

        b_pe : array, optional
            AR coefficients
            (initialized when fit_baseline is called)

        pkbas : array, optional
            baseline prediction error density coefficients
            cooresponding to bins (initialized when fit_baseline is called)
            

        bin_edges : array, optional
            baseline prediction error density bin edges corresponding
            to pkbas (initialized when fit_baseline is called)

            len(bins) == len(pkbas) + 1
            

        hbas : float, optional
            baseline entropy estimate (initialized when fit_baseline is called)

        cdf : CDF, optional
            Object holding the cumulative density function data of the
            baseline prediction errors. Used to build bins.
            (initialized when fit_baseline is called)

        Example
        -------
        >>> se_model = SteeringEntropyModel()
        >>> baseline_entropy = se_model.fit_baseline(baseline_steering_data)
        >>> task_entropy = se_model.get_entropy(task_steering_data)
        
        References
        ----------
        <NAME>., <NAME>., <NAME>., and <NAME>.
            (2005). Steering Entropy Revisited.  Proceedings of the
            Third International Driving Symposium on Human Factors in
            Driver Assessment, Training and Vehicle Design.  June 27-30,
            2005.  Rockport, Maine.

        <NAME>., Behavioral entropy as an index of workload
            Proceedings of the IEA 2000 /  HFES 2000 Congress.

        <NAME>., <NAME>., <NAME>., and <NAME>.,
            Development of a steering entropy method for evaluating
            driver workload. SAE Technical Paper Series #1999-01-0892.
            Presented at the International Congress and Exposition,
            Detriot, Michigan. March 1-4, 1999.

        Notes
        -----

        Expecting data to be in degrees. It may not matter but small
        values will sometimes cause overflow errors in arburg. If you
        your steering data is in radians it might be better to convert
        it to degrees.
        
        Loosely based off of Chris' SteeringEntropy.m script in ndaqTools.
        Users familiar with ndaqTools should note that the steeringentropy
        function in ndaqTools (Chris' matlab) uses the first 60 s to find
        the AR coeffs and the second 60 s to find baseline prediction error
        distribution. This module splits the baseline data in half. This
        class applies a 5th order lowpass to 3/7 the resample_fs as
        suggested by Boer et al. before resampling. The ndaqTools algorithm
        just applies an integer factor downsample. Because of these slight
        differences entropy estimates may differ.
        """
        self.resample_fs = kwds.get('resample_fs', 4.)
        self.alpha = kwds.get('alpha', 0.2)
        self.M = kwds.get('M', 6)
        self.b_pe = kwds.get('b_pe', None)
        self.pkbas = kwds.get('pkbas', None)
        self.bin_edges = kwds.get('bin_edges', None)
        self.hbas = kwds.get('hbas', None)
        self.cdf = kwds.get('cdf', None)

    def _build_lpfilter(self, fs):
        """
        builds low-pass filter with a cutoff frequency of 3/7th the resample
        frequency. The filter should be down 40 dB at 1.5 times the cutoff
        frequency (6/7th) the resample frequency.

        Parameters
        ----------
        fs : the base sampling rate

        Returns
        -------
        b, a : array_like
            Numerator (b) and denominator (a) polynomials of the IIR filter. 
        """
        nyq = fs/2. # nyquist frequency
        cutoff = (3./7.)*self.resample_fs # cutoff freq defined by Boer
        wp = cutoff * nyq # pass edge freq (pi radians / sample)
        ws = wp*2.        # pass edge freq (pi radians / sample)
        gpass = 1.5       # The maximum loss in the passband (dB)
        gstop = 40        # The minimum attenuation in the stopband (dB)
        n, wn = buttord(wp, ws, gpass, gstop)
        #print('n =',n,'wn =',wn)
        b, a = butter(n, wn, analog=True)

        return b, a
        
    def _resample(self, x, fs):
        """
        Private method applies 5th low-pass Butterworth filter to x
        and resamples and returns x at self.resample_fs.

        Parameters
        ----------
        x : array_like
            Input data.
        fs : float
            sampling rate of x in Hz
        
        Returns
        -------
        x_resampled : np.ndarray
            low-passed and resampled copy of x
        """
        b,a = self._build_lpfilter(fs)
        return decimate(lfilter(b, a, x).real, int(fs/self.resample_fs))
        
    def fit_baseline(self, x, fs=60., _tsplot=False):
        """
        fit_baseline(self, x[, fs=60.][, _tsplot=False])

        Finds AR coefficients to build prediction errors and estimates baseline
        prediction errors distribution. Returns the baseline entropy.

        Parameters
        ----------
        x : array_like
            Input data. Should specify steering wheel angle over at least 120 s.
            x[:N/2] is used to find the AR coefficients.
            x[N/2:] is used to build the baseline prediciton error distribution.
            
        fs : float
            sampling rate of x in Hz. Default is 60 Hz. Be sure to specify fs if
            x was not sampled at 60 Hz.

        Returns
        -------
        hbas : float
            baseline entropy
        """
        
        # unpack relevant parameters
        N = len(x)
        M = self.M
        alpha = self.alpha
        resample_fs = self.resample_fs
        
        # apply LP and downsample signal
        _x = self._resample(x, fs)
        Nx = len(_x)
        
        if len(_x) < resample_fs * 60:
            raise Exception('Need at least 60 seconds of steering '
                            'data to calculate baseline\n(ideally '
                            'need ~ 120 seconds of data).')
        
        # use first half of x to find coefficients of AR model
        # using Burg's method
        #
        # sign on coeffs returned by arburg is reversed
        b_pe = arburg(_x[:Nx/2], 3)
        
        # use second half of x to calculate baseline entropy
        # use AR coefficents to build prediction errors
        PE = lfilter(b_pe, 1, _x[Nx/2:])

        # need to build bins to approximate the PE distribution
        cdf = percentile(PE) # cdf is a CDF object
        pe_alpha = 0.5*(abs(cdf.find(alpha)) + abs(cdf.find(1.-alpha)))
        bin_edges = [-10e12]+list(np.linspace(-M, M, 2*M+1)*pe_alpha)+[10e12]

        # now we can calculate the baseline entropy
        # np.histogram returns a tuple of histogram counts and bin_edges
        Pk = np.histogram(PE, bins=bin_edges)[0]/float(len(PE))
        
        # replace small values to avoid excessively high entropy
        Pk[Pk < 1e-3] = 1e-3
        
        # and the baseline entropy is
        hbas = np.sum(np.multiply(-Pk, np.log2(Pk)))

        # store the relevant information
        self.bin_edges = bin_edges
        self.b_pe = b_pe
        self.cdf = cdf
        self.pkbas = Pk
        self.hbas = hbas

        if _tsplot:
            return hbas, self._baseline_tsplot(x[N/2:], _x[Nx/2:], PE, fs)

        return hbas
        
    def get_entropy(self, x, fs=60., _pedistplot=False):
        """
        get_entropy(self, x[, fs=60.][, _pedistplot=False])

        Returns steering entropy from given data vector. Specify fs if not
        collected at 60 Hz.

        Parameters
        ----------
        x : array_like
            Input data. Should specify steering wheel angle over at least 60 s
            
        fs : float
            sampling rate of x in Hz. Default is 60 Hz.
            Be sure to specify fs if x was not sampled at 60 Hz.

        Returns
        -------
        hbas : float
            baseline entropy
        """
        bin_edges = self.bin_edges
        pkbas = self.pkbas
        b_pe = self.b_pe

        if not x: # x is empty
            return 0.
        
        if b_pe is None:
            raise Exception('must first find build baseline AR model')

        # apply LP and downsample signal
        _x = self._resample(x, fs)
        
        # Use AR coefficents to build prediction errors
        PE = lfilter(self.b_pe, 1, _x)
        
        # Calculate and entropy
        Pk = np.histogram(PE, bins=bin_edges)[0]/float(len(PE))
        Pk[Pk < 1e-3] = 1e-3
        h = np.sum(np.multiply(-Pk, np.log2(pkbas)))
        
        if _pedistplot:
            return h, self._pedistplot(Pk)
        
        return h

    def _lpfilter_bode(self):
        """
        returns bode plot of the lp filter applied before downsampling
        
        Parameters
        ----------
        None
        
        Returns
        -------
        fig : matplotlib.figure.Figure
        """

        b, a = self._build_lpfilter(60.)        
        w, mag, phase = lti(b,a).bode()

        import matplotlib.pyplot as plt        
        plt.rc('font', family='serif')
        fig = plt.figure(figsize=(6,6))
        fig.subplots_adjust(bottom=.125, top=.92, right=.95, hspace=0.1)

        xticks = [.01, .03, .1, .3, 1., 3., 10.]
        xlim = [.01, 10.]
        
        # magnitude
        ax1 = fig.add_subplot(211)
        ax1.semilogx(w, mag)
        ax1.set_xlim(xlim)
        ax1.set_xticks(xticks)
        ax1.set_xticklabels(['' for t in xticks])
        ax1.set_ylabel('Gain (db)')
##        ax1.set_title('n = %i, wn = %.6f'%(n, wn) )
        ax1.grid()

        # phase
        ax2 = fig.add_subplot(212)
        ax2.semilogx(w, phase)
        ax2.set_xlim(xlim)
        ax2.set_xticks(xticks)
        ax2.set_xticklabels(['%.3f'%t for t in xticks], rotation=30)
        ax2.set_ylabel('Phase (deg)')
        ax2.set_xlabel('Frequency (Hz)')
        ax2.grid()

        return fig

    def _baseline_tsplot(self, x, _x, PE, fs):
        """
        returns ts plot to fit_baseline so it can be
        returned indirectly to user
        
        Parameters
        ----------
        x : array_like
            unfiltered data
            
        _x : array_like
            lowpassed and downsampled data
        
        PE : array_like
            prediction errors
        
        fs : float
            base sampling rate
        
        Returns
        -------
        fig : matplotlib.figure.Figure
        """
        pe_alpha = self.bin_edges[8] - self.bin_edges[7]
        bin_edges = self.bin_edges
        
        import matplotlib.pyplot as plt        
        plt.rc('font', family='serif')
        fig = plt.figure(figsize=(12, 12*(9/16.)))
        fig.subplots_adjust(left=.07, right=.97, bottom=.03, 
                            top=.96, hspace=0.35)
        
        # unfiltered data
        ax1 = fig.add_subplot(311)
        ax1.plot(x)
        ax1.set_xlim([0, len(x)])
        ax1.set_title('Unfiltered Data')
        ax1.grid()

        # unfiltered data
        ax2 = fig.add_subplot(312)
        ax2.plot(-1*_x)
        ax2.set_xlim([0, len(_x)])
        ax2.set_title('Lowpassed and Downsampled Data')
        ax2.grid()
        
        # phase
        ax3 = fig.add_subplot(313)
        ax3.plot(PE)
        ax3.set_xlim([0, len(PE)])
        ax3.set_yticks(bin_edges[1:-1])
        ax3.set_ylim([bin_edges[2], bin_edges[-2]])
        ax3.set_yticklabels([r'%i$PE(\alpha)$'%i for i in xrange(-6,7)])
        ax3.set_title('Prediction Errors')
        ax3.grid()

        return fig

    def _pedistplot(self, Pk):
        """
        returns plot to get_entropy so it can be
        returned indirectly to user
        """
        pkbas = self.pkbas
        M = self.M
        x = np.linspace(-(M+1), (M+1), 2*(M+1))
        h = np.multiply(-Pk, np.log2(pkbas))
        
        import matplotlib.pyplot as plt        
        plt.rc('font', family='serif')
        
        fig = plt.figure(figsize=(5,5))
        fig.subplots_adjust(left=.12)
        
        ax = fig.add_subplot(111)
        ax.plot(x, pkbas, color= 'b', alpha=.3, label='baseline')
        ax.plot(x, Pk, color= 'g', alpha=.3, label='task')
        ax.plot(x, h, color='r', alpha=.8, label='entropy')
        ax.scatter(x, pkbas, color= 'b', marker='*')
        ax.scatter(x, Pk, color='g', marker='+')
        ax.legend()

        
        return fig
    
    def bode(self):
        """
        returns bode plot of AR coeffs filter

        Parameters
        ----------
        None
        
        Returns
        -------
        fig : matplotlib.figure.Figure
        
        """
        b_pe = self.b_pe
        w, mag, phase = lti(b_pe, [1,1,1,1]).bode()
        w *= (.5*np.pi)
        iend = np.searchsorted(w, self.resample_fs)

        import matplotlib.pyplot as plt        
        plt.rc('font', family='serif')        
        fig = plt.figure(figsize=(6,6))
        fig.subplots_adjust(bottom=.125, top=.95, right=.95, hspace=0.1)

        xticks = [.1, .3, 1., 3., 10.]
        xlim = [.1, 10.]
        
        # magnitude
        ax1 = fig.add_subplot(211)
        ax1.semilogx(w[:iend], mag[:iend])
        ax1.set_xlim(xlim)
        ax1.set_xticks(xticks)
        ax1.set_xticklabels(['' for t in xticks])
        ax1.set_ylabel('Gain (db)')
        ax1.set_title('AR coeffs = [%s]'%' '.join('%.3f'%c for c in b_pe))
        ax1.grid()

        # phase
        ax2 = fig.add_subplot(212)
        ax2.semilogx(w[:iend], phase[:iend])  # Bode phase plot
        ax2.set_xlim(xlim)
        ax2.set_xticks(xticks)
        ax2.set_xticklabels(['%.3f'%t for t in xticks], rotation=30)
        ax2.set_ylabel('Phase (deg)')
        ax2.set_xlabel('Frequency (Hz)')
        ax2.grid()
        
##        # Nakamura et al. (1999) Taylor series coeffs
##        wt, magt, phaset = lti([1,-2.5,2,-.5], [1,1,1,1]).bode()
##        ax1.semilogx(w[:iend], magt[:iend])
##        ax2.semilogx(w[:iend], phaset[:iend])
##        
##        fig.savefig('bode.png')
##        plt.close('all')

        return fig

    def __str__(self):
        return '\n'.join(['b_pe = %s,'%str(self.b_pe),
                          'hbas = %s,'%str(self.hbas),
                          'pkbas = %s'%str(self.pkbas)])

    def __repr__(self):
        st = ('SteeringEntropyModel(resample_fs=%s, alpha=%s, M=%s,'\
                'b_pe=%s, pkbas=%s, bin_edges=%s, hbas=%s, '\
                %(repr(self.resample_fs), repr(self.alpha), repr(self.M),
                  repr(self.b_pe), repr(self.pkbas), repr(self.bin_edges),
                  repr(self.hbas) )).replace('array(','np.array(')

        st += 'cdf=%s)'%repr(self.cdf)

        return st

# Copyright (c) 2013, <NAME> # All rights reserved. SteeringEntropyModel(**kwds)                  Steering Entropy Model as described by Boer, Rakauskas, Ward, and         Goodrich (2005).          Model is calibrated to the unique spectral characteristics of the         driver. This makes it sensitive to a variety of coping strategies         employed by drivers in response to increased workload demands.          A model should be built for each participant. A baseline segment         of steering angle data is needed to fit the model via the baseline         method. This segment of data should be at least 2 minutes.         baseline() will raise an exception if less than 1 minute of data         is supplied.          Parameters         ----------         resample_fs : float, optional             Rate in Hz to resample input data. Default is 4. According to             Borg et al. this rate is optimizes the senstivity of the             entropy estimates.          alpha : float, optional             controls the spacing of the bins used to estimate the             prediction errors distribution. Must be between 0-1. The             default value is 0.2. According to Borg et al. this rate             is optimizes the senstivity of the entropy estimates.          M : int, optional             Controls the number of bins used to estimate the prediction             errors distribution. Number of bins is 2*M + 2. Default is 6             (resulting in 14 bins). This is set to avoid having an             excess of empty counts when the data set is small.           b_pe : array, optional             AR coefficients             (initialized when fit_baseline is called)          pkbas : array, optional             baseline prediction error density coefficients             cooresponding to bins (initialized when fit_baseline is called)                       bin_edges : array, optional             baseline prediction error density bin edges corresponding             to pkbas (initialized when fit_baseline is called)              len(bins) == len(pkbas) + 1                       hbas : float, optional             baseline entropy estimate (initialized when fit_baseline is called)          cdf : CDF, optional             Object holding the cumulative density function data of the             baseline prediction errors. Used to build bins.             (initialized when fit_baseline is called)          Example         -------         >>> se_model = SteeringEntropyModel()         >>> baseline_entropy = se_model.fit_baseline(baseline_steering_data)         >>> task_entropy = se_model.get_entropy(task_steering_data)                  References         ----------         <NAME>., <NAME>., <NAME>., and <NAME>.             (2005). Steering Entropy Revisited.  Proceedings of the             Third International Driving Symposium on Human Factors in             Driver Assessment, Training and Vehicle Design.  June 27-30,             2005.  Rockport, Maine.          <NAME>., Behavioral entropy as an index of workload             Proceedings of the IEA 2000 /  HFES 2000 Congress.          <NAME>., <NAME>., <NAME>., and <NAME>.,             Development of a steering entropy method for evaluating             driver workload. SAE Technical Paper Series #1999-01-0892.             Presented at the International Congress and Exposition,             Detriot, Michigan. March 1-4, 1999.          Notes         -----          Expecting data to be in degrees. It may not matter but small         values will sometimes cause overflow errors in arburg. If you         your steering data is in radians it might be better to convert         it to degrees.                  Loosely based off of Chris' SteeringEntropy.m script in ndaqTools.         Users familiar with ndaqTools should note that the steeringentropy         function in ndaqTools (Chris' matlab) uses the first 60 s to find         the AR coeffs and the second 60 s to find baseline prediction error         distribution. This module splits the baseline data in half. This         class applies a 5th order lowpass to 3/7 the resample_fs as         suggested by Boer et al. before resampling. The ndaqTools algorithm         just applies an integer factor downsample. Because of these slight         differences entropy estimates may differ. builds low-pass filter with a cutoff frequency of 3/7th the resample         frequency. The filter should be down 40 dB at 1.5 times the cutoff         frequency (6/7th) the resample frequency.          Parameters         ----------         fs : the base sampling rate          Returns         -------         b, a : array_like             Numerator (b) and denominator (a) polynomials of the IIR filter. # nyquist frequency # cutoff freq defined by Boer # pass edge freq (pi radians / sample) # pass edge freq (pi radians / sample) # The maximum loss in the passband (dB) # The minimum attenuation in the stopband (dB) #print('n =',n,'wn =',wn) Private method applies 5th low-pass Butterworth filter to x         and resamples and returns x at self.resample_fs.          Parameters         ----------         x : array_like             Input data.         fs : float             sampling rate of x in Hz                  Returns         -------         x_resampled : np.ndarray             low-passed and resampled copy of x fit_baseline(self, x[, fs=60.][, _tsplot=False])          Finds AR coefficients to build prediction errors and estimates baseline         prediction errors distribution. Returns the baseline entropy.          Parameters         ----------         x : array_like             Input data. Should specify steering wheel angle over at least 120 s.             x[:N/2] is used to find the AR coefficients.             x[N/2:] is used to build the baseline prediciton error distribution.                      fs : float             sampling rate of x in Hz. Default is 60 Hz. Be sure to specify fs if             x was not sampled at 60 Hz.          Returns         -------         hbas : float             baseline entropy # unpack relevant parameters # apply LP and downsample signal # use first half of x to find coefficients of AR model # using Burg's method # # sign on coeffs returned by arburg is reversed # use second half of x to calculate baseline entropy # use AR coefficents to build prediction errors # need to build bins to approximate the PE distribution # cdf is a CDF object # now we can calculate the baseline entropy # np.histogram returns a tuple of histogram counts and bin_edges # replace small values to avoid excessively high entropy # and the baseline entropy is # store the relevant information get_entropy(self, x[, fs=60.][, _pedistplot=False])          Returns steering entropy from given data vector. Specify fs if not         collected at 60 Hz.          Parameters         ----------         x : array_like             Input data. Should specify steering wheel angle over at least 60 s                      fs : float             sampling rate of x in Hz. Default is 60 Hz.             Be sure to specify fs if x was not sampled at 60 Hz.          Returns         -------         hbas : float             baseline entropy # x is empty # apply LP and downsample signal # Use AR coefficents to build prediction errors # Calculate and entropy returns bode plot of the lp filter applied before downsampling                  Parameters         ----------         None                  Returns         -------         fig : matplotlib.figure.Figure # magnitude ##        ax1.set_title('n = %i, wn = %.6f'%(n, wn) ) # phase returns ts plot to fit_baseline so it can be         returned indirectly to user                  Parameters         ----------         x : array_like             unfiltered data                      _x : array_like             lowpassed and downsampled data                  PE : array_like             prediction errors                  fs : float             base sampling rate                  Returns         -------         fig : matplotlib.figure.Figure # unfiltered data # unfiltered data # phase returns plot to get_entropy so it can be         returned indirectly to user returns bode plot of AR coeffs filter          Parameters         ----------         None                  Returns         -------         fig : matplotlib.figure.Figure # magnitude # phase # Bode phase plot ##        # Nakamura et al. (1999) Taylor series coeffs ##        wt, magt, phaset = lti([1,-2.5,2,-.5], [1,1,1,1]).bode() ##        ax1.semilogx(w[:iend], magt[:iend]) ##        ax2.semilogx(w[:iend], phaset[:iend]) ## ##        fig.savefig('bode.png') ##        plt.close('all')