def Chen_Yang(self, T, full=True, quick=True):
        r'''Method to calculate `a_alpha` and its first and second
        derivatives according to Hamid and Yang (2017) [1]_. Returns `a_alpha`,
        `da_alpha_dT`, and `d2a_alpha_dT2`. See `GCEOS.a_alpha_and_derivatives`
        for more documentation. Seven coefficients needed.
        
        .. math::
            \alpha = e^{\left(- c_{3}^{\log{\left (\frac{T}{Tc} \right )}} 
            + 1\right) \left(- \frac{T c_{2}}{Tc} + c_{1}\right)}

        References
        ----------
        .. [1] Chen, Zehua, and Daoyong Yang. "Optimization of the Reduced 
           Temperature Associated with Peng–Robinson Equation of State and 
           Soave-Redlich-Kwong Equation of State To Improve Vapor Pressure 
           Prediction for Heavy Hydrocarbon Compounds." Journal of Chemical & 
           Engineering Data, August 31, 2017. doi:10.1021/acs.jced.7b00496.
        '''
        c1, c2, c3, c4, c5, c6, c7 = self.alpha_function_coeffs
        T, Tc, a = self.T, self.Tc, self.a
        a_alpha = a*exp(c4*log((-sqrt(T/Tc) + 1)*(c5 + c6*omega + c7*omega**2) + 1)**2 + (-T/Tc + 1)*(c1 + c2*omega + c3*omega**2))
        if not full:
            return a_alpha
        else:
            da_alpha_dT = a*(-(c1 + c2*omega + c3*omega**2)/Tc - c4*sqrt(T/Tc)*(c5 + c6*omega + c7*omega**2)*log((-sqrt(T/Tc) + 1)*(c5 + c6*omega + c7*omega**2) + 1)/(T*((-sqrt(T/Tc) + 1)*(c5 + c6*omega + c7*omega**2) + 1)))*exp(c4*log((-sqrt(T/Tc) + 1)*(c5 + c6*omega + c7*omega**2) + 1)**2 + (-T/Tc + 1)*(c1 + c2*omega + c3*omega**2))
            d2a_alpha_dT2 = a*(((c1 + c2*omega + c3*omega**2)/Tc - c4*sqrt(T/Tc)*(c5 + c6*omega + c7*omega**2)*log(-(sqrt(T/Tc) - 1)*(c5 + c6*omega + c7*omega**2) + 1)/(T*((sqrt(T/Tc) - 1)*(c5 + c6*omega + c7*omega**2) - 1)))**2 - c4*(c5 + c6*omega + c7*omega**2)*((c5 + c6*omega + c7*omega**2)*log(-(sqrt(T/Tc) - 1)*(c5 + c6*omega + c7*omega**2) + 1)/(Tc*((sqrt(T/Tc) - 1)*(c5 + c6*omega + c7*omega**2) - 1)) - (c5 + c6*omega + c7*omega**2)/(Tc*((sqrt(T/Tc) - 1)*(c5 + c6*omega + c7*omega**2) - 1)) + sqrt(T/Tc)*log(-(sqrt(T/Tc) - 1)*(c5 + c6*omega + c7*omega**2) + 1)/T)/(2*T*((sqrt(T/Tc) - 1)*(c5 + c6*omega + c7*omega**2) - 1)))*exp(c4*log(-(sqrt(T/Tc) - 1)*(c5 + c6*omega + c7*omega**2) + 1)**2 - (T/Tc - 1)*(c1 + c2*omega + c3*omega**2))
            return a_alpha, da_alpha_dT, d2a_alpha_dT2
def Chen_Yang(self, T, full=True, quick=True):
        r'''Method to calculate `a_alpha` and its first and second
        derivatives according to Hamid and Yang (2017) [1]_. Returns `a_alpha`,
        `da_alpha_dT`, and `d2a_alpha_dT2`. See `GCEOS.a_alpha_and_derivatives`
        for more documentation. Seven coefficients needed.
        
        .. math::
            \alpha = e^{\left(- c_{3}^{\log{\left (\frac{T}{Tc} \right )}} 
            + 1\right) \left(- \frac{T c_{2}}{Tc} + c_{1}\right)}

        References
        ----------
        .. [1] Chen, Zehua, and Daoyong Yang. "Optimization of the Reduced 
           Temperature Associated with Peng–Robinson Equation of State and 
           Soave-Redlich-Kwong Equation of State To Improve Vapor Pressure 
           Prediction for Heavy Hydrocarbon Compounds." Journal of Chemical & 
           Engineering Data, August 31, 2017. doi:10.1021/acs.jced.7b00496.
        '''
        c1, c2, c3, c4, c5, c6, c7 = self.alpha_function_coeffs
        T, Tc, a = self.T, self.Tc, self.a
        a_alpha = a*exp(c4*log((-sqrt(T/Tc) + 1)*(c5 + c6*omega + c7*omega**2) + 1)**2 + (-T/Tc + 1)*(c1 + c2*omega + c3*omega**2))
        if not full:
            return a_alpha
        else:
            da_alpha_dT = a*(-(c1 + c2*omega + c3*omega**2)/Tc - c4*sqrt(T/Tc)*(c5 + c6*omega + c7*omega**2)*log((-sqrt(T/Tc) + 1)*(c5 + c6*omega + c7*omega**2) + 1)/(T*((-sqrt(T/Tc) + 1)*(c5 + c6*omega + c7*omega**2) + 1)))*exp(c4*log((-sqrt(T/Tc) + 1)*(c5 + c6*omega + c7*omega**2) + 1)**2 + (-T/Tc + 1)*(c1 + c2*omega + c3*omega**2))
            d2a_alpha_dT2 = a*(((c1 + c2*omega + c3*omega**2)/Tc - c4*sqrt(T/Tc)*(c5 + c6*omega + c7*omega**2)*log(-(sqrt(T/Tc) - 1)*(c5 + c6*omega + c7*omega**2) + 1)/(T*((sqrt(T/Tc) - 1)*(c5 + c6*omega + c7*omega**2) - 1)))**2 - c4*(c5 + c6*omega + c7*omega**2)*((c5 + c6*omega + c7*omega**2)*log(-(sqrt(T/Tc) - 1)*(c5 + c6*omega + c7*omega**2) + 1)/(Tc*((sqrt(T/Tc) - 1)*(c5 + c6*omega + c7*omega**2) - 1)) - (c5 + c6*omega + c7*omega**2)/(Tc*((sqrt(T/Tc) - 1)*(c5 + c6*omega + c7*omega**2) - 1)) + sqrt(T/Tc)*log(-(sqrt(T/Tc) - 1)*(c5 + c6*omega + c7*omega**2) + 1)/T)/(2*T*((sqrt(T/Tc) - 1)*(c5 + c6*omega + c7*omega**2) - 1)))*exp(c4*log(-(sqrt(T/Tc) - 1)*(c5 + c6*omega + c7*omega**2) + 1)**2 - (T/Tc - 1)*(c1 + c2*omega + c3*omega**2))
            return a_alpha, da_alpha_dT, d2a_alpha_dT2
def Chen_Yang ( self , T , full = True , quick = True ) : c1 , c2 , c3 , c4 , c5 , c6 , c7 = self . alpha_function_coeffs T , Tc , a = self . T , self . Tc , self . a a_alpha = a * exp ( c4 * log ( ( - sqrt ( T / Tc ) + 1 ) * ( c5 + c6 * omega + c7 * omega ** 2 ) + 1 ) ** 2 + ( - T / Tc + 1 ) * ( c1 + c2 * omega + c3 * omega ** 2 ) ) if not full : return a_alpha else : da_alpha_dT = a * ( - ( c1 + c2 * omega + c3 * omega ** 2 ) / Tc - c4 * sqrt ( T / Tc ) * ( c5 + c6 * omega + c7 * omega ** 2 ) * log ( ( - sqrt ( T / Tc ) + 1 ) * ( c5 + c6 * omega + c7 * omega ** 2 ) + 1 ) / ( T * ( ( - sqrt ( T / Tc ) + 1 ) * ( c5 + c6 * omega + c7 * omega ** 2 ) + 1 ) ) ) * exp ( c4 * log ( ( - sqrt ( T / Tc ) + 1 ) * ( c5 + c6 * omega + c7 * omega ** 2 ) + 1 ) ** 2 + ( - T / Tc + 1 ) * ( c1 + c2 * omega + c3 * omega ** 2 ) ) d2a_alpha_dT2 = a * ( ( ( c1 + c2 * omega + c3 * omega ** 2 ) / Tc - c4 * sqrt ( T / Tc ) * ( c5 + c6 * omega + c7 * omega ** 2 ) * log ( - ( sqrt ( T / Tc ) - 1 ) * ( c5 + c6 * omega + c7 * omega ** 2 ) + 1 ) / ( T * ( ( sqrt ( T / Tc ) - 1 ) * ( c5 + c6 * omega + c7 * omega ** 2 ) - 1 ) ) ) ** 2 - c4 * ( c5 + c6 * omega + c7 * omega ** 2 ) * ( ( c5 + c6 * omega + c7 * omega ** 2 ) * log ( - ( sqrt ( T / Tc ) - 1 ) * ( c5 + c6 * omega + c7 * omega ** 2 ) + 1 ) / ( Tc * ( ( sqrt ( T / Tc ) - 1 ) * ( c5 + c6 * omega + c7 * omega ** 2 ) - 1 ) ) - ( c5 + c6 * omega + c7 * omega ** 2 ) / ( Tc * ( ( sqrt ( T / Tc ) - 1 ) * ( c5 + c6 * omega + c7 * omega ** 2 ) - 1 ) ) + sqrt ( T / Tc ) * log ( - ( sqrt ( T / Tc ) - 1 ) * ( c5 + c6 * omega + c7 * omega ** 2 ) + 1 ) / T ) / ( 2 * T * ( ( sqrt ( T / Tc ) - 1 ) * ( c5 + c6 * omega + c7 * omega ** 2 ) - 1 ) ) ) * exp ( c4 * log ( - ( sqrt ( T / Tc ) - 1 ) * ( c5 + c6 * omega + c7 * omega ** 2 ) + 1 ) ** 2 - ( T / Tc - 1 ) * ( c1 + c2 * omega + c3 * omega ** 2 ) ) return a_alpha , da_alpha_dT , d2a_alpha_dT2
r'''Method to calculate `a_alpha` and its first and second
        derivatives according to Hamid and Yang (2017) [1]_. Returns `a_alpha`,
        `da_alpha_dT`, and `d2a_alpha_dT2`. See `GCEOS.a_alpha_and_derivatives`
        for more documentation. Seven coefficients needed.
        
        .. math::
            \alpha = e^{\left(- c_{3}^{\log{\left (\frac{T}{Tc} \right )}} 
            + 1\right) \left(- \frac{T c_{2}}{Tc} + c_{1}\right)}

        References
        ----------
        .. [1] Chen, Zehua, and Daoyong Yang. "Optimization of the Reduced 
           Temperature Associated with Peng–Robinson Equation of State and 
           Soave-Redlich-Kwong Equation of State To Improve Vapor Pressure 
           Prediction for Heavy Hydrocarbon Compounds." Journal of Chemical & 
           Engineering Data, August 31, 2017. doi:10.1021/acs.jced.7b00496.
r Method to calculate a_alpha and its first and second derivatives according to Hamid and Yang ( 2017 ) [ 1 ] _ . Returns a_alpha da_alpha_dT and d2a_alpha_dT2 . See GCEOS . a_alpha_and_derivatives for more documentation . Seven coefficients needed . .. math :: \ alpha = e^ { \ left ( - c_ { 3 } ^ { \ log { \ left ( \ frac { T } { Tc } \ right ) }} + 1 \ right ) \ left ( - \ frac { T c_ { 2 }} { Tc } + c_ { 1 } \ right ) }