Python scipy.exp方法代碼示例

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# 或者: from scipy import exp [as 別名]
def closed_loop_contours(Gcl_mags, Gcl_phases):
    """Contours of the function Gcl = Gol/(1+Gol), where
    Gol is an open-loop transfer function, and Gcl is a corresponding
    closed-loop transfer function.

    Parameters
    ----------
    Gcl_mags : array-like
        Array of magnitudes of the contours
    Gcl_phases : array-like
        Array of phases in radians of the contours

    Returns
    -------
    contours : complex array
        Array of complex numbers corresponding to the contours.
    """
    # Compute the contours in Gcl-space. Since we're given closed-loop
    # magnitudes and phases, this is just a case of converting them into
    # a complex number.
    Gcl = Gcl_mags*sp.exp(1.j*Gcl_phases)

    # Invert Gcl = Gol/(1+Gol) to map the contours into the open-loop space
    return Gcl/(1.0 - Gcl) 

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def calc_water_temperature(T_ambient_C, depth_m):
    """
    Calculates hourly ground temperature fluctuation over a year following [Kusuda, T. et al., 1965]_.
    ..[Kusuda, T. et al., 1965] Kusuda, T. and P.R. Achenbach (1965). Earth Temperatures and Thermal Diffusivity at
    Selected Stations in the United States. ASHRAE Transactions. 71(1):61-74
    """
    heat_capacity_soil = 2000  # _[A. Kecebas et al., 2011]
    conductivity_soil = 1.6  # _[A. Kecebas et al., 2011]
    density_soil = 1600  # _[A. Kecebas et al., 2011]

    T_max = max(T_ambient_C) + 273.15  # to K
    T_avg = np.mean(T_ambient_C) + 273.15  # to K
    e = depth_m * math.sqrt(
        (math.pi * heat_capacity_soil * density_soil) / (HOURS_IN_YEAR * conductivity_soil))  # soil constants
    Tg = [(T_avg + (T_max - T_avg) * math.exp(-e) * math.cos((2 * math.pi * (i + 1) / HOURS_IN_YEAR) - e)) - 274
          for i in range(HOURS_IN_YEAR)]

    return Tg  # in C 

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def _height(P):
    """
    Inverted _Pbar function

    Parameters
    ------------
    P : float
        Standard barometric pressure, [Pa]

    Returns
    -------
    Z : float
        Altitude, [m]

    Examples
    --------
    Selected point from Table 1 in [1]_

    >>> "%0.0f" % _height(107478)
    '-500'
    """
    P_atm = P/101325.
    Z = 1/2.25577e-5*(1-exp(log(P_atm)/5.2559))
    return unidades.Length(Z) 

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def _thermo0(self, rho, T, fase):
        rhol = 68.345
        B1 = -2.5370
        B2 = 0.05366
        C1 = 0.94215
        C2 = 0.14914
        deltaG = 2508.58
        lmax = 25.

        Drho = rhol-rho/self.M
        delta = rho/self.M-7.5114
        tau = T-299.28

        lg = (B1+B2*T)*(Drho/rhol)**C1
        lr = (rho/self.M/rhol)**C1*C2*rhol**2/Drho*T**0.5*exp(
                rho/self.M/Drho*deltaG/self.R.kJkgK/self.M/T)
        lc = 4*lmax/(exp(delta)+exp(-delta))/(exp(tau)+exp(-tau))
        return unidades.ThermalConductivity(lg+lr+lc, "mWmK") 

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def _tc(self, rho, T, fase):
        """Custom method for critical enhancement"""

        Tr = T/304.1282
        rhor = rho/467.6
        nc = 0.775547504

        # Table 4
        a = [0, 3, 6.70697, 0.94604, 0.3, 0.3, 0.39751, 0.33791, 0.77963,
             0.79857, 0.9, 0.02, 0.2]

        # Eq 6
        alfa = 1-a[10]*arccosh(1+a[11]*((1-Tr)**2)**a[12])

        # Eq 5
        num = rhor*exp(-rhor**a[1]/a[1]-(a[2]*(Tr-1))**2-(a[3]*(rhor-1))**2)
        den1 = pow(pow(1-1/Tr+a[4]*pow(pow(rhor-1, 2), 0.5/a[5]), 2), a[6])
        den2 = pow(pow(a[7]*(rhor-alfa), 2), a[8])
        lc = num / (den1+den2)**a[9]

        return lc*nc*4.81384e-3 

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def _vir(self, rho, T, fase):
        # The initial density dependence has a different expresion, without muo
        # and other normal method calculation so hardcoded here
        muB = 0
        if rho:
            for i, n in enumerate([13.2814, -10862.4, 1664060]):
                muB += n/T**i

        # Special exponential term for residual viscosity, Eq 5
        Ei = [-3.29316e-13, -2.92665e-13, 2.97768e-13, 1.76186e-18]
        ni = [4.6, 11.1, 5.6, 12.4]
        ki = [20.8, 10.6, 19.7, 21.9]
        Tr = T/617.12
        rhor = rho/self.M/2.741016

        # Eq 7
        g = 0
        for E, n, k in zip(Ei, ni, ki):
            g += E*rhor**n/Tr**k

        mur = g*exp(rhor**2)

        return muB*rho/self.M + mur 

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def Z_ShellOil(Tr, Pr):
    """Calculate gas compressibility factor using the Shell Oil Company
    correlation (2004)

    Parameters
    ------------
    Tr : float
        Reduced temperature [-]
    Pr : float
        Reduced pressure [-]

    Returns
    -------
    Z : float
        Gas compressibility factor [-]
    """
    A = -0.101 - 0.36*Tr + 1.3868*(Tr-0.919)**0.5
    B = 0.021 + 0.04275/(Tr-0.65)
    C = 0.6222 - 0.224*Tr
    D = 0.0657/(Tr-0.86) - 0.037
    E = 0.32*exp(-19.53*(Tr-1))
    F = 0.122*exp(-11.3*(Tr-1))
    G = Pr*(C + D*Pr + E*Pr**4)
    Z = A + B*Pr + (1-A)*exp(-G) - F*(Pr/10)**4
    return unidades.Dimensionless(Z) 

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def _physics(self, T, P, mezcla):
        """Properties of Gases calculation. Explanation in [1]_ section 1.4"""
        B, B1, B2 = self.B(T)
        C, C1, C2 = self.C(T)

        self.Z = 1+B*(P/R/T)+(C-B**2)*(P/R/T)**2
        V = self.Z*R*T/P
        self.U_exc = -R*T*(B1/V+C1/2/V**2)
        self.H_exc = R*T*((B-B1)/V+(2*C-C1)/2/V**2)
        self.Cv_exc = -R*((2*B1+B2)/V+(2*C1+C2)/2/V**2)
        self.Cp_exc = -R*(B2/V-((B-B1)**2-(C-C1)-C2/2)/V**2)
        self.S_exc = -R*(log(P)+B1/V+(B**2-C+C1)/2/V**2)
        self.A_exc = R*T*(log(P)+(B**2-C/2/V**2))
        self.G_exc = R*T*(log(P)+B/V+(B**2+C)/2/V**2)

        self.fug = P*exp(B/V+(C+B**2)/2/V**2) 

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def _fugacity(self, Z, zi, A, B, Ai, Bi):
        """Fugacity for individual components in a mixture using the GEoS in
        the Schmidt-Wenzel formulation, so the subclass must define the
        parameters u and w in the EoS

        Any other subclass with different formulation must overwrite this
        method
        """
        # Precalculation of inner sum in equation
        aij = []
        for ai, kiji in zip(Ai, self.kij):
            suma = 0
            for xj, aj, kij in zip(zi, Ai, kiji):
                suma += xj*(1-kij)*(ai*aj)**0.5
            aij.append(suma)

        tita = []
        for bi, aai in zip(Bi, aij):
            rhs = bi/B*(Z-1) - log(Z-B) + A/B/(self.u-self.w)*(
                    bi/B-2/A*aai) * log((Z+self.u*B)/(Z+self.w*B))
            tita.append(exp(rhs))

        return tita 

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def project_x(x_new, X, gamma, alphas, lambdas):
    pair_dist = np.array([np.sum((x_new-row)**2) for row in X])
    k = np.exp(-gamma * pair_dist)
    return k.dot(alphas / lambdas)

# projection of the "new" datapoint 

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def debye_func(x):
    """
    Calculate the debye function D(x) = 3*x**(-2)*Integral(z**3/exp(z-1)dz,2,x)
    """
    def func(z):
        f = z**3./(sp.exp(z)-1)
        return f

    integral,error = quad(func,0,x)
    D = integral*3.*x**(-3.)
    return D 

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def debye_S_vib(T,thetaD,natoms):
    """
    Returns the vibrational entropy of the Debeye model at a given temperature,
    T, in meV/atom/K.
    """
    S_vib = 4*debye_func(thetaD/T)-3*sp.log(1-sp.exp(-thetaD/T))
    S_vib = natoms*BOLTZCONST*S_vib
    return S_vib 

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def debye_C_V(T,thetaD,natoms):
    """
    Returns the heat capacity at constant volume, C_V, of the Debeye model at a
    given temperature, T, in meV/atom/K.
    """
    C_V = 4*debye_func(thetaD/T)-3*(thetaD/T)/(sp.exp(thetaD/T)-1.)
    C_V = 3*natoms*BOLTZCONST*C_V
    return C_V 

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def __call__(self, x):
        if not isinstance(x, float):
            x = float(x)

        return 1.0 / (1.0 + scipy.exp(-x)) 

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def calc_plate_HEX(NTU, cr):
    '''
    This function calculates the efficiency of exchange for a plate heat exchanger according to the NTU method of
    AShRAE 90.1

    :param NTU: number of transfer units
    :param cr: ratio between min and max capacity mass flow rates
    :return:
        eff: efficiency of heat exchange
    '''
    eff = 1 - scipy.exp((1 / cr) * (NTU ** 0.22) * (scipy.exp(-cr * (NTU) ** 0.78) - 1))
    return eff