added f-omega option to bds fit functions; closes #133
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Dominik Demuth
parent
070509c691
commit
dbb35cdba4
@ -10,14 +10,20 @@ class _AbstractBDS:
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equation = ''
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params = [r'\Delta\epsilon', r'\tau_{0}']
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bounds = [(0, None), (0, None)]
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choices = [
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('x axis', 'xaxis', {'Frequency': 'freq', 'Omega': 'omega'})
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]
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susceptibility = None
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iscomplex = True
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@classmethod
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def func(cls, x, *args, complex_mode: int = 0, **kwargs):
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def func(cls, x, *args, complex_mode: int = 0, xaxis: str = 'freq', **kwargs):
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# args[0] : Delta epsilon
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# args[1:] : every other parameter
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chi = args[0] * cls.susceptibility(2*np.pi*x, *args[1:], **kwargs)
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_w = _convert_x_to_omega(x, xaxis=xaxis)
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chi = args[0] * cls.susceptibility(_w, *args[1:], **kwargs)
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if complex_mode == 0:
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return chi
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elif complex_mode == 1:
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@ -64,11 +70,16 @@ class HavriliakNegamiAlphaGammaBDS:
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equation = r'\Delta\epsilon / [1-(i\omega\tau)^{\gamma}]^{\alpha}'
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params = [r'\Delta\epsilon', r'\tau_{0}', r'\alpha', r'\alpha\gamma']
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bounds = [(0, None), (0, None), (0, 1), (0, 1)]
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choices = [
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('x axis', 'xaxis', {'Frequency': 'freq', 'Omega': 'omega'})
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]
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iscomplex = True
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@staticmethod
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def func(x, deps, tau, alpha, alphagamma, complex_mode: int = 0, **kwargs):
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chi = deps * HavriliakNegami.susceptibility(2*np.pi*x, tau, alpha, alphagamma/alpha, **kwargs)
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def func(x, deps, tau, alpha, alphagamma, complex_mode: int = 0, xaxis: str = 'freq', **kwargs):
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_w = _convert_x_to_omega(x, xaxis=xaxis)
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chi = deps * HavriliakNegami.susceptibility(_w, tau, alpha, alphagamma/alpha, **kwargs)
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if complex_mode == 0:
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return chi
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elif complex_mode == 1:
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@ -115,13 +126,17 @@ class HNWithHF:
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equation = r'\Delta\epsilon HN(\omega, \tau, \alpha, \gamma) / CD(\omega, \tau_{c}, \alpha\gamma-\delta)'
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params = [r'\Delta\epsilon', r'\tau', r'\alpha', r'\gamma', r'\tau_{c}', '\delta']
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bounds = [(0, None), (0, None), (0, 1), (0, 1), (0, None), (0, 1)]
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choices = [
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('x axis', 'xaxis', {'Frequency': 'freq', 'Omega': 'omega'})
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]
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iscomplex = True
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@staticmethod
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def func(x, deps, tau, alpha, gamma, tauc, delta, complex_mode: int = 0):
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w = 2 * np.pi * x
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numerator = (1 + 1j*w*tauc) ** (gamma-delta)
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denominator = (1 + (1j*w*tau)**alpha) ** gamma
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def func(x, deps, tau, alpha, gamma, tauc, delta, complex_mode: int = 0, xaxis: str = 'freq'):
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_w = _convert_x_to_omega(x, xaxis=xaxis)
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numerator = (1 + 1j*_w*tauc) ** (gamma-delta)
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denominator = (1 + (1j*_w*tau)**alpha) ** gamma
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epsilon = deps * np.conjugate(numerator / denominator)
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@ -144,8 +159,8 @@ class _CCWithHF:
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iscomplex = True
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@staticmethod
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def func(x, deps, tau, alpha, tauc, delta, complex_mode: int = 0):
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return HNWithHF.func(x, deps, tau, alpha, 1, tauc, delta, complex_mode=complex_mode)
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def func(x, deps, tau, alpha, tauc, delta, complex_mode: int = 0, xaxis: str = 'freq'):
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return HNWithHF.func(x, deps, tau, alpha, 1, tauc, delta, complex_mode=complex_mode, xaxis=xaxis)
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class _CDWithHF:
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@ -157,8 +172,8 @@ class _CDWithHF:
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iscomplex = True
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@staticmethod
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def func(x, deps, tau, gamma, tauc, delta, complex_mode: int = 0):
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return HNWithHF.func(x, deps, tau, 1, gamma, tauc, delta, complex_mode=complex_mode)
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def func(x, deps, tau, gamma, tauc, delta, complex_mode: int = 0, xaxis: str = 'freq'):
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return HNWithHF.func(x, deps, tau, 1, gamma, tauc, delta, complex_mode=complex_mode, xaxis=xaxis)
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class PowerLawBDS:
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@ -167,16 +182,21 @@ class PowerLawBDS:
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equation = r'A / (i\omega)^{n}'
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params = ['A', 'n']
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bounds = [(None, None), (None, None)]
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choices = [
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('x axis', 'xaxis', {'Frequency': 'freq', 'Omega': 'omega'})
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]
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iscomplex = True
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@staticmethod
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def func(x, a, n, complex_mode: int = 0):
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def func(x, a, n, complex_mode: int = 0, xaxis: str = 'freq'):
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_w = _convert_x_to_omega(x, xaxis=xaxis)
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if complex_mode == 0:
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ret_val = np.exp(1j*n*np.pi/2) * a / x**n
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ret_val = np.exp(1j*n*np.pi/2) * a / _w**n
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elif complex_mode == 1:
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ret_val = np.cos(n*np.pi/2) * a / x**n
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ret_val = np.cos(n*np.pi/2) * a / _w**n
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elif complex_mode == 2:
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ret_val = np.sin(n*np.pi/2) * a / x**n
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ret_val = np.sin(n*np.pi/2) * a / _w**n
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else:
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raise ValueError(f'{complex_mode!r} is not 0, 1, 2')
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@ -189,17 +209,22 @@ class DCCondBDS:
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equation = r'i\sigma_{dc}/\epsilon_{0}\omega'
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params = [r'\sigma_{dc}']
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bounds = [(0, None)]
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choices = [
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('x axis', 'xaxis', {'Frequency': 'freq', 'Omega': 'omega'})
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]
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iscomplex = True
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@staticmethod
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def func(x, sigma, complex_mode: int = 0):
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def func(x, sigma, complex_mode: int = 0, xaxis: str = 'freq'):
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_w = _convert_x_to_omega(x, xaxis=xaxis)
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if complex_mode == 0:
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ret_val = np.zeros(x.shape, dtype=complex)
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ret_val += 1j * sigma / x / epsilon0
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ret_val += 1j * sigma / _w / epsilon0
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elif complex_mode == 1:
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ret_val = np.zeros(x.shape)
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elif complex_mode == 2:
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ret_val = sigma / x / epsilon0
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ret_val = sigma / _w / epsilon0
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else:
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raise ValueError(f'{complex_mode!r} is not 0, 1, 2')
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@ -210,11 +235,16 @@ class DerivativeHavriliakNegami:
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name = 'Derivative HN'
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type = 'Dielectric Spectroscopy'
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params = [r'\Delta\epsilon', r'\tau', r'\alpha', r'\gamma']
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choices = [
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('x axis', 'xaxis', {'Frequency': 'freq', 'Omega': 'omega'})
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]
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bounds = [(0, None), (0, None), (0, 1), (0, 1)]
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@staticmethod
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def func(x, eps, tau, a, g):
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omtau = 2*np.pi*x * tau
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def func(x, eps, tau, a, g, xaxis: str = 'freq'):
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w = _convert_x_to_omega(x, xaxis=xaxis)
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omtau = w * tau
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theta = np.arctan2(np.sin(np.pi*a/2.), omtau**(-a) + np.cos(np.pi*a/2.))
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numer = a*g * omtau**a * np.cos(np.pi*a/2. - (1+g)*theta)
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@ -228,10 +258,15 @@ class DerivativeColeCole:
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type = 'Dielectric Spectroscopy'
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params = [r'\Delta\epsilon', r'\tau', r'\alpha']
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bounds = [(0, None), (0, None), (0, 1)]
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choices = [
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('x axis', 'xaxis', {'Frequency': 'freq', 'Omega': 'omega'})
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]
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@staticmethod
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def func(x, eps, tau, alpha):
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omtau = 2*np.pi*x * tau
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def func(x, eps, tau, alpha, xaxis: str = 'freq'):
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w = _convert_x_to_omega(x, xaxis=xaxis)
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omtau = w * tau
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theta = np.arctan2(np.sin(np.pi*alpha/2.), omtau**(-alpha) + np.cos(np.pi*alpha/2.))
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numer = alpha * omtau**alpha * np.cos(np.pi*alpha/2. - 2*theta)
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@ -245,10 +280,14 @@ class DerivativeColeDavidson:
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type = 'Dielectric Spectroscopy'
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params = [r'\Delta\epsilon', r'\tau', r'\gamma']
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bounds = [(0, None), (0, None), (0, 1)]
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choices = [
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('x axis', 'xaxis', {'Frequency': 'freq', 'Omega': 'omega'})
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]
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@staticmethod
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def func(x, eps, tau, g):
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omtau = 2*np.pi*x * tau
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def func(x, eps, tau, g, xaxis: str = 'freq'):
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w = _convert_x_to_omega(x, xaxis=xaxis)
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omtau = w * tau
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numer = g * omtau * np.sin((1+g)*np.arctan(omtau))
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denom = (1 + omtau**2)**((1+g)/2.)
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@ -260,10 +299,13 @@ class _DerivativeHNWithHF:
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type = 'Dielectric Spectroscopy'
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params = [r'\Delta\epsilon', r'\tau', r'\alpha', r'\gamma', r'\tau_{c}', r'\delta']
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bounds = [(0, None), (0, None), (0, 1), (0, 1), (0, None), (0, 1)]
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choices = [
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('x axis', 'xaxis', {'Frequency': 'freq', 'Omega': 'omega'})
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]
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@staticmethod
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def func(x, deps, tau, alpha, gamma, tauc, delta):
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w = 2*np.pi*x
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def func(x, deps, tau, alpha, gamma, tauc, delta, xaxis: str = 'freq'):
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w = _convert_x_to_omega(x, xaxis=xaxis)
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a_pi2 = alpha*np.pi/2
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w_lamb = (w*tau)**alpha
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@ -287,10 +329,13 @@ class DerivativeCCWithHF:
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type = 'Dielectric Spectroscopy'
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params = [r'\Delta\epsilon', r'\tau', r'\alpha', r'\tau_{c}', r'\delta']
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bounds = [(0, None), (0, None), (0, 1), (0, None), (0, 1)]
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choices = [
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('x axis', 'xaxis', {'Frequency': 'freq', 'Omega': 'omega'})
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]
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@staticmethod
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def func(x, deps, tau, alpha, tauc, delta):
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return _DerivativeHNWithHF.func(x, deps, tau, alpha, 1, tauc, delta)
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def func(x, deps, tau, alpha, tauc, delta, xaxis: str = 'freq'):
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return _DerivativeHNWithHF.func(x, deps, tau, alpha, 1, tauc, delta, xaxis=xaxis)
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class DerivativeCDWithHF:
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@ -298,7 +343,22 @@ class DerivativeCDWithHF:
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type = 'Dielectric Spectroscopy'
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params = [r'\Delta\epsilon', r'\tau', r'\gamma', r'\tau_{c}', r'\delta']
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bounds = [(0, None), (0, None), (0, 1), (0, None), (0, 1)]
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choices = [
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('x axis', 'xaxis', {'Frequency': 'freq', 'Omega': 'omega'})
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]
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@staticmethod
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def func(x, deps, tau, gamma, tauc, delta):
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return _DerivativeHNWithHF.func(x, deps, tau, 1, gamma, tauc, delta)
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def func(x, deps, tau, gamma, tauc, delta, xaxis: str = 'freq'):
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return _DerivativeHNWithHF.func(x, deps, tau, 1, gamma, tauc, delta, xaxis=xaxis)
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def _convert_x_to_omega(x, xaxis: str = 'freq'):
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if xaxis not in ['freq', 'omega']:
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raise ValueError(f'Argument `xaxis` is `freq` or `omega`, given is {xaxis!r}')
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if xaxis == 'freq':
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_w = 2 * np.pi * x
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else:
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_w = x
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return _w
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