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m_resized = np.resize(m, newsize)
tau_resized = np.resize(tau, newsize)
c_resized = np.resize(c, newsize)
omega = np.atleast_2d(2 * np.pi * self.f).T
self.w = np.resize(omega, (len(m), nr_f)).T
self.rho0 = rho0
self.m = m_resized
self.tau = tau_resized
self.c = c_resized
# compute some common terms
self.otc = (self.w * self.tau) ** self.c
self.otc2 = (self.w * self.tau) ** (2 * self.c)
self.ang = self.c * np.pi / 2.0 # rad
self.denom = 1 + 2 * self.otc * np.cos(self.ang) + self.otc2"
249,"def response(self, parameters):
r""""""Complex response of the Cole-Cole model::
:math:`\hat{\rho} = \rho_0 \left(1 - \sum_i m_i (1 - \frac{1}{1 + (j
\omega \tau_i)^c_i})\right)`
Parameters
----------
parameters: list or tuple or numpy.ndarray
Cole-Cole model parameters: rho0, m, tau, c (all linear)
Returns
-------
response: :class:`sip_models.sip_response.sip_response`
model response object
""""""
# get a config object
self._set_parameters(parameters)
terms = self.m * (1 - (1 / (1 + (1j * self.w * self.tau) ** self.c)))
# sum up terms
specs = np.sum(terms, axis=1)
rcomplex = self.rho0 * (1 - specs)
response = sip_response.sip_response(self.f, rcomplex=rcomplex)
return response"
250,"def dre_drho0(self, pars):
r"""""" Compute partial derivative of real parts with respect to
:math:`\rho_0`
:math:`\frac{\partial \hat{\rho'}(\omega)}{\partial \rho_0} = 1 -
\frac{m (\omega \tau)^c cos(\frac{c \pi}{2}) + (\omega \tau)^c}{1 + 2
(\omega \tau)^c cos(\frac{c \pi}{2}) + (\omega \tau)^{2 c}}`
Note that partial derivatives towards :math:`\rho_0` are 1D, in
contrast to the other parameter derivatives, which usually return 2D
arrays!
Returns
-------
dre_drho0: :class:`numpy.ndarray`
Size N (nr of frequencies) array with the derivatives
""""""
self._set_parameters(pars)
numerator = self.m * self.otc * (np.cos(self.ang) + self.otc)
term = numerator / self.denom
specs = np.sum(term, axis=1)
result = 1 - specs
return result"
251,"def dre_dlog10rho0(self, pars):
""""""Compute partial derivative of real parts to log10(rho0)
""""""
# first call the linear response to set the parameters
linear_response = self.dre_drho0(pars)
result = np.log(10) * self.rho0 * linear_response
return result"
252,"def dre_dm(self, pars):
r""""""
:math:`\frac{\partial \hat{\rho'}(\omega)}{\partial m} = - \rho_0 m
(\omega \tau)^c \frac{(cos(\frac{c \pi}{2}) + (\omega \tau)^c)}{1 + 2
(\omega \tau)^c cos(\frac{c \pi}{2}) + (\omega \tau)^{2 c}}`
""""""
self._set_parameters(pars)
numerator = -self.otc * (np.cos(self.ang) + self.otc)
result = numerator / self.denom
result *= self.rho0
return result"
253,"def dim_dm(self, pars):
r""""""
:math:`\frac{\partial \hat{\rho''}(\omega)}{\partial m} = - \rho_0 m
(\omega \tau)^c \frac{sin(\frac{c \pi}{2})}{1 + 2 (\omega \tau)^c
cos(\frac{c \pi}{2}) + (\omega \tau)^{2 c}}`
""""""
self._set_parameters(pars)
numerator = -self.otc * np.sin(self.ang)
result = numerator / self.denom
result *= self.rho0
return result"
254,"def dim_dtau(self, pars):
r""""""
:math:`\frac{\partial \hat{\rho''}(\omega)}{\partial \tau} = \rho_0
\frac{-m \omega^c c \tau^{c-1} sin(\frac{c \pi}{2} }{1 + 2 (\omega
\tau)^c cos(\frac{c \pi}{2}) + (\omega \tau)^{2 c}} +