qdsfit/mathlib.py

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# -*- encoding: utf-8 -*-
__author__ = 'markusro'
from PyQt4.QtGui import QColor
from PyQt4.QtCore import QObject,pyqtSignal,QThread,pyqtSlot
import numpy as np
from scipy import optimize as opt, odr
import libyaff
def id_to_color(id):
colors = [
QColor(54,22,115),
QColor(160,16,36),
QColor(45,142,15),
QColor(168,149,17),
QColor(36,10,85),
QColor(118,8,23),
QColor(31,105,7),
QColor(124,109,8),
]
return colors[id % len(colors)]
class FitFunctionCreator(QObject):
new_data = pyqtSignal(np.ndarray, np.ndarray)
def __init__(self):
super(FitFunctionCreator,self).__init__()
self.data = None
self.functions = Functions()
def fitfcn(self, p0, x, *funcs):
if x.ndim == 2:
self.data = np.zeros( x.shape )
else:
self.data = np.zeros( (2,x.size) )
ndx = 0
for fn in funcs: # loop over functions and add the results
f, num_p = fn.function, fn.param_number
p = p0[ndx:ndx + num_p]
if x.ndim == 2:
x = x[0]
result = f(p, x)
self.data += result # fit functions take only 1-dim x
ndx += num_p
self.new_data.emit(x, self.data)
return self.data
def fitfcn_imag(self, p0, x, *funcs):
if x.ndim == 2:
self.data = np.zeros( x.shape )
else:
self.data = np.zeros( (2,x.size) )
ndx = 0
for fn in funcs: # loop over functions and add the results
f, num_p = fn.function, fn.param_number
p = p0[ndx:ndx + num_p]
if x.ndim == 2:
x = x[0]
result = f(p, x)
self.data += result # fit functions take only 1-dim x
ndx += num_p
self.new_data.emit(x, self.data)
return self.data[1]
class FitRoutine(QObject):
finished_fit = pyqtSignal()
data_ready = pyqtSignal(np.ndarray, np.ndarray)
def __init__(self):
super(FitRoutine,self).__init__()
self.f = FitFunctionCreator()
self.f.new_data.connect(self.data_ready.emit)
self._fitter = self.fit_odr_cmplx
self._odr_fit = None
@property
def fitter(self):
return self._fitter
@fitter.setter
def fitter(self, f):
self._fitter = f
def fit_odr_cmplx(self, x, y, p0, fixed, fcns):
#if x.ndim < 2:
# x = N.resize(x, (2,x.size))
if np.iscomplexobj(y) and y.ndim == 1:
weights = 1/np.abs(y)**2
we = np.resize(weights, (2, weights.size))
#we = 1/N.array([y.real**2, y.imag**2])
y = np.array([y.real, y.imag])
else:
raise NotImplementedError, "need complex input for now"
dat = odr.Data(x, y, we=we)
mod = odr.Model(self.f.fitfcn, extra_args=fcns)
self._odr_fit = odr.ODR(dat, mod, p0, ifixx=(0,), ifixb=fixed, maxit=800)
def fit_odr_imag(self, x, y, p0, fixed, fcns):
if np.iscomplexobj(y) and y.ndim == 1:
we = 1/np.imag(y)**2
else:
raise NotImplementedError, "need complex input for now"
dat = odr.Data(x, y.imag, we=we)
mod = odr.Model(self.f.fitfcn_imag, extra_args=fcns)
self._odr_fit = odr.ODR(dat, mod, p0, ifixx=(0,), ifixb=fixed, maxit=800)
@pyqtSlot()
def fit(self):
#print "TID in FitRoutine", QThread.thread()
self._odr_fit.run()
self.finished_fit.emit()
def result(self):
return self._odr_fit.output
class FunctionRegister:
def __init__(self):
self.registry = {}
def register_function(self, obj):
#print "FR: Registering:",obj
id_string = obj.id_label
if self.registry.has_key(obj):
raise AssertionError,"The object is already registered! This should NOT happen"
self.registry[obj]=id_string
#print "FR: ",self.registry
def unregister_function(self, obj):
#print "FR: UnRegistering:",obj
if self.registry.has_key(obj):
self.registry.pop(obj)
else:
obj.deleteLater()
raise AssertionError,"The object is not in the registry! This should NOT happen"
#print "FR: ",self.registry
def get_registered_functions(self):
return self.registry
############## deprecated #####################
def fit_odr_cmplx(x, y, p0, fixed, fcns):
f = FitFunctionCreator()
#if x.ndim < 2:
# x = N.resize(x, (2,x.size))
if np.iscomplexobj(y) and y.ndim == 1:
weights = 1/np.abs(y)**2
we = np.resize(weights, (2, weights.size))
#we = 1/N.array([y.real**2, y.imag**2])
y = np.array([y.real, y.imag])
else:
raise NotImplementedError, "need complex input for now"
dat = odr.Data(x, y, we=we)
mod = odr.Model(f.fitfcn, extra_args=fcns)
fit = odr.ODR(dat, mod, p0, ifixx=(0,), ifixb=fixed, maxit=8000)
fit.run()
#print fit.output.pprint()
return fit.output
### define funcs here
class Functions(QObject):
def __init__(self):
super(Functions,self).__init__()
self.list = {
# provides functions: "id_string":(function, number_of_parameters)
"hn":(self.hn_cmplx, 4),
"conductivity":(self.cond_cmplx, 3),
"power":(self.power_cmplx, 2),
"static":(self.static_cmplx, 1),
"yaff":(self.yaff, 8)
}
self.YAFF = libyaff.Yaff()
def hn_cmplx(self, p, x):
om = 2*np.pi*x
#hn = om*1j
eps,t,a,b = p
hn = eps/(1+(1j*om*t)**a)**b
cplx = np.array([hn.real, -hn.imag])
return cplx
def cond_cmplx(self, p, x):
om = 2*np.pi*x
sgma, isgma, n = p
cond = sgma/(om**n) + isgma/(1j*om**n) # Jonscher (Universal Dielectric Response: e",e' prop sigma/omega**n
cplx = np.array([cond.real, -cond.imag])
return cplx
def power_cmplx(self, p, x):
om = 2*np.pi*x
sgma,n = p
power = sgma/(om*1j)**n
cplx = np.array([power.real, -power.imag])
return cplx
def static_cmplx(self, p, x):
eps_inf = p[0]
static = np.ones( (2,x.size) )*eps_inf
static[1,:] *= 0 # set imag part zero
#cplx = N.array([static.real, static.imag])
return static
def yaff(self,p,x):
ya = self.YAFF.yaff(p[:8],x)
cplx = np.array([ya.imag, ya.real])
return cplx
def get(self,name):
return self.list[name]
def get_function(self,name):
return self.list[name][0]
def fit_anneal(x, y, p0, fixed, funcs):
raise NotImplementedError
bounds = [(0, 1e14), (0, 1)]
for i in xrange(len(p0[2:]) / 4):
bounds.append((1e-4, 1e12)) # delta_eps
bounds.append((1e-12, 1e3)) # tau
bounds.append((0.1, 1)) # a
bounds.append((0.1, 1)) # b
ret = opt.anneal(mini_func, p0,
args=(x, y),
maxeval=20000,
maxiter=30000,
lower=[b[0] for b in bounds],
upper=[b[1] for b in bounds],
dwell=100,
full_output=1)
#pmin, func_min, final_Temp, cooling_iters,accepted_tests, retval
#retval : int
#Flag indicating stopping condition::
# 0 : Points no longer changing
# 1 : Cooled to final temperature
# 2 : Maximum function evaluations
# 3 : Maximum cooling iterations reached
# 4 : Maximum accepted query locations reached
# 5 : Final point not the minimum amongst encountered points
print "Stop reason", ret
return ret[0]
def fit_lbfgsb(x, y, p0, fixed, funcs):
raise NotImplementedError
# TODO fixed parameters…
bounds = [(0, None), (0, 1)]
for i in xrange(len(p0[3:]) / 4):
bounds.append((1e-4, 1e12)) # delta_eps
bounds.append((1e-12, 1e3)) # tau
bounds.append((0.1, 1)) # a
bounds.append((0.1, 1)) # b
x, f_minvalue, info_dict = opt.fmin_l_bfgs_b(mini_func, p0,
fprime=None,
args=(x, y),
approx_grad=True,
bounds=bounds,
iprint=0,
maxfun=4000)
if info_dict['warnflag'] != 0:
print info_dict["task"]
return x
# Replaced with fit_odr_cmplx
#
#def fit_odr(x, y, p0, fixed, funcs):
# dat = odr.Data(x, y, 1.0 / y**2)
# mod = odr.Model(multi_hn)
# fit = odr.ODR(dat, mod, p0, ifixx=(0,), ifixb=fixed, maxit=2000)
# fit.run()
# return fit.output.beta
def hn(p, nu):
delta_eps, tau, a, b = p
om = 2 * np.pi * nu
Phi = np.arctan((om * tau) ** a * np.sin(np.pi * a / 2.) / (1. + (om * tau) ** a * np.cos(np.pi * a / 2.)))
e_loss = delta_eps * (1 + 2 * (om * tau) ** a * np.cos(np.pi * a / 2.) + (om * tau) ** (2. * a) ) ** (
-b / 2.) * np.sin(b * Phi)
e_stor = delta_eps * (1 + 2 * (om * tau) ** a * np.cos(np.pi * a / 2.) + (om * tau) ** (2. * a) ) ** (
-b / 2.) * np.cos(b * Phi)
return e_loss # 2* oder nicht?
def mini_func(p, x, y):
res = y - multi_hn(p, x)
# apply weights
res /= 1 / y
return np.sqrt(np.dot(res, res))
def multi_hn(p, nu):
conductivity = p[1]
cond_beta = p[2]
om = 2 * np.pi * nu
e_loss = conductivity / om ** cond_beta
e_loss += p[0]
#for key, igroup in groupby(p[3:], lambda x: x//4):
for i in xrange(len(p[3:]) / 4):
delta_eps, tau, a, b = p[3 + i * 4:3 + (i + 1) * 4]
#delta_eps, tau, a, b = list(igroup)
#print delta_eps,tau,a,b
#a = 0.5 *(1 + N.tanh(a))
#b = 0.5 *(1 + N.tanh(b))
Phi = np.arctan((om * tau) ** a * np.sin(np.pi * a / 2.) / (1. + (om * tau) ** a * np.cos(np.pi * a / 2.)))
e_loss += 2 * delta_eps * (1 + 2 * (om * tau) ** a * np.cos(np.pi * a / 2.) + (om * tau) ** (2. * a) ) ** (
-b / 2.) * np.sin(b * Phi)
#e_stor = delta_eps * (1+ 2*(om*tau)**a * N.cos(N.pi*a/2.) + (om*tau)**(2.*a) )**(-b/2.)*N.cos(b*Phi)
return e_loss
def tau_peak(f, a, b):
tau = (np.sin(np.pi * a / 2. / (b + 1)) / np.sin(np.pi * a * b / 2. / (b + 1))) ** (1 / a)
tau /= 2 * np.pi * f
return tau