def lmfit(self,maxfev=0,report_fit=True,cpus=1,epsfcn=None,xtol=1.e-7,ftol=1.e-7,
workdir=None, verbose=False, **kwargs):
""" Calibrate MATK model using lmfit package
:param maxfev: Max number of function evaluations, if 0, 100*(npars+1) will be used
:type maxfev: int
:param report_fit: If True, parameter statistics and correlations are printed to the screen
:type report_fit: bool
:param cpus: Number of cpus to use for concurrent simulations during jacobian approximation
:type cpus: int
:param epsfcn: jacobian finite difference approximation increment (single float of list of npar floats)
:type epsfcn: float or lst[float]
:param xtol: Relative error in approximate solution
:type xtol: float
:param ftol: Relative error in the desired sum of squares
:type ftol: float
:param workdir: Name of directory to use for model runs, calibrated parameters will be run there after calibration
:type workdir: str
:param verbose: If true, print diagnostic information to the screen
:type verbose: bool
:returns: lmfit minimizer object
Additional keyword argments will be passed to scipy leastsq function:
http://docs.scipy.org/doc/scipy-0.15.1/reference/generated/scipy.optimize.leastsq.html
"""
try: import lmfit
except ImportError as exc:
sys.stderr.write("Warning: failed to import lmfit module. ({})".format(exc))
return
self.cpus = cpus
# Create lmfit parameter object
params = lmfit.Parameters()
for k,p in self.pars.items():
params.add(k,value=p.value,vary=p.vary,min=p.min,max=p.max,expr=p.expr)
out = lmfit.minimize(self.__lmfit_residual, params, args=(cpus,epsfcn,workdir,verbose),
maxfev=maxfev,xtol=xtol,ftol=ftol,Dfun=self.__jacobian, **kwargs)
# Make sure that self.pars are set to final values of params
nm = [params[k].name for k in self.pars.keys()]
vs = [params[k].value for k in self.pars.keys()]
self.parvalues = dict(zip(nm,vs))
# Run forward model to set simulated values
if isinstance( cpus, int):
self.forward(workdir=workdir,reuse_dirs=True)
elif isinstance( cpus, dict):
hostname = cpus.keys()[0]
processor = cpus[hostname][0]
self.forward(workdir=workdir,reuse_dirs=True,
hostname=hostname,processor=processor)
else:
print 'Error: cpus argument type not recognized'
return
if report_fit:
print lmfit.report_fit(params)
print 'SSR: ',self.ssr
return out
def lmfit_psf(filename, wsname):
a = pd.read_excel(filename, wsname, header=None)
x = np.array(map(float, a[0]))
data = np.array(map(float, a[1]))
# create a set of Parameters
params = Parameters()
params.add('amp', value=100, min=0.0)
params.add('w0', value=0.25, min=0.0)
params.add('shift', value=0.35)
params.add('offset', value=0.0, min=0.0)
# do fit, here with leastsq model
result = minimize(fcn2min, params, args=(x, data))
# calculate final result
final = data + result.residual
# write error report
report_fit(params)
# try to plot results
try:
import pylab
pylab.plot(x, data, 'k+')
pylab.plot(x, final, 'r')
pylab.title(
'%s w0=%snm' %
(os.path.splitext(filename)[0], round(params['w0'].value * 1000)))
pylab.draw()
except:
pass
def Poly_fitting_Er(self):
def fcn2min(prms, rs, Es):
A = prms['A']
B = prms['B']
C = prms['C']
D = prms['D']
E_calc = []
E_poly = lambda r: A + B * r + C * r**2 + D * r**3
for ri in rs:
E_calc.append(E_poly(ri))
return np.array(E_calc) - Es
params = Parameters()
params.add('A', 0, vary=True)
params.add('B', 0, vary=True)
params.add('C', 0, vary=True)
params.add('D', 0, vary=True)
minner = Minimizer(fcn2min,
params=params,
fcn_args=(self._rexp, self._Eexp))
result = minner.minimize()
final = self._Eexp + result.residual
report_fit(result)
self.__A = result.params['A'].value
self.__B = result.params['B'].value
self.__C = result.params['C'].value
self.__D = result.params['D'].value
return final
def fit_nl_orthorhombic_cell(data_df, a, b, c, wavelength, verbose=True):
"""
perform non-linear fit
data_df = data in pandas DataFrame
a, b, c = cell parameter
wavelength = this ca be replaced with .get_base_ptn_wavelength()
"""
h = data_df['h']
k = data_df['k']
l = data_df['l']
param = Parameters()
param.add('a', value=a, min=0)
param.add('b', value=b, min=0)
param.add('c', value=c, min=0)
twoth_data = data_df['twoth']
minner = Minimizer(fcn2min_orthorhombic,
param,
fcn_args=(h, k, l, twoth_data, wavelength))
result = minner.minimize()
# calculate final result
# write error report
if verbose:
report_fit(result)
return result
def fit_phase_tau(self):
#fit_range_indices = np.where((self.time>=self.phase_fit_range[0])&(self.time<=self.phase_fit_range[1]))
fit_range_indices = np.arange(self.phase_fit_range[0], self.phase_fit_range[1])
fit_time = self.time[fit_range_indices]
fit_phase = self.phase[fit_range_indices]
self.lmfit_tau_result = minimizer.minimize(fn.phase_tau_func_residual, self.lmfit_init_tau_params, args=(fit_time, fit_phase), nan_policy='propagate', method='nelder')
report_fit(self.lmfit_tau_result)
def run(config, input, output):
dataFile = os.path.join(config['cwd'], input['fit.datafile'][0][0])
x, data = np.loadtxt(dataFile, usecols=(0, 1), unpack=True)
params = Parameters()
# Loop over parameters defined in input. Later, we might loop over
# all possible parameters and set which ones vary instead.
for param in input['fit.parameters']:
#minval = param[1]*0.5 if param[1] != 0 else -0.5
#maxval = param[1]*1.5 if param[1] != 0 else 0.5
#params.add(param[0],value=param[1],min=minval,max=maxval)
params.add(param[0], value=param[1])
#open('fitconvergence.dat', 'ab')
# do fit, here with the default leastsq algorithm
minner = Minimizer(Xanes2Min,
params,
fcn_args=(x, data, input, config, output))
#result = minner.minimize(epsfcn=0.0001,method='differential_evolution',workers=6)
result = minner.minimize(epsfcn=0.0001)
final = data + result.residual
report_fit(result)
with open('fit_result.txt', 'w') as fh:
fh.write(fit_report(result))
output['fit'] = [
x.tolist(), final.tolist(),
data.tolist()
] # For now set this as fit. Later we may want to make a statement about what is implemented and what is not for fit.
def das(tup, x0, from_t=0.4, uniform_fil=None, plot_result=True, fit_kws=None):
out = namedtuple('das_result', field_names=[
'fitter', 'result', 'minimizer'])
ti = dv.make_fi(tup.t)
if uniform_fil is not None:
tupf = filter.uniform_filter(tup, uniform_fil)
else:
tupf = tup
if fit_kws is None:
fit_kws = {}
import numpy as np
#ct = dv.tup(np.hstack((wl, wl)), tup.t[ti(t0):], np.hstack((pa[ti(t0):, :], se[ti(t0):, :])))
ct = dv.tup(tup.wl, tup.t[ti(from_t):], tupf.data[ti(from_t):, :])
f = fitter.Fitter(ct, model_coh=0, model_disp=0)
f.lsq_method = 'ridge'
kws = dict(full_model=0, lower_bound=0.2, fixed_names=['w'])
kws.update(fit_kws)
lm = f.start_lmfit(x0, **kws)
res = lm.leastsq()
import lmfit
lmfit.report_fit(res)
if plot_result:
plt.figure(figsize=(4, 7))
plt.subplot(211)
if is_montone(f.wl):
monotone = False
# Assume wl is repeated
N = len(f.wl)
else:
monotone = True
N = len(f.wl) // 2
print(N)
l = plt.plot(f.wl[:N], f.c[:N, :], lw=3)
if monotone:
l2 = plt.plot(f.wl[:N], f.c[N:, :], lw=1)
for i, j in zip(l, l2):
j.set_color(i.get_color())
plot_helpers.lbl_spec()
lbls = ['%.1f' % i for i in f.last_para[1:-1]] + ['const']
plt.legend(lbls)
plt.subplot(212)
wi = dv.make_fi(tup.wl)
for i in range(N)[::6]:
l, = plt.plot(tup.t, tupf.data[:, i], '-o', lw=0.7,
alpha=0.5, label='%.1f cm-1' % f.wl[i], mec='None', ms=3)
plt.plot(f.t, f.model[:, i], lw=3, c=l.get_color())
if monotone:
l, = plt.plot(tup.t, tupf.data[:, i+N], '-o', lw=0.7,
alpha=0.5, label='%.1f cm-1' % f.wl[i], mec='None', ms=3)
plt.plot(f.t, f.model[:, i+N], lw=3, c=l.get_color())
plt.xlim(-1)
plt.xscale('symlog', linthreshx=1, linscalex=0.5)
plot_helpers.lbl_trans()
plt.legend(loc='best')
return out(f, res, lm)
def analysis(meas, data=None, fig=None):
xs = meas.delays
ys, fig = meas.get_ys_fig(data, fig)
# fig.axes[0].plot(xs/1e3, ys, 'ks', ms=3)
amp0 = (np.max(ys) - np.min(ys)) / 2
fftys = np.abs(np.fft.fft(ys - np.average(ys)))
fftfs = np.fft.fftfreq(len(ys), xs[1] - xs[0])
f0 = np.abs(fftfs[np.argmax(fftys)])
print 'Delta f estimate: %.03f kHz' % (f0 * 1e6)
params = lmfit.Parameters()
params.add('ofs', value=amp0)
params.add('amp', value=amp0, min=0)
params.add('tau', value=xs[-1], min=10, max=200000)
params.add('freq', value=f0, min=0)
params.add('phi0', value=0, min=-1.2 * np.pi, max=1.2 * np.pi)
result = lmfit.minimize(t2_fit, params, args=(xs, ys))
lmfit.report_fit(params)
fig.axes[0].plot(xs / 1e3,
-t2_fit(params, xs, 0),
label='Fit, tau=%.03f us, df=%.03f kHz' %
(params['tau'].value / 1000, params['freq'].value * 1e6))
fig.axes[0].legend()
fig.axes[0].set_ylabel('Intensity [AU]')
fig.axes[0].set_xlabel('Time [us]')
fig.axes[1].plot(xs / 1e3, t2_fit(params, xs, ys), marker='s')
fig.canvas.draw()
return params
def fit(self, time_range: np.arange = None, parameters: [Parameters, tuple] = None, initial_conditions: list = None,
residual=None, verbose: bool = False, data: np.array = None):
"""
Fit the model based on data in the form np.array([X1,...,Xn])
"""
if data is None:
if self.data is None:
raise ValueError("No data to fit the model on!")
data = self.data
if initial_conditions is not None:
self.initial_conditions = initial_conditions
if self.initial_conditions is None:
raise ValueError("No initial conditions to fit the model with!")
if parameters is None:
if self.parameters is None:
raise ValueError("No parameters to fit the model with!")
parameters = self.parameters
if time_range is None:
time_range = np.arange(data.shape[0])
if residual is None:
residual = self.residual
result = minimize(residual, parameters, args=(time_range, data), method=self.fit_method)
self.result = result
self.fitted_parameters = result.params.valuesdict()
if verbose:
report_fit(result)
return result
def lmfitter(x, y):
params = Parameters()
params.add('m', value=0.01, vary=True)
out = minimize(residual, params, args=(x, y))
report_fit(params)
return out.params['m'].value, 0.0, out.params['m'].stderr, 0.0
def fit_my_func(sigma, like):
'''Fit my favorite function to the likelihood data'''
from lmfit import minimize, Parameters, Parameter, report_fit
params = Parameters()
params.add('amp', value= 2.5, min=0.0)
params.add('beta', value= 8.0,min=0.1)
params.add('core', value= 2.0, min=0.1,max=5.0)
print params
# do fit, here with leastsq model
result = minimize(func2min, params, args=(sigma, like))
print params
# calculate final result
final = like + result.residual
# write error report
report_fit(params)
# try to plot results
try:
plt.plot(sigma, like, 'k+')
plt.plot(sigma, final, 'r')
plt.draw()
plt.show()
print 'sleeping 1 sec'
time.sleep(1)
except:
pass
return params
def runFit(self):
## Initialize parameters
self.nb_calls = 0
## Run fit algorithm
if self.method=="least_square":
out = minimize(self.compute_diff, self.pars)
if self.method=="shgo":
out = minimize(self.compute_diff, self.pars,
method='shgo', sampling_method='sobol', options={"f_tol": 1e-16}, n = 100, iters=20)
if self.method=="differential_evolution":
out = minimize(self.compute_diff, self.pars,
method='differential_evolution')
if self.method=="ampgo":
out = minimize(self.compute_diff, self.pars,
method='ampgo')
else:
print("This method does not exist in the class")
## Display fit report
report_fit(out)
## Export final parameters from the fit
for param_name in self.ranges_dict.keys():
if param_name in self.init_member.keys():
self.member[param_name] = out.params[param_name].value
elif param_name in self.init_member["band_params"].keys():
self.member["band_params"][param_name] = out.params[param_name].value
## Save BEST member to JSON
self.save_member_to_json()
## Compute the FINAL member
self.fig_compare(fig_save=True)
def analysis(meas, data=None, fig=None):
ys, fig = meas.get_ys_fig(data, fig)
xs = meas.angles
fig.axes[0].plot(xs, ys, 'ks', ms=3)
r = fp.Sine(x_data=xs, y_data=ys)
result, params, ys_fit = r.fit(plot=False)
txt = 'Frequency = %.03f +- %.03e\nPhase = %.03f +- %.03f' %\
(params['frequency'].value, params['frequency'].stderr, \
params['phase'].value, params['phase'].stderr)
fig.axes[0].plot(xs, ys_fit, label=txt)
fig.axes[1].plot(xs, ys-ys_fit, marker='s')
lmfit.report_fit(params)
fig.axes[0].set_ylabel('Intensity [AU]')
fig.axes[0].set_xlabel('Rotation (Cycle)')
fig.axes[0].legend(loc=0)
fig.canvas.draw()
return params
def fit_eta(self, line, **run_args):
import lmfit
def model(v, x):
'''Eta orientation function.'''
m = v['prefactor'] * (1 - (v['eta']**2)) / ((
(1 + v['eta'])**2) - 4 * v['eta'] * (np.square(
np.cos((v['symmetry'] / 2.0) *
np.radians(x - v['x_center']))))) + v['baseline']
return m
def func2minimize(params, x, data):
v = params.valuesdict()
m = model(v, x)
return m - data
params = lmfit.Parameters()
params.add('prefactor', value=np.max(line.y) * 0.5, min=0)
params.add('x_center',
value=-90,
min=np.min(line.x),
max=np.max(line.x))
params.add('eta', value=0.2, min=0, max=1)
params.add('symmetry', value=2, min=0.5, max=20, vary=False)
params.add('baseline', value=0, min=0, max=np.max(line.y), vary=False)
lm_result = lmfit.minimize(func2minimize,
params,
args=(line.x, line.y))
if run_args['verbosity'] >= 5:
print('Fit results (lmfit):')
lmfit.report_fit(lm_result.params)
fit_x = line.x
fit_y = model(lm_result.params.valuesdict(), fit_x)
fit_line = DataLine(x=fit_x,
y=fit_y,
plot_args={
'linestyle': '-',
'color': 'r',
'marker': None,
'linewidth': 4.0
})
fit_x = np.linspace(np.min(line.x), np.max(line.x), num=1000)
fit_y = model(lm_result.params.valuesdict(), fit_x)
fit_line_extended = DataLine(x=fit_x,
y=fit_y,
plot_args={
'linestyle': '-',
'color': 'r',
'marker': None,
'linewidth': 4.0
})
return lm_result, fit_line, fit_line_extended
def calibrate_long_wG():
long_profile = load_data(calibration_shots_h5, 'wG/wG_profile')
magnification = load_data(calibrations_h5, 'magnification/M_bar')
def lmfit_gaussian_2d(xdata, ydata, zdata, u_zdata):
pars = Parameters()
pars.add('Tilt', value=-0.02, min=-0.1, max=0.1, vary=True)
pars.add('Amplitude', value=4e4, vary=True)
pars.add('wx', value=150, min=2, max=400, vary=True)
pars.add('wy', value=150, min=2, max=400, vary=True)
pars.add('x0', value=371, vary=True)
pars.add('y0', value=181, vary=True)
pars.add('offset', value=1e3, vary=True)
def residuals(pars, xdata, ydata, zdata, u_zdata):
theta = pars['Tilt']
amp = pars['Amplitude']
wx = pars['wx']
wy = pars['wy']
x0 = pars['x0']
y0 = pars['y0']
off = pars['offset']
zmodel = gaussian_2d(xdata, ydata, theta, amp, wx, wy, x0, y0, off)
return (zmodel - zdata) / u_zdata
return minimize(residuals,
pars,
args=(xdata, ydata, zdata, u_zdata),
method='leastsq',
nan_policy='omit')
def gaussian_2d(x, y, theta, amp, wx, wy, x0, y0, offset):
x = x[np.newaxis, :]
y = y[:, np.newaxis]
u, v = ((x - x0) * np.cos(theta) -
(y - y0) * np.sin(theta)), ((x - x0) * np.sin(theta) +
(y - y0) * np.cos(theta))
return amp * np.exp(-(2 * v**2 / wy**2) - (2 * u**2 / wx**2)) + offset
x_coords, y_coords = np.linspace(0, long_profile.shape[1],
long_profile.shape[1]), np.linspace(
0, long_profile.shape[0],
long_profile.shape[0])
result = lmfit_gaussian_2d(x_coords, y_coords, long_profile, 5)
parameters = np.array(
[result.params[key].value for key in result.params.keys()])
try:
u_params = np.sqrt(np.diag(result.covar))
except ValueError:
u_params = np.zeros_like(parameters)
report_fit(result)
x_waist = parameters[2] * pix_size / magnification
zR = pi * (x_waist)**2 / (1.064 * um)
u_x_waist = u_params[2] * pix_size / magnification
u_zR = pi * x_waist * u_x_waist / (1.064 * um)
with h5py.File(calibrations_h5) as calibrations:
h5_save(calibrations, 'wG/wx0', x_waist)
h5_save(calibrations, 'wG/u_wx0', u_x_waist)
def E_total_fitting_Er(
self): # fitting DFT data of E_V with the above function
def fcn2min(prms, rs, Es):
ls = prms['ls']
E_calc = []
for ri in rs:
E_calc.append(self.E_total(ri, ls))
return np.array(E_calc) - Es
params = Parameters()
_last_fitting = "/_last_fitting.json"
filename = current_folder + _last_fitting
if os.path.exists(filename):
with open(filename, 'r') as f:
dct = json.load(f)
if 'ls' in dct:
params.add('ls', dct['ls'], vary=True)
else:
params.add('ls', 0.5, vary=True)
minner = Minimizer(fcn2min,
params=params,
fcn_args=(self._rexp, self._Eexp))
result = minner.minimize()
final = self._Eexp + result.residual
_dct = {'ls': result.params['ls'].value}
with open(filename, 'w') as f:
json.dump(_dct, f)
report_fit(result)
self.LengthScale = result.params['ls'].value
return final
def cov_quasiparticle_occupation_fit_thermal(self, C):
n_qp = self.cov_calc_quasiparticle_occupation(C)
def objective_function(params, e, n_qp):
beta = params['beta']
mu = params['mu']
FD = np.exp(-beta * e + mu) / (1 + np.exp(-beta * e + mu))
return FD - n_qp
params = Parameters()
params.add('beta', value=3, min=0, max=100)
params.add('mu', value=0, min=-10, max=10)
minner = Minimizer(objective_function, params, fcn_args=(self.e, n_qp))
result = minner.minimize()
final = n_qp + result.residual
beta_opt = result.params['beta'].value
mu_opt = result.params['mu'].value
print "Inverse temp fit: ", beta_opt
print "Chemical potential fit fit: ", mu_opt
n_qp_thermal = [self.Fermi_Dirac(E, beta_opt, mu_opt) for E in self.e]
report_fit(result)
return [n_qp, n_qp_thermal, beta_opt, mu_opt]
def __lmfit_fit(residual_function,
params,
algo_choice,
args=None,
kws=None,
**fit_kws):
"""Process calls for [lmfit] fitting."""
method = "nelder" if algo_choice == "simplex" else \
"leastsq" if algo_choice == "levmar" else \
"emcee" if algo_choice == "mcmc" else \
"brute" if algo_choice == "grid" else None
if method is None:
raise ValueError("algo_choice invalid")
# Switch output channel to suppress printing during fitting process
old_stdout = sys.stdout
new_stdout = io.StringIO()
sys.stdout = new_stdout
# Call [lmfit.minimize()]
out = minimize(residual_function,
params,
method=method,
nan_policy='omit',
args=args,
kws=kws,
**fit_kws)
# Return to original output channel
sys.stdout = old_stdout
# Print report of fitting results
report_fit(out.params)
# Return value bindings
return out.params
def analysis(meas, data=None, fig=None, period=None):
ys, fig = meas.get_ys_fig(data, fig)
xs = meas.areas
fig.axes[0].plot(xs, ys, 'ks', ms=3)
amp0 = (np.max(ys) - np.min(ys)) / 2
if ys[0] > np.average(ys):
amp0 = -amp0
fftys = np.abs(np.fft.fft(ys - np.average(ys)))
fftfs = np.fft.fftfreq(len(ys), xs[1] - xs[0])
period0 = 1 / np.abs(fftfs[np.argmax(fftys)])
params = lmfit.Parameters()
params.add('ofs', value=np.average(ys))
params.add('amp', value=amp0)
if period is not None:
params.add('period', value=period, min=0, vary=False)
else:
params.add('period', value=period0, min=0)
params.add('decay', value=20000, min=0)
result = lmfit.minimize(fit_timerabi, params, args=(xs, ys))
lmfit.report_fit(params)
txt = 'Amp = %.03f +- %.03e\nPeriod = %.03f +- %.03e\nPi area = %.03f' % (
params['amp'].value, params['amp'].stderr, params['period'].value,
params['period'].stderr, params['period'].value / 2)
fig.axes[0].plot(xs, -fit_timerabi(params, xs, 0), label=txt)
fig.axes[0].set_ylabel('Intensity [AU]')
fig.axes[0].set_xlabel('Pulse area')
fig.axes[0].legend(loc=0)
fig.axes[1].plot(xs, fit_timerabi(params, xs, ys), marker='s')
fig.canvas.draw()
return params
def get_radial_dose(radial_dose_in, dwell_in, point_in):
"""
Calculate the radial dose function value
"""
R = pdist([[dwell_in.x, dwell_in.y, dwell_in.z],
[point_in.x, point_in.y, point_in.z]])
if R in radial_dose_in.r_cm:
return radial_dose_in.gL[radial_dose_in.r_cm.index(R)]
elif R < min(radial_dose_in.r_cm):
nrVal = find_nearest(np.array(radial_dose_in.r_cm), R)
return radial_dose_in.gL[radial_dose_in.r_cm.index(nrVal)]
elif R > max(radial_dose_in.r_cm):
pw = 2
params = Parameters()
params.add('pw', value=pw, vary=False)
params.add('adj1', value=1)
params.add('adj2', value=1)
xf = radial_dose_in.r_cm[-2:]
yf = radial_dose_in.gL[-2:]
result = minimize(fcn2min, params, args=(xf, yf))
report_fit(result.params)
adj1 = result.params['adj1']
adj2 = result.params['adj2']
next_y = adj1 * np.power(R + adj2, pw)
return next_y
else:
return log_interp(radial_dose_in.r_cm, radial_dose_in.gL, R)
def fit_model_with_adapter(method='nelder'):
"""
Test fit of a bare silicon with oxide.
These are the REFL1D results for the same model:
Chi2 = 1.307
SiOx thickness 6.7 +- 1.7
SiOx SLD 4.0 +- 0.3
SiOx roughness 1.0 +- 0.7
Si roughness 5.7 +- 2.0
"""
# This is how the interface will use its layer model
model_adapter = ModelAdapter(bare_silicon_model())
params = model_adapter.params_from_model()
# Load the data
q, r, dr, _ = np.loadtxt(os.path.join(os.path.dirname(__file__),
'data/Si_137848_1850_800.txt'),
unpack=True)
# Perform the fit
result = minimize(residual_with_adapter,
params,
args=(q, r, dr, model_adapter),
method=method)
report_fit(result)
def fit_data_sample():
# create a set of Parameters
params = Parameters()
params.add('amp', value=10, min=0)
params.add('decay', value=0.1)
params.add('shift', value=0.0, min=-np.pi / 2., max=np.pi / 2.)
params.add('omega', value=3.0)
# create data to be fitted
x = np.linspace(0, 15, 301)
data = (5.0 * np.sin(2.0 * x - 0.1) * np.exp(-x * x * 0.025) +
np.random.normal(size=x.size, scale=0.2))
# do fit, here with the default leastsq algorithm
minner = Minimizer(fcn2min, params, fcn_args=(x, data))
result = minner.minimize()
# calculate final result
final = data + result.residual
# write error report
report_fit(result)
# try to plot results
try:
import matplotlib.pyplot as plt
plt.plot(x, data, 'k+')
plt.plot(x, final, 'r')
plt.show()
except ImportError:
pass
def sineInfo(s, f = 3., report=True, debugPlot = False):
'''
f for repetition in s, input f = fft_f * tSpan
return amp, freql, shift, THD
real f = freql /tSpan
'''
l = len(s)
t = array(range(l))
a2 = ppv(s)
from lmfit import minimize, Parameters, report_fit
def err(params, t, s):
amp = params['amp'].value
shift = params['shift'].value
omega = params['freq'].value
model = amp * sin(t * omega * 2*pi + shift)
return model - s
params = Parameters()
params.add('amp', value= a2, min= a2 / 3)
params.add('shift', value= 0.) #, min=-pi, max=pi)
params.add('freq', value=f/l , min = 0.6*f/l, max = 1.4*f/l)
resd = minimize(err, params, args=(t, s)).residual
if report: report_fit(params)
if debugPlot:
figure()
plot(s)
plot(s+resd)
return (params['amp'].value, params['freq'].value * l , params['shift'].value % (2*pi) - pi, sum(resd**2)/sum(s**2))
def report_mcmc_fit(mcmc_res):
"""Report output of MCMC fit.
Code from https://lmfit.github.io/lmfit-py/fitting.html
"""
# -----------------------
# Median of distribution
print("median of posterior probability distribution")
print("--------------------------------------------")
lmfit.report_fit(mcmc_res.params)
p = mcmc_res.params.copy()
highest_prob = np.argmax(mcmc_res.lnprob)
hp_loc = np.unravel_index(highest_prob, mcmc_res.lnprob.shape)
mle_soln = mcmc_res.chain[hp_loc]
for i, par in enumerate(p):
p[par].value = mle_soln[i]
# -----------------------
# Max Likelihood
print("\nMaximum Likelihood Estimation from emcee ")
print("-------------------------------------------------")
print("Parameter MLE Value Median Value Uncertainty")
fmt = " {:5s} {:11.5f} {:11.5f} {:11.5f}".format
for name, param in p.items():
print(
fmt(
name,
param.value,
mcmc_res.params[name].value,
mcmc_res.params[name].stderr,
))
# -----------------------
# Error Estimate
print("\nError Estimates from emcee ")
print("------------------------------------------------------")
print("Parameter -2sigma -1sigma median +1sigma +2sigma ")
for name in p.keys():
quantiles = np.percentile(mcmc_res.flatchain[name],
[2.275, 15.865, 50, 84.135, 97.275])
median = quantiles[2]
err_m2 = quantiles[0] - median
err_m1 = quantiles[1] - median
err_p1 = quantiles[3] - median
err_p2 = quantiles[4] - median
fmt = " {:5s} {:8.4f} {:8.4f} {:8.4f} {:8.4f} {:8.4f}".format
print(fmt(name, err_m2, err_m1, median, err_p1, err_p2))
# /for
return
def main():
# Read in reference/model spectrum
ref = np.loadtxt('ref.txt', unpack=True)
# Read in input spectrum to be scaled
spec = np.loadtxt(sys.argv[1], unpack=True)
region = [[6507, 6512], [6560, 6565]] # Background or continuum region
ref_w, ref_f = region_around_line(ref[0], ref[1], region)
spec_w, spec_f = region_around_line(spec[0], spec[1], region)
divisor = np.max(ref_f) # To normalize spectrum
ref_f, spec_f = ref_f / divisor, spec_f / divisor
# Initial parameters
params = Parameters()
params.add('dx', value=0)
params.add('sigma', value=1)
params.add('amplitude', value=1)
# Minimize
fitout = minimize(fit_profile_err, params, args=(spec_w, spec_f, ref_f))
fitted_p = fitout.params
scaled = fit_profile(fitted_p, spec_w, spec_f)
# Best-fit parameters
report_fit(fitout)
# Save new scaled spectrum
save_scaled_spectrum = True
if save_scaled_spectrum:
ref_center = ref_w[np.argmax(ref_f)] # Model spectrum center
new_center = spec_w[np.argmax(scaled)] # This center is from the fit
shift = ref_center - new_center # Wavelength shift
spec_w_new = shift + spec[0] # Apply shift
scaling_factor = simps(ref_f, ref_w) / simps(
scaled, spec_w) # To scale the spectrum
spec_f_new = spec[1] * scaling_factor # Scaled
spec_e_new = spec[2] * scaling_factor
# Re-bin
spec_f_new = np.interp(ref[0], spec_w_new, spec_f_new)
spec_e_new = np.interp(ref[0], spec_w_new, spec_e_new)
out_name = os.path.splitext(
sys.argv[1])[0].split('.fits')[0] + '_scaled.txt'
# Save
np.savetxt(out_name, np.transpose([ref[0], spec_f_new, spec_e_new]))
plt.plot(ref_w, ref_f)
plt.plot(spec_w, scaled)
plt.show()
def fit_hawkes(event_times_dict_list, predefined_beta_matrix=None, pool=None):
'''Fit a multidimensional Hawkes Process to observed sequences
Parameters
----------
event_times_dict_list : list of dict of lists of floats
List of sequences of event dicts, with process dimension as key and list of ascending timestamps (floats) as values
predefined_beta_matrix : matrix of floats
Self-excitation decay per dimension^2. If equals None, then it will be a parameter to fit.
Returns
-------
fitted_hawkes : MultivariateHawkes
New Hawkes Process with fitted parameters
'''
parameters = lmfit.Parameters()
for dimension_m in event_times_dict_list[0]:
parameters.add("mu_{}".format(dimension_m), min=0, value=0.9)
for dimension_n in event_times_dict_list[0]:
parameters.add("alpha_{}{}".format(dimension_m, dimension_n), min=0, value=0.9)
if not predefined_beta_matrix:
parameters.add("beta_{}{}".format(dimension_m, dimension_n), min=0, value=0.9)
def __extract_parameters(parameters):
mu_list = []
alpha_matrix = []
beta_matrix = []
for dim_m in event_times_dict_list[0]:
mu_list.append(parameters["mu_{}".format(dim_m)])
alpha_matrix.append([])
beta_matrix.append([])
for dim_n in event_times_dict_list[0]:
alpha_matrix[dim_m].append(parameters["alpha_{}{}".format(dim_m, dim_n)])
if not predefined_beta_matrix:
beta_matrix[dim_m].append(parameters["beta_{}{}".format(dim_m, dim_n)])
return {"mu": mu_list,
"alpha": alpha_matrix,
"beta": beta_matrix if not predefined_beta_matrix else predefined_beta_matrix}
def log_likelihood_wrapper(parameters, event_times_dict_list, pool):
current_hawkes_process = MultivariateHawkes(**__extract_parameters(parameters))
current_hawkes_process.pprint()
'''
We compute -1 * log_likelihood, because we use algorithms that minimize,
and finding parameters that maximize likelihood is equivalent to finding those that minimize -log_likelihood
'''
result = pool.map(current_hawkes_process.log_likelihood, event_times_dict_list)
return list(np.array(result) * -1)
# return [-1 * current_hawkes_process.log_likelihood(event_times_dict) for event_times_dict in event_times_dict_list]
if not pool:
pool = multiprocessing.Pool(processes = constants.NUMBER_OF_PROCESSES)
minimizer = lmfit.Minimizer(log_likelihood_wrapper, parameters, fcn_args=(event_times_dict_list, pool))
result = minimizer.minimize(method="lbfgsb")
lmfit.report_fit(result)
return {"parameters": __extract_parameters(parameters),
"average_negativeloglikelihood": np.mean(log_likelihood_wrapper(parameters, event_times_dict_list, pool))}
def quadratic_planefit(x, y, z, err=None, pinit=None, method='leastsq',
report_fit=False):
"""
Fits a quadratic bivariate polynomial to 2D data
Parameters
----------
x : ndarray
array of x values
y : ndarray
array of y values
z : ndarray
data to be fit
err : ndarray (optional)
uncertainties on z data
pinit : ndarray (optional)
initial guesses for fitting. Format = [mmx, mx, mmy, my, c]
method : string (optional)
method used for the minimisation (default = leastsq)
"""
if pinit is None:
pars=lmfit.Parameters()
pars.add('mmx', value=1.0)
pars.add('mx', value=1.0)
pars.add('mmy', value=1.0)
pars.add('my', value=1.0)
pars.add('c', value=1.0)
else:
pars=lmfit.Parameters()
pars.add('mmx', value=pinit[0])
pars.add('mx', value=pinit[1])
pars.add('mmy', value=pinit[2])
pars.add('my', value=pinit[3])
pars.add('c', value=pinit[4])
fitter = lmfit.Minimizer(residual_quadratic_planefit, pars,
fcn_args=(x,y),
fcn_kws={'data':z, 'err':err},
nan_policy='propagate')
result = fitter.minimize(method=method)
if report_fit:
lmfit.report_fit(result)
popt = np.array([result.params['mmx'].value,
result.params['mx'].value,
result.params['mmy'].value,
result.params['my'].value,
result.params['c'].value])
perr = np.array([result.params['mmx'].stderr,
result.params['mx'].stderr,
result.params['mmy'].stderr,
result.params['my'].stderr,
result.params['c'].stderr])
return popt, perr, result
def prad_fe_fit():
cksbin = cksmet.io.load_table('cksbin-fe')
x = log10(cksbin.binc)
y = cksbin.fe_mean
yerr = cksbin.fe_mean_err
import lmfit
p0 = lmfit.Parameters()
p0.add('p1', 0.1)
p0.add('p0', 0.1)
def model_linear(params, x):
return params['p1'] * x + params['p0']
def model_step(params, x):
if isinstance(x, Iterable):
out = map(lambda x: model_step(params, x), x)
out = np.array(out)
return out
if x < log10(4):
return params['p0']
elif x >= log10(4):
return params['p1']
def resid(params, model, x, y, yerr):
return (y - model(params, x)) / yerr
res_linear = lmfit.minimize(resid, p0, args=(
model_linear,
x,
y,
yerr,
))
p1_linear = res_linear.params
print "linear model"
lmfit.report_fit(res_linear)
res_step = lmfit.minimize(resid, p0, args=(
model_step,
x,
y,
yerr,
))
p1_step = res_linear.params
print "step model"
lmfit.report_fit(res_step)
print "BIC(linear) - BIC(step) = {}".format(res_linear.bic - res_step.bic)
semilogx()
xerr = bins_to_xerr(cksbin.bin0, cksbin.binc, cksbin.bin1)
print xerr
errorbar(10**x, y, xerr=xerr, yerr=yerr, fmt='o')
plot(10**x, model_linear(p1_linear, x))
prad_fe_label()
xlim(0.5, 16)
def fitEPSC(self):
# create a set of Parameters
params = lmfit.Parameters()
params.add('amp',
value=self.ptreedata.param('Initial Fit Parameters').param(
'amp').value(),
min=-self.dmax,
max=self.dmax)
params.add('tau_rise',
value=self.ptreedata.param('Initial Fit Parameters').param(
'taurise').value(),
min=1e-4,
max=1e-1)
params.add('tau_fall',
value=self.ptreedata.param('Initial Fit Parameters').param(
'taufall').value(),
min=1e-4,
max=1e-1)
params.add('DC',
value=self.ptreedata.param('Initial Fit Parameters').param(
'DC').value(),
min=-1e3,
max=1e3)
dc = np.mean(self.dataY[0:10])
params.add('DC', value=dc, min=dc - dc * 1, max=dc + dc * 1)
t0 = self.T0.value()
t1 = self.T1.value()
it0 = int(t0 / self.dt)
it1 = int(t1 / self.dt)
if it0 > it1:
t = it0
it0 = it1
it1 = t
# do fit, here with the default leastsq algorithm
time_zero = int(self.time_zero / self.dt)
print('timezero: ', time_zero, self.dataX[time_zero])
print(self.dataX[it0:it1] - self.time_zero)
print(self.dataY[it0:it1])
minner = lmfit.Minimizer(
self._fcn_EPSC,
params,
fcn_args=(self.dataX[it0:it1] - self.dataX[time_zero],
self.dataY[it0:it1]))
self.fitresult = minner.minimize(method='least_squares', )
# calculate final result
final = self.dataY[it0:it1] + self.fitresult.residual
# write error report
lmfit.report_fit(self.fitresult)
self.updateFit(self.fitresult)
self.fitx = self.dataX[it0:it1]
self.fity = final
self.showFit()
def paramOptimization(self, data, time, ts=None):
warnings.filterwarnings("ignore")
# set parameters including bounds; you can also fix parameters (use vary=False)
S0, E0, I0, R10, R20, D0 = self.y0
_, a0, b0, c0, f0, mu0, xi0 = self.modele.getParam()
params = Parameters()
params.add('N', value=self.N, vary=False)
params.add('E0', value=E0, vary=False)
params.add('I0', value=I0, vary=False)
params.add('R10', value=R10, vary=False)
params.add('R20', value=R20, vary=False)
params.add('D0', value=D0, vary=False)
params.add('a', value=a0, vary=True, min=0.0, max=0.99)
params.add('b', value=b0, vary=True, min=0.0, max=0.99)
params.add('c', value=c0, vary=True, min=0.0, max=0.99)
params.add('f', value=f0, vary=True, min=0.0, max=0.99)
params.add('mu', value=mu0, vary=True, min=0.00001, max=0.15)
params.add('xi', value=xi0, vary=True, min=0.000001, max=0.1)
# The time delay is only used for the first period (otherwise it is 0 and doesn't need to be estimated)
if ts != None:
params.add('ts', value=ts, vary=False)
else:
params.add('ts',
value=self.TS,
vary=True,
min=0,
max=len(time) - np.shape(data)[0] - 2)
# Fit the model by minimization
result = minimize(residual,
params,
args=(time, data, self, self.indexdata),
method='powell') #powell, least_squares
if self.verbose > 1:
result.params.pretty_print()
# display fitted statistics
report_fit(result)
# Update params with the optimized values
self.setParamInit(result.params['N'].value, result.params['E0'].value,
result.params['I0'].value,
result.params['R10'].value,
result.params['R20'].value,
result.params['D0'].value)
self.modele.setParam(
result.params['N'].value, result.params['a'].value,
result.params['b'].value, result.params['c'].value,
result.params['f'].value, result.params['mu'].value,
result.params['xi'].value)
self.TS = result.params['ts'].value
warnings.filterwarnings("default")
def diag(subf, subs, cat_freqs, cat_K, cat_J, cat_En):
'''
vdopler shift!
'''
cat_freqs = cat_freqs.copy()
xy = []
constants = []
params = Parameters()
params.add('w0', 0.0105, min=-0.01, max=0.04)
params.add('I0', 0.050, min=0.01, max=10)
params.add('I1', 0.050, min=0.01, max=10)
params.add('I2', 0.050, min=0.01, max=10)
params.add('I3', 0.050, min=0.01, max=10)
params.add('I4', 0.050, min=0.01, max=10)
params.add('sigma', 0.0001, min=0.00001, max=0.01)
minm = minimize(resCH3C2H, params, args=(subf, subs, cat_freqs / 1e9))
lines = fitCH3C2H(minm.params, subf, cat_freqs / 1e9)
report_fit(minm.params)
I = []
for i in range(len(cat_freqs)):
I.append(minm.params.get('I{0}'.format(i)).value)
for i in range(len(cat_freqs)):
f = cat_freqs[i] / 1e9
par = minm.params.copy()
for j in range(len(cat_freqs)):
par['I{0}'.format(j)].value = 0
par['I{0}'.format(i)].value = I[i]
integ = ((fitCH3C2H(minm.params, subf, cat_freqs / 1e9) > 0) *
fitCH3C2H(minm.params, subf, cat_freqs / 1e9))
intl, eu, error = rot(integ.sum(), cat_K[i], cat_J[i], cat_En[i],
cat_freqs[i], (subs - lines).std())
xy.append((intl, eu, error))
xy = np.array(xy)
xy = np.flipud(xy)
fitfunc = lambda x, k, b: -x / k + b
def residual(params, x, yd, error):
k = params['k'].value
b = params['b'].value
model = fitfunc(x, k, b)
return (yd - model)
params = Parameters()
params.add('k', value=40)
params.add('b', value=-0.8)
minm = minimize(residual, params, args=(xy[:-1, 1], xy[:-1, 0], []))
report_fit(minm.params)
x = xy[:, 1]
y = xy[:, 0]
dy = xy[:, 2]
Dx = len(x) * ((x**2).sum()) + (x.sum())**2
su = 0
for i in range(len(dy)):
su += (dy[i] * (x[i] - x.sum()) / Dx)**2
dB = math.sqrt(su)
return (minm.params['k'].value.dB, xy)
def fit_all(t, p):
params = lmfit.Parameters()
params.add('lnkappa', value=2.)
params.add('n_avrami', value=1.)
out = lmfit.minimize(residual, params, args=(t, p, )) # lmfit minimizer
lmfit.report_fit(params)
# return out.params['chi0'].value
return out
def polar_plot(dataset,
fig_name=None,
polar=True,
ax=None,
reset_scaling=False,
fit_mask=np.ones(16, dtype=bool)):
if ax is None:
fig = plt.figure(fig_name)
fig.clf()
ax = fig.add_subplot(111, polar=polar)
else:
fig = ax.figure
phi = np.linspace(0, 2 * np.pi, 16, endpoint=False)
phi_line = np.linspace(0, 2 * np.pi, 2**10)
if reset_scaling:
det_factors = dataset.det_factors.copy()
dataset.det_factors = np.ones_like(det_factors)
auger = dataset.auger_amplitudes.mean(axis=0)
photo = dataset.photo_amplitudes.mean(axis=0)
if reset_scaling:
det_calib = auger.max() / auger
ax.plot(phi, auger, 'gx')
auger *= det_calib
ax.plot(phi, photo, 'rx')
photo *= det_calib
ax.plot(phi, auger, 'gs', label='auger')
ax.plot(phi, photo, 'ro', label='photo')
params = cookie_box.initial_params(photo)
params['beta'].vary = False
params['beta'].value = 2
lmfit.minimize(cookie_box.model_function,
params,
args=(phi[fit_mask], photo[fit_mask]))
lmfit.report_fit(params)
ax.plot(phi_line,
cookie_box.model_function(params, phi_line),
'-m',
label='{:.1f} % lin {:.1f} deg'.format(
params['linear'].value * 100,
np.rad2deg(params['tilt'].value)))
ax.grid(True)
ax.legend(loc='center', bbox_to_anchor=(0, 0), fontsize='medium')
plt.tight_layout()
if reset_scaling:
dataset.det_factors = det_factors
return fig
def fit_peaks(self, line, num_curves=1, **run_args):
# Usage: lm_result, fit_line, fit_line_extended = self.fit_peaks(line, **run_args)
line_full = line
#if 'fit_range' in run_args:
#line = line.sub_range(run_args['fit_range'][0], run_args['fit_range'][1])
import lmfit
def model(v, x):
'''Gaussians with constant background.'''
m = v['m']*x + v['b']
for i in range(num_curves):
m += v['prefactor{:d}'.format(i+1)]*np.exp( -np.square(x-v['x_center{:d}'.format(i+1)])/(2*(v['sigma{:d}'.format(i+1)]**2)) )
return m
def func2minimize(params, x, data):
v = params.valuesdict()
m = model(v, x)
return m - data
params = lmfit.Parameters()
params.add('m', value=0)
params.add('b', value=np.min(line.y), min=0, max=np.max(line.y))
xspan = np.max(line.x) - np.min(line.x)
xpeak, ypeak = line.target_y(np.max(line.y))
for i in range(num_curves):
#xpos = np.min(line.x) + xspan*(1.*i/num_curves)
#xpos, ypos = line.target_x(xpeak*(i+1))
xpos, ypos = xpeak, ypeak
params.add('prefactor{:d}'.format(i+1), value=ypos-np.min(line.y), min=0, max=np.max(line.y)*10)
params.add('x_center{:d}'.format(i+1), value=xpos, min=np.min(line.x), max=np.max(line.x))
params.add('sigma{:d}'.format(i+1), value=xspan*0.20, min=0, max=xspan*0.50)
lm_result = lmfit.minimize(func2minimize, params, args=(line.x, line.y))
if run_args['verbosity']>=5:
print('Fit results (lmfit):')
lmfit.report_fit(lm_result.params)
fit_x = line.x
fit_y = model(lm_result.params.valuesdict(), fit_x)
fit_line = DataLine(x=fit_x, y=fit_y, plot_args={'linestyle':'-', 'color':'b', 'marker':None, 'linewidth':4.0})
fit_x = np.linspace(np.min(line_full.x), np.max(line_full.x), num=200)
fit_y = model(lm_result.params.valuesdict(), fit_x)
fit_line_extended = DataLine(x=fit_x, y=fit_y, plot_args={'linestyle':'-', 'color':'b', 'alpha':0.5, 'marker':None, 'linewidth':2.0})
return lm_result, fit_line, fit_line_extended
def fit(self):
# set everything up, then call the fit function, finally print out the results in the table
self.setParametersFromTable()
import Fitting
xData,yData = self.getCurrentData()
result = Fitting.FitOne(self.getCurrentFunctionName(),self.params,xData,yData)
import lmfit
lmfit.report_fit(self.params)
self.updateParametersTable()
self.updatePlot()
def lmfitter(x , y, y_error):
params = Parameters()
params.add('phiStar', value=0.1, vary=True)
params.add('LStar', value=1.0, vary=True)
params.add('alpha', value=-1, vary=True)
# remove inf values in errors
out = minimize(residual, params, args=(x, y, y_error))
report_fit(params)
return out
def test_peakfit():
from lmfit.utilfuncs import gaussian
def residual(pars, x, data=None):
g1 = gaussian(x, pars['a1'].value, pars['c1'].value, pars['w1'].value)
g2 = gaussian(x, pars['a2'].value, pars['c2'].value, pars['w2'].value)
model = g1 + g2
if data is None:
return model
return (model - data)
n = 601
xmin = 0.
xmax = 15.0
noise = np.random.normal(scale=.65, size=n)
x = np.linspace(xmin, xmax, n)
org_params = Parameters()
org_params.add_many(('a1', 12.0, True, None, None, None),
('c1', 5.3, True, None, None, None),
('w1', 1.0, True, None, None, None),
('a2', 9.1, True, None, None, None),
('c2', 8.1, True, None, None, None),
('w2', 2.5, True, None, None, None))
data = residual(org_params, x) + noise
fit_params = Parameters()
fit_params.add_many(('a1', 8.0, True, None, 14., None),
('c1', 5.0, True, None, None, None),
('w1', 0.7, True, None, None, None),
('a2', 3.1, True, None, None, None),
('c2', 8.8, True, None, None, None))
fit_params.add('w2', expr='2.5*w1')
myfit = Minimizer(residual, fit_params,
fcn_args=(x,), fcn_kws={'data':data})
myfit.prepare_fit()
init = residual(fit_params, x)
myfit.leastsq()
print(' N fev = ', myfit.nfev)
print(myfit.chisqr, myfit.redchi, myfit.nfree)
report_fit(fit_params)
fit = residual(fit_params, x)
check_paras(fit_params, org_params)
def example():
'''
Make a "noisy" hologram. Then fit the noisy hologram. Plot the results.
'''
## Make Noisy Hologram.
# Create hologram to be fitted.
x,y,z = 0., 0., 100.
a_p = 0.5
n_p = 1.5
n_m = 1.339
dim = [201,201]
lamb = 0.447
mpp = 0.135
hologram = sph.spheredhm([x,y,z], a_p, n_p, n_m, dim, mpp, lamb)
# Add noise.
std = 0.03
noise = np.random.normal(size=hologram.shape)*std
noisy_hologram = hologram + noise
## Fit the noisy hologram.
init_params = {'x':x, 'y':y, 'z':z, 'a_p':a_p, 'n_p':n_p, 'n_m':n_m,
'mpp':mpp, 'lamb':lamb}
mie_fit = Mie_Fitter(init_params)
result = mie_fit.fit(noisy_hologram)
# Calculate the resulting image.
residual = result.residual.reshape(*dim)
final = hologram + residual
# Write error report.
report_fit(result)
## Make plots.
# Plot images.
sns.set(style='white', font_scale=1.4)
plt.imshow(np.hstack([hologram, final, residual+1]))
plt.title('Image, Fit, Residual')
plt.gray()
plt.show()
# Plot Covariance.
f, ax = plt.subplots()
#cmap = sns.diverging_palette(220, 10, as_cmap=True)
sns.set(font_scale=1.5)
plt.title('Log Covariance Matrix')
sns.heatmap(np.log(result.covar), cmap='PuBu',
square=True, cbar_kws={}, ax=ax)
ax.set_xticklabels(['x', 'y', 'z', r'a$_p$', r'n$_p$'])
ax.set_yticklabels([r'n$_p$', r'a$_p$', 'z', 'y', 'x'])
plt.show()
def run_minimize(paramdic, maxlimitdic, minlimitdic, datadic, extrakeys, extrakeyssolv, rsolvtest, outfile, nptype, mintotalerror):
mintotalerror = mintotalerror
params = Parameters()
for ikey, ivalue in paramdic.iteritems():
maxlimit = maxlimitdic[ikey]
minlimit = minlimitdic[ikey]
ikey = ikey.replace("@","zzz") #replace @ with zzz because this character is not supported by lmfit library
ikey = ikey.replace(".","xxx") #replace . with xxx because this character is not supported by lmfit library
#~ params.add(ikey, value=ivalue)
#~ if "rczzz" in ikey:
#~ params.add(ikey, value=ivalue, min=minlimit, max=maxlimit)
#~ else:
#~ params.add(ikey, ivalue, False)
params.add(ikey, value=ivalue, min=minlimit, max=maxlimit)
print params
#experimental data
datacompoundnamelist = []
for ikey, ivalue in datadic.iteritems():
datacompoundnamelist.append(ikey) #to convert in error function to a dictionary
#~ extra_kwargs={}
#~ extra_kwargs['epsfcn'] = 0.5
#~ result = minimize(fcn2min, params, args=(extrakeys, extrakeyssolv, rsolvtest, outfile, nptype, datacompoundnamelist), method='lbfgs', **extra_kwargs)
#~ extra_kwargs={}
#~ extra_kwargs['T'] = 300.0
#~ extra_kwargs['stepsize']=0.1
#~ result = minimize(fcn2min, params, args=(extrakeys, extrakeyssolv, rsolvtest, outfile, nptype, datacompoundnamelist), method='basinhopping', **extra_kwargs)
result = minimize(fcn2min, params, args=(extrakeys, extrakeyssolv, outfile, nptype, datacompoundnamelist, limitcycle), method='powell')
#~ #calculate final result
#~ final = data + result.residual
# write error report
report_fit(params)
#~ # try to plot results
#~ try:
#~ import pylab
#~ pylab.plot(x, data, 'k+')
#~ pylab.plot(x, final, 'r')
#~ pylab.show()
#~ except:
#~ pass
return datadic
def polar_plot(dataset, fig_name=None, polar=True, ax=None,
reset_scaling=False,
fit_mask=np.ones(16, dtype=bool)):
if ax is None:
fig = plt.figure(fig_name)
fig.clf()
ax = fig.add_subplot(111, polar=polar)
else:
fig = ax.figure
phi = np.linspace(0, 2 * np.pi, 16, endpoint=False)
phi_line = np.linspace(0, 2 * np.pi, 2**10)
if reset_scaling:
det_factors = dataset.det_factors.copy()
dataset.det_factors = np.ones_like(det_factors)
auger = dataset.auger_amplitudes.mean(axis=0)
photo = dataset.photo_amplitudes.mean(axis=0)
if reset_scaling:
det_calib = auger.max() / auger
ax.plot(phi, auger, 'gx')
auger *= det_calib
ax.plot(phi, photo, 'rx')
photo *= det_calib
ax.plot(phi, auger, 'gs', label='auger')
ax.plot(phi, photo, 'ro', label='photo')
params = cookie_box.initial_params(photo)
params['beta'].vary = False
params['beta'].value = 2
lmfit.minimize(cookie_box.model_function, params,
args=(phi[fit_mask], photo[fit_mask]))
lmfit.report_fit(params)
ax.plot(phi_line, cookie_box.model_function(params, phi_line),
'-m', label='{:.1f} % lin {:.1f} deg'.format(
params['linear'].value*100,
np.rad2deg(params['tilt'].value)))
ax.grid(True)
ax.legend(loc='center', bbox_to_anchor=(0, 0), fontsize='medium')
plt.tight_layout()
if reset_scaling:
dataset.det_factors = det_factors
return fig
def fit_decision_model(df):
import lmfit
fit_params = lmfit.Parameters()
fit_params.add('alpha1', value=.5, min=0, max=1)
fit_params.add('alpha2', value=.5, min=0, max=1)
fit_params.add('lam', value = .5, min=0, max=1)
fit_params.add('W', value = .5, min=0, max=1)
fit_params.add('p', value = 0)
fit_params.add('B1', value = 3)
#fit_params.add('B2', value = 3)
out = lmfit.minimize(get_likelihood, fit_params, method = 'lbfgsb', kws={'df': df})
lmfit.report_fit(out)
return out.params.valuesdict()
def lmfitter(x , y, y_error):
params = Parameters()
params.add('a', value=-1., vary=True)
params.add('b', value=1., vary=True)
params.add('c', value=1., vary=True)
params.add('d', value=1., vary=True)
params.add('e', value=0.0, vary=False)
# remove inf values in errors
y_error[y_error == np.float('inf')] = 1.0
out = minimize(residual, params, args=(x, y, y_error))
report_fit(params)
return out
def _fit_one_file(self, data_orders, rv_guess=0.0, alpha_guess=1.0):
# Create parameters
params = lmfit.Parameters()
params.add('rv', value=rv_guess, min=-5, max=5)
params.add('alpha', value=alpha_guess, min=0, max=3)
# Perform the fit
result = lmfit.minimize(self._errfcn, params, args=(data_orders, self.telluric_model))
logger = logging.getLogger()
if logger.level <= logging.DEBUG:
lmfit.report_fit(params)
return params
def r_fit(time, R, volume_params,far_field=True):
volume_params = volume_params.valuesdict()
t_long = volume_params['tau_long']
params = Parameters()
params.add('Rinf', value=-0.01, )
params.add('R0', value=-0.05, )
params.add('tau_long', value=t_long, vary=False)
result = minimize(residual_r, params, args=(time, R,True,far_field), method='leastsq', maxfev=int(1e5), xtol=1e-9,
ftol=1e-9)
report_fit(result.params, min_correl=0.5)
v = result.params.valuesdict()
t = time
R_th = residual_r(params, time, R, fit=False)
return result.params, R_th
def fit_hi_vel_range(guesses=None, av_image=None, av_image_error=None,
hi_cube=None, hi_velocity_axis=None, hi_noise_cube=None, dgr=None):
from scipy.optimize import curve_fit
from scipy import stats
from lmfit import minimize, Parameters, report_fit, report_errors
from pprint import pprint
params = Parameters()
params.add('low_vel',
value=guesses[0],
min=-100,
max=100,
vary=True)
params.add('high_vel',
value=guesses[1],
min=-100,
max=100,
vary=True)
result = minimize(calc_model_chisq,
params,
kws={'av_image': av_image,
'av_image_error': av_image_error,
'hi_cube': hi_cube,
'hi_velocity_axis': hi_velocity_axis,
'hi_noise_cube': hi_noise_cube,
'dgr': dgr},
#method='BFGS',
method='anneal',
#method='powell',
#method='SLSQP',
options={'gtol': 1e-6,
'disp': True,
'maxiter' : 1e9}
)
report_fit(params)
report_errors(params)
print result.values
print result.errorbars
#print(result.__dict__)
#print(dir(result))
#print result.vars
#print help(result)
print result.view_items()
print result.Bopt
def fitcurve(val0):
if elem.matchX is False:
return
ydat = measdata.D1complex[:, measdata.findex]
data = np.empty(len(ydat) * 2, dtype='float64')
data[0::2] = ydat.real
data[1::2] = ydat.imag
preFit(False)
xaxis3 = np.linspace(squid.start, squid.stop, (squid.pt * 2))
# Using standard curve_fit settings
# Define fitting parameters
params = Parameters()
params.add('CapfF', value=squid.Cap*1e15, vary=True, min=30, max=90)
params.add('IcuA', value=squid.Ic*1e6, vary=True, min=3.0, max=4.5)
params.add('WbpH', value=squid.Wb*1e12, vary=True, min=0, max=1500)
params.add('LooppH', value=squid.LOOP*1e12, vary=False, min=0.0, max=100)
params.add('alpha', value=squid.ALP, vary=False, min=0.98, max=1.02)
params.add('R', value=squid.R, vary=True, min=1, max=20e3)
params.add('Z1', value=elem.Z1, vary=False, min=40, max=60)
params.add('Z2', value=elem.Z2, vary=False, min=40, max=60)
params.add('Z3', value=elem.Z3, vary=False, min=40, max=60)
params.add('L2', value=elem.L2, vary=False, min=0.00, max=0.09)
# Crop region to fit
elem.midx = find_nearest(xaxis3, elem.xmin)
elem.madx = find_nearest(xaxis3, elem.xmax)
# Do Fit
result = minimize(gta1, params, args=(xaxis3[elem.midx:elem.madx], data))
# Present results of fitting
print report_fit(result)
paramsToMem(result.params)
update2(0)
preFit(True)
# Calculate and plot residual there
S11 = getfit()
residual = data - S11
plt.figure(4)
plt.clf()
plt.plot(xaxis3[elem.midx:elem.madx], residual[elem.midx:elem.madx])
plt.axis('tight')
plt.draw()
print 'Avg-sqr Residuals', abs(np.mean((residual * residual))) * 1e8
return
def sineFITwLINEARbackground(param1, param2, **kwargs):
"""
Bounded LS minimisation for the fitting of a sinefunction to a given dataset *with a linear background instead of a constant background*. It is assumed that you can represent param2 as a function of param1. The lmfit package is used to perform the bounded LS minimisation.
DANGER this routine assumes you have a fixed frequency of 1 [unit**-1]. For example:
- if param1 is time and param2 is flux, you will have a sine with a frequency of 1 c/d.
- if param1 is position and param2 is flux, you will have a sine with a frequency of 1 c/pix.
Returns: The optimal lmfit parameter class.
TODO provide options through kwargs to set the boundaries
Returns: The optimal lmfit parameter class.
@param param1: param1 measurements [???]
@type param1: numpy array of length N
@param param2: param2 measurements [???]
@type param2: numpy array of length N
@return: paramSINE
@rtype: lmfit parameter class
@kwargs: show_ME: Boolean to indicate if you want to see the report_fit - Default is False [Boolean]
"""
show_ME = kwargs.get('show_ME', False)
# Determination of the guesses to start your bounded LS fit with.
constantGUESS = np.median(param2) # param2
amplitudeGUESS = np.max(np.abs(constantGUESS-param2))/2. # param2
frequencyGUESS = 1. # DANGER Here is the frequency assumption assumption.
phaseGUESS = 0.1 # Using the param1[np.where(param2==np.max(param2))]-param1[0]%1-0.5 is best, when there is no scatter on param2
slopeGUESS, constantGUESS = np.polyfit(param1, param2, 1)
paramSINE = Parameters()
#Make a params class for lmfit.
# (Name, Value, Vary, Min, Max, Expr)
paramSINE.add_many(('amplitude', amplitudeGUESS, True, amplitudeGUESS*0.1, amplitudeGUESS*1.2, None),
('frequency', frequencyGUESS, False, frequencyGUESS-0.05, frequencyGUESS+0.05, None), # DANGER Here is the frequency assumption assumption. (It is set to non-vary.)
('constant', constantGUESS, True, -abs(constantGUESS)*1.5, abs(constantGUESS)*1.5, None),
('phase', phaseGUESS, True, 0., 1., None),
('slope', slopeGUESS, True, -2*slopeGUESS, +2*slopeGUESS, None))
resultSIN = minimize(BRITE.fitfunctions.ff_lmfitlmfit_sinslope_vs_data, paramSINE, args=(param1, param2))
if show_ME:
report_fit(paramsSIN, show_correl=False)
return paramSINE
def optimize(self, optimization_iterations=10, fcn_callback=None):
params = Parameters()
params.add("density", value=self.density, min=self.density_min, max=self.density_max)
params.add("background_scaling", value=self.background_scaling, min=self.bkg_min, max=self.bkg_max)
def fcn_optimization(params):
density = params['density'].value
background_scaling = params['background_scaling'].value
self.background_spectrum.scaling = background_scaling
calculator = StandardCalculator(
original_spectrum=self.original_spectrum,
background_spectrum=self.background_spectrum,
elemental_abundances=self.elemental_abundances,
density=density,
r=self.r,
interpolation_method=self.interpolation_method,
interpolation_parameters=self.interpolation_parameters,
use_modification_fcn=self.use_modification_fcn
)
calculator.optimize(
r=self.minimization_r,
iterations=optimization_iterations
)
if fcn_callback is not None:
fr_spectrum = calculator.calc_fr()
gr_spectrum = calculator.calc_gr()
fcn_callback(background_scaling, density, fr_spectrum, gr_spectrum)
r, fr = calculator.calc_fr(self.minimization_r).data
output = (-fr - 4 * np.pi * convert_density_to_atoms_per_cubic_angstrom(self.elemental_abundances, density) *
self.minimization_r) ** 2
self.write_output(u'{} X: {:.3f} Den: {:.3f}'.format(self.iteration, np.sum(output)/(r[1]-r[0]), density))
self.iteration+=1
return output
self.output_txt.setPlainText('')
minimize(fcn_optimization, params)
self.write_fit_result(params)
report_fit(params)
def volume_fit(time, volumeexp,far_field=True):
params = Parameters()
params.add('V0', value=-1e-5,)
params.add('delta',value=0.0001,min=0)
params.add('Vinf', expr='V0-delta')
params.add('tau_long', value=0.1)
result = minimize(residual_volume, params, args=(time, volumeexp,True,far_field), method='leastsq', maxfev=int(1e5), xtol=1e-9,
ftol=1e-9)
v = result.params.valuesdict()
t = time
V_th = residual_volume(params, t, volumeexp, fit=False)
# plt.plot(time - t0, volumeexp, 'ro', label="Experimental")
# plt.plot(t_th - t0, V_th, 'b-', label="Theoretical")
# plt.title("Volume")
# plt.legend()
# plt.show()
report_fit(result.params, min_correl=0.5)
return result.params, V_th
def far_field_fit(time, yg, volume_params, R_params, rho, k, g=9.81, mass=0, manip_name=None):
# yg = savgol_filter(yg,11,3)
volume_params = volume_params.valuesdict()
R_params = R_params.valuesdict()
Finf = volume_params['Vinf'] * rho * g
F0 = volume_params['V0'] * rho * g
deltaF = -(Finf - F0)
Rinf = R_params['Rinf']
R0 = R_params['R0']
deltaR =-(Rinf - R0)
print deltaF
params = Parameters()
Amin = 0.05
params.add('q0', value=0.1)
params.add('q0p', value=0.1)
params.add('k', value=8.33)
params.add('massTot', value=0.036, min=0.01,max= 1)
params.add('deltaprim', value=-0.1)
params.add('deltaF', value=deltaF, vary=False)
params.add('Finf', value=Finf, vary=False)
params.add('deltaR', value=deltaR, vary=False)
params.add('Rinf', value=Rinf, vary=False)
params.add('tau_v', value=volume_params['tau_long'], vary=False)
params.add('tau_R', value=R_params['tau_long'], vary=False)
params.add('C1', expr="Finf/k", )
params.add('C2', expr="deltaF/(massTot*((1/tau_v)**2-(2*lamda/tau_v)+omega0**2))")
params.add('D1', expr="Rinf" )
params.add('D2', expr="(omega0**2)*deltaR/((1/tau_R)**2-(2*lamda/tau_R)+omega0**2)")
params.add('omega0', expr="(k/massTot)**0.5")
params.add('lamda', value=1)
params.add('deltaprim', expr='lamda**2-omega0**2')
result = minimize(residual_far_field, params, args=(time, yg), method='leastsq', maxfev=int(1e5), xtol=1e-9,
ftol=1e-9)
report_fit(result.params, min_correl=0.5)
print result.success
v = params.valuesdict()
yg_th = residual_far_field(params, time, yg, fit=False)
v["added_mass"] =0
v['real_mass'] = mass
v["added_mass"] = v['massTot'] - v['real_mass']
# yg_f,ygdot_fa,ygdotdot_f = filterer(yg,win_size,pol_order,double_filter)
return params, yg_th
def run_main():
x1, x2, x3 = dw['target fuel_consumptions'].values, dw['target engine_speeds_out'].values, dw.velocities.values
data = dw['target engine_coolant_temperatures'].values #.diff().fillna(0)
temperature_threshold = 95
temperature_max, initial_engine_temperature = data.max(), data[0]
t_init = initial_engine_temperature
# do fit, here with leastsq model
_t0 = datetime.datetime.now()
result = minimize(fcn2min, params, args=(x1, x2, x3, data, t_init))
_t1 = datetime.datetime.now()
print("Elapsed time: %s"%(_t1-_t0))
# calculate final result
final = fcn(result.params, x1, x2, x3, t_init)
# write error report
report_fit(result.params)
n1, n2, n3 = dn['target fuel_consumptions'].values, dn['target engine_speeds_out'].values, dn.velocities.values
nedc_data = dn['target engine_coolant_temperatures'].values
nedc_t_init = nedc_data[0]
nedc_final = fcn(result.params, n1, n2, n3, nedc_t_init)
# try to plot results
try:
import pylab
pylab.plot(data, 'k+')
pylab.plot(final, 'r')
pylab.plot(nedc_data, 'g+')
pylab.plot(nedc_final, 'b')
pylab.show()
except:
pass
def test_1var():
rands = [-0.21698284, 0.41900591, 0.02349374, -0.218552, -0.3513699,
0.33418304, 0.04226855, 0.213303, 0.45948731, 0.33587736]
x = numpy.arange(10)+1
y = numpy.arange(10)+1+rands
y_errs = numpy.sqrt(y)/2
params = lmfit.Parameters()
params.add(name="m", value=1.0, vary=True)
params.add(name="c", value=0.0, vary=False)
out = lmfit.minimize(linear_chisq, params, args=(x, y))
lmfit.report_fit(out)
assert_allclose(params['m'].value, 1.025, rtol=0.02, atol=0.02)
assert(len(params)==2)
assert(out.nvarys == 1)
assert(out.chisqr > 0.01)
assert(out.chisqr < 5.00)
def test_simple():
# create data to be fitted
np.random.seed(1)
x = np.linspace(0, 15, 301)
data = (5. * np.sin(2 * x - 0.1) * np.exp(-x*x*0.025) +
np.random.normal(size=len(x), scale=0.2) )
# define objective function: returns the array to be minimized
def fcn2min(params, x, data):
""" model decaying sine wave, subtract data"""
amp = params['amp'].value
shift = params['shift'].value
omega = params['omega'].value
decay = params['decay'].value
model = amp * np.sin(x * omega + shift) * np.exp(-x*x*decay)
return model - data
# create a set of Parameters
params = Parameters()
params.add('amp', value= 10, min=0)
params.add('decay', value= 0.1)
params.add('shift', value= 0.0, min=-pi / 2., max=pi / 2)
params.add('omega', value= 3.0)
# do fit, here with leastsq model
result = minimize(fcn2min, params, args=(x, data))
# calculate final result
final = data + result.residual
# write error report
print(" --> SIMPLE --> ")
print(result.params)
report_fit(result.params)
#assert that the real parameters are found
for para, val in zip(result.params.values(), [5, 0.025, -.1, 2]):
check(para, val)
def fit_hi_vel_range(
guesses=None, av_image=None, av_image_error=None, hi_cube=None, hi_velocity_axis=None, hi_noise_cube=None, dgr=None
):
from scipy.optimize import curve_fit
from scipy import stats
from lmfit import minimize, Parameters, report_fit, report_errors
from pprint import pprint
params = Parameters()
params.add("low_vel", value=guesses[0], min=-100, max=100, vary=True)
params.add("high_vel", value=guesses[1], min=-100, max=100, vary=True)
result = minimize(
calc_model_chisq,
params,
kws={
"av_image": av_image,
"av_image_error": av_image_error,
"hi_cube": hi_cube,
"hi_velocity_axis": hi_velocity_axis,
"hi_noise_cube": hi_noise_cube,
"dgr": dgr,
},
# method='BFGS',
method="anneal",
# method='powell',
# method='SLSQP',
options={"gtol": 1e-6, "disp": True, "maxiter": 1e9},
)
report_fit(params)
report_errors(params)
print result.values
print result.errorbars
# print(result.__dict__)
# print(dir(result))
# print result.vars
# print help(result)
print result.view_items()
print result.Bopt
def generate(mod_pars, body_pars, photo_data, rv_data, fit_method, ncores, fname):
nbodies, epoch, max_h, orbit_error, rv_body, rv_corr = mod_pars
masses, radii, fluxes, u1, u2, a, e, inc, om, ln, ma = body_pars
lmparams = lmParameters()
# lmparams.add('N', value=N, vary=False)
# lmparams.add('epoch', value=epoch, vary=False)
# lmparams.add('maxh', value=maxh, vary=False)
# lmparams.add('orbit_error', value=orbit_error, vary=False)
for i in range(nbodies):
lmparams.add('mass_{0}'.format(i), value=masses[i], min=0.0, max=0.1, vary=False)
lmparams.add('radius_{0}'.format(i), value=radii[i], min=0.0, max=1.0, vary=False)
lmparams.add('flux_{0}'.format(i), value=fluxes[i], min=0.0, max=1.0, vary=False)
lmparams.add('u1_{0}'.format(i), value=u1[i], min=0.0, max=1.0, vary=False)
lmparams.add('u2_{0}'.format(i), value=u2[i], min=0.0, max=1.0, vary=False)
# if i < N-1:
# params['flux_{0}'.format(i)].vary = False
# params['u1_{0}'.format(i)].vary = False
# params['u2_{0}'.format(i)].vary = False
if i > 0:
lmparams.add('a_{0}'.format(i), value=a[i - 1], min=0.0, max=10.0, vary=False)
lmparams.add('e_{0}'.format(i), value=e[i - 1], min=0.0, max=1.0, vary=False)
lmparams.add('inc_{0}'.format(i), value=inc[i - 1], min=0.0, max=np.pi, vary=False)
lmparams.add('om_{0}'.format(i), value=om[i - 1], min=0.0, max=twopi)
lmparams.add('ln_{0}'.format(i), value=ln[i - 1], min=0.0, max=twopi)
lmparams.add('ma_{0}'.format(i), value=ma[i - 1], min=0.0, max=twopi)
print('Generating maximum likelihood values...')
results = minimize(residual, lmparams, args=(mod_pars, photo_data, rv_data, ncores, fname),
iter_cb=per_iteration, method=fit_method)
# Save the final outputs
print "Writing report..."
report_fit(results.params)
utilfuncs.report_as_input(mod_pars, utilfuncs.get_lmfit_parameters(mod_pars, results.params), fname)
# Return best fit values
return utilfuncs.get_lmfit_parameters(mod_pars, results.params)
def exp_fit(x, y, start_taus = [1], use_constant=True, amp_max=None, amp_min=None, weights=None, amp_penalty=0,
verbose=True):
num_exp = len(start_taus)
para = lmfit.Parameters()
if use_constant:
para.add('const', y[-1] )
for i in range(num_exp):
para.add('tau' + str(i), start_taus[i], min=0)
y_c = y - y[-1]
a = y_c[fi(x, start_taus[i])]
para.add('amp' + str(i), a)
if amp_max is not None:
para['amp' + str(i)].max = amp_max
if amp_min is not None:
para['amp' + str(i)].min = amp_min
def fit(p):
y_fit = np.zeros_like(y)
if use_constant:
y_fit += p['const'].value
for i in range(num_exp):
amp = p['amp'+str(i)].value
tau = p['tau'+str(i)].value
y_fit += amp * np.exp(-x/tau) + amp_penalty/y.size
return y_fit
def res(p):
if weights is None:
return y - fit(p)
else:
return (y - fit(p)) / weights
mini = lmfit.minimize(res, para)
if verbose:
lmfit.report_fit(mini)
y_fit = fit(mini.params)
return mini, y_fit
def r_fit(time, R, volume_params,far_field):
t_short = volume_params['tau_short']
omega = volume_params['omega']
t_long = volume_params['tau_long']
params = Parameters()
params.add('amp', value=-0.02)
params.add('tau_short', value=t_short, vary=True)
params.add('omega', value=omega, vary=True)
# params.add('omega', expr='omega0*sqrt(1-(1/(tau_short*omega0)**2))')
params.add('shift', value=1, min=0, max=2 * np.pi)
params.add('Rinf', value=-0.01, )
params.add('R0', value=-0.05, )
params.add('tau_long', value=t_long, vary=True)
result = minimize(residual_r, params, args=(time, R,far_field), method='leastsq', maxfev=int(5e4), xtol=1e-8,
ftol=1e-8)
report_fit(result.params, min_correl=0.5)
v = result.params.valuesdict()
t = time
R_th = residual_r(params, time, R, fit=False)
return v, R_th
def example():
# create data to be fitted
x = np.linspace(0, 15, 301)
data = (5. * np.sin(2 * x - 0.1) * np.exp(-x*x*0.025) +
np.random.normal(size=len(x), scale=0.2) )
# define objective function: returns the array to be minimized
def fcn2min(params, x, data):
""" model decaying sine wave, subtract data"""
amp = params['amp'].value
shift = params['shift'].value
omega = params['omega'].value
decay = params['decay'].value
model = amp * np.sin(x * omega + shift) * np.exp(-x*x*decay)
return model - data
# create a set of Parameters
params = Parameters()
params.add('amp', value= 10, min=0)
params.add('decay', value= 0.1)
params.add('shift', value= 0.0, min=-np.pi/2., max=np.pi/2)
params.add('omega', value= 3.0)
# do fit, here with leastsq model
result = minimize(fcn2min, params, args=(x, data))
# calculate final result
final = data + result.residual
plt.plot(x,data)
#plt.plot(x,final)
plt.show()
print result.residual
resultparams = result.params
print resultparams
amp = resultparams['amp'].value
decay = resultparams['decay'].value
shift = resultparams['shift'].value
omega = resultparams['omega'].value
model = amp * np.sin(x * omega + shift) * np.exp(-x*x*decay)
plt.plot(x,model)
plt.show()
report_fit(result.params)
def lmfit_fit(group, x_fit, y_interp):
'''set initial value is important, and more sepcified value can be set down ward'''
para = [1]*group #P initial value
para.extend([1]*group) #a initial value
para.extend([3]*group) #b initial value
################
params = Parameters()
for i in np.arange(len(para)/3):
p = 'p'+str(i)
a = 'a'+str(i)
b = 'b'+str(i)
if i == 0:
params.add(p, value=abs(para[i]), min=10**-1)
params.add(a, value=abs(para[i+len(para)/3]), min=0.5)
params.add(b, value=0.5, min=0.1, max=1.1)
else:
params.add(p, value=abs(para[i]), min=10**-10)
params.add(a, value=abs(para[i+len(para)/3]), min=10**-5)
params.add(b, value=abs(para[i + 2*len(para)/3]), min=0.5, max=5)
#using lmfit to get the final result without negtive values
result = minimize(residuals, params, args=(x_fit, y_interp), method='leastsq')
report_fit(result.params)
return result
