class LmModel(object):
"""
Base class for all models.
Models take x and y and return
"""
def __init__(self,x,y):
self.x, self.y=x,y
self.parameters=Parameters()
self.min=Minimizer(self.residual, self.parameters)
def print_para(self):
for i in self.parameters.values:
print i
def func(self,paras):
raise NotImplementedError
def est_startvals(self):
raise NotImplementedError
def residual(self,paras):
return self.func(paras)-self.y
def fit(self):
self.min.leastsq()
self.y_model=self.func(self.parameters)
def test_multidimensional_fit_GH205():
# test that you don't need to flatten the output from the objective
# function. Tests regression for GH205.
pos = np.linspace(0, 99, 100)
xv, yv = np.meshgrid(pos, pos)
f = lambda xv, yv, lambda1, lambda2: (np.sin(xv * lambda1)
+ np.cos(yv * lambda2))
data = f(xv, yv, 0.3, 3)
assert_(data.ndim, 2)
def fcn2min(params, xv, yv, data):
""" model decaying sine wave, subtract data"""
lambda1 = params['lambda1'].value
lambda2 = params['lambda2'].value
model = f(xv, yv, lambda1, lambda2)
return model - data
# create a set of Parameters
params = Parameters()
params.add('lambda1', value=0.4)
params.add('lambda2', value=3.2)
mini = Minimizer(fcn2min, params, fcn_args=(xv, yv, data))
res = mini.minimize()
def NIST_Test(DataSet, start='start2', plot=True):
NISTdata = ReadNistData(DataSet)
resid, npar, dimx = Models[DataSet]
y = NISTdata['y']
x = NISTdata['x']
params = Parameters()
for i in range(npar):
pname = 'b%i' % (i+1)
cval = NISTdata['cert_values'][i]
cerr = NISTdata['cert_stderr'][i]
pval1 = NISTdata[start][i]
params.add(pname, value=pval1)
myfit = Minimizer(resid, params, fcn_args=(x,), fcn_kws={'y':y},
scale_covar=True)
myfit.prepare_fit()
myfit.leastsq()
digs = Compare_NIST_Results(DataSet, myfit, params, NISTdata)
if plot and HASPYLAB:
fit = -resid(params, x, )
pylab.plot(x, y, 'r+')
pylab.plot(x, fit, 'ko--')
pylab.show()
return digs > 2
def setup(self):
self.x = np.linspace(1, 10, 250)
np.random.seed(0)
self.y = (3.0 * np.exp(-self.x / 2)
- 5.0 * np.exp(-(self.x - 0.1) / 10.)
+ 0.1 * np.random.randn(len(self.x)))
self.p = Parameters()
self.p.add_many(('a1', 4., True, 0., 10.),
('a2', 4., True, -10., 10.),
('t1', 3., True, 0.01, 10.),
('t2', 3., True, 0.01, 20.))
self.p_emcee = deepcopy(self.p)
self.p_emcee.add('noise', 0.2, True, 0.001, 1.)
self.mini_de = Minimizer(Minimizer_Residual,
self.p,
fcn_args=(self.x, self.y),
kws={'seed': 1,
'polish': False,
'maxiter': 100})
self.mini_emcee = Minimizer(Minimizer_lnprob,
self.p_emcee,
fcn_args=(self.x, self.y))
def fit_single_line(self, x, y, zero_lev, err_continuum, fitting_parameters, bootstrap_iterations = 1000):
#Simple fit
if self.fit_dict['MC_iterations'] == 1:
fit_output = lmfit_minimize(residual_gauss, fitting_parameters, args=(x, y, zero_lev, err_continuum))
self.fit_dict['area_intg'] = simps(y, x) - simps(zero_lev, x)
self.fit_dict['area_intg_err'] = 0.0
#Bootstrap
else:
mini_posterior = Minimizer(lnprob_gaussCurve, fitting_parameters, fcn_args = ([x, y, zero_lev, err_continuum]))
fit_output = mini_posterior.emcee(steps=200, params = fitting_parameters)
#Bootstrap for the area of the lines
area_array = empty(bootstrap_iterations)
len_x_array = len(x)
for i in range(bootstrap_iterations):
y_new = y + np_normal_dist(0.0, err_continuum, len_x_array)
area_array[i] = simps(y_new, x) - simps(zero_lev, x)
self.fit_dict['area_intg'] = mean(area_array)
self.fit_dict['area_intg_err'] = std(area_array)
#Store the fitting parameters
output_params = fit_output.params
for key in self.fit_dict['parameters_list']:
self.fit_dict[key + '_norm'] = output_params[key].value
self.fit_dict[key + '_norm_er'] = output_params[key].stderr
return
def polyfit(x,y,u=None):
'''Determine the weighted least-squares fit for 2nd order polynomial'''
x = np.asarray(x)
y = np.asarray(y)
if u is not None:
u[u==0]=1
weight = 1./np.asarray(u)
else:
weight = np.ones_like(x)
params = Parameters()
params.add('a', value=0)
params.add('b', value=(y.max()-y.min())/(x.max()-x.min()))
params.add('c', value=0.0)
def residual(pars, x, data=None,w=None):
model = pars['a'].value + pars['b'].value*x + pars['c'].value*x**2
if data is None:
return model
return (model - data) #* w
myfit = Minimizer(residual, params,fcn_args=(x,), fcn_kws={'data':y,'w':weight})
myfit.leastsq()
return [params['c'].value,params['b'].value,params['a'].value]
def autobk(energy, mu, rbkg=1, nknots=None, group=None, e0=None,
kmin=0, kmax=None, kw=1, dk=0, win=None, vary_e0=True,
chi_std=None, nfft=2048, kstep=0.05, _larch=None):
if _larch is None:
raise Warning("cannot calculate autobk spline -- larch broken?")
# get array indices for rkbg and e0: irbkg, ie0
rgrid = np.pi/(kstep*nfft)
if rbkg < 2*rgrid: rbkg = 2*rgrid
irbkg = int(1.01 + rbkg/rgrid)
if e0 is None:
e0 = find_e0(energy, mu, group=group, _larch=_larch)
ie0 = _index_nearest(energy, e0)
# save ungridded k (kraw) and grided k (kout)
# and ftwin (*k-weighting) for FT in residual
kraw = np.sqrt(ETOK*(energy[ie0:] - e0))
if kmax is None:
kmax = max(kraw)
kout = kstep * np.arange(int(1.01+kmax/kstep))
ftwin = kout**kw * ftwindow(kout, xmin=kmin, xmax=kmax,
window=win, dx=dk)
# calc k-value and initial guess for y-values of spline params
nspline = max(4, min(60, 2*int(rbkg*(kmax-kmin)/np.pi) + 1))
spl_y = np.zeros(nspline)
spl_k = np.zeros(nspline)
for i in range(nspline):
q = kmin + i*(kmax-kmin)/(nspline - 1)
ik = _index_nearest(kraw, q)
i1 = min(len(kraw)-1, ik + 5)
i2 = max(0, ik - 5)
spl_k[i] = kraw[ik]
spl_y[i] = (2*mu[ik] + mu[i1] + mu[i2] ) / 4.0
# get spline represention: knots, coefs, order=3
# coefs will be varied in fit.
knots, coefs, order = splrep(spl_k, spl_y)
# set fit parameters from initial coefficients
fparams = Parameters()
for i, v in enumerate(coefs):
fparams.add("c%i" % i, value=v, vary=i<len(spl_y))
fitkws = dict(knots=knots, order=order, kraw=kraw, mu=mu[ie0:],
irbkg=irbkg, kout=kout, ftwin=ftwin, nfft=nfft)
# do fit
fit = Minimizer(__resid, fparams, fcn_kws=fitkws)
fit.leastsq()
# write final results
coefs = [p.value for p in fparams.values()]
bkg, chi = spline_eval(kraw, mu[ie0:], knots, coefs, order, kout)
obkg = np.zeros(len(mu))
obkg[:ie0] = mu[:ie0]
obkg[ie0:] = bkg
if _larch.symtable.isgroup(group):
setattr(group, 'bkg', obkg)
setattr(group, 'chie', mu-obkg)
setattr(group, 'k', kout)
setattr(group, 'chi', chi)
def test_constraints1():
def residual(pars, x, sigma=None, data=None):
yg = gaussian(x, pars['amp_g'], pars['cen_g'], pars['wid_g'])
yl = lorentzian(x, pars['amp_l'], pars['cen_l'], pars['wid_l'])
model = yg + yl + pars['line_off'] + x * pars['line_slope']
if data is None:
return model
if sigma is None:
return (model - data)
return (model - data)/sigma
n = 601
xmin = 0.
xmax = 20.0
x = linspace(xmin, xmax, n)
data = (gaussian(x, 21, 8.1, 1.2) +
lorentzian(x, 10, 9.6, 2.4) +
random.normal(scale=0.23, size=n) +
x*0.5)
pfit = Parameters()
pfit.add(name='amp_g', value=10)
pfit.add(name='cen_g', value=9)
pfit.add(name='wid_g', value=1)
pfit.add(name='amp_tot', value=20)
pfit.add(name='amp_l', expr='amp_tot - amp_g')
pfit.add(name='cen_l', expr='1.5+cen_g')
pfit.add(name='wid_l', expr='2*wid_g')
pfit.add(name='line_slope', value=0.0)
pfit.add(name='line_off', value=0.0)
sigma = 0.021 # estimate of data error (for all data points)
myfit = Minimizer(residual, pfit,
fcn_args=(x,), fcn_kws={'sigma':sigma, 'data':data},
scale_covar=True)
myfit.prepare_fit()
init = residual(myfit.params, x)
result = myfit.leastsq()
print(' Nfev = ', result.nfev)
print( result.chisqr, result.redchi, result.nfree)
report_fit(result.params)
pfit= result.params
fit = residual(result.params, x)
assert(pfit['cen_l'].value == 1.5 + pfit['cen_g'].value)
assert(pfit['amp_l'].value == pfit['amp_tot'].value - pfit['amp_g'].value)
assert(pfit['wid_l'].value == 2 * pfit['wid_g'].value)
def test_minizers():
"""
test scale minimizers except newton-cg (needs jacobian) and
anneal (doesn't work out of the box).
"""
methods = ['Nelder-Mead', 'Powell', 'CG', 'BFGS',
'L-BFGS-B', 'TNC', 'COBYLA', 'SLSQP']
p_true = Parameters()
p_true.add('amp', value=14.0)
p_true.add('period', value=5.33)
p_true.add('shift', value=0.123)
p_true.add('decay', value=0.010)
def residual(pars, x, data=None):
amp = pars['amp'].value
per = pars['period'].value
shift = pars['shift'].value
decay = pars['decay'].value
if abs(shift) > pi/2:
shift = shift - np.sign(shift)*pi
model = amp*np.sin(shift + x/per) * np.exp(-x*x*decay*decay)
if data is None:
return model
return (model - data)
n = 2500
xmin = 0.
xmax = 250.0
noise = np.random.normal(scale=0.7215, size=n)
x = np.linspace(xmin, xmax, n)
data = residual(p_true, x) + noise
fit_params = Parameters()
fit_params.add('amp', value=11.0, min=5, max=20)
fit_params.add('period', value=5., min=1., max=7)
fit_params.add('shift', value=.10, min=0.0, max=0.2)
fit_params.add('decay', value=6.e-3, min=0, max=0.1)
init = residual(fit_params, x)
mini = Minimizer(residual, fit_params, [x, data])
for m in methods:
print(m)
mini.scalar_minimize(m, x)
fit = residual(fit_params, x)
for name, par in fit_params.items():
nout = "%s:%s" % (name, ' '*(20-len(name)))
print("%s: %s (%s) " % (nout, par.value, p_true[name].value))
for para, true_para in zip(fit_params.values(), p_true.values()):
check_wo_stderr(para, true_para.value)
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 fit_axis(image_nparray2D,axis,minim_method="nelder"):
axis_data = np.sum(pic_data,axis = 1) if (axis == 0) else np.sum(pic_data,axis = 0)
axis_points = np.linspace(1,len(axis_data),len(axis_data))
param_estimates = startparams_estimate(axis_data)
params_for_fit = Parameters()
params_for_fit.add('I_zero',value=param_estimates[0],min=0,max=np.amax(axis_data))
params_for_fit.add('r_zero',value=param_estimates[1],min=1,max=len(axis_data))
params_for_fit.add('omega_zero',value=param_estimates[2],min=1,max=len(axis_data))
params_for_fit.add('backgr',value=param_estimates[3])
fit = Minimizer(residual,params_for_fit,fcn_args=(axis_points,),\
fcn_kws={"data":axis_data})
fit_res = fit.minimize(minim_method)
return (axis_points,axis_data,fit_res)
def fitevent(self, edat, initguess):
try:
dt = 1000./self.Fs # time-step in ms.
# control numpy error reporting
np.seterr(invalid='ignore', over='ignore', under='ignore')
ts = np.array([ t*dt for t in range(0,len(edat)) ], dtype='float64')
self.nStates=len(initguess)
initRCConst=dt*5.
# setup fit params
params=Parameters()
for i in range(0, len(initguess)):
params.add('a'+str(i), value=initguess[i][0])
params.add('mu'+str(i), value=initguess[i][1])
if self.LinkRCConst:
if i==0:
params.add('tau'+str(i), value=initRCConst)
else:
params.add('tau'+str(i), value=initRCConst, expr='tau0')
else:
params.add('tau'+str(i), value=initRCConst)
params.add('b', value=self.baseMean )
igdict=params.valuesdict()
optfit=Minimizer(self._objfunc, params, fcn_args=(ts,edat,))
optfit.prepare_fit()
result=optfit.leastsq(xtol=self.FitTol,ftol=self.FitTol,maxfev=self.FitIters)
if result.success:
tt=[init[0] for init, final in zip(igdict.items(), (result.params.valuesdict()).items()) if init==final]
if len(tt) > 0:
self.flagEvent('wInitGuessUnchanged')
self._recordevent(result)
else:
#print optfit.message, optfit.lmdif_message
self.rejectEvent('eFitConvergence')
except KeyboardInterrupt:
self.rejectEvent('eFitUserStop')
raise
except InvalidEvent:
self.rejectEvent('eInvalidEvent')
except:
self.rejectEvent('eFitFailure')
def __fit2D(self,minim_method="nelder",rotation=False):
self.__fit_axis(0,minim_method)
self.__fit_axis(1,minim_method)
# we first take all the initial parameters from 1D fits
bgr2D_est = self.axis0fitparams.valuesdict()["backgr"]/len(self.axis0pts)
x2D_est = self.axis0fitparams.valuesdict()["r_zero"]
omegaX2D_est = self.axis0fitparams.valuesdict()["omega_zero"]
y2D_est = self.axis1fitparams.valuesdict()["r_zero"]
omegaY2D_est = self.axis1fitparams.valuesdict()["omega_zero"]
smoothened_image = gaussian_filter(self.image_array,50)
peakheight2D_est = np.amax(smoothened_image)
#now we need to programatically cut out the region of interest out of the
#whole picture so that fitting takes way less time
# NOTE! In this implementation, if the beam is small compared to picture size
# and is very close to the edge, the fitting will fail, because the x and y
# center position estimates will be off
self.__format_picture(x2D_est,omegaX2D_est,y2D_est,omegaY2D_est)
cropped_data = self.formatted_array
xvals = np.linspace(1,cropped_data.shape[0],cropped_data.shape[0])
yvals = np.linspace(1,cropped_data.shape[1],cropped_data.shape[1])
x, y = np.meshgrid(yvals,xvals)
# NOTE! there's apparently some weird convention, this has to do with
# Cartesian vs. matrix indexing, which is explain in numpy.meshgrid manual
estimates_2D = Parameters()
estimates_2D.add("I_zero",value=peakheight2D_est,min=bgr2D_est)
estimates_2D.add("x_zero",value=0.5*len(yvals),min=0,max=len(yvals)) # NOTE! weird indexing conventions
estimates_2D.add("y_zero",value=0.5*len(xvals),min=0,max=len(xvals)) # NOTE! weird indexing conventions
estimates_2D.add("omegaX_zero",value=omegaX2D_est)
estimates_2D.add("omegaY_zero",value=omegaY2D_est)
estimates_2D.add("theta_rot",value=0*np.pi,min = 0,max = np.pi) #just starting with 0
estimates_2D.add("backgr",value=bgr2D_est)
if rotation:
fit2D = Minimizer(residual_G2D,estimates_2D,fcn_args=(x,y),fcn_kws={"data":cropped_data})
print("Including rotation")
else:
fit2D = Minimizer(residual_G2D_norotation,estimates_2D,fcn_args=(x,y),fcn_kws={"data":cropped_data})
print("Not including rotation")
fit_res2D = fit2D.minimize(minim_method)
self.x2Dgrid = x
self.y2Dgrid = y
self.fit2Dparams = fit_res2D.params
def fit(self, image):
"""Fit a image of a hologram with the current attribute
parameters.
Example:
>>> p = {'x':0, 'y':0, 'z':100, 'a_p':0.5, 'n_p':1.5, 'n_m':1.337,
... 'mpp':0.135, 'lamb':0.447}
>>> mie_fit = Mie_Fitter(p)
>>> mit_fit.result(image)
"""
dim = image.shape
minner = Minimizer(mie_loss, self.p, fcn_args=(image, dim))
self.result = minner.minimize()
return self.result
def __call__(self):
#out = minimize(self.residual,
# self.params,
# scale_covar = False
# #method = 'cg'
# )
mini = Minimizer(self.residual, self.params)
out = mini.emcee(burn = 10000, steps = 60000, thin = 1, workers = 1, params = self.params)
self.H0 = 10**(out.params['a_nu'].value + 5 +
0.2 * (out.params['m04258'].value - 5*log10(out.params['mu_geometric'].value) - 25))
#print 5*log10(out.params['mu_geometric'].value) + 25
self.e_H0 = model.H0 * sqrt((out.params['a_nu'].stderr * log(10))**2
+ (log(10)/5 *out.params['m04258'].stderr )**2
+ (out.params['mu_geometric'].stderr/out.params['mu_geometric'].value)**2)
return out
def setUp(self):
"""
test scale minimizers except newton-cg (needs jacobian) and
anneal (doesn't work out of the box).
"""
p_true = Parameters()
p_true.add('amp', value=14.0)
p_true.add('period', value=5.33)
p_true.add('shift', value=0.123)
p_true.add('decay', value=0.010)
self.p_true = p_true
n = 2500
xmin = 0.
xmax = 250.0
noise = np.random.normal(scale=0.7215, size=n)
self.x = np.linspace(xmin, xmax, n)
self.data = self.residual(p_true, self.x) + noise
fit_params = Parameters()
fit_params.add('amp', value=11.0, min=5, max=20)
fit_params.add('period', value=5., min=1., max=7)
fit_params.add('shift', value=.10, min=0.0, max=0.2)
fit_params.add('decay', value=6.e-3, min=0, max=0.1)
self.fit_params = fit_params
self.mini = Minimizer(self.residual, fit_params, [self.x, self.data])
def test_bounds():
if not HAS_LEAST_SQUARES:
raise nose.SkipTest
p_true = Parameters()
p_true.add('amp', value=14.0)
p_true.add('period', value=5.4321)
p_true.add('shift', value=0.12345)
p_true.add('decay', value=0.01000)
def residual(pars, x, data=None):
amp = pars['amp']
per = pars['period']
shift = pars['shift']
decay = pars['decay']
if abs(shift) > pi/2:
shift = shift - sign(shift)*pi
model = amp*sin(shift + x/per) * exp(-x*x*decay*decay)
if data is None:
return model
return (model - data)
n = 1500
xmin = 0.
xmax = 250.0
random.seed(0)
noise = random.normal(scale=2.80, size=n)
x = linspace(xmin, xmax, n)
data = residual(p_true, x) + noise
fit_params = Parameters()
fit_params.add('amp', value=13.0, max=20, min=0.0)
fit_params.add('period', value=2, max=10)
fit_params.add('shift', value=0.0, max=pi/2., min=-pi/2.)
fit_params.add('decay', value=0.02, max=0.10, min=0.00)
min = Minimizer(residual, fit_params, (x, data))
out = min.least_squares()
assert(out.nfev > 10)
assert(out.nfree > 50)
assert(out.chisqr > 1.0)
print(fit_report(out, show_correl=True, modelpars=p_true))
assert_paramval(out.params['decay'], 0.01, tol=1.e-2)
assert_paramval(out.params['shift'], 0.123, tol=1.e-2)
def test_scalar_minimize_has_no_uncertainties():
# scalar_minimize doesn't calculate uncertainties.
# when a scalar_minimize is run the stderr and correl for each parameter
# should be None. (stderr and correl are set to None when a Parameter is
# initialised).
# This requires a reset after a leastsq fit has been done.
# Only when scalar_minimize calculates stderr and correl can this test
# be removed.
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)
mini = Minimizer(fcn2min, params, fcn_args=(x, data))
out = mini.minimize()
assert_(np.isfinite(out.params['amp'].stderr))
print(out.errorbars)
assert_(out.errorbars == True)
out2 = mini.minimize(method='nelder-mead')
assert_(out2.params['amp'].stderr is None)
assert_(out2.params['decay'].stderr is None)
assert_(out2.params['shift'].stderr is None)
assert_(out2.params['omega'].stderr is None)
assert_(out2.params['amp'].correl is None)
assert_(out2.params['decay'].correl is None)
assert_(out2.params['shift'].correl is None)
assert_(out2.params['omega'].correl is None)
assert_(out2.errorbars == False)
def fit(self, y, x=None, dy=None, **kws):
fcn_kws={'y':y, 'x':x, 'dy':dy}
fcn_kws.update(kws)
self.minimizer = Minimizer(self.__objective, self.params,
fcn_kws=fcn_kws, scale_covar=True)
self.minimizer.prepare_fit()
self.init = self.model(self.params, x=x, **kws)
self.minimizer.leastsq()
def time_confinterval(self):
np.random.seed(0)
x = np.linspace(0.3,10,100)
y = 1/(0.1*x)+2+0.1*np.random.randn(x.size)
p = Parameters()
p.add_many(('a', 0.1), ('b', 1))
def residual(p):
a = p['a'].value
b = p['b'].value
return 1/(a*x)+b-y
minimizer = Minimizer(residual, p)
out = minimizer.leastsq()
return conf_interval(minimizer, out)
def test_scalar_minimize_neg_value():
x0 = 3.14
fmin = -1.1
xtol = 0.001
ftol = 2.0 * xtol
def objective(pars):
return (pars['x'] - x0) ** 2.0 + fmin
params = Parameters()
params.add('x', value=2*x0)
minr = Minimizer(objective, params)
result = minr.scalar_minimize(method='Nelder-Mead',
options={'xatol': xtol, 'fatol': ftol})
assert abs(result.params['x'].value - x0) < xtol
assert abs(result.fun - fmin) < ftol
def __FitEvent(self):
try:
dt = 1000./self.Fs # time-step in ms.
# edat=np.asarray( np.abs(self.eventData), dtype='float64' )
edat=self.dataPolarity*np.asarray( self.eventData, dtype='float64' )
# control numpy error reporting
np.seterr(invalid='ignore', over='ignore', under='ignore')
ts = np.array([ t*dt for t in range(0,len(edat)) ], dtype='float64')
# estimate initial guess for events
initguess=self._characterizeevent(edat, np.abs(util.avg(edat[:10])), self.baseSD, self.InitThreshold, 6.)
self.nStates=len(initguess)-1
# setup fit params
params=Parameters()
for i in range(1, len(initguess)):
params.add('a'+str(i-1), value=initguess[i][0]-initguess[i-1][0])
params.add('mu'+str(i-1), value=initguess[i][1]*dt)
params.add('tau'+str(i-1), value=dt*7.5)
params.add('b', value=initguess[0][0])
optfit=Minimizer(self.__objfunc, params, fcn_args=(ts,edat,))
optfit.prepare_fit()
optfit.leastsq(xtol=self.FitTol,ftol=self.FitTol,maxfev=self.FitIters)
if optfit.success:
self.__recordevent(optfit)
else:
#print optfit.message, optfit.lmdif_message
self.rejectEvent('eFitConvergence')
except KeyboardInterrupt:
self.rejectEvent('eFitUserStop')
raise
except InvalidEvent:
self.rejectEvent('eInvalidEvent')
except:
self.rejectEvent('eFitFailure')
raise
def fit(self, params0):
r"""Perform a fit with the provided parameters.
Parameters
----------
params0 : list
Initial fitting parameters
"""
self.params0 = params0
p = Parameters()
if self.parinfo is None:
self.parinfo = [None] * len(self.params0)
else:
assert (len(self.params0) == len(self.parinfo))
for i, (p0, parin) in enumerate(zip(self.params0, self.parinfo)):
p.add(name='p{0}'.format(i), value=p0)
if parin is not None:
if 'limits' in parin:
p['p{0}'.format(i)].set(min=parin['limits'][0])
p['p{0}'.format(i)].set(max=parin['limits'][1])
if 'fixed' in parin:
p['p{0}'.format(i)].set(vary=not parin['fixed'])
if np.all([not value.vary for value in p.values()]):
raise Exception('All parameters are fixed!')
self.lmfit_minimizer = Minimizer(self.residuals, p, nan_policy=self.nan_policy, fcn_args=(self.data,))
self.result.orignorm = np.sum(self.residuals(params0, self.data) ** 2)
result = self.lmfit_minimizer.minimize(Dfun=self.deriv, method='leastsq', ftol=self.ftol,
xtol=self.xtol, gtol=self.gtol, maxfev=self.maxfev, epsfcn=self.epsfcn,
factor=self.stepfactor)
self.result.bestnorm = result.chisqr
self.result.redchi = result.redchi
self._m = result.ndata
self.result.nfree = result.nfree
self.result.resid = result.residual
self.result.status = result.ier
self.result.covar = result.covar
self.result.xerror = [result.params['p{0}'.format(i)].stderr for i in range(len(result.params))]
self.result.params = [result.params['p{0}'.format(i)].value for i in range(len(result.params))]
self.result.message = result.message
self.lmfit_result = result
if not result.errorbars or not result.success:
warnings.warn(self.result.message)
return result.success
def fit(self, y, x=None, dy=None, **kws):
fcn_kws={'y':y, 'x':x, 'dy':dy}
fcn_kws.update(kws)
if not self.has_initial_guess:
self.guess_starting_values(y, x=x, **kws)
self.minimizer = Minimizer(self.__objective, self.params,
fcn_kws=fcn_kws, scale_covar=True)
self.minimizer.prepare_fit()
self.init = self.model(self.params, x=x, **kws)
self.minimizer.leastsq()
def fit2D(image_nparray2D,fit_axis0=None,fit_axis1=None,minim_method="nelder"):
if fit_axis0 is None:
fit_axis0 = fit_axis(image_nparray2D,0,minim_method)
if fit_axis1 is None:
fit_axis1 = fit_axis(image_nparray2D,1,minim_method)
# we first take all the initial parameters from 1D fits
bgr2D_est = fit_axis0[2].params.valuesdict()["backgr"]/len(fit_axis1[0])
x2D_est = fit_resultsA0[2].params.valuesdict()["r_zero"]
omegaX2D_est = fit_axis0[2].params.valuesdict()["omega_zero"]
y2D_est = fit_axis1[2].params.valuesdict()["r_zero"]
omegaY2D_est = fit_axis1[2].params.valuesdict()["omega_zero"]
smoothened_image = gaussian_filter(image_nparray2D,50)
peakheight2D_est = np.amax(smoothened_image)
#now we need to programatically cut out the region of interest out of the
#whole picture so that fitting takes way less time
# NOTE! In this implementation, if the beam is small compared to picture size
# and is very close to the edge, the fitting will fail, because the x and y
# center position estimates will be off
cropped_data = format_picture(image_nparray2D,x2D_est,omegaX2D_est,y2D_est,omegaY2D_est)
xvals = np.linspace(1,cropped_data.shape[0],cropped_data.shape[0])
yvals = np.linspace(1,cropped_data.shape[1],cropped_data.shape[1])
x, y = np.meshgrid(yvals,xvals)
# NOTE! there's apparently some weird convention, this has to do with
# Cartesian vs. matrix indexing, which is explain in numpy.meshgrid manual
estimates_2D = Parameters()
estimates_2D.add("I_zero",value=peakheight2D_est,min=bgr2D_est)
estimates_2D.add("x_zero",value=0.5*len(yvals),min=0,max=len(xvals)) # NOTE! weird indexing conventions
estimates_2D.add("y_zero",value=0.5*len(xvals),min=0,max=len(yvals)) # NOTE! weird indexing conventions
estimates_2D.add("omegaX_zero",value=omegaX2D_est)
estimates_2D.add("omegaY_zero",value=omegaY2D_est)
estimates_2D.add("backgr",value=bgr2D_est)
fit2D = Minimizer(residual_2D,estimates_2D,fcn_args=(x,y),fcn_kws={"data":cropped_data})
fit_res2D = fit2D.minimize(minim_method)
print(estimates_2D.valuesdict()["x_zero"])
return (x,y,fit_res2D)
def fit_axis(image_nparray2D,axis,minim_method="nelder"):
"""
This function fits one axis of a 2D array representing an image by doing
a summation along the other axis
fit_axis(image_nparray2D,axis,minim_method="nelder")
"""
axis_data = np.sum(image_nparray2D,axis = 1) if (axis == 0) else np.sum(image_nparray2D,axis = 0)
axis_points = np.linspace(1,len(axis_data),len(axis_data))
param_estimates = startparams_estimate(axis_data)
params_for_fit = Parameters()
params_for_fit.add('I_zero',value=param_estimates[0],min=0,max=np.amax(axis_data))
params_for_fit.add('r_zero',value=param_estimates[1],min=1,max=len(axis_data))
params_for_fit.add('omega_zero',value=param_estimates[2],min=1,max=len(axis_data))
params_for_fit.add('backgr',value=param_estimates[3])
fit = Minimizer(residual_G1D,params_for_fit,fcn_args=(axis_points,),\
fcn_kws={"data":axis_data})
fit_res = fit.minimize(minim_method)
return (axis_points,axis_data,fit_res)
def test_derive():
def func(pars, x, data=None):
model = pars['a'] * np.exp(-pars['b'] * x) + pars['c']
if data is None:
return model
return model - data
def dfunc(pars, x, data=None):
v = np.exp(-pars['b']*x)
return np.array([v, -pars['a']*x*v, np.ones(len(x))])
def f(var, x):
return var[0] * np.exp(-var[1] * x) + var[2]
params1 = Parameters()
params1.add('a', value=10)
params1.add('b', value=10)
params1.add('c', value=10)
params2 = Parameters()
params2.add('a', value=10)
params2.add('b', value=10)
params2.add('c', value=10)
a, b, c = 2.5, 1.3, 0.8
x = np.linspace(0, 4, 50)
y = f([a, b, c], x)
data = y + 0.15*np.random.normal(size=len(x))
# fit without analytic derivative
min1 = Minimizer(func, params1, fcn_args=(x,), fcn_kws={'data': data})
out1 = min1.leastsq()
# fit with analytic derivative
min2 = Minimizer(func, params2, fcn_args=(x,), fcn_kws={'data': data})
out2 = min2.leastsq(Dfun=dfunc, col_deriv=1)
check_wo_stderr(out1.params['a'], out2.params['a'].value, 0.00005)
check_wo_stderr(out1.params['b'], out2.params['b'].value, 0.00005)
check_wo_stderr(out1.params['c'], out2.params['c'].value, 0.00005)
def test_peakfit():
def residual(pars, x, data=None):
g1 = gaussian(x, pars['a1'], pars['c1'], pars['w1'])
g2 = gaussian(x, pars['a2'], pars['c2'], pars['w2'])
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()
out = myfit.leastsq()
check_paras(out.params, org_params)
def test_ci_report():
"""test confidence interval report"""
def residual(pars, x, data=None):
argu = (x*pars['decay'])**2
shift = pars['shift']
if abs(shift) > np.pi/2:
shift = shift - np.sign(shift)*np.pi
model = pars['amp']*np.sin(shift + x/pars['period']) * np.exp(-argu)
if data is None:
return model
return model - data
p_true = Parameters()
p_true.add('amp', value=14.0)
p_true.add('period', value=5.33)
p_true.add('shift', value=0.123)
p_true.add('decay', value=0.010)
n = 2500
xmin = 0.
xmax = 250.0
x = np.linspace(xmin, xmax, n)
data = residual(p_true, x) + np.random.normal(scale=0.7215, size=n)
fit_params = Parameters()
fit_params.add('amp', value=13.0)
fit_params.add('period', value=2)
fit_params.add('shift', value=0.0)
fit_params.add('decay', value=0.02)
mini = Minimizer(residual, fit_params, fcn_args=(x,),
fcn_kws={'data': data})
out = mini.leastsq()
report = fit_report(out)
assert(len(report) > 500)
ci, tr = conf_interval(mini, out, trace=True)
report = ci_report(ci)
assert(len(report) > 250)
def minimize(fcn, paramgroup, method='leastsq', args=None, kws=None,
scale_covar=True, iter_cb=None, reduce_fcn=None, nan_polcy='omit',
_larch=None, **fit_kws):
"""
wrapper around lmfit minimizer for Larch
"""
fiteval = _larch.symtable._sys.fiteval
if isinstance(paramgroup, ParameterGroup):
params = paramgroup.__params__
elif isgroup(paramgroup):
params = group2params(paramgroup, _larch=_larch)
elif isinstance(Parameters):
params = paramgroup
else:
raise ValueError('minimize takes ParamterGroup or Group as first argument')
if args is None:
args = ()
if kws is None:
kws = {}
def _residual(params):
params2group(params, paramgroup)
return fcn(paramgroup, *args, **kws)
fitter = Minimizer(_residual, params, iter_cb=iter_cb,
reduce_fcn=reduce_fcn, nan_policy='omit', **fit_kws)
result = fitter.minimize(method=method)
params2group(result.params, paramgroup)
out = Group(name='minimize results', fitter=fitter, fit_details=result,
chi_square=result.chisqr, chi_reduced=result.redchi)
for attr in ('aic', 'bic', 'covar', 'params', 'nvarys',
'nfree', 'ndata', 'var_names', 'nfev', 'success',
'errorbars', 'message', 'lmdif_message', 'residual'):
setattr(out, attr, getattr(result, attr, None))
return out
plt.grid()
plt.legend()
plt.tight_layout()
plt.show()
# %%
# Least-squares minimization with LMFIT
# -------------------------------------
# Use the :func:`~mrsimulator.utils.spectral_fitting.make_LMFIT_params` for a quick
# setup of the fitting parameters.
params = make_LMFIT_params(sim, processor)
print(params.pretty_print(columns=["value", "min", "max", "vary", "expr"]))
# %%
# **Solve the minimizer using LMFIT**
minner = Minimizer(LMFIT_min_function, params, fcn_args=(sim, processor))
result = minner.minimize()
report_fit(result)
# %%
# The best fit solution
# ---------------------
sim.run()
processed_data = processor.apply_operations(
data=sim.methods[0].simulation).real
# Plot the spectrum
ax = plt.subplot(projection="csdm")
ax.plot(experiment, "k", alpha=0.5, linewidth=2, label="Experiment")
ax.plot(processed_data, "r--", label="Best Fit")
ax.set_xlim(50, -25)
pfit = [Parameter(name='amp_g', value=10),
Parameter(name='cen_g', value=9),
Parameter(name='wid_g', value=1),
Parameter(name='amp_tot', value=20),
Parameter(name='amp_l', expr='amp_tot - amp_g'),
Parameter(name='cen_l', expr='1.5+cen_g'),
Parameter(name='wid_l', expr='2*wid_g'),
Parameter(name='line_slope', value=0.0),
Parameter(name='line_off', value=0.0)]
sigma = 0.021 # estimate of data error (for all data points)
myfit = Minimizer(residual, pfit,
fcn_args=(x,), fcn_kws={'sigma':sigma, 'data':data},
scale_covar=True)
myfit.prepare_fit()
init = residual(myfit.params, x)
if HASPYLAB:
pylab.plot(x, init, 'b--')
myfit.leastsq()
print(' Nfev = ', myfit.nfev)
print( myfit.chisqr, myfit.redchi, myfit.nfree)
report_fit(myfit.params)
# -------------------------------------
# Use the :func:`~mrsimulator.utils.spectral_fitting.make_LMFIT_params` for a quick
# setup of the fitting parameters. Note, the first two arguments of this function is
# the simulator object and a list of SignalProcessor objects, ``processors``. The
# fitting parameters corresponding to the signal processor objects are generated using
# ``SP_i_operation_j_FunctionName_FunctionArg``, where *i* is the *ith* signal
# processor within the list, *j* is the operation index of the *ith* processor, and
# *FunctionName* and *FunctionArg* are the operation function name and function
# argument, respectively.
params = sf.make_LMFIT_params(sim, processors, include={"rotor_frequency"})
print(params.pretty_print(columns=["value", "min", "max", "vary", "expr"]))
# %%
# **Solve the minimizer using LMFIT**
minner = Minimizer(sf.LMFIT_min_function,
params,
fcn_args=(sim, processors, sigmas))
result = minner.minimize()
result
# %%
# The best fit solution
# ---------------------
all_best_fit = sf.bestfit(sim, processors) # a list of best fit simulations
all_residuals = sf.residuals(sim, processors) # a list of residuals
# Plot the spectrum
fig, ax = plt.subplots(1,
3,
figsize=(12, 3),
subplot_kw={"projection": "csdm"})
def fit(x_tofit, y_tofit, func='Growth', daystofit=60, nfreq=7):
y0 = y_tofit[0]
y1 = y_tofit[-1]
x1 = x_tofit[-1]
pars = Parameters()
pars.add('a', value=y1, min=y1)
pars.add('b', value=0., min=0.)
pars.add('c', value=y0, min=0.)
if func == 'Growth':
lfunc = lmfunc
growf = growth
elif func == 'Sigmoid':
lfunc = lmsig
growf = sigm
mfit = Minimizer(lfunc,
pars,
fcn_args=(x_tofit, ),
fcn_kws={'y': y_tofit},
reduce_fcn='neglogcauchy')
nfit = mfit.minimize(method='nedeler')
#nfit = mfit.minimize(method='leastsq')
#nfit = mfit.leastsq()
dfit = mfit.minimize(method='leastsq', params=nfit.params)
print(fit_report(dfit))
a = dfit.params['a']
b = dfit.params['b']
c = dfit.params['c']
## to look ahead
nstd = 3
a_err = nstd * a.stderr
b_err = nstd * b.stderr
c_err = nstd * c.stderr
xfit = np.arange(0, daystofit, 1.)
yfit = lfunc(dfit.params, xfit)
fig, ax = plt.subplots()
#yfit1 = growf(a+a_err,b-b_err,c+c_err,xfit)
#yfit2 = growf(a-a_err,b+b_err,c-c_err,xfit)
yfit1 = growf(a + a_err, b, c, xfit)
yfit2 = growf(a - a_err, b, c, xfit)
#plt.fill_between(xfit, yfit2,yfit1, color="#ABABAB")
plt.fill_between(xfit, yfit2, yfit1, color="#ABABAB", label='CI: 99.75%')
ax.plot(xfit, yfit, 'r-', label="Best fit")
ax.scatter(x_tofit,
y_tofit,
c='black',
s=50,
label="# Diagnosed in Mainland China")
#xlabel = [date[s].date() for s in range(daystofit) if s%7==0]
#print(date.astype(str)[0][5:])
nfreq = 3
date = pd.date_range('2020-01-16', periods=daystofit)
datestr = date.astype(str)
ypred = lfunc(dfit.params, x1 + 1)
yerr = a.stderr / a
ypred_1 = ypred * (1 + 1.732 * yerr)
ypred_2 = ypred * (1 - 1.732 * yerr)
print("Predicted diagnosed number on %s: %d (total: %d-%d, 95%% CI)" %
(datestr[x1 + 1], ypred - y1, ypred_2, ypred_1))
xticks = [xfit[s] for s in range(daystofit) if s % nfreq == 0]
xlabel = [datestr[s][5:] for s in range(daystofit) if s % nfreq == 0]
plt.xticks(xticks, xlabel, rotation=60)
plt.legend()
fig.tight_layout()
plt.show()
fig.savefig('FitbyGompertzGrowth.pdf')
plt.close()
def grid_fit(src_y, src_x, ncols, nrows, params, vary_theta=False, method='least_squares', bbox=None,
normalized_shifts=None):
"""Optimize grid model parameters to match detected source centroids.
Parameters
----------
src_y : `numpy.ndarray`, (N,)
An array of Y-axis centroid coordinates.
src_x : `numpy.ndarray`, (N,)
An array of X-axis centroid coordinates.
ncols : `int`
Number of grid columns.
nrows : `int`
Number of grid rows.
params: `list` or `tuple`
Sequence of initial guesses for the grid model parameters.
vary_theta : `bool`, optional
Allow the grid rotation angle parameter to vary during model fit if
`True`.
method : `str`, optional
Name of the fitting method to use (the default is 'least_squares').
bbox : `lsst.geom.Box2I`, optional
An integer coordinate rectangle corresponding to detector geometry
(the default is `None`, which implies no detector geometry information
will be used).
normalized_shifts : `tuple` [`numpy.ndarray`], optional
A sequence of arrays of normalized shifts in Y-axis and X-axis (the
default is `None`, which implies no normalized shifts to be included).
Returns
-------
grid : `mixcoatl.sourcegrid.DistortedGrid`
Optimized grid model.
result : `lmfit.minimizer.MinimizerResult`
The results of the grid model optimization.
"""
ystep, xstep, theta, y0, x0 = params
## Define fit parameters
params = Parameters()
params.add('ystep', value=ystep, vary=False)
params.add('xstep', value=xstep, vary=False)
params.add('y0', value=y0, min=y0 - 3., max=y0 + 3., vary=True)
params.add('x0', value=x0, min=x0 - 3., max=x0 + 3., vary=True)
params.add('theta', value=theta, min=theta - 0.5*np.pi/180., max=theta + 0.5*np.pi/180., vary=False)
minner = Minimizer(fit_error, params, fcn_args=(src_y, src_x, ncols, nrows),
fcn_kws={'normalized_shifts' : normalized_shifts, 'bbox' : bbox}, nan_policy='omit')
result = minner.minimize(params=params, method=method, max_nfev=None)
if vary_theta:
result_params = result.params
result_values = result_params.valuesdict()
params['y0'].set(value=result_values['y0'], vary=False)
params['x0'].set(value=result_values['x0'], vary=False)
params['theta'].set(vary=True)
theta_minner = Minimizer(fit_error, params, fcn_args=(src_y, src_x, ncols, nrows),
fcn_kws={'normalized_shifts' : normalized_shifts, 'bbox' : bbox},
nan_policy='omit')
theta_result = theta_minner.minimize(params=params, method=method, max_nfev=None)
result.params['theta'] = theta_result.params['theta']
parvals = result.params.valuesdict()
grid = DistortedGrid(parvals['ystep'], parvals['xstep'], parvals['theta'], parvals['y0'], parvals['x0'],
ncols, nrows, normalized_shifts=normalized_shifts)
return grid, result
def BIC_minimisation_region_full(ind1, uc, peak_regions, grouped_peaks, total_spectral_ydata, corr_distance, std):
################################################################################################################
# initialise process
################################################################################################################
# print("minimising region " + str(ind1) + " of " + str(len(peak_regions)))
BIC_param = 15
region = np.array(peak_regions[ind1])
region_y = total_spectral_ydata[region]
fit_y = np.zeros(len(region_y))
copy_peaks = np.array(grouped_peaks[ind1])
params = Parameters()
fitted_peaks = []
ttotal = 0
################################################################################################################
# build initial model
################################################################################################################
# params.add('vregion' + str(ind1), value=2.5, max=5, min=1)
params.add('vregion' + str(ind1), value=0.5, max=1, min=0)
distance = uc(0, "hz") - uc(5, "hz")
std_upper = uc(0, "hz") - uc(1, "hz")
av_std = uc(0, "hz") - uc(0.2, "hz")
std_lower = uc(0, "hz") - uc(0.1, "hz")
# build model
while (len(copy_peaks) > 0):
# pick peak that is furthest from fitted data:
diff_array = region_y - fit_y
ind2 = np.argmax(diff_array[copy_peaks - region[0]])
maxpeak = copy_peaks[ind2]
copy_peaks = np.delete(copy_peaks, ind2)
# only allow params < distance away vary at a time
# add new params
fitted_peaks.append(maxpeak)
fitted_peaks = sorted(fitted_peaks)
params.add('A' + str(maxpeak), value=total_spectral_ydata[maxpeak], min=0, max=1, vary=True)
# params.add('std' + str(maxpeak), value=av_std, vary=True, min = std_lower,
# max = std_upper)
params.add('std' + str(maxpeak), value=av_std, vary=True)
params.add('mu' + str(maxpeak), value=maxpeak, vary=True
, min=maxpeak - 4 * corr_distance, max=maxpeak + 4 * corr_distance)
# adjust amplitudes and widths of the current model
initial_y = p7sim(params, region, fitted_peaks, ind1)
inty = np.sum(region_y[region_y > 0])
intmodel = np.sum(initial_y)
# check the region can be optimised this way
# find peak with max amplitude
maxamp = 0
for peak in fitted_peaks:
amp = params['A' + str(peak)]
if amp > maxamp:
maxamp = copy.copy(amp)
maxintegral = maxamp * len(region)
if maxintegral > inty:
# set initial conditions
while (intmodel / inty < 0.99) or (intmodel / inty > 1.01):
for f in fitted_peaks:
params['std' + str(f)].set(value=params['std' + str(f)] * inty / intmodel)
initial_y = p7sim(params, region, fitted_peaks, ind1)
for f in fitted_peaks:
params['A' + str(f)].set(
value=params['A' + str(f)] * region_y[int(params['mu' + str(f)]) - region[0]] / (
initial_y[f - region[0]]))
initial_y = p7sim(params, region, fitted_peaks, ind1)
intmodel = np.sum(initial_y)
# print('built model region ' + str(ind1))
################################################################################################################
# now relax all params
################################################################################################################
# allow all params to vary
params['vregion' + str(ind1)].set(vary=True)
for peak in fitted_peaks:
params['A' + str(peak)].set(vary=False, min=max(0, params['A' + str(peak)] - 0.01),
max=min(params['A' + str(peak)] + 0.01, 1))
params['mu' + str(peak)].set(vary=False)
params['std' + str(peak)].set(vary=False, min=min(std_lower, params['std' + str(peak)] - av_std),
max=max(params['std' + str(peak)] + av_std, std_upper))
out = Minimizer(p7residual, params,
fcn_args=(region, fitted_peaks, region_y, ind1, False))
results = out.minimize()
params = results.params
# print('relaxed params region ' + str(ind1))
################################################################################################################
# now remove peaks in turn
################################################################################################################
trial_y = p7sim(params, region, fitted_peaks, ind1)
trial_peaks = np.array(fitted_peaks)
amps = []
for peak in trial_peaks:
amps.append(params['A' + str(peak)])
r = trial_y - region_y
chi2 = r ** 2
N = len(chi2)
BIC = N * np.log(np.sum(chi2) / N) + np.log(N) * (3 * len(fitted_peaks) + 2)
while (len(trial_peaks) > 0):
new_params = copy.copy(params)
# find peak with smallest amp
minpeak = trial_peaks[np.argmin(amps)]
# remove this peak from the set left to try
trial_peaks = np.delete(trial_peaks, np.argmin(amps))
amps = np.delete(amps, np.argmin(amps))
# remove this peak from the trial peaks list and the trial params
new_params.__delitem__('A' + str(minpeak))
new_params.__delitem__('mu' + str(minpeak))
new_params.__delitem__('std' + str(minpeak))
new_fitted_peaks = np.delete(fitted_peaks, np.where(fitted_peaks == minpeak))
# simulate data with one fewer peak
new_trial_y = p7sim(new_params, region, new_fitted_peaks, ind1)
r = new_trial_y - region_y
chi2 = np.sum(r ** 2)
N = len(new_trial_y)
new_BIC = N * np.log(chi2 / N) + np.log(N) * (3 * len(new_fitted_peaks) + 2)
# if the fit is significantly better remove this peak
if new_BIC < BIC - BIC_param:
fitted_peaks = copy.copy(new_fitted_peaks)
params = copy.copy(new_params)
BIC = copy.copy(new_BIC)
fitted_peaks = sorted(fitted_peaks)
fit_y = p7sim(params, region, fitted_peaks, ind1)
################################################################################################################
print(" done region " + str(ind1 + 1) + "of" + str(len(peak_regions)))
return fitted_peaks, params, fit_y
def ACMEWLRhybrid(y, corr_distance):
def residual_function(params, im, real):
# phase the region
data = ps(params, im, real, 0)
# make new baseline for this region
r = np.linspace(data[0], data[-1], len(real))
# find negative area
data -= r
ds1 = np.abs((data[1:] - data[:-1]))
p1 = ds1 / np.sum(ds1)
# Calculation of entropy
p1[p1 == 0] = 1
h1 = -p1 * np.log(p1)
h1s = np.sum(h1)
# Calculation of penalty
pfun = 0.0
as_ = data - np.abs(data)
sumas = np.sum(as_)
if sumas < 0:
pfun = (as_[1:] / 2) ** 2
p = np.sum(pfun)
return h1s + 1000 * p
# find regions
classification, sigma = baseline_find_signal(y, corr_distance, True, 1)
c1 = np.roll(classification, 1)
diff = classification - c1
s_start = np.where(diff == 1)[0]
s_end = np.where(diff == -1)[0] - 1
peak_regions = []
for r in range(len(s_start)):
peak_regions.append(np.arange(s_start[r], s_end[r]))
# for region in peak_regions:
# plt.plot(region,y[region],color = 'C1')
# phase each region independently
phase_angles = []
weights = []
centres = []
for region in peak_regions:
params = Parameters()
params.add('p0', value=0, min=-np.pi, max=np.pi)
out = Minimizer(residual_function, params,
fcn_args=(np.imag(y[region]), np.real(y[region])))
results = out.minimize('brute')
p = results.params
phase_angles.append(p['p0'] * 1)
# find weight
data = ps(p, np.imag(y[region]), np.real(y[region]), 0)
# make new baseline for this region
r = np.linspace(data[0], data[-1], len(data))
# find negative area
res = data - r
weights.append(abs(np.sum(res[res > 0] / np.sum(y[y > 0]))))
centres.append(np.median(region) / len(y))
sw = sum(weights)
weights = [w / sw for w in weights]
# do weighted linear regression on the regions
# do outlier analysis
switch = 0
centres = np.array(centres)
weights = np.array(weights)
sweights = np.argsort(weights)[::-1]
phase_angles = np.array(phase_angles)
ind1 = 0
while switch == 0:
intercept, gradient = np.polynomial.polynomial.polyfit(centres, phase_angles, deg=1, w=weights)
predicted_angles = gradient * centres + intercept
weighted_res = np.abs(predicted_angles - phase_angles) * weights
# find where largest weighted residual is
max_res = sweights[ind1]
s = 0
if phase_angles[max_res] > 0:
s = -1
phase_angles[max_res] -= 2 * np.pi
else:
s = +1
phase_angles[max_res] += 2 * np.pi
intercept1, gradient1 = np.polynomial.polynomial.polyfit(centres, phase_angles, deg=1, w=weights)
new_predicted_angles = gradient1 * centres + intercept1
new_weighted_res = np.abs(new_predicted_angles - phase_angles) * weights
if np.sum(new_weighted_res) > np.sum(weighted_res):
switch = 1
phase_angles[max_res] += -2*np.pi*s
ind1 +=1
# phase the data
p_final = Parameters()
p_final.add('p0', value=intercept)
p_final.add('p1', value=gradient)
# p_final.pretty_print()
y = ps(p_final, np.imag(y), np.real(y), 1)
classification, sigma = baseline_find_signal(y, corr_distance, True, 1)
r = gen_baseline(np.real(y), classification, corr_distance)
y -= r
return np.real(y)
def acme(y, corr_distance):
params = Parameters()
phase_order = 3
for p in range(phase_order + 1):
params.add('p' + str(p), value=0, min=-np.pi, max=np.pi)
def acmescore(params, im, real, phase_order):
"""
Phase correction using ACME algorithm by Chen Li et al.
Journal of Magnetic Resonance 158 (2002) 164-168
Parameters
----------
pd : tuple
Current p0 and p1 values
data : ndarray
Array of NMR data.
Returns
-------
score : float
Value of the objective function (phase score)
"""
data = ps(params, im, real, phase_order)
##########
# calculate entropy of non corrected data, calculate penalty for baseline corrected data
# - keep as vector to use the default lmfit method
# Calculation of first derivatives of signal regions
ds1 = np.abs((data[1:] - data[:-1]))
p1 = ds1 / np.sum(ds1)
# Calculation of entropy
p1[p1 == 0] = 1
h1 = -p1 * np.log(p1)
# h1s = np.sum(h1)
# Calculation of penalty
pfun = 0.0
as_ = data - np.abs(data)
# as_ = databl - np.abs(databl)
sumas = np.sum(as_)
if sumas < 0:
# pfun = pfun + np.sum((as_ / 2) ** 2)
pfun = (as_[1:] / 2) ** 2
p = 1000 * pfun
return h1 + p
out = Minimizer(acmescore, params,
fcn_args=(np.imag(y), np.real(y), phase_order))
results = out.minimize()
p = results.params
p.pretty_print()
y = ps(p, np.imag(y), np.real(y), phase_order)
classification, sigma = baseline_find_signal(y, corr_distance, True, 1)
r = gen_baseline(np.real(y), classification, corr_distance)
y -= r
return y
class CommonMinimizerTest(unittest.TestCase):
def setUp(self):
"""
test scale minimizers except newton-cg (needs jacobian) and
anneal (doesn't work out of the box).
"""
p_true = Parameters()
p_true.add('amp', value=14.0)
p_true.add('period', value=5.33)
p_true.add('shift', value=0.123)
p_true.add('decay', value=0.010)
self.p_true = p_true
n = 2500
xmin = 0.
xmax = 250.0
noise = np.random.normal(scale=0.7215, size=n)
self.x = np.linspace(xmin, xmax, n)
data = self.residual(p_true, self.x) + noise
fit_params = Parameters()
fit_params.add('amp', value=11.0, min=5, max=20)
fit_params.add('period', value=5., min=1., max=7)
fit_params.add('shift', value=.10, min=0.0, max=0.2)
fit_params.add('decay', value=6.e-3, min=0, max=0.1)
self.fit_params = fit_params
init = self.residual(fit_params, self.x)
self.mini = Minimizer(self.residual, fit_params, [self.x, data])
def residual(self, pars, x, data=None):
amp = pars['amp'].value
per = pars['period'].value
shift = pars['shift'].value
decay = pars['decay'].value
if abs(shift) > pi / 2:
shift = shift - np.sign(shift) * pi
model = amp * np.sin(shift + x / per) * np.exp(-x * x * decay * decay)
if data is None:
return model
return (model - data)
def test_diffev_bounds_check(self):
# You need finite (min, max) for each parameter if you're using
# differential_evolution.
self.fit_params['decay'].min = None
self.minimizer = 'differential_evolution'
np.testing.assert_raises(ValueError, self.scalar_minimizer)
def test_scalar_minimizers(self):
# test all the scalar minimizers
for method in SCALAR_METHODS:
if method in ['newton', 'dogleg', 'trust-ncg']:
continue
self.minimizer = SCALAR_METHODS[method]
if method == 'Nelder-Mead':
sig = 0.2
else:
sig = 0.15
self.scalar_minimizer(sig=sig)
def scalar_minimizer(self, sig=0.15):
try:
from scipy.optimize import minimize as scipy_minimize
except ImportError:
raise SkipTest
print(self.minimizer)
self.mini.scalar_minimize(method=self.minimizer)
fit = self.residual(self.fit_params, self.x)
for name, par in self.fit_params.items():
nout = "%s:%s" % (name, ' ' * (20 - len(name)))
print("%s: %s (%s) " % (nout, par.value, self.p_true[name].value))
for para, true_para in zip(self.fit_params.values(),
self.p_true.values()):
check_wo_stderr(para, true_para.value, sig=sig)
n = 2500
xmin = 0.
xmax = 250.0
noise = random.normal(scale=0.7215, size=n)
x = linspace(xmin, xmax, n)
data = residual(p_true, x) + noise
fit_params = Parameters()
fit_params.add('amp', value=13.0)
fit_params.add('period', value=2)
fit_params.add('shift', value=0.0)
fit_params.add('decay', value=0.02)
mini = Minimizer(residual, fit_params, fcn_args=(x, ), fcn_kws={'data': data})
out = mini.leastsq()
fit = residual(out.params, x)
report_fit(out)
ci, tr = conf_interval(mini, out, trace=True)
report_ci(ci)
if HASPYLAB:
names = out.params.keys()
i = 0
gs = plt.GridSpec(4, 4)
sx = {}
sy = {}
for fixed in names:
def solve_general(self, nh, delfstar, overlayer, prop_guess={}):
'''
solve the property of a single test.
nh: list of int
delfstar: dict {harm(int): complex, ...}
overlayer: dicr e.g.: {'drho': 0, 'grho_rh': 0, 'phi': 0}
return drho, grho_rh, phi, dlam_rh, err
'''
# input variables - this is helpfulf for the error analysis
# define sensibly names partial derivatives for further use
deriv = {}
err = {}
err_names = ['drho', 'grho_rh', 'phi']
# first pass at solution comes from rh and rd
rd_exp = self.rdexp(nh, delfstar) # nh[2]
rh_exp = self.rhexp(nh, delfstar) # nh[0], nh[1]
logger.info('rd_exp', rd_exp)
logger.info('rh_exp', rh_exp)
n1 = nh[0]
n2 = nh[1]
n3 = nh[2]
# solve the problem
if ~np.isnan(rd_exp) or ~np.isnan(rh_exp):
logger.info('rd_exp, rh_exp is not nan')
# TODO change here for the model selection
if prop_guess: # value{'drho', 'grho_rh', 'phi'}
dlam_rh, phi = self.guess_from_props(**prop_guess)
elif rd_exp > 0.5:
dlam_rh, phi = self.bulk_guess(delfstar)
else:
dlam_rh, phi = self.thinfilm_guess(delfstar)
logger.info('dlam_rh', dlam_rh)
logger.info('phi', phi)
if fit_method == 'lmfit':
params1 = Parameters()
params1.add('dlam_rh',
value=dlam_rh,
min=dlam_rh_range[0],
max=dlam_rh_range[1])
params1.add('phi',
value=phi,
min=phi_range[0],
max=phi_range[1])
def residual1(params, rh_exp, rd_exp):
# dlam_rh = params['dlam_rh'].value
# phi = params['phi'].value
return [
self.rhcalc(nh, dlam_rh, phi) - rh_exp,
self.rdcalc(nh, dlam_rh, phi) - rd_exp
]
mini = Minimizer(
residual1,
params1,
fcn_args=(rh_exp, rd_exp),
# nan_policy='omit',
)
soln1 = mini.leastsq(
# xtol=1e-7,
# ftol=1e-7,
)
print(fit_report(soln1)) #testprint
logger.info('success', soln1.success)
logger.info('message', soln1.message)
logger.info('lmdif_message', soln1.lmdif_message)
dlam_rh = soln1.params.get('dlam_rh').value
phi = soln1.params.get('phi').value
drho = self.drho(n1, delfstar, dlam_rh, phi)
grho_rh = self.grho_from_dlam(self.rh, drho, dlam_rh, phi)
else: # scipy
lb = np.array([dlam_rh_range[0],
phi_range[0]]) # lower bounds on dlam3 and phi
ub = np.array([dlam_rh_range[1],
phi_range[1]]) # upper bonds on dlam3 and phi
def ftosolve(x):
return [
self.rhcalc(nh, x[0], x[1]) - rh_exp,
self.rdcalc(nh, x[0], x[1]) - rd_exp
]
x0 = np.array([dlam_rh, phi])
logger.info(x0)
soln1 = least_squares(ftosolve, x0, bounds=(lb, ub))
logger.info(soln1['x'])
dlam_rh = soln1['x'][0]
phi = soln1['x'][1]
drho = self.drho(n1, delfstar, dlam_rh, phi)
grho_rh = self.grho_from_dlam(self.rh, drho, dlam_rh, phi)
logger.info('solution of 1st solving:')
logger.info('dlam_rh', dlam_rh)
logger.info('phi', phi)
logger.info('drho', phi)
logger.info('grho_rh', grho_rh)
# we solve it again to get the Jacobian with respect to our actual
if drho_range[0] <= drho <= drho_range[1] and grho_rh_range[
0] <= grho_rh <= grho_rh_range[1] and phi_range[
0] <= phi <= phi_range[1]:
logger.info('1st solution in range')
if fit_method == 'lmfit':
params2 = Parameters()
params2.add('drho',
value=dlam_rh,
min=drho_range[0],
max=drho_range[1])
params2.add('grho_rh',
value=grho_rh,
min=grho_rh_range[0],
max=grho_rh_range[1])
params2.add('phi',
value=phi,
min=phi_range[0],
max=phi_range[1])
def residual2(params, delfstar, overlayer, n1, n2, n3):
drho = params['drho'].value
grho_rh = params['grho_rh'].value
phi = params['phi'].value
return ([
np.real(delfstar[n1]) - np.real(
self.delfstarcalc(n1, drho, grho_rh, phi,
overlayer)),
np.real(delfstar[n2]) - np.real(
self.delfstarcalc(n2, drho, grho_rh, phi,
overlayer)),
np.imag(delfstar[n3]) - np.imag(
self.delfstarcalc(n3, drho, grho_rh, phi,
overlayer))
])
mini = Minimizer(
residual2,
params2,
fcn_args=(delfstar, overlayer, n1, n2, n3),
# nan_policy='omit',
)
soln2 = mini.least_squares(
# xtol=1e-7,
# ftol=1e-7,
)
logger.info(soln2.params.keys())
logger.info(soln2.params['drho'])
print(fit_report(soln2))
print('success', soln2.success)
print('message', soln2.message)
print('lmdif_message', soln1.lmdif_message)
# put the input uncertainties into a 3 element vector
delfstar_err = np.zeros(3)
delfstar_err[0] = np.real(self.fstar_err_calc(
delfstar[n1]))
delfstar_err[1] = np.real(self.fstar_err_calc(
delfstar[n2]))
delfstar_err[2] = np.imag(self.fstar_err_calc(
delfstar[n3]))
# initialize the uncertainties
# recalculate solution to give the uncertainty, if solution is viable
drho = soln2.params.get('drho').value
grho_rh = soln2.params.get('grho_rh').value
phi = soln2.params.get('phi').value
dlam_rh = self.d_lamcalc(self.rh, drho, grho_rh, phi)
jac = soln2.params.get('jac') #TODO ???
logger.info('jac', jac)
jac_inv = np.linalg.inv(jac)
for i, k in enumerate(err_names):
deriv[k] = {
0: jac_inv[i, 0],
1: jac_inv[i, 1],
2: jac_inv[i, 2]
}
err[k] = ((jac_inv[i, 0] * delfstar_err[0])**2 +
(jac_inv[i, 1] * delfstar_err[1])**2 +
(jac_inv[i, 2] * delfstar_err[2])**2)**0.5
else: # scipy
x0 = np.array([drho, grho_rh, phi])
lb = np.array(
[drho_range[0], grho_rh_range[0],
phi_range[0]]) # lower bounds drho, grho3, phi
ub = np.array(
[drho_range[1], grho_rh_range[1],
phi_range[1]]) # upper bounds drho, grho3, phi
def ftosolve2(x):
return ([
np.real(delfstar[n1]) - np.real(
self.delfstarcalc(n1, x[0], x[1], x[2],
overlayer)),
np.real(delfstar[n2]) - np.real(
self.delfstarcalc(n2, x[0], x[1], x[2],
overlayer)),
np.imag(delfstar[n3]) - np.imag(
self.delfstarcalc(n3, x[0], x[1], x[2],
overlayer))
])
# put the input uncertainties into a 3 element vector
delfstar_err = np.zeros(3)
delfstar_err[0] = np.real(self.fstar_err_calc(
delfstar[n1]))
delfstar_err[1] = np.real(self.fstar_err_calc(
delfstar[n2]))
delfstar_err[2] = np.imag(self.fstar_err_calc(
delfstar[n3]))
# recalculate solution to give the uncertainty, if solution is viable
soln2 = least_squares(ftosolve2, x0, bounds=(lb, ub))
drho = soln2['x'][0]
grho_rh = soln2['x'][1]
phi = soln2['x'][2]
dlam_rh = self.d_lamcalc(self.rh, drho, grho_rh, phi)
jac = soln2['jac']
logger.info('jac', jac)
jac_inv = np.linalg.inv(jac)
logger.info('jac_inv', jac_inv)
for i, k in enumerate(err_names):
deriv[k] = {
0: jac_inv[i, 0],
1: jac_inv[i, 1],
2: jac_inv[i, 2]
}
err[k] = ((jac_inv[i, 0] * delfstar_err[0])**2 +
(jac_inv[i, 1] * delfstar_err[1])**2 +
(jac_inv[i, 2] * delfstar_err[2])**2)**0.5
if np.isnan(rd_exp) or np.isnan(
rh_exp) or not deriv or not err: # failed to solve the problem
print('2nd solving failed')
# assign the default value first
drho = np.nan
grho_rh = np.nan
phi = np.nan
dlam_rh = np.nan
for k in err_names:
err[k] = np.nan
logger.info('drho', drho)
logger.info('grho_rh', grho_rh)
logger.info('phi', phi)
logger.info('dlam_rh', phi)
logger.info('err', err)
return drho, grho_rh, phi, dlam_rh, err
OutputFormatter.printConfig(configJson)
# close config file
configFile.close()
config = Config(configJson)
# retrieve params from config
params = config.getParams()
data = config.getData()
soly = config.getSoly()
OutputFormatter.printExperimentaldata(data, soly)
minimizer = Minimizer(ExcessSaltSolubilityModel.residual,
params,
fcn_args=(data, soly))
out = minimizer.leastsq()
# show output
#lmfit.printfuncs.report_fit(out.params)
print(lmfit.fit_report(out))
# confidence
# ci = lmfit.conf_interval(minimizer, out)
# show output
# lmfit.printfuncs.report_ci(ci)
# print results
def f(params):
return f1(params) + f2(params) + f3(params)
###############################################################################
# Just as in the documentation we will do a grid search between ``-4`` and
# ``4`` and use a stepsize of ``0.25``. The bounds can be set as usual with
# the ``min`` and ``max`` attributes, and the stepsize is set using
# ``brute_step``.
params['x'].set(min=-4, max=4, brute_step=0.25)
params['y'].set(min=-4, max=4, brute_step=0.25)
###############################################################################
# Performing the actual grid search is done with:
fitter = Minimizer(f, params)
result = fitter.minimize(method='brute')
###############################################################################
# , which will increment ``x`` and ``y`` between ``-4`` in increments of
# ``0.25`` until ``4`` (not inclusive).
grid_x, grid_y = (np.unique(par.ravel()) for par in result.brute_grid)
print(grid_x)
###############################################################################
# The objective function is evaluated on this grid, and the raw output from
# ``scipy.optimize.brute`` is stored in the MinimizerResult as
# ``brute_<parname>`` attributes. These attributes are:
#
# ``result.brute_x0`` -- A 1-D array containing the coordinates of a point at
# which the objective function had its minimum value.
"""Calculate cubic growth and subtract data"""
#Get an ordered dictionary of parameter values
v = params.valuesdict()
#Cubic model
model = v['a'] * t**3 + v['b'] * t**2 + v['c'] * t + v['d']
return model - data #Return residuals
# In[7]:
#Create a Minimizer object
minner = Minimizer(residuals_linear,
params_linear,
fcn_args=(t, np.log(N_rand)))
#Perform the minimization
fit_linear_NLLS = minner.minimize()
# The variable `fit_linear` belongs to a class called [`MinimizerResult`](https://lmfit.github.io/lmfit-py/fitting.html#lmfit.minimizer.MinimizerResult), which include data such as status and error messages, fit statistics, and the updated (i.e., best-fit) parameters themselves in the params attribute.
#
# Now get the summary of the fit:
# In[8]:
report_fit(fit_linear_NLLS)
# ### Using OLS
#
def fit_multigaussian(spec,
vcent=None,
err=None,
max_comp=10,
amp_const=None,
cent_const=None,
sigma_const=None,
sigma_init=10.,
verbose=True,
plot_fit=True,
min_delta_BIC=5.,
min_sigma_intensity=5,
return_model=False,
discrete_fitter=False,
discrete_oversamp=2):
'''
Increase the number of fitted Gaussians to find a minimum
in AIC or BIC.
'''
spec = spec.with_spectral_unit(u.km / u.s)
vels = spec.spectral_axis
# Set parameter limits:
if amp_const is None:
amp_min = 0.
amp_max = 1.1 * np.nanmax(spec.filled_data[:].value)
else:
amp_min = amp_const[0]
amp_max = amp_const[1]
if cent_const is None:
cent_min = vels.value.min() - 0.1 * np.ptp(vels.value)
cent_max = vels.value.max() + 0.1 * np.ptp(vels.value)
else:
cent_min = cent_const[0]
cent_max = cent_const[1]
if sigma_const is None:
sig_min = np.abs(np.diff(vels.value)[0])
sig_max = 0.3 * np.ptp(vels.value)
else:
sig_min = sigma_const[0]
sig_max = sigma_const[1]
if vcent is None:
vcent = np.mean(vels.value)
else:
vcent = vcent.to(u.km / u.s).value
# Currently assuming all spectra have some signal in them.
aics = []
bics = []
fit_outputs = []
pfit = Parameters()
valid_data = np.isfinite(spec.filled_data[:])
yfit = spec.filled_data[:].value[valid_data]
xfit = spec.spectral_axis.value[valid_data]
# Upsample for computing over discrete bins
chan_width = np.abs(np.diff(vels.value)[0])
order_sign = 1. if vels[-1] > vels[0] else -1.
# You really need to rewrite this to be faster.
assert discrete_oversamp > 1.
xfit_upsamp = np.linspace(vels.value[0] - order_sign * 0.5 * chan_width,
vels.value[-1] + order_sign * 0.5 * chan_width,
vels.size * discrete_oversamp)
for nc in range(1, max_comp + 1):
if verbose:
print(f"Now fitting with {nc} components.")
# Place the centre at the largest positive residual within the bounds.
if nc > 1:
tpeak = 20
vel_peakresid = spec.spectral_axis.value[np.argmax(fit_residual)]
if vel_peakresid >= cent_min and vel_peakresid <= cent_max:
v_guess = vel_peakresid
tpeak = fit_residual[np.argmax(fit_residual)]
else:
v_guess = vcent
if tpeak < amp_min:
tpeak = 20.
pfit.add(name=f'amp{nc}', value=tpeak,
min=amp_min, max=amp_max)
pfit.add(name=f'cent{nc}', value=v_guess,
min=cent_min, max=cent_max)
else:
tpeak = 20.
pfit.add(name=f'amp{nc}', value=tpeak,
min=amp_min, max=amp_max)
pfit.add(name=f'cent{nc}', value=vcent,
min=cent_min, max=cent_max)
# Setup a minimum relation between the amp. and line width.
# pfit.add(name=f'integral{nc}',
# value=sigma_init * tpeak,
# min=err.value * sig_min * min_sigma_intensity,
# max=amp_max * sig_max)
# # expr=f'amp{nc} * sigma{nc}')
pfit.add(name=f'sigma{nc}',
value=np.random.uniform(sigma_init - 2, sigma_init + 2),
# expr=f'integral{nc} / amp{nc}',
min=sig_min, max=sig_max,)
mini = Minimizer(residual_multigauss, pfit,
fcn_args=(xfit, xfit_upsamp, yfit,
err if err is not None else 1.,
discrete_fitter),
max_nfev=vels.size * 1000)
out = mini.leastsq()
# out = mini.minimize(method='differential_evolution')
if not out.success:
raise ValueError("Fit failed.")
if verbose:
report_fit(out)
model = multigaussian(vels.value, out.params)
if plot_fit:
plt.plot(vels.value, spec.filled_data[:], drawstyle='steps-mid')
plt.plot(vels.value, model)
for n in range(1, nc + 1):
plt.plot(vels.value, gaussian(vels.value,
out.params[f"amp{n}"],
out.params[f"cent{n}"],
out.params[f"sigma{n}"]))
plt.plot(vels.value, spec.filled_data[:].value - model, '--',
zorder=-10)
plt.draw()
input(f"{nc}?")
plt.clf()
if nc > 1:
if verbose:
print(f"BIC1: {out.bic}; BIC0: {bics[-1]}")
if bics[-1] - out.bic < min_delta_BIC:
if verbose:
print(f"Final model with {nc - 1} components.")
break
else:
# n=1 cases tests against a noise model.
err_norm = err.value if err is not None else 1.
no_model_rss = np.nansum((yfit / err_norm)**2)
no_model_bic = yfit.size * np.log(no_model_rss / yfit.size)
no_fit_model = False
if verbose:
print(f"BIC1: {out.bic}; BIC0: {no_model_bic}")
if no_model_bic - out.bic < min_delta_BIC:
if verbose:
print("No components preferred. Consistent with noise.")
no_fit_model = True
bics.append(no_model_bic)
pfit = Parameters()
pfit.add('amp1', value=0.)
pfit.add('cent1', value=0.)
# pfit.add('integral1', value=0.)
pfit.add('sigma1', value=0.)
fit_outputs.append(pfit)
break
# Smooth the residual to ensure the peak chosen for
# the next component
# is not a single large noise value
# fit_residual = np.abs(convolve_fft(yfit - model,
# Gaussian1DKernel(3)))
fit_residual = yfit - model
aics.append(out.aic)
bics.append(out.bic)
fit_outputs.append(out)
# Exit if max residual is small
# if fit_residual.max() < 3 * err.value:
# if verbose:
# print("Max residual below 3-sigma.")
# break
fit_residual = convolve_fft(fit_residual,
Gaussian1DKernel(3))
# Update parameters for next fit
# With too few components, we often get bright, extremely wide
# components
# To avoid their influence, we will update the component amp and
# cent, only.
for ncc in range(1, nc + 1):
pfit[f'amp{ncc}'].value = out.params[f'amp{ncc}'].value
pfit[f'cent{ncc}'].value = out.params[f'cent{ncc}'].value
# if out.params[f'sigma{ncc}'].value > sigma_init:
# pfit[f'integral{ncc}'].value = sigma_init * out.params[f'amp{ncc}'].value
# else:
# pfit[f'integral{ncc}'].value = out.params[f'integral{ncc}'].value
# pfit[f'sigma{ncc}'].value = min(out.params[f'sigma{ncc}'].value,
# sigma_init)
# new_sigma = out.params[f'sigma{ncc}'].value
# if new_sigma < sig_min:
new_sigma = np.random.uniform(sigma_init - 2, sigma_init + 2)
pfit[f'sigma{ncc}'].value = max(new_sigma, 2 * sig_min)
# pfit = out.params.copy()
if return_model:
if no_fit_model:
return fit_outputs[0], vels.value, np.zeros_like(vels.value)
model = multigaussian(vels.value, fit_outputs[-1].params)
return fit_outputs[-1], vels.value, model
if no_fit_model:
return fit_outputs[0]
return fit_outputs[-1]
params.add('satco1', value=5e-06, max=1e-04, min=1e-07) # , vary=False)
params.add('poros1', value=0.450, max=0.5, min=0.3) # , vary=False)
params.add('bee26', value=7.12, max=15.0, min=2.0)
params.add('phsat26', value=-0.2, max=-0.01, min=-0.5)
params.add('satco26', value=5e-06, max=1e-04, min=1e-07)
params.add('poros2', value=0.450, max=0.5, min=0.3)
params.add('poros3', value=0.450, max=0.5, min=0.3)
params.add('poros4', value=0.450, max=0.5, min=0.3)
params.add('poros5', value=0.450, max=0.5, min=0.3)
params.add('poros6', value=0.450, max=0.5, min=0.3)
otimiza = Minimizer(residualSiB2,
params,
reduce_fcn=None,
calc_covar=True,
fcn_args=(www1_o, swc_o, posval, nlinha))
# out_leastsq = otimiza.leastsq()
out_leastsq = otimiza.minimize(method='leastsq') # Levenberg-Marquardt
# report_fit(out_leastsq.params)
# report_fit(out_leastsq)
print('###################################################')
print('Modulo: Umidade do solo')
print('---Parametros---')
params.pretty_print()
print('---Otimizacao---')
report_fit(out_leastsq)
def fit_gaussian(spec,
vels=None,
vcent=None,
err=None,
amp_const=None,
cent_const=None,
sigma_const=None,
verbose=True,
plot_fit=True,
use_emcee=False,
emcee_kwargs={}):
'''
'''
if vels is None:
spec = spec.with_spectral_unit(u.km / u.s)
vels = spec.spectral_axis
# Set parameter limits:
if amp_const is None:
amp_min = 0.
amp_max = 1.1 * np.nanmax(spec.value)
else:
amp_min = amp_const[0]
amp_max = amp_const[1]
if cent_const is None:
cent_min = vels.value.min() - 0.1 * np.ptp(vels.value)
cent_max = vels.value.max() + 0.1 * np.ptp(vels.value)
else:
cent_min = cent_const[0]
cent_max = cent_const[1]
if sigma_const is None:
sig_min = np.abs(np.diff(vels.value)[0])
sig_max = 0.3 * np.ptp(vels.value)
else:
sig_min = sigma_const[0]
sig_max = sigma_const[1]
if vcent is None:
vcent = np.mean(vels.value)
else:
vcent = vcent.to(u.km / u.s).value
pfit = Parameters()
pfit.add(name='amp', value=20.,
min=amp_min, max=amp_max)
pfit.add(name='cent', value=vcent,
min=cent_min, max=cent_max)
pfit.add(name='sigma', value=10.,
min=sig_min, max=sig_max)
# valid_data = np.isfinite(spec.filled_data[:])
# yfit = spec.filled_data[:].value[valid_data]
# xfit = spec.spectral_axis.value[valid_data]
yfit = spec.value
xfit = vels.value
mini = Minimizer(residual_single, pfit,
fcn_args=(xfit, yfit,
err if err is not None else 1.))
out = mini.leastsq()
if use_emcee:
mini = Minimizer(residual_single, out.params,
fcn_args=(xfit, yfit,
err if err is not None else 1.))
out = mini.emcee(**emcee_kwargs)
if plot_fit:
plt.plot(vels.value, spec.value, drawstyle='steps-mid')
model = gaussian(vels.value,
out.params["amp"],
out.params["cent"],
out.params["sigma"])
plt.plot(vels.value, model)
plt.plot(vels.value, spec.value - model, '--',
zorder=-10)
plt.draw()
return out
def main(raft_id, directory):
sensor_names = [
'S00', 'S01', 'S02', 'S10', 'S11', 'S12', 'S20', 'S21', 'S22'
]
for sensor_name in sensor_names:
sensor_id = '{0}_{1}'.format(raft_id, sensor_name)
print("Starting sensor {0}".format(sensor_id))
try:
####
##
## Fit Local Electronic Offset Effect
##
####
## Config variables
start = 3
stop = 13
max_signal = 150000.
error = 7.0 / np.sqrt(2000.)
## Get existing overscan analysis results
hdulist = fits.open(
join(directory, raft_id, sensor_name,
'{0}_overscan_results.fits'.format(sensor_id)))
cti_results = {i: 0.0 for i in range(1, 17)}
drift_scales = {i: 0.0 for i in range(1, 17)}
decay_times = {i: 0.0 for i in range(1, 17)}
## CCD geometry info
ncols = ITL_AMP_GEOM.nx + ITL_AMP_GEOM.prescan_width
for amp in range(1, 17):
## Signals
all_signals = hdulist[amp].data['FLATFIELD_SIGNAL']
signals = all_signals[all_signals < max_signal]
## Data
data = hdulist[amp].data['COLUMN_MEAN'][
all_signals < max_signal, start:stop + 1]
params = Parameters()
params.add('ctiexp', value=-6, min=-7, max=-5, vary=False)
params.add('trapsize', value=0.0, min=0., max=10., vary=False)
params.add('scaling', value=0.08, min=0, max=1.0, vary=False)
params.add('emissiontime',
value=0.4,
min=0.1,
max=1.0,
vary=False)
params.add('driftscale', value=0.00022, min=0., max=0.001)
params.add('decaytime', value=2.4, min=0.1, max=4.0)
model = SimpleModel()
minner = Minimizer(model.difference,
params,
fcn_args=(signals, data, error, ncols),
fcn_kws={
'start': start,
'stop': stop
})
result = minner.minimize()
if result.success:
cti = 10**result.params['ctiexp']
drift_scale = result.params['driftscale']
decay_time = result.params['decaytime']
cti_results[amp] = cti
drift_scales[amp] = drift_scale.value
decay_times[amp] = decay_time.value
else:
print("Electronics fitting failure: Amp{0}".format(amp))
cti = 10**result.params['ctiexp']
cti_results[amp] = cti
drift_scales[amp] = 0.0
decay_times[amp] = 2.4
param_results = OverscanParameterResults(sensor_id, cti_results,
drift_scales, decay_times)
####
##
## Fit Global CTI
##
####
start = 1
stop = 2
max_signal = 10000.
error = 7.0 / np.sqrt(2000.)
num_transfers = ITL_AMP_GEOM.nx + ITL_AMP_GEOM.prescan_width
cti_results = {amp: 0.0 for amp in range(1, 17)}
drift_scales = param_results.drift_scales
decay_times = param_results.decay_times
ncols = ITL_AMP_GEOM.nx + ITL_AMP_GEOM.prescan_width
for amp in range(1, 17):
## Signals
all_signals = hdulist[amp].data['FLATFIELD_SIGNAL']
signals = all_signals[all_signals < max_signal]
## Data
data = hdulist[amp].data['COLUMN_MEAN'][
all_signals < max_signal, start:stop + 1]
## CTI test
lastpixel = signals
overscan1 = data[:, 0]
overscan2 = data[:, 1]
test = (overscan1 + overscan2) / (ncols * lastpixel)
if np.median(test) > 5.E-6:
params = Parameters()
params.add('ctiexp', value=-6, min=-7, max=-5, vary=True)
params.add('trapsize',
value=5.0,
min=0.,
max=30.,
vary=True)
params.add('scaling',
value=0.08,
min=0,
max=1.0,
vary=True)
params.add('emissiontime',
value=0.35,
min=0.1,
max=1.0,
vary=True)
params.add('driftscale',
value=drift_scales[amp],
min=0.,
max=0.001,
vary=False)
params.add('decaytime',
value=decay_times[amp],
min=0.1,
max=4.0,
vary=False)
model = SimulatedModel()
minner = Minimizer(model.difference,
params,
fcn_args=(signals, data, error,
num_transfers, ITL_AMP_GEOM),
fcn_kws={
'start': start,
'stop': stop,
'trap_type': 'linear'
})
result = minner.minimize()
else:
params = Parameters()
params.add('ctiexp', value=-6, min=-7, max=-5, vary=True)
params.add('trapsize',
value=0.0,
min=0.,
max=10.,
vary=False)
params.add('scaling',
value=0.08,
min=0,
max=1.0,
vary=False)
params.add('emissiontime',
value=0.35,
min=0.1,
max=1.0,
vary=False)
params.add('driftscale',
value=drift_scales[amp],
min=0.,
max=0.001,
vary=False)
params.add('decaytime',
value=decay_times[amp],
min=0.1,
max=4.0,
vary=False)
model = SimulatedModel()
minner = Minimizer(model.difference,
params,
fcn_args=(signals, data, error,
num_transfers, ITL_AMP_GEOM),
fcn_kws={
'start': start,
'stop': stop,
'trap_type': 'linear'
})
result = minner.minimize()
cti_results[amp] = 10**result.params['ctiexp'].value
param_results.cti_results = cti_results
outfile = join(directory, raft_id, sensor_name,
'{0}_parameter_results.fits'.format(sensor_id))
param_results.write_fits(outfile, overwrite=True)
####
##
## Determine Localized Trapping
##
####
start = 1
stop = 20
max_signal = 150000.
for amp in range(1, 17):
## Signals
all_signals = hdulist[amp].data['FLATFIELD_SIGNAL']
signals = all_signals[all_signals < max_signal]
## Data
data = hdulist[amp].data['COLUMN_MEAN'][
all_signals < max_signal, start:stop + 1]
## Second model: model with electronics
params = Parameters()
params.add('ctiexp',
value=np.log10(param_results.cti_results[amp]),
min=-7,
max=-4,
vary=False)
params.add('trapsize', value=0.0, min=0., max=10., vary=False)
params.add('scaling', value=0.08, min=0, max=1.0, vary=False)
params.add('emissiontime',
value=0.35,
min=0.1,
max=1.0,
vary=False)
params.add('driftscale',
value=param_results.drift_scales[amp],
min=0.,
max=0.001,
vary=False)
params.add('decaytime',
value=param_results.decay_times[amp],
min=0.1,
max=4.0,
vary=False)
model = SimpleModel.model_results(params,
signals,
num_transfers,
start=start,
stop=stop)
res = np.sum((data - model)[:, :3], axis=1)
new_signals = hdulist[amp].data['COLUMN_MEAN'][
all_signals < max_signal, 0]
rescale = param_results.drift_scales[amp] * new_signals
new_signals = np.asarray(new_signals - rescale,
dtype=np.float64)
x = new_signals
y = np.maximum(0, res)
# Pad left with ramp
y = np.pad(y, (10, 0), 'linear_ramp', end_values=(0, 0))
x = np.pad(x, (10, 0), 'linear_ramp', end_values=(0, 0))
# Pad right with constant
y = np.pad(y, (1, 1), 'constant', constant_values=(0, y[-1]))
x = np.pad(x, (1, 1),
'constant',
constant_values=(-1, 200000.))
f = interp.interp1d(x, y)
spltrap = SplineTrap(f, 0.4, 1)
pickle.dump(
spltrap,
open(
join(directory, raft_id, sensor_name,
'{0}_amp{1}_trap.pkl'.format(sensor_id, amp)),
'wb'))
hdulist.close()
except Exception as e:
print("Error occurred for {0}!".format(sensor_id))
print(e)
continue
def pre_edge(energy,
mu=None,
group=None,
e0=None,
step=None,
nnorm=3,
nvict=0,
pre1=None,
pre2=-50,
norm1=100,
norm2=None,
make_flat=True,
_larch=None):
"""pre edge subtraction, normalization for XAFS
This performs a number of steps:
1. determine E0 (if not supplied) from max of deriv(mu)
2. fit a line of polymonial to the region below the edge
3. fit a polymonial to the region above the edge
4. extrapolae the two curves to E0 to determine the edge jump
Arguments
----------
energy: array of x-ray energies, in eV, or group (see note)
mu: array of mu(E)
group: output group
e0: edge energy, in eV. If None, it will be determined here.
step: edge jump. If None, it will be determined here.
pre1: low E range (relative to E0) for pre-edge fit
pre2: high E range (relative to E0) for pre-edge fit
nvict: energy exponent to use for pre-edg fit. See Note
norm1: low E range (relative to E0) for post-edge fit
norm2: high E range (relative to E0) for post-edge fit
nnorm: degree of polynomial (ie, nnorm+1 coefficients will be found) for
post-edge normalization curve. Default=3 (quadratic), max=5
make_flat: boolean (Default True) to calculate flattened output.
Returns
-------
None
The following attributes will be written to the output group:
e0 energy origin
edge_step edge step
norm normalized mu(E)
flat flattened, normalized mu(E)
pre_edge determined pre-edge curve
post_edge determined post-edge, normalization curve
dmude derivative of mu(E)
(if the output group is None, _sys.xafsGroup will be written to)
Notes
-----
1 nvict gives an exponent to the energy term for the fits to the pre-edge
and the post-edge region. For the pre-edge, a line (m * energy + b) is
fit to mu(energy)*energy**nvict over the pre-edge region,
energy=[e0+pre1, e0+pre2]. For the post-edge, a polynomial of order
nnorm will be fit to mu(energy)*energy**nvict of the post-edge region
energy=[e0+norm1, e0+norm2].
2 If the first argument is a Group, it must contain 'energy' and 'mu'.
If it exists, group.e0 will be used as e0.
See First Argrument Group in Documentation
"""
energy, mu, group = parse_group_args(energy,
members=('energy', 'mu'),
defaults=(mu, ),
group=group,
fcn_name='pre_edge')
if len(energy.shape) > 1:
energy = energy.squeeze()
if len(mu.shape) > 1:
mu = mu.squeeze()
pre_dat = preedge(energy,
mu,
e0=e0,
step=step,
nnorm=nnorm,
nvict=nvict,
pre1=pre1,
pre2=pre2,
norm1=norm1,
norm2=norm2)
group = set_xafsGroup(group, _larch=_larch)
e0 = pre_dat['e0']
norm = pre_dat['norm']
norm1 = pre_dat['norm1']
norm2 = pre_dat['norm2']
# generate flattened spectra, by fitting a quadratic to .norm
# and removing that.
flat = norm
ie0 = index_nearest(energy, e0)
p1 = index_of(energy, norm1 + e0)
p2 = index_nearest(energy, norm2 + e0)
if p2 - p1 < 2:
p2 = min(len(energy), p1 + 2)
if make_flat and p2 - p1 > 4:
enx, mux = remove_nans2(energy[p1:p2], norm[p1:p2])
# enx, mux = (energy[p1:p2], norm[p1:p2])
fpars = Parameters()
fpars.add('c0', value=0, vary=True)
fpars.add('c1', value=0, vary=True)
fpars.add('c2', value=0, vary=True)
fit = Minimizer(flat_resid, fpars, fcn_args=(enx, mux))
result = fit.leastsq(xtol=1.e-6, ftol=1.e-6)
fc0 = result.params['c0'].value
fc1 = result.params['c1'].value
fc2 = result.params['c2'].value
flat_diff = fc0 + energy * (fc1 + energy * fc2)
flat = norm - flat_diff + flat_diff[ie0]
flat[:ie0] = norm[:ie0]
group.e0 = e0
group.norm = norm
group.flat = flat
group.dmude = np.gradient(mu) / np.gradient(energy)
group.edge_step = pre_dat['edge_step']
group.pre_edge = pre_dat['pre_edge']
group.post_edge = pre_dat['post_edge']
group.pre_edge_details = Group()
group.pre_edge_details.pre1 = pre_dat['pre1']
group.pre_edge_details.pre2 = pre_dat['pre2']
group.pre_edge_details.nnorm = pre_dat['nnorm']
group.pre_edge_details.norm1 = pre_dat['norm1']
group.pre_edge_details.norm2 = pre_dat['norm2']
group.pre_edge_details.pre_slope = pre_dat['precoefs'][0]
group.pre_edge_details.pre_offset = pre_dat['precoefs'][1]
for i in range(MAX_NNORM):
if hasattr(group, 'norm_c%i' % i):
delattr(group, 'norm_c%i' % i)
for i, c in enumerate(pre_dat['norm_coefs']):
setattr(group.pre_edge_details, 'norm_c%i' % i, c)
return
def test_constraints(with_plot=True):
with_plot = with_plot and WITHPLOT
def residual(pars, x, sigma=None, data=None):
yg = gaussian(x, pars['amp_g'].value,
pars['cen_g'].value, pars['wid_g'].value)
yl = lorentzian(x, pars['amp_l'].value,
pars['cen_l'].value, pars['wid_l'].value)
slope = pars['line_slope'].value
offset = pars['line_off'].value
model = yg + yl + offset + x * slope
if data is None:
return model
if sigma is None:
return (model - data)
return (model - data) / sigma
n = 201
xmin = 0.
xmax = 20.0
x = linspace(xmin, xmax, n)
data = (gaussian(x, 21, 8.1, 1.2) +
lorentzian(x, 10, 9.6, 2.4) +
random.normal(scale=0.23, size=n) +
x*0.5)
if with_plot:
pylab.plot(x, data, 'r+')
pfit = Parameters()
pfit.add(name='amp_g', value=10)
pfit.add(name='cen_g', value=9)
pfit.add(name='wid_g', value=1)
pfit.add(name='amp_tot', value=20)
pfit.add(name='amp_l', expr='amp_tot - amp_g')
pfit.add(name='cen_l', expr='1.5+cen_g')
pfit.add(name='wid_l', expr='2*wid_g')
pfit.add(name='line_slope', value=0.0)
pfit.add(name='line_off', value=0.0)
sigma = 0.021 # estimate of data error (for all data points)
myfit = Minimizer(residual, pfit,
fcn_args=(x,), fcn_kws={'sigma':sigma, 'data':data},
scale_covar=True)
myfit.prepare_fit()
init = residual(myfit.params, x)
result = myfit.leastsq()
print(' Nfev = ', result.nfev)
print( result.chisqr, result.redchi, result.nfree)
report_fit(result.params, min_correl=0.3)
fit = residual(result.params, x)
if with_plot:
pylab.plot(x, fit, 'b-')
assert(result.params['cen_l'].value == 1.5 + result.params['cen_g'].value)
assert(result.params['amp_l'].value == result.params['amp_tot'].value - result.params['amp_g'].value)
assert(result.params['wid_l'].value == 2 * result.params['wid_g'].value)
# now, change fit slightly and re-run
myfit.params['wid_l'].expr = '1.25*wid_g'
result = myfit.leastsq()
report_fit(result.params, min_correl=0.4)
fit2 = residual(result.params, x)
if with_plot:
pylab.plot(x, fit2, 'k')
pylab.show()
assert(result.params['cen_l'].value == 1.5 + result.params['cen_g'].value)
assert(result.params['amp_l'].value == result.params['amp_tot'].value - result.params['amp_g'].value)
assert(result.params['wid_l'].value == 1.25 * result.params['wid_g'].value)
m2 = parvals['poly']
b = parvals['intercept']
a = parvals['amp']
newe = m1 * channel + m2 * channel * channel + b
newe[0] = 0.0001
model = np.interp(energy, newe, counts)
return model * a - simcount
params = Parameters()
params.add('slope', value=0)
params.add('intercept', value=0)
params.add('poly', value=0)
params.add('amp', value=100, min=0)
minner = Minimizer(residual,
params,
fcn_args=(channel, simcount, counts),
iter_cb=1000,
nan_policy='propagate')
result = minner.minimize()
final = simcount + result.residual
"""
report_fit(result)
plt.semilogy(energy, simcount, 'r')
plt.semilogy(channel, counts, 'b')
plt.show()
"""
print(len(simcount))
def refit_multigaussian(spec, init_params,
vels=None,
vcent=None,
err=None,
amp_const=None,
cent_const=None,
sigma_const=None,
component_sigma=5.,
nchan_component_sigma=3.,
discrete_fitter=False):
'''
Given full set of initial parameters, refit the spectrum.
'''
# if len(init_params) < 3:
# raise ValueError("Less than 3 initial parameters given.")
if vels is None:
spec = spec.with_spectral_unit(u.m / u.s)
vels = spec.spectral_axis
chan_width = np.abs(np.diff(vels)[:1]).value
if err is None:
# Can't remove components if we don't know what the error is
def comp_sig(amp, sigma):
return True
else:
def comp_sig(amp, sigma):
return (amp * sigma) / \
(err * chan_width * nchan_component_sigma)
# Set parameter limits:
if amp_const is None:
amp_min = 0.
amp_max = 1.1 * np.nanmax(spec.value)
else:
amp_min = amp_const[0]
amp_max = amp_const[1]
if cent_const is None:
cent_min = vels.value.min() - 0.1 * np.ptp(vels.value)
cent_max = vels.value.max() + 0.1 * np.ptp(vels.value)
else:
cent_min = cent_const[0]
cent_max = cent_const[1]
if sigma_const is None:
sig_min = np.abs(np.diff(vels.value)[0])
sig_max = 0.5 * np.ptp(vels.value) / 2.35
else:
sig_min = sigma_const[0]
sig_max = sigma_const[1]
# Create the fit parameter
pars = Parameters()
for i in range(len(init_params) // 3):
pars.add(name=f'amp{i + 1}', value=init_params[3 * i],
min=amp_min, max=amp_max)
pars.add(name=f'cent{i + 1}', value=init_params[3 * i + 1],
min=cent_min, max=cent_max)
pars.add(name=f'sigma{i + 1}', value=init_params[3 * i + 2],
min=sig_min, max=sig_max)
valid_data = np.isfinite(spec.filled_data[:])
yfit = spec.filled_data[:].value[valid_data]
xfit = vels.value[valid_data]
if discrete_fitter:
vels = xfit.copy()
# Upsample for computing over discrete bins
chan_width = np.abs(np.diff(vels.value)[0])
order_sign = 1. if vels[-1] > vels[0] else -1.
# You really need to rewrite this to be faster.
discrete_oversamp = 4
assert discrete_oversamp > 1.
xfit_upsamp = np.linspace(vels.value[0] - order_sign * 0.5 * chan_width,
vels.value[-1] + order_sign * 0.5 * chan_width,
vels.size * discrete_oversamp)
else:
xfit_upsamp = None
comp_deletes = []
while True:
mini = Minimizer(residual_multigauss, pars,
fcn_args=(xfit, xfit_upsamp, yfit,
err if err is not None else 1.,
discrete_fitter),
max_nfev=vels.size * 1000)
out = mini.leastsq()
# Testing null model. Nothing to check
if len(pars) == 0:
break
params_fit = [value.value for value in out.params.values()]
params_fit = np.array(params_fit)
# Make sure all components are significant
component_signif = comp_sig(params_fit[::3],
params_fit[2::3])
if np.all(component_signif >= component_sigma):
break
comp_del = np.argmin(component_signif)
comp_deletes.append(comp_del)
remain_comps = np.arange(len(init_params) // 3)
for dcomp in comp_deletes:
remain_comps = np.delete(remain_comps, dcomp)
pars = Parameters()
for i, comp in enumerate(remain_comps):
pars.add(name=f'amp{i + 1}', value=init_params[3 * i],
min=amp_min, max=amp_max)
pars.add(name=f'cent{i + 1}', value=init_params[3 * i + 1],
min=cent_min, max=cent_max)
pars.add(name=f'sigma{i + 1}', value=init_params[3 * i + 2],
min=sig_min, max=sig_max)
return out
shift = params['shift']
omega = params['omega']
decay = params['decay']
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
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:
data = residual(fit_params, x) + noise
if HASPYLAB:
pylab.plot(x, data, 'r+')
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)
if HASPYLAB:
pylab.plot(x, init, 'b--')
myfit.leastsq()
print ' N fev = ', myfit.nfev
print myfit.chisqr, myfit.redchi, myfit.nfree
report_errors(fit_params)
def fret_fit(self, ax, vary):
dis_peak_n = len(self.x_ini)
params = Parameters()
if dis_peak_n == 1:
params.add('h', value=self.y_ini[0]) # height
params.add('c', value=self.x_ini[0]) # center
params.add('w', value=.05) # width
#params.add('o', value = 0) # offset
minner = Minimizer(one_gau,
params,
fcn_args=(self.xhist, self.yhist))
if dis_peak_n == 2:
params.add('h1', value=self.y_ini[0])
params.add('h2', value=self.y_ini[1])
params.add('c1', value=self.x_ini[0])
params.add('c2', value=self.x_ini[1], vary=vary)
params.add('w1', value=.05)
params.add('w2', value=.05)
params.add('o', value=0)
minner = Minimizer(two_gau,
params,
fcn_args=(self.xhist, self.yhist))
if dis_peak_n == 3:
params.add('h1', value=self.y_ini[0])
params.add('h2', value=self.y_ini[1])
params.add('h3', value=self.y_ini[2])
params.add('c1', value=self.x_ini[0])
params.add('c2', value=self.x_ini[1], vary=vary)
params.add('c3', value=self.x_ini[2])
params.add('w1', value=.05)
params.add('w2', value=.05)
params.add('w3', value=.05)
params.add('o', value=0)
minner = Minimizer(three_gau,
params,
fcn_args=(self.xhist, self.yhist))
self.fret_fit_result = minner.minimize()
self.yhist_fit = self.yhist + self.fret_fit_result.residual
ax.plot(self.xhist, self.yhist_fit, 'black')
ax.set_ylabel('Frequency')
if dis_peak_n == 1:
params1 = Parameters()
params1.add('h', value=self.fret_fit_result.params['h'].value)
params1.add('c', value=self.fret_fit_result.params['c'].value)
params1.add('w', value=self.fret_fit_result.params['w'].value)
#params1.add('o', value = self.fret_fit_result.params['o'].value)
params1.add('h_std', value=self.fret_fit_result.params['h'].stderr)
params1.add('c_std', value=self.fret_fit_result.params['c'].stderr)
params1.add('w_std', value=self.fret_fit_result.params['w'].stderr)
#params1.add('o_std', value = self.fret_fit_result.params['o'].stderr)
self.fit_notes = '\npeak 1:\n' \
+'center: '+str(round(params1['c'].value, 2))+'+/-'+str(round(params1['c_std'].value, 2))+' ('+str(round(params1['c_std'].value/params1['c'].value, 2)*100)+'%)\n' \
+'height: '+str(round(params1['h'].value, 2))+'+/-'+str(round(params1['h_std'].value, 2))+' ('+str(round(params1['h_std'].value/params1['h'].value, 2)*100)+'%)\n' \
+'sigma: '+str(round(params1['w'].value, 2))+'+/-'+str(round(params1['w_std'].value, 2))+' ('+str(round(params1['w_std'].value/params1['w'].value, 2)*100)+'%)\n' \
+'area: '+str(round(params1['h'].value*params1['w'].value/0.3989, 2))+'\n\n' \
+'reduced chisqr: '+str(self.fret_fit_result.redchi)
#+'offset: '+str(round(params1['o'].value, 2))+'+/-'+str(round(params1['o_std'].value, 2))+' ('+str(round(params1['o_std'].value/params1['o'].value, 2)*100)+'%)\n' \
if dis_peak_n == 2:
params1 = Parameters()
params2 = Parameters()
params1.add('h', value=self.fret_fit_result.params['h1'].value)
params1.add('c', value=self.fret_fit_result.params['c1'].value)
params1.add('w', value=self.fret_fit_result.params['w1'].value)
params1.add('h_std',
value=self.fret_fit_result.params['h1'].stderr)
params1.add('c_std',
value=self.fret_fit_result.params['c1'].stderr)
params1.add('w_std',
value=self.fret_fit_result.params['w1'].stderr)
params2.add('h', value=self.fret_fit_result.params['h2'].value)
params2.add('c', value=self.fret_fit_result.params['c2'].value)
params2.add('w', value=self.fret_fit_result.params['w2'].value)
params2.add('h_std',
value=self.fret_fit_result.params['h2'].stderr)
params2.add('c_std',
value=self.fret_fit_result.params['c2'].stderr)
params2.add('w_std',
value=self.fret_fit_result.params['w2'].stderr)
params1.add('o', value=self.fret_fit_result.params['o'].value)
params2.add('o', value=self.fret_fit_result.params['o'].value)
params1.add('o_std', value=self.fret_fit_result.params['o'].stderr)
params2.add('o_std', value=self.fret_fit_result.params['o'].stderr)
self.fit_notes = '\npeak 1:\n' \
+'center: '+str(round(params1['c'].value, 2))+'+/-'+str(round(params1['c_std'].value, 2))+' ('+str(round(params1['c_std'].value/params1['c'].value, 2)*100)+'%)\n' \
+'height: '+str(round(params1['h'].value, 2))+'+/-'+str(round(params1['h_std'].value, 2))+' ('+str(round(params1['h_std'].value/params1['h'].value, 2)*100)+'%)\n' \
+'sigma: '+str(round(params1['w'].value, 2))+'+/-'+str(round(params1['w_std'].value, 2))+' ('+str(round(params1['w_std'].value/params1['w'].value, 2)*100)+'%)\n' \
+'area: '+str(round(params1['h'].value*params1['w'].value/0.3989, 2)) \
+'\n\npeak 2:\n' \
+'center: '+str(round(params2['c'].value, 2))+'+/-'+str(round(params2['c_std'].value, 2))+' ('+str(round(params2['c_std'].value/params2['c'].value, 2)*100)+'%)\n' \
+'height: '+str(round(params2['h'].value, 2))+'+/-'+str(round(params2['h_std'].value, 2))+' ('+str(round(params2['h_std'].value/params2['h'].value, 2)*100)+'%)\n' \
+'sigma: '+str(round(params2['w'].value, 2))+'+/-'+str(round(params2['w_std'].value, 2))+' ('+str(round(params2['w_std'].value/params2['w'].value, 2)*100)+'%)\n' \
+'area: '+str(round(params2['h'].value*params2['w'].value/0.3989, 2))+'\n\n' \
+'reduced chisqr: '+str(self.fret_fit_result.redchi) +'\n\n' \
+'offset: '+str(round(params1['o'].value, 2))+'+/-'+str(round(params1['o_std'].value, 2))+' ('+str(round(params1['o_std'].value/params1['o'].value, 2)*100)+'%)\n' \
mask1 = (self.xhist > params1['c'] - params1['w'] * 3) & (
self.xhist < params1['c'] + params1['w'] * 3)
mask2 = (self.xhist > params2['c'] - params2['w'] * 3) & (
self.xhist < params2['c'] + params2['w'] * 3)
ax.plot(self.xhist[mask1],
one_gau(params1, self.xhist[mask1], self.yhist[mask1]) +
self.yhist[mask1],
color='blue')
ax.plot(self.xhist[mask2],
one_gau(params2, self.xhist[mask2], self.yhist[mask2]) +
self.yhist[mask2],
color='blue')
if dis_peak_n == 3:
params1 = Parameters()
params2 = Parameters()
params3 = Parameters()
params1.add('h', value=self.fret_fit_result.params['h1'].value)
params1.add('c', value=self.fret_fit_result.params['c1'].value)
params1.add('w', value=self.fret_fit_result.params['w1'].value)
params1.add('h_std',
value=self.fret_fit_result.params['h1'].stderr)
params1.add('c_std',
value=self.fret_fit_result.params['c1'].stderr)
params1.add('w_std',
value=self.fret_fit_result.params['w1'].stderr)
params2.add('h', value=self.fret_fit_result.params['h2'].value)
params2.add('c', value=self.fret_fit_result.params['c2'].value)
params2.add('w', value=self.fret_fit_result.params['w2'].value)
params2.add('h_std',
value=self.fret_fit_result.params['h2'].stderr)
params2.add('c_std',
value=self.fret_fit_result.params['c2'].stderr)
params2.add('w_std',
value=self.fret_fit_result.params['w2'].stderr)
params3.add('h', value=self.fret_fit_result.params['h3'].value)
params3.add('c', value=self.fret_fit_result.params['c3'].value)
params3.add('w', value=self.fret_fit_result.params['w3'].value)
params3.add('h_std',
value=self.fret_fit_result.params['h3'].stderr)
params3.add('c_std',
value=self.fret_fit_result.params['c3'].stderr)
params3.add('w_std',
value=self.fret_fit_result.params['w3'].stderr)
params1.add('o', value=self.fret_fit_result.params['o'].value)
params2.add('o', value=self.fret_fit_result.params['o'].value)
params3.add('o', value=self.fret_fit_result.params['o'].value)
params1.add('o_std', value=self.fret_fit_result.params['o'].stderr)
params2.add('o_std', value=self.fret_fit_result.params['o'].stderr)
params3.add('o_std', value=self.fret_fit_result.params['o'].stderr)
self.fit_notes = '\npeak 1:\n' \
+'center: '+str(round(params1['c'].value, 2))+'+/-'+str(round(params1['c_std'].value, 2))+' ('+str(round(params1['c_std'].value/params1['c'].value, 2)*100)+'%)\n' \
+'height: '+str(round(params1['h'].value, 2))+'+/-'+str(round(params1['h_std'].value, 2))+' ('+str(round(params1['h_std'].value/params1['h'].value, 2)*100)+'%)\n' \
+'sigma: '+str(round(params1['w'].value, 2))+'+/-'+str(round(params1['w_std'].value, 2))+' ('+str(round(params1['w_std'].value/params1['w'].value, 2)*100)+'%)\n' \
+'area: '+str(round(params1['h'].value*params1['w'].value/0.3989, 2)) \
+'\n\npeak 2:\n' \
+'center: '+str(round(params2['c'].value, 2))+'+/-'+str(round(params2['c_std'].value, 2))+' ('+str(round(params2['c_std'].value/params2['c'].value, 2)*100)+'%)\n' \
+'height: '+str(round(params2['h'].value, 2))+'+/-'+str(round(params2['h_std'].value, 2))+' ('+str(round(params2['h_std'].value/params2['h'].value, 2)*100)+'%)\n' \
+'sigma: '+str(round(params2['w'].value, 2))+'+/-'+str(round(params2['w_std'].value, 2))+' ('+str(round(params2['w_std'].value/params2['w'].value, 2)*100)+'%)\n' \
+'area: '+str(round(params2['h'].value*params2['w'].value/0.3989, 2)) \
+'\n\npeak 3:\n' \
+'center: '+str(round(params3['c'].value, 2))+'+/-'+str(round(params3['c_std'].value, 2))+' ('+str(round(params3['c_std'].value/params3['c'].value, 2)*100)+'%)\n' \
+'height: '+str(round(params3['h'].value, 2))+'+/-'+str(round(params3['h_std'].value, 2))+' ('+str(round(params3['h_std'].value/params3['h'].value, 2)*100)+'%)\n' \
+'sigma: '+str(round(params3['w'].value, 2))+'+/-'+str(round(params3['w_std'].value, 2))+' ('+str(round(params3['w_std'].value/params3['w'].value, 2)*100)+'%)\n' \
+'area: '+str(round(params3['h'].value*params3['w'].value/0.3989, 2))+'\n\n' \
+'reduced chisqr: '+str(self.fret_fit_result.redchi)+'\n\n' \
+'offset: '+str(round(params1['o'].value, 2))+'+/-'+str(round(params1['o_std'].value, 2))+' ('+str(round(params1['o_std'].value/params1['o'].value, 2)*100)+'%)\n' \
mask1 = (self.xhist > params1['c'] - params1['w'] * 3) & (
self.xhist < params1['c'] + params1['w'] * 3)
mask2 = (self.xhist > params2['c'] - params2['w'] * 3) & (
self.xhist < params2['c'] + params2['w'] * 3)
mask3 = (self.xhist > params3['c'] - params3['w'] * 3) & (
self.xhist < params3['c'] + params3['w'] * 3)
ax.plot(self.xhist[mask1],
one_gau(params1, self.xhist[mask1], self.yhist[mask1]) +
self.yhist[mask1],
color='blue')
ax.plot(self.xhist[mask2],
one_gau(params2, self.xhist[mask2], self.yhist[mask2]) +
self.yhist[mask2],
color='blue')
ax.plot(self.xhist[mask3],
one_gau(params3, self.xhist[mask3], self.yhist[mask3]) +
self.yhist[mask3],
color='blue')
def optimize(function: Callable,
cte: settings.Settings,
average: bool = False,
material_text: str = '',
N_samples: int = None,
full_path: str = None) -> OptimSolution:
''' Minimize the error between experimental data and simulation for the settings in cte
average = True -> optimize average rate equations instead of microscopic ones.
function returns the error vector and accepts: parameters, sim, and average.
'''
logger = logging.getLogger(__name__)
optim_progress = [] # type: List[str]
def callback_fun(params: Parameters,
iter_num: int,
resid: np.array,
sim: simulations.Simulations,
average: bool = False,
N_samples: int = None) -> None:
''' This function is called after every minimization step
It prints the current parameters and error from the cache
'''
optim_progbar.update(1)
if not cte['no_console']:
val_list = ', '.join('{:.3e}'.format(par.value)
for par in params.values())
error = np.sqrt((resid * resid).sum())
msg = '{}, \t\t{}, \t{:.4e},\t[{}]'.format(
iter_num,
datetime.datetime.now().strftime('%H:%M:%S'), error, val_list)
tqdm.tqdm.write(msg)
logger.info(msg)
optim_progress.append(msg)
start_time = datetime.datetime.now()
logger.info('Decay curves optimization of ' + material_text)
cte['no_plot'] = True
sim = simulations.Simulations(cte, full_path=full_path)
method, parameters, options_dict = setup_optim(cte)
optim_progbar = tqdm.tqdm(desc='Optimizing',
unit='points',
disable=cte['no_console'])
param_names = ', '.join(name for name in parameters.keys())
header = 'Iter num\tTime\t\tRMSD\t\tParameters ({})'.format(param_names)
optim_progress.append(header)
tqdm.tqdm.write(header)
minimizer = Minimizer(function,
parameters,
fcn_args=(sim, average, N_samples),
iter_cb=callback_fun)
# minimize logging only warnings or worse to console.
with disable_loggers([
'simetuc.simulations', 'simetuc.precalculate', 'simetuc.lattice',
'simetuc.simulations.conc_dep'
]):
with disable_console_handler(__name__):
result = minimizer.minimize(method=method, **options_dict)
optim_progbar.update(1)
optim_progbar.close()
# fit results
report_fit(result.params)
logger.info(fit_report(result))
best_x = np.array([par.value for par in result.params.values()])
if 'brute' in method:
min_f = np.sqrt(result.candidates[0].score)
else:
min_f = np.sqrt((result.residual**2).sum())
total_time = datetime.datetime.now() - start_time
hours, remainder = divmod(total_time.total_seconds(), 3600)
minutes, seconds = divmod(remainder, 60)
tqdm.tqdm.write('')
formatted_time = '{:.0f}h {:02.0f}m {:02.0f}s'.format(
hours, minutes, seconds)
logger.info('Minimum reached! Total time: %s.', formatted_time)
logger.info('Optimized RMS error: %.3e.', min_f)
logger.info('Parameters name and value:')
for name, best_val in zip(parameters.keys(), best_x.T):
logger.info('%s: %.3e.', name, best_val)
optim_solution = OptimSolution(result, cte, optim_progress,
total_time.total_seconds())
return optim_solution
def fit_temp_sta(temporal_sta,
time,
fit_time,
tau1=None,
tau2=None,
amp1=None,
amp2=None,
min_time=None,
max_time=None,
min_amp=-1,
max_amp=1,
max_n=20):
"""Fit the temporal integration of the sta.
Use the difference of two cascades of low-pass filters to fit
the raw temporal integration of STA. It uses the time before
of the spike to compute the fitting.
Parameters
----------
temporal_sta: ndarray
array with the raw temporal integration of the sta.
time: ndarray
array with the time of the raw temporal integration.
fit_time: ndarray
array with the time of fitting curve.
tau1: float default:None
estimated time for positive peak of temporal integration
tau2: float default:None
estimated time for negative peak of temporal integration
amp1: float default:None
estimated amplitude for positive peak of temporal integration
amp2: float default:None
estimated amplitude for negative peak of temporal integration
min_time: float default:None
minimum time to fit tau1 or tau2
max_time: float default:None
maximum time to fit tau1 or tau2
min_amp: float default:-1
minimum amplitude to fit amp1 or amp2
max_amp: float default:1
minimum amplitude to fit amp1 or amp2
max_n=: float default:20
maximum order of a model to fit
Returns
-------
fit_parameters: lmfit.Params.params
parameters of the fitting for two_cascades model
fit_temp: ndarray
array with the values of the fitting using fit_time
"""
tau1 = tau1 if tau1 else time[temporal_sta.argmax()]
tau2 = tau2 if tau2 else time[temporal_sta.argmin()]
amp1 = amp1 if amp1 else np.abs(temporal_sta.max())
amp2 = amp2 if amp2 else np.abs(temporal_sta.min())
min_time = min_time if min_time else time[1]
max_time = max_time if max_time else time[-2]
params_fit = Parameters()
params_fit.add('amp1', value=amp1, min=min_amp, max=max_amp)
params_fit.add('amp2', value=amp2, min=min_amp, max=max_amp)
params_fit.add('tau1', value=tau1, min=min_time, max=max_time)
params_fit.add('tau2', value=tau2, min=min_time, max=max_time)
params_fit.add('n', value=3, max=max_n)
minner = Minimizer(two_cascades_min,
params_fit,
fcn_args=(time, temporal_sta))
try:
result = minner.minimize(method='Nelder')
fit_parameters = result.params
fit_temp = two_cascades(fit_parameters, fit_time)
except ValueError:
try:
result = minner.minimize()
fit_parameters = result.params
fit_temp = two_cascades(fit_parameters, fit_time)
except ValueError:
for key in params_fit:
params_fit[key].set(value=0)
fit_parameters = params_fit
fit_temp = np.full_like(fit_time, np.nan)
return fit_parameters, fit_temp
np.random.normal(scale=0.1, size=x.size)) ############################################################################### # Create the fitting parameters and set an inequality constraint for ``cen_l``. # First, we add a new fitting parameter ``peak_split``, which can take values # between 0 and 5. Afterwards, we constrain the value for ``cen_l`` using the # expression to be ``'peak_split+cen_g'``: pfit = Parameters() pfit.add(name='amp_g', value=10) pfit.add(name='amp_l', value=10) pfit.add(name='cen_g', value=5) pfit.add(name='peak_split', value=2.5, min=0, max=5, vary=True) pfit.add(name='cen_l', expr='peak_split+cen_g') pfit.add(name='wid_g', value=1) pfit.add(name='wid_l', expr='wid_g') mini = Minimizer(residual, pfit, fcn_args=(x, data)) out = mini.leastsq() best_fit = data + out.residual ############################################################################### # Performing a fit, here using the ``leastsq`` algorithm, gives the following # fitting results: report_fit(out.params) ############################################################################### # and figure: plt.plot(x, data, 'o') plt.plot(x, best_fit, '--', label='best fit') plt.legend()
def test_derive():
def func(pars, x, data=None):
a = pars['a'].value
b = pars['b'].value
c = pars['c'].value
model = a * np.exp(-b * x) + c
if data is None:
return model
return (model - data)
def dfunc(pars, x, data=None):
a = pars['a'].value
b = pars['b'].value
c = pars['c'].value
v = np.exp(-b * x)
return [v, -a * x * v, np.ones(len(x))]
def f(var, x):
return var[0] * np.exp(-var[1] * x) + var[2]
params1 = Parameters()
params1.add('a', value=10)
params1.add('b', value=10)
params1.add('c', value=10)
params2 = Parameters()
params2.add('a', value=10)
params2.add('b', value=10)
params2.add('c', value=10)
a, b, c = 2.5, 1.3, 0.8
x = np.linspace(0, 4, 50)
y = f([a, b, c], x)
data = y + 0.15 * np.random.normal(size=len(x))
# fit without analytic derivative
min1 = Minimizer(func, params1, fcn_args=(x, ), fcn_kws={'data': data})
min1.leastsq()
fit1 = func(params1, x)
# fit with analytic derivative
min2 = Minimizer(func, params2, fcn_args=(x, ), fcn_kws={'data': data})
min2.leastsq(Dfun=dfunc, col_deriv=1)
fit2 = func(params2, x)
print('''Comparison of fit to exponential decay
with and without analytic derivatives, to
model = a*exp(-b*x) + c
for a = %.2f, b = %.2f, c = %.2f
==============================================
Statistic/Parameter| Without | With |
----------------------------------------------
N Function Calls | %3i | %3i |
Chi-square | %.4f | %.4f |
a | %.4f | %.4f |
b | %.4f | %.4f |
c | %.4f | %.4f |
----------------------------------------------
''' % (a, b, c, min1.nfev, min2.nfev, min1.chisqr, min2.chisqr,
params1['a'].value, params2['a'].value, params1['b'].value,
params2['b'].value, params1['c'].value, params2['c'].value))
check_wo_stderr(min1.params['a'], min2.params['a'].value, 0.00005)
check_wo_stderr(min1.params['b'], min2.params['b'].value, 0.00005)
check_wo_stderr(min1.params['c'], min2.params['c'].value, 0.00005)
def _fit(self):
import numpy as np
x0, x1 = self.lr.getRegion()
start_idx = fi(self.spectrum.data[:, 0], x0)
end_idx = fi(self.spectrum.data[:, 0], x1) + 1
x_data = self.spectrum.data[start_idx:end_idx, 0]
y_data = self.spectrum.data[start_idx:end_idx, 1]
tab_idx = self.tabWidget.currentIndex()
if tab_idx == 0:
self._setup_model()
# fill the parameters from fields
for i, p in enumerate((self.current_model.params if tab_idx == 0 else
self.general_model_params).values()):
p.value = float(self.value_list[i][tab_idx].text())
p.min = float(self.lower_bound_list[i][tab_idx].text())
p.max = float(self.upper_bound_list[i][tab_idx].text())
p.vary = not self.fixed_list[i][tab_idx].isChecked()
def y_fit(params):
if tab_idx == 0:
y = self.current_model.wrapper_func(x_data, params)
else:
init, coefs, rates, y0 = self.get_values_from_params(params)
sol = self._simul_custom_model(init, rates, x_data)
y = (coefs * sol).sum(axis=1, keepdims=False) + y0
return y
def residuals(params):
y = y_fit(params)
e = y - y_data
if self.cbPropWeighting.isChecked():
e /= y * y
return e
minimizer = Minimizer(
residuals, self.current_model.params
if tab_idx == 0 else self.general_model_params)
method = self.methods[self.cbMethod.currentIndex()]['abbr']
result = minimizer.minimize(method=method) # fit
if tab_idx == 0:
self.current_model.params = result.params
else:
self.general_model_params = result.params
# fill fields
values_errors = np.zeros((len(result.params), 2), dtype=np.float64)
for i, p in enumerate(result.params.values()):
values_errors[i, 0] = p.value
values_errors[i, 1] = p.stderr if p.stderr is not None else 0
self.value_list[i][tab_idx].setText(f"{p.value:.4g}")
self.error_list[i][tab_idx].setText(
f"{p.stderr:.4g}" if p.stderr else '')
y_fit_data = y_fit(result.params)
y_residuals = y_data - y_fit_data
# self.remove_last_fit()
self.clear_plot()
self.plot_fit = self.plot_widget.plotItem.plot(
x_data,
y_fit_data,
pen=pg.mkPen(color=QColor(0, 0, 0, 200), width=2.5),
name="Fit of {}".format(self.spectrum.name))
self.plot_residuals = self.plot_widget.plotItem.plot(
x_data,
y_residuals,
pen=pg.mkPen(color=QColor(255, 0, 0, 150), width=1),
name="Residuals of {}".format(self.spectrum.name))
self.fitted_spectrum = SpectrumItem.from_xy_values(
x_data,
y_fit_data,
name="Fit of {}".format(self.spectrum.name),
color='black',
line_width=2.5,
line_type=Qt.SolidLine)
self.residual_spectrum = SpectrumItem.from_xy_values(
x_data,
y_residuals,
name="Residuals of {}".format(self.spectrum.name),
color='red',
line_width=1,
line_type=Qt.SolidLine)
self.fit_result = FitResult(result,
minimizer,
values_errors,
(self.current_model if tab_idx == 0 else
self.current_general_model),
data_item=self.spectrum,
fit_item=self.fitted_spectrum,
residuals_item=self.residual_spectrum)