def group2params(paramgroup, _larch=None):
"""take a Group of Parameter objects (and maybe other things)
and put them into Larch's current fiteval namespace
returns a lmfit Parameters set, ready for use in fitting
"""
if _larch is None:
return None
if isinstance(paramgroup, ParameterGroup):
return paramgroup.__params__
fiteval = _larch.symtable._sys.fiteval
params = Parameters(asteval=fiteval)
if paramgroup is not None:
for name in dir(paramgroup):
par = getattr(paramgroup, name)
if isParameter(par):
params.add(name, value=par.value, vary=par.vary,
min=par.min, max=par.max,
brute_step=par.brute_step)
else:
fiteval.symtable[name] = par
# now set any expression (that is, after all symbols are defined)
for name in dir(paramgroup):
par = getattr(paramgroup, name)
if isParameter(par) and par.expr is not None:
params[name].expr = par.expr
return params
def NIST_Test(DataSet, method='leastsq', 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 = minimize(resid, params, method=method, args=(x,), kws={'y':y})
digs = Compare_NIST_Results(DataSet, myfit, params, NISTdata)
if plot and HASPYLAB:
fit = -resid(params, x, )
pylab.plot(x, y, 'ro')
pylab.plot(x, fit, 'k+-')
pylab.show()
return digs > 2
def __extract_pars(self):
"""
__extract_pars()
Extracts the paramers from the function list and converts them to
a single lmfit Parameters instance, which can then be manipulated
by the residual minimization routines.
Parameters
----------
None
Returns
-------
An lmfit `Parameters` instance containing the parameters
of *all* the fittable functions in a single place.
"""
oPars=Parameters()
for indFunc,cFunc in enumerate(self.funclist):
cParlist = cFunc['params']
for cPar in cParlist.values():
oPars.add(self.__func_ident(indFunc)+cPar.name,
value=cPar.value,vary=cPar.vary,
min=cPar.min,max=cPar.max,
expr=cPar.expr)
return oPars
def test_pickle_parameters(self):
# test that we can pickle a Parameters object
p = Parameters()
p.add('a', 10, True, 0, 100)
p.add('b', 10, True, 0, 100, 'a * sin(1)')
p.update_constraints()
p._asteval.symtable['abc'] = '2 * 3.142'
pkl = pickle.dumps(p, -1)
q = pickle.loads(pkl)
q.update_constraints()
assert_(p == q)
assert_(not p is q)
# now test if the asteval machinery survived
assert_(q._asteval.symtable['abc'] == '2 * 3.142')
# check that unpickling of Parameters is not affected by expr that
# refer to Parameter that are added later on. In the following
# example var_0.expr refers to var_1, which is a Parameter later
# on in the Parameters OrderedDict.
p = Parameters()
p.add('var_0', value=1)
p.add('var_1', value=2)
p['var_0'].expr = 'var_1'
pkl = pickle.dumps(p)
q = pickle.loads(pkl)
def test_bounded_jacobian():
pars = Parameters()
pars.add('x0', value=2.0)
pars.add('x1', value=2.0, min=1.5)
global jac_count
jac_count = 0
def resid(params):
x0 = params['x0']
x1 = params['x1']
return np.array([10 * (x1 - x0*x0), 1-x0])
def jac(params):
global jac_count
jac_count += 1
x0 = params['x0']
return np.array([[-20*x0, 10], [-1, 0]])
out0 = minimize(resid, pars, Dfun=None)
assert_paramval(out0.params['x0'], 1.2243, tol=0.02)
assert_paramval(out0.params['x1'], 1.5000, tol=0.02)
assert(jac_count == 0)
out1 = minimize(resid, pars, Dfun=jac)
assert_paramval(out1.params['x0'], 1.2243, tol=0.02)
assert_paramval(out1.params['x1'], 1.5000, tol=0.02)
assert(jac_count > 5)
def lmfitter(x, y):
params = Parameters()
params.add('m', value=0.01, vary=True)
out = minimize(residual, params, args=(x, y))
report_fit(params)
return out.params['m'].value, 0.0, out.params['m'].stderr, 0.0
def parameters(ini_values):
from lmfit import Parameters
k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, UA, mu_0, E, q, prim_stab_0, LDH_0 = ini_values
p = Parameters()
# ( Name, Value, Vary, Min, Max)
p.add_many(( 'k1', k1, True, 1.6, 2.1),
( 'k2', k2, True, 8.0, 46.0),
( 'k3', k3, True, 0.0, 6.0),
( 'k4', k4, True, 0.0, 2.1),
( 'k5', k5, True, 0.0, 0.03),
( 'k6', k6, True, 0.0, 39.0),
( 'k7', k7, True, 0.0, 2.7),
( 'k8', k8, True, 0.0, 7.9),
( 'k9', k9, True, 0.0, 13.1),
( 'k10', k10, True, 0.7, 10.9),
( 'k11', k11, True, 2.0, 3.6),
( 'UA', UA, True, 275.0, 402.0),
( 'mu_0', mu_0, False, 0.0, 0.1),
( 'E', E, False, 5000.0, None),
( 'q', q, False, 0.0, 17.0),
('prim_stab_0', prim_stab_0, False, 0.5, 1.3),
( 'LDH_0', LDH_0, False, None, None))
return p
def setup_model_params(self):
""" Setup parameters """
params = Parameters()
params.add('g0', value=0.0, vary=False)
params.add('g1', value=2.0, min=0.0)
return params
def amplitude_of_best_fit_greybody(Trf = None, b = 2.0, Lrf = None, zin = None):
'''
Same as single_simple_flux_from_greybody, but to made an amplitude lookup table
'''
nsed = 1e4
lambda_mod = loggen(1e3, 8.0, nsed) # microns
nu_mod = c * 1.e6/lambda_mod # Hz
#cosmo = Planck15#(H0 = 70.5 * u.km / u.s / u.Mpc, Om0 = 0.273)
conversion = 4.0 * np.pi *(1.0E-13 * cosmo.luminosity_distance(zin) * 3.08568025E22)**2.0 / L_sun # 4 * pi * D_L^2 units are L_sun/(Jy x Hz)
Lir = Lrf / conversion # Jy x Hz
Ain = 1.0e-36 #good starting parameter
betain = b
alphain= 2.0
fit_params = Parameters()
fit_params.add('Ain', value= Ain)
#THE LM FIT IS HERE
Pfin = minimize(sedint, fit_params, args=(nu_mod,Lir.value,Trf/(1.+zin),b,alphain))
#pdb.set_trace()
return Pfin.params['Ain'].value
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 build_fitmodel(self):
""" use fit components to build model"""
dgroup = self.get_datagroup()
model = None
params = Parameters()
self.summary = {"components": [], "options": {}}
for comp in self.fit_components.values():
if comp.usebox is not None and comp.usebox.IsChecked():
for parwids in comp.parwids.values():
params.add(parwids.param)
self.summary["components"].append((comp.mclass.__name__, comp.mclass_kws))
thismodel = comp.mclass(**comp.mclass_kws)
if model is None:
model = thismodel
else:
model += thismodel
self.fit_model = model
self.fit_params = params
self.plot1 = self.larch.symtable._plotter.plot1
if dgroup is not None:
i1, i2, xv1, xv2 = self.get_xranges(dgroup.x)
xsel = dgroup.x[slice(i1, i2)]
dgroup.xfit = xsel
dgroup.yfit = self.fit_model.eval(self.fit_params, x=xsel)
dgroup.ycomps = self.fit_model.eval_components(params=self.fit_params, x=xsel)
return dgroup
def isotropic(filename, v0, x0, rho, g=9.81):
try:
results = read_results_file(filename)
Volume_array_normalized = v0 - results['External_volume']
spring_position_array_normalized = x0 - results['Ylow']
params = Parameters()
params.add('A', value=1)
params.add('B', value=0)
try:
result = minimize(residual_isotropic, params, args=(spring_position_array_normalized, Volume_array_normalized))
except TypeError:
result = minimize(residual_isotropic, params, args=(spring_position_array_normalized, Volume_array_normalized),method="nelder")
v = result.params.valuesdict()
x_th = np.arange(np.amin(Volume_array_normalized), np.amax(Volume_array_normalized), 0.0000001)
y_th = v['A'] * x_th + v['B']
# report_fit(result.params, min_correl=0.5)
filename_list = filename.split("\\")
txt = filename_list[-1].split("_")
txt = "_".join(txt[0:-1])
k = -rho * g / v['A']
print "Stiffness: " + str(k)
list_results = [txt, k, v['B']]
return list_results
except:
return None
def Fit_frvsT(temp, freq, fitpara):
# create a set of Parameters
params = Parameters()
print fitpara
params.add_many(('CPWC', fitpara[0], False, None, None, None),
('CPWG', fitpara[1], False, None, None, None),
('thick', fitpara[2], False, None, None, None),
('BCS', fitpara[3], False, None, None, None),
('Tc', fitpara[4], True, None, None, None),
('f0', fitpara[5], False, None, None, None),
('sigman',fitpara[6], False, None, None, None),
('A', fitpara[7], True, fitpara[7]*0.9, fitpara[7]*1.1, None))
# do fit, here with leastsq model
result = minimize(Fit_frvsT_Func, params, args=(temp, freq))
# calculate final result
residual = result.residual
Tc = result.params['Tc'].value
Tc_err = np.abs(result.params['Tc'].stderr/Tc)
A = result.params['A'].value
A_err = np.abs(result.params['A'].stderr/A)
print fit_report(result)
return Tc, Tc_err, A, A_err, fit_report(result)
def optimize_density_and_scaling(self, density_min, density_max, bkg_min, bkg_max, iterations,
callback_fcn = None, output_txt=None):
params = Parameters()
params.add("density", value=self.density, min=density_min, max=density_max)
params.add("background_scaling", value=self.background_scaling, min=bkg_min, max=bkg_max)
self.iteration = 0
def optimization_fcn(params):
density = params['density'].value
background_scaling = params['background_scaling'].value
self.background_spectrum.scaling = background_scaling
self.calculate_spectra()
self.optimize_sq(iterations,fcn_callback=callback_fcn)
r, fr = self.limit_spectrum(self.fr_spectrum, 0, self.r_cutoff).data
output = (-fr - 4 * np.pi * convert_density_to_atoms_per_cubic_angstrom(self.composition, density) *
r) ** 2
self.write_output(u'{} X: {:.3f} Den: {:.3f}'.format(self.iteration, np.sum(output)/(r[1]-r[0]), density))
self.iteration+=1
return output
minimize(optimization_fcn, params)
self.write_fit_results(params)
class rabifit:
def __init__(self, nmax=10000):
self.params = Parameters()
self.params.add('nbar', value=.1, vary=False, min=0.)
self.params.add('delta', value=0, min=-0.05,
max=.1, vary=False)
self.params.add('time_2pi', value=20, vary=True, min=0.1)
self.params.add('coh_time', value=2000, vary=False, min=0)
self.params.add('eta', value=0.06, vary=False, min=0)
self.eta = 0.06
self.sideband = 0
self.result = None
self.nmax = nmax
def residual(self, params, x, data=None, eps=None):
# unpack parameters:
# extract .value attribute for each parameter
nbar = params['nbar'].value
delta = params['delta'].value
time_2pi = params['time_2pi'].value
coh_time = params['coh_time'].value
eta = params['eta'].value
te = rabi_flop_time_evolution(self.sideband ,eta, nmax=self.nmax)
model = te.compute_evolution_decay_thermal(abs(coh_time), nbar = nbar, delta = delta,
time_2pi = time_2pi, t = x)
if data is None:
return model
if eps is None:
return (model - data)
return (model - data)/eps
def minimize(self, data):
self.result = minimize(self.residual,self.params, args = (data[:,0], data[:,1], data[:,2]+.01))
def rescale_reframe(scisub, refsub, verbose=False):
"""Example function with types documented in the docstring.
`PEP 484`_ type annotations are supported. If attribute, parameter, and
return types are annotated according to `PEP 484`_, they do not need to be
included in the docstring:
Args:
param1 (int): The first parameter.
param2 (str): The second parameter.
Returns:
bool: The return value. True for success, False otherwise.
.. _PEP 484:
https://www.python.org/dev/peps/pep-0484/
"""
params = Parameters()
params.add('sigma', 1.0, True, 0.0, inf)
image_sub = Model(res_sigma_image_flat, independent_vars=['scisub', 'refsub'])
image_sub_results = image_sub.fit(data=scisub.ravel(), params=params, scisub=scisub, refsub=refsub)
if verbose: print('Sigma of Rescale: {}'.format(image_sub_results.params['sigma'].value))
return partial_res_sigma_image(image_sub_results.params['sigma'].value)
def fit_for_b(bins, x, y, error=None):
"""
Fit a fractional energy loss histogram for the parameter b
"""
magic_ice_const = 0.917
outer_bounds = (min(bins), max(bins)) # Beginning and ending position
select_bounds = np.vectorize(lambda xx: mlc.get_bounding_elements(xx, bins)) # Returns the bin edges on either side of a point
E_diff = lambda xx, b: np.exp(-b*xx[1]) - np.exp(-b*xx[0]) # Proportional to Delta E (comes from -dE/dx=a+b*E)
fit_func = lambda xx, b: E_diff(select_bounds(xx), b*magic_ice_const) / E_diff(outer_bounds, b*magic_ice_const) # We are fitting to the ratio of differences
params = Parameters()
params.add('b', value=0.4*10**(-3)) # Add b as a fit parameter
if error is not None:
l_fit_func = lambda params, x, data: np.sqrt((fit_func(x, params['b']) - data)**2 / error**2)
else:
l_fit_func = lambda params, x, data: fit_func(x, params['b']) - data
result = minimize(l_fit_func, params, args=(x, y))
b = result.params['b'].value
if b == 0.4*10**(-3):
print fit
print x
print y
print fit_func(x, 0.36*10**(-3))
print w
raise ValueError("Fit doesn't make sense.")
return b
def replot(self):
params = Parameters()
for key,value in self.paramDict.items():
params.add(key, value=float(value.text()))
for i in np.arange(self.fitNumber):
sequence = 'g'+str(i+1)+'_'
center_value = params[sequence+'center'].value
params[sequence+'center'].set(center_value, min=center_value-0.05,
max=center_value+0.05)
sigma_value = params[sequence+'sigma'].value
params[sequence+'sigma'].set(sigma_value, min=sigma_value-0.05,
max=sigma_value+0.05)
ampl_value = params[sequence+'amplitude'].value
params[sequence+'amplitude'].set(ampl_value, min=ampl_value-0.5,
max=ampl_value+0.5)
result = minimize(lmLeast(self.fitNumber).residuals, params, args=(self.fitResult.fitDf['field'], self.fitResult.fitDf['IRM_norm']),
method='cg')
self.params = result.params
#FitMplCanvas.fitPlot(self)
pdf_adjust = lmLeast(self.fitNumber).func(self.fitResult.fitDf['field'].values,self.params)
pdf_adjust = pdf_adjust/np.max(np.sum(pdf_adjust,axis=0))
ax=self.axes
fit_plots(ax=ax,
xfit=self.fitResult.fitDf['field'],
xraw=self.fitResult.rawDf['field_log'],
yfit=np.array(pdf_adjust).transpose(),
yraw=self.fitResult.rawDf['rem_grad_norm'])
def test_args_kwds_are_used(self):
# check that user defined args and kwds make their way into the user
# function
a = [1., 2.]
x = np.linspace(0, 10, 11)
y = a[0] + 1 + 2 * a[1] * x
par = Parameters()
par.add('p0', 1.5)
par.add('p1', 2.5)
def fun(x, p, *args, **kwds):
assert_equal(args, a)
return args[0] + p['p0'] + p['p1'] * a[1] * x
g = CurveFitter(fun, (x, y), par, fcn_args=a)
res = g.fit()
assert_almost_equal(values(res.params), [1., 2.])
d = {'a': 1, 'b': 2}
def fun(x, p, *args, **kwds):
return kwds['a'] + p['p0'] + p['p1'] * kwds['b'] * x
g = CurveFitter(fun, (x, y), par, fcn_kws=d)
res = g.fit()
assert_almost_equal(values(res.params), [1., 2.])
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 as_parameter_dict(self) -> Parameters:
"""
Creates a lmfit.Parameters dictionary from the group.
Notes
-----
Only for internal use.
"""
params = Parameters()
for label, p in self.all(seperator="_"):
p.name = "_" + label
if p.non_neg:
p = copy.deepcopy(p)
if p.value == 1:
p.value += 1e-10
if p.min == 1:
p.min += 1e-10
if p.max == 1:
p.max += 1e-10
else:
try:
p.value = log(p.value)
p.min = log(p.min) if np.isfinite(p.min) else p.min
p.max = log(p.max) if np.isfinite(p.max) else p.max
except Exception:
raise Exception("Could not take log of parameter"
f" '{label}' with value '{p.value}'")
params.add(p)
return params
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 pca_fit(group, pca_model, ncomps=None, rescale=True, _larch=None):
"""
fit a spectrum from a group to a PCA training model from pca_train()
Arguments
---------
group group with data to fit
pca_model PCA model as found from pca_train()
ncomps number of components to included
rescale whether to allow data to be renormalized (True)
Returns
-------
None, the group will have a subgroup name `pca_result` created
with the following members:
x x or energy value from model
ydat input data interpolated onto `x`
yfit linear least-squares fit using model components
weights weights for PCA components
chi_square goodness-of-fit measure
pca_model the input PCA model
"""
# get first nerate arrays and interpolate components onto the unknown x array
xdat, ydat = get_arrays(group, pca_model.arrayname)
if xdat is None or ydat is None:
raise ValueError("cannot get arrays for arrayname='%s'" % arrayname)
ydat = interp(xdat, ydat, pca_model.x, kind='cubic')
params = Parameters()
params.add('scale', value=1.0, vary=True, min=0)
if ncomps is None:
ncomps=len(pca_model.components)
comps = pca_model.components[:ncomps].transpose()
if rescale:
weights, chi2, rank, s = np.linalg.lstsq(comps, ydat-pca_model.mean)
yfit = (weights * comps).sum(axis=1) + pca_model.mean
result = minimize(_pca_scale_resid, params, method='leastsq',
gtol=1.e-5, ftol=1.e-5, xtol=1.e-5, epsfcn=1.e-5,
kws = dict(ydat=ydat, comps=comps, pca_model=pca_model))
scale = result.params['scale'].value
ydat *= scale
weights, chi2, rank, s = np.linalg.lstsq(comps, ydat-pca_model.mean)
yfit = (weights * comps).sum(axis=1) + pca_model.mean
else:
weights, chi2, rank, s = np.linalg.lstsq(comps, ydat-pca_model.mean)
yfit = (weights * comps).sum(axis=1) + pca_model.mean
scale = 1.0
group.pca_result = Group(x=pca_model.x, ydat=ydat, yfit=yfit,
pca_model=pca_model, chi_square=chi2[0],
data_scale=scale, weights=weights)
return
def define_orientation_matrix(self):
from lmfit import Parameters
p = Parameters()
for i in range(3):
for j in range(3):
p.add('U%d%d' % (i,j), self.Umat[i,j])
self.init_p = self.Umat
return p
def parameters(ini_values):
from lmfit import Parameters
from Adjust_Kinetics import params
p = Parameters()
pi = params(ini_values)
for i,tup in enumerate(pi):
p.add_many(tup)
return p
def simple_flux_from_greybody(lambdavector, Trf = None, b = None, Lrf = None, zin = None, ngal = None): ''' Return flux densities at any wavelength of interest (in the range 1-10000 micron), assuming a galaxy (at given redshift) graybody spectral energy distribution (SED), with a power law replacing the Wien part of the spectrum to account for the variability of dust temperatures within the galaxy. The two different functional forms are stitched together by imposing that the two functions and their first derivatives coincide. The code contains the nitty-gritty details explicitly. Cosmology assumed: H0=70.5, Omega_M=0.274, Omega_L=0.726 (Hinshaw et al. 2009) Inputs: alphain = spectral index of the power law replacing the Wien part of the spectrum, to account for the variability of dust temperatures within a galaxy [default = 2; see Blain 1999 and Blain et al. 2003] betain = spectral index of the emissivity law for the graybody [default = 2; see Hildebrand 1985] Trf = rest-frame temperature [in K; default = 20K] Lrf = rest-frame FIR bolometric luminosity [in L_sun; default = 10^10] zin = galaxy redshift [default = 0.001] lambdavector = array of wavelengths of interest [in microns; default = (24, 70, 160, 250, 350, 500)]; AUTHOR: Lorenzo Moncelsi [[email protected]] HISTORY: 20June2012: created in IDL November2015: converted to Python ''' nwv = len(lambdavector) nuvector = c * 1.e6 / lambdavector # Hz nsed = 1e4 lambda_mod = loggen(1e3, 8.0, nsed) # microns nu_mod = c * 1.e6/lambda_mod # Hz #Lorenzo's version had: H0=70.5, Omega_M=0.274, Omega_L=0.726 (Hinshaw et al. 2009) cosmo = FlatLambdaCDM(H0 = 70.5 * u.km / u.s / u.Mpc, Om0 = 0.273) conversion = 4.0 * np.pi *(1.0E-13 * cosmo.luminosity_distance(zin) * 3.08568025E22)**2.0 / L_sun # 4 * pi * D_L^2 units are L_sun/(Jy x Hz) Lir = Lrf / conversion # Jy x Hz Ain = np.zeros(ngal) + 1.0e-36 #good starting parameter betain = np.zeros(ngal) + b alphain= np.zeros(ngal) + 2.0 fit_params = Parameters() fit_params.add('Ain', value= Ain) #fit_params.add('Tin', value= Trf/(1.+zin), vary = False) #fit_params.add('betain', value= b, vary = False) #fit_params.add('alphain', value= alphain, vary = False) #pdb.set_trace() #THE LM FIT IS HERE #Pfin = minimize(sedint, fit_params, args=(nu_mod,Lir.value,ngal)) Pfin = minimize(sedint, fit_params, args=(nu_mod,Lir.value,ngal,Trf/(1.+zin),b,alphain)) #pdb.set_trace() flux_mJy=sed(Pfin.params,nuvector,ngal,Trf/(1.+zin),b,alphain) return flux_mJy
def test_add_many_params(self):
# test that we can add many parameters, but only parameters are added.
a = Parameter('a', 1)
b = Parameter('b', 2)
p = Parameters()
p.add_many(a, b)
assert_(list(p.keys()) == ['a', 'b'])
def buildLmfitParameters(self, parameters):
lp = Parameters()
for p in parameters:
lp.add(p.name, value=p.init, min=p.min, max=p.max)
for k in p.kws:
setattr(lp[p.name], k, p.kws[k])
return lp
def FPolyp(x, data, Np): #generate parameters for FD2
params = FPolypGuess(x, data, Np)
p = Parameters()
p.add('Np', value=Np, vary=False)
for ii in range(Np + 1):
p.add('c%s' % ii, value = params[ii+1], vary=True)
return p
def test_eval(self):
# check that eval() works with usersyms and parameter values
def myfun(x):
return 2.0 * x
p = Parameters(usersyms={"myfun": myfun})
p.add("a", value=4.0)
p.add("b", value=3.0)
assert_almost_equal(p.eval("myfun(2.0) * a"), 16)
assert_almost_equal(p.eval("b / myfun(3.0)"), 0.5)
def fitcorrplot(quadScanPath, fitNoiseQ=False):
# path to CSV with 2-quad scan data
#quadScanPath = 'CorrelationPlot-QUAD_IN20_511_BCTRL-2016-10-20-053315.mat';
nquads = 2
# maybe one day we'll try 3 quad scans
# import data to be fitted
[data, legend] = corrplot(quadScanPath) # read in corrplot data
# meshgrid for the fit
#x = y = np.linspace(-3, 3, ngrid)
x = np.array([a for a in data[0]])
y = np.array([a for a in data[1]])
z = np.array([a for a in data[2]])
dz = np.array([a for a in data[3]])
# grab peak value & locate peak
zpeak = np.max(z)
elpeak = (z == zpeak).nonzero()
xpeak = np.mean(x[elpeak])
ypeak = np.mean(y[elpeak])
dzpeak = np.mean(dz[elpeak])
# grab half-max region & find width of peak
elhm = (z >= 0.5 * zpeak).nonzero()
xfwhm = np.max(x[elhm]) - np.min(x[elhm])
yfwhm = np.max(y[elhm]) - np.min(y[elhm])
# in case we want to fit the map of fluctuations
if (fitNoiseQ):
z = dz
dzpeak = 1.
# define objective function: returns the array to be minimized
def fcn2min(params, x, y, z, dz):
""" model decaying sine wave, subtract data"""
amp = params['amp']
xm = params['xm']
sx = params['sx']
ym = params['ym']
sy = params['sy']
rho = params['rho']
if fitNoiseQ:
bg = params['bg']
model = bg + amp * np.exp(-0.5 * ((x - xm) * (x - xm) / sx / sx +
(y - ym) *
(y - ym) / sy / sy - 2. * rho *
(x - xm) * (y - ym) / sx / sy) /
(1. - rho * rho))
else:
model = amp * np.exp(-0.5 *
((x - xm) * (x - xm) / sx / sx + (y - ym) *
(y - ym) / sy / sy - 2. * rho * (x - xm) *
(y - ym) / sx / sy) / (1. - rho * rho))
resid = (
model - z
) / dzpeak # replace dzpeak with dz to include some uncertainty in the fit
#print(np.sum(resid**2))
return resid.flatten()
# create a set of Parameters
params = Parameters()
params.add('amp', value=zpeak, min=0., max=zpeak + 3. * dzpeak)
params.add('xm', value=xpeak, min=xpeak - xfwhm, max=xpeak + xfwhm)
params.add('sx',
value=xfwhm / 2.35,
min=0.5 * xfwhm / 2.35,
max=2. * xfwhm)
params.add('ym', value=ypeak, min=ypeak - yfwhm, max=ypeak + yfwhm)
params.add('sy',
value=yfwhm / 2.35,
min=0.5 * yfwhm / 2.35,
max=2. * yfwhm)
params.add('rho', value=0., min=-1., max=1.)
if fitNoiseQ: params.add('bg', value=0., min=-0.1, max=0.1)
# do fit, here with leastsq model
minner = Minimizer(fcn2min, params, fcn_args=(x, y, z, dz))
kws = {'options': {'maxiter': 100}}
result = minner.minimize()
# calculate final result
#final = data + result.residual
# write error report
report_fit(result)
#print(result.params.items())
#print([par for pname,par in result.params.items()])
if fitNoiseQ:
parnames = ['amp', 'xm', 'sx', 'ym', 'sy', 'rho', 'bg']
else:
parnames = ['amp', 'xm', 'sx', 'ym', 'sy', 'rho']
parvals = [result.params.valuesdict()[p] for p in parnames]
#print(parnames)
#print(parvals)
return parvals
I = current[0]
sol = [ t*k*I/Cr + k*I*Jr/Cr**2*np.exp(-t*Cr/Jr) - k*I*Jr/Cr**2 for t in time]
print(k*I/Cr)
return sol
def energy(params, data):
E = 0.
for run in data:
y = predict(params, run[0], run[1])
for i in range(len(run[2])):
E = E + ((y[i]-run[2][i])/run[2][-1]) **2
print(params.valuesdict(),"\n", E)
return E
params = Parameters()
#params.add('k', value=0.0369, min=.0001, max=.5)
params.add('Jr', value=0.001184, min=.00001, max=.5)
params.add('Cr', value=0.00001, min=.0, max=.5)
runs = []
runs = runs + ['vise-constant-0.25a.csv']
#runs = runs + ['vise-constant-0.375a.csv']
runs = runs + ['vise-constant-0.5a.csv']
#runs = runs + ['vise-constant-0.625a.csv']
runs = runs + ['vise-constant-0.75a.csv']
#runs = runs + ['vise-constant-0.875a.csv']
runs = runs + ['vise-constant-1a.csv']
#runs = runs + ['vise-constant--1a.csv']
print(runs)
from lmfit import Parameters, minimize, report_fit
from numpy import linspace, zeros, sin, exp, random, sqrt, pi, sign
try:
import pylab
HASPYLAB = True
except ImportError:
HASPYLAB = False
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):
argu = (x * pars['decay'])**2
shift = pars['shift']
if abs(shift) > pi / 2:
shift = shift - sign(shift) * pi
model = pars['amp'] * sin(shift + x / pars['period']) * exp(-argu)
if data is None:
return model
return (model - data)
n = 2500
xmin = 0.
xmax = 250.0
def get_params(Ug, Ue, Dg, De, vary_groundstate):
# make parameters
params = Parameters()
if vary_groundstate:
print("Don't vary groundstate")
asd
# ground state
for k in range(len(Ug)):
for l in range(len(Ug[k])):
val = Ug[k][l]
params.add('Ug' + str(k) + str(l), value=val, vary=True)
# adding Born-Oppenheimer correction
params.add('Dg' + str(k) + str(l), value=0.0, vary=False)
else:
# use Bernath values and don't vary the values
Ug, Dg = get_Ug_Bernath()
for k in range(len(Ug)):
for l in range(len(Ug[k])):
val = Ug[k][l]
params.add('Ug' + str(k) + str(l), value=val, vary=False)
# adding Born-Oppenheimer correction
val = Dg[k][l]
params.add('Dg' + str(k) + str(l), value=val, vary=False)
# excited state
for k in range(len(Ue)):
for l in range(len(Ue[k])):
val = Ue[k][l]
params.add('Ue' + str(k) + str(l), value=val, vary=True)
# Born-Oppenheimer corrections for excited state
# Should throw error if Ue and De don't have the same dimensions
val = De[k][l]
# adding Born-Oppenheimer correction
if not val == 0.0:
params.add('De' + str(k) + str(l), value=val, vary=True)
else:
params.add('De' + str(k) + str(l), value=0.0, vary=False)
return params
def create_model(self):
params = Parameters()
params.add('ocv', value=self.voltage[-1], min=0, max=10)
taus = [math.pow(10, i) for i in range(self.circuits)]
weights = np.zeros(self.circuits)
params.add('t0', value=taus[0], min=0.01)
params.add('w0', value=weights[0])
for i in range(1, self.circuits):
params.add('delta' + str(i), value=taus[i] - taus[i - 1], min=0.0)
params.add('t' + str(i), expr='delta' + str(i) + '+t' + str(i - 1))
params.add('w' + str(i), value=weights[i])
for i in range(self.circuits, 5):
params.add('t' + str(i), value=1, vary=False)
params.add('w' + str(i), value=0, vary=False)
self.params = params
self.model = Model(self._model)
def lcf(collection: Collection,
fit_region: str = 'xanes',
fit_range: list = [-inf, inf],
scantag: str = 'scan',
reftag: str = 'ref',
kweight: int = 2,
sum_one: bool = True,
method: str = 'leastsq') -> Dataset:
"""Performs linear combination fitting on a XAFS spectrum.
Parameters
----------
collection
Collection containing the group for LCF analysis and the groups
with the reference scans.
fit_region
XAFS region to perform the LCF. Accepted values are 'dxanes',
'xanes', or 'exafs'. The default is 'xanes'.
fit_range
Domain range in absolute values. Energy units are expected
for 'dxanes' or 'xanes', while wavenumber (k) units are expected
for 'exafs'.
The default is [-:data:`~numpy.inf`, :data:`~numpy.inf`].
scantag
Key to filter the scan group in the collection based on the ``tags``
attribute. The default is 'scan'.
reftag
Key to filter the reference groups in the collection based on the ``tags``
attribute. The default is 'scan'.
kweight
Exponent for weighting chi(k) by k^kweight. Only valid for ``fit_region='exafs'``.
The default is 2.
sum_one
Conditional to force sum of fractions to be one.
The default is True.
method
Fitting method. Currently only local optimization methods are supported.
See the :func:`~lmfit.minimizer.minimize` function of ``lmfit`` for a list
of valid methods.
The default is ``leastsq``.
Returns
-------
:
Fit group with the following arguments:
- ``energy`` : array with energy values.
Returned only if ``fit_region='xanes'`` or ``fit_region='dxanes'``.
- ``k`` : array with wavenumber values.
Returned only if ``fit_region='exafs'``.
- ``scangroup``: name of the group containing the fitted spectrum.
- ``refgroups``: list with names of groups containing reference spectra.
- ``scan`` : array with values of the fitted spectrum.
- ``ref`` : array with interpolated values for each reference spectrum.
- ``fit`` : array with fit result.
- ``min_pars`` : object with the optimized parameters and goodness-of-fit statistics.
- ``lcf_pars`` : dictionary with lcf parameters.
Raises
------
TypeError
If ``collection`` is not a valid Collection instance.
AttributeError
If ``collection`` has no ``tags`` attribute.
AttributeError
If groups have no ``energy`` or ``norm`` attribute.
Only verified if ``fit_region='dxanes'`` or ``fit_region='xanes'``.
AttributeError
If groups have no ``k`` or ``chi`` attribute.
Only verified if and ``fit_region='exafs'``.
KeyError
If ``scantag`` or ``refttag`` are not keys of the ``tags`` attribute.
ValueError
If ``fit_region`` is not recognized.
ValueError
If ``fit_range`` is outside the doamin of a reference group.
Important
---------
If more than one group in ``collection`` is tagged with ``scantag``,
a warning will be raised and only the first group will be fitted.
Notes
-----
The ``min_pars`` object is returned by the :func:`minimize` function of
``lmfit``, and contains the following attributes (non-exhaustive list):
- ``params`` : dictionary with the optimized parameters.
- ``var_names`` : ordered list of parameter names used in optimization.
- ``covar`` : covariance matrix from minimization.
- ``init_vals`` : list of initial values for variable parameters using
``var_names``.
- ``success`` : True if the fit succeeded, otherwise False.
- ``nvarys`` : number of variables.
- ``ndata`` : number of data points.
- ``chisqr`` : chi-square.
- ``redchi`` : reduced chi-square.
- ``residual`` : array with fit residuals.
Example
-------
>>> from numpy.random import seed, normal
>>> from numpy import arange, sin, pi
>>> from araucaria import Group, Dataset, Collection
>>> from araucaria.fit import lcf
>>> from araucaria.utils import check_objattrs
>>> seed(1234) # seed of random values
>>> k = arange(0, 12, 0.05)
>>> eps = normal(0, 0.1, len(k))
>>> f1 = 1.2 # freq 1
>>> f2 = 2.6 # freq 2
>>> amp1 = 0.4 # amp 1
>>> amp2 = 0.6 # amp 2
>>> group1 = Group(**{'name': 'group1', 'k': k, 'chi': sin(2*pi*f1*k)})
>>> group2 = Group(**{'name': 'group2', 'k': k, 'chi': sin(2*pi*f2*k)})
>>> group3 = Group(**{'name': 'group3', 'k': k,
... 'chi' : amp1 * group1.chi + amp2 * group2.chi + eps})
>>> collection = Collection()
>>> tags = ['ref', 'ref', 'scan']
>>> for i, group in enumerate((group1,group2, group3)):
... collection.add_group(group, tag=tags[i])
>>> # performing lcf
>>> out = lcf(collection, fit_region='exafs', fit_range=[3,10],
... kweight=0, sum_one=False)
>>> check_objattrs(out, Dataset,
... attrlist=['k', 'scangroup', 'refgroups',
... 'scan', 'ref1', 'ref2', 'fit', 'min_pars', 'lcf_pars'])
[True, True, True, True, True, True, True, True, True]
>>> for key, val in out.min_pars.params.items():
... print('%1.4f +/- %1.4f' % (val.value, val.stderr))
0.4003 +/- 0.0120
0.5943 +/- 0.0120
"""
# checking class and attributes
check_objattrs(collection, Collection, attrlist=['tags'], exceptions=True)
# verifying fit type
fit_valid = ['dxanes', 'xanes', 'exafs']
if fit_region not in fit_valid:
raise ValueError('fit_region %s not recognized.' % fit_region)
# required groups
# at least a spectrum and a single reference must be provided
for tag in (scantag, reftag):
if tag not in collection.tags:
raise KeyError("'%s' is not a valid key for the collection." % tag)
# scan and ref tags
scangroup = collection.tags[scantag]
if len(scangroup) > 1:
warn(
"More than one group is tagged as scan. Only the first group will be considered."
)
scangroup = scangroup[0]
refgroups = collection.tags[reftag]
refgroups.sort()
# the first element is the scan group
groups = [scangroup] + refgroups
# storing report parameters
lcf_pars = {
'fit_region': fit_region,
'fit_range': fit_range,
'sum_one': sum_one
}
# report parameters for exafs lcf
if fit_region == 'exafs':
lcf_pars['kweight'] = kweight
# storing name of x-variable (exafs)
xvar = 'k'
# report parameters for xanes/dxanes lcf
else:
# storing name of x-variable (xanes/dxanes)
xvar = 'energy'
# content dictionary
content = {'scangroup': scangroup, 'refgroups': refgroups}
# reading and processing spectra
for i, name in enumerate(groups):
dname = 'scan' if i == 0 else 'ref' + str(i)
group = collection.get_group(name).copy()
if fit_region == 'exafs':
check_objattrs(group,
Group,
attrlist=['k', 'chi'],
exceptions=True)
else:
# fit_region == 'xanes' or 'dxanes'
check_objattrs(group,
Group,
attrlist=['energy', 'norm'],
exceptions=True)
if i == 0:
# first value is the spectrum, so we extract the
# interpolation values from xvar
xvals = getattr(group, xvar)
index = index_xrange(fit_range, xvals)
xvals = xvals[index]
# storing the y-variable
if fit_region == 'exafs':
yvals = xvals**kweight * group.chi[index]
elif fit_region == 'xanes':
yvals = group.norm[index]
else:
# derivative lcf
yvals = gradient(group.norm[index]) / gradient(
group.energy[index])
else:
# spline interpolation of references
if fit_region == 'exafs':
s = interp1d(group.k,
group.k**kweight * group.chi,
kind='cubic')
elif fit_region == 'xanes':
s = interp1d(group.energy, group.norm, kind='cubic')
else:
s = interp1d(group.energy,
gradient(group.norm) / gradient(group.energy),
kind='cubic')
# interpolating in the fit range
try:
yvals = s(xvals)
except:
raise ValueError(
'fit_range is outside the domain of group %s' % name)
# saving yvals in the dictionary
content[dname] = yvals
# setting xvar as an attribute of datgroup
content[xvar] = xvals
# setting initial values and parameters for fit model
initval = around(1 / (len(groups) - 1), decimals=1)
params = Parameters()
expr = str(1)
for i in range(len(groups) - 1):
parname = 'amp' + str(i + 1)
if ((i == len(groups) - 2) and (sum_one == True)):
params.add(parname, expr=expr)
else:
params.add(parname, value=initval, min=0, max=1, vary=True)
expr += ' - amp' + str(i + 1)
# perform fit
min = minimize(residuals, params, method=method, args=(content, ))
# storing fit data, parameters, and results
content['fit'] = sum_references(min.params, content)
content['lcf_pars'] = lcf_pars
content['min_pars'] = min
out = Dataset(**content)
return out
def Lorentz_params(p0):
pars = Parameters()
f, A, f0, df, y0 = p0[0], p0[1], p0[2], p0[3], p0[4]
pars.add('A', value=A)
pars.add('f', value=f.tolist(), vary=False)
pars.add('f0', value=f0)
pars.add('df', value=df, min=0.)
pars.add('y0', value=y0)
return pars
def S21p0i2params(f, p0i):
pars = Parameters()
(A, f0, Q, Qe, dx, theta) = p0i
pars.add('A', value=1.e-3)
pars.add('f', value=f, vary=False)
pars.add('f0', value=6.28, min=0.)
pars.add('Q', value=Q, min=0.)
pars.add('Qe', value=Qe, min=0.)
pars.add('Qi', expr='1./(1./Q-1./Qe*cos(theta))', vary=False)
pars.add('Qc', expr='Qe/cos(theta)', vary=False)
pars.add('df', value=dx)
pars.add('theta', value=theta, min=-np.pi / 2, max=np.pi / 2)
return pars
def _Parameters(*arg, _larch=None, **kws):
return Parameters(*arg, **kws)
def test_bounded_parameters():
# create data to be fitted
np.random.seed(1)
x = np.linspace(0, 15, 301)
data = (5. * np.sin(2 * x - 0.1) * np.exp(-x * x * 0.025) +
np.random.normal(size=len(x), scale=0.2))
# define objective function: returns the array to be minimized
def fcn2min(params, x, data):
""" model decaying sine wave, subtract data"""
amp = params['amp']
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, max=50)
params.add('decay', value=0.1, min=0, max=10)
params.add('shift', value=0.0, min=-pi / 2., max=pi / 2.)
params.add('omega', value=3.0, min=0, max=np.inf)
# do fit, here with leastsq model
result = minimize(fcn2min, params, args=(x, data))
# assert that the real parameters are found
for para, val in zip(result.params.values(), [5, 0.025, -.1, 2]):
check(para, val)
# assert that the covariance matrix is correct [cf. lmfit v0.9.10]
cov_x = np.array(
[[1.42428250e-03, 9.45395985e-06, -4.33997922e-05, 1.07362106e-05],
[9.45395985e-06, 1.84110424e-07, -2.90588963e-07, 7.19107184e-08],
[-4.33997922e-05, -2.90588963e-07, 9.53427031e-05, -2.37750362e-05],
[1.07362106e-05, 7.19107184e-08, -2.37750362e-05, 9.60952336e-06]])
assert_allclose(result.covar, cov_x, rtol=1e-6)
# assert that stderr and correlations are correct [cf. lmfit v0.9.10]
assert_almost_equal(result.params['amp'].stderr, 0.03773967, decimal=6)
assert_almost_equal(result.params['decay'].stderr, 4.2908e-04, decimal=6)
assert_almost_equal(result.params['shift'].stderr, 0.00976436, decimal=6)
assert_almost_equal(result.params['omega'].stderr, 0.00309992, decimal=6)
assert_almost_equal(result.params['amp'].correl['decay'],
0.5838166760743324,
decimal=6)
assert_almost_equal(result.params['amp'].correl['shift'],
-0.11777303073961824,
decimal=6)
assert_almost_equal(result.params['amp'].correl['omega'],
0.09177027400788784,
decimal=6)
assert_almost_equal(result.params['decay'].correl['shift'],
-0.0693579417651835,
decimal=6)
assert_almost_equal(result.params['decay'].correl['omega'],
0.05406342001021014,
decimal=6)
assert_almost_equal(result.params['shift'].correl['omega'],
-0.7854644476455469,
decimal=6)
import shelve
import numpy as np
import matplotlib.pyplot as plt
# custom imports
from lmfit import Parameters # not a standard library -- install using PIP
import pygisaxs.io.pilatus as pil # from my (very small) library
import pygisaxs.utilities as util # from my (very small) library
# geometry of interest in Pilatus Files
pilatus_rectangle = [361, 7]
valid_pixels = range(0, 166) + range(195, 361)
# fitting function and parameter guesses
fnc2min = util.ode1sol
localguess = Parameters()
localguess.add('R', value=-5e-4)
localguess.add('beta', value=1e-8, min=0.0)
localguess.add('I0', value=1e-4, min=0.0)
# global parameters for hierarchical fitting
globalguess = None
globalguess = Parameters(
) # COMMENT OUT THESE TWO LINES TO FIT ALL PARAMETERS LOCALLY
globalguess.add(
'beta', value=1e-8,
min=0.0) # (useful to identify potential global parameters and guesses)
# in principle this can be run over multiple directories in sequence (just to save typing and waiting)
directories = sys.argv[1:]
for directory in directories:
field_residuum_telluric[idx_correction_skip] = 0
# resample and shift residuals from observed to restframe
field_residuum_telluric = spectra_resample(
field_residuum_telluric,
wvl_read_finer / (1 + velocity_shift * 1000. / C_LIGHT), wvl_read)
field_residuum_telluric_binary = spectra_resample(
np.logical_not(idx_correction_skip), wvl_read_finer /
(1 + velocity_shift * 1000. / C_LIGHT), wvl_read) > 0.5
# set the residuum outside observed wavelengths to 0
object_spectra_corrected_s1 = object_spectra - field_residuum_telluric
template_res_before_s1 = template_spectra - object_spectra
template_res_after_s1 = template_spectra - object_spectra_corrected_s1
# the best residuum scaling factor based on reference spectra
fit_param = Parameters()
fit_param.add('scale', value=1, min=0., max=10., brute_step=0.1)
fit_res = minimize(
minimize_scale,
fit_param, # method='brute',
args=(template_res_before_s1, field_residuum_telluric),
**{'nan_policy': 'omit'})
fit_res.params.pretty_print()
residuum_scale = fit_res.params['scale'].value
object_spectra_corrected_s1_scaled = object_spectra - residuum_scale * field_residuum_telluric
template_res_after_s1_scaled = template_spectra - object_spectra_corrected_s1_scaled
print np.nansum(template_res_after_s1**2), np.nansum(
template_res_after_s1_scaled**2)
fig, axes = plt.subplots(2, 1)
def fitz_galaxy_emcee(spec, zguess, fluxpoly=True, steps=5000, burn=2000, progress=True, printReport=True, saveCorner='', zMin=None, zMax=None, saveSpecPlot=''):
flux_median = np.median(spec['flux'])
parameters = Parameters()
# (Name, Value, Vary, Min, Max, Expr)
parameters.add_many(('z', zguess, True, zMin, zMax, None),
('eigen1', flux_median*0.4, True, None, None, None),
('eigen2', flux_median*0.4, True, None, None, None),
('eigen3', flux_median*0.1, True, None, None, None),
('eigen4', flux_median*0.1, True, None, None, None),
('fluxcal0', 0.0, fluxpoly, None, None, None),
('fluxcal1', 0.0, fluxpoly, None, None, None),
('fluxcal2', 0.0, fluxpoly, None, None, None))
galaxy_model = Model(eigensum_galaxy, missing='drop')
result = galaxy_model.fit(spec['flux'], wave=spec['wave'], weights=1/spec['error'],
params=parameters, missing='drop')
emcee_kws = dict(steps=steps, burn=burn, is_weighted=True,
progress=progress)
emcee_params = result.params.copy()
result_emcee = galaxy_model.fit(spec['flux'], wave=spec['wave'], weights=1/spec['error'],
params=emcee_params, method='emcee', nan_policy='omit',
missing='drop', fit_kws=emcee_kws, show_titles=True)
result_emcee.conf_interval
# find the maximum likelihood solution
highest_prob = np.argmax(result_emcee.lnprob)
hp_loc = np.unravel_index(highest_prob, result_emcee.lnprob.shape)
mle_soln = result_emcee.chain[hp_loc]
#result_emcee.conf_interval()
if printReport:
print('Initial results')
print(result.fit_report())
print('MCMC results')
print(result_emcee.fit_report())
#print(result_emcee.ci_report())
z_marginalized = np.percentile(result_emcee.flatchain['z'], [50])[0]
zErrUp = np.percentile(result_emcee.flatchain['z'], [84.1])[0] - np.percentile(result_emcee.flatchain['z'], [50])[0]
zErrDown = np.percentile(result_emcee.flatchain['z'], [50])[0] - np.percentile(result_emcee.flatchain['z'], [15.9])[0]
std_z = np.std(result_emcee.flatchain['z'])
print('z = {:0.5f} +{:0.5f} -{:0.5f} sigma(v) & +/- = {:0.1f} & +{:0.1f} -{:0.1f} km/s'.format(z_marginalized, zErrUp, zErrDown, std_z/(1 + z_marginalized)*c_kms, zErrUp/(1 + z_marginalized)*c_kms, zErrDown/(1 + z_marginalized)*c_kms))
interval68 = np.percentile(result_emcee.flatchain['z'], [15.9, 84.1])
interval95 = np.percentile(result_emcee.flatchain['z'], [2.28, 97.7])
print('68% C.I:')
print(interval68)
print('95% C.I:')
print(interval95)
if saveCorner != '':
emcee_corner = corner.corner(result_emcee.flatchain, labels=['z', 'eigen1', 'eigen2', 'eigen3', 'eigen4', 'fluxcal0', 'fluxcal1', 'fluxcal2'],
truths=mle_soln)
emcee_corner.savefig(saveCorner)
plt.close()
if saveSpecPlot != '':
fig, ax = plt.subplots(2, figsize=(7, 10))
ax[0].plot(spec['wave'], spec['flux'], color='black', drawstyle='steps-mid')
ax[0].plot(spec['wave'], spec['error'], color='blue', drawstyle='steps-mid')
ax[0].plot(spec['wave'], result_emcee.best_fit, color='red')
ax[0].minorticks_on()
ax[0].set_xlabel(r'$\rm observed\ wavelength\ [\AA]$')
ax[0].set_ylabel(r'$f_\lambda\ [{\rm arbitrary}]$')
tempString = saveSpecPlot.replace('.pdf', '').replace('_', '\ ').replace('spec', '')
titleString = r'$\rm {}'.format(tempString) + r'$z={:0.5f} +{:0.5f} -{:0.5f}$'.format(z_marginalized, zErrUp, zErrDown)
titleString = titleString.split('/')[1]
ax[0].set_title(titleString)
ax[0].minorticks_on()
ax[1].hist(result_emcee.flatchain['z'], color='black', histtype='step', density=True)
ax[1].minorticks_on()
ax[1].set_xlabel(r'$\rm marginalized\ redshift\ posterior$')
ax[1].set_ylabel(r'$P$')
fig.tight_layout()
plt.savefig(saveSpecPlot)
return result_emcee
def getParams(N, p, beta, gamma, sigma, tc, eps):
fit_params = Parameters()
fit_params.add('N', value=N, vary=False)
fit_params.add('p', value=p, min=1, max=1e6)
fit_params.add('beta', value=beta, min=0, max=10) #0.2
fit_params.add('gamma', value=gamma, min=0, max=1.0) #0.02
fit_params.add('sigma', value=sigma, min=0, max=1.0) #0.01
fit_params.add('tc', value=tc, vary=False) #20
fit_params.add('eps', value=eps, vary=False) #8
return fit_params
def chemical_potential(n_e: u.m**-3, T: u.K):
r"""
Calculate the ideal chemical potential.
Parameters
----------
n_e: ~astropy.units.Quantity
Electron number density.
T : ~astropy.units.Quantity
The temperature.
Returns
-------
beta_mu: ~astropy.units.Quantity
The dimensionless ideal chemical potential. That is the ratio of
the ideal chemical potential to the thermal energy.
Raises
------
TypeError
If argument is not a `~astropy.units.Quantity`.
~astropy.units.UnitConversionError
If argument is in incorrect units.
ValueError
If argument contains invalid values.
Warns
-----
~astropy.units.UnitsWarning
If units are not provided, SI units are assumed.
Notes
-----
The ideal chemical potential is given by [1]_:
.. math::
\chi_a = I_{1/2}(\beta \mu_a^{ideal})
where :math:`\chi` is the degeneracy parameter, :math:`I_{1/2}` is the
Fermi integral with order 1/2, :math:`\beta` is the inverse thermal
energy :math:`\beta = 1/(k_B T)`, and :math:`\mu_a^{ideal}`
is the ideal chemical potential.
The definition for the ideal chemical potential is implicit, so it must
be obtained numerically by solving for the Fermi integral for values
of chemical potential approaching the degeneracy parameter. Since values
returned from the Fermi_integral are complex, a nonlinear
Levenberg-Marquardt least squares method is used to iteratively approach
a value of :math:`\mu` which minimizes
:math:`I_{1/2}(\beta \mu_a^{ideal}) - \chi_a`
This function returns :math:`\beta \mu^{ideal}` the dimensionless
ideal chemical potential.
Warning: at present this function is limited to relatively small
arguments due to limitations in the `~mpmath` package's implementation
of `~mpmath.polylog`, which PlasmaPy uses in calculating the Fermi
integral.
References
----------
.. [1] Bonitz, Michael. Quantum kinetic theory. Stuttgart: Teubner, 1998.
Example
-------
>>> from astropy import units as u
>>> chemical_potential(n_e=1e21*u.cm**-3,T=11000*u.K)
<Quantity 2.00039985e-12>
"""
from lmfit import minimize, Parameters
# deBroglie wavelength
lambdaDB = thermal_deBroglie_wavelength(T)
# degeneracy parameter
degen = (n_e * lambdaDB**3).to(u.dimensionless_unscaled)
def residual(params, data, eps_data):
"""Residual function for fitting parameters to Fermi_integral."""
alpha = params['alpha'].value
# note that alpha = mu / (k_B * T)
model = mathematics.Fermi_integral(alpha, 0.5)
complexResidue = (data - model) / eps_data
return complexResidue.view(np.float)
# setting parameters for fitting along with bounds
alphaGuess = 1 * u.dimensionless_unscaled
params = Parameters()
params.add('alpha', value=alphaGuess, min=0.0)
# calling minimize function from lmfit to fit by minimizing the residual
data = np.array([degen]) # result of Fermi_integral - degen should be zero
eps_data = np.array([1e-15]) # numerical error
minFit = minimize(residual, params, args=(data, eps_data))
beta_mu = minFit.params['alpha'].value * u.dimensionless_unscaled
return beta_mu
n = 601
xmin = 0.
xmax = 20.0
random.seed(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 HASPYLAB:
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)
class FittingProfile(object):
def __init__(self, wave, flux, restWave, lineName, zone, rp, fluxError=None, xAxis='vel', initVals='vel'):
"""The input vel and flux must be limited to a single emission line profile"""
self.flux = flux
self.fluxError = fluxError
self.restWave = restWave
self.lineName = lineName
self.zone = zone
self.weights = self._weights()
self.rp = rp
self.xAxis = xAxis
self.initVals = initVals
if xAxis == 'vel':
if fluxError is None:
vel, self.flux = wave_to_vel(restWave, wave, flux)
else:
vel, self.flux, self.fluxError = wave_to_vel(restWave, wave, flux, fluxError)
self.x = vel
else:
self.x = wave
self.linGaussParams = Parameters()
def _weights(self):
if self.fluxError is None:
return None
else:
fluxErrorCR = self.fluxError# - self.continuum
return 1./fluxErrorCR
def _get_amplitude(self, numOfComponents, modelFit):
amplitudeTotal = 0.
for i in range(numOfComponents):
amplitudeTotal = amplitudeTotal + modelFit.best_values['g%d_amplitude' % (i+1)]
print("Amplitude Total is %f" % amplitudeTotal)
return amplitudeTotal
def _gaussian_component(self, pars, prefix, c, s, a, limits):
"""Fits a gaussian with given parameters.
pars is the lmfit Parameters for the fit, prefix is the label of the gaussian, c is the center, s is sigma,
a is amplitude. Returns the Gaussian model"""
varyCentre = True
varySigma = True
varyAmp = True
if limits['c'] is False:
varyCentre = False
cMin, cMax = -np.inf, np.inf
elif type(limits['c']) is tuple:
cMin = limits['c'][0]
cMax = limits['c'][1]
else:
cMin = c - c*limits['c']
cMax = c + c*limits['c']
if limits['s'] is False:
varySigma = False
sMin, sMax = -np.inf, np.inf
elif type(limits['s']) is tuple:
sMin = limits['s'][0]
sMax = limits['s'][1]
else:
sMin = s - s * limits['s']
sMax = s + s * limits['s']
if limits['a'] is False:
varyAmp = False
aMin, aMax = -np.inf, np.inf
elif type(limits['a']) is tuple:
aMin = limits['a'][0]
aMax = limits['a'][1]
else:
aMin = a - a * limits['a']
aMax = a + a * limits['a']
g = GaussianModel(prefix=prefix)
pars.update(g.make_params())
if isinstance(c, str):
pars[prefix + 'center'].set(expr=c, min=cMin, max=cMax, vary=varyCentre)
else:
pars[prefix + 'center'].set(c, min=cMin, max=cMax, vary=varyCentre)
if isinstance(s, str):
pars[prefix + 'sigma'].set(expr=s, min=sMin, max=sMax, vary=varySigma)
else:
pars[prefix + 'sigma'].set(s, min=sMin, max=sMax, vary=varySigma)
if isinstance(a, str):
pars[prefix + 'amplitude'].set(expr=a, min=aMin, max=aMax, vary=varyAmp)
else:
pars[prefix + 'amplitude'].set(a, min=aMin, max=aMax, vary=varyAmp)
return g
def multiple_close_emission_lines(self, lineNames, cListInit, sListInit, lS, lI):
"""All lists should be the same length"""
gList = []
# Assume initial parameters are in velocity
lin = LinearModel(prefix='lin_')
self.linGaussParams = lin.guess(self.flux, x=self.x)
self.linGaussParams.update(lin.make_params())
self.linGaussParams['lin_slope'].set(lS, vary=True)
self.linGaussParams['lin_intercept'].set(lI, vary=True)
for j, lineName in enumerate(lineNames):
numComps = self.rp.emProfiles[lineName]['numComps']
restWave = self.rp.emProfiles[lineName]['restWavelength']
copyFrom = self.rp.emProfiles[lineName]['copyFrom']
if copyFrom is not None:
copyFromRestWave = self.rp.emProfiles[copyFrom]['restWavelength']
cList = ['g{0}{1}_center*{2}'.format(copyFrom.replace('-', ''), (i + 1), (restWave / copyFromRestWave)) for i in range(numComps)]
sList = ['g{0}{1}_sigma'.format(copyFrom.replace('-', ''), i + 1) for i in range(numComps)]
if type(self.rp.emProfiles[lineName]['ampList']) is list:
aList = self.rp.emProfiles[lineName]['ampList']
if self.xAxis == 'vel':
aList = vel_to_wave(restWave, vel=0, flux=np.array(aList))[1]
else:
ampRatio = self.rp.emProfiles[lineName]['ampList']
aList = ['g{0}{1}_amplitude*{2}'.format(copyFrom.replace('-', ''), i + 1, ampRatio) for i in range(numComps)]
else:
cList = vel_to_wave(restWave, vel=np.array(cListInit), flux=0)[0]
sList = vel_to_wave(restWave, vel=np.array(sListInit), flux=0, delta=True)[0]
aListInit = self.rp.emProfiles[lineName]['ampList']
aList = vel_to_wave(restWave, vel=0, flux=np.array(aListInit))[1]
limits = self.rp.emProfiles[lineName]['compLimits']
for i in range(numComps):
if type(limits['c']) is list:
cLimit = limits['c'][i]
else:
cLimit = limits['c']
if type(limits['s']) is list:
sLimit = limits['s'][i]
else:
sLimit = limits['s']
if type(limits['a']) is list:
aLimit = limits['a'][i]
else:
aLimit = limits['a']
lims = {'c': cLimit, 's': sLimit, 'a': aLimit}
if len(lineNames) == 1:
prefix = 'g{0}_'.format(i + 1)
else:
prefix = 'g{0}{1}_'.format(lineName.replace('-', ''), i + 1)
gList.append(self._gaussian_component(self.linGaussParams, prefix, cList[i], sList[i], aList[i], lims))
gList = np.array(gList)
mod = lin + gList.sum()
init = mod.eval(self.linGaussParams, x=self.x)
out = mod.fit(self.flux, self.linGaussParams, x=self.x, weights=self.weights)
f = open(os.path.join(constants.OUTPUT_DIR, self.rp.regionName, "{0}_Log.txt".format(self.rp.regionName)), "a")
print("######## %s %s Linear and Multi-gaussian Model ##########\n" % (self.rp.regionName, self.lineName))
print(out.fit_report())
f.write("######## %s %s Linear and Multi-gaussian Model ##########\n" % (self.rp.regionName, self.lineName))
f.write(out.fit_report())
f.close()
components = out.eval_components()
if not hasattr(self.rp, 'plotResiduals'):
self.rp.plotResiduals = True
numComps = self.rp.emProfiles[lineName]['numComps']
self.plot_emission_line(numComps, components, out, self.rp.plotResiduals, lineNames, init=init, scaleFlux=self.rp.scaleFlux)
return out, components
def lin_and_multi_gaussian(self, numOfComponents, cList, sList, aList, lS, lI, limits):
"""All lists should be the same length"""
gList = []
if self.xAxis == 'wave' and self.initVals == 'vel':
cList = vel_to_wave(self.restWave, vel=np.array(cList), flux=0)[0]
sList = vel_to_wave(self.restWave, vel=np.array(sList), flux=0, delta=True)[0]
aList = vel_to_wave(self.restWave, vel=0, flux=np.array(aList))[1]
elif self.xAxis == 'vel' and self.initVals == 'wave':
cList = wave_to_vel(self.restWave, wave=np.array(cList), flux=0)[0]
sList = wave_to_vel(self.restWave, wave=np.array(sList), flux=0, delta=True)[0]
aList = wave_to_vel(self.restWave, wave=0, flux=np.array(aList))[1]
lin = LinearModel(prefix='lin_')
self.linGaussParams = lin.guess(self.flux, x=self.x)
self.linGaussParams.update(lin.make_params())
self.linGaussParams['lin_slope'].set(lS, vary=True)
self.linGaussParams['lin_intercept'].set(lI, vary=True)
for i in range(numOfComponents):
if type(limits['c']) is list:
cLimit = limits['c'][i]
else:
cLimit = limits['c']
if type(limits['s']) is list:
sLimit = limits['s'][i]
else:
sLimit = limits['s']
if type(limits['a']) is list:
aLimit = limits['a'][i]
else:
aLimit = limits['a']
lims = {'c': cLimit, 's': sLimit, 'a': aLimit}
prefix = 'g{0}_'.format(i+1)
gList.append(self._gaussian_component(self.linGaussParams, prefix, cList[i], sList[i], aList[i], lims))
gList = np.array(gList)
mod = lin + gList.sum()
init = mod.eval(self.linGaussParams, x=self.x)
out = mod.fit(self.flux, self.linGaussParams, x=self.x, weights=self.weights)
f = open(os.path.join(constants.OUTPUT_DIR, self.rp.regionName, "{0}_Log.txt".format(self.rp.regionName)), "a")
print("######## %s %s Linear and Multi-gaussian Model ##########\n" % (self.rp.regionName, self.lineName))
print(out.fit_report())
f.write("######## %s %s Linear and Multi-gaussian Model ##########\n" % (self.rp.regionName, self.lineName))
f.write(out.fit_report())
f.close()
components = out.eval_components()
if not hasattr(self.rp, 'plotResiduals'):
self.rp.plotResiduals = True
self.plot_emission_line(numOfComponents, components, out, self.rp.plotResiduals, init=init, scaleFlux=self.rp.scaleFlux)
self._get_amplitude(numOfComponents, out)
return out, components
def plot_emission_line(self, numOfComponents, components, out, plotResiduals=True, lineNames=None, init=None, scaleFlux=1e14):
ion, lambdaZero = line_label(self.lineName, self.restWave)
fig = plt.figure("%s %s %s" % (self.rp.regionName, ion, lambdaZero))
if plotResiduals is True:
frame1 = fig.add_axes((.1, .3, .8, .6))
plt.title("%s %s" % (ion, lambdaZero))
if self.xAxis == 'wave':
x = self.x
xLabel = constants.WAVE_AXIS_LABEL
yLabel = constants.FluxUnitsLabels(scaleFlux).FLUX_WAVE_AXIS_LABEL
elif self.xAxis == 'vel':
if hasattr(self.rp, 'showSystemicVelocity') and self.rp.showSystemicVelocity is True:
x = self.x - self.rp.systemicVelocity
xLabel = constants.DELTA_VEL_AXIS_LABEL
else:
x = self.x
xLabel = constants.VEL_AXIS_LABEL
if hasattr(self.rp, 'rp.plottingXRange') and self.rp.plottingXRange is not None:
plt.xlim(self.rp.plottingXRange)
yLabel = constants.FluxUnitsLabels(scaleFlux).FLUX_VEL_AXIS_LABEL
else:
raise Exception("Invalid xAxis argument. Must be either 'wave' or 'vel'. ")
plt.plot(x, self.flux, label='Data')
for i in range(numOfComponents):
labelComp = self.rp.componentLabels
if lineNames is None:
plt.plot(x, components['g%d_' % (i+1)]+components['lin_'], color=self.rp.componentColours[i], linestyle=':', label=labelComp[i])
else:
for j, lineName in enumerate(lineNames):
plt.plot(x, components['g{0}{1}_'.format(lineName.replace('-', ''), i + 1)] + components['lin_'], color=self.rp.componentColours[i], linestyle=':', label=labelComp[i])
# plt.plot(x, components['lin_'], label='lin_')
plt.plot(x, out.best_fit, color='black', linestyle='--', label='Fit')
# plt.plot(x, init, label='init')
plt.legend(loc='upper left')
plt.ylabel(yLabel)
if plotResiduals is True:
frame1 = plt.gca()
frame1.axes.get_xaxis().set_visible(False)
frame2 = fig.add_axes((.1, .1, .8, .2))
plt.plot(x, self.flux - out.best_fit)
plt.axhline(y=0, linestyle='--', color='black')
plt.ylabel('Residuals')
# plt.locator_params(axis='y', nbins=3)
# nbins = len(frame2.get_yticklabels())
frame2.yaxis.set_major_locator(MaxNLocator(nbins=3, prune='upper'))
plt.xlabel(xLabel)
plt.savefig(os.path.join(constants.OUTPUT_DIR, self.rp.regionName, self.lineName + " {0} Component Linear-Gaussian Model".format(numOfComponents)), bbox_inches='tight')
return ((data - model) / data_err)**2
from lmfit import Parameters, Minimizer
from multiprocessing import cpu_count
res = op.minimize(chisq_sp, params, args=(args), method='powell')
nrg_ratio_fit, temp_night_fit, delta_T_fit = res.x
fit_model = generate_spiderman_model(times, planet_info, nrg_ratio_fit,
temp_night_fit, delta_T_fit, T_star,
spider_params)
print('Initializing Parameters')
initialParams = Parameters()
initialParams.add_many(
('nrg_ratio', np.max([nrg_ratio_fit, 0.0]), True, 0.0, 1.0),
('temp_night', temp_night_fit, True, 0.0, np.inf),
('delta_T', delta_T_fit, True, 0.0, np.inf))
from functools import partial
partial_residuals = partial(chisq_lmfit, args=args)
mle0 = Minimizer(partial_residuals, initialParams, nan_policy='omit')
fitResult = mle0.leastsq(initialParams)
def logprior_func(p):
for key, val in p.items():
def chemical_potential(n_e: u.m**-3, T: u.K) -> u.dimensionless_unscaled:
r"""
Calculate the ideal chemical potential.
Parameters
----------
n_e : `~astropy.units.Quantity`
Electron number density.
T : ~astropy.units.Quantity
The temperature.
Returns
-------
beta_mu : `~astropy.units.Quantity`
The dimensionless ideal chemical potential. That is the ratio of
the ideal chemical potential to the thermal energy.
Raises
------
`TypeError`
If argument is not a `~astropy.units.Quantity`.
`~astropy.units.UnitConversionError`
If argument is in incorrect units.
`ValueError`
If argument contains invalid values.
Warns
-----
: `~astropy.units.UnitsWarning`
If units are not provided, SI units are assumed.
Notes
-----
The ideal chemical potential is given by [1]_:
.. math::
χ_a = I_{1/2}(β μ_a^{ideal})
where :math:`χ` is the degeneracy parameter, :math:`I_{1/2}` is the
Fermi integral with order 1/2, :math:`β` is the inverse thermal
energy :math:`β = 1/(k_B T)`, and :math:`μ_a^{ideal}`
is the ideal chemical potential.
The definition for the ideal chemical potential is implicit, so it must
be obtained numerically by solving for the Fermi integral for values
of chemical potential approaching the degeneracy parameter. Since values
returned from the Fermi_integral are complex, a nonlinear
Levenberg-Marquardt least squares method is used to iteratively approach
a value of :math:`μ` which minimizes
:math:`I_{1/2}(β μ_a^{ideal}) - χ_a`
This function returns :math:`β μ^{ideal}` the dimensionless
ideal chemical potential.
Warning: at present this function is limited to relatively small
arguments due to limitations in the `~mpmath` package's implementation
of `~mpmath.polylog`, which PlasmaPy uses in calculating the Fermi
integral.
References
----------
.. [1] Bonitz, Michael. Quantum kinetic theory. Stuttgart: Teubner, 1998.
Example
-------
>>> from astropy import units as u
>>> chemical_potential(n_e=1e21*u.cm**-3,T=11000*u.K) # doctest: +SKIP
<Quantity 2.00039985e-12>
"""
raise NotImplementedError(
"This function has been temporarily disabled due to a bug.\n"
"Please refer to https://github.com/PlasmaPy/PlasmaPy/issues/726 \n"
"and https://github.com/astropy/astropy/issues/9721 "
"for progress in fixing it.")
# deBroglie wavelength
lambdaDB = thermal_deBroglie_wavelength(T)
# degeneracy parameter
degen = (n_e * lambdaDB**3).to(u.dimensionless_unscaled)
def residual(params, data, eps_data):
"""Residual function for fitting parameters to Fermi_integral."""
alpha = params["alpha"].value
# note that alpha = mu / (k_B * T)
model = mathematics.Fermi_integral(alpha, 0.5)
complexResidue = (data - model) / eps_data
return complexResidue.view(np.float)
# setting parameters for fitting along with bounds
alphaGuess = 1 * u.dimensionless_unscaled
try:
from lmfit import minimize, Parameters
except (ImportError, ModuleNotFoundError) as e:
from plasmapy.optional_deps import lmfit_import_error
raise lmfit_import_error from e
params = Parameters()
params.add("alpha", value=alphaGuess, min=0.0)
# calling minimize function from lmfit to fit by minimizing the residual
data = np.array([degen]) # result of Fermi_integral - degen should be zero
eps_data = np.array([1e-15]) # numerical error
minFit = minimize(residual, params, args=(data, eps_data))
beta_mu = minFit.params["alpha"].value * u.dimensionless_unscaled
return beta_mu
# Pre1 -------------------------------------------------------------------------
pre1_time = numpy.memmap("orion331-TP2B-48000.raw", dtype="float32", mode='r')
pre1_freq = numpy.fft.rfft(pre1_time)
pre1_reference = pre1_freq
samples = pre1_time.size
delta_time = numpy.zeros(samples)
delta_time[0] = 1.0
x_freq = numpy.linspace(0.0, sample_rate / 2, (samples / 2) + 1)
pre1_filters = '-eadb:-{adb} -el:RThighshelf,{RThighshelf_A},{RThighshelf_f0},{RThighshelf_Q} -el:RTlowshelf,{RTlowshelf_A},{RTlowshelf_f0},{RTlowshelf_Q}'
fmin = 20
fmax = 22000
pre1 = Parameters()
# (Name, Value, Vary, Min, Max, Expr)
pre1.add_many(('adb', 9.28136887, True, 0, None, None),
('RThighshelf_A', 4.38211718, True, 0, None, None),
('RThighshelf_f0', 134.645409, True, 100, 200, None),
('RThighshelf_Q', 0.48178881, True, 0.1, 3, None),
('RTlowshelf_A', 3.42318251, True, 0, None, None),
('RTlowshelf_f0', 1747.22195, True, 1600, 1800, None),
('RTlowshelf_Q', 0.48331721, True, 0.1, 3, None),
('sample_rate', sample_rate, False, None, None, None))
#out = minimize(residual, pre1, args=(pre1_filters, x_freq, fmin, fmax, delta_time), kws={'data':pre1_reference}, method='nelder')
#pre1 = out.params
#print(fit_report(out))
data_file_name_3 = "70mM_cleaneddata_RAD_F.csv"
#create arrays from signal data
signal1 = create_numpy_array(data_file_path,
data_file_name_1) #columns Time / ns, D, C, F
signal2 = create_numpy_array(data_file_path,
data_file_name_2) #columns Time / ns, D, C, F
signal3 = create_numpy_array(data_file_path,
data_file_name_3) #columns Time / ns, D, F
#take time series from signal data
t1 = signal1[:, 0] * (1e-9)
t2 = signal2[:, 0] * (1e-9)
t3 = signal3[:, 0] * (1e-9)
#Initilaise parameter class and add parameters to model
params = Parameters()
#rate coefficients
k = [1e9, 1.3e10, 1.5e9, 1e6, 3.03e11, 3.1e5]
params.add('k1', value=k[0])
params.add('k2', value=k[1], vary=False)
params.add('k3', value=k[2])
params.add('k4', value=k[3])
params.add('k5', value=k[4], vary=False)
params.add('k6', value=k[5], vary=False)
#static and diffusive radical conentrations
params.add('radical', value=3.8e-5, vary=False) #radical conc in M
params.add('static_radical', value=1e-5, vary=False) #static radical conc
#amplitudes to convert from concentration to integrated signal
params.add('amp_C', value=30)
params.add('amp_F', value=17)
params.add('amp_D', value=5700)
# Variable Definitions
Z = 18 # Atomic Number of Argon
X_0 = 14.1 # Radiation length
# Energy
Energy = np.arange(200, 3200, 200)
E_s = 0.511 * np.sqrt(137 * 4 * np.pi) # Scale energy
E_c = 35.2 # Critical Energy
TMax_Truth = np.array([18, 26, 30, 34, 42, 42, 42, 42, 54, 42, 42, 54, 54, 54, 54])
params = Parameters()
params.add('X0', value = X_0, min = 0, max = 30, vary = True )
params.add('Ec', value = E_c, min = 10, max = 60, vary = True)
# do fit, here with leastsq model
minner = Minimizer(fTmax_Residual, params, fcn_args=(Energy, TMax_Truth))
result = minner.minimize()
# calculate final result
final = TMax_Truth + result.residual
result.params.pretty_print()
print result.params['X0'].value
# =============================================================================
path_data = "../data/"
df_fahey = pd.read_csv(path_data + "fahey_data.csv")
df_fahey.loc[df_fahey["cell"] == "NonTfh", "cell"] = "nonTfh"
data_arm = df_fahey[df_fahey.name == "Arm"]
data_cl13 = df_fahey[df_fahey.name == "Cl13"]
# get model
time = np.arange(0, 80, 0.1)
sim = Sim(time=time, name=today, params=d, virus_model=vir_model_const)
# =============================================================================
# set parameters
# =============================================================================
params = Parameters()
params.add('death_tr1', value=0.05, min=0, max=0.2)
params.add('death_tfhc', value=0.01, min=0, max=0.2)
params.add('prolif_tr1', value=2.8, min=2, max=4.0)
params.add('prolif_tfhc', value=4.1, min=3, max=5.0)
params.add("pth1", value=0.06, min=0, max=1.0)
params.add("ptfh", value=0.04, min=0, max=1.0)
params.add("ptr1", value=0.89, min=0, max=1.0)
params.add("ptfhc", expr="1.0-pth1-ptfh-ptr1")
params.add("r_mem", value=0.01, min=0, max=0.2)
params.add("deg_myc", value=0.32, min=0.28, max=0.35)
# =============================================================================
# run fitting procedure
# =============================================================================
modelname = "fahey"
ndata, _ = data.shape
resid = 0.0 * data[:]
# make residual per data set
for i in range(ndata):
resid[i, :] = data[i, :] - gauss_dataset(params, i, x)
# now flatten this to a 1D array, as minimize() needs
return resid.flatten()
#Create five simulated Gaussian data sets
x = np.linspace(-1, 2, 151)
data = []
for i in np.arange(5):
params = Parameters()
amp = 0.60 + 9.50 * np.random.rand()
cen = -0.20 + 1.20 * np.random.rand()
sig = 0.25 + 0.03 * np.random.rand()
dat = gauss(x, amp, cen, sig) + np.random.normal(size=x.size, scale=0.1)
data.append(dat)
data = np.array(data)
#Create five sets of fitting parameters, one per data set
fit_params = Parameters()
for iy, y in enumerate(data):
fit_params.add('amp_%i' % (iy + 1), value=0.5, min=0.0, max=200)
fit_params.add('cen_%i' % (iy + 1), value=0.4, min=-2.0, max=2.0)
fit_params.add('sig_%i' % (iy + 1), value=0.3, min=0.01, max=3.0)
#Constrain the values of sigma to be the same for all peaks by assigning sig_2, …, sig_5 to be equal to sig_1.
def main(self,
ID0,
PA0,
zgal,
flag_m,
zprev,
Cz0,
Cz1,
mcmcplot=True,
fzvis=1,
specplot=1,
fneld=0,
ntemp=5,
sigz=1.0,
ezmin=0.01,
f_move=False,
f_disp=False
): # flag_m related to redshift error in redshift check func.
#
# sigz (float): confidence interval for redshift fit.
# ezmin (float): minimum error in redshift.
#
print('########################')
print('### Fitting Function ###')
print('########################')
start = timeit.default_timer()
inputs = self.inputs
DIR_TMP = inputs['DIR_TEMP']
if os.path.exists(DIR_TMP) == False:
os.mkdir(DIR_TMP)
# For error parameter
ferr = 0
#
# Age
#
age = inputs['AGE']
age = [float(x.strip()) for x in age.split(',')]
nage = np.arange(0, len(age), 1)
#
# Metallicity
#
Zmax, Zmin = float(inputs['ZMAX']), float(inputs['ZMIN'])
delZ = float(inputs['DELZ'])
Zall = np.arange(Zmin, Zmax, delZ) # in logZsun
# For minimizer.
delZtmp = delZ
#delZtmp = 0.4 # to increase speed.
# For z prior.
delzz = 0.001
zlimu = 6.
snlim = 1
zliml = zgal - 0.5
agemax = cd.age(zgal, use_flat=True, **cosmo) / cc.Gyr_s
# N of param:
try:
ndim = int(inputs['NDIM'])
print('No of params are : %d' % (ndim))
except:
if int(inputs['ZEVOL']) == 1:
ndim = int(len(nage) * 2 + 1)
print('Metallicity evolution is on.')
if int(inputs['ZMC']) == 1:
ndim += 1
print('No of params are : %d' % (ndim))
else:
ndim = int(len(nage) + 1 + 1)
print('Metallicity evolution is off.')
if int(inputs['ZMC']) == 1:
ndim += 1
print('No of params are : %d' % (ndim))
pass
#
# Line
#
LW0 = inputs['LINE']
LW0 = [float(x.strip()) for x in LW0.split(',')]
#
# Params for MCMC
#
nmc = int(inputs['NMC'])
nwalk = int(inputs['NWALK'])
nmc_cz = int(inputs['NMCZ'])
nwalk_cz = int(inputs['NWALKZ'])
f_Zevol = int(inputs['ZEVOL'])
#f_zvis = int(inputs['ZVIS'])
try:
fzmc = int(inputs['ZMC'])
except:
fzmc = 0
#
# If FIR data;
#
try:
DT0 = float(inputs['TDUST_LOW'])
DT1 = float(inputs['TDUST_HIG'])
dDT = float(inputs['TDUST_DEL'])
Temp = np.arange(DT0, DT1, dDT)
f_dust = True
print('FIR fit is on.')
except:
f_dust = False
pass
#
# Tau for MCMC parameter; not as fitting parameters.
#
tau0 = inputs['TAU0']
tau0 = [float(x.strip()) for x in tau0.split(',')]
#
# Dust model specification;
#
try:
dust_model = int(inputs['DUST_MODEL'])
except:
dust_model = 0
from .function_class import Func
from .basic_func import Basic
fnc = Func(Zall, nage, dust_model=dust_model,
DIR_TMP=DIR_TMP) # Set up the number of Age/ZZ
bfnc = Basic(Zall)
# Open ascii file and stock to array.
#lib = open_spec(ID0, PA0)
lib = fnc.open_spec_fits(ID0, PA0, fall=0, tau0=tau0)
lib_all = fnc.open_spec_fits(ID0, PA0, fall=1, tau0=tau0)
if f_dust:
lib_dust = fnc.open_spec_dust_fits(ID0,
PA0,
Temp,
fall=0,
tau0=tau0)
lib_dust_all = fnc.open_spec_dust_fits(ID0,
PA0,
Temp,
fall=1,
tau0=tau0)
#################
# Observed Data
#################
##############
# Spectrum
##############
dat = np.loadtxt(DIR_TMP + 'spec_obs_' + ID0 + '_PA' + PA0 + '.cat',
comments='#')
NR = dat[:, 0]
x = dat[:, 1]
fy00 = dat[:, 2]
ey00 = dat[:, 3]
con0 = (NR < 1000)
fy0 = fy00[con0] * Cz0
ey0 = ey00[con0] * Cz0
con1 = (NR >= 1000) & (NR < 10000)
fy1 = fy00[con1] * Cz1
ey1 = ey00[con1] * Cz1
# BB data in spec_obs are not in use.
#con2 = (NR>=10000) # BB
#fy2 = fy00[con2]
#ey2 = ey00[con2]
##############
# Broadband
##############
dat = np.loadtxt(DIR_TMP + 'bb_obs_' + ID0 + '_PA' + PA0 + '.cat',
comments='#')
NRbb = dat[:, 0]
xbb = dat[:, 1]
fybb = dat[:, 2]
eybb = dat[:, 3]
exbb = dat[:, 4]
fy2 = fybb
ey2 = eybb
fy01 = np.append(fy0, fy1)
fy = np.append(fy01, fy2)
ey01 = np.append(ey0, ey1)
ey = np.append(ey01, ey2)
wht = 1. / np.square(ey)
wht2 = check_line_man(fy, x, wht, fy, zprev, LW0)
sn = fy / ey
#####################
# Function fo MCMC
#####################
def residual(
pars,
fy,
wht2,
f_fir,
out=False): # x, y, wht are taken from out of the definition.
#
# Returns: residual of model and data.
# out: model as second output. For lnprob func.
# f_fir: syntax. If dust component is on or off.
vals = pars.valuesdict()
model, x1 = fnc.tmp04(ID0, PA0, vals, zprev, lib, tau0=tau0)
if f_fir:
model_dust, x1_dust = fnc.tmp04_dust(ID0,
PA0,
vals,
zprev,
lib_dust,
tau0=tau0)
n_optir = len(model)
# Add dust flux to opt/IR grid.
model[:] += model_dust[:n_optir]
#print(model_dust)
# then append only FIR flux grid.
model = np.append(model, model_dust[n_optir:])
x1 = np.append(x1, x1_dust[n_optir:])
#plt.plot(x1,model,'r.')
#plt.show()
if ferr == 1:
f = vals['f']
else:
f = 0 # temporary... (if f is param, then take from vals dictionary.)
con_res = (model > 0) & (wht2 > 0) #& (fy>0)
sig = np.sqrt(1. / wht2 + f**2 * model**2)
'''
contmp = x1>1e6 & (wht2>0)
try:
print(x1[contmp],model[contmp],fy[contmp],np.log10(vals['MDUST']))
except:
pass
'''
if not out:
if fy is None:
print('Data is none')
return model[con_res]
else:
return (model - fy)[con_res] / sig[
con_res] # i.e. residual/sigma. Because is_weighted = True.
if out:
if fy is None:
print('Data is none')
return model[con_res], model
else:
return (model - fy)[con_res] / sig[
con_res], model # i.e. residual/sigma. Because is_weighted = True.
def lnprob(pars, fy, wht2, f_fir):
#
# Returns: posterior.
#
vals = pars.valuesdict()
if ferr == 1:
f = vals['f']
else:
f = 0 # temporary... (if f is param, then take from vals dictionary.)
resid, model = residual(pars, fy, wht2, f_fir, out=True)
con_res = (model > 0) & (wht2 > 0)
sig = np.sqrt(1. / wht2 + f**2 * model**2)
lnlike = -0.5 * np.sum(resid**2 +
np.log(2 * 3.14 * sig[con_res]**2))
#print(np.log(2 * 3.14 * 1) * len(sig[con_res]), np.sum(np.log(2 * 3.14 * sig[con_res]**2)))
#Av = vals['Av']
#if Av<0:
# return -np.inf
#else:
# respr = 0 #np.log(1)
respr = 0 # Flat prior...
return lnlike + respr
###############################
# Add parameters
###############################
fit_params = Parameters()
for aa in range(len(age)):
if age[aa] == 99 or age[aa] > agemax:
fit_params.add('A' + str(aa), value=0, min=0, max=1e-10)
else:
fit_params.add('A' + str(aa), value=1, min=0, max=1e3)
#####################
# Dust attenuation
#####################
try:
Avmin = float(inputs['AVMIN'])
Avmax = float(inputs['AVMAX'])
fit_params.add('Av', value=Avmin, min=Avmin, max=Avmax)
except:
fit_params.add('Av', value=0.2, min=0, max=4.0)
#####################
# Metallicity
#####################
if int(inputs['ZEVOL']) == 1:
for aa in range(len(age)):
if age[aa] == 99 or age[aa] > agemax:
fit_params.add('Z' + str(aa), value=0, min=0, max=1e-10)
else:
fit_params.add('Z' + str(aa),
value=0,
min=np.min(Zall),
max=np.max(Zall))
elif inputs['ZFIX']:
#print('Z is fixed')
ZFIX = float(inputs['ZFIX'])
aa = 0
fit_params.add('Z' + str(aa), value=0, min=ZFIX, max=ZFIX + 0.01)
else:
aa = 0
fit_params.add('Z' + str(aa),
value=0,
min=np.min(Zall),
max=np.max(Zall))
####################################
# Initial Metallicity Determination
####################################
chidef = 1e5
Zbest = 0
fwz = open('Z_' + ID0 + '_PA' + PA0 + '.cat', 'w')
fwz.write('# ID Zini chi/nu AA Av Zbest\n')
fwz.write('# FNELD = %d\n' % fneld)
nZtmp = int((Zmax - Zmin) / delZtmp)
ZZtmp = np.arange(Zmin, Zmax, delZtmp)
# How to get initial parameters?
# Nelder;
if fneld == 1:
fit_name = 'nelder'
for zz in range(len(ZZtmp)):
ZZ = ZZtmp[zz]
if int(inputs['ZEVOL']) == 1:
for aa in range(len(age)):
fit_params['Z' + str(aa)].value = ZZ
else:
aa = 0
fit_params['Z' + str(aa)].value = ZZ
out_tmp = minimize(
residual,
fit_params,
args=(fy, wht2, False),
method=fit_name) # nelder is the most efficient.
keys = fit_report(out_tmp).split('\n')
csq = 99999
rcsq = 99999
for key in keys:
if key[4:7] == 'chi':
skey = key.split(' ')
csq = float(skey[14])
if key[4:7] == 'red':
skey = key.split(' ')
rcsq = float(skey[7])
fitc = [csq, rcsq] # Chi2, Reduced-chi2
fwz.write('%s %.2f %.5f' % (ID0, ZZ, fitc[1]))
AA_tmp = np.zeros(len(age), dtype='float32')
ZZ_tmp = np.zeros(len(age), dtype='float32')
for aa in range(len(age)):
AA_tmp[aa] = out_tmp.params['A' + str(aa)].value
fwz.write(' %.5f' % (AA_tmp[aa]))
Av_tmp = out_tmp.params['Av'].value
fwz.write(' %.5f' % (Av_tmp))
if int(inputs['ZEVOL']) == 1:
for aa in range(len(age)):
ZZ_tmp[aa] = out_tmp.params['Z' + str(aa)].value
fwz.write(' %.5f' % (ZZ_tmp[aa]))
else:
aa = 0
ZZ_tmp[aa] = out_tmp.params['Z' + str(aa)].value
fwz.write(' %.5f' % (ZZ_tmp[aa]))
fwz.write('\n')
if fitc[1] < chidef:
chidef = fitc[1]
out = out_tmp
# Or
# Powell;
else:
fit_name = 'powell'
for zz in range(0, nZtmp, 2):
ZZ = zz * delZtmp + np.min(Zall)
if int(inputs['ZEVOL']) == 1:
for aa in range(len(age)):
fit_params['Z' + str(aa)].value = ZZ
else:
aa = 0
fit_params['Z' + str(aa)].value = ZZ
out_tmp = minimize(
residual,
fit_params,
args=(fy, wht2, False),
method=fit_name) # powel is the more accurate.
keys = fit_report(out_tmp).split('\n')
csq = 99999
rcsq = 99999
for key in keys:
if key[4:7] == 'chi':
skey = key.split(' ')
csq = float(skey[14])
if key[4:7] == 'red':
skey = key.split(' ')
rcsq = float(skey[7])
fitc = [csq, rcsq] # Chi2, Reduced-chi2
fwz.write('%s %.2f %.5f' % (ID0, ZZ, fitc[1]))
AA_tmp = np.zeros(len(age), dtype='float32')
ZZ_tmp = np.zeros(len(age), dtype='float32')
for aa in range(len(age)):
AA_tmp[aa] = out_tmp.params['A' + str(aa)].value
fwz.write(' %.5f' % (AA_tmp[aa]))
Av_tmp = out_tmp.params['Av'].value
fwz.write(' %.5f' % (Av_tmp))
if int(inputs['ZEVOL']) == 1:
for aa in range(len(age)):
ZZ_tmp[aa] = out_tmp.params['Z' + str(aa)].value
fwz.write(' %.5f' % (ZZ_tmp[aa]))
else:
aa = 0
fwz.write(' %.5f' % (ZZ_tmp[aa]))
fwz.write('\n')
if fitc[1] < chidef:
chidef = fitc[1]
out = out_tmp
#
# Best fit
#
keys = fit_report(out).split('\n')
for key in keys:
if key[4:7] == 'chi':
skey = key.split(' ')
csq = float(skey[14])
if key[4:7] == 'red':
skey = key.split(' ')
rcsq = float(skey[7])
fitc = [csq, rcsq] # Chi2, Reduced-chi2
#fitc = fit_report_chi(out) # Chi2, Reduced-chi2
ZZ = Zbest # This is really important/does affect lnprob/residual.
print('\n\n')
print('#####################################')
print('Zbest, chi are;', Zbest, chidef)
print('Params are;', fit_report(out))
print('#####################################')
print('\n\n')
fwz.close()
Av_tmp = out.params['Av'].value
AA_tmp = np.zeros(len(age), dtype='float32')
ZZ_tmp = np.zeros(len(age), dtype='float32')
fm_tmp, xm_tmp = fnc.tmp04_val(ID0, PA0, out, zprev, lib, tau0=tau0)
########################
# Check redshift
########################
zrecom = zprev
# Observed data.
con_cz = (NR < 10000) #& (sn>snlim)
fy_cz = fy[con_cz]
ey_cz = ey[con_cz]
x_cz = x[con_cz] # Observed range
NR_cz = NR[con_cz]
xm_s = xm_tmp / (1 + zprev) * (1 + zrecom)
fm_s = np.interp(x_cz, xm_s, fm_tmp)
if fzvis == 1:
plt.plot(x_cz / (1 + zprev) * (1. + zrecom),
fm_s,
'gray',
linestyle='--',
linewidth=0.5,
label='Default ($z=%.5f$)' %
(zprev)) # Model based on input z.
plt.plot(x_cz,
fy_cz,
'b',
linestyle='-',
linewidth=0.5,
label='Obs.') # Observation
plt.errorbar(x_cz,
fy_cz,
yerr=ey_cz,
color='b',
capsize=0,
linewidth=0.5) # Observation
if flag_m == 0:
dez = 0.5
else:
dez = 0.2
#
# For Eazy
#
'''
dprob = np.loadtxt(eaz_path + 'photz_' + str(int(ID0)) + '.pz', comments='#')
zprob = dprob[:,0]
cprob = dprob[:,1]
zz_prob = np.arange(0,13,delzz)
cprob_s = np.interp(zz_prob, zprob, cprob)
prior_s = 1/cprob_s
prior_s /= np.sum(prior_s)
'''
zz_prob = np.arange(0, 13, delzz)
prior_s = zz_prob * 0 + 1.
prior_s /= np.sum(prior_s)
try:
print('############################')
print('Start MCMC for redshift fit')
print('############################')
res_cz, fitc_cz = check_redshift(fy_cz, ey_cz, x_cz, fm_tmp,
xm_tmp / (1 + zprev), zprev, dez,
prior_s, NR_cz, zliml, zlimu,
delzz, nmc_cz, nwalk_cz)
z_cz = np.percentile(res_cz.flatchain['z'], [16, 50, 84])
scl_cz0 = np.percentile(res_cz.flatchain['Cz0'], [16, 50, 84])
scl_cz1 = np.percentile(res_cz.flatchain['Cz1'], [16, 50, 84])
zrecom = z_cz[1]
Czrec0 = scl_cz0[1]
Czrec1 = scl_cz1[1]
# Switch to peak redshift:
from scipy import stats
from scipy.stats import norm
# find minimum and maximum of xticks, so we know
# where we should compute theoretical distribution
ser = res_cz.flatchain['z']
xmin, xmax = zprev - 0.2, zprev + 0.2
lnspc = np.linspace(xmin, xmax, len(ser))
print('\n\n')
print(
'Recommended redshift, Cz0 and Cz1, %.5f %.5f %.5f, with chi2/nu=%.3f'
% (zrecom, Cz0 * Czrec0, Cz1 * Czrec1, fitc_cz[1]))
print('\n\n')
except:
print('z fit failed. No spectral data set?')
try:
ezl = float(inputs['EZL'])
ezu = float(inputs['EZU'])
print('Redshift error is taken from input file.')
if ezl < ezmin:
ezl = ezmin #0.03
if ezu < ezmin:
ezu = ezmin #0.03
except:
ezl = ezmin
ezu = ezmin
print('Redshift error is assumed to %.1f.' % (ezl))
z_cz = [zprev - ezl, zprev, zprev + ezu]
zrecom = z_cz[1]
scl_cz0 = [1., 1., 1.]
scl_cz1 = [1., 1., 1.]
Czrec0 = scl_cz0[1]
Czrec1 = scl_cz1[1]
'''
try:
# lets try the normal distribution first
m, s = stats.norm.fit(ser) # get mean and standard deviation
pdf_g = stats.norm.pdf(lnspc, m, s) # now get theoretical values in our interval
z_cz[:] = [m-s, m, m+s]
zrecom = z_cz[1]
f_fitgauss = 1
except:
print('Guassian fitting to z distribution failed.')
f_fitgauss=0
'''
f_fitgauss = 0
xm_s = xm_tmp / (1 + zprev) * (1 + zrecom)
fm_s = np.interp(x_cz, xm_s, fm_tmp)
whtl = 1 / np.square(ey_cz)
try:
wht3, ypoly = check_line_cz_man(fy_cz, x_cz, whtl, fm_s, zrecom,
LW0)
except:
wht3, ypoly = whtl, fy_cz
con_line = (wht3 == 0)
if fzvis == 1:
plt.plot(x_cz,
fm_s,
'r',
linestyle='-',
linewidth=0.5,
label='Updated model ($z=%.5f$)' %
(zrecom)) # Model based on recomended z.
plt.plot(x_cz[con_line],
fm_s[con_line],
color='orange',
marker='o',
linestyle='',
linewidth=3.)
# Plot lines for reference
for ll in range(len(LW)):
try:
conpoly = (x_cz /
(1. + zrecom) > 3000) & (x_cz /
(1. + zrecom) < 8000)
yline = np.max(ypoly[conpoly])
yy = np.arange(yline / 1.02, yline * 1.1)
xxpre = yy * 0 + LW[ll] * (1. + zprev)
xx = yy * 0 + LW[ll] * (1. + zrecom)
plt.plot(xxpre,
yy / 1.02,
linewidth=0.5,
linestyle='--',
color='gray')
plt.text(LW[ll] * (1. + zprev),
yline / 1.05,
'%s' % (LN[ll]),
fontsize=8,
color='gray')
plt.plot(xx,
yy,
linewidth=0.5,
linestyle='-',
color='orangered')
plt.text(LW[ll] * (1. + zrecom),
yline,
'%s' % (LN[ll]),
fontsize=8,
color='orangered')
except:
pass
plt.plot(xbb,
fybb,
'.r',
linestyle='',
linewidth=0,
zorder=4,
label='Obs.(BB)')
plt.plot(xm_tmp,
fm_tmp,
color='gray',
marker='.',
ms=0.5,
linestyle='',
linewidth=0.5,
zorder=4,
label='Model')
try:
xmin, xmax = np.min(x_cz) / 1.1, np.max(x_cz) * 1.1
except:
xmin, xmax = 2000, 10000
plt.xlim(xmin, xmax)
try:
plt.ylim(0, yline * 1.1)
except:
pass
plt.xlabel('Wavelength ($\mathrm{\AA}$)')
plt.ylabel('$F_\\nu$ (arb.)')
plt.legend(loc=0)
zzsigma = ((z_cz[2] - z_cz[0]) / 2.) / zprev
zsigma = np.abs(zprev - zrecom) / (zprev)
C0sigma = np.abs(Czrec0 - Cz0) / Cz0
eC0sigma = ((scl_cz0[2] - scl_cz0[0]) / 2.) / Cz0
C1sigma = np.abs(Czrec1 - Cz1) / Cz1
eC1sigma = ((scl_cz1[2] - scl_cz1[0]) / 2.) / Cz1
print('Input redshift is %.3f per cent agreement.' %
((1. - zsigma) * 100))
print('Error is %.3f per cent.' % (zzsigma * 100))
print('Input Cz0 is %.3f per cent agreement.' %
((1. - C0sigma) * 100))
print('Error is %.3f per cent.' % (eC0sigma * 100))
print('Input Cz1 is %.3f per cent agreement.' %
((1. - C1sigma) * 100))
print('Error is %.3f per cent.' % (eC1sigma * 100))
plt.show()
#
# Ask interactively;
#
flag_z = raw_input(
'Do you want to continue with original redshift, Cz0 and Cz1, %.5f %.5f %.5f? ([y]/n/m) '
% (zprev, Cz0, Cz1))
else:
flag_z = 'y'
#################################################
# Gor for mcmc phase
#################################################
if flag_z == 'y' or flag_z == '':
zrecom = zprev
Czrec0 = Cz0
Czrec1 = Cz1
#######################
# Added
#######################
if fzmc == 1:
out_keep = out
#sigz = 1.0 #3.0
fit_params.add('zmc',
value=zrecom,
min=zrecom - (z_cz[1] - z_cz[0]) * sigz,
max=zrecom + (z_cz[2] - z_cz[1]) * sigz)
#print(zrecom,zrecom-(z_cz[1]-z_cz[0])*sigz,zrecom+(z_cz[2]-z_cz[1])*sigz)
#####################
# Error parameter
#####################
try:
ferr = int(inputs['F_ERR'])
if ferr == 1:
fit_params.add('f', value=1e-2, min=0, max=1e2)
ndim += 1
except:
ferr = 0
pass
#####################
# Dust;
#####################
if f_dust:
Tdust = np.arange(DT0, DT1, dDT)
fit_params.add('TDUST',
value=len(Tdust) / 2.,
min=0,
max=len(Tdust) - 1)
#fit_params.add('TDUST', value=1, min=0, max=len(Tdust)-1)
fit_params.add('MDUST', value=1e6, min=0, max=1e10)
ndim += 2
# Append data;
dat_d = np.loadtxt(DIR_TMP + 'spec_dust_obs_' + ID0 +
'_PA' + PA0 + '.cat',
comments='#')
x_d = dat_d[:, 1]
fy_d = dat_d[:, 2]
ey_d = dat_d[:, 3]
fy = np.append(fy, fy_d)
x = np.append(x, x_d)
wht = np.append(wht, 1. / np.square(ey_d))
wht2 = check_line_man(fy, x, wht, fy, zprev, LW0)
# Then, minimize again.
out = minimize(
residual,
fit_params,
args=(fy, wht2, f_dust),
method=fit_name
) # It needs to define out with redshift constrain.
print(fit_report(out))
# Fix params to what we had before.
out.params['zmc'].value = zrecom
out.params['Av'].value = out_keep.params['Av'].value
for aa in range(len(age)):
out.params['A' +
str(aa)].value = out_keep.params['A' +
str(aa)].value
try:
out.params['Z' + str(aa)].value = out_keep.params[
'Z' + str(aa)].value
except:
out.params['Z0'].value = out_keep.params['Z0'].value
##############################
# Save fig of z-distribution.
##############################
try: # if spectrum;
fig = plt.figure(figsize=(6.5, 2.5))
fig.subplots_adjust(top=0.96,
bottom=0.16,
left=0.09,
right=0.99,
hspace=0.15,
wspace=0.25)
ax1 = fig.add_subplot(111)
#n, nbins, patches = ax1.hist(res_cz.flatchain['z'], bins=200, normed=False, color='gray',label='')
n, nbins, patches = ax1.hist(res_cz.flatchain['z'],
bins=200,
normed=True,
color='gray',
label='')
if f_fitgauss == 1:
ax1.plot(lnspc,
pdf_g,
label='Gaussian fit',
color='g',
linestyle='-') # plot it
ax1.set_xlim(m - s * 3, m + s * 3)
yy = np.arange(0, np.max(n), 1)
xx = yy * 0 + z_cz[1]
ax1.plot(
xx,
yy,
linestyle='-',
linewidth=1,
color='orangered',
label='$z=%.5f_{-%.5f}^{+%.5f}$\n$C_z0=%.3f$\n$C_z1=%.3f$'
% (z_cz[1], z_cz[1] - z_cz[0], z_cz[2] - z_cz[1], Czrec0,
Czrec1))
xx = yy * 0 + z_cz[0]
ax1.plot(xx,
yy,
linestyle='--',
linewidth=1,
color='orangered')
xx = yy * 0 + z_cz[2]
ax1.plot(xx,
yy,
linestyle='--',
linewidth=1,
color='orangered')
xx = yy * 0 + zprev
ax1.plot(xx, yy, linestyle='-', linewidth=1, color='royalblue')
ax1.set_xlabel('Redshift')
ax1.set_ylabel('$dn/dz$')
ax1.legend(loc=0)
plt.savefig('zprob_' + ID0 + '_PA' + PA0 + '.pdf', dpi=300)
plt.close()
except:
print('z-distribution figure is not generated.')
pass
##############################
print('\n\n')
print('###############################')
print('Input redshift is adopted.')
print('Starting long journey in MCMC.')
print('###############################')
print('\n\n')
#################
# Initialize mm.
#################
mm = 0
# add a noise parameter
# out.params.add('f', value=1, min=0.001, max=20)
wht2 = wht
################################
print('\nMinimizer Defined\n')
mini = Minimizer(lnprob,
out.params,
fcn_args=[fy, wht2, f_dust],
f_disp=f_disp,
f_move=f_move)
print('######################')
print('### Starting emcee ###')
print('######################')
import multiprocess
ncpu0 = int(multiprocess.cpu_count() / 2)
try:
ncpu = int(inputs['NCPU'])
if ncpu > ncpu0:
print('!!! NCPU is larger than No. of CPU. !!!')
#print('Now set to %d'%(ncpu0))
#ncpu = ncpu0
except:
ncpu = ncpu0
pass
print('No. of CPU is set to %d' % (ncpu))
start_mc = timeit.default_timer()
res = mini.emcee(burn=int(nmc / 2),
steps=nmc,
thin=10,
nwalkers=nwalk,
params=out.params,
is_weighted=True,
ntemps=ntemp,
workers=ncpu)
stop_mc = timeit.default_timer()
tcalc_mc = stop_mc - start_mc
print('###############################')
print('### MCMC part took %.1f sec ###' % (tcalc_mc))
print('###############################')
#----------- Save pckl file
#-------- store chain into a cpkl file
start_mc = timeit.default_timer()
import corner
burnin = int(nmc / 2)
savepath = './'
cpklname = 'chain_' + ID0 + '_PA' + PA0 + '_corner.cpkl'
savecpkl(
{
'chain': res.flatchain,
'burnin': burnin,
'nwalkers': nwalk,
'niter': nmc,
'ndim': ndim
}, savepath + cpklname) # Already burn in
stop_mc = timeit.default_timer()
tcalc_mc = stop_mc - start_mc
print('#################################')
print('### Saving chain took %.1f sec' % (tcalc_mc))
print('#################################')
Avmc = np.percentile(res.flatchain['Av'], [16, 50, 84])
#Zmc = np.percentile(res.flatchain['Z'], [16,50,84])
Avpar = np.zeros((1, 3), dtype='float32')
Avpar[0, :] = Avmc
out = res
####################
# Best parameters
####################
Amc = np.zeros((len(age), 3), dtype='float32')
Ab = np.zeros(len(age), dtype='float32')
Zmc = np.zeros((len(age), 3), dtype='float32')
Zb = np.zeros(len(age), dtype='float32')
NZbest = np.zeros(len(age), dtype='int')
f0 = fits.open(DIR_TMP + 'ms_' + ID0 + '_PA' + PA0 + '.fits')
sedpar = f0[1]
ms = np.zeros(len(age), dtype='float32')
for aa in range(len(age)):
Ab[aa] = out.params['A' + str(aa)].value
Amc[aa, :] = np.percentile(res.flatchain['A' + str(aa)],
[16, 50, 84])
try:
Zb[aa] = out.params['Z' + str(aa)].value
Zmc[aa, :] = np.percentile(res.flatchain['Z' + str(aa)],
[16, 50, 84])
except:
Zb[aa] = out.params['Z0'].value
Zmc[aa, :] = np.percentile(res.flatchain['Z0'],
[16, 50, 84])
NZbest[aa] = bfnc.Z2NZ(Zb[aa])
ms[aa] = sedpar.data['ML_' + str(NZbest[aa])][aa]
Avb = out.params['Av'].value
if f_dust:
Mdust_mc = np.zeros(3, dtype='float32')
Tdust_mc = np.zeros(3, dtype='float32')
Mdust_mc[:] = np.percentile(res.flatchain['MDUST'],
[16, 50, 84])
Tdust_mc[:] = np.percentile(res.flatchain['TDUST'],
[16, 50, 84])
print(Mdust_mc)
print(Tdust_mc)
####################
# MCMC corner plot.
####################
if mcmcplot:
fig1 = corner.corner(res.flatchain, labels=res.var_names, \
label_kwargs={'fontsize':16}, quantiles=[0.16, 0.84], show_titles=False, \
title_kwargs={"fontsize": 14}, truths=list(res.params.valuesdict().values()), \
plot_datapoints=False, plot_contours=True, no_fill_contours=True, \
plot_density=False, levels=[0.68, 0.95, 0.997], truth_color='gray', color='#4682b4')
fig1.savefig('SPEC_' + ID0 + '_PA' + PA0 + '_corner.pdf')
plt.close()
#########################
msmc0 = 0
for aa in range(len(age)):
msmc0 += res.flatchain['A' + str(aa)] * ms[aa]
msmc = np.percentile(msmc0, [16, 50, 84])
# Do analysis on MCMC results.
# Write to file.
stop = timeit.default_timer()
tcalc = stop - start
# Load writing package;
from .writing import Analyze
wrt = Analyze(inputs) # Set up for input
start_mc = timeit.default_timer()
wrt.get_param(res,
lib_all,
zrecom,
Czrec0,
Czrec1,
z_cz[:],
scl_cz0[:],
scl_cz1[:],
fitc[:],
tau0=tau0,
tcalc=tcalc)
stop_mc = timeit.default_timer()
tcalc_mc = stop_mc - start_mc
print('##############################################')
print('### Writing params tp file took %.1f sec ###' % (tcalc_mc))
print('##############################################')
return 0, zrecom, Czrec0, Czrec1
###################################################################
elif flag_z == 'm':
zrecom = float(
raw_input('What is your manual input for redshift? '))
Czrec0 = float(raw_input('What is your manual input for Cz0? '))
Czrec1 = float(raw_input('What is your manual input for Cz1? '))
print('\n\n')
print('Generate model templates with input redshift and Scale.')
print('\n\n')
return 1, zrecom, Czrec0, Czrec1
else:
print('\n\n')
print('Terminated because of redshift estimate.')
print('Generate model templates with recommended redshift.')
print('\n\n')
flag_gen = raw_input(
'Do you want to make templates with recommended redshift, Cz0, and Cz1 , %.5f %.5f %.5f? ([y]/n) '
% (zrecom, Czrec0, Czrec1))
if flag_gen == 'y' or flag_gen == '':
#return 1, zrecom, Cz0 * Czrec0, Cz1 * Czrec1
return 1, zrecom, Czrec0, Czrec1
else:
print('\n\n')
print('There is nothing to do.')
print('\n\n')
return 0, zprev, Czrec0, Czrec1
def main():
# sets up command line argument parser
args = init_argparse()
# The file format is:
# X values of size n
# Number of replicates
# A values
# Y values with n values on each line
if (args.input): # has i flag, read from specified file
f = open(args.input, 'r')
x = array([float(val) for val in f.readline().split()])
num_rep = int(f.readline())
a = array([float(val) for val in f.readline().split()])
y = zeros((len(a), len(x)))
stddev = zeros((len(a), len(x)))
for i in range(len(a)):
all_y = zeros((num_rep, len(x)))
for j in range(num_rep):
all_y[j] = array([float(val) for val in f.readline().split()])
y[i] = average(all_y, axis=0)
stddev[i] = std(all_y, axis=0)
f.close()
else: #read from cmdline
x = array([float(val) for val in raw_input().split()])
num_rep = int(raw_input())
a = array([float(val) for val in raw_input().split()])
y = zeros((len(a), len(x)))
stddev = zeros((len(a), len(x)))
for i in range(len(a)):
all_y = zeros((num_rep, len(x)))
for j in range(num_rep):
all_y[j] = array([float(val) for val in raw_input().split()])
y[i] = average(all_y, axis=0)
stddev[i] = std(all_y, axis=0)
#adding parameters, initial guesses, and constraints
params = Parameters()
params.add('Kd', value=1, min=0)
params.add('EmFRETMAX', value=1, min=0)
return_data = {}
ci = []
emfretmax = []
emfretmax_error = []
#run fitting procedure and display results
#this needs to be repeated for each A value. Note that A[i] corresponds to Y[i]
#X is assumed to hold constant across all of these, so it remains unchanged across iterations
for i in range(len(a)):
result = minimize(residuals, params, args=(x, y[i], a[i]))
ci.append(conf_interval(result, maxiter=1000))
emfretmax.append(params['EmFRETMAX'].value)
emfretmax_error.append(params['EmFRETMAX'].stderr)
# generate table of results with tabulate
return_data[a[i]] = [
a[i],
round(params['Kd'].value, 4),
round(params['Kd'].stderr, 4),
round(params['EmFRETMAX'].value, 4),
round(params['EmFRETMAX'].stderr, 4),
round(1 - result.residual.var() / var(y), 4)
]
# plots data and curve on graph and displays if output file is given
if (args.scatter):
create_scatter(args.scatter, result, x, y[i], a[i], stddev[i], i,
args.unit)
if (args.bar):
create_bar(args.bar, emfretmax, emfretmax_error, a, args.unit)
print(json.dumps(return_data))
slope = params['slope'].value
intercept = params['intercept'].value
return slope * x + intercept
def residual(params, x, data, error):
return (data - analyticLinear(params, x)
) #/error # this is where I weight the error.
def residualError(params, x, data, error):
return (data - analyticLinear(
params, x)) / error # this is where I weight the error.
params = Parameters()
# you can add attributes to the fitting dictionary in such a way
params.add('slope', value=1)
params.add('intercept', value=0.5)
### I make an nddata set of a T1 of power measurement
# The arrays for data, error, and, x-dim (power).
dataArray = array(
[0.48909572, 0.43322032, 0.3944982, 0.37726134, 0.36782925, 0.48865151])
dataError = array(
[0.00304622, 0.00074815, 0.00119058, 0.00384469, 0.00288963, 0.00680168])
dataPower = array([
1.18040107e-01, 1.49209244e+00, 2.91886587e+00, 4.44269384e+00,
5.02700108e+00, 4.13047502e-10
])
# Throw everything into an nddata set - Zach this is cool and a nice way to handle your data with axes and associated error.
def __init__(self, model):
self.model = model
self.lmfitparams = Parameters()
self.parameterdict = {}
self.seriesdict = {}
p = np.random.uniform(0,1,size=4)
p = enzyme_total*(p/(p[0]+p[1]+p[2]+p[3]))
#Add the random parameter set 'p' to a permanent list of all random parameter sets
Params.append(p)
f6p = simulate(p,enzyme_total)
#add the resulting F6P value to a permanent list of parameters
F6ps.append(f6p)
#Sorting F6P values and rearranging parameters to match accordingly
F6ps = np.asarray(F6ps)
Params = np.asarray(Params)
indices = F6ps.argsort()
Params = Params[indices]
F6ps = F6ps[indices]
'''Levenberg-Marquardt Algorithm'''
#setting initial parameters to be used for LM simulation
pi = Parameters()
pi.add('protALDPase', value=Params[-1,0], min=0.0, max=1.0)
pi.add('protGAPDH', value=Params[-1,1], min=0.0, max=1.0)
pi.add('protPGK', value=Params[-1,2], min=0.0, max=1.0)
pi.add('protTIM', value=Params[-1,3], min=0.0, max=1.0)
#Run the LM algorithm using lmfit:
result = minimize(objFunction,pi)
print '\n',"The following is the set of enzyme concentrations which result in optimal production of F6P for the reconstituted system:",'\n',result.params
print '\n',"The above parameters result in a theoretical F6P concentration of:",1/(result.residual[0]),"ug/mL"
class ParameterGroup(Group):
"""
Group for Fitting Parameters
"""
def __init__(self, name=None, _larch=None, **kws):
if name is not None:
self.__name__ = name
self._larch = _larch
self.__params__ = None
if _larch is not None:
self.__params__ = Parameters(asteval=_larch.symtable._sys.fiteval)
Group.__init__(self)
self.__exprsave__ = {}
for key, val in kws.items():
expr = getattr(val, 'expr', None)
if expr is not None:
self.__exprsave__[key] = expr
val.expr = None
setattr(self, key, val)
for key, val in self.__exprsave__.items():
self.__params__[key].expr = val
def __repr__(self):
return '<Param Group {:s}>'.format(self.__name__)
def __setattr__(self, name, val):
if isinstance(val, Parameter):
if val.name != name:
# allow 'a=Parameter(2, ..)' to mean Parameter(name='a', value=2, ...)
nval = None
try:
nval = float(val.name)
except (ValueError, TypeError):
pass
if nval is not None:
val.value = nval
self.__params__.add(name,
value=val.value,
vary=val.vary,
min=val.min,
max=val.max,
expr=val.expr,
brute_step=val.brute_step)
val = self.__params__[name]
self.__dict__[name] = val
def __add(self,
name,
value=None,
vary=True,
min=-np.inf,
max=np.inf,
expr=None,
stderr=None,
correl=None,
brute_step=None):
if expr is None and isinstance(value, str):
expr = value
value = None
if self.__params__ is not None:
self.__params__.add(name,
value=value,
vary=vary,
min=min,
max=max,
expr=expr,
brute_step=brute_step)
self.__params__[name].stderr = stderr
self.__params__[name].correl = correl
self.__dict__[name] = self.__params__[name]
