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 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)
def model3_fits(fitData, exc, outf, c_included, beta_included, beta2_included, end_diff=False):
# Set up paramters
bval = 0
b2val = 0
if beta_included:
bval = -1.0
if beta2_included:
b2val = -1.0
pars = Parameters()
pars.add('alpha', value=5.0, vary=True)
pars.add('const', value=0.0, vary=c_included)
pars.add('beta', value=bval, vary=beta_included)
pars.add('beta2', value=b2val, vary=beta2_included)
pars.add('delta', value=0.0, vary=end_diff)
fit_result = cross_validate(model3, fitData, pars, outf)
parvals = pars.valuesdict()
beta_mod3 = (parvals['const'], parvals['beta'], parvals['beta2'])
name = 'Thiophene model3: delta varied=%r\n' % end_diff
write_statistics(name, outf, pars, fit_result)
#title = "Coupling = const + beta2 cos^2(theta) \n"
plot_something(model3, pars, exc, title="", filename='thio_mod3%r_%r_%r_%r.eps' % (c_included,beta_included,beta2_included,end_diff))
return beta_mod3
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 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 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
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 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 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 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 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 neon_init(x_list, y_list):
""" Initialize parameters for neon peaks
x_list: list of x peaks
y_list: list of y peaks
returns: params
"""
params = Parameters()
BG = 100.
params.add("BG", value = BG)
n = len(x_list)
A_variables = []
X_variables = []
W_variables = []
MU_variables = []
for i in range(n):
A_variables.append("A%d"%i)
X_variables.append("X%d"%i)
W_variables.append("W%d"%i)
MU_variables.append("MU%d"%i)
W = np.ones(n)
MU = W*0.5
for i in range(n):
params.add(X_variables[i], value = x_list[i], min = x_list[i]-2., max = x_list[i]+2.)
params.add(A_variables[i], value = y_list[i])
params.add(W_variables[i], value = W[i])
params.add(MU_variables[i], value = MU[i])
print "number of params: %d"%len(params.keys())
return params
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 __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_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 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 gaussian_constant_delta_chi_squared(light_curve, num_attempts=1):
""" Compute the difference in chi-squared between a Gaussian and a straight (constant) line. """
gaussian_chisqr = 1E6
for ii in range(num_attempts):
gaussian_params = Parameters()
t0 = np.random.normal(light_curve.mjd[np.argmin(light_curve.mag)], 1.)
if t0 > light_curve.mjd.max() or t0 < light_curve.mjd.min():
t0 = light_curve.mjd[np.argmin(light_curve.mag)]
gaussian_params.add('A', value=np.random.uniform(-1., -20.), min=-1E4, max=0.)
gaussian_params.add('mu', value=t0, min=light_curve.mjd.min(), max=light_curve.mjd.max())
gaussian_params.add('sigma', value=abs(np.random.normal(10., 2.)), min=1.)
gaussian_params.add('B', value=np.random.normal(np.median(light_curve.mag), 0.5))
gaussian_result = minimize(gaussian_error_func, gaussian_params, args=(light_curve.mjd, light_curve.mag, light_curve.error))
if gaussian_result.chisqr < gaussian_chisqr:
gaussian_chisqr = gaussian_result.chisqr
constant_chisqr = 1E6
for ii in range(num_attempts):
constant_params = Parameters()
constant_params.add('b', value=np.random.normal(np.median(light_curve.mag), 0.5))
constant_result = minimize(constant_error_func, constant_params, args=(light_curve.mjd, light_curve.mag, light_curve.error))
if constant_result.chisqr < constant_chisqr:
constant_chisqr = constant_result.chisqr
return constant_chisqr - gaussian_chisqr
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 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 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 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 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 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 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 fit(self, params0):
r"""Perform a fit with the provided parameters.
Parameters
----------
params0 : list
Initial fitting parameters
"""
self.params0 = params0
p = Parameters()
if self.parinfo is None:
self.parinfo = [None] * len(self.params0)
else:
assert (len(self.params0) == len(self.parinfo))
for i, (p0, parin) in enumerate(zip(self.params0, self.parinfo)):
p.add(name='p{0}'.format(i), value=p0)
if parin is not None:
if 'limits' in parin:
p['p{0}'.format(i)].set(min=parin['limits'][0])
p['p{0}'.format(i)].set(max=parin['limits'][1])
if 'fixed' in parin:
p['p{0}'.format(i)].set(vary=not parin['fixed'])
if np.all([not value.vary for value in p.values()]):
raise Exception('All parameters are fixed!')
self.lmfit_minimizer = Minimizer(self.residuals, p, nan_policy=self.nan_policy, fcn_args=(self.data,))
self.result.orignorm = np.sum(self.residuals(params0, self.data) ** 2)
result = self.lmfit_minimizer.minimize(Dfun=self.deriv, method='leastsq', ftol=self.ftol,
xtol=self.xtol, gtol=self.gtol, maxfev=self.maxfev, epsfcn=self.epsfcn,
factor=self.stepfactor)
self.result.bestnorm = result.chisqr
self.result.redchi = result.redchi
self._m = result.ndata
self.result.nfree = result.nfree
self.result.resid = result.residual
self.result.status = result.ier
self.result.covar = result.covar
self.result.xerror = [result.params['p{0}'.format(i)].stderr for i in range(len(result.params))]
self.result.params = [result.params['p{0}'.format(i)].value for i in range(len(result.params))]
self.result.message = result.message
self.lmfit_result = result
if not result.errorbars or not result.success:
warnings.warn(self.result.message)
return result.success
def 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 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 fit_jd_hist(
hists: list,
dt: float,
D: list,
fit_D: list,
F: list,
fit_F: list,
sigma: float,
fit_sigma: bool,
verbose=False,
):
"""
Fits jd probability functions to a jd histograms.
Parameters:
hist (list): histogram values
D (list): init values for MSD
F (list): fractions for D, sum = 1
sigma (float): localization precision guess
funcs (dict): dictionary with functions sigma, gamma, center, amplitude
Returns:
popt (lmfit.minimizerResult): optimized parameters
"""
from lmfit import Parameters, Parameter, minimize
def residual(fit_params, data):
res = cumulative_error_jd_hist(fit_params, data, len(D))
return res
fit_params = Parameters()
# fit_params.add('sigma', value=sigma, vary=fit_sigma, min=0.)
fit_params.add("dt", value=dt, vary=False)
try:
fit_params.add("max_lag", value=max([h.lag for h in hists]), vary=False)
except TypeError as e:
logger.error(
f"problem with `hists`: expected `list`,\
got `{type(hists)}`"
)
raise e
for i, (d, f_d, f, f_f) in enumerate(zip(D, fit_D, F, fit_F)):
fit_params.add(f"D{i}", value=d, vary=f_d, min=0.0)
fit_params.add(f"F{i}", value=f, min=0.0, max=1.0, vary=f_f)
f_expr = "1"
for i, f in enumerate(F[:-1]):
f_expr += f" - F{i}"
fit_params[f"F{i+1}"] = Parameter(name=f"F{i+1}", min=0.0, max=1.0, expr=f_expr)
for i, (s, f_s, min_s, max_s) in enumerate(
zip(sigma, fit_sigma, (0, sigma[0]), (3 * sigma[0], D[-1]))
):
fit_params.add(f"sigma{i}", value=s, min=min_s, max=max_s, vary=f_s)
logger.debug("start minimize")
minimizer_result = minimize(residual, fit_params, args=(hists,))
if verbose:
logger.info(f"completed in {minimizer_result.nfev} steps")
minimizer_result.params.pretty_print()
return minimizer_result
model = yg + offset + x * slope
if data is None:
return model
if sigma is None:
return (model - data)
return (model - data) / sigma
n = 201
xmin = 0.
xmax = 20.0
x = linspace(xmin, xmax, n)
p_true = Parameters()
p_true.add('amp_g', value=21.0)
p_true.add('cen_g', value=8.1)
p_true.add('wid_g', value=1.6)
p_true.add('line_off', value=-1.023)
p_true.add('line_slope', value=0.62)
data = (gaussian(x, p_true['amp_g'].value, p_true['cen_g'].value,
p_true['wid_g'].value) + random.normal(scale=0.23, size=n) +
x * p_true['line_slope'].value + p_true['line_off'].value)
if HASPYLAB:
pylab.plot(x, data, 'r+')
p_fit = Parameters()
p_fit.add('amp_g', value=10.0)
p_fit.add('cen_g', value=9)
class XRF_Model:
"""model for X-ray fluorescence data
consists of parameterized components for
incident beam (energy, angle_in, angle_out)
matrix (list of material, thickness)
filters (list of material, thickness)
detector (material, thickness, step, tail, beta, gamma)
"""
def __init__(self,
xray_energy=None,
energy_min=1.5,
energy_max=30.,
count_time=1,
bgr=None,
iter_callback=None,
**kws):
self.xray_energy = xray_energy
self.energy_min = energy_min
self.energy_max = energy_max
self.count_time = count_time
self.iter_callback = None
self.params = Parameters()
self.elements = []
self.scatter = []
self.comps = {}
self.eigenvalues = {}
self.transfer_matrix = None
self.matrix_layers = []
self.matrix = None
self.matrix_atten = 1.0
self.filters = []
self.fit_iter = 0
self.fit_toler = 1.e-5
self.fit_log = False
self.bgr = None
self.use_pileup = False
self.use_escape = False
self.escape_scale = None
self.script = ''
self.mca = None
if bgr is not None:
self.add_background(bgr)
def set_detector(self,
material='Si',
thickness=0.40,
noise=0.05,
peak_step=1e-3,
peak_tail=0.01,
peak_gamma=0,
peak_beta=0.5,
cal_offset=0,
cal_slope=10.,
cal_quad=0,
vary_thickness=False,
vary_noise=True,
vary_peak_step=True,
vary_peak_tail=True,
vary_peak_gamma=False,
vary_peak_beta=False,
vary_cal_offset=True,
vary_cal_slope=True,
vary_cal_quad=False):
"""
set up detector material, calibration, and general settings for
the hypermet functions for the fluorescence and scatter peaks
"""
self.detector = XRF_Material(material, thickness)
matname = material.title()
if matname not in FanoFactors:
matname = 'Si'
self.efano = FanoFactors[matname]
self.params.add('det_thickness',
value=thickness,
vary=vary_thickness,
min=0)
self.params.add('det_noise', value=noise, vary=vary_noise, min=0)
self.params.add('cal_offset',
value=cal_offset,
vary=vary_cal_offset,
min=-500,
max=500)
self.params.add('cal_slope',
value=cal_slope,
vary=vary_cal_slope,
min=0)
self.params.add('cal_quad', value=cal_quad, vary=vary_cal_quad)
self.params.add('peak_step',
value=peak_step,
vary=vary_peak_step,
min=0,
max=10)
self.params.add('peak_tail',
value=peak_tail,
vary=vary_peak_tail,
min=0,
max=10)
self.params.add('peak_beta',
value=peak_beta,
vary=vary_peak_beta,
min=0)
self.params.add('peak_gamma',
value=peak_gamma,
vary=vary_peak_gamma,
min=0)
def add_scatter_peak(self,
name='elastic',
amplitude=1000,
center=None,
step=0.010,
tail=0.5,
sigmax=1.0,
beta=0.5,
vary_center=True,
vary_step=True,
vary_tail=True,
vary_sigmax=True,
vary_beta=False):
"""add Rayleigh (elastic) or Compton (inelastic) scattering peak
"""
if name not in self.scatter:
self.scatter.append(
xrf_peak(name, amplitude, center, step, tail, sigmax, beta,
0.0, vary_center, vary_step, vary_tail, vary_sigmax,
vary_beta, False))
if center is None:
center = self.xray_energy
self.params.add('%s_amp' % name, value=amplitude, vary=True, min=0)
self.params.add('%s_center' % name,
value=center,
vary=vary_center,
min=center * 0.5,
max=center * 1.25)
self.params.add('%s_step' % name,
value=step,
vary=vary_step,
min=0,
max=10)
self.params.add('%s_tail' % name,
value=tail,
vary=vary_tail,
min=0,
max=20)
self.params.add('%s_beta' % name,
value=beta,
vary=vary_beta,
min=0,
max=20)
self.params.add('%s_sigmax' % name,
value=sigmax,
vary=vary_sigmax,
min=0,
max=100)
def add_element(self, elem, amplitude=1.e6, vary_amplitude=True):
"""add Element to XRF model
"""
self.elements.append(
XRF_Element(elem,
xray_energy=self.xray_energy,
energy_min=self.energy_min))
self.params.add('amp_%s' % elem.lower(),
value=amplitude,
vary=vary_amplitude,
min=0)
def add_filter(self,
material,
thickness,
density=None,
vary_thickness=False):
self.filters.append(
XRF_Material(material=material,
density=density,
thickness=thickness))
self.params.add('filterlen_%s' % material,
value=thickness,
min=0,
vary=vary_thickness)
def set_matrix(self, material, thickness, density=None):
self.matrix = XRF_Material(material=material,
density=density,
thickness=thickness)
self.matrix_atten = 1.0
def add_background(self, data, vary=True):
self.bgr = data
self.params.add('background_amp', value=1.0, min=0, vary=vary)
def add_escape(self, scale=1.0, vary=True):
self.use_escape = True
self.params.add('escape_amp', value=scale, min=0, vary=vary)
def add_pileup(self, scale=1.0, vary=True):
self.use_pileup = True
self.params.add('pileup_amp', value=scale, min=0, vary=vary)
def clear_background(self):
self.bgr = None
self.params.pop('background_amp')
def calc_matrix_attenuation(self, energy):
"""
calculate beam attenuation by a matrix built from layers
note that matrix layers and composition cannot be variable
so the calculation can be done once, ahead of time.
"""
atten = 1.0
if self.matrix is not None:
ixray_en = index_of(energy, self.xray_energy)
print("MATRIX ", ixray_en, self.matrix)
# layer_trans = self.matrix.transmission(energy) # transmission through layer
# incid_trans = layer_trans[ixray_en] # incident beam trans to lower layers
# ncid_absor = 1.0 - incid_trans # incident beam absorption by layer
# atten = layer_trans * incid_absor
self.matrix_atten = atten
def calc_escape_scale(self, energy, thickness=None):
"""
calculate energy dependence of escape effect
X-rays penetrate a depth 1/mu(material, energy) and the
detector fluorescence escapes from that depth as
exp(-mu(material, KaEnergy)*thickness)
with a fluorecence yield of the material
"""
det = self.detector
# note material_mu, xray_edge, xray_line work in eV!
escape_energy_ev = xray_line(det.material, 'Ka').energy
mu_emit = material_mu(det.material, escape_energy_ev)
self.escape_energy = 0.001 * escape_energy_ev
mu_input = material_mu(det.material, 1000 * energy)
edge = xray_edge(det.material, 'K')
self.escape_scale = edge.fyield * np.exp(-mu_emit / (2 * mu_input))
self.escape_scale[np.where(energy < 0.001 * edge.energy)] = 0.0
def det_sigma(self, energy, noise=0):
""" energy width of peak """
return np.sqrt(self.efano * energy + noise**2)
def calc_spectrum(self, energy, params=None):
if params is None:
params = self.params
pars = params.valuesdict()
self.comps = {}
self.eigenvalues = {}
det_noise = pars['det_noise']
step = pars['peak_step']
tail = pars['peak_tail']
beta = pars['peak_beta']
gamma = pars['peak_gamma']
# detector attenuation
atten = self.detector.absorbance(energy,
thickness=pars['det_thickness'])
# filters
for f in self.filters:
thickness = pars.get('filterlen_%s' % f.material, None)
if thickness is not None and int(thickness * 1e6) > 1:
atten *= f.transmission(energy, thickness=thickness)
self.atten = atten
# matrix
# if self.matrix_atten is None:
# self.calc_matrix_attenuation(energy)
# atten *= self.matrix_atten
if self.use_escape:
if self.escape_scale is None:
self.calc_escape_scale(energy, thickness=pars['det_thickness'])
escape_amp = pars.get('escape_amp', 0.0) * self.escape_scale
for elem in self.elements:
comp = 0. * energy
amp = pars.get('amp_%s' % elem.symbol.lower(), None)
if amp is None:
continue
for key, line in elem.lines.items():
ecen = 0.001 * line.energy
line_amp = line.intensity * elem.mu * elem.fyields[
line.initial_level]
sigma = self.det_sigma(ecen, det_noise)
comp += hypermet(energy,
amplitude=line_amp,
center=ecen,
sigma=sigma,
step=step,
tail=tail,
beta=beta,
gamma=gamma)
comp *= amp * atten * self.count_time
if self.use_escape:
comp += escape_amp * interp(energy - self.escape_energy, comp,
energy)
self.comps[elem.symbol] = comp
self.eigenvalues[elem.symbol] = amp
# scatter peaks for Rayleigh and Compton
for peak in self.scatter:
p = peak.name
amp = pars.get('%s_amp' % p, None)
if amp is None:
continue
ecen = pars['%s_center' % p]
step = pars['%s_step' % p]
tail = pars['%s_tail' % p]
beta = pars['%s_beta' % p]
sigma = pars['%s_sigmax' % p]
sigma *= self.det_sigma(ecen, det_noise)
comp = hypermet(energy,
amplitude=1.0,
center=ecen,
sigma=sigma,
step=step,
tail=tail,
beta=beta,
gamma=gamma)
comp *= amp * atten * self.count_time
if self.use_escape:
comp += escape_amp * interp(energy - self.escape_energy, comp,
energy)
self.comps[p] = comp
self.eigenvalues[p] = amp
if self.bgr is not None:
bgr_amp = pars.get('background_amp', 0.0)
self.comps['background'] = bgr_amp * self.bgr
self.eigenvalues['background'] = bgr_amp
# calculate total spectrum
total = 0. * energy
for comp in self.comps.values():
total += comp
if self.use_pileup:
pamp = pars.get('pileup_amp', 0.0)
npts = len(energy)
pileup = pamp * 1.e-9 * np.convolve(total, total * 1.0,
'full')[:npts]
self.comps['pileup'] = pileup
self.eigenvalues['pileup'] = pamp
total += pileup
# remove tiny values so that log plots are usable
floor = 1.e-10 * max(total)
total[np.where(total < floor)] = floor
self.current_model = total
return total
def __resid(self, params, data, index):
pars = params.valuesdict()
self.best_en = (pars['cal_offset'] + pars['cal_slope'] * index +
pars['cal_quad'] * index**2)
self.fit_iter += 1
model = self.calc_spectrum(self.best_en, params=params)
if callable(self.iter_callback):
self.iter_callback(iter=self.fit_iter, pars=pars)
return ((data - model) * self.fit_weight)[self.imin:self.imax]
def set_fit_weight(self, energy, counts, emin, emax, ewid=0.050):
"""
set weighting factor to smoothed square-root of data
"""
ewin = ftwindow(energy,
xmin=emin,
xmax=emax,
dx=ewid,
window='hanning')
self.fit_window = ewin
fit_wt = 0.5 + savitzky_golay(np.sqrt(counts + 1.0), 25, 1)
self.fit_weight = 1.0 / fit_wt
def fit_spectrum(self, mca, energy_min=None, energy_max=None):
self.mca = mca
work_energy = 1.0 * mca.energy
work_counts = 1.0 * mca.counts
floor = 1.e-10 * np.percentile(work_counts, [99])[0]
work_counts[np.where(work_counts < floor)] = floor
if max(work_energy) > 250.0: # if input energies are in eV
work_energy /= 1000.0
imin, imax = 0, len(work_counts)
if energy_min is None:
energy_min = self.energy_min
if energy_min is not None:
imin = index_of(work_energy, energy_min)
if energy_max is None:
energy_max = self.energy_max
if energy_max is not None:
imax = index_of(work_energy, energy_max)
self.imin = max(0, imin - 5)
self.imax = min(len(work_counts), imax + 5)
self.npts = (self.imax - self.imin)
self.set_fit_weight(work_energy, work_counts, energy_min, energy_max)
self.fit_iter = 0
# reset attenuation calcs for matrix, detector, filters
self.matrix_atten = 1.0
self.escape_scale = None
self.detector.mu_total = None
for f in self.filters:
f.mu_total = None
self.init_fit = self.calc_spectrum(work_energy, params=self.params)
index = np.arange(len(work_counts))
userkws = dict(data=work_counts, index=index)
tol = self.fit_toler
self.result = minimize(self.__resid,
self.params,
kws=userkws,
method='leastsq',
maxfev=10000,
scale_covar=True,
gtol=tol,
ftol=tol,
epsfcn=1.e-5)
self.fit_report = fit_report(self.result, min_correl=0.5)
pars = self.result.params
self.best_en = (pars['cal_offset'] + pars['cal_slope'] * index +
pars['cal_quad'] * index**2)
self.fit_iter += 1
self.best_fit = self.calc_spectrum(work_energy,
params=self.result.params)
# calculate transfer matrix for linear analysis using this model
tmat = []
for key, val in self.comps.items():
arr = val / self.eigenvalues[key]
floor = 1.e-12 * max(arr)
arr[np.where(arr < floor)] = 0.0
tmat.append(arr)
self.transfer_matrix = np.array(tmat).transpose()
return self.get_fitresult()
def get_fitresult(self,
label='XRF fit result',
script='# no script supplied'):
"""a simple compilation of fit settings results
to be able to easily save and inspect"""
out = XRFFitResult(label=label, script=script, mca=self.mca)
for attr in ('filename', 'label'):
setattr(out, 'mca' + attr, getattr(self.mca, attr, 'unknown'))
for attr in ('params', 'var_names', 'chisqr', 'redchi', 'nvarys',
'nfev', 'ndata', 'aic', 'bic', 'aborted', 'covar', 'ier',
'message', 'method', 'nfree', 'init_values', 'success',
'residual', 'errorbars', 'lmdif_message', 'nfree'):
setattr(out, attr, getattr(self.result, attr, None))
for attr in ('atten', 'best_en', 'best_fit', 'bgr', 'comps',
'count_time', 'eigenvalues', 'energy_max', 'energy_min',
'fit_iter', 'fit_log', 'fit_report', 'fit_toler',
'fit_weight', 'fit_window', 'init_fit', 'scatter',
'script', 'transfer_matrix', 'xray_energy'):
setattr(out, attr, getattr(self, attr, None))
elem_attrs = ('all_lines', 'edges', 'fyields', 'lines', 'mu', 'symbol',
'xray_energy')
out.elements = []
for el in self.elements:
out.elements.append(
{attr: getattr(el, attr)
for attr in elem_attrs})
mater_attrs = ('material', 'mu_photo', 'mu_total', 'thickness')
out.detector = {
attr: getattr(self.detector, attr)
for attr in mater_attrs
}
out.matrix = None
if self.matrix is not None:
out.matrix = {
attr: getattr(self.matrix, attr)
for attr in mater_attrs
}
out.filters = []
for ft in self.filters:
out.filters.append(
{attr: getattr(ft, attr)
for attr in mater_attrs})
return out
ADMRObject = ADMR([condObject])
ADMRObject.Btheta_array = Btheta_array
ADMRObject.runADMR()
print("ADMR time : %.6s seconds" % (time.time() - start_total_time))
diff_0 = rzz_0 - ADMRObject.rzz_array[0, :]
diff_15 = rzz_15 - ADMRObject.rzz_array[1, :]
diff_30 = rzz_30 - ADMRObject.rzz_array[2, :]
diff_45 = rzz_45 - ADMRObject.rzz_array[3, :]
return np.concatenate((diff_0, diff_15, diff_30, diff_45))
## Initialize
pars = Parameters()
pars.add("gamma_0", value=gamma_0_ini, vary=gamma_0_vary, min=0)
pars.add("gamma_dos", value=gamma_dos_ini, vary=gamma_dos_vary, min=0)
pars.add("gamma_k", value=gamma_k_ini, vary=gamma_k_vary, min=0)
pars.add("power", value=power_ini, vary=power_vary, min=2)
pars.add("mu", value=mu_ini, vary=mu_vary)
pars.add("M", value=M_ini, vary=M_vary, min=0.001)
## Run fit algorithm
out = minimize(residualFunc,
pars,
args=(bandObject, rzz_0, rzz_15, rzz_30, rzz_45))
## Display fit report
print(fit_report(out.params))
## Export final parameters from the fit
def fit_lm(self): # use Levenberg Mardquart method # define objective function: returns the array to be minimized def fcn2min(params, x, y, yerr): n = len(x) model = np.zeros(n,dtype=ctypes.c_double) model = np.require(model,dtype=ctypes.c_double,requirements='C') occultquadC( x,params['RpRs'].value,params['aRs'].value, params['period'].value, params['inc'].value, params['gamma1'].value, params['gamma2'].value, params['ecc'].value, params['omega'].value, params['tmid'].value, n, model ) model *= (params['a0'] + x*params['a1'] + x*x*params['a2']) return (model - y)/yerr #Rp,aR,P,i,u1,u2,e,omega,tmid,a0,a1,a2 = self.p_init v = [ (i[0] != i[1]) for i in self.bounds ] # boolean array to vary parameters pnames = ['RpRs','aRs','period','inc','gamma1','gamma2','ecc','omega','tmid','a0','a1','a2'] params = Parameters() for j in range(len(self.p_init)): # algorithm does not like distance between min and max to be zero if v[j] == True: params.add(pnames[j], value= self.p_init[j], vary=v[j], min=self.bounds[j][0], max=self.bounds[j][1] ) else: if (self.bounds[j][0] == None): if (self.bounds[j][1] == None): # no upper bound params.add(pnames[j], value= self.p_init[j], vary=True ) else: # upper bound params.add(pnames[j], value= self.p_init[j], vary=True,max = self.bounds[j][1] ) elif (self.bounds[j][1] == None): if (self.bounds[j][0] == None): # no lower bound params.add(pnames[j], value= self.p_init[j], vary=True ) else: # lower bound params.add(pnames[j], value= self.p_init[j], vary=True,min = self.bounds[j][0] ) else: params.add(pnames[j], value= self.p_init[j], vary=v[j] ) # do fit, here with leastsq model result = lminimize(fcn2min, params, args=(self.t,self.y,self.yerr)) params = result.params n = len(self.t) model = np.zeros(n,dtype=ctypes.c_double) model = np.require(model,dtype=ctypes.c_double,requirements='C') occultquadC( self.t,params['RpRs'].value,params['aRs'].value, params['period'].value, params['inc'].value, params['gamma1'].value, params['gamma2'].value, params['ecc'].value, params['omega'].value, params['tmid'].value, n, model ) self.final_model = model self.residuals = result.residual self.params = result.params self.result = result A0 = params['a0'].value A1 = params['a1'].value A2 = params['a2'].value self.amcurve = A0 + self.t*A1 + self.t*self.t*A2 self.final_curve = self.final_model/self.amcurve self.phase = (self.t-params['tmid'].value)/params['period']
https://lmfit.github.io/lmfit-py/bounds.html
The example below shows how to set boundaries using the ``min`` and ``max``
attributes to fitting parameters.
"""
import matplotlib.pyplot as plt
from numpy import exp, linspace, pi, random, sign, sin
from lmfit import Parameters, minimize
from lmfit.printfuncs import report_fit
###############################################################################
# Define the 'correct' Parameter values and residual function:
p_true = Parameters()
p_true.add('amp', value=14.0)
p_true.add('period', value=5.4321)
p_true.add('shift', value=0.12345)
p_true.add('decay', value=0.01000)
def residual(pars, x, data=None):
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
class SphereAtInterface: #Please put the class name same as the function name
def __init__(self,
x=0.1,
lam=1.0,
Rc=10,
Rsig=0.0,
rhoc=4.68,
D=60.0,
cov=100,
Zo=20.0,
decay=3.0,
rho_up=0.333,
rho_down=0.38,
zmin=-50,
zmax=100,
dz=1,
roughness=3.0,
rrf=1,
mpar={},
qoff=0):
"""
Calculates X-ray reflectivity from a system of nanoparticle at an interface between two media
x : array of wave-vector transfer along z-direction
lam : wavelength of x-rays in invers units of x
Rc : Radius of nanoparticles in inverse units of x
rhoc : Electron density of the nanoparticles
cov : Coverate of the nanoparticles in %
D : The lattice constant of the two dimensional hcp structure formed by the particles
Zo : Average distance between the center of the nanoparticles and the interface
decay : Assuming exponential decay of the distribution of nanoparticles away from the interface
rho_up : Electron density of the upper medium
rho_down : Electron density of the lower medium
zmin : Minimum z value for the electron density profile
zmax : Maximum z value for the electron density profile
dz : minimum slab thickness
roughness : Roughness of the interface
rrf : 1 for Frensnel normalized refelctivity and 0 for just reflectivity
qoff : offset in the value of qz due to alignment errors
"""
if type(x) == list:
self.x = np.array(x)
else:
self.x = x
self.Rc = Rc
self.lam = lam
self.rhoc = rhoc
self.Zo = Zo
self.cov = cov
self.D = D
self.decay = decay
self.rho_up = rho_up
self.rho_down = rho_down
self.zmin = zmin
self.zmax = zmax
self.dz = dz
self.roughness = roughness
self.rrf = rrf
self.qoff = qoff
self.choices = {'rrf': [1, 0]}
self.output_params = {}
self.__mpar__ = mpar
def init_params(self):
"""
Define all the fitting parameters like
self.param.add('sig',value=0,vary=0)
"""
self.params = Parameters()
self.params.add('Rc',
value=self.Rc,
vary=0,
min=-np.inf,
max=np.inf,
expr=None,
brute_step=0.1)
self.params.add('rhoc',
value=self.rhoc,
vary=0,
min=-np.inf,
max=np.inf,
expr=None,
brute_step=0.1)
self.params.add('Zo',
value=self.Zo,
vary=0,
min=-np.inf,
max=np.inf,
expr=None,
brute_step=0.1)
self.params.add('D',
value=self.D,
vary=0,
min=-np.inf,
max=np.inf,
expr=None,
brute_step=0.1)
self.params.add('cov',
value=self.cov,
vary=0,
min=-np.inf,
max=np.inf,
expr=None,
brute_step=0.1)
self.params.add('decay',
value=self.decay,
vary=0,
min=-np.inf,
max=np.inf,
expr=None,
brute_step=0.1)
self.params.add('roughness',
value=self.roughness,
vary=0,
min=-np.inf,
max=np.inf,
expr=None,
brute_step=0.1)
self.params.add('qoff',
value=self.qoff,
vary=0,
min=-np.inf,
max=np.inf,
expr=None,
brute_step=0.1)
def decayNp(self,
z,
Rc=10,
D=30.0,
z0=0.0,
xi=1.0,
cov=100.0,
rhoc=4.65,
rhos=[0.334, 0.38],
sig=1.0):
if sig < 1e-3:
z2 = z
else:
zmin = z[0] - 5 * sig
zmax = z[-1] + 5 * sig
z2 = np.arange(zmin, zmax, self.dz)
intf = np.where(z2 <= 0, rhos[0], rhos[1])
if z0 <= 0:
z1 = np.linspace(-5 * xi + z0, z0, 101)
dec = np.exp((z1 - z0) / xi) / xi
else:
z1 = np.linspace(z0, z0 + 5 * xi, 101)
dec = np.exp((z0 - z1) / xi) / xi
rhoz = np.zeros_like(z2)
for i in range(len(z1)):
rhoz = rhoz + self.rhoNPz(
z2, z0=z1[i], rhoc=rhoc, Rc=Rc, D=D,
rhos=rhos) * dec[i] / sum(dec)
rhoz = cov * rhoz / 100.0 + (100 - cov) * intf / 100.0
x = np.arange(-5 * sig, 5 * sig, self.dz)
if sig > 1e-3:
rough = np.exp(-x**2 / 2.0 / sig**2) / np.sqrt(2 * np.pi) / sig
res = np.convolve(rhoz, rough, mode='valid') * self.dz
if len(res) > len(z):
return res[0:len(z)]
else:
return res
else:
return rhoz
def rhoNPz(self, z, z0=0, rhoc=4.65, Rc=10.0, D=28.0, rhos=[0.334, 0.38]):
rhob = np.where(z > 0, rhos[1], rhos[0])
#D=D/2
return np.where(
np.abs(z - z0) <= Rc,
(2 * np.pi * (rhoc - rhob) *
(Rc**2 - (z - z0)**2) + 1.732 * rhob * D**2) / (1.732 * D**2),
rhob)
def y(self):
"""
Define the function in terms of x to return some value
"""
Rc = self.params['Rc'].value
D = self.params['D'].value
Zo = self.params['Zo'].value
cov = self.params['cov'].value
sig = self.params['roughness'].value
xi = self.params['decay'].value
rhoc = self.params['rhoc'].value
qoff = self.params['qoff'].value
rhos = [self.rho_up, self.rho_down]
lam = self.lam
z = np.arange(self.zmin, self.zmax, self.dz)
d = np.ones_like(z) * self.dz
edp = self.decayNp(z,
Rc=Rc,
z0=Zo,
xi=xi,
cov=cov,
rhos=rhos,
rhoc=rhoc,
sig=sig,
D=D)
self.output_params['EDP'] = {'x': z, 'y': edp}
beta = np.zeros_like(z)
rho = np.array(edp, dtype='float')
refq, r2 = parratt(self.x + qoff, lam, d, rho, beta)
if self.rrf > 0:
ref, r2 = parratt(self.x + qoff, lam, [0.0, 1.0], rhos, [0.0, 0.0])
refq = refq / ref
return refq
def diag_results(cube_id):
def f_doublet(x, c, i1, i2, sigma_gal, z, sigma_inst):
""" function for Gaussian doublet """
dblt_mu = [3727.092, 3729.875] # the actual non-redshifted wavelengths
l1 = dblt_mu[0] * (1 + z)
l2 = dblt_mu[1] * (1 + z)
sigma = np.sqrt(sigma_gal**2 + sigma_inst**2)
norm = (sigma * np.sqrt(2 * np.pi))
term1 = (i1 / norm) * np.exp(-(x - l1)**2 / (2 * sigma**2))
term2 = (i2 / norm) * np.exp(-(x - l2)**2 / (2 * sigma**2))
return (c * x + term1 + term2)
with PdfPages('diagnostics/cube_' + str(cube_id) +
'_diagnostic.pdf') as pdf:
analysis = cube_reader.analysis(
"/Volumes/Jacky_Cao/University/level4/" +
"project/cubes_better/cube_" + str(cube_id) + ".fits",
"data/skyvariance_csub.fits")
# calling data into variables
icd = analysis['image_data']
segd = analysis['spectra_data']['segmentation']
sr = analysis['sr']
df_data = analysis['df_data']
gs_data = analysis['gs_data']
snw_data = analysis['snw_data']
# images of the galaxy
f, (ax1, ax2) = plt.subplots(1, 2)
ax1.imshow(icd['median'], cmap='gray_r')
ax1.set_title(r'\textbf{Galaxy Image: Median}', fontsize=13)
ax1.set_xlabel(r'\textbf{Pixels}', fontsize=13)
ax1.set_ylabel(r'\textbf{Pixels}', fontsize=13)
ax2.imshow(icd['sum'], cmap='gray_r')
ax2.set_title(r'\textbf{Galaxy Image: Sum}', fontsize=13)
ax2.set_xlabel(r'\textbf{Pixels}', fontsize=13)
ax2.set_ylabel(r'\textbf{Pixels}', fontsize=13)
f.subplots_adjust(wspace=0.4)
pdf.savefig()
plt.close()
# ---------------------------------------------------------------------- #
# segmentation area used to extract the 1D spectra
segd_mask = ((segd == cube_id))
plt.figure()
plt.title(r'\textbf{Segmentation area used to extract 1D spectra}',
fontsize=13)
plt.imshow(np.rot90(segd_mask, 1), cmap='Paired')
plt.xlabel(r'\textbf{Pixels}', fontsize=13)
plt.ylabel(r'\textbf{Pixels}', fontsize=13)
pdf.savefig()
plt.close()
# ---------------------------------------------------------------------- #
# spectra plotting
f, (ax1, ax2) = plt.subplots(2, 1)
# --- redshifted data plotting
cbd_x = np.linspace(sr['begin'], sr['end'], sr['steps'])
## plotting our cube data
cbs_y = gs_data['gd_shifted']
ax1.plot(cbd_x, cbs_y, linewidth=0.5, color="#000000")
## plotting our sky noise data
snd_y = snw_data['sky_regions'][:, 1]
ax1.plot(cbd_x, snd_y, linewidth=0.5, color="#f44336", alpha=0.5)
## plotting our [OII] region
ot_x = df_data['x_region']
ot_y = df_data['y_region']
ax1.plot(ot_x, ot_y, linewidth=0.5, color="#00c853")
## plotting the standard deviation region in the [OII] section
std_x = df_data['std_x']
std_y = df_data['std_y']
ax1.plot(std_x, std_y, linewidth=0.5, color="#00acc1")
pu_lines = gs_data['pu_peaks']
for i in range(len(pu_lines)):
srb = sr['begin']
ax1.axvline(x=(pu_lines[i]),
linewidth=0.5,
color="#ec407a",
alpha=0.2)
ax1.set_title(r'\textbf{Spectra: cross-section redshifted}',
fontsize=13)
ax1.set_xlabel(r'\textbf{Wavelength (\AA)}', fontsize=13)
ax1.set_ylabel(r'\textbf{Flux}', fontsize=13)
ax1.set_ylim([-1000, 5000]) # setting manual limits for now
# --- corrected redshift
crs_x = np.linspace(sr['begin'], sr['end'], sr['steps'])
rdst = gs_data['redshift']
sp_lines = gs_data['spectra']
## corrected wavelengths
corr_x = crs_x / (1 + rdst)
## plotting our cube data
cps_y = gs_data['gd_shifted']
ax2.plot(corr_x, cps_y, linewidth=0.5, color="#000000")
## plotting our sky noise data
sn_y = gs_data['sky_noise']
ax2.plot(corr_x, sn_y, linewidth=0.5, color="#e53935")
## plotting spectra lines
for e_key, e_val in sp_lines['emis'].items():
spec_line = float(e_val)
ax2.axvline(x=spec_line, linewidth=0.5, color="#00c853")
ax2.text(spec_line - 10, 4800, e_key, rotation=-90)
ax2.set_title(r'\textbf{Spectra: cross-section corrected}',
fontsize=13)
ax2.set_xlabel(r'\textbf{Wavelength (\AA)}', fontsize=13)
ax2.set_ylabel(r'\textbf{Flux}', fontsize=13)
ax2.set_ylim([-500, 5000]) # setting manual limits for now
f.subplots_adjust(hspace=0.5)
pdf.savefig()
plt.close()
# ---------------------------------------------------------------------- #
# OII doublet region
ot_fig = plt.figure()
# plotting the data for the cutout [OII] region
ot_x = df_data['x_region']
ot_y = df_data['y_region']
plt.plot(ot_x, ot_y, linewidth=0.5, color="#000000")
## plotting the standard deviation region in the [OII] section
std_x = df_data['std_x']
std_y = df_data['std_y']
plt.plot(std_x, std_y, linewidth=0.5, color="#00acc1")
dblt_rng = df_data['doublet_range']
ot_x_b, ot_x_e = dblt_rng[0], dblt_rng[-1]
x_ax_vals = np.linspace(ot_x_b, ot_x_e, 1000)
# lmfit
lm_init = df_data['lm_init_fit']
lm_best = df_data['lm_best_fit']
plt.plot(ot_x, lm_best, linewidth=0.5, color="#1e88e5")
plt.plot(ot_x, lm_init, linewidth=0.5, color="#43a047", alpha=0.5)
lm_params = df_data['lm_best_param']
lm_params = [prm_value for prm_key, prm_value in lm_params.items()]
c, i_val1, i_val2, sig_g, rdsh, sig_i = lm_params
dblt_mu = [3727.092,
3729.875] # the actual non-redshifted wavelengths for OII
l1 = dblt_mu[0] * (1 + rdsh)
l2 = dblt_mu[1] * (1 + rdsh)
sig = np.sqrt(sig_g**2 + sig_i**2)
norm = (sig * np.sqrt(2 * np.pi))
lm_y1 = c + (i_val1 / norm) * np.exp(-(ot_x - l1)**2 / (2 * sig**2))
lm_y2 = c + (i_val2 / norm) * np.exp(-(ot_x - l2)**2 / (2 * sig**2))
plt.plot(ot_x, lm_y1, linewidth=0.5, color="#e64a19", alpha=0.7)
plt.plot(ot_x, lm_y2, linewidth=0.5, color="#1a237e", alpha=0.7)
# plotting signal-to-noise straight line and gaussian to verify it works
sn_line = df_data['sn_line']
sn_gauss = df_data['sn_gauss']
plt.title(r'\textbf{OII doublet region}', fontsize=13)
plt.xlabel(r'\textbf{Wavelength (\AA)}', fontsize=13)
plt.ylabel(r'\textbf{Flux}', fontsize=13)
plt.ylim([-500, 5000]) # setting manual limits for now
pdf.savefig()
plt.close()
# ---------------------------------------------------------------------- #
# plotting pPXF data
# defining wavelength as the x-axis
x_data = np.load("ppxf_results/cube_" + str(int(cube_id)) + "/cube_" +
str(int(cube_id)) + "_lamgal.npy")
# defining the flux from the data and model
y_data = np.load("ppxf_results/cube_" + str(int(cube_id)) + "/cube_" +
str(int(cube_id)) + "_flux.npy")
y_model = np.load("ppxf_results/cube_" + str(int(cube_id)) + "/cube_" +
str(int(cube_id)) + "_model.npy")
# scaled down y data
y_data_scaled = y_data / np.median(y_data)
# opening cube to obtain the segmentation data
cube_file = (
"/Volumes/Jacky_Cao/University/level4/project/cubes_better/cube_" +
str(cube_id) + ".fits")
hdu = fits.open(cube_file)
segmentation_data = hdu[2].data
seg_loc_rows, seg_loc_cols = np.where(segmentation_data == cube_id)
signal_pixels = len(seg_loc_rows)
# noise spectra will be used as in the chi-squared calculation
noise = np.load("ppxf_results/cube_" + str(int(cube_id)) + "/cube_" +
str(int(cube_id)) + "_noise.npy")
noise_median = np.median(noise)
noise_stddev = np.std(noise)
residual = y_data_scaled - y_model
res_median = np.median(residual)
res_stddev = np.std(residual)
noise = noise
mask = ((residual < res_stddev) & (residual > -res_stddev))
chi_sq = (y_data_scaled[mask] - y_model[mask])**2 / noise[mask]**2
total_chi_sq = np.sum(chi_sq)
total_points = len(chi_sq)
reduced_chi_sq = total_chi_sq / total_points
# spectral lines
sl = spectra_data.spectral_lines()
# parameters from lmfit
lm_params = spectra_data.lmfit_data(cube_id)
c = lm_params['c']
i1 = lm_params['i1']
i2 = lm_params['i2']
sigma_gal = lm_params['sigma_gal']
z = lm_params['z']
sigma_inst = lm_params['sigma_inst']
plt.figure()
plt.plot(x_data, y_data_scaled, linewidth=1.1, color="#000000")
plt.plot(x_data,
y_data_scaled + noise_stddev,
linewidth=0.1,
color="#616161",
alpha=0.1)
plt.plot(x_data,
y_data_scaled - noise_stddev,
linewidth=0.1,
color="#616161",
alpha=0.1)
# plotting over the OII doublet
doublets = np.array([3727.092, 3728.875])
#dblt_av = np.average(doublets) * (1+z)
dblt_av = np.average(doublets)
dblt_x_mask = ((x_data > dblt_av - 20) & (x_data < dblt_av + 20))
doublet_x_data = x_data[dblt_x_mask]
doublet_data = f_doublet(doublet_x_data, c, i1, i2, sigma_gal, z,
sigma_inst)
doublet_data = doublet_data / np.median(y_data)
plt.plot(doublet_x_data, doublet_data, linewidth=0.5, color="#9c27b0")
max_y = np.max(y_data_scaled)
# plotting spectral lines
for e_key, e_val in sl['emis'].items():
spec_line = float(e_val)
#spec_line = float(e_val) * (1+z)
spec_label = e_key
if (e_val in str(doublets)):
alpha_line = 0.2
else:
alpha_line = 0.7
alpha_text = 0.75
plt.axvline(x=spec_line,
linewidth=0.5,
color="#1e88e5",
alpha=alpha_line)
plt.text(spec_line - 3,
max_y,
spec_label,
rotation=-90,
alpha=alpha_text,
weight="bold",
fontsize=15)
for e_key, e_val in sl['abs'].items():
spec_line = float(e_val)
#spec_line = float(e_val) * (1+z)
spec_label = e_key
plt.axvline(x=spec_line, linewidth=0.5, color="#ff8f00", alpha=0.7)
plt.text(spec_line - 3,
max_y,
spec_label,
rotation=-90,
alpha=0.75,
weight="bold",
fontsize=15)
# iron spectral lines
for e_key, e_val in sl['iron'].items():
spec_line = float(e_val)
#spec_line = float(e_val) * (1+z)
plt.axvline(x=spec_line, linewidth=0.5, color="#bdbdbd", alpha=0.3)
plt.plot(x_data, y_model, linewidth=1.5, color="#b71c1c")
residuals_mask = (residual > res_stddev)
rmask = residuals_mask
#plt.scatter(x_data[rmask], residual[rmask], s=3, color="#f44336", alpha=0.5)
plt.scatter(x_data[mask], residual[mask] - 1, s=3, color="#43a047")
plt.tick_params(labelsize=13)
plt.title(r'\textbf{Spectra with pPXF overlayed}', fontsize=13)
plt.xlabel(r'\textbf{Wavelength (\AA)}', fontsize=13)
plt.ylabel(r'\textbf{Relative Flux}', fontsize=13)
plt.tight_layout()
pdf.savefig()
plt.close()
# ---------------------------------------------------------------------- #
# Voigt fitted region
# Running pPXF fitting routine
best_fit = ppxf_fitter_kinematics_sdss.kinematics_sdss(
cube_id, 0, "all")
best_fit_vars = best_fit['variables']
data_wl = np.load("cube_results/cube_" + str(int(cube_id)) + "/cube_" +
str(int(cube_id)) + "_cbd_x.npy") # 'x-data'
data_spec = np.load("cube_results/cube_" + str(int(cube_id)) +
"/cube_" + str(int(cube_id)) +
"_cbs_y.npy") # 'y-data'
# y-data which has been reduced down by median during pPXF running
galaxy = best_fit['y_data']
model_wl = np.load("ppxf_results/cube_" + str(int(cube_id)) +
"/cube_" + str(int(cube_id)) + "_lamgal.npy")
model_spec = np.load("ppxf_results/cube_" + str(int(cube_id)) +
"/cube_" + str(int(cube_id)) + "_model.npy")
# parameters from lmfit
lm_params = spectra_data.lmfit_data(cube_id)
z = lm_params['z']
sigma_inst = lm_params['sigma_inst']
# masking out the region of CaH and CaK
calc_rgn = np.array([3900, 4000])
data_rgn = calc_rgn * (1 + z)
data_mask = ((data_wl > data_rgn[0]) & (data_wl < data_rgn[1]))
data_wl_masked = data_wl[data_mask]
data_spec_masked = data_spec[data_mask]
data_spec_masked = data_spec_masked / np.median(data_spec_masked)
model_rgn = calc_rgn
model_mask = ((model_wl > calc_rgn[0]) & (model_wl < calc_rgn[1]))
model_wl_masked = model_wl[model_mask]
model_spec_masked = model_spec[model_mask]
z_wl_masked = model_wl_masked * (1 + z) # redshifted wavelength range
galaxy_masked = galaxy[model_mask]
# Applying the lmfit routine to fit two Voigt profiles over our spectra data
vgt_pars = Parameters()
vgt_pars.add('sigma_inst', value=sigma_inst, vary=False)
vgt_pars.add('sigma_gal', value=1.0, min=0.0)
vgt_pars.add('z', value=z)
vgt_pars.add('v1_amplitude', value=-0.1, max=0.0)
vgt_pars.add('v1_center', expr='3934.777*(1+z)')
vgt_pars.add('v1_sigma',
expr='sqrt(sigma_inst**2 + sigma_gal**2)',
min=0.0)
#vgt_pars.add('v1_gamma', value=0.01)
vgt_pars.add('v2_amplitude', value=-0.1, max=0.0)
vgt_pars.add('v2_center', expr='3969.588*(1+z)')
vgt_pars.add('v2_sigma', expr='v1_sigma')
#vgt_pars.add('v2_gamma', value=0.01)
vgt_pars.add('c', value=0)
voigt = VoigtModel(prefix='v1_') + VoigtModel(
prefix='v2_') + ConstantModel()
vgt_result = voigt.fit(galaxy_masked, x=z_wl_masked, params=vgt_pars)
opt_pars = vgt_result.best_values
best_fit = vgt_result.best_fit
# Plotting the spectra
fig, ax = plt.subplots()
ax.plot(z_wl_masked, galaxy_masked, lw=1.5, c="#000000", alpha=0.3)
ax.plot(z_wl_masked, model_spec_masked, lw=1.5, c="#00c853")
ax.plot(z_wl_masked, best_fit, lw=1.5, c="#e53935")
ax.tick_params(labelsize=13)
ax.set_ylabel(r'\textbf{Relative Flux}', fontsize=13)
ax.set_xlabel(r'\textbf{Wavelength (\AA)}', fontsize=13)
plt.title(r'\textbf{Voigt Fitted Region}', fontsize=15)
fig.tight_layout()
pdf.savefig()
plt.close()
# ---------------------------------------------------------------------- #
# Values for diagnostics
catalogue = np.load("data/matched_catalogue.npy")
cat_loc = np.where(catalogue[:, 0] == cube_id)[0]
cube_data = catalogue[cat_loc][0]
vmag = cube_data[5]
sigma_sn_data = np.load("data/ppxf_fitter_data.npy")
sigma_sn_loc = np.where(sigma_sn_data[:][:, 0][:, 0] == cube_id)[0]
ss_indiv_data = sigma_sn_data[sigma_sn_loc][0][0]
ssid = ss_indiv_data
plt.figure()
plt.title('Variables and numbers for cube ' + str(cube_id),
fontsize=15)
plt.text(0.0, 0.9, "HST V-band magnitude: " + str(vmag))
plt.text(0.0, 0.85, "S/N from spectra: " + str(ssid[7]))
plt.text(0.0, 0.75, "OII sigma lmfit: " + str(ssid[1]))
plt.text(0.0, 0.7, "OII sigma pPXF: " + str(ssid[5]))
plt.text(0.0, 0.6, "Voigt sigma lmfit: " + str(ssid[11]))
plt.text(0.0, 0.55, "Voigt sigma pPXF: " + str(ssid[10]))
plt.axis('off')
pdf.savefig()
plt.close()
# We can also set the file's metadata via the PdfPages object:
d = pdf.infodict()
d['Title'] = 'cube_' + str(cube_id) + ' diagnostics'
d['Author'] = u'Jacky Cao'
#d['Subject'] = 'How to create a multipage pdf file and set its metadata'
#d['Keywords'] = 'PdfPages multipage keywords author title subject'
#d['CreationDate'] = datetime.datetime(2009, 11, 13)
d['CreationDate'] = datetime.datetime.today()
def fit_sine(t, data):
params = Parameters()
params.add('frequency', value = rabi)
params.add('phaseShift', value = 0)
params.add('amplitude', value = 0.01)
params.add('offset', value = 0.005)
params.add('frequency2', value = rabi_2)
params.add('amp2', value = 0.1)
params.add('phase2', value = 0)
out = minimize(residual, params, args = (t, data))
return out
1.6762046817955716 * 100e-6, 1.538489775708743 * 100e-6,
1.2667996551684635 * 100e-6, 0.9227732749310865 * 100e-6,
0.8606704620816109 * 100e-6, 0.6315702583843055 * 100e-6,
1.0875502579337843 * 100e-6, 2.364140282852443 * 100e-6,
2.319778855771209 * 100e-6, 3.8146331190426035 * 100e-6,
3.458809626725272 * 100e-6
]
sigma_y_error = [
0.004200939478237076, 0.002775160952841804, 0.005456730565488788,
0.006134716355516601, 0.013508877486089588, 0.0019198433852926633,
0.005618933751150967, 0.053682807653258724, 0.017732913060791056,
0.007950141650115095, 0.004731836802477574
]
z = np.linspace(5, 16)
#params, cov = curve_fit(omega, height, sigma_y, p_0=[1e-4])
#error = np.sqrt(np.diag(cov))
params = Parameters()
params.add('omega', value=1e-4)
out = minimize(omega, params, args=(height, sigma_y))
#plt.errorbar( height, sigma_y, xerr = 0.05, yerr = sigma_y_error, fmt ='x')
print('Parameter', params)
print('errors', error)
plt.plot(z, omega(params[0], z))
plt.show()
def lmfit2(record):
import numpy as np
from datetime import datetime
from lmfit import Minimizer, Parameters
now = datetime.now()
#first get globally used values
tfreq = record['tfreq'] * 1000.0
mpinc = record['mpinc'] / 1000000.0
smsep = record['smsep'] / 1000000.0
lagfr = record['lagfr'] / 1000000.0
nrang = record['nrang']
ltab = record['ltab']
mplgs = record['mplgs']
nave = record['nave']
acfd = record['acfd']
lag0_power = np.array(record['pwr0'])
#ignore the second lag 0 in the lag table
ltab = ltab[0:-1]
fit_record = build_fit_record(record)
c = 299792458.0
lamda = c/tfreq
k = 2*np.pi/lamda
nyquist_velocity = lamda/(4.*mpinc)
lags=[]
for pair in ltab:
lags.append(pair[1]-pair[0])
lags.sort()
max_lag = lags[-1]
t = np.array(lags)*mpinc
ranges = np.arange(0,nrang)
#Estimate the noise
noise = estimate_noise(lag0_power)
#Setup the fitted parameter lists
fitted_power = list()
fitted_width = list()
fitted_vels = list()
fitted_phis = list()
fitted_power_e = list()
fitted_width_e = list()
fitted_vels_e = list()
fitted_phis_e = list()
slist = list()
#next, iterate through all range gates and do fitting
for gate in ranges:
print gate
re = [x[0] for x in acfd[gate]]
im = [x[1] for x in acfd[gate]]
time = list(t)
#estimate the upper limit of the self clutter
clutter = list(estimate_selfclutter(nrang,ltab,smsep,mpinc,lagfr/2,gate,lag0_power)[lags])
#find lags blanked due to Tx and identify "good" lags
blanked = determine_tx_blanked(nrang,ltab,smsep,mpinc,lagfr/2,gate)
blank_lags = [0 if len(blanked[x])==0 else 1 for x in blanked]
#don't include any lags that are blanked
j=0
for i,bl in enumerate(blank_lags):
if (bl == 1):
re.pop(i-j)
im.pop(i-j)
time.pop(i-j)
clutter.pop(i-j)
j += 1
re = np.array(re)
im = np.array(im)
time = np.array(time)
clutter = np.array(clutter)
#Now fit each acf using first order errors
first_error = first_order_errors(lag0_power[gate],noise,clutter,nave)
#set up the fitter and fit for the first time
init_vels = np.linspace(-nyquist_velocity/2.,nyquist_velocity/2.,num=30)
outs = list()
for vel in init_vels:
params = Parameters()
params.add('power', value=lag0_power[gate])
params.add('width', value=200.0,min=-100) #Need minimum, to stop magnitude model from diverging to infinity
params.add('velocity', value=vel, min=-nyquist_velocity/2., max=nyquist_velocity/2.)
minner = Minimizer(acf_residual, params, fcn_args=(time, re, im, first_error, first_error, lamda))
outs.append(minner.minimize())
chi2 = np.array([out.chisqr for out in outs])
ind = np.where(chi2 == np.min(chi2))[0]
if (ind.size != 1):
print "SOMETHING WEIRD IS HAPPENING"
else:
ind = ind[0]
pwr_fit = outs[ind].params['power'].value
wid_fit = outs[ind].params['width'].value
vel_fit = outs[ind].params['velocity'].value
#Now get proper errorbars using fitted parameters and model
acf_model = pwr_fit*np.exp(-time*2.*np.pi*wid_fit/lamda)*np.exp(1j*4.*np.pi*vel_fit*time/lamda)
mag_model = np.abs(acf_model)
rho_re = np.cos(4.*np.pi*vel_fit*time/lamda)
rho_im = np.sin(4.*np.pi*vel_fit*time/lamda)
rho = mag_model/mag_model[0]
for i in range(len(rho)):
if (rho[i] > 0.999):
rho[i] = 0.999
rho[i] = rho[i] * pwr_fit / (pwr_fit + noise + clutter[i])
re_error = acf_error(pwr_fit,noise,clutter,nave,rho,rho_re)
im_error = acf_error(pwr_fit,noise,clutter,nave,rho,rho_im)
#Now second LMFIT
outs2 = list()
for vel in init_vels:
params = Parameters()
params.add('power', value=pwr_fit)
params.add('width', value=wid_fit,min=-100)
params.add('velocity', value=vel, min=-nyquist_velocity/2., max=nyquist_velocity/2.)
minner = Minimizer(acf_residual, params, fcn_args=(time, re, im, re_error, im_error, lamda))
outs2.append(minner.minimize())
chi2 = np.array([out.chisqr for out in outs2])
ind = np.where(chi2 == np.min(chi2))[0]
if (ind.size != 1):
print "SOMETHING WEIRD IS HAPPENING"
else:
ind = ind[0]
pwr_fit = outs2[ind].params['power'].value
wid_fit = outs2[ind].params['width'].value
vel_fit = outs2[ind].params['velocity'].value
# TO DO, implement errors that compare relative chi2 of the
# multiple minima found. Just like in the C version.
pwr_e = outs2[ind].params['power'].stderr
wid_e = outs2[ind].params['width'].stderr
vel_e = outs2[ind].params['velocity'].stderr
#Now save fitted quantities into array
slist.append(gate)
fitted_power.append(pwr_fit)
fitted_width.append(wid_fit)
fitted_vels.append(vel_fit)
fitted_power_e.append(pwr_e)
fitted_width_e.append(wid_e)
fitted_vels_e.append(vel_e)
print "It took "+str((datetime.now()-now).total_seconds())+" to fit one beam."
#set ground scatter flags
gflg = list()
p_l = list()
p_l_e = list()
for i in range(len(slist)):
if (np.abs(fitted_vels[i])-(30.-1./3.*np.abs(fitted_width[i])) < 0.):
gflg.append(1)
else:
gflg.append(0)
p_l.append(10.0*np.log10(fitted_power[i]/noise))
p_l_e.append(10.0*np.log10((fitted_power_e[i]+fitted_power[i])/noise)-10.0*np.log10(fitted_power[i]/noise))
#construct the fitted data dictionary that will be written to the fit file
fit_record['slist'] = np.array(slist,dtype=np.int16)
fit_record['nlag'] = mplgs * np.ones(len(slist),dtype=np.int16)
fit_record['qflg'] = [1]*len(slist)
fit_record['gflg'] = gflg
fit_record['p_l'] = np.array(p_l,dtype=np.float32)
fit_record['p_l_e'] = np.array(p_l_e,dtype=np.float32)
fit_record['noise.sky'] = noise
fit_record['noise.search'] = noise
fit_record['noise.mean'] = noise
# fit_record['p_s']
# fit_record['p_s_e']
fit_record['v'] = np.array(fitted_vels,dtype=np.float32)
fit_record['v_e'] = np.array(fitted_vels_e,dtype=np.float32)
fit_record['w_l'] = np.array(fitted_width,dtype=np.float32)
fit_record['w_l_e'] = np.array(fitted_width_e,dtype=np.float32)
# fit_record['w_s'] =
# fit_record['w_s_e'] =
# fit_record['sd_l'] =
# fit_record['sd_s'] =
# fit_record['sd_phi'] =
# fit_record['x_qflg'] =
# fit_record['x_gflg'] =
# fit_record['x_p_l'] =
# fit_record['x_p_l_e'] =
# fit_record['x_p_s'] =
# fit_record['x_p_s_e'] =
# fit_record['x_v'] =
# fit_record['x_v_e'] =
# fit_record['x_w_l'] =
# fit_record['x_w_l_e'] =
# fit_record['x_w_s'] =
# fit_record['x_w_s_e'] =
# fit_record['phi0'] =
# fit_record['phi0_e'] =
# fit_record['elv'] =
# fit_record['elv_low'] =
# fit_record['elv_high'] =
# fit_record['x_sd_l'] =
# fit_record['x_sd_s'] =
# fit_record['x_sd_phi'] =
return fit_record
offset = pars['line_off'].value
model = (1 - frac) * yg + frac * yl + offset + x * slope
if data is None:
return model
if sigma is None:
return (model - data)
return (model - data) / sigma
n = 601
xmin = 0.
xmax = 20.0
x = linspace(xmin, xmax, n)
p_true = Parameters()
p_true.add('amp_g', value=21.0)
p_true.add('cen_g', value=8.1)
p_true.add('wid_g', value=1.6)
p_true.add('frac', value=0.37)
p_true.add('line_off', value=-1.023)
p_true.add('line_slope', value=0.62)
data = (pvoigt(x, p_true['amp_g'].value, p_true['cen_g'].value,
p_true['wid_g'].value, p_true['frac'].value) +
random.normal(scale=0.23, size=n) + x * p_true['line_slope'].value +
p_true['line_off'].value)
if HASPYLAB:
pylab.plot(x, data, 'r+')
pfit = [
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.linspace(0,80,300)
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=2.5, min=1, max=5.0)
params.add('prolif_tfhc', value=2.5, min=1, max=5.0)
params.add("pth1", value=0.3, min=0, max=1.0)
params.add("ptfh", value=0.2, min=0, max=1.0)
params.add("ptr1", value=0.3, min=0, max=1.0)
params.add("ptfhc", expr="1.0-pth1-ptfh-ptr1")
params.add("K_il2", value = 0.0001, min = 1e-7, max=1)
# =============================================================================
# run fitting procedure
# =============================================================================
out = minimize(fit_fun, params, args=(sim, data_arm, data_cl13))
out_values = out.params.valuesdict()
print(out_values)
def test_constraints(with_plot=True):
with_plot = with_plot and WITHPLOT
def residual(pars, x, sigma=None, data=None):
yg = gaussian(x, pars['amp_g'], pars['cen_g'], pars['wid_g'])
yl = lorentzian(x, pars['amp_l'], pars['cen_l'], pars['wid_l'])
model = yg + yl + pars['line_off'] + x * pars['line_slope']
if data is None:
return model
if sigma is None:
return (model - data)
return (model - data) / sigma
n = 201
xmin = 0.
xmax = 20.0
x = linspace(xmin, xmax, n)
data = (gaussian(x, 21, 8.1, 1.2) +
lorentzian(x, 10, 9.6, 2.4) +
random.normal(scale=0.23, size=n) +
x*0.5)
if with_plot:
pylab.plot(x, data, 'r+')
pfit = Parameters()
pfit.add(name='amp_g', value=10)
pfit.add(name='cen_g', value=9)
pfit.add(name='wid_g', value=1)
pfit.add(name='amp_tot', value=20)
pfit.add(name='amp_l', expr='amp_tot - amp_g')
pfit.add(name='cen_l', expr='1.5+cen_g')
pfit.add(name='wid_l', expr='2*wid_g')
pfit.add(name='line_slope', value=0.0)
pfit.add(name='line_off', value=0.0)
sigma = 0.021 # estimate of data error (for all data points)
myfit = Minimizer(residual, pfit,
fcn_args=(x,), fcn_kws={'sigma':sigma, 'data':data},
scale_covar=True)
myfit.prepare_fit()
init = residual(myfit.params, x)
result = myfit.leastsq()
print(' Nfev = ', result.nfev)
print( result.chisqr, result.redchi, result.nfree)
report_fit(result.params, min_correl=0.3)
fit = residual(result.params, x)
if with_plot:
pylab.plot(x, fit, 'b-')
assert(result.params['cen_l'].value == 1.5 + result.params['cen_g'].value)
assert(result.params['amp_l'].value == result.params['amp_tot'].value - result.params['amp_g'].value)
assert(result.params['wid_l'].value == 2 * result.params['wid_g'].value)
# now, change fit slightly and re-run
myfit.params['wid_l'].expr = '1.25*wid_g'
result = myfit.leastsq()
report_fit(result.params, min_correl=0.4)
fit2 = residual(result.params, x)
if with_plot:
pylab.plot(x, fit2, 'k')
pylab.show()
assert(result.params['cen_l'].value == 1.5 + result.params['cen_g'].value)
assert(result.params['amp_l'].value == result.params['amp_tot'].value - result.params['amp_g'].value)
assert(result.params['wid_l'].value == 1.25 * result.params['wid_g'].value)
def fitcurve(val0):
if elem.matchX is False:
return
ydat = measdata.D1complex[:, measdata.findex]
data = np.empty(len(ydat) * 2, dtype='float64')
data[0::2] = ydat.real
data[1::2] = ydat.imag
preFit(False)
xaxis3 = np.linspace(squid.start, squid.stop, (squid.pt * 2))
# Using standard curve_fit settings
# Define fitting parameters
params = Parameters()
params.add('CapfF', value=squid.Cap * 1e15, vary=True, min=30, max=90)
params.add('IcuA', value=squid.Ic * 1e6, vary=True, min=3.0, max=4.5)
params.add('WbpH', value=squid.Wb * 1e12, vary=True, min=0, max=1500)
params.add('LooppH', value=squid.LOOP * 1e12, vary=False, min=0.0, max=100)
params.add('alpha', value=squid.ALP, vary=False, min=0.98, max=1.02)
params.add('R', value=squid.R, vary=True, min=1, max=20e3)
params.add('Z1', value=elem.Z1, vary=False, min=40, max=60)
params.add('Z2', value=elem.Z2, vary=False, min=40, max=60)
params.add('Z3', value=elem.Z3, vary=False, min=40, max=60)
params.add('L2', value=elem.L2, vary=False, min=0.00, max=0.09)
# Crop region to fit
elem.midx = find_nearest(xaxis3, elem.xmin)
elem.madx = find_nearest(xaxis3, elem.xmax)
# Do Fit
result = minimize(gta1, params, args=(xaxis3[elem.midx:elem.madx], data))
# Present results of fitting
print report_fit(result)
paramsToMem(result.params)
update2(0)
preFit(True)
# Calculate and plot residual there
S11 = getfit()
residual = data - S11
plt.figure(4)
plt.clf()
plt.plot(xaxis3[elem.midx:elem.madx], residual[elem.midx:elem.madx])
plt.axis('tight')
plt.draw()
print 'Avg-sqr Residuals', abs(np.mean((residual * residual))) * 1e8
return
class FieldFitter:
"""Input field measurements, perform parametric fit, return relevant quantities.
The :class:`mu2e.fieldfitter.FieldFitter` takes a 3D set of field measurements and their
associated position values, and performs a parametric fit. The parameters and fit model are
handled by the :mod:`lmfit` package, which in turn wraps the :mod:`scipy.optimize` module, which
actually performs the parameter optimization. The default optimizer is the Levenberg-Marquardt
algorithm.
The :func:`mu2e.fieldfitter.FieldFitter.fit` requires multiple cfg `namedtuples`, and performs
the actual fitting (or recreates a fit for a given set of saved parameters). After fitting, the
generated class members can be used for further analysis.
Args:
input_data (pandas.DataFrame): DF that contains the field component values to be fit.
cfg_geom (namedtuple): namedtuple with the following members:
'geom z_steps r_steps phi_steps x_steps y_steps bad_calibration'
Attributes:
input_data (pandas.DataFrame): The input DF, with possible modifications.
phi_steps (List[float]): The axial values of the field data (cylindrial coords)
r_steps (List[float]): The radial values of the field data (cylindrial coords)
x_steps (List[float]): The x values of the field data (cartesian coords)
y_steps (List[float]): The y values of the field data (cartesian coords)
pickle_path (str): Location to read/write the pickled fit parameter values
params (lmfit.Parameters): Set of Parameters, inherited from `lmfit`
result (lmfit.ModelResult): Container for resulting fit information, inherited from `lmfit`
"""
def __init__(self, input_data, cfg_geom):
self.input_data = input_data
if cfg_geom.geom == 'cyl':
self.phi_steps = cfg_geom.phi_steps
self.r_steps = cfg_geom.r_steps
elif cfg_geom.geom == 'cart':
self.x_steps = cfg_geom.x_steps
self.y_steps = cfg_geom.y_steps
self.pickle_path = mu2e_ext_path + 'fit_params/'
self.geom = cfg_geom.geom
def fit(self, geom, cfg_params, cfg_pickle):
"""Helper function that chooses one of the subsequent fitting functions."""
self.fit_solenoid(cfg_params, cfg_pickle)
def fit_solenoid(self, cfg_params, cfg_pickle):
"""Main fitting function for FieldFitter class.
The typical magnetic field geometry for the Mu2E experiment is determined by one or more
solenoids, with some contaminating external fields. The purpose of this function is to fit
a set of sparse magnetic field data that would, in practice, be generated by a field
measurement device.
The following assumptions must hold for the input data:
* The data is represented in a cylindrical coordiante system.
* The data forms a series of planes, where all planes intersect at R=0.
* All planes has the same R and Z values.
* All positive Phi values have an associated negative phi value, which uniquely defines a
single plane in R-Z space.
Args:
cfg_params (namedtuple): 'ns ms cns cms Reff func_version'
cfg_pickle (namedtuple): 'use_pickle save_pickle load_name save_name recreate'
Returns:
Nothing. Generates class attributes after fitting, and saves parameter values, if
saving is specified.
"""
func_version = cfg_params.func_version
Bz = []
Br = []
Bphi = []
RR = []
ZZ = []
PP = []
XX = []
YY = []
# Load pre-defined starting values for parameters, or start a new set
if cfg_pickle.use_pickle or cfg_pickle.recreate:
try:
self.params = pkl.load(
open(
self.pickle_path + cfg_pickle.load_name + '_results.p',
"rb"))
except UnicodeDecodeError:
self.params = pkl.load(open(
self.pickle_path + cfg_pickle.load_name + '_results.p',
"rb"),
encoding='latin1')
else:
self.params = Parameters()
self.add_params_default(cfg_params)
ZZ = self.input_data.Z.values
RR = self.input_data.R.values
PP = self.input_data.Phi.values
Bz = self.input_data.Bz.values
Br = self.input_data.Br.values
Bphi = self.input_data.Bphi.values
if func_version in [
6, 8, 105, 110, 115, 116, 117, 118, 119, 120, 121, 122, 1000
]:
XX = self.input_data.X.values
YY = self.input_data.Y.values
# Choose the type of fitting function we'll be using.
pvd = self.params.valuesdict(
) # Quicker way to grab params and init the fit functions
if func_version == 5:
fit_func = ff.brzphi_3d_producer_modbessel_phase(
ZZ, RR, PP, pvd['R'], pvd['ns'], pvd['ms'])
elif func_version == 6:
fit_func = ff.brzphi_3d_producer_modbessel_phase_ext(
ZZ, RR, PP, pvd['R'], pvd['ns'], pvd['ms'], pvd['cns'],
pvd['cms'])
elif func_version == 7:
fit_func = ff.brzphi_3d_producer_modbessel_phase_hybrid(
ZZ, RR, PP, pvd['R'], pvd['ns'], pvd['ms'], pvd['cns'],
pvd['cms'])
elif func_version == 8:
fit_func = ff.brzphi_3d_producer_modbessel_v8(
ZZ, RR, PP, pvd['R'], pvd['ns'], pvd['ms'], pvd['cns'],
pvd['cms'])
elif func_version == 100:
fit_func = ff.brzphi_3d_producer_hel_v0(ZZ, RR, PP, pvd['R'],
pvd['ns'], pvd['ms'])
elif func_version == 115:
fit_func = ff.brzphi_3d_producer_hel_v15(ZZ, RR, PP, pvd['R'],
pvd['ns'], pvd['ms'],
pvd['n_scale'])
elif func_version == 117:
fit_func = ff.brzphi_3d_producer_hel_v17(ZZ, RR, PP, pvd['R'],
pvd['ns'], pvd['ms'],
pvd['n_scale'])
elif func_version == 118:
fit_func = ff.brzphi_3d_producer_hel_v18(ZZ, RR, PP, pvd['R'],
pvd['ns'], pvd['ms'],
pvd['cns'], pvd['cms'],
pvd['n_scale'])
elif func_version == 119:
fit_func = ff.brzphi_3d_producer_hel_v19(ZZ, RR, PP, pvd['R'],
pvd['ns'], pvd['ms'],
pvd['cns'], pvd['cms'],
pvd['n_scale'])
elif func_version == 120:
fit_func = ff.brzphi_3d_producer_hel_v20(ZZ, RR, PP, pvd['R'],
pvd['ns'], pvd['ms'],
pvd['cns'], pvd['cms'],
pvd['n_scale'],
pvd['m_scale'])
elif func_version == 121:
fit_func = ff.brzphi_3d_producer_hel_v21(ZZ, RR, PP, pvd['R'],
pvd['ns'], pvd['ms'],
pvd['cns'], pvd['cms'],
pvd['n_scale'],
pvd['m_scale'])
elif func_version == 122:
fit_func = ff.brzphi_3d_producer_hel_v22(ZZ, RR, PP, pvd['R'],
pvd['ns'], pvd['ms'],
pvd['cns'], pvd['cms'],
pvd['n_scale'],
pvd['m_scale'])
else:
raise NotImplementedError(
f'Function version={func_version} not implemented.')
# Generate an lmfit Model
if func_version in [6, 8, 110, 115, 116, 117, 118, 119, 120, 121, 122]:
self.mod = Model(fit_func,
independent_vars=['r', 'z', 'phi', 'x', 'y'])
else:
self.mod = Model(fit_func, independent_vars=['r', 'z', 'phi'])
# Start loading in additional parameters based on the function version.
# Functions with version < 100 are cyclindrical expansions.
# Functions with version > 100 are helical expansions.
if func_version == 5:
self.add_params_AB()
self.add_params_phase_shift()
elif func_version == 6:
self.add_params_AB()
self.add_params_phase_shift()
self.add_params_cart_simple(on_list=['k3'])
if func_version == 7:
self.add_params_AB()
self.add_params_phase_shift()
elif func_version == 8:
self.add_params_AB()
self.add_params_phase_shift()
self.add_params_cart_simple(on_list=['k3'])
self.add_params_biot_savart(xyz_tuples=((1000, 0, -4600), (1000, 0,
4600)))
elif func_version == 100:
self.add_params_ABCD()
elif func_version == 115:
self.add_params_AB(skip_zero_n=True)
self.add_params_cart_simple(all_on=True)
elif func_version == 116:
self.add_params_AB(skip_zero_n=True)
self.add_params_finite_wire()
elif func_version == 117:
self.add_params_AB(skip_zero_n=True)
self.add_params_cart_simple(all_on=True)
self.add_params_phase_shift()
elif func_version == 118:
self.add_params_AB(skip_zero_n=True)
self.add_params_CD(skip_zero_cn=True)
self.add_params_cart_simple(all_on=True)
elif func_version == 119:
self.add_params_AB(skip_zero_n=True)
self.add_params_CD(skip_zero_cn=True)
self.add_params_cart_simple(on_list=['k3'])
# self.add_params_cart_simple(all_on=False)
# self.add_params_biot_savart(xyz_tuples=(
# (1000, 0, -4600),
# (1000, 0, 4600)))
# self.add_params_biot_savart(xyz_tuples=(
# (0.25, 0, -46),
# (0.25, 0, 46)),
# xy_bounds=0.05, z_bounds=0.05, v_bounds=100)
# self.add_params_biot_savart(
# xyz_tuples=(
# # (0, 0, 3532.85),
# # (0, 1000, 3963.66),
# # (0, 0, 4393.47),
# # (0, 0, 5034.67),
# # (0, 0, 5691.88),
# # (0, 0, 6382.01),
# # (0, 0, 7208.56),
# # (-100, -100, 7868.01),
# # (-500, 1150, 7868.01),
# # (-400, 1050, 7868.01),
# # (100, 100, 9710.86),
# # (-500, 1150, 9710.86),
# # (-400, 1050, 9710.86),
# # (-200, 1000, 10000),
# # (-500, 1150, 11553.71),
# # (-400, 1050, 11553.71),
# # (-200, 1000, 13454.53),
# # (200, -1000, 7868.01),
# # (200, -1000, 9710.86),
# # (200, -1000, 11553.71),
# # (200, -1000, 13454.53),
# ),
# xy_bounds=500, z_bounds=20, v_bounds=100)
elif func_version == 120:
self.add_params_AB(skip_zero_n=False, skip_zero_m=False)
self.add_params_CD(skip_zero_cn=True)
self.add_params_cart_simple(on_list=['k3'])
# self.add_params_cart_simple(all_on=True)
self.add_params_biot_savart(
xyz_tuples=((0.25, 0, -46), (0.25, 0, 46)),
# (0.25, 0, -4.6),
# (0.25, 0, 4.6)),
xy_bounds=0.1,
z_bounds=46,
v_bounds=100)
elif func_version == 121:
self.add_params_AB(skip_zero_n=False, skip_zero_m=False)
self.add_params_phase_shift()
self.add_params_cart_simple(on_list=['k3'])
# self.add_params_cart_simple(all_on=True)
self.add_params_biot_savart(xyz_tuples=((0.25, 0, -46), (0.25, 0,
46)),
xy_bounds=0.1,
z_bounds=46,
v_bounds=100)
elif func_version == 122:
self.add_params_AB(skip_zero_n=False, skip_zero_m=False)
self.add_params_CD(skip_zero_cn=False)
self.add_params_cart_simple(on_list=['k3'])
# self.add_params_cart_simple(all_on=True)
self.add_params_biot_savart(xyz_tuples=((0.25, 0, -46), (0.25, 0,
46)),
xy_bounds=0.01,
z_bounds=0.01,
v_bounds=100)
if not cfg_pickle.recreate:
print(
f'fitting with func_version={func_version},\n'
f'n={cfg_params.ns}, m={cfg_params.ms}, cn={cfg_params.cns}, cm={cfg_params.cms}'
)
else:
print(
f'recreating fit with func_version={func_version},\n'
f'n={cfg_params.ns}, m={cfg_params.ms}, cn={cfg_params.cns}, cm={cfg_params.cms}'
)
start_time = time()
# Functions with r, z, phi dependence only
if func_version in [5, 100]:
if cfg_pickle.recreate:
for param in self.params:
self.params[param].vary = False
self.result = self.mod.fit(np.concatenate([Br, Bz,
Bphi]).ravel(),
r=RR,
z=ZZ,
phi=PP,
params=self.params,
method='leastsq',
fit_kws={'maxfev': 1})
elif cfg_pickle.use_pickle:
# mag = 1/np.sqrt(Br**2+Bz**2+Bphi**2)
self.result = self.mod.fit(
np.concatenate([Br, Bz, Bphi]).ravel(),
# weights=np.concatenate([mag, mag, mag]).ravel(),
r=RR,
z=ZZ,
phi=PP,
params=self.params,
method='leastsq',
fit_kws={'maxfev': 10000})
else:
self.result = self.mod.fit(
np.concatenate([Br, Bz, Bphi]).ravel(),
# weights=np.concatenate(
# [np.ones(Br.shape), np.ones(Bz.shape),
# np.ones(Bphi.shape)*100000]).ravel(),
r=np.abs(RR),
z=ZZ,
phi=PP,
params=self.params,
# method='leastsq', fit_kws={'maxfev': 10000})
method='least_squares',
fit_kws={'max_nfev': 100})
# Functions with r, z, phi, x, y dependence
elif func_version in [
6, 8, 105, 115, 116, 117, 118, 119, 120, 121, 122
]:
if cfg_pickle.recreate:
for param in self.params:
self.params[param].vary = False
self.result = self.mod.fit(np.concatenate([Br, Bz,
Bphi]).ravel(),
r=RR,
z=ZZ,
phi=PP,
x=XX,
y=YY,
params=self.params,
method='leastsq',
fit_kws={'maxfev': 1})
elif cfg_pickle.use_pickle:
# mag = 1/np.sqrt(Br**2+Bz**2+Bphi**2)
self.result = self.mod.fit(
np.concatenate([Br, Bz, Bphi]).ravel(),
# weights=np.concatenate([mag, mag, mag]).ravel(),
r=RR,
z=ZZ,
phi=PP,
x=XX,
y=YY,
params=self.params,
method='leastsq',
fit_kws={'maxfev': 10000})
else:
# mag = 1/np.sqrt(Br**2+Bz**2+Bphi**2)
self.result = self.mod.fit(
np.concatenate([Br, Bz, Bphi]).ravel(),
# weights=np.concatenate([mag, mag, mag]).ravel(),
r=RR,
z=ZZ,
phi=PP,
x=XX,
y=YY,
params=self.params,
# method='leastsq', fit_kws={'maxfev': 10000})
method='least_squares',
fit_kws={
'verbose': 1,
'gtol': 1e-15,
'ftol': 1e-15,
'xtol': 1e-15,
# 'tr_solver': 'lsmr',
# 'tr_options':
# {'regularize': True}
})
self.params = self.result.params
end_time = time()
print(("Elapsed time was %g seconds" % (end_time - start_time)))
report_fit(self.result, show_correl=False)
if cfg_pickle.save_pickle: # and not cfg_pickle.recreate:
self.pickle_results(self.pickle_path + cfg_pickle.save_name)
def fit_external(self, cfg_params, cfg_pickle, profile=False):
raise NotImplementedError('Oh no! you got lazy during refactoring')
def pickle_results(self, pickle_name='default'):
"""Pickle the resulting Parameters after a fit is performed."""
pkl.dump(self.result.params, open(pickle_name + '_results.p', "wb"),
pkl.HIGHEST_PROTOCOL)
def merge_data_fit_res(self):
"""Combine the fit results and the input data into one dataframe for easier
comparison of results.
Adds three columns to input_data: `Br_fit, Bphi_fit, Bz_fit` or `Bx_fit, By_fit, Bz_fit`,
depending on the geometry.
"""
bf = self.result.best_fit
self.input_data.loc[:, 'Br_fit'] = bf[0:len(bf) // 3]
self.input_data.loc[:, 'Bz_fit'] = bf[len(bf) // 3:2 * len(bf) // 3]
self.input_data.loc[:, 'Bphi_fit'] = bf[2 * len(bf) // 3:]
def add_params_default(self, cfg_params):
if 'R' not in self.params:
self.params.add('R', value=cfg_params.Reff, vary=False)
if 'ns' not in self.params:
self.params.add('ns', value=cfg_params.ns, vary=False)
if 'ms' not in self.params:
self.params.add('ms', value=cfg_params.ms, vary=False)
if 'n_scale' not in self.params:
self.params.add('n_scale', value=cfg_params.n_scale, vary=False)
if 'm_scale' not in self.params:
self.params.add('m_scale', value=cfg_params.m_scale, vary=False)
if 'cns' not in self.params:
self.params.add('cns', value=cfg_params.cns, vary=False)
if 'cms' not in self.params:
self.params.add('cms', value=cfg_params.cms, vary=False)
def add_params_AB(self, skip_zero_n=False, skip_zero_m=False):
if skip_zero_n:
ns_range = range(1, self.params['ns'].value)
else:
ns_range = range(self.params['ns'].value)
if skip_zero_m:
ms_range = range(1, self.params['ms'].value)
else:
ms_range = range(self.params['ms'].value)
for n in ns_range:
for m in ms_range:
if n == m == 0:
if f'A_{n}_{m}' not in self.params:
self.params.add(f'A_{n}_{m}', value=0, vary=False)
if f'B_{n}_{m}' not in self.params:
self.params.add(f'B_{n}_{m}', value=0, vary=False)
else:
if f'A_{n}_{m}' not in self.params:
self.params.add(f'A_{n}_{m}', value=0, vary=True)
if f'B_{n}_{m}' not in self.params:
self.params.add(f'B_{n}_{m}', value=0, vary=True)
def add_params_CD(self, skip_zero_cn=False):
if skip_zero_cn:
cns_range = range(1, self.params['cns'].value)
else:
cns_range = range(self.params['cns'].value)
cms_range = range(self.params['cms'].value)
for cn in cns_range:
for cm in cms_range:
if f'C_{cn}_{cm}' not in self.params:
self.params.add(f'C_{cn}_{cm}', value=0, vary=True)
if f'D_{cn}_{cm}' not in self.params:
self.params.add(f'D_{cn}_{cm}', value=0, vary=True)
def add_params_phase_shift(self):
# `D` parameter is a scaling parameters that is equivalent to a phase shift.
# Instead of using a term like cos(phi+D), it is D*cos(phi)+(1-D)*sin(phi).
# This allows the free paramns to remain linear, and greatly decreases run time.
for n in range(self.params['ns'].value):
if f'D_{n}' not in self.params:
self.params.add(f'D_{n}', value=0.5, min=0, max=1, vary=True)
def add_params_ABCD(self):
# Add parameters A,B,C,D, and turn off the off-diagonals that are unphysical.
ns_range = range(self.params['ns'].value)
ms_range = range(self.params['ms'].value)
n_scale = self.params['n_scale'].value
m_scale = self.params['m_scale'].value
for n in ns_range:
for m in ms_range:
if f'A_{n}_{m}' not in self.params:
self.params.add(f'A_{n}_{m}', value=0, vary=True)
if f'B_{n}_{m}' not in self.params:
self.params.add(f'B_{n}_{m}', value=0, vary=True)
if f'C_{n}_{m}' not in self.params:
self.params.add(f'C_{n}_{m}', value=0, vary=True)
if f'D_{n}_{m}' not in self.params:
self.params.add(f'D_{n}_{m}', value=0, vary=True)
if (n * n_scale > m * m_scale) or n * n_scale == 0:
self.params[f'A_{n}_{m}'].vary = False
self.params[f'A_{n}_{m}'].value = 0
self.params[f'B_{n}_{m}'].vary = False
self.params[f'B_{n}_{m}'].value = 0
self.params[f'C_{n}_{m}'].vary = False
self.params[f'C_{n}_{m}'].value = 0
self.params[f'D_{n}_{m}'].vary = False
self.params[f'D_{n}_{m}'].value = 0
def add_params_cart_simple(self, all_on=False, on_list=None):
cart_names = [f'k{i}' for i in range(1, 11)]
if on_list is None:
on_list = []
for k in cart_names:
if all_on:
if k not in self.params:
self.params.add(k, value=0, vary=True)
else:
if k not in self.params:
self.params.add(k, value=0, vary=(k in on_list))
def add_params_finite_wire(self):
if 'k1' not in self.params:
self.params.add('k1', value=0, vary=True)
if 'k2' not in self.params:
self.params.add('k2', value=0, vary=True)
if 'xp1' not in self.params:
self.params.add('xp1', value=1050, vary=False, min=900, max=1200)
if 'xp2' not in self.params:
self.params.add('xp2', value=1050, vary=False, min=900, max=1200)
if 'yp1' not in self.params:
self.params.add('yp1', value=0, vary=False, min=-100, max=100)
if 'yp2' not in self.params:
self.params.add('yp2', value=0, vary=False, min=-100, max=100)
if 'zp1' not in self.params:
self.params.add('zp1', value=4575, vary=False, min=4300, max=4700)
if 'zp2' not in self.params:
self.params.add('zp2',
value=-4575,
vary=False,
min=-4700,
max=-4300)
def add_params_biot_savart(self,
xyz_tuples=None,
v_tuples=None,
xy_bounds=100,
z_bounds=100,
v_bounds=100):
if v_tuples and len(v_tuples) != len(xyz_tuples):
raise AttributeError(
'If v_tuples is specified it must be same size as xyz_tuples')
for i in range(1, len(xyz_tuples) + 1):
x, y, z = xyz_tuples[i - 1]
if f'x{i}' not in self.params:
self.params.add(f'x{i}',
value=x,
vary=True,
min=x - xy_bounds,
max=x + xy_bounds)
if f'y{i}' not in self.params:
self.params.add(f'y{i}',
value=y,
vary=True,
min=y - xy_bounds,
max=y + xy_bounds)
if f'z{i}' not in self.params:
self.params.add(f'z{i}',
value=z,
vary=True,
min=z - z_bounds,
max=z + z_bounds)
if v_tuples:
vx, vy, vz = v_tuples[i - 1]
else:
vx = vy = vz = 0
if f'vx{i}' not in self.params:
self.params.add(f'vx{i}',
value=vx,
vary=True,
min=vx - v_bounds,
max=vx + v_bounds)
if f'vy{i}' not in self.params:
self.params.add(f'vy{i}',
value=vy,
vary=True,
min=vy - v_bounds,
max=vy + v_bounds)
if f'vz{i}' not in self.params:
self.params.add(f'vz{i}',
value=vz,
vary=True,
min=vz - v_bounds,
max=vz + v_bounds)
minner = Minimizer(fcn2min, params, fcn_args=(x, y, func))
result = minner.minimize()
## Store the Confidence data from the fit
#con_report = lmfit.fit_report(result.params)
(x_plot, model) = fcn2min(result.params, x, y, func=func, plot_fit=True)
return (x_plot, model, result)
if __name__ == '__main__':
params = Parameters()
params.add('p0', value=2.4, min=-2.0, max=4.0, vary=True)
params.add('p1', value=100.0, min=0.0, max=2000.0, vary=True)
params.add('p2', value=0.0, min=-2, max=2, vary=True)
params.add('p3', value=2.3, min=-2.0, max=4.0, vary=True)
x = np.linspace(-10, 10, 100)
y = 2.4 + 0.2 * np.exp(-x**2 / (2 * 2.3**2))
(x_fit, y_fit, result) = fit_func(x, y, params, gauss)
print(result.params)
import matplotlib.pyplot as plt
plt.plot(x, y, 'o')
plt.plot(x_fit, y_fit)
def fit_isoturbHI_model_simple(vels,
spec,
vcent,
delta_vcent=5 * u.km / u.s,
err=None,
verbose=True,
plot_fit=True,
return_model=False,
use_emcee=False,
emcee_kwargs={}):
vels = vels.copy().to(u.km / u.s)
vel_min = (vcent - delta_vcent).to(vels.unit).value
vel_max = (vcent + delta_vcent).to(vels.unit).value
# Create the parameter list.
pfit = Parameters()
# pfit.add(name='Ts', value=100., min=10**1.2, max=8000)
pfit.add(name='Ts', value=np.nanmax(spec.value), min=10**1.2, max=8000)
pfit.add(name='sigma', value=15., min=0.30, max=31.6) # min v at Ts=16 K
# pfit.add(name='log_NH', value=21., min=20., max=23.5)
pfit.add(name='Tpeak',
value=np.nanmax(spec.value),
min=0,
max=5. * np.nanmax(spec.value))
pfit.add(name='vcent',
value=vcent.to(vels.unit).value,
min=vel_min,
max=vel_max)
try:
finite_mask = np.isfinite(spec.filled_data[:])
except AttributeError:
finite_mask = np.isfinite(spec)
# Some cases are failing with a TypeError due to a lack
# of data. This really shouldn't happen, but I'll throw in this
# to catch those cases.
if finite_mask.sum() <= 4:
return None
if err is not None:
fcn_args = (vels[finite_mask].value, spec[finite_mask].value,
err.value)
else:
fcn_args = (vels[finite_mask].value, spec[finite_mask].value, 1.)
try:
mini = Minimizer(residual,
pfit,
fcn_args=fcn_args,
max_nfev=vels.size * 1000,
nan_policy='omit')
out = mini.leastsq()
except TypeError:
return None
if use_emcee:
mini = Minimizer(residual,
out.params,
fcn_args=fcn_args,
max_nfev=vels.size * 1000)
out = mini.emcee(**emcee_kwargs)
if verbose:
report_fit(out)
pars = out.params
model = isoturbHI_simple(vels.value, pars['Ts'].value, pars['sigma'].value,
pars['Tpeak'].value, pars['vcent'].value)
if plot_fit:
plt.plot(vels.value, spec.value, drawstyle='steps-mid')
plt.plot(vels.value, model)
if return_model:
return out, vels.value, model
return out
def mback(energy,
mu=None,
group=None,
order=3,
z=None,
edge='K',
e0=None,
emin=None,
emax=None,
whiteline=None,
leexiang=False,
tables='chantler',
fit_erfc=False,
return_f1=False,
_larch=None):
"""
Match mu(E) data for tabulated f''(E) using the MBACK algorithm and,
optionally, the Lee & Xiang extension
Arguments:
energy, mu: arrays of energy and mu(E)
order: order of polynomial [3]
group: output group (and input group for e0)
z: Z number of absorber
edge: absorption edge (K, L3)
e0: edge energy
emin: beginning energy for fit
emax: ending energy for fit
whiteline: exclusion zone around white lines
leexiang: flag to use the Lee & Xiang extension
tables: 'chantler' (default) or 'cl'
fit_erfc: True to float parameters of error function
return_f1: True to put the f1 array in the group
Returns:
group.f2: tabulated f2(E)
group.f1: tabulated f1(E) (if return_f1 is True)
group.fpp: matched data
group.mback_params: Group of parameters for the minimization
References:
* MBACK (Weng, Waldo, Penner-Hahn): http://dx.doi.org/10.1086/303711
* Lee and Xiang: http://dx.doi.org/10.1088/0004-637X/702/2/970
* Cromer-Liberman: http://dx.doi.org/10.1063/1.1674266
* Chantler: http://dx.doi.org/10.1063/1.555974
"""
order = int(order)
if order < 1: order = 1 # set order of polynomial
if order > MAXORDER: order = MAXORDER
### implement the First Argument Group convention
energy, mu, group = parse_group_args(energy,
members=('energy', 'mu'),
defaults=(mu, ),
group=group,
fcn_name='mback')
if len(energy.shape) > 1:
energy = energy.squeeze()
if len(mu.shape) > 1:
mu = mu.squeeze()
group = set_xafsGroup(group, _larch=_larch)
if e0 is None: # need to run find_e0:
e0 = xray_edge(z, edge, _larch=_larch)[0]
if e0 is None:
e0 = group.e0
if e0 is None:
find_e0(energy, mu, group=group)
### theta is an array used to exclude the regions <emin, >emax, and
### around white lines, theta=0.0 in excluded regions, theta=1.0 elsewhere
(i1, i2) = (0, len(energy) - 1)
if emin is not None: i1 = index_of(energy, emin)
if emax is not None: i2 = index_of(energy, emax)
theta = np.ones(len(energy)) # default: 1 throughout
theta[0:i1] = 0
theta[i2:-1] = 0
if whiteline:
pre = 1.0 * (energy < e0)
post = 1.0 * (energy > e0 + float(whiteline))
theta = theta * (pre + post)
if edge.lower().startswith('l'):
l2 = xray_edge(z, 'L2', _larch=_larch)[0]
l2_pre = 1.0 * (energy < l2)
l2_post = 1.0 * (energy > l2 + float(whiteline))
theta = theta * (l2_pre + l2_post)
## this is used to weight the pre- and post-edge differently as
## defined in the MBACK paper
weight1 = 1 * (energy < e0)
weight2 = 1 * (energy > e0)
weight = np.sqrt(sum(weight1)) * weight1 + np.sqrt(sum(weight2)) * weight2
## get the f'' function from CL or Chantler
if tables.lower() == 'chantler':
f1 = f1_chantler(z, energy, _larch=_larch)
f2 = f2_chantler(z, energy, _larch=_larch)
else:
(f1, f2) = f1f2(z, energy, edge=edge, _larch=_larch)
group.f2 = f2
if return_f1:
group.f1 = f1
em = xray_line(z, edge.upper(), _larch=_larch)[0] # erfc centroid
params = Parameters()
params.add(name='s', value=1, vary=True) # scale of data
params.add(name='xi', value=50, vary=fit_erfc, min=0) # width of erfc
params.add(name='a', value=0, vary=False) # amplitude of erfc
if fit_erfc:
params['a'].value = 1
params['a'].vary = True
for i in range(order): # polynomial coefficients
params.add(name='c%d' % i, value=0, vary=True)
out = minimize(match_f2,
params,
method='leastsq',
gtol=1.e-5,
ftol=1.e-5,
xtol=1.e-5,
epsfcn=1.e-5,
kws=dict(en=energy,
mu=mu,
f2=f2,
e0=e0,
em=em,
order=order,
weight=weight,
theta=theta,
leexiang=leexiang))
opars = out.params.valuesdict()
eoff = energy - e0
norm_function = opars['a'] * erfc(
(energy - em) / opars['xi']) + opars['c0']
for i in range(order):
j = i + 1
attr = 'c%d' % j
if attr in opars:
norm_function += opars[attr] * eoff**j
group.e0 = e0
group.fpp = opars['s'] * mu - norm_function
group.mback_params = opars
tmp = Group(energy=energy, mu=group.f2 - norm_function, e0=0)
# calculate edge step from f2 + norm_function: should be very smooth
pre_f2 = preedge(energy, group.f2 + norm_function, e0=e0, nnorm=2, nvict=0)
group.edge_step = pre_f2['edge_step'] / opars['s']
pre_fpp = preedge(energy, mu, e0=e0, nnorm=2, nvict=0)
group.norm = (mu - pre_fpp['pre_edge']) / group.edge_step
def setup_model_params(self,
jmax_guess=None,
vcmax_guess=None,
rd_guess=None,
hd_guess=None,
ea_guess=None,
dels_guess=None):
""" Setup lmfit Parameters object
Parameters
----------
jmax_guess : value
initial parameter guess, if nothing is passed, i.e. it is None,
then parameter is not fitted
vcmax_guess : value
initial parameter guess, if nothing is passed, i.e. it is None,
then parameter is not fitted
rd_guess : value
initial parameter guess, if nothing is passed, i.e. it is None,
then parameter is not fitted
hd_guess : value
initial parameter guess, if nothing is passed, i.e. it is None,
then parameter is not fitted
ea_guess : value
initial parameter guess, if nothing is passed, i.e. it is None,
then parameter is not fitted
dels_guess : value
initial parameter guess, if nothing is passed, i.e. it is None,
then parameter is not fitted
Returns
-------
params : object
lmfit object containing parameters to fit
"""
params = Parameters()
if jmax_guess is not None:
params.add('Jmax', value=jmax_guess, min=0.0)
if vcmax_guess is not None:
params.add('Vcmax', value=vcmax_guess, min=0.0)
if rd_guess is not None:
params.add('Rd', value=rd_guess, min=0.0)
if ea_guess is not None:
params.add('Ea', value=ea_guess, min=0.0)
if hd_guess is not None:
params.add('Hd', value=hd_guess, vary=False)
if dels_guess is not None:
params.add('delS', value=dels_guess, min=0.0, max=700.0)
return params
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.
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 = 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 = 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 plot():
set_plot_properties() # change style
cs = palettable.colorbrewer.qualitative.Set1_8.mpl_colors
with open('/home/lc585/qsosed/input.yml', 'r') as f:
parfile = yaml.load(f)
fittingobj = load(parfile)
wavlen = fittingobj.get_wavlen()
lin = fittingobj.get_lin()
galspc = fittingobj.get_galspc()
ext = fittingobj.get_ext()
galcnt = fittingobj.get_galcnt()
ignmin = fittingobj.get_ignmin()
ignmax = fittingobj.get_ignmax()
ztran = fittingobj.get_ztran()
lyatmp = fittingobj.get_lyatmp()
lybtmp = fittingobj.get_lybtmp()
lyctmp = fittingobj.get_lyctmp()
whmin = fittingobj.get_whmin()
whmax = fittingobj.get_whmax()
qsomag = fittingobj.get_qsomag()
flxcorr = fittingobj.get_flxcorr()
cosmo = fittingobj.get_cosmo()
params = Parameters()
params.add('plslp1', value = -0.478)
params.add('plslp2', value = -0.199)
params.add('plbrk', value = 2.40250)
params.add('bbt', value = 1.30626)
params.add('bbflxnrm', value = 2.673)
params.add('elscal', value = 1.240)
params.add('scahal',value = 0.713)
params.add('galfra',value = 0.0)
params.add('bcnrm',value = 0.135)
params.add('ebv',value = 0.0)
params.add('imod',value = 18.0)
# Load median magnitudes
with open('/home/lc585/qsosed/sdss_ukidss_wise_medmag_ext.dat') as f:
datz = np.loadtxt(f, usecols=(0,))
datz = datz[:-5]
# Load filters
ftrlst = fittingobj.get_ftrlst()[2:-2]
lameff = fittingobj.get_lameff()[2:-2]
bp = fittingobj.get_bp()[2:-2] # these are in ab and data is in vega
dlam = fittingobj.get_bp()[2:-2]
zromag = fittingobj.get_zromag()[2:-2]
with open('ftgd_dr7.dat') as f:
ftgd = np.loadtxt(f, skiprows=1, usecols=(1,2,3,4,5,6,7,8,9))
modarr = residual(params,
parfile,
wavlen,
datz,
lin,
bp,
dlam,
zromag,
galspc,
ext,
galcnt,
ignmin,
ignmax,
ztran,
lyatmp,
lybtmp,
lyctmp,
ftrlst,
whmin,
whmax,
cosmo,
flxcorr,
qsomag,
ftgd)
fname = '/home/lc585/qsosed/sdss_ukidss_wise_medmag_ext.dat'
datarr = np.genfromtxt(fname, usecols=(5,7,9,11,13,15,17,19,21))
datarr[datarr < 0.0] = np.nan
datarr = datarr[:-5, :]
# remove less than lyman break
col1 = np.arange(8)
col2 = col1 + 1
col_label = ['$r$ - $i$',
'$i$ - $z$',
'$z$ - $Y$',
'$Y$ - $J$',
'$J$ - $H$',
'$H$ - $K$',
'$K$ - $W1$',
'$W1$ - $W2$']
df = get_data()
df = df[(df.z_HW > 1) & (df.z_HW < 3)]
colstr1 = ['rVEGA',
'iVEGA',
'zVEGA',
'YVEGA',
'JVEGA',
'HVEGA',
'KVEGA',
'W1VEGA']
colstr2 = ['iVEGA',
'zVEGA',
'YVEGA',
'JVEGA',
'HVEGA',
'KVEGA',
'W1VEGA',
'W2VEGA']
ylims = [[0, 0.6],
[-0.1, 0.5],
[-0.1, 0.5],
[-0.1, 0.5],
[0.2, 0.9],
[0.2, 0.9],
[0.5, 1.6],
[0.8, 1.5]]
fig, axs = plt.subplots(4, 2, figsize=figsize(1, vscale=2), sharex=True)
for i, ax in enumerate(axs.flatten()):
#data definition
ydat = datarr[:, col1[i]] - datarr[:, col2[i]]
ax.scatter(datz,
ydat,
color='black',
s=5,
label='Data')
ax.plot(datz,
modarr[:,col1[i]] - modarr[:, col2[i]],
color=cs[1],
label='Model')
# ax.scatter(df.z_HW, df[colstr1[i]] - df[colstr2[i]], s=1, alpha=0.1)
ax.set_title(col_label[i], size=10)
ax.set_ylim(ylims[i])
ax.set_xlim(0.75, 3.25)
axs[0, 0].legend(bbox_to_anchor=(0.7, 0.99),
bbox_transform=plt.gcf().transFigure,
fancybox=True,
shadow=True,
scatterpoints=1,
ncol=2)
axs[3, 0].set_xlabel(r'Redshift $z$')
axs[3, 1].set_xlabel(r'Redshift $z$')
fig.tight_layout()
fig.subplots_adjust(wspace=0.2, hspace=0.15, top=0.93)
fig.savefig('/home/lc585/thesis/figures/chapter05/sed_color_plot.pdf')
plt.show()
return None
class FeffPathGroup(Group):
def __init__(self,
filename=None,
_larch=None,
label=None,
s02=None,
degen=None,
e0=None,
ei=None,
deltar=None,
sigma2=None,
third=None,
fourth=None,
**kws):
kwargs = dict(name='FeffPath: %s' % filename)
kwargs.update(kws)
Group.__init__(self, **kwargs)
self._larch = _larch
self.filename = filename
self.params = None
self.label = label
self.spline_coefs = None
def_degen = 1
self._feffdat = None
if filename is not None:
self._feffdat = FeffDatFile(filename=filename, _larch=_larch)
self.geom = self._feffdat.geom
def_degen = self._feffdat.degen
if self.label is None:
self.label = self.__geom2label()
self.degen = def_degen if degen is None else degen
self.s02 = 1.0 if s02 is None else s02
self.e0 = 0.0 if e0 is None else e0
self.ei = 0.0 if ei is None else ei
self.deltar = 0.0 if deltar is None else deltar
self.sigma2 = 0.0 if sigma2 is None else sigma2
self.third = 0.0 if third is None else third
self.fourth = 0.0 if fourth is None else fourth
self.k = None
self.chi = None
if self._feffdat is not None:
self.create_spline_coefs()
def __geom2label(self):
"""generate label by hashing path geometry"""
rep = []
if self.geom is not None:
for atom in self.geom:
rep.extend(atom)
if self._feffdat is not None:
rep.append(self._feffdat.degen)
rep.append(self._feffdat.reff)
for attr in ('s02', 'e0', 'ei', 'deltar', 'sigma2', 'third', 'fourth'):
rep.append(getattr(self, attr, '_'))
s = "|".join([str(i) for i in rep])
return "p%s" % (b32hash(s)[:8].lower())
def __copy__(self):
return FeffPathGroup(filename=self.filename,
_larch=self._larch,
s02=self.s02,
degen=self.degen,
e0=self.e0,
ei=self.ei,
deltar=self.deltar,
sigma2=self.sigma2,
third=self.third,
fourth=self.fourth)
def __deepcopy__(self, memo):
return FeffPathGroup(filename=self.filename,
_larch=self._larch,
s02=self.s02,
degen=self.degen,
e0=self.e0,
ei=self.ei,
deltar=self.deltar,
sigma2=self.sigma2,
third=self.third,
fourth=self.fourth)
@property
def reff(self):
return self._feffdat.reff
@reff.setter
def reff(self, val):
pass
@property
def nleg(self):
return self._feffdat.nleg
@nleg.setter
def nleg(self, val):
pass
@property
def rmass(self):
return self._feffdat.rmass
@rmass.setter
def rmass(self, val):
pass
def __repr__(self):
if self.filename is not None:
return '<FeffPath Group %s>' % self.filename
return '<FeffPath Group (empty)>'
def create_path_params(self):
"""
create Path Parameters within the current fiteval
"""
self.params = Parameters(asteval=self._larch.symtable._sys.fiteval)
if self.label is None:
self.label = self.__geom2label()
self.store_feffdat()
for pname in PATH_PARS:
val = getattr(self, pname)
attr = 'value'
if isinstance(val, six.string_types):
attr = 'expr'
kws = {'vary': False, attr: val}
parname = fix_varname(PATHPAR_FMT % (pname, self.label))
self.params.add(parname, **kws)
def create_spline_coefs(self):
"""pre-calculate spline coefficients for feff data"""
self.spline_coefs = {}
fdat = self._feffdat
self.spline_coefs['pha'] = UnivariateSpline(fdat.k, fdat.pha, s=0)
self.spline_coefs['amp'] = UnivariateSpline(fdat.k, fdat.amp, s=0)
self.spline_coefs['rep'] = UnivariateSpline(fdat.k, fdat.rep, s=0)
self.spline_coefs['lam'] = UnivariateSpline(fdat.k, fdat.lam, s=0)
def store_feffdat(self):
"""stores data about this Feff path in the fiteval
symbol table for use as `reff` and in sigma2 calcs
"""
fiteval = self._larch.symtable._sys.fiteval
fdat = self._feffdat
fiteval.symtable['feffpath'] = fdat
fiteval.symtable['reff'] = fdat.reff
return fiteval
def __path_params(self, **kws):
"""evaluate path parameter value. Returns
(degen, s02, e0, ei, deltar, sigma2, third, fourth)
"""
# put 'reff' and '_feffdat' into the symboltable so that
# they can be used in constraint expressions, and get
# fiteval evaluator
self.store_feffdat()
if self.params is None:
self.create_path_params()
out = []
for pname in PATH_PARS:
val = kws.get(pname, None)
parname = fix_varname(PATHPAR_FMT % (pname, self.label))
if val is None:
val = self.params[parname]._getval()
out.append(val)
return out
def path_paramvals(self, **kws):
(deg, s02, e0, ei, delr, ss2, c3, c4) = self.__path_params()
return dict(degen=deg,
s02=s02,
e0=e0,
ei=ei,
deltar=delr,
sigma2=ss2,
third=c3,
fourth=c4)
def report(self):
"return text report of parameters"
(deg, s02, e0, ei, delr, ss2, c3, c4) = self.__path_params()
geomlabel = ' atom x y z ipot'
geomformat = ' %4s % .4f, % .4f, % .4f %i'
out = [' Path %s, Feff.dat file = %s' % (self.label, self.filename)]
out.append(geomlabel)
for atsym, iz, ipot, amass, x, y, z in self.geom:
s = geomformat % (atsym, x, y, z, ipot)
if ipot == 0: s = "%s (absorber)" % s
out.append(s)
stderrs = {}
out.append(' {:7s}= {:.5f}'.format('reff', self._feffdat.reff))
for pname in ('degen', 's02', 'e0', 'r', 'deltar', 'sigma2', 'third',
'fourth', 'ei'):
val = strval = getattr(self, pname, 0)
parname = fix_varname(PATHPAR_FMT % (pname, self.label))
std = None
if pname == 'r':
parname = fix_varname(PATHPAR_FMT % ('deltar', self.label))
par = self.params.get(parname, None)
val = par.value + self._feffdat.reff
strval = 'reff + ' + getattr(self, 'deltar', 0)
std = par.stderr
else:
par = self.params.get(parname, None)
if par is not None:
val = par.value
std = par.stderr
if std is None or std <= 0:
svalue = "{: 5f}".format(val)
else:
svalue = "{: 5f} +/- {:5f}".format(val, std)
if pname == 's02': pname = 'n*s02'
svalue = " {:7s}= {:s}".format(pname, svalue)
if isinstance(strval, six.string_types):
svalue = "{:s} '{:s}'".format(svalue, strval)
if val == 0 and pname in ('third', 'fourth', 'ei'):
continue
out.append(svalue)
return '\n'.join(out)
def _calc_chi(self,
k=None,
kmax=None,
kstep=None,
degen=None,
s02=None,
e0=None,
ei=None,
deltar=None,
sigma2=None,
third=None,
fourth=None,
debug=False,
interp='cubic',
**kws):
"""calculate chi(k) with the provided parameters"""
fdat = self._feffdat
if fdat.reff < 0.05:
self._larch.writer.write('reff is too small to calculate chi(k)')
return
# make sure we have a k array
if k is None:
if kmax is None:
kmax = 30.0
kmax = min(max(fdat.k), kmax)
if kstep is None: kstep = 0.05
k = kstep * np.arange(int(1.01 + kmax / kstep), dtype='float64')
reff = fdat.reff
# get values for all the path parameters
(degen, s02, e0, ei, deltar, sigma2, third, fourth) = \
self.__path_params(degen=degen, s02=s02, e0=e0, ei=ei,
deltar=deltar, sigma2=sigma2,
third=third, fourth=fourth)
# create e0-shifted energy and k, careful to look for |e0| ~= 0.
en = k * k - e0 * ETOK
if min(abs(en)) < SMALL:
try:
en[np.where(abs(en) < 2 * SMALL)] = SMALL
except ValueError:
pass
# q is the e0-shifted wavenumber
q = np.sign(en) * np.sqrt(abs(en))
# lookup Feff.dat values (pha, amp, rep, lam)
if interp.startswith('lin'):
pha = np.interp(q, fdat.k, fdat.pha)
amp = np.interp(q, fdat.k, fdat.amp)
rep = np.interp(q, fdat.k, fdat.rep)
lam = np.interp(q, fdat.k, fdat.lam)
else:
pha = self.spline_coefs['pha'](q)
amp = self.spline_coefs['amp'](q)
rep = self.spline_coefs['rep'](q)
lam = self.spline_coefs['lam'](q)
if debug:
self.debug_k = q
self.debug_pha = pha
self.debug_amp = amp
self.debug_rep = rep
self.debug_lam = lam
# p = complex wavenumber, and its square:
pp = (rep + 1j / lam)**2 + 1j * ei * ETOK
p = np.sqrt(pp)
# the xafs equation:
cchi = np.exp(-2 * reff * p.imag - 2 * pp *
(sigma2 - pp * fourth / 3) + 1j *
(2 * q * reff + pha + 2 * p *
(deltar - 2 * sigma2 / reff - 2 * pp * third / 3)))
cchi = degen * s02 * amp * cchi / (q * (reff + deltar)**2)
cchi[0] = 2 * cchi[1] - cchi[2]
# outputs:
self.k = k
self.p = p
self.chi = cchi.imag
self.chi_imag = -cchi.real
# =============================================================================
# get data
# =============================================================================
path_data = "../../data/"
df_fahey = pd.read_csv(path_data + "fahey_data.csv")
data_arm = df_fahey[df_fahey.name == "Arm"]
data_cl13 = df_fahey[df_fahey.name == "Cl13"]
# get model
sim = Sim(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
# =============================================================================
out = minimize(fit_fun, params, args=(sim, data_arm, data_cl13))
out_values = out.params.valuesdict()
print(out_values)
class LMFitModel():
"""
Wrapper class for the lmfit package. Acts both as module usable in
scripts as well as core logic class for the lmfit part in kMap.py.
For an example on how to use it please see the 'test_PTCDA' test in
the 'kmap.tests.test_lmfit' file.
ATTENTION: Please do not set any attributes manually. Instead use
the appropriate "set_xxx" method instead.
"""
def __init__(self, sliced_data, orbitals):
"""
Args:
sliced_data (SlicedData): A single SlicedData object.
orbitals (OrbitalData or list): A single OrbitalData object
or a list of OrbitalData objects.
ATTENTION: An Orbital object is NOT sufficient. Please
use the OrbitalData wrapping class instead.
"""
self.axis = None
self.crosshair = None
self.symmetrization = 'no'
self.background_equation = ['0', []]
self.Ak_type = 'no'
self.polarization = 'p'
self.slice_policy = [0, [0], False]
self.method = ['leastsq', 1e-12]
self.region = ['all', False]
self._set_sliced_data(sliced_data)
self._add_orbitals(orbitals)
self._set_parameters()
def set_crosshair(self, crosshair):
"""A setter method to set a custom crosshair. If none is set
when a region restriction is applied, a CrosshairAnnulusModel
will be created.
Args:
crosshair (CrosshairModel): A crosshair model for cutting
the data for any region-restriction.
ATTENTION: The passed CrosshairModel has to support the
region restriction you want to use.
"""
if crosshair is None or isinstance(crosshair, CrosshairModel):
self.crosshair = crosshair
else:
raise TypeError(
'crosshair has to be of type %s (is %s)' % (
type(CrosshairModel), type(crosshair)))
def set_axis(self, axis):
"""A setter method to set an axis for the interpolation onto a
common grid. Default is the x-axis of the first slice in the
list of slices chosen to be fitted.
Args:
axis (np.array): 1D array defining the common axis (and grid
as only square kmaps are supported) for the subtraction.
"""
self.axis = axis
def set_axis_by_step_size(self, range_, step_size):
"""A convenience setter method to set an axis by defining the
range and the step size.
Args:
range_ (list): A list of min and max value.
step_size (float): A number denoting the step size.
"""
num = step_size_to_num(range_, step_size)
self.set_axis(axis_from_range(range_, num))
def set_axis_by_num(self, range_, num):
"""A convenience setter method to set an axis by defining the
range and the number of grid points.
Args:
range_ (list): A list of min and max value.
num (int): An integer denoting the number of grid points.
"""
self.set_axis(axis_from_range(range_, num))
def set_symmetrization(self, symmetrization):
"""A setter method to set the type of symmetrization for the
orbital kmaps. Default is 'no'.
Args:
symmetrization (str): See 'get_kmap' from
'kmap.library.orbital.py' for information.
"""
self.symmetrization = symmetrization
def set_region(self, region, inverted=False):
"""A setter method to set the region restriction for the lmfit
process. Default is no region restriction ('all').
Args:
region (str): Supports all regions the crosshair model you
supplied supports. See there for documentation. (default
is a CrosshairAnnulusModel).
inverted (bool): See your CrosshairModel for documentation.
"""
self.region = [region, inverted]
if region != 'all' and self.crosshair is None:
self.crosshair = CrosshairAnnulusModel()
def set_polarization(self, Ak_type, polarization):
"""A setter method to set the type of polarization for the
orbital kmaps. Default is 'toroid' and 'p'.
Args:
Ak_type (str): See 'get_kmap' from
'kmap.library.orbital.py' for information.
polarization (str): See 'get_kmap' from
'kmap.library.orbital.py' for information.
"""
self.Ak_type = Ak_type
self.polarization = polarization
def set_slices(self, slice_indices, axis_index=0, combined=False):
"""A setter method to chose the slices to be fitted next time
'fit()' is called. Default is [0], 0 and False.
Args:
slice_indices (int or list or str): Either one or more
indices for the slices to be fitted next. Pass 'all' to use
all slices in this axis.
axis_index (int): Which axis in the SlicedData is used as
slice axis.
combined (bool): Whether to fit all slices individually or
add all the slices for one fit instead.
"""
if isinstance(slice_indices, str) and slice_indices == 'all':
self.slice_policy = [axis_index,
range(self.sliced_data.axes[axis_index].num),
combined]
elif isinstance(slice_indices, list):
self.slice_policy = [axis_index, slice_indices, combined]
elif isinstance(slice_indices, range):
self.slice_policy = [axis_index, list(slice_indices), combined]
else:
self.slice_policy = [axis_index, [slice_indices], combined]
def set_fit_method(self, method, xtol=1e-7):
"""A setter method to set the method and the tolerance for the
fitting process. Default is 'leastsq' and 1e-7.
Args:
method (str): See the documentation for the lmfit module.
polarization (str): See the documentation for the lmfit
module.
"""
self.method = [method, xtol]
def set_background_equation(self, equation):
"""A setter method to set an custom background equation.
Default is '1'.
Args:
equation (str): An equation used to calculate the background
profile. Can use python function (e.g. abs()) and basics
methods from the numpy module (prefix by 'np.';
e.g. np.sqrt()). Can contain variables to be fitted.
Variables have can only contain lower or upper case letters,
underscores and numbers. They cannot start with numbers.
The variables 'x' and 'y' are special and denote the x and
y axis respectively. No variables already used outside the
background equation (like phi) can be used.
Here are some examples of valid variable names:
x_s, x2, x_2, foo, this_is_a_valid_variable.
Each variables starts with following default values:
value=0, min=-99999.9, max=99999.9, vary=False, expr=None
The equation will be parsed by eval. Please don't injected
any code as it would be really easy to do so. There are no
safeguards in place whatsoever so we (have to) trust you.
Thanks, D.B.
"""
try:
compile(equation, '', 'exec')
except:
raise ValueError(
'Equation is not parseable. Check for syntax errors.')
# Pattern matches all numpy, math and builtin methods
clean_pattern = 'np\\.[a-z1-9\\_]+|math\\.[a-z1-9\\_]+'
for builtin in dir(builtins):
clean_pattern += '|' + str(builtin)
cleaned_equation = re.sub(clean_pattern, '', equation)
# Pattern matches all text including optional underscore with
# numbers.
variable_pattern = '[a-zA-Z\\_]+[0-9]*'
variables = list(set(re.findall(variable_pattern, cleaned_equation)))
# x and y need special treatment
if 'x' in variables:
variables.remove('x')
if 'y' in variables:
variables.remove('y')
new_variables = np.setdiff1d(variables, self.background_equation[1])
self.background_equation = [equation, variables]
for variable in new_variables:
self.parameters.add(variable, value=0, min=-99999.9,
max=99999.9, vary=False, expr=None)
return [self.parameters[variable] for variable in new_variables]
def edit_parameter(self, parameter, *args, **kwargs):
"""A setter method to edit fitting settings for one parameter.
Use this method to enable a parameter for fitting (vary=True)
Args:
parameter (str): Name of the parameter to be editted.
*args & **kwargs (): Are being passed to the
'parameter.set' method of the lmfit module. See there
for more documentation.
"""
self.parameters[parameter].set(*args, **kwargs)
def fit(self):
"""Calling this method will trigger a lmfit with the current
settings.
Returns:
(list): A list of MinimizerResults. One for each slice
fitted.
"""
lmfit_padding = float(config.get_key('lmfit', 'padding'))
for parameter in self.parameters.values():
if parameter.vary and parameter.value <= parameter.min:
padded_value = parameter.min + lmfit_padding
print('WARNING: Initial value for parameter \'%s\' had to be corrected to %f (was %f)' % (
parameter.name, padded_value, parameter.value))
parameter.value = padded_value
results = []
for index in self.slice_policy[1]:
slice_ = self.get_sliced_kmap(index)
result = minimize(self._chi2,
copy.deepcopy(self.parameters),
kws={'slice_': slice_},
nan_policy='omit',
method=self.method[0],
xtol=self.method[1])
results.append([index, result])
return results
def transpose(self, constant_axis):
axis_order = transpose_axis_order(constant_axis)
self.sliced_data.transpose(axis_order)
def get_settings(self):
settings = {'crosshair': self.crosshair,
'background': self.background_equation,
'symmetrization': self.symmetrization,
'polarization': [self.Ak_type, self.polarization],
'slice_policy': self.slice_policy,
'method': self.method,
'region': self.region,
'axis': self.axis}
return copy.deepcopy(settings)
def set_settings(self, settings):
self.set_crosshair(settings['crosshair'])
self.set_background_equation(settings['background'][0])
self.set_polarization(*settings['polarization'])
slice_policy = settings['slice_policy']
self.set_slices(slice_policy[1], slice_policy[0], slice_policy[2])
self.set_region(*settings['region'])
self.set_symmetrization(settings['symmetrization'])
self.set_fit_method(*settings['method'])
self.set_axis(settings['axis'])
def get_sliced_kmap(self, slice_index):
axis_index, slice_indices, is_combined = self.slice_policy
if is_combined:
kmaps = []
for slice_index in slice_indices:
kmaps.append(self.sliced_data.slice_from_index(slice_index,
axis_index))
kmap = np.nansum(kmaps, axis=axis_index)
else:
kmap = self.sliced_data.slice_from_index(slice_index,
axis_index)
if self.axis is not None:
kmap = kmap.interpolate(self.axis, self.axis)
else:
self.axis = kmap.x_axis
return kmap
def get_orbital_kmap(self, ID, param=None):
if param is None:
param = self.parameters
orbital = self.ID_to_orbital(ID)
kmap = orbital.get_kmap(E_kin=param['E_kin'].value,
dk=(self.axis, self.axis),
phi=param['phi_' + str(ID)].value,
theta=param['theta_' + str(ID)].value,
psi=param['psi_' + str(ID)].value,
alpha=param['alpha'].value,
beta=param['beta'].value,
Ak_type=self.Ak_type,
polarization=self.polarization,
symmetrization=self.symmetrization)
return kmap
def get_weighted_sum_kmap(self, param=None, with_background=True):
if param is None:
param = self.parameters
orbital_kmaps = []
for orbital in self.orbitals:
ID = orbital.ID
weight = param['w_' + str(ID)].value
kmap = weight * self.get_orbital_kmap(ID, param)
orbital_kmaps.append(kmap)
orbital_kmap = np.nansum(orbital_kmaps)
if with_background:
variables = {}
for variable in self.background_equation[1]:
variables.update({variable: param[variable].value})
background = self._get_background(variables)
return orbital_kmap + background
else:
return orbital_kmap
def get_residual(self, slice_, param=None, weight_sum_data=None):
if param is None:
param = self.parameters
if weight_sum_data is None:
orbital_kmap = self.get_weighted_sum_kmap(param)
else:
orbital_kmap = weight_sum_data
if isinstance(slice_, int):
sliced_kmap = self.get_sliced_kmap(slice_)
residual = sliced_kmap - orbital_kmap
else:
residual = slice_ - orbital_kmap
residual = self._cut_region(residual)
return residual
def get_reduced_chi2(self, slice_index, weight_sum_data=None):
n = self._get_degrees_of_freedom()
residual = self.get_residual(
slice_index, weight_sum_data=weight_sum_data)
reduced_chi2 = get_reduced_chi2(residual.data, n)
return reduced_chi2
def ID_to_orbital(self, ID):
for orbital in self.orbitals:
if orbital.ID == ID:
return orbital
return None
def _chi2(self, param=None, slice_=0):
if param is None:
param = self.parameters
residual = self.get_residual(slice_, param)
return residual.data
def _get_degrees_of_freedom(self):
n = 0
for parameter in self.parameters.values():
if parameter.vary:
n += 1
return n
def _get_background(self, variables=[]):
variables.update({'x': self.axis, 'y': np.array([self.axis]).T})
background = eval(self.background_equation[0], None, variables)
return background
def _cut_region(self, data):
if self.crosshair is None or self.region[0] == 'all':
return data
else:
return self.crosshair.cut_from_data(
data, region=self.region[0], inverted=self.region[1])
def _set_sliced_data(self, sliced_data):
if isinstance(sliced_data, SlicedData):
self.sliced_data = sliced_data
else:
raise TypeError(
'sliced_data has to be of type %s (is %s)' % (
type(SlicedData), type(sliced_data)))
def _add_orbitals(self, orbitals):
if (isinstance(orbitals, list) and
all(isinstance(element, OrbitalData)
for element in orbitals)):
self.orbitals = orbitals
elif isinstance(orbitals, OrbitalData):
self.orbitals = [orbitals]
else:
raise TypeError(
'orbital has to be of (or list of) type %s (is %s)' % (
type(OrbitalData), type(orbitals)))
def _set_parameters(self):
self.parameters = Parameters()
for orbital in self.orbitals:
ID = orbital.ID
self.parameters.add('w_' + str(ID), value=1,
min=0, vary=False, expr=None)
for angle in ['phi_', 'theta_', 'psi_']:
self.parameters.add(angle + str(ID), value=0,
min=90, max=-90, vary=False, expr=None)
# LMFit doesn't work when the initial value is exactly the same
# as the minimum value. For this reason the initial value will
# be set ever so slightly above 0 to circumvent this problem.
self.parameters.add('c', value=0,
min=0, vary=False, expr=None)
self.parameters.add('E_kin', value=30,
min=5, max=150, vary=False, expr=None)
for angle in ['alpha', 'beta']:
self.parameters.add(angle, value=0,
min=90, max=-90, vary=False, expr=None)
def _fit_punkt(n):
"""
:type n: int
:return: Gefittete Amplitude und gefittete oder geglättete Phase im Bereich um Resonanzfrequenz +/- Versatz
:rtype: list
"""
if not _weiter:
return None
# ----------------------------------------
# ----------- AMPLITUDE fitten -----------
# ----------------------------------------
amplitude = savgol_filter(_bereich(_amplitude_voll[n]), _par.filter_breite,
_par.filter_ordnung)
index_max = numpy.argmax(amplitude)
start_freq = _frequenz[index_max]
start_amp = amplitude[index_max]
start_off = amplitude[
0] # Erster betrachteter Wert ist bereits eine gute Näherung für den Untergrund
# Fitparameter für die Fitfunktion
par_amp = Parameters()
par_amp.add('resfreq', value=start_freq, min=_par.fmin, max=_par.fmax)
par_amp.add('amp', value=start_amp, min=_par.amp_min, max=_par.amp_max)
par_amp.add('guete',
value=0.5 * (_par.amp.guete_max + _par.amp.guete_min),
min=_par.amp.guete_min,
max=_par.amp.guete_max)
par_amp.add('untergrund',
value=start_off,
min=_par.amp.off_min,
max=_par.amp.off_max)
amp = _mod_amp.fit(data=amplitude,
freq=_frequenz,
params=par_amp,
fit_kws=_fit_genauigkeit)
_puls(n)
# Wenn keine Phase gefittet werden soll:
if _mod_ph is KEIN_FIT:
return Ergebnis(amp=amp.params['amp'].value,
amp_fhlr=amp.params['amp'].stderr,
resfreq=amp.params['resfreq'].value,
resfreq_fhlr=amp.params['resfreq'].stderr,
guete_amp=amp.params['guete'].value,
guete_amp_fhlr=amp.params['guete'].stderr,
untergrund=amp.best_values['untergrund'])
# Resonanzfrequenz
resfreq = amp.best_values['resfreq']
# ----------------------------------------
# ------------- PHASE fitten -------------
# ----------------------------------------
halb = abs(_par.phase_versatz
) + 10 * _par.df # Halbe Frequenzbreite des Phasenversatzes
# +df, weil der Fit auch bei Versatz = 0 funktionieren muss
von = resfreq - halb # Untere Versatzgrenze
bis = resfreq + halb # Obere Versatzgrenze
if von < _par.fmin: # Die Resonanzfrequenz liegt zu weit links:
# Auswahlbereich nach rechts verschieben, aber nicht über den Frequenzbereich hinaus
bis = min(bis - von + _par.fmin, _par.fmax)
von = _par.fmin
elif bis > _par.fmax: # Die Resonanz lieg zu weit rechts:
von = max(von - bis + _par.fmax,
_par.fmin) # Verschieben, aber nicht über linken Rand hinaus
bis = _par.fmax
# Phase beschneiden
index_von = index_freq(_par, von)
index_bis = index_freq(_par, bis)
wahl_phase = _bereich(_phase_voll[n])[index_von:index_bis]
if _mod_ph is GLAETTEN: # Nur glätten:
phase = savgol_filter(wahl_phase, _par.filter_breite,
_par.filter_ordnung)
return Ergebnis(amp=amp.params['amp'].value,
amp_fhlr=amp.params['amp'].stderr,
resfreq=amp.params['resfreq'].value,
resfreq_fhlr=amp.params['resfreq'].stderr,
guete_amp=amp.params['guete'].value,
guete_amp_fhlr=amp.params['guete'].stderr,
untergrund=amp.best_values['untergrund'],
phase=randwert(phase, _par.phase_versatz))
else:
# Fitparameter für die Fitfunktion
par_ph = Parameters()
par_ph.add('resfreq', value=resfreq, min=von, max=bis)
par_ph.add('guete',
value=3,
min=_par.phase.guete_min,
max=_par.phase.guete_max)
par_ph.add('rel',
value=200,
min=_par.phase.off_min,
max=_par.phase.off_max)
ph = _mod_ph.fit(
data=wahl_phase,
freq=_frequenz[index_von:index_bis],
params=par_ph,
method='cg' # 'differential_evolution' passt auch gut
# TODO fit_kws=self.fit_genauigkeit
)
return Ergebnis(amp=amp.params['amp'].value,
amp_fhlr=amp.params['amp'].stderr,
resfreq=amp.params['resfreq'].value,
resfreq_fhlr=amp.params['resfreq'].stderr,
guete_amp=amp.params['guete'].value,
guete_amp_fhlr=amp.params['guete'].stderr,
untergrund=amp.best_values['untergrund'],
phase=randwert(ph.best_fit, _par.phase_versatz),
guete_ph=ph.best_values['guete'],
phase_rel=ph.best_values['rel'],
phase_fhlr=ph.params['resfreq'].stderr)
def formatParameters(rVec, tVec, linearCoeffs, distCoeffs):
'''
puts all intrinsic and extrinsic parameters in Parameters() format
if there are several extrinsica paramters they are correctly
Inputs
rVec, tVec : arrays of shape (n,3,1) or (3,1)
distCoeffs must have be reshapable to (5)
'''
params = Parameters()
if prod(rVec.shape) == 9:
rVec = Rodrigues(rVec)[0]
rVec = rVec.reshape(3)
for i in range(3):
params.add('rvec%d' % i, value=rVec[i], vary=False)
params.add('tvec%d' % i, value=tVec[i], vary=False)
if len(rVec.shape) == 3:
for j in range(len(rVec)):
for i in range(3):
params.add('rvec%d%d' % (j, i),
value=rVec[j, i, 0],
vary=False)
params.add('tvec%d%d' % (j, i),
value=tVec[j, i, 0],
vary=False)
params.add('fX', value=linearCoeffs[0, 0], vary=False)
params.add('fY', value=linearCoeffs[1, 1], vary=False)
params.add('cX', value=linearCoeffs[0, 2], vary=False)
params.add('cY', value=linearCoeffs[1, 2], vary=False)
# (k1,k2,p1,p2[,k3[,k4,k5,k6[,s1,s2,s3,s4[,τx,τy]]]])
distCoeffs = distCoeffs.reshape(5)
for i in range(5):
params.add('distCoeffs%d' % i, value=distCoeffs[i], vary=False)
return params
def helium_abundance_elementalScheme(self,
Te,
ne,
lineslog_frame,
metal_ext=''):
#Check temperatures are not nan before starting the treatment
if (not isinstance(Te, float)) and (not isinstance(ne, float)):
#HeI_indices = (lineslog_frame.Ion.str.contains('HeI_')) & (lineslog_frame.index != 'He1_8446A') & (lineslog_frame.index != 'He1_7818A') & (lineslog_frame.index != 'He1_5016A')
HeI_indices = (lineslog_frame.Ion.str.contains('HeI_')) & (
lineslog_frame.index.isin(
['He1_4472A', 'He1_5876A', 'He1_6678A']))
HeI_labels = lineslog_frame.loc[HeI_indices].index.values
HeI_ions = lineslog_frame.loc[HeI_indices].Ion.values
Emis_Hbeta = self.H1_atom.getEmissivity(tem=Te,
den=ne,
label='4_2',
product=False)
#--Generating matrices with fluxes and emissivities
for i in range(len(HeI_labels)):
pyneb_code = float(HeI_ions[i][HeI_ions[i].find('_') +
1:len(HeI_ions[i])])
line_relative_Flux = self.lines_dict[
HeI_labels[i]] / self.Hbeta_flux
line_relative_emissivity = self.He1_atom.getEmissivity(
tem=Te, den=ne, wave=pyneb_code,
product=False) / Emis_Hbeta
line_relative_emissivity = self.check_nan_entries(
line_relative_emissivity)
if i == 0:
matrix_HeI_fluxes = copy(line_relative_Flux)
matrix_HeI_emis = copy(line_relative_emissivity)
else:
matrix_HeI_fluxes = vstack(
(matrix_HeI_fluxes, line_relative_Flux))
matrix_HeI_emis = vstack(
(matrix_HeI_emis, line_relative_emissivity))
matrix_HeI_fluxes = transpose(matrix_HeI_fluxes)
matrix_HeI_emis = transpose(matrix_HeI_emis)
#Perform the fit
params = Parameters()
params.add('Y', value=0.01)
HeII_HII_array = zeros(len(matrix_HeI_fluxes))
HeII_HII_error = zeros(len(matrix_HeI_fluxes))
for i in range(len(matrix_HeI_fluxes)):
fit_Output = lmfit_minimmize(residual_Y_v3,
params,
args=(matrix_HeI_emis[i],
matrix_HeI_fluxes[i]))
HeII_HII_array[i] = fit_Output.params['Y'].value
HeII_HII_error[i] = fit_Output.params['Y'].stderr
#NO SUMANDO LOS ERRORES CORRECTOS?
#self.abunData['HeII_HII_from_' + metal_ext] = random.normal(mean(HeII_HII_array), mean(HeII_HII_error), size = self.MC_array_len)
ionic_abund = random.normal(mean(HeII_HII_array),
mean(HeII_HII_error),
size=self.MC_array_len)
#Evaluate the nan array
nan_count = np_sum(isnan(ionic_abund))
if nan_count == 0:
self.abunData['HeII_HII_from_' + metal_ext] = ionic_abund
#Remove the nan entries performing a normal distribution
elif nan_count < 0.90 * self.MC_array_len:
mag, error = nanmean(ionic_abund), nanstd(ionic_abund)
self.abunData['HeII_HII_from_' + metal_ext] = random.normal(
mag, error, size=self.MC_array_len)
if nan_count > self.MC_warning_limit:
print '-- {} calculated with {}'.format(
'HeII_HII_from_' + metal_ext, nan_count)
#Calculate the He+2 abundance
if self.lines_dict.viewkeys() >= {'He2_4686A'}:
#self.abunData['HeIII_HII_from_' + metal_ext] = self.He2_atom.getIonAbundance(int_ratio = self.lines_dict['He2_4686A'], tem=Te, den=ne, wave = 4685.6, Hbeta = self.Hbeta_flux)
self.determine_ionic_abundance('HeIII_HII_from_' + metal_ext,
self.He2_atom, 'L(4685)',
self.lines_dict['He2_4686A'],
Te, ne)
#Calculate elemental abundance
Helium_element_keys = [
'HeII_HII_from_' + metal_ext, 'HeIII_HII_from_' + metal_ext
]
if set(self.abunData.index) >= set(Helium_element_keys):
self.abunData['HeI_HI_from_' +
metal_ext] = self.abunData[Helium_element_keys[
0]] + self.abunData[Helium_element_keys[1]]
else:
self.abunData['HeI_HI_from_' + metal_ext] = self.abunData[
Helium_element_keys[0]]
#Proceed to get the Helium mass fraction Y
Element_abund = metal_ext + 'I_HI'
Y_fraction, Helium_abund = 'Ymass_' + metal_ext, 'HeI_HI_from_' + metal_ext
if set(self.abunData.index) >= {Helium_abund, Element_abund}:
self.abunData[Y_fraction] = (
4 * self.abunData[Helium_abund] *
(1 - 20 * self.abunData[Element_abund])) / (
1 + 4 * self.abunData[Helium_abund])
print("Max surface strain = {:.5f}".format(strain[np.nonzero(surface)].max()))
hist, bin_edges = np.histogram(
strain[np.nonzero(surface)],
bins=int(
(strain[np.nonzero(surface)].max() - strain[np.nonzero(surface)].min())
/ bin_step),
)
hist = hist.astype(float)
if normalize:
hist = hist / nb_surface # normalize the histogram to the number of points
x_axis = bin_edges[:-1] + (bin_edges[1] - bin_edges[0]) / 2
fit_params = Parameters()
if fit_pdf == "skewed_gaussian":
fit_params.add("amp_0", value=0.0005, min=0.000001, max=10000)
fit_params.add("loc_0", value=0, min=-0.1, max=0.1)
fit_params.add("sig_0", value=0.0005, min=0.0000001, max=0.1)
fit_params.add("alpha_0", value=0, min=-10, max=10)
else: # 'pseudovoigt'
fit_params.add("amp_0", value=0.0005, min=0.000001, max=10000)
fit_params.add("cen_0", value=0, min=-0.1, max=0.1)
fit_params.add("sig_0", value=0.0005, min=0.0000001, max=0.1)
fit_params.add("ratio_0", value=0.5, min=0, max=1)
# run the global fit to all the data sets
result = minimize(util.objective_lmfit,
fit_params,
args=(x_axis, hist, fit_pdf))
report_fit(result.params)
strain_fit = util.function_lmfit(params=result.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)
