def dask_fit_fourier_pl_c(power_spectrum):
"""
Fits the power law + constant observation model
Parameters
----------
power_spectrum :
Return
------
"""
# Make the random data into a Powerspectrum object
ps = Powerspectrum()
ps.freq = power_spectrum[0]
ps.power = power_spectrum[1]
ps.df = ps.freq[1] - ps.freq[0]
ps.m = 1
# Define the log-likelihood of the data given the model
loglike = PSDLogLikelihood(ps.freq, ps.power, observation_model, m=ps.m)
# Parameter estimation object
parameter_estimate = PSDParEst(ps, fitmethod="L-BFGS-B", max_post=False)
# Estimate the starting parameters
ipe = InitialParameterEstimatePlC(ps.freq, ps.power)
return parameter_estimate.fit(loglike, [ipe.amplitude, ipe.index, ipe.background],
scipy_optimize_options=scipy_optimize_options)
def test_fit_method_returns_optimization_results_object(self):
pe = PSDParEst(self.ps)
lpost = PSDPosterior(self.ps, self.model, self.priors)
t0 = [2.0, 1, 1, 1]
res = pe.fit(self.lpost, t0)
assert isinstance(res, OptimizationResults), "res must be of type " \
"OptimizationResults"
def test_fit_method_works_with_correct_parameter(self):
pe = PSDParEst(self.ps)
lpost = PSDPosterior(self.ps.freq, self.ps.power,
self.model, self.priors, m=self.ps.m)
t0 = [2.0, 1, 1, 1]
res = pe.fit(lpost, t0)
assert isinstance(res, OptimizationResults), "res must be of type " \
"OptimizationResults"
pe.plotfits(res, save_plot=True)
assert os.path.exists("test_ps_fit.png")
os.unlink("test_ps_fit.png")
pe.plotfits(res, save_plot=True, log=True)
assert os.path.exists("test_ps_fit.png")
os.unlink("test_ps_fit.png")
pe.plotfits(res, res2=res, save_plot=True)
assert os.path.exists("test_ps_fit.png")
os.unlink("test_ps_fit.png")
pe.plotfits(res, res2=res, log=True, save_plot=True)
assert os.path.exists("test_ps_fit.png")
os.unlink("test_ps_fit.png")
def test_simulate_highest_outlier_works(self):
m = 1
nfreq = 100000
seed = 100
freq = np.linspace(1, 10, nfreq)
rng = np.random.RandomState(seed)
noise = rng.exponential(size=nfreq)
model = models.Const1D()
model.amplitude = 2.0
p = model(freq)
power = noise * p
ps = Powerspectrum()
ps.freq = freq
ps.power = power
ps.m = m
ps.df = freq[1] - freq[0]
ps.norm = "leahy"
nsim = 10
loglike = PSDLogLikelihood(ps.freq, ps.power, model, m=1)
s_all = np.atleast_2d(np.ones(nsim) * 2.0).T
pe = PSDParEst(ps)
res = pe.fit(loglike, [2.0], neg=True)
maxpow_sim = pe.simulate_highest_outlier(s_all, loglike, [2.0],
max_post=False, seed=seed)
assert maxpow_sim.shape[0] == nsim
assert np.all(maxpow_sim > 20.00) and np.all(maxpow_sim < 31.0)
def test_compute_highest_outlier_works(self):
mp_ind = 5
max_power = 1000.0
ps = Powerspectrum()
ps.freq = np.arange(10)
ps.power = np.ones_like(ps.freq)
ps.power[mp_ind] = max_power
ps.m = 1
ps.df = ps.freq[1]-ps.freq[0]
ps.norm = "leahy"
model = models.Const1D()
p_amplitude = lambda amplitude: \
scipy.stats.norm(loc=1.0, scale=1.0).pdf(
amplitude)
priors = {"amplitude": p_amplitude}
lpost = PSDPosterior(ps.freq, ps.power, model, 1)
lpost.logprior = set_logprior(lpost, priors)
pe = PSDParEst(ps)
res = pe.fit(lpost, [1.0])
res.mfit = np.ones_like(ps.freq)
max_y, max_x, max_ind = pe._compute_highest_outlier(lpost, res)
assert np.isclose(max_y[0], 2*max_power)
assert np.isclose(max_x[0], ps.freq[mp_ind])
assert max_ind == mp_ind
def test_fit_method_returns_optimization_results_object(self):
pe = PSDParEst(self.ps)
t0 = [2.0, 1, 1, 1]
res = pe.fit(self.lpost, t0)
assert isinstance(res, OptimizationResults), "res must be of type " \
"OptimizationResults"
def test_compute_highest_outlier_works(self):
mp_ind = 5
max_power = 1000.0
ps = Powerspectrum()
ps.freq = np.arange(10)
ps.power = np.ones_like(ps.freq)
ps.power[mp_ind] = max_power
ps.m = 1
ps.df = ps.freq[1]-ps.freq[0]
ps.norm = "leahy"
model = models.Const1D()
p_amplitude = lambda amplitude: \
scipy.stats.norm(loc=1.0, scale=1.0).pdf(
amplitude)
priors = {"amplitude": p_amplitude}
lpost = PSDPosterior(ps.freq, ps.power, model, 1)
lpost.logprior = set_logprior(lpost, priors)
pe = PSDParEst(ps)
res = pe.fit(lpost, [1.0])
res.mfit = np.ones_like(ps.freq)
max_y, max_x, max_ind = pe._compute_highest_outlier(lpost, res)
assert np.isclose(max_y[0], 2*max_power)
assert np.isclose(max_x[0], ps.freq[mp_ind])
assert max_ind == mp_ind
def test_fit_method_works_with_correct_parameter(self):
pe = PSDParEst(self.ps)
lpost = PSDPosterior(self.ps.freq,
self.ps.power,
self.model,
self.priors,
m=self.ps.m)
t0 = [2.0, 1, 1, 1]
res = pe.fit(lpost, t0)
def test_plotfits_log_leahy(self):
pe = PSDParEst(self.ps)
t0 = [2.0, 1, 1, 1]
res = pe.fit(self.lpost, t0)
pe.plotfits(res, save_plot=True, log=True)
assert os.path.exists("test_ps_fit.png")
os.unlink("test_ps_fit.png")
def test_plotfits_leahy(self):
pe = PSDParEst(self.ps)
t0 = [2.0, 1, 1, 1]
lpost = PSDPosterior(self.ps, self.model, self.priors)
res = pe.fit(lpost, t0)
pe.plotfits(res, save_plot=True)
assert os.path.exists("test_ps_fit.png")
os.unlink("test_ps_fit.png")
def test_plotfits_leahy(self):
pe = PSDParEst(self.ps)
t0 = [2.0, 1, 1, 1]
lpost = PSDPosterior(self.ps.freq, self.ps.power,
self.model, self.priors, m=self.ps.m)
res = pe.fit(lpost, t0)
pe.plotfits(res, save_plot=True)
assert os.path.exists("test_ps_fit.png")
os.unlink("test_ps_fit.png")
def test_fitting_with_ties_and_bounds(self, capsys):
double_f = lambda model: model.x_0_0 * 2
model = self.model.copy()
model = self.model + models.Lorentz1D(amplitude=model.amplitude_0,
x_0=model.x_0_0 * 2,
fwhm=model.fwhm_0)
model.x_0_0 = self.model.x_0_0
model.amplitude_0 = self.model.amplitude_0
model.amplitude_1 = self.model.amplitude_1
model.fwhm_0 = self.model.fwhm_0
model.x_0_2.tied = double_f
model.fwhm_0.bounds = [0, 10]
model.amplitude_0.fixed = True
p = model(self.ps.freq)
noise = np.random.exponential(size=len(p))
power = noise * p
ps = Powerspectrum()
ps.freq = self.ps.freq
ps.power = power
ps.m = self.ps.m
ps.df = self.ps.df
ps.norm = "leahy"
pe = PSDParEst(ps)
llike = PSDLogLikelihood(ps.freq, ps.power, model)
true_pars = [
self.amplitude_0, self.x_0_0, self.fwhm_0, self.amplitude_1,
model.amplitude_2.value, model.x_0_2.value, model.fwhm_2.value
]
res = pe.fit(llike, true_pars)
res.print_summary(llike)
out, err = capsys.readouterr()
assert "100.00000 (Fixed)" in out
pattern = \
re.compile(r"5\) Parameter x_0_2\s+: [0-9]\.[0-9]{5}\s+\(Tied\)")
assert pattern.search(out)
compare_pars = [
self.x_0_0, self.fwhm_0, self.amplitude_1, model.amplitude_2.value,
model.fwhm_2.value
]
assert np.all(np.isclose(compare_pars, res.p_opt, rtol=0.5))
def test_plotfits_log_pow(self):
ps = Powerspectrum()
ps.freq = self.ps.freq
ps.power = self.ps.power
ps.m = self.ps.m
ps.df = self.ps.df
ps.norm = "none"
pe = PSDParEst(ps)
t0 = [2.0, 1, 1, 1]
res = pe.fit(self.lpost, t0)
pe.plotfits(res, res2=res, save_plot=True, log=True)
assert os.path.exists("test_ps_fit.png")
os.unlink("test_ps_fit.png")
def test_plotfits_pow(self):
t0 = [2.0, 1, 1, 1]
ps = Powerspectrum()
ps.freq = self.ps.freq
ps.power = self.ps.power
ps.m = self.ps.m
ps.df = self.ps.df
ps.norm = "none"
pe = PSDParEst(ps)
lpost = PSDPosterior(self.ps, self.model, self.priors)
res = pe.fit(self.lpost, t0)
pe.plotfits(res, res2=res, save_plot=True)
assert os.path.exists("test_ps_fit.png")
os.unlink("test_ps_fit.png")
def test_fitting_with_ties_and_bounds(self, capsys, rebin):
double_f = lambda model : model.x_0_0 * 2
model = self.model.copy()
model += models.Lorentz1D(amplitude=model.amplitude_0,
x_0 = model.x_0_0 * 2,
fwhm = model.fwhm_0)
model.x_0_0 = self.model.x_0_0
model.amplitude_0 = self.model.amplitude_0
model.amplitude_1 = self.model.amplitude_1
model.fwhm_0 = self.model.fwhm_0
model.x_0_2.tied = double_f
model.fwhm_0.bounds = [0, 10]
model.amplitude_0.fixed = True
p = model(self.ps.freq)
noise = np.random.exponential(size=len(p))
power = noise*p
ps = Powerspectrum()
ps.freq = self.ps.freq
ps.power = power
ps.m = self.ps.m
ps.df = self.ps.df
ps.norm = "leahy"
if rebin != 0:
ps = ps.rebin_log(rebin)
pe = PSDParEst(ps, fitmethod="TNC")
llike = PSDLogLikelihood(ps.freq, ps.power, model)
true_pars = [self.x_0_0, self.fwhm_0,
self.amplitude_1,
model.amplitude_2.value,
model.fwhm_2.value]
res = pe.fit(llike, true_pars, neg=True)
compare_pars = [self.x_0_0, self.fwhm_0,
self.amplitude_1,
model.amplitude_2.value,
model.fwhm_2.value]
assert np.allclose(compare_pars, res.p_opt, rtol=0.5)
def test_fitting_with_ties_and_bounds(self, capsys):
double_f = lambda model : model.x_0_0 * 2
model = self.model.copy()
model += models.Lorentz1D(amplitude=model.amplitude_0,
x_0 = model.x_0_0 * 2,
fwhm = model.fwhm_0)
model.x_0_0 = self.model.x_0_0
model.amplitude_0 = self.model.amplitude_0
model.amplitude_1 = self.model.amplitude_1
model.fwhm_0 = self.model.fwhm_0
model.x_0_2.tied = double_f
model.fwhm_0.bounds = [0, 10]
model.amplitude_0.fixed = True
p = model(self.ps.freq)
noise = np.random.exponential(size=len(p))
power = noise*p
ps = Powerspectrum()
ps.freq = self.ps.freq
ps.power = power
ps.m = self.ps.m
ps.df = self.ps.df
ps.norm = "leahy"
pe = PSDParEst(ps, fitmethod="TNC")
llike = PSDLogLikelihood(ps.freq, ps.power, model)
true_pars = [self.x_0_0, self.fwhm_0,
self.amplitude_1,
model.amplitude_2.value,
model.fwhm_2.value]
res = pe.fit(llike, true_pars, neg=True)
compare_pars = [self.x_0_0, self.fwhm_0,
self.amplitude_1,
model.amplitude_2.value,
model.fwhm_2.value]
assert np.allclose(compare_pars, res.p_opt, rtol=0.5)
ps.freq = freq
ps.power = powers
ps.df = ps.freq[1] - ps.freq[0]
ps.m = 1
# Define the log-likelihood of the data given the model
loglike = PSDLogLikelihood(ps.freq,
ps.power,
observation_model,
m=ps.m)
# Parameter estimation object
parameter_estimate = PSDParEst(ps,
fitmethod="L-BFGS-B",
max_post=False)
# Estimate the starting parameters - will be replaced with a function
# starting_parameters = starting_parameter_selector(model_name)
starting_pars = [
amplitude, alpha, white_noise, ll_amplitude, ll_log_x_0, ll_fwhm
]
# Do the fit and store the results
z.append(parameter_estimate.fit(loglike, starting_pars))
t_end = Time.now()
print('Time taken ', (t_end - t_start).to(u.s))
# Save the results
#sp.save('/Users/Desktop/')
# flat prior for the power law amplitude
p_amplitude = lambda amplitude: ((0.01 <= amplitude) & (amplitude <= 10.0))
# normal prior for the white noise parameter
p_whitenoise = lambda white_noise: scipy.stats.norm(2.0, 0.1).pdf(white_noise)
priors = {}
priors["alpha_0"] = p_alpha
priors["amplitude_0"] = p_amplitude
priors["amplitude_1"] = p_whitenoise
starting_pars = [3.0, 1.0, 2.4]
lpost = PSDPosterior(ps.freq, ps.power, plc, priors=priors, m=ps.m)
parest = PSDParEst(ps, fitmethod='BFGS', max_post=True)
res = parest.fit(lpost, starting_pars)
sample = parest.sample(lpost,
res.p_opt,
cov=res.cov,
nwalkers=400,
niter=100,
burnin=200,
namestr="psd_modeling_test")
max_power, max_freq, max_ind = parest._compute_highest_outlier(lpost, res)
print(max_power)
pval = parest.calibrate_highest_outlier(lpost,
starting_pars,
sample=sample,
max_post=True,
def test_fit_fails_when_object_is_not_posterior_or_likelihood(self):
x = np.ones(10)
y = np.ones(10)
pe = PSDParEst(self.ps)
with pytest.raises(TypeError):
res = pe.fit(x, y)
def test_fit_fails_without_t0(self):
pe = PSDParEst(self.ps)
with pytest.raises(TypeError):
res = pe.fit(np.ones(10))
def fit_powerspectrum(ps, model, starting_pars=None, max_post=False,
priors=None, fitmethod="L-BFGS-B"):
"""
Fit a number of Lorentzians to a power spectrum, possibly including white
noise. Each Lorentzian has three parameters (amplitude, centroid position,
full-width at half maximum), plus one extra parameter if the white noise
level should be fit as well. Priors for each parameter can be included in
case `max_post = True`, in which case the function will attempt a
Maximum-A-Posteriori fit. Priors must be specified as a dictionary with one
entry for each parameter.
The parameter names are `(amplitude_i, x_0_i, fwhm_i)` for each `i` out of
a total of `N` Lorentzians. The white noise level has a parameter
`amplitude_(N+1)`. For example, a model with two Lorentzians and a
white noise level would have parameters:
[amplitude_0, x_0_0, fwhm_0, amplitude_1, x_0_1, fwhm_1, amplitude_2].
Parameters
----------
ps : Powerspectrum
A Powerspectrum object with the data to be fit
model: astropy.modeling.models class instance
The parametric model supposed to represent the data. For details
see the astropy.modeling documentation
starting_pars : iterable, optional, default None
The list of starting guesses for the optimizer. If it is not provided,
then default parameters are taken from `model`. See explanation above
for ordering of parameters in this list.
fit_whitenoise : bool, optional, default True
If True, the code will attempt to fit a white noise level along with
the Lorentzians. Be sure to include a starting parameter for the
optimizer in `starting_pars`!
max_post : bool, optional, default False
If True, perform a Maximum-A-Posteriori fit of the data rather than a
Maximum Likelihood fit. Note that this requires priors to be specified,
otherwise this will cause an exception!
priors : {dict | None}, optional, default None
Dictionary with priors for the MAP fit. This should be of the form
{"parameter name": probability distribution, ...}
fitmethod : string, optional, default "L-BFGS-B"
Specifies an optimization algorithm to use. Supply any valid option for
`scipy.optimize.minimize`.
Returns
-------
parest : PSDParEst object
A PSDParEst object for further analysis
res : OptimizationResults object
The OptimizationResults object storing useful results and quantities
relating to the fit
Examples
--------
We start by making an example power spectrum with three Lorentzians
>>> m = 1
>>> nfreq = 100000
>>> freq = np.linspace(1, 1000, nfreq)
>>> np.random.seed(100) # set the seed for the random number generator
>>> noise = np.random.exponential(size=nfreq)
>>> model = models.PowerLaw1D() + models.Const1D()
>>> model.x_0_0.fixed = True
>>> alpha_0 = 2.0
>>> amplitude_0 = 100.0
>>> amplitude_1 = 2.0
>>> model.alpha_0 = alpha_0
>>> model.amplitude_0 = amplitude_0
>>> model.amplitude_1 = amplitude_1
>>> p = model(freq)
>>> power = noise * p
>>> ps = Powerspectrum()
>>> ps.freq = freq
>>> ps.power = power
>>> ps.m = m
>>> ps.df = freq[1] - freq[0]
>>> ps.norm = "leahy"
Now we have to guess starting parameters. For each Lorentzian, we have
amplitude, centroid position and fwhm, and this pattern repeats for each
Lorentzian in the fit. The white noise level is the last parameter.
>>> t0 = [80, 1.5, 2.5]
Let's also make a model to test:
>>> model_to_test = models.PowerLaw1D() + models.Const1D()
>>> model_to_test.amplitude_1.fixed = True
We're ready for doing the fit:
>>> parest, res = fit_powerspectrum(ps, model_to_test, t0)
`res` contains a whole array of useful information about the fit, for
example the parameters at the optimum:
>>> p_opt = res.p_opt
"""
if not (isinstance(starting_pars, np.ndarray) or isinstance(starting_pars,
list)):
starting_pars = model.parameters
if priors:
lpost = PSDPosterior(ps.freq, ps.power, model, priors=priors,
m=ps.m)
else:
lpost = PSDLogLikelihood(ps.freq, ps.power, model, m=ps.m)
parest = PSDParEst(ps, fitmethod=fitmethod, max_post=max_post)
res = parest.fit(lpost, starting_pars, neg=True)
return parest, res
def test_fit_method_works_with_correct_parameter(self):
pe = PSDParEst(self.ps)
lpost = PSDPosterior(self.ps.freq, self.ps.power,
self.model, self.priors, m=self.ps.m)
t0 = [2.0, 1, 1, 1]
res = pe.fit(lpost, t0)
def test_fit_fails_without_t0(self):
pe = PSDParEst(self.ps)
with pytest.raises(TypeError):
res = pe.fit(np.ones(10))
def test_fit_fails_when_object_is_not_posterior_or_likelihood(self):
x = np.ones(10)
y = np.ones(10)
pe = PSDParEst(self.ps)
with pytest.raises(TypeError):
res = pe.fit(x, y)
def fit_crossspectrum(cs,
model,
starting_pars=None,
max_post=False,
priors=None,
fitmethod="L-BFGS-B"):
"""
Fit a number of Lorentzians to a cross spectrum, possibly including white
noise. Each Lorentzian has three parameters (amplitude, centroid position,
full-width at half maximum), plus one extra parameter if the white noise
level should be fit as well. Priors for each parameter can be included in
case `max_post = True`, in which case the function will attempt a
Maximum-A-Posteriori fit. Priors must be specified as a dictionary with one
entry for each parameter.
The parameter names are `(amplitude_i, x_0_i, fwhm_i)` for each `i` out of
a total of `N` Lorentzians. The white noise level has a parameter
`amplitude_(N+1)`. For example, a model with two Lorentzians and a
white noise level would have parameters:
[amplitude_0, x_0_0, fwhm_0, amplitude_1, x_0_1, fwhm_1, amplitude_2].
Parameters
----------
cs : Crossspectrum
A Crossspectrum object with the data to be fit
model: astropy.modeling.models class instance
The parametric model supposed to represent the data. For details
see the astropy.modeling documentation
starting_pars : iterable, optional, default None
The list of starting guesses for the optimizer. If it is not provided,
then default parameters are taken from `model`. See explanation above
for ordering of parameters in this list.
max_post : bool, optional, default False
If True, perform a Maximum-A-Posteriori fit of the data rather than a
Maximum Likelihood fit. Note that this requires priors to be specified,
otherwise this will cause an exception!
priors : {dict | None}, optional, default None
Dictionary with priors for the MAP fit. This should be of the form
{"parameter name": probability distribution, ...}
fitmethod : string, optional, default "L-BFGS-B"
Specifies an optimization algorithm to use. Supply any valid option for
`scipy.optimize.minimize`.
Returns
-------
parest : PSDParEst object
A PSDParEst object for further analysis
res : OptimizationResults object
The OptimizationResults object storing useful results and quantities
relating to the fit
"""
if not (isinstance(starting_pars, np.ndarray)
or isinstance(starting_pars, list)):
starting_pars = model.parameters
if priors:
lgauss = GaussianPosterior(cs.freq, np.abs(cs.power), cs.power_err,
model, priors)
else:
lgauss = GaussianLogLikelihood(cs.freq,
np.abs(cs.power),
model=model,
yerr=cs.power_err)
parest = PSDParEst(cs, fitmethod=fitmethod, max_post=max_post)
res = parest.fit(lgauss, starting_pars, neg=True)
return parest, res
def test_fit_fails_without_lpost_or_t0(self):
pe = PSDParEst(self.ps)
with pytest.raises(TypeError):
res = pe.fit()
ps = Powerspectrum()
ps.freq = freq
ps.power = powers
ps.df = ps.freq[1] - ps.freq[0]
ps.m = 1
# Define the log-likelihood of the data given the model
from stingray.modeling import PSDLogLikelihood
loglike = PSDLogLikelihood(ps.freq, ps.power, observation_model, m=ps.m)
loglike(true_parameters)
# Parameter estimation
from stingray.modeling import PSDParEst
parest = PSDParEst(ps, fitmethod="L-BFGS-B", max_post=False)
starting_pars = true_parameters
res = parest.fit(loglike, starting_pars)
print(true_parameters)
print(res.p_opt)
print(res.err)
print("AIC: " + str(res.aic))
print("BIC: " + str(res.bic))
res.print_summary(loglike)
plt.figure(figsize=(12, 8))
plt.loglog(ps.freq, psd_shape, label="true power spectrum", lw=3)
plt.loglog(ps.freq, ps.power, label="simulated data")
plt.loglog(ps.freq, res.mfit, label="best fit", lw=3)
plt.legend()
plt.show()
def test_fit_fails_with_incorrect_number_of_parameters(self):
pe = PSDParEst(self.ps)
t0 = [1,2]
with pytest.raises(ValueError):
res = pe.fit(self.lpost, t0)
def test_fit_fails_without_lpost_or_t0(self):
pe = PSDParEst(self.ps)
with pytest.raises(TypeError):
res = pe.fit()
def fit_crossspectrum(cs, model, starting_pars=None, max_post=False,
priors=None, fitmethod="L-BFGS-B"):
"""
Fit a number of Lorentzians to a cross spectrum, possibly including white
noise. Each Lorentzian has three parameters (amplitude, centroid position,
full-width at half maximum), plus one extra parameter if the white noise
level should be fit as well. Priors for each parameter can be included in
case `max_post = True`, in which case the function will attempt a
Maximum-A-Posteriori fit. Priors must be specified as a dictionary with one
entry for each parameter.
The parameter names are `(amplitude_i, x_0_i, fwhm_i)` for each `i` out of
a total of `N` Lorentzians. The white noise level has a parameter
`amplitude_(N+1)`. For example, a model with two Lorentzians and a
white noise level would have parameters:
[amplitude_0, x_0_0, fwhm_0, amplitude_1, x_0_1, fwhm_1, amplitude_2].
Parameters
----------
cs : Crossspectrum
A Crossspectrum object with the data to be fit
model: astropy.modeling.models class instance
The parametric model supposed to represent the data. For details
see the astropy.modeling documentation
starting_pars : iterable, optional, default None
The list of starting guesses for the optimizer. If it is not provided,
then default parameters are taken from `model`. See explanation above
for ordering of parameters in this list.
max_post : bool, optional, default False
If True, perform a Maximum-A-Posteriori fit of the data rather than a
Maximum Likelihood fit. Note that this requires priors to be specified,
otherwise this will cause an exception!
priors : {dict | None}, optional, default None
Dictionary with priors for the MAP fit. This should be of the form
{"parameter name": probability distribution, ...}
fitmethod : string, optional, default "L-BFGS-B"
Specifies an optimization algorithm to use. Supply any valid option for
`scipy.optimize.minimize`.
Returns
-------
parest : PSDParEst object
A PSDParEst object for further analysis
res : OptimizationResults object
The OptimizationResults object storing useful results and quantities
relating to the fit
"""
if not (isinstance(starting_pars, np.ndarray) or isinstance(starting_pars,
list)):
starting_pars = model.parameters
if priors:
lgauss = GaussianPosterior(cs.freq, np.abs(cs.power), cs.power_err,
model, priors)
else:
lgauss = GaussianLogLikelihood(cs.freq, np.abs(cs.power), model=model,
yerr=cs.power_err)
parest = PSDParEst(cs, fitmethod=fitmethod, max_post=max_post)
res = parest.fit(lgauss, starting_pars, neg=True)
return parest, res
def test_fit_fails_with_incorrect_number_of_parameters(self):
pe = PSDParEst(self.ps)
t0 = [1,2]
with pytest.raises(ValueError):
res = pe.fit(self.lpost, t0)
def fit_powerspectrum(ps,
model,
starting_pars,
max_post=False,
priors=None,
fitmethod="L-BFGS-B"):
"""
Fit a number of Lorentzians to a power spectrum, possibly including white
noise. Each Lorentzian has three parameters (amplitude, centroid position,
full-width at half maximum), plus one extra parameter if the white noise
level should be fit as well. Priors for each parameter can be included in
case `max_post = True`, in which case the function will attempt a
Maximum-A-Posteriori fit. Priors must be specified as a dictionary with one
entry for each parameter.
The parameter names are `(amplitude_i, x_0_i, fwhm_i)` for each `i` out of
a total of `N` Lorentzians. The white noise level has a parameter
`amplitude_(N+1)`. For example, a model with two Lorentzians and a
white noise level would have parameters:
[amplitude_0, x_0_0, fwhm_0, amplitude_1, x_0_1, fwhm_1, amplitude_2].
Parameters
----------
ps : Powerspectrum
A Powerspectrum object with the data to be fit
model: astropy.modeling.models class instance
The parametric model supposed to represent the data. For details
see the astropy.modeling documentation
starting_pars : iterable
The list of starting guesses for the optimizer. See explanation above
for ordering of parameters in this list.
fit_whitenoise : bool, optional, default True
If True, the code will attempt to fit a white noise level along with
the Lorentzians. Be sure to include a starting parameter for the
optimizer in `starting_pars`!
max_post : bool, optional, default False
If True, perform a Maximum-A-Posteriori fit of the data rather than a
Maximum Likelihood fit. Note that this requires priors to be specified,
otherwise this will cause an exception!
priors : {dict | None}, optional, default None
Dictionary with priors for the MAP fit. This should be of the form
{"parameter name": probability distribution, ...}
fitmethod : string, optional, default "L-BFGS-B"
Specifies an optimization algorithm to use. Supply any valid option for
`scipy.optimize.minimize`.
Returns
-------
parest : PSDParEst object
A PSDParEst object for further analysis
res : OptimizationResults object
The OptimizationResults object storing useful results and quantities
relating to the fit
Example
-------
We start by making an example power spectrum with three Lorentzians
>>> m = 1
>>> nfreq = 100000
>>> freq = np.linspace(1, 1000, nfreq)
>>> np.random.seed(100) # set the seed for the random number generator
>>> noise = np.random.exponential(size=nfreq)
>>> model = models.PowerLaw1D() + models.Const1D()
>>> model.x_0_0.fixed = True
>>> alpha_0 = 2.0
>>> amplitude_0 = 100.0
>>> amplitude_1 = 2.0
>>> model.alpha_0 = alpha_0
>>> model.amplitude_0 = amplitude_0
>>> model.amplitude_1 = amplitude_1
>>> p = model(freq)
>>> power = noise * p
>>> ps = Powerspectrum()
>>> ps.freq = freq
>>> ps.power = power
>>> ps.m = m
>>> ps.df = freq[1] - freq[0]
>>> ps.norm = "leahy"
Now we have to guess starting parameters. For each Lorentzian, we have
amplitude, centroid position and fwhm, and this pattern repeats for each
Lorentzian in the fit. The white noise level is the last parameter.
>>> t0 = [80, 1.5, 2.5]
Let's also make a model to test:
>>> model_to_test = models.PowerLaw1D() + models.Const1D()
>>> model_to_test.x_0_0.fixed = True
We're ready for doing the fit:
>>> parest, res = fit_powerspectrum(ps, model_to_test, t0)
`res` contains a whole array of useful information about the fit, for
example the parameters at the optimum:
>>> p_opt = res.p_opt
"""
if priors:
lpost = PSDPosterior(ps, model, priors=priors)
else:
lpost = PSDLogLikelihood(ps.freq, ps.power, model, m=ps.m)
parest = PSDParEst(ps, fitmethod=fitmethod, max_post=max_post)
res = parest.fit(lpost, starting_pars, neg=True)
return parest, res
powers = psd_shape * np.random.chisquare(2,
size=psd_shape.shape[0]) / 2.0
# Make the random data into a Powerspectrum object
ps = Powerspectrum()
ps.freq = freq
ps.power = powers
ps.df = ps.freq[1] - ps.freq[0]
ps.m = 1
# Define the log-likelihood of the data given the model
loglike = PSDLogLikelihood(ps.freq,
ps.power,
observation_model,
m=ps.m)
# Parameter estimation object
parameter_estimate = PSDParEst(ps,
fitmethod="L-BFGS-B",
max_post=False)
# Estimate the starting parameters - will be replaced with a function
# starting_parameters = starting_parameter_selector(model_name)
starting_pars = [ll_amplitude / 2.0, -1.0, ll_fwhm / 5.0]
# Do the fit and store the results
sp.store(i, j, parameter_estimate.fit(loglike, starting_pars))
# Save the results
sp.save('/Users/Desktop/')
