def approx(self, type="norm", from_samples=False, samples=25000, n_components=2):
types = ["norm", "uniform", "loggamma", "gaussian_mixture"]
if type not in types:
raise NotImplementedError("allowed types are " + str(types))
if type == "gaussian_mixture":
if n_components <= 1:
return self.approx(type="norm",
from_samples=from_samples,
samples=samples)
from_samples=True
if from_samples:
rv = self.rvs(samples)
mean, std, skewness = np.mean(rv), np.std(rv), skew(rv)
else:
mean, std, skewness = self.mean(), self.std(), self.stats(moments="s")
if type == "norm":
return norm(mean, std)
elif type == "uniform":
return uniform(mean - np.sqrt(3) * std, np.sqrt(12) * std)
elif type == "loggamma":
if skewness == 0:
return self.approx(type="norm",
from_samples=from_samples,
samples=samples)
c = get_loggamma_c(skewness)
a = loggamma(c)
a = scale(
offset(a, - a.mean()),
-np.sign(skewness) / a.std())
a = offset(
scale(a, std),
mean)
return a
elif type == "gaussian_mixture":
gm = GaussianMixture(n_components=n_components)
gm.fit(np.atleast_2d(rv).T)
mean = gm.means_[:, 0]
var = gm.covariances_[:,0, 0]
weights = gm.weights_
return combination([norm(m, np.sqrt(v))
for m, v in zip(mean, var)],
list(weights))
else:
raise NotImplementedError('approximation not defined for input type')
c = 0.414 mean, var, skew, kurt = loggamma.stats(c, moments='mvsk') # Display the probability density function (``pdf``): x = np.linspace(loggamma.ppf(0.01, c), loggamma.ppf(0.99, c), 100) ax.plot(x, loggamma.pdf(x, c), 'r-', lw=5, alpha=0.6, label='loggamma pdf') # Alternatively, the distribution object can be called (as a function) # to fix the shape, location and scale parameters. This returns a "frozen" # RV object holding the given parameters fixed. # Freeze the distribution and display the frozen ``pdf``: rv = loggamma(c) ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf') # Check accuracy of ``cdf`` and ``ppf``: vals = loggamma.ppf([0.001, 0.5, 0.999], c) np.allclose([0.001, 0.5, 0.999], loggamma.cdf(vals, c)) # True # Generate random numbers: r = loggamma.rvs(c, size=1000) # And compare the histogram: ax.hist(r, normed=True, histtype='stepfilled', alpha=0.2)
def all_dists():
# dists param were taken from scipy.stats official
# documentaion examples
# Total - 89
return {
"alpha":
stats.alpha(a=3.57, loc=0.0, scale=1.0),
"anglit":
stats.anglit(loc=0.0, scale=1.0),
"arcsine":
stats.arcsine(loc=0.0, scale=1.0),
"beta":
stats.beta(a=2.31, b=0.627, loc=0.0, scale=1.0),
"betaprime":
stats.betaprime(a=5, b=6, loc=0.0, scale=1.0),
"bradford":
stats.bradford(c=0.299, loc=0.0, scale=1.0),
"burr":
stats.burr(c=10.5, d=4.3, loc=0.0, scale=1.0),
"cauchy":
stats.cauchy(loc=0.0, scale=1.0),
"chi":
stats.chi(df=78, loc=0.0, scale=1.0),
"chi2":
stats.chi2(df=55, loc=0.0, scale=1.0),
"cosine":
stats.cosine(loc=0.0, scale=1.0),
"dgamma":
stats.dgamma(a=1.1, loc=0.0, scale=1.0),
"dweibull":
stats.dweibull(c=2.07, loc=0.0, scale=1.0),
"erlang":
stats.erlang(a=2, loc=0.0, scale=1.0),
"expon":
stats.expon(loc=0.0, scale=1.0),
"exponnorm":
stats.exponnorm(K=1.5, loc=0.0, scale=1.0),
"exponweib":
stats.exponweib(a=2.89, c=1.95, loc=0.0, scale=1.0),
"exponpow":
stats.exponpow(b=2.7, loc=0.0, scale=1.0),
"f":
stats.f(dfn=29, dfd=18, loc=0.0, scale=1.0),
"fatiguelife":
stats.fatiguelife(c=29, loc=0.0, scale=1.0),
"fisk":
stats.fisk(c=3.09, loc=0.0, scale=1.0),
"foldcauchy":
stats.foldcauchy(c=4.72, loc=0.0, scale=1.0),
"foldnorm":
stats.foldnorm(c=1.95, loc=0.0, scale=1.0),
# "frechet_r": stats.frechet_r(c=1.89, loc=0.0, scale=1.0),
# "frechet_l": stats.frechet_l(c=3.63, loc=0.0, scale=1.0),
"genlogistic":
stats.genlogistic(c=0.412, loc=0.0, scale=1.0),
"genpareto":
stats.genpareto(c=0.1, loc=0.0, scale=1.0),
"gennorm":
stats.gennorm(beta=1.3, loc=0.0, scale=1.0),
"genexpon":
stats.genexpon(a=9.13, b=16.2, c=3.28, loc=0.0, scale=1.0),
"genextreme":
stats.genextreme(c=-0.1, loc=0.0, scale=1.0),
"gausshyper":
stats.gausshyper(a=13.8, b=3.12, c=2.51, z=5.18, loc=0.0, scale=1.0),
"gamma":
stats.gamma(a=1.99, loc=0.0, scale=1.0),
"gengamma":
stats.gengamma(a=4.42, c=-3.12, loc=0.0, scale=1.0),
"genhalflogistic":
stats.genhalflogistic(c=0.773, loc=0.0, scale=1.0),
"gilbrat":
stats.gilbrat(loc=0.0, scale=1.0),
"gompertz":
stats.gompertz(c=0.947, loc=0.0, scale=1.0),
"gumbel_r":
stats.gumbel_r(loc=0.0, scale=1.0),
"gumbel_l":
stats.gumbel_l(loc=0.0, scale=1.0),
"halfcauchy":
stats.halfcauchy(loc=0.0, scale=1.0),
"halflogistic":
stats.halflogistic(loc=0.0, scale=1.0),
"halfnorm":
stats.halfnorm(loc=0.0, scale=1.0),
"halfgennorm":
stats.halfgennorm(beta=0.675, loc=0.0, scale=1.0),
"hypsecant":
stats.hypsecant(loc=0.0, scale=1.0),
"invgamma":
stats.invgamma(a=4.07, loc=0.0, scale=1.0),
"invgauss":
stats.invgauss(mu=0.145, loc=0.0, scale=1.0),
"invweibull":
stats.invweibull(c=10.6, loc=0.0, scale=1.0),
"johnsonsb":
stats.johnsonsb(a=4.32, b=3.18, loc=0.0, scale=1.0),
"johnsonsu":
stats.johnsonsu(a=2.55, b=2.25, loc=0.0, scale=1.0),
"ksone":
stats.ksone(n=1e03, loc=0.0, scale=1.0),
"kstwobign":
stats.kstwobign(loc=0.0, scale=1.0),
"laplace":
stats.laplace(loc=0.0, scale=1.0),
"levy":
stats.levy(loc=0.0, scale=1.0),
"levy_l":
stats.levy_l(loc=0.0, scale=1.0),
"levy_stable":
stats.levy_stable(alpha=0.357, beta=-0.675, loc=0.0, scale=1.0),
"logistic":
stats.logistic(loc=0.0, scale=1.0),
"loggamma":
stats.loggamma(c=0.414, loc=0.0, scale=1.0),
"loglaplace":
stats.loglaplace(c=3.25, loc=0.0, scale=1.0),
"lognorm":
stats.lognorm(s=0.954, loc=0.0, scale=1.0),
"lomax":
stats.lomax(c=1.88, loc=0.0, scale=1.0),
"maxwell":
stats.maxwell(loc=0.0, scale=1.0),
"mielke":
stats.mielke(k=10.4, s=3.6, loc=0.0, scale=1.0),
"nakagami":
stats.nakagami(nu=4.97, loc=0.0, scale=1.0),
"ncx2":
stats.ncx2(df=21, nc=1.06, loc=0.0, scale=1.0),
"ncf":
stats.ncf(dfn=27, dfd=27, nc=0.416, loc=0.0, scale=1.0),
"nct":
stats.nct(df=14, nc=0.24, loc=0.0, scale=1.0),
"norm":
stats.norm(loc=0.0, scale=1.0),
"pareto":
stats.pareto(b=2.62, loc=0.0, scale=1.0),
"pearson3":
stats.pearson3(skew=0.1, loc=0.0, scale=1.0),
"powerlaw":
stats.powerlaw(a=1.66, loc=0.0, scale=1.0),
"powerlognorm":
stats.powerlognorm(c=2.14, s=0.446, loc=0.0, scale=1.0),
"powernorm":
stats.powernorm(c=4.45, loc=0.0, scale=1.0),
"rdist":
stats.rdist(c=0.9, loc=0.0, scale=1.0),
"reciprocal":
stats.reciprocal(a=0.00623, b=1.01, loc=0.0, scale=1.0),
"rayleigh":
stats.rayleigh(loc=0.0, scale=1.0),
"rice":
stats.rice(b=0.775, loc=0.0, scale=1.0),
"recipinvgauss":
stats.recipinvgauss(mu=0.63, loc=0.0, scale=1.0),
"semicircular":
stats.semicircular(loc=0.0, scale=1.0),
"t":
stats.t(df=2.74, loc=0.0, scale=1.0),
"triang":
stats.triang(c=0.158, loc=0.0, scale=1.0),
"truncexpon":
stats.truncexpon(b=4.69, loc=0.0, scale=1.0),
"truncnorm":
stats.truncnorm(a=0.1, b=2, loc=0.0, scale=1.0),
"tukeylambda":
stats.tukeylambda(lam=3.13, loc=0.0, scale=1.0),
"uniform":
stats.uniform(loc=0.0, scale=1.0),
"vonmises":
stats.vonmises(kappa=3.99, loc=0.0, scale=1.0),
"vonmises_line":
stats.vonmises_line(kappa=3.99, loc=0.0, scale=1.0),
"wald":
stats.wald(loc=0.0, scale=1.0),
"weibull_min":
stats.weibull_min(c=1.79, loc=0.0, scale=1.0),
"weibull_max":
stats.weibull_max(c=2.87, loc=0.0, scale=1.0),
"wrapcauchy":
stats.wrapcauchy(c=0.0311, loc=0.0, scale=1.0),
}
def _set_rvdist_(self):
""" set the rvdistribution.
This method defines which kind of rv_continuous distribution you use
"""
return stats.loggamma(
*stats.loggamma.fit(self.samplers, loc=np.median(self.samplers)))
def get_massestimator(photopoints=None,
samplers=None,
dist_param=None,
nsamples=10000,
**kwargs):
""" Get the photopoint collection instance that enables
to derive the stellar mass of a galaxy.
The natural non-parametrized mass estimation is based on
rest-frame 'i' and 'g' band measurements following
eq. 8 of Taylor et al 2011 (2011MNRAS.418.1587T)
```
log M∗/[M⊙] = 1.15 + 0.70(g − i) − 0.4Mi
```
You can otherwize provide 'samplers' of the mass estimate
or a parametrized version of the 'samplers' using 'dist_param'.
It has been tested, the natural method returns a galaxy mass
pdf well described by a loggamma distribution (3-parameters).
By providing a 'dist_param', which parametrizes the scipy's loggamma
object, this will draw a fake sampler to set the MassEstimate.
Parameters
----------
= One of these must be set. If several are given, the first is used. =
photopoints: [2 PhotoPoints: photopoint_g,photopoint_i]
Astrobject's PhotoPoint of the g and i band measurements of the galaxy
Magnitude should be rest-frame magnitude in the sdss system.
samplers: [N-float array]
Array of potential mass estimate. From this sampling of masses is drawn
the pdf of the galaxy's stellar mass estimate.
dist_param: [3-floats]
Parameters defining scipy's loggamma functions. The mass estimate
will be base on the random drawing of samplers from this distribution.
= other options =
nsamples: [int] -optional-
Number of sampler used to estimae the galaxy's stellar mass.
If you set the MassEstimator with the 'samplers' input, nsamples
is ignored.
**kwargs goes to MassEstimate's __init__ method
Return
------
MassEstimate (PhotoPointCollection's child)
"""
# ------------- #
# - Setting - #
# ------------- #
if photopoints is not None:
photopoint_g, photopoint_i = photopoints
if photopoint_i is not None and "i" not in photopoint_i.bandname:
warnings.warn(
"The PhotoPoint with the bandname %s is used as a 'i' band photopoint for the MassEstimator"
% photopoint_i.bandname)
if photopoint_g is not None and "g" not in photopoint_g.bandname:
warnings.warn(
"The PhotoPoint with the bandname %s is used as a 'g' band photopoint for the MassEstimator"
% photopoint_g.bandname)
return MassEstimate(photopoint_g, photopoint_i, **kwargs)
if samplers is not None:
m = MassEstimate(**kwargs)
m.set_samplers(samplers)
return m
if dist_param is not None:
samplers = stats.loggamma(*dist_param).rvs(nsamples)
return get_massestimator(samplers=samplers, **kwargs)
if "empty" in kwargs.keys():
return MassEstimate(**kwargs)
raise ValueError(
"You need to provide a setter (photopoints, samplers or dist_param) or to set empty=True"
)
def _set_rvdist_(self):
""" set the rvdistribution.
This method defines which kind of rv_continuous distribution you use
"""
return stats.loggamma(*stats.loggamma.fit(self.samplers,
loc=np.median(self.samplers)))
def get_massestimator(photopoints=None,samplers=None,dist_param=None,
nsamples=10000,
**kwargs):
""" Get the photopoint collection instance that enables
to derive the stellar mass of a galaxy.
The natural non-parametrized mass estimation is based on
rest-frame 'i' and 'g' band measurements following
eq. 8 of Taylor et al 2011 (2011MNRAS.418.1587T)
```
log M∗/[M⊙] = 1.15 + 0.70(g − i) − 0.4Mi
```
You can otherwize provide 'samplers' of the mass estimate
or a parametrized version of the 'samplers' using 'dist_param'.
It has been tested, the natural method returns a galaxy mass
pdf well described by a loggamma distribution (3-parameters).
By providing a 'dist_param', which parametrizes the scipy's loggamma
object, this will draw a fake sampler to set the MassEstimate.
Parameters
----------
= One of these must be set. If several are given, the first is used. =
photopoints: [2 PhotoPoints: photopoint_g,photopoint_i]
Astrobject's PhotoPoint of the g and i band measurements of the galaxy
Magnitude should be rest-frame magnitude in the sdss system.
samplers: [N-float array]
Array of potential mass estimate. From this sampling of masses is drawn
the pdf of the galaxy's stellar mass estimate.
dist_param: [3-floats]
Parameters defining scipy's loggamma functions. The mass estimate
will be base on the random drawing of samplers from this distribution.
= other options =
nsamples: [int] -optional-
Number of sampler used to estimae the galaxy's stellar mass.
If you set the MassEstimator with the 'samplers' input, nsamples
is ignored.
**kwargs goes to MassEstimate's __init__ method
Return
------
MassEstimate (PhotoPointCollection's child)
"""
# ------------- #
# - Setting - #
# ------------- #
if photopoints is not None:
photopoint_g, photopoint_i = photopoints
if photopoint_i is not None and "i" not in photopoint_i.bandname:
warnings.warn("The PhotoPoint with the bandname %s is used as a 'i' band photopoint for the MassEstimator"%photopoint_i.bandname)
if photopoint_g is not None and "g" not in photopoint_g.bandname:
warnings.warn("The PhotoPoint with the bandname %s is used as a 'g' band photopoint for the MassEstimator"%photopoint_g.bandname)
return MassEstimate(photopoint_g, photopoint_i,**kwargs)
if samplers is not None:
m = MassEstimate(**kwargs)
m.set_samplers(samplers)
return m
if dist_param is not None:
samplers = stats.loggamma(*dist_param).rvs(nsamples)
return get_massestimator(samplers=samplers, **kwargs)
if "empty" in kwargs.keys():
return MassEstimate(**kwargs)
raise ValueError("You need to provide a setter (photopoints, samplers or dist_param) or to set empty=True")