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Add z_obs output (#119)
* Update SN model to output zobs too * Add TF predicted zobs * Add imoprt * Update nb * Calculate chi2 * Update nb * Update script
This commit is contained in:
Richard Stiskalek
GitHub
parent
f7285b2600
commit
4093186f9a
@ -17,4 +17,4 @@ from .flow_model import (DataLoader, radial_velocity_los, dist2redshift,
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SD_PV_validation_model, SN_PV_validation_model, # noqa
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TF_PV_validation_model, radec_to_galactic, # noqa
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sample_prior, make_loss, get_model, # noqa
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optimize_model_with_jackknife) # noqa
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optimize_model_with_jackknife, distmodulus2dist) # noqa
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@ -19,7 +19,7 @@ References
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----------
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[1] https://arxiv.org/abs/1912.09383.
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"""
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from abc import ABC
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from abc import ABC, abstractmethod
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from datetime import datetime
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from warnings import catch_warnings, simplefilter, warn
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@ -35,11 +35,12 @@ from jax import numpy as jnp
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from jax import vmap
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from jax.lax import cond, scan
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from jax.random import PRNGKey
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from numdifftools import Hessian
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from numpyro.infer import Predictive, util
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from scipy.interpolate import interp1d
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from scipy.optimize import fmin_powell
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from sklearn.model_selection import KFold
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from tqdm import trange
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from numdifftools import Hessian
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from ..params import simname2Omega_m
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@ -426,17 +427,45 @@ def dist2distmodulus(dist, Omega_m):
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return 5 * jnp.log10(luminosity_distance) + 25
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# def distmodulus2dist(distmodulus, Omega_m):
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# """
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# Copied from Supranta. Make sure this actually works.
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#
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#
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# """
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# dL = 10 ** ((distmodulus - 25.) / 5.)
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# r_hMpc = dL
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# for i in range(4):
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# r_hMpc = dL / (1.0 + dist2redshift(r_hMpc, Omega_m))
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# return r_hMpc
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def distmodulus2dist(mu, Omega_m, ninterp=10000, zmax=0.1, mu2comoving=None,
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return_interpolator=False):
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"""
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Convert distance modulus to comoving distance. Note that this is a costly
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implementation, as it builts up the interpolator every time it is called
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unless it is provided.
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Parameters
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----------
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mu : float or 1-dimensional array
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Distance modulus.
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Omega_m : float
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Matter density parameter.
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ninterp : int, optional
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Number of points to interpolate the mapping from distance modulus to
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comoving distance.
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zmax : float, optional
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Maximum redshift for the interpolation.
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mu2comoving : callable, optional
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Interpolator from distance modulus to comoving distance. If not
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provided, it is built up every time the function is called.
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return_interpolator : bool, optional
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Whether to return the interpolator as well.
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Returns
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-------
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float (or 1-dimensional array) and callable (optional)
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"""
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if mu2comoving is None:
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zrange = np.linspace(1e-15, zmax, ninterp)
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cosmo = FlatLambdaCDM(H0=100, Om0=Omega_m)
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mu2comoving = interp1d(
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cosmo.distmod(zrange).value, cosmo.comoving_distance(zrange).value,
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kind="cubic")
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if return_interpolator:
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return mu2comoving(mu), mu2comoving
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return mu2comoving(mu)
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def project_Vext(Vext_x, Vext_y, Vext_z, RA, dec):
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@ -549,6 +578,29 @@ def calculate_ll_zobs(zobs, zobs_pred, sigma_v):
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return jnp.exp(-0.5 * (dcz / sigma_v)**2) / jnp.sqrt(2 * np.pi) / sigma_v
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def stack_normal(mus, stds):
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"""
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Stack the normal distributions and approximate the stacked distribution
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by a single Gaussian.
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Parameters
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----------
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mus : 1-dimensional array
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Means of the normal distributions.
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stds : 1-dimensional array
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Standard deviations of the normal distributions.
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Returns
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-------
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mu, std : floats
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"""
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if mus.ndim > 1 or stds.ndim > 1 and mus.shape != stds.shape:
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raise ValueError("Shape of `mus` and `stds` must be the same and 1D.")
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mu = np.mean(mus)
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std = (np.sum(stds**2 + (mus - mu)**2) / len(mus))**0.5
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return mu, std
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class BaseFlowValidationModel(ABC):
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"""
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Base class for the flow validation models.
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@ -556,8 +608,90 @@ class BaseFlowValidationModel(ABC):
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@property
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def ndata(self):
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"""
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Number of PV objects in the catalogue.
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Returns
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-------
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int
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"""
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return len(self._RA)
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@abstractmethod
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def predict_zobs_single(self, **kwargs):
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pass
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def predict_zobs(self, samples):
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"""
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Predict the observed redshifts given the samples from the posterior.
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Parameters
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----------
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samples : dict of 1-dimensional arrays
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Posterior samples.
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Returns
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-------
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zobs_mean : 2-dimensional array of shape (ndata, nsamples)
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Mean of the predicted redshifts.
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zobs_std : 2-dimensional array of shape (ndata, nsamples)
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Standard deviation of the predicted redshifts.
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"""
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keys = list(samples.keys())
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nsamples = len(samples[keys[0]])
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zobs_mean = np.empty((self.ndata, nsamples), dtype=np.float32)
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zobs_std = np.empty_like(zobs_mean)
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# JIT compile the function, it is called many times.
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f = jit(self.predict_zobs_single)
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for i in trange(nsamples):
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x = {key: samples[key][i] for key in keys}
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if "alpha" not in keys:
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x["alpha"] = 1.0
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e_z = samples["sigma_v"][i] / SPEED_OF_LIGHT
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mu, var = f(**x)
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zobs_mean[:, i] = mu
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zobs_std[:, i] = (var + e_z**2)**0.5
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return zobs_mean, zobs_std
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def summarize_zobs_pred(self, zobs_mean, zobs_pred):
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"""
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Summarize the predicted observed redshifts from each posterior sample
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by stacking their Gaussian distribution and approximating the stacked
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distribution by a single Gaussian.
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Parameters
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----------
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zobs_mean : 2-dimensional array of shape (ndata, nsamples)
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Mean of the predicted redshifts.
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zobs_pred : 2-dimensional array of shape (ndata, nsamples)
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Predicted redshifts.
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Returns
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-------
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mu : 1-dimensional array
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Mean of predicted redshift, averaged over the posterior samples.
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std : 1-dimensional array
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Standard deviation of the predicted redshift, averaged over the
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posterior samples.
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"""
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mu = np.empty(self.ndata, dtype=np.float32)
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std = np.empty_like(mu)
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for i in range(self.ndata):
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mu[i], std[i] = stack_normal(zobs_mean[i], zobs_pred[i])
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return mu, std
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@abstractmethod
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def __call__(self, **kwargs):
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pass
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class SD_PV_validation_model(BaseFlowValidationModel):
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"""
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@ -625,6 +759,9 @@ class SD_PV_validation_model(BaseFlowValidationModel):
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# Distribution of velocity uncertainty sigma_v
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self._sv = dist.LogNormal(*lognorm_mean_std_to_loc_scale(150, 100))
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def predict_zobs_single(self, **kwargs):
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raise NotImplementedError("This method is not implemented yet.")
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def __call__(self, sample_alpha=False):
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"""
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The simple distance NumPyro PV validation model.
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@ -714,11 +851,15 @@ class SN_PV_validation_model(BaseFlowValidationModel):
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raise ValueError("The radial step size must be constant.")
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dr = dr[0]
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# Get the various vmapped functions
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# Get the various functions, also vmapped
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self._f_ptilde_wo_bias = lambda mu, err: calculate_ptilde_wo_bias(mu_xrange, mu, err, r2_xrange, True) # noqa
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self._f_simps = lambda y: simps(y, dr) # noqa
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self._f_zobs = lambda beta, Vr, vpec_rad: predict_zobs(r_xrange, beta, Vr, vpec_rad, Omega_m) # noqa
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self._vmap_ptilde_wo_bias = vmap(lambda mu, err: calculate_ptilde_wo_bias(mu_xrange, mu, err, r2_xrange, True)) # noqa
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self._vmap_simps = vmap(lambda y: simps(y, dr))
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self._vmap_zobs = vmap(lambda beta, Vr, vpec_rad: predict_zobs(r_xrange, beta, Vr, vpec_rad, Omega_m), in_axes=(None, 0, 0)) # noqa
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# Distribution of external velocity components
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self._Vext = dist.Uniform(-500, 500)
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# Distribution of velocity and density bias parameters
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@ -733,6 +874,83 @@ class SN_PV_validation_model(BaseFlowValidationModel):
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self._beta_cal = dist.Normal(3.112, 1.0)
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self._e_mu = dist.LogNormal(*lognorm_mean_std_to_loc_scale(0.1, 0.05))
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self._Omega_m = Omega_m
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self._r_xrange = r_xrange
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def mu(self, mag_cal, alpha_cal, beta_cal):
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"""
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Distance modulus of each object the given SALT2 calibration parameters.
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Parameters
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----------
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mag_cal, alpha_cal, beta_cal : floats
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SALT2 calibration parameters.
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Returns
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-------
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1-dimensional array
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"""
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return self._mB - mag_cal + alpha_cal * self._x1 - beta_cal * self._c
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def squared_e_mu(self, alpha_cal, beta_cal, e_mu_intrinsic):
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"""
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Linearly-propagated squared error on the SALT2 distance modulus.
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Parameters
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----------
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alpha_cal, beta_cal, e_mu_intrinsic : floats
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SALT2 calibration parameters.
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Returns
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-------
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1-dimensional array
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"""
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return (self._e2_mB + alpha_cal**2 * self._e2_x1
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+ beta_cal**2 * self._e2_c + e_mu_intrinsic**2)
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def predict_zobs_single(self, Vext_x, Vext_y, Vext_z, alpha, beta,
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e_mu_intrinsic, mag_cal, alpha_cal, beta_cal,
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**kwargs):
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"""
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Predict the observed redshifts given the samples from the posterior.
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Parameters
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----------
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Vext_x, Vext_y, Vext_z : floats
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Components of the external velocity.
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alpha, beta : floats
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Density and velocity bias parameters.
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e_mu_intrinsic, mag_cal, alpha_cal, beta_cal : floats
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Calibration parameters.
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kwargs : dict
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Additional arguments (for compatibility).
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Returns
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-------
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zobs_mean : 1-dimensional array
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Mean of the predicted redshifts.
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zobs_var : 1-dimensional array
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Variance of the predicted redshifts.
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"""
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mu = self.mu(mag_cal, alpha_cal, beta_cal)
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squared_e_mu = self.squared_e_mu(alpha_cal, beta_cal, e_mu_intrinsic)
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Vext_rad = project_Vext(Vext_x, Vext_y, Vext_z, self._RA, self._dec)
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# Calculate p(r) (Malmquist bias)
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ptilde = self._vmap_ptilde_wo_bias(mu, squared_e_mu)
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ptilde *= self._los_density**alpha
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ptilde /= self._vmap_simps(ptilde).reshape(-1, 1)
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# Predicted mean z_obs
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zobs_pred = self._vmap_zobs(beta, Vext_rad, self._los_velocity)
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zobs_mean = self._vmap_simps(zobs_pred * ptilde)
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# Variance of the predicted z_obs
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zobs_pred -= zobs_mean.reshape(-1, 1)
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zobs_var = self._vmap_simps(zobs_pred**2 * ptilde)
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return zobs_mean, zobs_var
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def __call__(self, sample_alpha=True, fix_calibration=False):
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"""
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The supernova NumPyro PV validation model with SALT2 calibration.
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@ -777,9 +995,8 @@ class SN_PV_validation_model(BaseFlowValidationModel):
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Vext_rad = project_Vext(Vx, Vy, Vz, self._RA, self._dec)
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mu = self._mB - mag_cal + alpha_cal * self._x1 - beta_cal * self._c
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squared_e_mu = (self._e2_mB + alpha_cal**2 * self._e2_x1
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+ beta_cal**2 * self._e2_c + e_mu_intrinsic**2)
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mu = self.mu(mag_cal, alpha_cal, beta_cal)
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squared_e_mu = self.squared_e_mu(alpha_cal, beta_cal, e_mu_intrinsic)
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def scan_body(ll, i):
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# Calculate p(r) and multiply it by the galaxy bias
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@ -857,6 +1074,10 @@ class TF_PV_validation_model(BaseFlowValidationModel):
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self._f_simps = lambda y: simps(y, dr) # noqa
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self._f_zobs = lambda beta, Vr, vpec_rad: predict_zobs(r_xrange, beta, Vr, vpec_rad, Omega_m) # noqa
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self._vmap_ptilde_wo_bias = vmap(lambda mu, err: calculate_ptilde_wo_bias(mu_xrange, mu, err, r2_xrange, True)) # noqa
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self._vmap_simps = vmap(lambda y: simps(y, dr))
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self._vmap_zobs = vmap(lambda beta, Vr, vpec_rad: predict_zobs(r_xrange, beta, Vr, vpec_rad, Omega_m), in_axes=(None, 0, 0)) # noqa
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# Distribution of external velocity components
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self._Vext = dist.Uniform(-1000, 1000)
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# Distribution of velocity and density bias parameters
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@ -870,6 +1091,83 @@ class TF_PV_validation_model(BaseFlowValidationModel):
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self._b = dist.Normal(-5.95, 0.1)
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self._e_mu = dist.LogNormal(*lognorm_mean_std_to_loc_scale(0.3, 0.1)) # noqa
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self._Omega_m = Omega_m
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self._r_xrange = r_xrange
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def mu(self, a, b):
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"""
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Distance modulus of each object the given Tully-Fisher calibration.
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Parameters
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----------
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a, b : floats
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Tully-Fisher calibration parameters.
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Returns
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-------
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1-dimensional array
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"""
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return self._mag - (a + b * self._eta)
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def squared_e_mu(self, b, e_mu_intrinsic):
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"""
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Squared error on the Tully-Fisher distance modulus.
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Parameters
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----------
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b, e_mu_intrinsic : floats
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Tully-Fisher calibration parameters.
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Returns
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-------
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1-dimensional array
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"""
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return (self._e2_mag + b**2 * self._e2_eta + e_mu_intrinsic**2)
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def predict_zobs_single(self, Vext_x, Vext_y, Vext_z, alpha, beta,
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e_mu_intrinsic, a, b, **kwargs):
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"""
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Predict the observed redshifts given the samples from the posterior.
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Parameters
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----------
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Vext_x, Vext_y, Vext_z : floats
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Components of the external velocity.
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alpha, beta : floats
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Density and velocity bias parameters.
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e_mu_intrinsic, a, b : floats
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Calibration parameters.
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kwargs : dict
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Additional arguments (for compatibility).
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Returns
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-------
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zobs_mean : 1-dimensional array
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Mean of the predicted redshifts.
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zobs_var : 1-dimensional array
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Variance of the predicted redshifts.
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"""
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mu = self.mu(a, b)
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squared_e_mu = self.squared_e_mu(b, e_mu_intrinsic)
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Vext_rad = project_Vext(Vext_x, Vext_y, Vext_z, self._RA, self._dec)
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# Calculate p(r) (Malmquist bias)
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ptilde = self._vmap_ptilde_wo_bias(mu, squared_e_mu)
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ptilde *= self._los_density**alpha
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ptilde /= self._vmap_simps(ptilde).reshape(-1, 1)
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# Predicted mean z_obs
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zobs_pred = self._vmap_zobs(beta, Vext_rad, self._los_velocity)
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zobs_mean = self._vmap_simps(zobs_pred * ptilde)
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# Variance of the predicted z_obs
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zobs_pred -= zobs_mean.reshape(-1, 1)
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zobs_var = self._vmap_simps(zobs_pred**2 * ptilde)
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return zobs_mean, zobs_var
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def __call__(self, sample_alpha=True):
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"""
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The Tully-Fisher NumPyro PV validation model.
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@ -893,9 +1191,8 @@ class TF_PV_validation_model(BaseFlowValidationModel):
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Vext_rad = project_Vext(Vx, Vy, Vz, self._RA, self._dec)
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mu = self._mag - (a + b * self._eta)
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squared_e_mu = (self._e2_mag + b**2 * self._e2_eta
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+ e_mu_intrinsic**2)
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mu = self.mu(a, b)
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squared_e_mu = self.squared_e_mu(b, e_mu_intrinsic)
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def scan_body(ll, i):
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# Calculate p(r) and multiply it by the galaxy bias
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File diff suppressed because one or more lines are too long
@ -30,7 +30,7 @@ def read_samples(catalogue, simname, ksmooth, include_calibration=False,
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nsims = paths.get_ics(simname)
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Vx, Vy, Vz, beta, sigma_v, alpha = [], [], [], [], [], []
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BIC, AIC, logZ = [], [], []
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BIC, AIC, logZ, chi2 = [], [], [], []
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if catalogue in ["LOSS", "Foundation", "Pantheon+"]:
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alpha_cal, beta_cal, mag_cal, e_mu_intrinsic = [], [], [], []
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@ -69,6 +69,10 @@ def read_samples(catalogue, simname, ksmooth, include_calibration=False,
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BIC.append(f[f"sim_{nsim}/BIC"][...])
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AIC.append(f[f"sim_{nsim}/AIC"][...])
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logZ.append(f[f"sim_{nsim}/logZ"][...])
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try:
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chi2.append(f[f"sim_{nsim}/chi2"][...])
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except KeyError:
|
||||
chi2.append([0.])
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|
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if catalogue in ["LOSS", "Foundation", "Pantheon+"]:
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alpha_cal.append(f[f"sim_{nsim}/alpha_cal"][:])
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@ -84,7 +88,7 @@ def read_samples(catalogue, simname, ksmooth, include_calibration=False,
|
||||
|
||||
Vx, Vy, Vz, alpha, beta, sigma_v = np.hstack(Vx), np.hstack(Vy), np.hstack(Vz), np.hstack(alpha), np.hstack(beta), np.hstack(sigma_v) # noqa
|
||||
|
||||
gof = np.hstack(BIC), np.hstack(AIC), np.hstack(logZ)
|
||||
gof = np.hstack(BIC), np.hstack(AIC), np.hstack(logZ), np.hstack(chi2)
|
||||
|
||||
if catalogue in ["LOSS", "Foundation", "Pantheon+"]:
|
||||
alpha_cal, beta_cal, mag_cal, e_mu_intrinsic = np.hstack(alpha_cal), np.hstack(beta_cal), np.hstack(mag_cal), np.hstack(e_mu_intrinsic) # noqa
|
||||
@ -116,6 +120,7 @@ def read_samples(catalogue, simname, ksmooth, include_calibration=False,
|
||||
print("BIC = {:4f} +- {:4f}".format(np.mean(gof[0]), np.std(gof[0])))
|
||||
print("AIC = {:4f} +- {:4f}".format(np.mean(gof[1]), np.std(gof[1])))
|
||||
print("logZ = {:4f} +- {:4f}".format(np.mean(gof[2]), np.std(gof[2])))
|
||||
print("chi2 = {:4f} +- {:4f}".format(np.mean(gof[3]), np.std(gof[3])))
|
||||
|
||||
data = np.vstack(data).T
|
||||
|
||||
|
||||
@ -104,11 +104,19 @@ def run_model(model, nsteps, nburn, nchains, nsim, dump_folder,
|
||||
samples = mcmc.get_samples()
|
||||
thinned_samples = csiborgtools.thin_samples_by_acl(samples)
|
||||
|
||||
# Calculate the chi2
|
||||
keys = list(thinned_samples.keys())
|
||||
nsamples = len(thinned_samples[keys[0]])
|
||||
zobs_mean, zobs_std = model.predict_zobs(thinned_samples)
|
||||
nu = model.ndata - len(keys)
|
||||
chi2 = [np.sum((zobs_mean[:, i] - model._z_obs)**2 / zobs_std[:, i]**2) / nu # noqa
|
||||
for i in range(nsamples)]
|
||||
|
||||
gof = csiborgtools.numpyro_gof(model, mcmc, model_kwargs)
|
||||
|
||||
# Save the samples to the temporary folder.
|
||||
fname = join(dump_folder, f"samples_{nsim}.npz")
|
||||
np.savez(fname, **thinned_samples, **gof)
|
||||
np.savez(fname, **thinned_samples, **gof, chi2=chi2)
|
||||
|
||||
|
||||
def combine_from_simulations(catalogue_name, simname, nsims, outfolder,
|
||||
|
||||
@ -1,5 +1,5 @@
|
||||
memory=4
|
||||
on_login=0
|
||||
on_login=1
|
||||
nthreads=${1}
|
||||
ksmooth=${2}
|
||||
|
||||
@ -7,8 +7,8 @@ queue="berg"
|
||||
env="/mnt/users/rstiskalek/csiborgtools/venv_csiborg/bin/python"
|
||||
file="flow_validation.py"
|
||||
|
||||
catalogue="Pantheon+"
|
||||
simname="csiborg2_main"
|
||||
catalogue="LOSS"
|
||||
simname="Carrick2015"
|
||||
|
||||
|
||||
pythoncm="$env $file --catalogue $catalogue --simname $simname --ksmooth $ksmooth"
|
||||
|
||||
Loading…
Reference in New Issue
Block a user