import numpy as np
from matplotlib import pyplot as plt
from scipy.stats import lognorm
from sklearn.linear_model import LinearRegression, Ridge, Lasso
from astroML.cosmology import Cosmology
from astroML.datasets import generate_mu_z
import matplotlib
#----------------------------------------------------------------------
# generate data
np.random.seed(0)
z_sample, mu_sample, dmu = generate_mu_z(100, random_state=0)
cosmo = Cosmology()
z = np.linspace(0.01, 2, 1000)
mu = np.asarray(map(cosmo.mu, z))
#------------------------------------------------------------
# Manually convert data to a gaussian basis
# note that we're ignoring errors here, for the sake of example.
def gaussian_basis(x, mu, sigma):
return np.exp(-0.5 * ((x - mu) / sigma) ** 2)
centers = np.linspace(0, 1.8, 100)
widths = 0.2
X = gaussian_basis(z_sample[:, np.newaxis], centers, widths)
from astroML.cosmology import Cosmology
from astroML.plotting.mcmc import convert_to_stdev
from astroML.decorators import pickle_results
#----------------------------------------------------------------------
# This function adjusts matplotlib settings for a uniform feel in the textbook.
# Note that with usetex=True, fonts are rendered with LaTeX. This may
# result in an error if LaTeX is not installed on your system. In that case,
# you can set usetex to False.
from astroML.plotting import setup_text_plots
setup_text_plots(fontsize=8, usetex=True)
#------------------------------------------------------------
# Generate the data
z_sample, mu_sample, dmu = generate_mu_z(100, z0=0.3,
dmu_0=0.05, dmu_1=0.004,
random_state=1)
#------------------------------------------------------------
# define a log likelihood in terms of the parameters
# beta = [omegaM, omegaL]
def compute_logL(beta):
cosmo = Cosmology(omegaM=beta[0], omegaL=beta[1])
mu_pred = np.array(map(cosmo.mu, z_sample))
return - np.sum(0.5 * ((mu_sample - mu_pred) / dmu) ** 2)
#------------------------------------------------------------
# Define a function to compute (and save to file) the log-likelihood
@pickle_results('mu_z_nonlinear.pkl')
from sklearn.gaussian_process import GaussianProcess
from astroML.cosmology import Cosmology
from astroML.datasets import generate_mu_z
#----------------------------------------------------------------------
# This function adjusts matplotlib settings for a uniform feel in the textbook.
# Note that with usetex=True, fonts are rendered with LaTeX. This may
# result in an error if LaTeX is not installed on your system. In that case,
# you can set usetex to False.
from astroML.plotting import setup_text_plots
setup_text_plots(fontsize=8, usetex=True)
#------------------------------------------------------------
# Generate data
z_sample, mu_sample, dmu = generate_mu_z(100, random_state=0)
cosmo = Cosmology()
z = np.linspace(0.01, 2, 1000)
mu_true = np.asarray(map(cosmo.mu, z))
#------------------------------------------------------------
# fit the data
# Mesh the input space for evaluations of the real function,
# the prediction and its MSE
z_fit = np.linspace(0, 2, 1000)
gp = GaussianProcess(corr='squared_exponential',
theta0=1e-1,
thetaL=1e-2,
thetaU=1,
normalize=False,
# from astroML.cosmology import Cosmology from astropy.cosmology import FlatLambdaCDM as Cosmology from astroML.datasets import generate_mu_z #---------------------------------------------------------------------- # This function adjusts matplotlib settings for a uniform feel in the textbook. # Note that with usetex=True, fonts are rendered with LaTeX. This may # result in an error if LaTeX is not installed on your system. In that case, # you can set usetex to False. from astroML.plotting import setup_text_plots setup_text_plots(fontsize=8, usetex=True) #------------------------------------------------------------ # Generate data # z_sample, mu_sample, dmu = generate_mu_z(100, random_state=0) z_sample, mu_sample, dmu = generate_mu_z(100, random_state=0, Om0=0.27, H0=71) # cosmo = Cosmology() cosmo = Cosmology(Om0=0.27, H0=71) z = np.linspace(0.01, 2, 1000) # mu_true = np.asarray([cosmo.mu(zi) for zi in z]) mu_true = np.asarray(cosmo.distmod(z).value) #------------------------------------------------------------ # fit the data # Mesh the input space for evaluations of the real function, # the prediction and its MSE z_fit = np.linspace(0, 2, 1000) #------------------------------------------------------------ # using scikit-learn
