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apetri · May 4, 2016 · 3372283 · 3372283
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diff --git a/.travis.yml b/.travis.yml
@@ -34,7 +34,7 @@ before_install:
 
 #Install packages
 install:
-- conda install --yes python=$TRAVIS_PYTHON_VERSION atlas numpy scipy matplotlib nose dateutil pandas statsmodels astropy
+- conda install --yes python=$TRAVIS_PYTHON_VERSION atlas numpy scipy sqlalchemy matplotlib nose dateutil pandas statsmodels astropy
 
 #Coverage packages are on Dan Blanchard binstar channel
 - conda install --yes -c dan_blanchard python-coveralls nose-cov

diff --git a/docs/source/examples/parameter_priors.rst b/docs/source/examples/parameter_priors.rst
@@ -0,0 +1,25 @@
+A quick and dirty way to incorporate parameter priors
+=====================================================
+
+Suppose you carried on your weak lensing analysis all the way to the parameter constraints, and you were able to estimate your parameter covariance matrix :math:`\Sigma_{lens}` (either from simulated or real data). Now suppose you are interested in understanding how these constraints change when you add prior information from say CMB observations from Planck. These prior results will become available through their own parameter covariance matrix :math:`\Sigma_{CMB}`, which may, or may not, have the same dimensions and parametrization as :math:`\Sigma_{lens}`. Applying the prior to the parameters considered in the weak lensing analysis and fixing all the others is equivalent to take the appropriate parameter slice of :math:`\Sigma_{CMB}^{-1}` and adding the Fisher matrices
+
+.. math:: \Sigma_{lens+CMB} = (\Sigma_{lens}^{-1}+\Sigma_{CMB}^{-1})^{-1}
+
+This can be readily done with the functionality embedded in the :py:class:`~lenstools.statistics.ensemble.SquareMatrix` class, with the following code
+
+::
+
+	from lenstools.statistics.ensemble import SquareMatrix
+
+	#Read in parameter covariances
+	lens_pcov = SquareMatrix.read("lenscov.pkl")
+	cmb_cov = SquareMatrix.read("cmbcov.pkl")
+
+	#Parametrization
+	parameters = ["Om","w","sigma8"]
+
+	#Add the Fisher matrices
+	fisher_lens_cmb = lens_pcov.invert()[parameters] + cmb_cov.invert()[parameters]
+
+	#pcov_lens_cmb is the parameter covariance subject to the prior
+	pcov_lens_cmb = fisher_lens_cmb.invert()
diff --git a/docs/source/examples/sampling.rst b/docs/source/examples/sampling.rst
@@ -0,0 +1,84 @@
+Three different ways to do parameter sampling
+=============================================
+
+This code snipped shows how to use LensTools to perform cosmological parameter sampling with three diffenent methods: direct evaluation of the likelihood, Fisher Matrix and MCMC
+
+::
+
+
+	from lenstools.statistics.ensemble import Series,Ensemble
+	from lenstools.statistics.constraints import Emulator
+	from lenstools.statistics.contours import ContourPlot
+	
+	import numpy as np
+	import matplotlib.pyplot as plt
+
+
+	def lt_sample(emulator,test_data,covariance,p_value=0.68):
+
+		#Check that the data types are correct
+		assert isinstance(emulator,Emulator)
+		assert isinstance(test_data,Series)
+		assert isinstance(covariance,Ensemble)
+
+		#Plot setup
+		fig,ax = plt.subplots(figsize=(8,8))
+	
+
+		#Map the likelihood in the OmegaM-sigma8 plane, fix w to -1
+		p = Ensemble.meshgrid({
+			"Om":np.linspace(0.2,0.5,50),
+			"sigma8":np.linspace(0.6,0.9,50)
+		})
+
+		p["w"] = -1.
+
+		#Compute the chi squared scores of the test data on a variety of parameter points
+		scores = emulator.score(p,test_data,covariance,correct=1000,method="chi2")
+		scores["likelihood"] = np.exp(-0.5*scores[emulator.feature_names[0]])
+
+		contour = ContourPlot.from_scores(scores,parameters=["Om","sigma8"],
+			feature_names=["likelihood"],
+			plot_labels=[r"$\Omega_m$",
+			r"$\sigma_8$"],fig=fig,ax=ax)
+
+		contour.getLikelihoodValues([p_value],precision=0.01)
+		contour.plotContours(colors=["red"])
+		contour.labels()
+
+		#Approximate the emulator linearly around the maximum (Fisher matrix)
+		fisher = emulator.approximate_linear(center=(0.26,-1.,0.8))
+
+		#Consider (OmegaM,sigma8) only
+		fisher.pop(("parameters","w"))
+		fisher = fisher.iloc[[0,1,3]]
+
+		#Fisher confidence ellipse
+		ellipse = fisher.confidence_ellipse(covariance,
+			correct=1000,
+			observed_feature=test_data,
+			parameters=["Om","sigma8"],
+			p_value=p_value,
+			fill=False,
+			edgecolor="blue")
+
+		ax.add_artist(ellipse)
+
+		#MCMC sampling of (OmegaM,sigma8)
+		samples = emulator.sample_posterior(test_data,
+			features_covariance=covariance,
+			correct=1000,
+			pslice={"w":-1},
+			sample="emcee")[emulator.feature_names[0]]	
+
+		ax.scatter(samples["Om"],samples["sigma8"],marker=".",color="black",s=1)
+		ax.set_xlim(0.2,0.5)
+		ax.set_ylim(0.6,0.9)
+
+		#Save the figure
+		fig.tight_layout()
+		fig.savefig("parameter_sampling.png")
+
+And this is the resulting figure: 
+
+.. figure:: ../figures/parameter_sampling.png
diff --git a/docs/source/figures/parameter_sampling.png b/docs/source/figures/parameter_sampling.png
diff --git a/docs/source/gallery.rst b/docs/source/gallery.rst
@@ -13,4 +13,6 @@ Gallery
 	examples/eb_decomposition
 	examples/design
 	examples/gadget_io
-	examples/confidence_contours
+	examples/confidence_contours
+	examples/sampling
+	examples/parameter_priors
diff --git a/docs/source/index.rst b/docs/source/index.rst
@@ -78,6 +78,7 @@ Dependencies
 
 .. _numpy: http://www.numpy.org
 .. _scipy: http://www.scipy.org
+.. _sqlalchemy: http://www.sqlalchemy.org 
 .. _astropy: http://www.astropy.org
 .. _pandas: http://pandas.pydata.org
 .. _emcee: http://dan.iel.fm/emcee/current/
@@ -90,12 +91,12 @@ Dependencies
 .. _NICAEA: http://www.cosmostat.org/software/nicaea/
 .. _fftw3: http://www.fftw.org
 
-The core features require the standard numpy_, scipy_ , and additionally  astropy_ (mainly for the cosmology and measure units support) and emcee_ (from which LensTools borrows the MPI Pool utility), and the Test suite requires additionally the matplotlib_ package. matpoltlib should eventually be installed if you want to use the plotting engines of LensTools. If you want to run the calculations in parallel on a computer cluster you will need to install mpi4py_ (a python wrapper for the MPI library). Installation of all these packages is advised (if you run astrophysical data analyses you should use them anyway). One of the lenstools features, namely the :py:class:`~lenstools.simulations.Design` class, requires that you have a working version of GSL_ to link to; if you don't have one, just hit *enter* during the installation process and the package will work correctly without this additional feature. The installation if the NICAEA_ bindings additionally requires a working installation of the fftw3_ library. 
+The core features require the standard numpy_, scipy_ , and additionally  astropy_ (mainly for the cosmology and measure units support) and emcee_ (from which LensTools borrows the MPI Pool utility), and the Test suite requires additionally the matplotlib_ package. matpoltlib should eventually be installed if you want to use the plotting engines of LensTools. If you want to use the SQL database querying shortcuts embedded in LensTools, you will need the sqlalchemy_ package too. If you want to run the calculations in parallel on a computer cluster you will need to install mpi4py_ (a python wrapper for the MPI library). Installation of all these packages is advised (if you run astrophysical data analyses you should use them anyway). One of the lenstools features, namely the :py:class:`~lenstools.simulations.Design` class, requires that you have a working version of GSL_ to link to; if you don't have one, just hit *enter* during the installation process and the package will work correctly without this additional feature. The installation if the NICAEA_ bindings additionally requires a working installation of the fftw3_ library. 
 
 Test
 ----
 
-To check that everything works before installing you can run the pre implemented test suite that comes with the source code. First you will need to install pytest_, then you need to download some data files (mainly FITS images) that the test suite depends on. You need to set the environment variable LENSTOOLS_DATA to the path where you want your data to be downloaded (for a manual download the data file can be found here_, it is almost 250MB). After that, in a python shell, type
+To check that everything works before installing you can run the pre implemented test suite that comes with the source code. First you will need to install pytest_, then you need to download some data files (mainly FITS images) that the test suite depends on. You need to set the environment variable LENSTOOLS_DATA to the path where you want your data to be downloaded (for a manual download the data file can be found here_, it is roughly 300MB). After that, in a python shell, type
 
 ::