diff --git a/.travis.yml b/.travis.yml new file mode 100644 index 0000000..391c6ed --- /dev/null +++ b/.travis.yml @@ -0,0 +1,11 @@ +language: python +python: + - "2.7" + - "3.4" + - "3.5" + - "3.6" + +# command to install dependencies +#install: "pip install -r requirements.txt" +# command to run tests +script: py.test diff --git a/LAB2.pdf b/LAB2.pdf new file mode 100644 index 0000000..4285622 Binary files /dev/null and b/LAB2.pdf differ diff --git a/README.md b/README.md index 476b991..6af0cb3 100644 --- a/README.md +++ b/README.md @@ -1 +1,6 @@ -# MCMC-for-Brown-Dwarf-WISE-data +# MCMC for Brown Dwarf WISE data + +Exercise in using Markov Chain Monte Carlo via the emcee module. The code is meant for the exploration of the MCMC algorithm in general, its advantages and limitations and as a lesson in building a functioning repository, working testing via travis CI. + +### Referencing +line.py from http://dan.iel.fm/emcee/current/ diff --git a/chains.dat b/chains.dat new file mode 100644 index 0000000..5146fa4 --- /dev/null +++ b/chains.dat @@ -0,0 +1,100001 @@ +col0 col1 +74.3208687261473 -56.344810272695184 +73.34593767880021 -55.93993398012154 +73.34593767880021 -55.93993398012154 +73.34593767880021 -55.93993398012154 +76.37851496609066 -54.94222932812573 +76.37851496609066 -54.94222932812573 +76.37851496609066 -54.94222932812573 +84.23953226568872 -53.929469479807906 +84.23953226568872 -53.929469479807906 +86.32015084199206 -52.37408671708897 +105.61562166301385 -50.00682334868801 +117.35782947769329 -48.53306463578704 +118.7040583102206 -47.36116049625225 +121.319996527789 -46.685077373125544 +123.89653977309153 -46.57995956883873 +123.89653977309153 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emcee +import corner +import numpy as np +import scipy.optimize as op +import matplotlib.pyplot as pl +from matplotlib.ticker import MaxNLocator + +# Reproducible results! +np.random.seed(123) + +# Choose the "true" parameters. +m_true = -0.9594 +b_true = 4.294 +f_true = 0.534 + +# Generate some synthetic data from the model. + +y_list = [] +x_list = [] +yerr_list = [] + +N = 50 +x = np.sort(10*np.random.rand(N)) +yerr = 0.1+0.5*np.random.rand(N) +y = m_true*x+b_true +y += np.abs(f_true*y) * np.random.randn(N) +y += yerr * np.random.randn(N) + +# Plot the dataset and the true model. +xl = np.array([0, 10]) +pl.errorbar(x, y, yerr=yerr, fmt=".k") +pl.plot(xl, m_true*xl+b_true, "k", lw=3, alpha=0.6) +pl.ylim(-9, 9) +pl.xlabel("$x$") +pl.ylabel("$y$") +pl.tight_layout() +pl.savefig("line-data.png") + +# Do the least-squares fit and compute the uncertainties. +A = np.vstack((np.ones_like(x), x)).T +C = np.diag(yerr * yerr) +cov = np.linalg.inv(np.dot(A.T, np.linalg.solve(C, A))) +b_ls, m_ls = np.dot(cov, np.dot(A.T, np.linalg.solve(C, y))) +print("""Least-squares results: + m = {0} ± {1} (truth: {2}) + b = {3} ± {4} (truth: {5}) +""".format(m_ls, np.sqrt(cov[1, 1]), m_true, b_ls, np.sqrt(cov[0, 0]), b_true)) + +# Plot the least-squares result. +print(m_ls*xl+b_ls,xl,"this is it") +pl.plot(xl, m_ls*xl+b_ls, "--k") +pl.savefig("line-least-squares.png") + +# Define the probability function as likelihood * prior. +# log of prior distribution +# m -> slope +# b -> y-axis intercept +# lnf -> log of the fractional amount that the likelyhood function is understimated by + +def lnprior(theta): + m, b, lnf = theta + if -5.0 < m < 0.5 and 0.0 < b < 10.0 and -10.0 < lnf < 1.0: + return 0.0 + return -np.inf + +# log of the likelyhood function is a Guassian understimated by fractional amount + +def lnlike(theta, x, y, yerr): + m, b, lnf = theta + model = m * x + b + inv_sigma2 = 1.0/(yerr**2 + model**2*np.exp(2*lnf)) + return -0.5*(np.sum((y-model)**2*inv_sigma2 - np.log(inv_sigma2))) + +# using the log of prior and lilyhood function to determine the log of the probability + +def lnprob(theta, x, y, yerr): + lp = lnprior(theta) + if not np.isfinite(lp): + return -np.inf + print(lp + loglikechain[0]) + return lp + lnlike(theta, x, y, yerr) + +# Find the maximum likelihood value. +chi2 = lambda *args: -2 * lnlike(*args) +result = op.minimize(chi2, [m_true, b_true, np.log(f_true)], args=(x, y, yerr)) +m_ml, b_ml, lnf_ml = result["x"] +print("""Maximum likelihood result: + m = {0} (truth: {1}) + b = {2} (truth: {3}) + f = {4} (truth: {5}) +""".format(m_ml, m_true, b_ml, b_true, np.exp(lnf_ml), f_true)) + +# Plot the maximum likelihood result. +pl.plot(xl, m_ml*xl+b_ml, "k", lw=2) +pl.savefig("line-max-likelihood.png") + +# Set up the sampler. +ndim, nwalkers = 3, 100 +pos = [result["x"] + 1e-4*np.random.randn(ndim) for i in range(nwalkers)] +sampler = emcee.EnsembleSampler(nwalkers, ndim, lnprob, args=(x, y, yerr)) + +# Clear and run the production chain. +print("Running MCMC...") +sampler.run_mcmc(pos, 500, rstate0=np.random.get_state()) +print("Done.") + +pl.clf() +fig, axes = pl.subplots(3, 1, sharex=True, figsize=(8, 9)) +axes[0].plot(sampler.chain[:, :, 0].T, color="k", alpha=0.4) +axes[0].yaxis.set_major_locator(MaxNLocator(5)) +axes[0].axhline(m_true, color="#888888", lw=2) +axes[0].set_ylabel("$m$") + +axes[1].plot(sampler.chain[:, :, 1].T, color="k", alpha=0.4) +axes[1].yaxis.set_major_locator(MaxNLocator(5)) +axes[1].axhline(b_true, color="#888888", lw=2) +axes[1].set_ylabel("$b$") + +axes[2].plot(np.exp(sampler.chain[:, :, 2]).T, color="k", alpha=0.4) +axes[2].yaxis.set_major_locator(MaxNLocator(5)) +axes[2].axhline(f_true, color="#888888", lw=2) +axes[2].set_ylabel("$f$") +axes[2].set_xlabel("step number") + +fig.tight_layout(h_pad=0.0) +fig.savefig("line-time.png") + +# Make the triangle plot. +burnin = 50 +samples = sampler.chain[:, burnin:, :].reshape((-1, ndim)) + +fig = corner.corner(samples, labels=["$m$", "$b$", "$\ln\,f$"], + truths=[m_true, b_true, np.log(f_true)]) +fig.savefig("line-triangle.png") + +# Plot some samples onto the data. +pl.figure() +for m, b, lnf in samples[np.random.randint(len(samples), size=100)]: + pl.plot(xl, m*xl+b, color="k", alpha=0.1) +pl.plot(xl, m_true*xl+b_true, color="r", lw=2, alpha=0.8) +pl.errorbar(x, y, yerr=yerr, fmt=".k") +pl.ylim(-9, 9) +pl.xlabel("$x$") +pl.ylabel("$y$") +pl.tight_layout() +pl.savefig("line-mcmc.png") + +# Compute the quantiles. +samples[:, 2] = np.exp(samples[:, 2]) +m_mcmc, b_mcmc, f_mcmc = map(lambda v: (v[1], v[2]-v[1], v[1]-v[0]), + zip(*np.percentile(samples, [16, 50, 84], + axis=0))) +print("""MCMC result: + m = {0[0]} +{0[1]} -{0[2]} (truth: {1}) + b = {2[0]} +{2[1]} -{2[2]} (truth: {3}) + f = {4[0]} +{4[1]} -{4[2]} (truth: {5}) +""".format(m_mcmc, m_true, b_mcmc, b_true, f_mcmc, f_true)) diff --git a/mcmc.ipynb b/mcmc.ipynb new file mode 100644 index 0000000..3635889 --- /dev/null +++ b/mcmc.ipynb @@ -0,0 +1,465 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from astropy.io import ascii\n", + "import scipy.constants as con\n", + "\n", + "# Get the data using the astropy ascii\n", + "data = ascii.read(\"SED.dat\",data_start=4)\n", + "lam=data[0][:] # Wavelength column\n", + "logf=data[1][:] # log10(flux)\n", + "errlogf=data[2][:] # Error on log10(flux)\n", + "\n", + "# Shape parameters for priors\n", + "Teffmin = 10.0\n", + "Teffmax = 1000.0\n", + "logfacmin = -100.0\n", + "logfacmax = 0.0\n", + "thetashape=np.array([[Teffmin,Teffmax],[logfacmin,logfacmax]])" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Set a definition for the model\n", + "def model(microns,Teff,logfactor):\n", + " wavelength = microns*1.0e-6\n", + " flux=np.empty([len(wavelength)])\n", + " logflux=np.empty([len(wavelength)])\n", + " for i in range(len(wavelength)):\n", + " # Flux is just the Planck function\n", + " flux[i] = ( (2.0*con.h*con.c**2)/(wavelength[i]**5) )/( np.exp( (con.h*con.c)/(con.k*Teff*wavelength[i]) ) - 1.0 )\n", + " # So logflux (which is what we want) is just the log of this\n", + " logflux[i] = logfactor + np.log10(flux[i])\n", + " return logflux" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Set a definition for the loglikelihood, assuming normally distributed data\n", + "def log_like(lam,logf,errlogf,theta):\n", + " residuals = logf - model(lam,theta[0],theta[1])\n", + " loglike=0.0\n", + " for i in range(len(lam)):\n", + " loglike = loglike - np.log(errlogf[i]) - 0.5*(residuals[i]/errlogf[i])**2\n", + " loglike = loglike - 0.5*len(lam)*np.log(2.0*np.pi)\n", + " return loglike" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Set a definition for the logpriors\n", + "def log_prior(theta,thetashape):\n", + " \n", + " logpriors=np.empty([len(theta)])\n", + " #logprior=0.0\n", + " \n", + " # Prior for theta[0]: Teff~logU[Teffmin,Teffmax]\n", + " Teff = theta[0]\n", + " Teffmin = thetashape[0][0]\n", + " Teffmax = thetashape[0][1]\n", + " if Teffmin < Teff < Teffmax:\n", + " logpriors[0] = ( 1.0/(np.log(Teffmax) - np.log(Teffmin)) )/Teff\n", + " else:\n", + " logpriors[0] = -1.0e99 # -infinity\n", + " \n", + " # Prior for theta[1]: logfac~U[logfacmin,logfacmax]\n", + " logfac = theta[1]\n", + " logfacmin = thetashape[1][0]\n", + " logfacmax = thetashape[1][1]\n", + " if logfacmin < logfac < logfacmax:\n", + " logpriors[1] = 1.0/(logfacmax - logfacmin)\n", + " else:\n", + " logpriors[1] = -1.0e99 # -infinity\n", + " \n", + " #logprior = np.sum(logpriors)\n", + " return np.sum(logpriors)" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Initialize the MCMC from a random point drawn from the prior\n", + "Teffinitial = np.exp( np.random.uniform(np.log(thetashape[0][0]),np.log(thetashape[0][1])) )\n", + "logfacinitial=np.random.uniform(thetashape[1][0],thetashape[1][1])\n", + "thetachain=np.array([[Teffinitial,logfacinitial]])\n", + "# Calculate the associated modified loglike\n", + "loglikechain=np.empty([1])\n", + "loglikechain[0]=log_prior(thetachain[0],thetashape) + log_like(lam,logf,errlogf,thetachain[0])" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Define the proposal jump size\n", + "Teffjump=5\n", + "logfacjump=0.1\n", + "thetajump=np.array([Teffjump,logfacjump])\n", + "\n", + "# Starting walking\n", + "j=0\n", + "jmax=10000\n", + "while True:\n", + " \n", + " # Generate a proposal (or jump)\n", + " thetatrial=np.array([np.random.normal(thetachain[j][0],thetajump[0]),np.random.normal(thetachain[j][1],thetajump[1])])\n", + " logliketrial=log_prior(thetatrial,thetashape) + log_like(lam,logf,errlogf,thetatrial)\n", + " deltaloglike=logliketrial-loglikechain[j]\n", + "\n", + " # Compute Metropolis Rule\n", + " if deltaloglike > 0:\n", + " probjump = 1.0\n", + " else:\n", + " probjump = np.exp(deltaloglike)\n", + "\n", + " if probjump>np.random.uniform(0,1):\n", + " # Accept the jump\n", + " j = j + 1\n", + " loglikechain = np.append(loglikechain,logliketrial)\n", + " thetachain = np.vstack((thetachain,thetatrial))\n", + " \n", + " if j==jmax:\n", + " break" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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FInIRMAt4K3FhKadDeOzuCQzqn9Ki5Wb3evalzVTX6JxWSqm216zEYYz5P+Ap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\niqzlccNvv6G0LMihBTlMP6U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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "%matplotlib inline\n", + "\n", + "plt.plot(loglikechain)\n", + "plt.xlabel('Chain number')\n", + "plt.ylabel('loglike')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Burn point = 180\n" + ] + } + ], + "source": [ + "loglikeburn=np.median(loglikechain)\n", + "j=-1\n", + "while True:\n", + " j=j+1\n", + " if loglikechain[j] > loglikeburn:\n", + " break\n", + "burnj=j\n", + "print( 'Burn point = ',burnj)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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mjmSxiU4CUBozbcGUo4Lmrh4mDMi3hpTjgkAZoiSgqiyIQgeacmixRVp3n0Uh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\n49xr1zz//wZ+50td3xSvP3zlO5b5T594I2/qPkiSpKgI3b6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PTLXUEDXspDQWNSOqbhGa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\n4ziOsyJcQHEcx3FWxP8PoGMzDuiRNK4AAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Temperature [K] = 251.7 - 3.5 + 3.6\n", + "log10(factor) = -22.462 - 0.08 + 0.082\n" + ] + } + ], + "source": [ + "%matplotlib inline\n", + "\n", + "jlist=np.arange(len(thetachain))\n", + "plt.scatter(thetachain[burnj:,0], thetachain[burnj:,1], c=jlist[burnj:], cmap='coolwarm',alpha=0.5)\n", + "plt.xlabel('Temperature [K]')\n", + "plt.ylabel('log10(factor)')\n", + "plt.show()\n", + "print( 'Temperature [K] = ',np.round(np.median(thetachain[burnj:,0]),1),'-',np.round(np.median(thetachain[burnj:,0])-np.percentile(thetachain[burnj:,0],15.9),1),'+',np.round(np.percentile(thetachain[burnj:,0],84.1)-np.median(thetachain[burnj:,0]),1))\n", + "print( 'log10(factor) = ',np.round(np.median(thetachain[burnj:,1]),3),'-',np.round(np.median(thetachain[burnj:,1])-np.percentile(thetachain[burnj:,1],15.9),3),'+',np.round(np.percentile(thetachain[burnj:,1],84.1)-np.median(thetachain[burnj:,1]),3))" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "ascii.write(thetachain[burnj:,:], \"chains.dat\")" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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J22CJDwL9Wdx7OnvFBq54bgbXvPh54GNd9uxnFU4WlQKFEqcaUfWth94+gbI8pLOPmkiV\nhYjUw1EUY1R1nLt6OTBOHaYA5UArYAXQOW73Tu66SDn7kU/ofcPrUZ8mKVt3+Fdu8Qnh7nnL6ZbG\nK6k3565K3CUtYl39ZF36+Dpi7ZadTF/6XcXvWGs+iOKL8drsb7jq+ZmByr47/1te9Wk5Zuuz/GZD\negOpExd8G8hskVh/bNmxm9dnf5Oy/NUhKtMZWZikKJ3e666y1PvUiatddsddfEyph/HIg+ruvvFs\n3bk7pddiIlFX48u/28aOiOaayeesjlF6QwnwKDBPVe+O2/QSMNwt0xOoD6wB/gucKSINRKQb0AOI\nfOT3w4VrA7dIf/f8TB56/6vQ53hs0mI+i6tgwxDfeclm1tPYccvcAJ9k6XLilVJs8fbX5/PDBz6i\n2hYf0YbdMYFzH50cWs6fPPEplz4TLD1GJh29jdt3Mfgv3pHKyerSFeu3ccHjn3LlWH/lF+tZfLtx\nO1MWr2PUuFn84ulpVcqEHUtYtXE790/4kpNDTlKU7DSLVm+uvtKHSQsr424Sb49feplsDpv94unp\nHPfXD8JV0kXW+N9dVp7XWR2jTPcxBDgXmCUisUT31wKPAY+JyGxgJ3C+Ok2aOSIyFpiL40l1qarm\n1a6QOEnK83GmkzAv+s2vzAVgyW0nhJch7nsrz8IwSWwwPSZ+92vHc1LfDhzRyzHphW1dxuQrV+99\nl63bxrJ16aep8MJL5KB174c+wYap2OZO+PNViIp2y84yTn/oY/p3aVZtW1iFd+boT6rNmeL1HGIN\njnQUa+JRF37r3cotqZO8LRrkmUxc8C0XPB4sdboITFnseC+FMf94Nb4y1SNRpEEvy7NTSpTeUJNU\nVVT1e6raz/0br6o7VfUcVe2jqgNUdULcPn9S1e6q2ktVU8/cUgAomtUXInGuhWXrtrIyIQAu1asy\nYf4qnp2yNNT51m/dxfUvzQacwUOvDzhIj2bwX97h7EeS9xyO/2tw18f/zFhB6TWvRuZbn4pLxqSf\n3A+y2EgN+UolMxs+l6OxjjMe8s5iXKdqt7gaCvz7s+pjV5O+XJNUUaQzRjhm8tcpvaVqkENgTrAI\n7kzIYuMhcZ7lYXe8yyF/mVBFIaVqMV74xFRGjZsV+pxPfVLd/Tfo9xPzbonPKfRRnG/6+Fkr+Xy5\nY0efG9CWDJUV3ZeJg5kehK1EguTKCj7DYfovQTYqq2TXvuy76Gb0u+WVuYxzPbVSxRqt3LCtWuNn\nR1zZeJF/81x18905aZgrY6zZtJPR7y9CVdm2s4zr/j2bY+59P6mXX+z2L16zpVovKdNPO/Zcxkz+\nOucNn6gwZZEJOWiZ5CqjSGIvqbxc+XBhZeWfKMfh/zfR83i/HDOdk+7/kI8WhjPvhK1Ay8o1pbtv\nMt7/YjVH3DmRlz7z9p2YmWTAOJlsExe4YUIB5A4yU1/Y3mqyAeYg9zD52Ij/uR+dtLhyfCZF8SG3\nTajW+MkkU24YLn/uM/48fj5zV26s6BFv3VnGDf+tDKBMvD/D75zIiLurjgXEF1mxflsob7/YOVas\n38Z1/57Nz56qOi41duqyogz6M2WRgkWrNzP16/QGpbPJd1srA5LCVKRBMsQmI3aOhz/4imv/PSv0\neRP5cQrTVPXzKk99vKTieoNWmcfe+36lP3qSnbYkOC984XqTzPKpuIMq6ekhHBeCZHYN0zhINxgt\n9Xm8H3TQ9yDosEEUrs6b3PQum7fvriLvK0niNJL11JPdlyG3TeDCNKae3bU7eUr6q1/4nLMeDjcR\n2VF3TeR0j8DFXGDKwmXn7nK27qwMEjrLZ1a5TxevS2vAaf43GwNF8sZYub6yCxvETx9gzv82cFrI\nFytxQpi/vFYZvLcyTZfSMMxduZHr/zOH+d+Ecw30M1f9MsVYhN+tDOqVNH6W4/q6butOLh0z3dOF\ntnmj+r7HC6orSq95lWF3vBuo7D1vfZFRfqZscfYjzjcVu7XzvwlunkxGskcYGyc5Y/QnzFzu7U6c\nuP83G7bzVgpX9I+S9AQufWZ60jEXSPAkFKdXee6jk6uY7u59+wu6jQqWtHLR6i3MXJ7ZHPKZktIb\nSkTuTrUtjo2qemP2xMkfpz74EZ8v31DhseTX7Xx3wWoeej98xPCx935A270aMPnaEaH3DaqaYik9\n0iFZaysXAUY7IoqIT2ZOAv9B+2cnL+Wkvh0C77N+6y5enbWSA7s258Kh3ZIXStAE8b3GKPnrO058\nTrw3XnKlFM4EFtZCGjNrxl6xxFdt/dadgXslqYh3142PPUl22MTzh23tv/r5Sl79fCWn9O/kWe7r\ntVu5+oXPmbtyY0XPFuDet4Ol8zjUx6U7V3i5zv4IuNln/98CN2ZNmjzyuYfWTjWwvCihVbt4zRYW\nfbuZEb3bep5r1cbgeX9en1MZtBXrWXy6xNv0kc70qYWebj1bVMxl4FMpffxV9m3Kic/l67XVzUhR\nP4ZseQCd++hkNvpk9A17qn43v+W5/YT7JjHmpwd7lgn0HqcQLJlTw6w8tObjx+AKKV2+l7L4m6o+\n6rWziDTPsjx5547X53PFiJ6ByiYbKIP04imCnTBY4FRG80ynv2tBsGN3Gd9t2UWDkjqs3ZL7zLqx\n+7dywzbuevML/nzKARXb6gSox6Lwz09+oszO80GacSmZ8nKSsQfBP+dVulcb776+aPVmurduXK3M\nsfe+z0uXDqm2PlmAa5Bv8443FoQVMyd4KYtnU20QkeNU9TVVvTMCmfLKAxMX0XSPehl3hzMhVU9G\ngW0R5T/y+5jGTo0msV2MrLiRIvz6mc94c+4q2u3VkG+SuCy+HwtKTOOE46av4I5T+wYqe/1Lc3h7\n3qpAg9rxZCNKv1AUfj76qql0YLr3pG6chj/qrveSNgTnf7Op2jS1IjBj2XdVfjty+Evybh4mNgqC\nl7J4W0SOUdUq0V4ich6O6WnvKAXLJ/GDu15EZXOe87/UA39+ddw781YljZ8ITBHXNC99tqJCQSRT\nFPGkc5m702hBhE0/n+ocu8vKA7+XqSgvr6yq7n0r+oymUbxK8cogaC4oL1LFQCz8djO922/l7+8m\nT6zph2rVGJIvvkltEbj7rS8Yuk8rGpTUYWTItC25xMsb6mochVGhFETkd8DvgSMilqsomL40+eBp\nzOvDj283VX9Rb3ttfkpPrMVrtvi6xF70z6lMXBA+dXuYlk8mpHYcCH/eX46p6r/upyDiefLjrymP\nsPuYrIUbxMSUqjHw9rxVPDppcaBzpzrG3teOr8jcujaER142mTB/lefcFWGImcKem1oZsR5/3xev\n9g+sHHp7co+y/3tjAcPueDflN57Isfd6ZynYGcv2nOTZ3PfOl5z+0Me8OTd1UslCIKWyUNWXgV8D\nb7gz3N2JM+h9WGJvw6jKhwvX8vsX/DOGnnR/9VbEg+8tYpNHnv935mcny2wisYpMFd8sr5mw7/XZ\nyfCrqhVuq+nS/xbvAdV08DJvZTJMkE6vBqhI6ZIPkl3u718Mn2nAj69Wb6mojOOdCJ5PkQY/vkG0\nM+Qc7S9MWx7IhJkq6NNrTvhCTz/iGWehqm8APwPeB/YDhqtq8YUe5oH41k4ytoSY+CWebCQTTEZ8\nRRY0y2uU+LXCg6Y49yJdF+MgrsTJpM+kMkjmOZWK5z6tbMuFMUlm6omVeH3JLtersgxGciH9Brg3\nhZyLPRW/fX4mb8zxb6QsTREwWcxzvHvFWXyH87wFaAQMBVa4qcdVVVvkRsT88/Tkpbz8ufdDThWc\nE8+GrZWV0+H/FyygKpGozURe8xNESbKK1Gu+g3HTI5/qJCmPfPCVZ1Dllh1l1SJ2w5Cqsvu/EB4y\n323N75SgXqzPULZZK3zMQjlwAd+wbRdv+8wjkypgN9+ZYzPBa4C7Vc6kKHCSueslkiwhWiJ9b36z\nYjnVvMJ+RGVmj31iQaPEs03iWbfvLuNI1xUZYOqSdZz64Mf891dD+F6n6qm9c8Wtr87z3H7P219w\nz9tfcMz+1WNtakkoSwWTI4hVmb3Ce1A7F7e4XGGKz9hhlONh+cJrzKLM6y+XQhqVeNlL053pDSor\nslzWZ6rK81OX8c2G7fw7wcZ70ROfVsnr9I7rTnjJ0/k3kUXFSfdPSmtyrUIifsbE+1JM0RsluVDI\nt7rz03gRm0o3Ea+2WPBMx/nByww1RVUHee0cpIyRXbyiv4+4Mz3TVjy5bP2+8vlKfpfCESBVwyxX\n2UvzgVcWgWKh2jzZOcbv9f10ybpAKeq92LKzjNFpKnWvxt5rHlPsFgJeZqgDRMSrGSdAyyzLY/iQ\nauAMYPuuzEe/c2mF8oonqYnU9JQqazbvYHqeMzV73ePFa7aETrBpVOKlLPoE2D87LgZGAZD7iuzB\n98InYiwWcpa2I4tkQ2K/MZ2o8RpzO+quibkTJAVFPL6dWlmoas39ko2UhHmX3w8ZnVybeD2Je2Xx\nqY/i4zOPILpCGHOO2psxSmw+iwLit1mIHUiXdCwk5z02JfuCpOAfE63tYhQ/haCw0sWURQHxQoqI\n01ySL9fZ2kCYucgNo9AIpCxEpJOIDHeXG4jIntGKZeSLdPJK1VQKaS6BXBB1ZmGjuPFVFiJyIfBf\n4BF3VVfgP1EKZRhG7qnJDgeFwrAe2Yt1ziRTQDoE6VlcBgwGNgKo6hdAmyiFMnKPDb4aRvQ0rFc3\na8eal+Ec5mEJoiy2q2qFChORutSAumXbzjL6x6XfMIqH9Tmau9owss1jAdPMFyJBlMWHInI10NAd\nt3gOeCVasaJn8ZotBZ1wLdcUU8CY31zNRmas3LCNS8fU3LQq+WTyYu+cUmHIdSxPEGVxNbAJmA9c\nDrwDXOe3k4h0FpF3RWSuiMwRkcvd9TeKyAoRmeH+He+uLxWRbXHrH0z/sgzDSJc/j5/Pq7Oim9PE\nKE68IrhjJqfHVPV84B8hj70buEpVp4tIE2CaiMSahPekmL97kar2C3metCjm4JgomPO/4s9LZGSH\ndOYnN2o+nspCVctEpL2I1FPVUDYbVV0JrHSXN4nIPKBj+qIaUXLv21/mWwSjAFjmkXvMKCxybTkO\nYob6CvhAREaJyGWxvzAnEZFSoD8w2V31KxH5XEQeE5HmcUW7ichnIvKeiAxLcayLRWSqiExdvTr9\nmIBizN1jGFGTbjZVo+YTRFmsBt7CmS2vddxfIESkMfAicIWqbsQxZ3UH+uH0PO5yi64Euqhqf+BK\n4BkR2SvxeKo6WlUHqurA1q0Di5F4DK7/T/7mJjaMQkXRok52Z0SHpxkKQFWvT/fgIlIPR1GMUdVx\n7vFWxW1/GNezSlV3ADvc5WkisgjoCUxN9/yp2FlWzrQ8p1I2jELk6U+W+hcyCoJc20Z8lYU7KF2t\nraGqR/vsJ8CjwDxVvTtufXt3PAPgFGC2u741sM4dJ9kb6IFjAjMMwzASyLW7u6+yAP4Qt9wQ+BEQ\nZP7OIcC5wCwRmeGuuxY4S0T64SigJcDP3W2HATeLyC6gHPiFqmbPKdkwDKMGkesB7iBmqMkJq94T\nkYkB9ptE8p7S+BTlX8QxWUWO2WQNwzDCEcQMFT/IXAc4EOgQmUSGYRiGLwU3ZgHMwTEZCU6g3WLg\nZ1EKZRiGYXhTcGYoYO/EgDwRCbKfYRiGUUMIEmeROGYBkLv5NCPAxiwMwyh+CsQbSkTaAO2BPUTk\nACol2wsnQM8wDMPIE4VkhjoBuBDoBDwQt34TkHagXiFgSQQNwzDCkVJZqOrjwOMicrqqjs2hTIZh\nGIYP23aW5fR8QeIsxorIMcD+OEF5sfV/jlKwKLExC8Mwip2rX/icD685MmfnCxJn8QDQDCfC+nGc\nCO5PIpbLMAzD8GDF+m05PV8Qb6ihqvpjYK2bVPBgnHGMosU6FoZhGOEIoixieaC2i0g793dpZBIZ\nhmEYBUeQ4LrxItIMuBOYAZQB/4xUqoixaSMNwzDC4TcHdx3gNVVdDzwvIq8Ae1g2WMMwjNqFpxlK\nVcuBe+N+b6sJisL6FYZhGOEIMmbxtoiMjFwSwzAMo2AJMmbxK6CpiOwAtuGk/VBVbRGpZBFiQxaG\nYRjhCKIsWkUuRY6ZMH+VfyHDMAyjAl8zlKqWAacBv3eX2wP9ohYsSjZu251vEQzDMIoKX2UhIvcD\nw3Hm0wZbsYxOAAAgAElEQVTYCjwYpVBRY66zhmEY4QhihjpUVQeIyGcAqrpOROpHLJdhGIZRQATx\nhtrlxlsogIi0BMojlSpirF9hGIYRjiDK4u/Ai0BrEbkJmATcHqlUEWNWKMMwjHAESVH+pIhMA0a4\nq05T1dnRimUYhmEUEkHGLADqArtwLDhBeiMFjXUsDMMwwhHEG+o64FmgA05q8mdEZFTUgkWJeUMZ\nhmGEI0jP4hzgQFXdCiAifwKmAX+JUjDDMAyjcAhiUvqaqkqlBPjKbycR6Swi74rIXBGZIyKXu+tv\nFJEVIjLD/Ts+bp9RIrJQRBa4U7kahmEYBUCQnsVWYI6IvIFj7j8amCQidwOo6pUp9tsNXKWq00Wk\nCTBNRN5yt92jqnfGFxaR3sCZOHN9d8BJYNjTjRrPKmaFMgzDCEcQZfGq+xcj0PzbqroSWOkubxKR\neUBHj11GAv9S1R3AYhFZCAwCPg5yvjB0b7Nntg9pGIZRowniOvtopicRkVKgPzAZGAL8SkTOA6bi\n9D6+w1Ek8YpoOUmUi4hcDFwM0KVLl7TkaVhSN639DMMwaitBvKGOFZFPReRbEVknIt+JSOAJkESk\nMU5Q3xWquhH4B9AdJxnhSuCuMAKr6mhVHaiqA1u3bh1m1wrKzA5lGIYRiiBmqPuB04FZhEzzISL1\ncBTFGFUdB6Cqq+K2Pwy84v5cAXSO272Tuy7rlJuuMAzDCEUQb6jlwAxV3aWqZbE/v51ERIBHgXmq\nenfc+vZxxU4BYtHg/wXOFJEGItIN6AFMCXohYSi3noVhGEYogvQsrgZeFpGJwI7YSlW9z2e/IThp\nzWeJyAx33bXAWSLSD8ezagnwc/d4c0RkLDAXx5Pq0ig8oQC6tbQBbsMwjDAEURY34aT6aEYIM5Sq\nTsKZgjWR8R77/An4U9BzpEtpK1MWhmEUNz8c4OVcmn2CKIs2qnpg5JIYhmEYwcmxNT3ImMUEETky\nckkMwzCMgiWIsvgpTjT15nRcZw2jJrNvuyb5FsEwckIQM1SryKUwjCJlQNfmzP9mU77FMGohufbp\n9O1ZuB5JpwG/d5fb4wTUGYZhGLWEIBHc9wPDcdxgwUks+GCUQhnFQ2nLRvkWwTCMHBDEDHWoqg4Q\nkc8AVHWdiNSPWC7DMAzDg1xP4hZkgHuXiNTBNZGJSEtCpv0wai516iQLpalkwlWH50iS/OB99QbA\nfu33yrcIRhZIqSxEJNbr+DtOfqfWInITMAm4PQeyGUWAX2XZqkmDnMiRLyxxjD/zVm7MtwgZM7xX\neklLaxJeZqgpwABVfVJEpgEjcOqG01R1tsd+Ri3CSQHmsT1HchhGlLRruke+RahGIXlDVXznqjpH\nVf+qqveaoqh9dGjaMOU2P2Xgp0wKjbevDGc2C3J1R/dum54wRgFhfUivnkVrEUk1ZSrxmWSNms1H\no46i+7XjKUuS291PFxSXqoB92jTO+jHbeyhbwygWvHoWdYHGQJMUfzWeMwZ29i9UyxEfdVBkHQvD\nSErDeja7plfPYqWq3pwzSQqQ20/9Hs9NXZZvMQoa/55FYWiL0wd2YuzU5Xk5d7GZ4nJNr7ZNWLCq\nsKPgzzuklMc/XJJvMfJKoDELozrdW+9Jz7bZN1nkgh/2D5/aOF2f7kKpJ+84ta9vmWl/GJEDSYxE\ntAjGA1o2rs/B3VrkW4wq5HoONy9lcVTOpChCRIRBBfbyBOXQfcKn+0r1XhZ7q3n/DpUxAC0b12w3\n33wQJMYik0rv3jOizzz01zP7sVfDegWn0grGG0pVLbNsRPz8sL3zev4OTRty68l9snKsq4/tlZXj\nhGFoGsouFQeVZqbwzZadOZlMc9ynY9MsSlKd647fj5H9UvfEW+yZv2QWPvGw2T9fbk9nQPQveBB6\nd8g8qnbv1nsyvFcbzzJRdDwKqUd35fd7Bip3x6nfi+T8L106JJLjJuPArs2Trm/SoITfjAh2H5JR\naC32VCR7lUf265BzOWLkuk9vyiJNMnlQvbI0B8IFh5amva9fY27WjUf7lt+ntf+YTRQD3F4tqmP3\nb1fl99ifH8Lzvzgk6zLE2LOBf3o1ETg9Is+6fp2bcVyfdv4Fs8CLlxyatFf85EWDaNIwSJq5FESg\nLU5JY1wuHc4d3DUn50lGrk3ApizyQKss2cZvPGn/9HYM8I41aVgv5bbvdXJ6Rr84orv/qSJ4n70+\nkr1bV86vXq+uM66UqamptlKvbrCH179L8h5HUHaWZTfV3MI/HUfbvXIT29Igj2ZI61kUCZcO3yft\ngbkmDUv4Qd/8dV8d0m/Oxa67bgBNkOkLnUmLdfDeLX3LxLy8vKLUMyVq9+HEYMkzD8pOLyZJDGYk\nNVR50hOlx3mHdKWkbp2UHlbv/2645/5Lbjuhyu8gnlofXO19zKjon8IsGBWmLNLk5Lhu7i0hB4vr\niFAvg9Gpxy4YyMPnDUx7/1yST2+pswZ1CVTuqYsGpWX7L5RsqokDxF0KaI6RIE8/i7qCAbFejnvM\nw3u2rhKVH39vsqFUBejcIvP7nU6j6JyDg73f2cKURQJhbJAxhXFod/8WbDxBq89E+3uMw3q05vsB\n8w01KEn+iL16Rcns0u3cbv1dp/nHK2SLKddm5r19/AHtA5Ub1qM1bdIwWzz7s4MDlYtaX15z3L6R\nHDeZGSpbvaR7zuhLw3rOuxn2+6lK1Rc5VnHHFOiQfVqmdK89vGfhZJL9ZNRRjP15uLE1G7PIM2Hu\n/0GlLVhy2wl0DzDQm845jtqv0tOof5dmoc4RY8GtxyVd79WYO/eQ6gqzT0enFT2sZ6uKrnnsOjq3\nSJ2RM/FSLx3uP84B0LVlI9rs1TByu2wmjdpmjYK5TUZ9Dfu0qeowEbZCT5UPK9lxggbQxRoXFwwp\nTVlmL3dc7LfH9KJ+ikaNH/GNnjd/c1iFx1ast1LH42Pzm4sll+zZoCQzJ4EcYMoigVy8PiKS8kT3\nnNG3ajng5H4dePEXh1ZbD3D36cFb+oP3rhzoDTvecu+Z/Xn2Z4Np06SyBR6rTF67/DAOS9FKS/xW\nD+/p7WobI/bRF2PQ31mD8ptTLGxEdM+2jWlUv/pAbZjjNGtU1SHi/auHs+S2EwJ5gdWtI3RqnnkK\n8J5tK5VmkPe7e5wzRCr8jpPN1zPXEdlhqbXKIqwWv2JED567eHD2BEjyYsy7+VhO6d+p4nfsPawj\nQp06kvTFrFc3+COMfxmDerrEaNyghENcc0Gvtk4vI3YPGzcoSam0cl3Zh/3e0v1AX79iWLV1sWDB\nxGsudH3XqH4Jc28+1rPMyW48Qapey8kJgWt+iib+OJlUkql2rez9pr75iT2yfFPoaU8iUxYi0llE\n3hWRuSIyR0QuT9h+lYioiLRyfx8hIhtEZIb7d0NUsgGMv6z6x+7KkXT9CQe05+AA3jWpuPrYXinH\nD2LskaR1FxX9OjdjVJyt+84QYxF/OqUP/7p4MKWtKltmQevDHgkmj1RjRImVjxfNG6V28/Uj5gYc\nln3bVR/cPmdwF0b268AvE1yKC713lOq9rO82RAaVtuDeM/t7HiPRpBNEAWRyW2KypTqPVpih0j9H\nrmjV2DFnxl9LUOeMXBKlkWw3cJWqTheRJsA0EXlLVeeKSGfgaGBpwj4fqOqJEcpUQboeDC9dOsTX\nZfSIXq2ZuGB1lXW/PGIfTj2wEwu+cbNr+rzEforFixH7teXteas8y4gIPz+8O395bT4AzfYIXuE2\nrFe3mluqV4X4/u+GU6cOdGpe/Z4f0as1T33ydZV1vz9235RmrWRcc9y+/P7FWY4cgfeCXx7RnVMP\n7ORfMCCN6pfw1zP7s2XH7qwdMxd0TeE91Wavhtx6So8q6VXyrfdu/9EBfLlqMxcMKWXJmq0pW+Ox\nAW6vMYtUnH1wF8ZMXkrXlo2qeD0mO1SQ8aFOzfdg+Xfbqq1fctsJLFu3tWLsJp6SAtRykfUsVHWl\nqk53lzcB84DYnb8HuJoCi/Q/vGfraq3CGLEXpV/nZhyQZmu0TZOGDOvhVIL16lS99fFmsacuGsQ7\nV1XO2Ba7Sclen+SmKb+pTqtvT2azzpTYvezSslFSRRHfyzhy3zb8/PDqXlhBeg3ptty7tGiUlVZ/\nYm/J75AHdGwaaWUQ1qyTqsJTVU7q2yGt/Ed+5lEReODsAzm6d1taN2kQWMmfcVAX/nBibzo1b8TQ\nHq3o0Cz5WEelsgiv4G49uQ8L/3Qc7/1ueJXgvnTMZRcO6cYbVxyWcnvnFo1o6vOOx49j5pOcjFmI\nSCnQH5gsIiOBFao6M0nRQ0Rkpoi8JiJJw5NF5GIRmSoiU1evXp2sSNr888JBablQJhLkparmCx+3\nz7AerenUvFG1l/zHrl+137sfJu5j9k3H8KdT+lSMR6RLshTmXp4wAC/+8lDP7QBP/9TfPTW+9Rik\nYkiV4yhdYhWK37mfvHAQfzurPy//eqhncrpMSRxszgd1AyjDA7s2Z/R5AwOVTUWyVjnAoG7O+5xO\nLIyIUBJwLNDvmd/wg97s2aCEZ352MJ+MOoq5Nx+TsmyqeqNzkoZWPohcWYhIY+BF4Aoc09S1QLLx\niOlAV1XtC/wNeCnZ8VR1tKoOVNWBrVvn0k/a+63INIVHskCq4w9oz8n9OlSMLdx8Uh/m33Ksr8tf\nGFkaNyjh7IO7ZtzCTiewqtqHnuQYyXokiYSta4LktArDLSf34ejebSsSHKZqqR/Ws7Vn5P6FQ7pl\nRZ7j+7TnrtP6Vriv+pHq0V97/H5ZkSeYDNntaZ3UtwOfXjeCgXGpXvIZRHlo91a0a9qQRvWDWf79\nFGg+gnIjVRYiUg9HUYxR1XFAd6AbMFNElgCdgOki0k5VN6rqZgBVHQ/Uiw1+FwNnHJS+7fvh8wby\nzwsHVVvfsF5d7j2zf0Vvp04dqZYSO4xPfZQ2v3QnR0q2W2K98dOhVSvRxHOlY5eG4PfjgbMHAKnH\nkbq12pPR5w2kQUlyU97FAVPS3/CD3p7bX7p0SCCTRN26wo8O7ES9kswq4KP2qx74GZXxLMhxHzxn\nQKhjtm5StdGU7jsaI5fjNXvFmaWTSR00KDebROkNJcCjwDxVvRtAVWepahtVLVXVUmA5MEBVvxGR\ndu4+iMggV7a1UcmXba76fq8Kj6Kwr+T3e7fNWnLBIKR66TPJj5RpyoZ4kRK/6T+cWLUS9XNNvfO0\nvp524rAMLG3ODwd0DGQSSyZPtp5tv87NqrhWp6IQB0cTCdqTePwnBwFOTMSxfZJH5B+7fztaeoyr\neDWobvvhAYHTzCdt2ATaMxipBusLJf4iyp7FEOBc4Mg4d9jjPcqfCswWkZnAfcCZmmlTIIv4vdt1\n6kicC1zBiJ2UVOJlYgqIz08U+3CD9HqG9WzFD/p2cDLopnn6xJ7FqQd2CpQGPsjp2jRpQJsmDbn7\n9H4cVNqCib89gjEBlUYmnDM4fdfJmAmjUOY/j3HNcfsyIEUmglSvXqcUA9jxPHjugUy7/vtpyXTm\noC5cdlSPtPaNp9Q1Iz954aBqPZpMKZT6JDLXWVWdhM/36PYuYsv3A/dHJU+mdGvpH+0ZprLNVpc2\n366MMWLKomOzPdixuyzwfg1K6vK3s7x9+BNJ/HjapdkjCvIJJs7KV9pqzyrxJeniF4B168kH8Msj\n9uHQ2yZU2/bB1cMZdse7KfctqVNYsbbNGtVj/dZdnHpgJ2at2ABL1wfet8ITsABedC8R3vzN4ZSr\n0rBeXT69bgSl17ya9nliqXXACQaul4EbfTYpDCmKgCB5ZPL/Ogcjiu8uVn+LpN9tjqWqDmtFiZ+v\nItvBYPls06WS0y9GqNCsUPE9vwaul1FYU1kmlxSpnnGPXb+kTtam2E3sEfbv3IzrT/Qez8oFpiyS\n0Ldzekn7Cp2j3UGxbOThSSTm2XR078pMuWE/0l1lTtXs57b4vU6F/XzCXPf5SZI2Zn5+CSVH84AJ\nEQF6tM3Mk+z6E3vz88P2rngX/cimBcbrWAO7NvdVYPmyBokIFyU4eeSDwk5zmCee/dnBfLd1V9r7\nB3mp0vXgSSTxKJcduU/KshcN7cZpAzvTNEW0diZR400b1WPqH0bQvFF9XpqxIq1j7C53ZkzzCir8\n7Prve05lGuZ7DtQLCXG8ZMdNnEwnkQM6NQO+9iwThr//OJzH0L1n9As1j/TJ/Trym+eShUj5I0Dz\nPeszKolLrt/4SiafS3yvNxUvXOIf85OMyMaFCsDsloj1LJLQqH4JHQMMrCUS/3xf+fVQRp97IHed\n1pdLkkSFn5flFuWQfVqy+C/Hc+XRvTzkk5SKAhzPk8uP6pHWtYPj9ZNJgNUx7vwdB3dLHSDYPIXX\ny+UhBimjNkM1KKlD387NQrt6ZoMTvuc9h0f/Ls04oldlfNLJ/TuGHGtLXTaZ+zfA6HMP5PgD2oXq\nwWST2HhapuMeUdff8Y2M8w7pyiF7t+ScPM7xnYj1LCJAUfp0bEqfjqnTggQNzglK4wYlGX8MXVvu\nyW/i3Ahf+fVQ1mzekalogRnWo7VvSxySf7SnHtiJ0e9/FSjXU9TmBBHhP2nMvAdOTMkjkxZXW3+f\njxPAa5cPY/43G6us2yOJDf3fv3TkenbKUs/I4MYevbdUpJpMaGBpiyrBccnw9TbM4N0ucXuqe2Vp\nvohLjujOPyYuysqxUtGqcQOezWaW6yxgyiKLxLqkubRtRtna8VJ2QYhKtGT3t3OLRsy7xTvNdjHw\nhxN7V8SVxN6nNk0acJLPnO37td+rWoTyI+cP5N/TV/Di9OUsWbuVl381tGKbX1bTIEFfb195GIvX\nbPUtF4aLhnbjlP4dOfFvkwAn79ZFQ7uFmsEykV5tmzDquH05ZUBmKVY6NmsErOO4Pu147tNlrNuy\nM6vfX5+OTTlncBd+OjRYEGeuqdXKolXj+qzZvDNrx4u9OAXiFm2kIMwHni0Pl2pk6LXVvmlD39Z6\np+aN+PVRPTh7cFeWrdvqmwDzsQsGcvmzM9gUMGvuPm2aZH1OiB8N6ETvDnvxwdXD2b6rjDp1JGNP\noFiG5RhTrktvut5bTt6fI/dtE5mDRd06wq0nHxDJsbNBrVYW+7Xfiw++XJNvMbJCbVBQUXhxeXHF\niB6Re6Gk2zD9eFTwCq/FnvUDZY49ct+23DRyf64cm94AdiYcuW8b5n+zqSKwNd0pBIIQP9tjGBrV\nL/EdE6rJ1GplkW12l8dcP3PpyVB4XhNRRJxOufYoGrl29Gx1/f0C464YESwNRNTUgnYAVx3diwsO\nLc1K1udcUnhfX3SYssgisSjvY/u08ykZPc9dPJitO4NHUmeTKKJus1uJFMcnHpvj5IcZ2tqLgbp1\npKgURSYNog+vOZKtRTZBFpiyyCpdWjZi7s3HJPVCiZrEVzeTKWALnXQT5fVs25gmDevh11Z//Yph\nKTPIRkX9JDEujeqXMO/mYzOKf8k1Q/dpRbcspEOpyaTrmp5vTFn4MOn3w3FjxQKRbZdYPwowdidy\n0u2xvPkbZ/bBUeM+9yyXbH7tKHnmpwfTNUUFm8t52bNB0My8xU4+clW9etlQTrhvUs7PG6N4mix5\nolPzRkknJio0CmmAO+bmmY8eVjDyr2HjH9eh+7Qq2tamkTv279CU34zoWZHhNtdYz6LIyX+1V50/\n/mB/rvp+r6JrFeeD2tgzNNLn8hE9uHxE5inV06FW9ywKIe1xTaRuHfGdhN4wjOKiViuLmkUB2aGK\nhHya7trs5UyQU20e8gKhUCbcMQqHWm2Gqgn9CusdhacQbtmV3+/Jvu2acNR+bfItShVi0+MGmb/F\nqF1Yz8IoSv74AycFRDqDfYXQaG5QUpdT+ncqOGXf1u3x9MhyGg+j+KnVPYuaRCFUgEGZcu1RFdHu\n6fKTId3o1bYJPdpapZZNhvVozXMXD64y+6BhQC1XFgXWqKs1ZCtS99CE+bGDYs/dm5oc0Gmkj5mh\nDMMwDF9qdc8i3zx10aC0M2DGiDWSi8gKVTDYPTOM4JiyyCPDeiSfWcyIFrNCGUZ4arUZqiZVGjXp\nWgzDKDxqtbIwaieDujmePvu1M08qwwiKmaGMWsfIfh05ZO+WRTV/gmHkm8h6FiLSWUTeFZG5IjJH\nRC5P2H6ViKiItHJ/i4jcJyILReRzERkQlWw1CRukTQ9TFIYRjih7FruBq1R1uog0AaaJyFuqOldE\nOgNHA0vjyh8H9HD/Dgb+4f6PjEKLns2EGnQphmEUIJH1LFR1papOd5c3AfOA2PyQ9wBXU7VhPBJ4\nUh0+AZqJSKSzo1v9ahiGEYycDHCLSCnQH5gsIiOBFao6M6FYR2BZ3O/lVCqX+GNdLCJTRWTq6tWr\nM5IrNsdxMWPZQQ2j8Dj/kK41bkKryJWFiDQGXgSuwDFNXQvckO7xVHW0qg5U1YGtW2cWp3DTyD6M\nOm5f2pn92jCMLHLTyD58eM2R+RYjq0TatBaRejiKYoyqjhORA4BuwEx3vKATMF1EBgErgM5xu3dy\n10VG0z3q8fPDu/Pjg7uwecfuKE+VA1I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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "%matplotlib inline\n", + "\n", + "plt.plot(thetachain[burnj:,0])\n", + "plt.title('Check mixing')\n", + "plt.xlabel('Chain number')\n", + "plt.ylabel('Temperature [K]')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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SC2p9LyJfi8iDIuJtSDQKzsdFGPE0DJmOWRSSWwdPzriHNX9FduvIGEZtIp0p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\nGvT47sGD6Cf2aM+JPernQHtdwhRLHml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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "%matplotlib inline\n", + "\n", + "plt.plot(thetachain[burnj:,1])\n", + "plt.title('Check mixing')\n", + "plt.xlabel('Chain number')\n", + "plt.ylabel('log10(factor)')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "%matplotlib inline\n", + "\n", + "temp=np.empty([len(thetachain)-burnj])\n", + "temp[0]=thetachain[burnj,0]\n", + "for i in range(burnj+1,len(thetachain)):\n", + " temp[i-burnj]=np.mean(thetachain[burnj:i,0])\n", + "plt.plot(temp)\n", + "plt.title('Check mixing')\n", + "plt.xlabel('Chain number')\n", + "plt.ylabel('Temperature [K]')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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OmWn8c+EG3llRP8AMD2opIwd05YpgZNpj1x7HqcP7MCA3O+5rjBkYem+npCw0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\nJIyCjoiIJIyCjoiIJIyCjoi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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "%matplotlib inline\n", + "\n", + "temp=np.empty([len(thetachain)-burnj])\n", + "temp[0]=thetachain[burnj,1]\n", + "for i in range(burnj+1,len(thetachain)):\n", + " temp[i-burnj]=np.mean(thetachain[burnj:i,1])\n", + "plt.plot(temp)\n", + "plt.title('Check mixing')\n", + "plt.xlabel('Chain number')\n", + "plt.ylabel('log10(factor)')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.2" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/mcmc.py b/mcmc.py new file mode 100644 index 0000000..ebfe031 --- /dev/null +++ b/mcmc.py @@ -0,0 +1,198 @@ + +import numpy as np +import matplotlib.pyplot as plt +from astropy.io import ascii +import scipy.constants as con + +# Get the data using the astropy ascii +data = ascii.read("SED.dat", data_start=4) +lam = data[0][:] # Wavelength column +logf = data[1][:] # log10(flux) +errlogf = data[2][:] # Error on log10(flux) + +# Shape parameters for priors +Teffmin = 10.0 +Teffmax = 1000.0 +logfacmin = -100.0 # log factor minimum +logfacmax = 0.0 # log factor maximum +thetashape=np.array([[Teffmin, Teffmax], [logfacmin, logfacmax]]) + +# Set a definition for the model +# model function creates an array with 6 values of log of flux +def model(microns, Teff, logfactor): + + wavelength = microns*1.0e-6 + flux=np.empty([len(wavelength)]) + logflux=np.empty([len(wavelength)]) + for i in range(len(wavelength)): + # Flux is just the Planck function + flux[i] = ( (2.0*con.h*con.c**2)/(wavelength[i]**5) )/( np.exp( (con.h*con.c)/(con.k*Teff*wavelength[i]) ) - 1.0 ) + # So logflux (which is what we want) is just the log of this + logflux[i] = logfactor + np.log10(flux[i]) + return logflux + +# Set a definition for the loglikelihood, assuming normally distributed data +# +def log_prior(theta, thetashape): + + logpriors=np.empty([len(theta)]) + #logprior=0.0 + + # Prior for theta[0]: Teff~logU[Teffmin,Teffmax] + Teff = theta[0] + Teffmin = thetashape[0][0] + Teffmax = thetashape[0][1] + if Teffmin < Teff < Teffmax: + logpriors[0] = ( 1.0/(np.log(Teffmax) - np.log(Teffmin)) )/Teff + else: + logpriors[0] = -1.0e99 # -infinity + + # Prior for theta[1]: logfac~U[logfacmin,logfacmax] + logfac = theta[1] + logfacmin = thetashape[1][0] + logfacmax = thetashape[1][1] + if logfacmin < logfac < logfacmax: + logpriors[1] = 1.0/(logfacmax - logfacmin) + else: + logpriors[1] = -1.0e99 # -infinity + + #logprior = np.sum(logpriors) + + return np.sum(logpriors) + +# Set a definition for the logpriors +Teffinitial = np.exp( np.random.uniform(np.log(thetashape[0][0]), np.log(thetashape[0][1])) ) + +# Initialize the MCMC from a random point drawn from the prior +# np.random.uniform draws samples from a uniform distribution between low and high values +# Teffinitial draws a random uniformly distibuted number between the log of minimum and maximum values +# for the temperature +# logfacinitial draws a random uniformly distributed value from the minimu and maximum of the log factor +# thetachain setsup and 2 value array of teffinitial and loffactinitial +def log_like(lam,logf,errlogf,theta): + residuals = logf - model(lam,theta[0],theta[1]) + loglike=0.0 + for i in range(len(lam)): + loglike = loglike - np.log(errlogf[i]) - 0.5*(residuals[i]/errlogf[i])**2 + loglike = loglike - 0.5*len(lam)*np.log(2.0*np.pi) + return loglike +logfacinitial = np.random.uniform(thetashape[1][0], thetashape[1][1]) +thetachain = np.array([[Teffinitial, logfacinitial]]) + +# Calculate the associated modified loglike + +loglikechain = np.empty([1]) +loglikechain[0] = log_prior(thetachain[0], thetashape) + log_like(lam, logf, errlogf, thetachain[0]) + +# Define the proposal jump size +Teffjump=5 +logfacjump=0.1 +thetajump=np.array([Teffjump,logfacjump]) + +# Starting walking +j=0 +jmax=10000 +while True: + + # Generate a proposal (or jump) + thetatrial=np.array([np.random.normal(thetachain[j][0],thetajump[0]),np.random.normal(thetachain[j][1],thetajump[1])]) + logliketrial=log_prior(thetatrial,thetashape) + log_like(lam,logf,errlogf,thetatrial) + deltaloglike=logliketrial-loglikechain[j] + + # Compute Metropolis Rule + if deltaloglike > 0: + probjump = 1.0 + else: + probjump = np.exp(deltaloglike) + + if probjump>np.random.uniform(0,1): + # Accept the jump + j = j + 1 + loglikechain = np.append(loglikechain,logliketrial) + thetachain = np.vstack((thetachain,thetatrial)) + + if j==jmax: + break + +jlist=np.arange(len(thetachain)) +plt.scatter(thetachain[:,0], thetachain[:,1], c=jlist, cmap='coolwarm') +plt.xlabel('Temperature [K]') +plt.ylabel('log10(factor)') +plt.savefig("1 Temperatur vs log10(factor) A") +#plt.show() +plt.close() + +np.max(loglikechain) + +plt.plot(loglikechain) +plt.xlabel('Chain number') +plt.ylabel('loglike') +plt.savefig("2 Chain number vs loglike") +#plt.show() +plt.close() + +loglikeburn=np.median(loglikechain) +j=-1 +while True: + j=j+1 + if loglikechain[j] > loglikeburn: + break +burnj=j +print( 'Burn point = ',burnj) + + +jlist=np.arange(len(thetachain)) +plt.scatter(thetachain[burnj:,0], thetachain[burnj:,1], c=jlist[burnj:], cmap='coolwarm',alpha=0.5) +plt.xlabel('Temperature [K]') +plt.ylabel('log10(factor)') +plt.savefig("3 Temperatur vs log10(factor) B") +#plt.show() +plt.close() + +print( 'Temperature [K] = ',np.round(np.median(thetachain[burnj:,0]),1),'-',np.round(np.median(thetachain[burnj:,0])-np.percentile(thetachain[burnj:,0],15.9),1),'+',np.round(np.percentile(thetachain[burnj:,0],84.1)-np.median(thetachain[burnj:,0]),1)) +print( 'log10(factor) = ',np.round(np.median(thetachain[burnj:,1]),3),'-',np.round(np.median(thetachain[burnj:,1])-np.percentile(thetachain[burnj:,1],15.9),3),'+',np.round(np.percentile(thetachain[burnj:,1],84.1)-np.median(thetachain[burnj:,1]),3)) + +ascii.write(thetachain[burnj:,:], "chains.dat") + + +plt.plot(thetachain[burnj:,0]) +plt.title('Check mixing') +plt.xlabel('Chain number') +plt.ylabel('Temperature [K]') +plt.savefig("4 Check mixing, Temperature A") +#plt.show() +plt.close() + + +plt.plot(thetachain[burnj:,1]) +plt.title('Check mixing') +plt.xlabel('Chain number') +plt.ylabel('log10(factor)') +plt.savefig("5 Check mixing, log10(factor) A") +#plt.show() +plt.close() + + +temp=np.empty([len(thetachain)-burnj]) +temp[0]=thetachain[burnj,0] +for i in range(burnj+1,len(thetachain)): + temp[i-burnj]=np.mean(thetachain[burnj:i,0]) +plt.plot(temp) +plt.title('Check mixing') +plt.xlabel('Chain number') +plt.ylabel('Temperature [K]') +plt.savefig("6 Check mixing, Temperature B") +#plt.show() +plt.close() + +temp=np.empty([len(thetachain)-burnj]) +temp[0]=thetachain[burnj,1] +for i in range(burnj+1,len(thetachain)): + temp[i-burnj]=np.mean(thetachain[burnj:i,1]) +plt.plot(temp) +plt.title('Check mixing') +plt.xlabel('Chain number') +plt.ylabel('log10(factor)') +plt.savefig("7 Check mixing, log10(factor) B") +#plt.show() +plt.close() diff --git a/mcmc_test/Log_of_planck_function.py b/mcmc_test/Log_of_planck_function.py new file mode 100644 index 0000000..ec4ced3 --- /dev/null +++ b/mcmc_test/Log_of_planck_function.py @@ -0,0 +1,72 @@ +from __future__ import print_function + +import emcee +import corner +import numpy as np +import scipy.optimize as op +import matplotlib.pyplot as pl +from matplotlib.ticker import MaxNLocator +from scipy.optimize import curve_fit +import PyAstronomy +from astropy.io import ascii + +np.seterr(divide='ignore', invalid='ignore') + +h = 6.626e-34 # J*s +c = 3.0e+8 # m/s +k = 1.38e-23 # m^2*kg*s^-2*K^-1 + +# using the planck function to caculate the intensity of spectral density +def planck(wav, T): + a = 2.0*h*c**2 + b = h*c/(wav*k*T) + intensity = a/ ( (wav**5) * (np.exp(b) - 1.0) ) + return intensity + +def model(microns,Teff,logfactor): + flux = ( (2.0*h*c**2)/(microns**5) )/( np.exp( (h*c)/(k*Teff*microns) ) - 1.0 ) + logflux = logfactor + np.log10(flux) + return logflux + +X = np.linspace(1,25,256,endpoint=True) + +results_temperature = ascii.read("results_temperature.dat") +results_logfactor = ascii.read("results_logfactor.dat") + +# Temperatures of other Brown Dwarfs used for comparison +MCMC_Temp = results_temperature[0][0] +MCMC_logfactor = results_logfactor[0][0] +T1, T1_name = 227, "WISE 1506+7027" +T2, T2_name = 450, "WISE 0410+1502" +T3, T3_name = 350, "WISE 1541−2250" + +# temperature and Brown Dwarf decriptions +T1_description = T1_name + " (" + str(T1)+"K" + ")" +T2_description = T2_name + " (" + str(T2)+"K" + ")" +T3_description = T3_name + " (" + str(T3)+"K" + ")" +MCMC_description = "WISE 0855-0714" + " (" + str(MCMC_Temp)+"K" + ")" + +# Ys used for plotting +Y1 = (np.log10(planck(X*10**-6,T1))) +Y2 = (np.log10(planck(X*10**-6,T2))) +Y3 = (np.log10(planck(X*10**-6,T3))) +Y4 = (model(X*10**-6, MCMC_Temp, MCMC_logfactor)) +# Given data for WISE 0855-0714 +data = ascii.read("SED.dat", data_start=6) +x = data[0][:] +y = data[1][:] +yerr = data[2][:] + +# Plotting the error bars for WISE 0855-0714 +pl.errorbar(x, y, yerr=yerr, fmt=".k") + +# Plotting the log of planck function for each brown dwarf +plot1, = pl.plot(X,Y1, color="red", label=T1_description ) +plot2, = pl.plot(X,Y2, color="green", label=T2_description ) +plot3, = pl.plot(X,Y3, color="blue", label=T3_description ) +plot4, = pl.plot(X,Y4, color="black", label=MCMC_description ) +pl.legend([plot1,plot2,plot3,plot4],[T1_description, T2_description, T3_description, MCMC_description]) +pl.xlabel("Wavelength (um)") +pl.ylabel("LOG10(Spectral Radiance)") + +pl.show() diff --git a/mcmc_test/SED.dat b/mcmc_test/SED.dat new file mode 100644 index 0000000..6ad0ef9 --- /dev/null +++ b/mcmc_test/SED.dat @@ -0,0 +1,13 @@ +Data collected of the WISE 0855-071 brown dwarf. + +Column #1 = Wavelength [microns] +Column #2 = Log10( Flux [erg s^-1 cm^-2 Angstroms^-1] ) +Column #3 = Error on Column 2 + +Col #1 Col #2 Col #3 +3.368 -18.435 0.087 +4.618 -17.042 0.087 +12.082 -15.728 0.087 +22.194 -16.307 0.087 +3.6 -18.063 0.043 +4.5 -17.173 0.043 diff --git a/mcmc_test/Spectral_Radiance.py b/mcmc_test/Spectral_Radiance.py new file mode 100644 index 0000000..40f4d66 --- /dev/null +++ b/mcmc_test/Spectral_Radiance.py @@ -0,0 +1,72 @@ +from __future__ import print_function + +import emcee +import corner +import numpy as np +import scipy.optimize as op +import matplotlib.pyplot as pl +from matplotlib.ticker import MaxNLocator +from scipy.optimize import curve_fit +import PyAstronomy +import subprocess +from astropy.io import ascii +import os + +np.seterr(divide='ignore', invalid='ignore') +np.seterr(over='ignore', invalid='ignore') + +results = ascii.read(os.path.dirname(os.path.realpath(__file__))+"\\results.dat") + +h = 6.626070040*(10**(-34)) #J*s +c = 299792458 #m/s +k_b = 1.38064852*(10**(-23)) #m^2*kg*s^-2*K^-1 + +a = 2*h*(c**2) +b = (h*c)/k_b + +def my_own_Planck(x,T): + #x is the wavelength + #returns spectral radiance per sr + return((a/x**5)*(1/((np.exp(b/(T*x))-1)))) + +h = 6.626e-34 +c = 3.0e+8 +k = 1.38e-23 + +def planck(wav, T): + a = 2.0*h*c**2 + b = h*c/(wav*k*T) + intensity = a/ ( (wav**5) * (np.exp(b) - 1.0) ) + return intensity + +X = np.linspace(0,50,1000,endpoint=True) + +# Temperatures of other Brown Dwarfs used for comparison +MCMC_Temp = results_temperature[0][0] + +T1, T1_name = 227, "WISE 1506+7027" +T2, T2_name = 450, "WISE 0410+1502" +T3, T3_name = 350, "WISE 1541−2250" + +# temperature and Brown Dwarf decriptions +T1_description = T1_name + " (" + str(T1)+"K" + ")" +T2_description = T2_name + " (" + str(T2)+"K" + ")" +T3_description = T3_name + " (" + str(T3)+"K" + ")" +MCMC_description = "WISE 0855-0714" + " (" + str(MCMC_Temp)+"K" + ")" + +# Ys used for plotting +Y1 = (planck(X*10**-6,T1)) +Y2 = (planck(X*10**-6,T2)) +Y3 = (planck(X*10**-6,T3)) +Y4 = (planck(X*10**-6,MCMC_Temp)) + +# Plotting the planck function for each brown dwarf +plot1, = pl.plot(X,Y1, color="red", label=T1_description ) +plot2, = pl.plot(X,Y2, color="green", label=T2_description ) +plot3, = pl.plot(X,Y3, color="blue", label=T3_description ) +plot4, = pl.plot(X,Y4, color="black", label=MCMC_description ) +pl.legend([plot1,plot2,plot3,plot4],[T1_description, T2_description, T3_description, MCMC_description]) +pl.xlabel("Wavelength (um)") +pl.ylabel("Spectral Radiance") + +pl.show() diff --git a/mcmc_test/__init__.py b/mcmc_test/__init__.py 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a/mcmc_test/emcee_model_graphs/Initial Guess Result.png b/mcmc_test/emcee_model_graphs/Initial Guess Result.png new file mode 100644 index 0000000..08f57f8 Binary files /dev/null and b/mcmc_test/emcee_model_graphs/Initial Guess Result.png differ diff --git a/mcmc_test/emcee_model_graphs/Line-Triangle.png b/mcmc_test/emcee_model_graphs/Line-Triangle.png new file mode 100644 index 0000000..f2143a1 Binary files /dev/null and b/mcmc_test/emcee_model_graphs/Line-Triangle.png differ diff --git a/mcmc_test/emcee_model_graphs/MCMC results.png b/mcmc_test/emcee_model_graphs/MCMC results.png new file mode 100644 index 0000000..53c454d Binary files /dev/null and b/mcmc_test/emcee_model_graphs/MCMC results.png differ diff --git a/mcmc_test/mcmc_clone_emceee.py b/mcmc_test/mcmc_clone_emceee.py new file mode 100644 index 0000000..b94d657 --- /dev/null +++ b/mcmc_test/mcmc_clone_emceee.py @@ -0,0 +1,473 @@ +import sys +import numpy as np +import matplotlib.pyplot as plt +from astropy.io import ascii +import scipy.constants as con +import emcee +import corner +import scipy.optimize as op +import random +import os + +# Get the data using the astropy ascii +data = ascii.read(os.path.dirname(os.path.realpath(__file__))+"\\SED.dat", data_start=6) + +x = data[0][:] # Wavelength column +y = data[1][:] # log10(flux) +yerr = data[2][:] # Error on log10(flux) + +#Constants +h = 6.626e-34 +c = 3.0e+8 +k = 1.38e-23 + +Teffmin = 10.0 #effective temperature minimum +Teffmax = 1000.0 #effective temperature maximum +logfacmin = -100.0 #log factor minimum +logfacmax = 0.0 #log factor maximum + +#theatshape is 2 X 2 array +thetashape=np.array([[Teffmin,Teffmax],[logfacmin,logfacmax]]) + + +#Model for the log of the Spectral Radiance +def model(x, T,logfactor): + + #takes in the wavelength array approximate Temp and the log factor and returns and array of logflux + wav = x * 1.0e-6 + flux = np.empty([len(wav)]) + logflux = np.empty([len(wav)]) + + a = 2.0*h*c**2 + b = h*c/(wav*k*T) + for i in range(len(wav)): + a = 2.0*h*c**2 + b = h*c/(wav[i]*k*T) + flux[i] = a/ ( (wav[i]**5) * (np.exp(b) - 1.0) ) + logflux[i] = logfactor + np.log10(flux[i]) + return logflux + + +#log of likelyhood function +def log_like(x,logf,errlogf,theta): + residuals = logf - model(x,theta[0],theta[1]) + loglike=0.0 + for i in range(len(x)): + loglike = loglike - np.log(errlogf[i]) - 0.5*(residuals[i]/errlogf[i])**2 + loglike = loglike - 0.5*len(x)*np.log(2.0*np.pi) + return loglike + +#log of the priors +def log_prior(theta,thetashape): + + logpriors=np.empty([len(theta)]) + #logprior=0.0 + + # Prior for theta[0]: Teff~logU[Teffmin,Teffmax] + Teff = theta[0] + Teffmin = thetashape[0][0] + Teffmax = thetashape[0][1] + if Teffmin < Teff < Teffmax: + logpriors[0] = ( 1.0/(np.log(Teffmax) - np.log(Teffmin)) )/Teff + else: + logpriors[0] = -1.0e99 # -infinity + + # Prior for theta[1]: logfac~U[logfacmin,logfacmax] + logfac = theta[1] + logfacmin = thetashape[1][0] + logfacmax = thetashape[1][1] + if logfacmin < logfac < logfacmax: + logpriors[1] = 1.0/(logfacmax - logfacmin) + else: + logpriors[1] = -1.0e99 # -infinity + + #logprior = np.sum(logpriors) + + return np.sum(logpriors) + +# Initialize the MCMC from a random point drawn from the prior +Teffinitial = np.exp( np.random.uniform(np.log(thetashape[0][0]),np.log(thetashape[0][1])) ) +logfacinitial=np.random.uniform(thetashape[1][0],thetashape[1][1]) +samples=np.array([[Teffinitial,logfacinitial]]) +# Calculate the associated modified loglike +loglikechain=np.empty([1]) +loglikechain[0]=log_prior(samples[0],thetashape) + log_like(x,y,yerr,samples[0]) + +#log of the probability function +def lnprob(theta, x, y, yerr): + lp = log_prior(theta,thetashape) + + loglikechain=np.empty([1]) + loglikechain[0]=log_prior(samples[0],thetashape) + log_like(x,y,yerr,samples[0]) + if not np.isfinite(lp): + return -np.inf + + return lp + log_like(x,y,yerr,theta) #loglikechain[0] + +#Set the number of dimensions the MCMC algorithm will look for and the number of walkers +ndim, nwalkers = 2, 5 +#Conversion Matrix required for the MHSampler to run +neg_lnprob = lambda *args: -lnprob(*args) +#!!!! +res = op.minimize(neg_lnprob, x0=[200,-20], args=(x, y, yerr)) +cov = res.hess_inv +#identify the initial position for MCMC algorithm +pos = [[Teffinitial,logfacinitial] + 1e-4*np.random.randn(ndim) for i in range(nwalkers)] +#Set up the sampler function +sampler = emcee.MHSampler(cov, dim = ndim, lnprobfn = lnprob, args=(x, y, yerr)) +# Clear and run the production chain. +number_of_samples = 12500 +print("Running MCMC...") +sampler.run_mcmc(pos[0], number_of_samples, rstate0=np.random.get_state()) +print("Done.") + +acceptfrac = sampler.acceptance_fraction +print("Acceptance Fraction: " + str(acceptfrac)) + +# Give a generic burning point and choose the sample points used and identify the final result +burnin = 500 +samples = sampler.chain[burnin:,:].reshape((-1, 2)) +# Compute the quantiles. +samples[:] #= np.exp(samples[:]) +T_mcmc, logfac_mcmc = list(map(lambda v: (v[1], v[2]-v[1], v[1]-v[0]), + zip(*np.percentile(samples, [16, 50, 84], + axis=0)))) + +print("""MCMC result: + T = {0[0]} +{0[1]} -{0[2]} + Log Factor = {1[0]} +{1[1]} -{1[2]} +""".format(T_mcmc, logfac_mcmc)) + +# Calculate the bruning point and use it to calculate the final result once again +loglikeburn=np.median(samples[:,1]) +j=-1 +while True: + j=j+1 + if samples[:,1][j] > loglikeburn: + break +burnj=j +print( 'Burn point = ',burnj) + +samples = sampler.chain[burnj:,:].reshape((-1, 2)) + +# Compute the quantiles. +samples[:] #= np.exp(samples[:]) +T_mcmc, logfac_mcmc = list(map(lambda v: (v[1], v[2]-v[1], v[1]-v[0]), + zip(*np.percentile(samples, [16, 50, 84], + axis=0)))) + +print("""MCMC result with calculated burn point: + T = {0[0]} +{0[1]} -{0[2]} + Log Factor = {1[0]} +{1[1]} -{1[2]} +""".format(T_mcmc, logfac_mcmc)) + + + + + + +################################################################################ + + + + + +dir_path = os.path.dirname(os.path.realpath(__file__)) + "\\emcee_model_graphs" +os.makedirs(dir_path, exist_ok=True) + +# Ploting MCMC +plotting_wavelength = np.arange(x[0], 25.0, 0.01) + +# Plot the initial guess results. +fig, ax = plt.subplots() + +ax.spines['top'].set_visible(False) +ax.spines['bottom'].set_visible(False) +ax.spines['right'].set_visible(False) +ax.spines['left'].set_visible(False) +ax.tick_params(colors='#302B2B',top="off",bottom="off") +ax.yaxis.label.set_color('#302B2B') +ax.xaxis.label.set_color('#302B2B') +ax.grid(color='959595', linestyle='-', linewidth=.3) +plt.tick_params( + axis='both', # changes apply to the x-axis + which='both', # both major and minor ticks are affected + left='off', # ticks along the bottom edge are off + right='off', # ticks along the top edge are off + bottom= 'off', # ticks along the bottom edge are off + top= 'off') # tick along the top edhe are off + +data_1 = plt.errorbar(x, y, yerr=yerr, fmt=".r",color="#C80013") +line_1, = plt.plot(plotting_wavelength, model(plotting_wavelength,samples[0][0],samples[0][1]), "--",color="#0A40AB", lw=1) +plt.ylabel('log10(fulx[erg s^-1 cm^-1 A^-1] )') +plt.xlabel("wavelength [um]") +plt.title('Initial Guess Result',color= "#302B2B", fontweight="bold") +plt.legend([data_1, line_1],['Available data','Curve with temperature from the initial guess']) +plt.savefig(dir_path+"\Initial Guess Result.png") +plt.close() + +# Plot the MCMC results. +fig, ax = plt.subplots() + +ax.spines['top'].set_visible(False) +ax.spines['bottom'].set_visible(False) +ax.spines['right'].set_visible(False) +ax.spines['left'].set_visible(False) +ax.tick_params(colors='#302B2B',top="off",bottom="off") +ax.yaxis.label.set_color('#302B2B') +ax.xaxis.label.set_color('#302B2B') +ax.grid(color='959595', linestyle='-', linewidth=.3) +plt.tick_params( + axis='both', # changes apply to the x-axis + which='both', # both major and minor ticks are affected + left='off', # ticks along the bottom edge are off + right='off', # ticks along the top edge are off + bottom= 'off', # ticks along the bottom edge are off + top= 'off') # tick along the top edhe are off + +data_2 = plt.errorbar(x, y, yerr=yerr,fmt='.',color="#C80013",ms="6") +line_2, = plt.plot(plotting_wavelength, model(plotting_wavelength,T_mcmc[0],logfac_mcmc[0]), "--",color="#0A40AB", lw=1) +plt.ylabel('log10(fulx[erg s^-1 cm^-1 A^-1] )') +plt.xlabel("wavelength [um]") +plt.title('MCMC Result',color= "#302B2B", fontweight="bold") +plt.legend([data_2, line_2],['Available data','Curve with temperature from MCMC']) +plt.savefig(dir_path+"\MCMC results.png") +plt.close() + +# Plot the path toward the MCMC results as vaules of logfactor and temperature without the burn point +fig, ax = plt.subplots() + +ax.spines['top'].set_visible(False) +ax.spines['bottom'].set_visible(False) +ax.spines['right'].set_visible(False) +ax.spines['left'].set_visible(False) +ax.tick_params(colors='#302B2B',top="off",bottom="off") +ax.yaxis.label.set_color('#302B2B') +ax.xaxis.label.set_color('#302B2B') +ax.grid(color='959595', linestyle='-', linewidth=.3) +plt.tick_params( + axis='both', # changes apply to the x-axis + which='both', # both major and minor ticks are affected + left='off', # ticks along the bottom edge are off + right='off', # ticks along the top edge are off + bottom= 'off', # ticks along the bottom edge are off + top= 'off') # tick along the top edhe are off + +jlist=np.arange(len(samples)) +plt.scatter(samples[:,0], samples[:,1], c=jlist, cmap='coolwarm') +plt.xlabel('Temperature [K]') +plt.ylabel('log10(factor)') +plt.title('Temperature vs log10(factor)',color= "#302B2B", fontweight="bold") +plt.colorbar().ax.set_title("Chain Number") +plt.savefig(dir_path+"\\1B Temperature vs logfactor.png") +plt.close() + +np.max(samples[:,1]) + +#plotting log of likelyhood versus the chain number +fig, ax = plt.subplots() + +ax.spines['top'].set_visible(False) +ax.spines['bottom'].set_visible(False) +ax.spines['right'].set_visible(False) +ax.spines['left'].set_visible(False) +ax.tick_params(colors='#302B2B',top="off",bottom="off") +ax.yaxis.label.set_color('#302B2B') +ax.xaxis.label.set_color('#302B2B') +ax.grid(color='959595', linestyle='-', linewidth=.3) +plt.tick_params( + axis='both', # changes apply to the x-axis + which='both', # both major and minor ticks are affected + left='off', # ticks along the bottom edge are off + right='off', # ticks along the top edge are off + bottom= 'off', # ticks along the bottom edge are off + top= 'off') # tick along the top edhe are off + +plt.plot(samples[:,1],color="#3513B6", lw=1) +plt.xlabel('Chain number') +plt.ylabel('loglike') +plt.title('Chain number vs loglike',color= "#302B2B", fontweight="bold") +plt.savefig(dir_path+"\\2B Chain number vs loglike.png") +#plt.show() +plt.close() + +# Plot the path toward the MCMC results as vaules of logfactor and temperature with the burn point +fig, ax = plt.subplots() + +ax.spines['top'].set_visible(False) +ax.spines['bottom'].set_visible(False) +ax.spines['right'].set_visible(False) +ax.spines['left'].set_visible(False) +ax.tick_params(colors='#302B2B',top="off",bottom="off") +ax.yaxis.label.set_color('#302B2B') +ax.xaxis.label.set_color('#302B2B') +ax.grid(color='959595', linestyle='-', linewidth=.3) +plt.tick_params( + axis='both', # changes apply to the x-axis + which='both', # both major and minor ticks are affected + left='off', # ticks along the bottom edge are off + right='off', # ticks along the top edge are off + bottom= 'off', # ticks along the bottom edge are off + top= 'off') # tick along the top edhe are off + +jlist=np.arange(len(samples)) +plt.scatter(samples[burnj:,0], samples[burnj:,1], c=jlist[burnj:], cmap='coolwarm',alpha=0.5) +plt.xlabel('Temperature [K]') +plt.ylabel('log10(factor)') +plt.title('Temperature vs log10(factor)',color= "#302B2B", fontweight="bold") +plt.colorbar().ax.set_title("Chain Number") +plt.savefig(dir_path+"\\3B Temperature vs log10(factor).png") +#plt.show() +plt.close() + +ascii.write(samples[burnj:,:], "chains.dat", overwrite= True) + +# check mixing of temperature values +fig, ax = plt.subplots() + +ax.spines['top'].set_visible(False) +ax.spines['bottom'].set_visible(False) +ax.spines['right'].set_visible(False) +ax.spines['left'].set_visible(False) +ax.tick_params(colors='#302B2B',top="off",bottom="off") +ax.yaxis.label.set_color('#302B2B') +ax.xaxis.label.set_color('#302B2B') +ax.grid(color='959595', linestyle='-', linewidth=.3) +plt.tick_params( + axis='both', # changes apply to the x-axis + which='both', # both major and minor ticks are affected + left='off', # ticks along the bottom edge are off + right='off', # ticks along the top edge are off + bottom= 'off', # ticks along the bottom edge are off + top= 'off') # tick along the top edhe are off +plt.plot(samples[burnj:,0], color="#3513B6", lw=1) +plt.xlabel('Chain number') +plt.ylabel('Temperature [K]') +plt.title('Check mixing',color= "#302B2B", fontweight="bold") +plt.savefig(dir_path+"\\4B Check mixing, Temperature.png") +#plt.show() +plt.close() + +# check mixing of log factor values +fig, ax = plt.subplots() + +ax.spines['top'].set_visible(False) +ax.spines['bottom'].set_visible(False) +ax.spines['right'].set_visible(False) +ax.spines['left'].set_visible(False) +ax.tick_params(colors='#302B2B',top="off",bottom="off") +ax.yaxis.label.set_color('#302B2B') +ax.xaxis.label.set_color('#302B2B') +ax.grid(color='959595', linestyle='-', linewidth=.3) +plt.tick_params( + axis='both', # changes apply to the x-axis + which='both', # both major and minor ticks are affected + left='off', # ticks along the bottom edge are off + right='off', # ticks along the top edge are off + bottom= 'off', # ticks along the bottom edge are off + top= 'off') # tick along the top edhe are off +plt.plot(samples[burnj:,1], color="#3513B6", lw=1) +plt.xlabel('Chain number') +plt.ylabel('log10(factor)') +plt.title('Check mixing',color= "#302B2B", fontweight="bold") +plt.savefig(dir_path+"\\5B Check mixing, log10(factor).png") +#plt.show() +plt.close() + +# check mixing of log factor values using the mean +fig, ax = plt.subplots() + +ax.spines['top'].set_visible(False) +ax.spines['bottom'].set_visible(False) +ax.spines['right'].set_visible(False) +ax.spines['left'].set_visible(False) +ax.tick_params(colors='#302B2B',top="off",bottom="off") +ax.yaxis.label.set_color('#302B2B') +ax.xaxis.label.set_color('#302B2B') +ax.grid(color='959595', linestyle='-', linewidth=.3) +plt.tick_params( + axis='both', # changes apply to the x-axis + which='both', # both major and minor ticks are affected + left='off', # ticks along the bottom edge are off + right='off', # ticks along the top edge are off + bottom= 'off', # ticks along the bottom edge are off + top= 'off') # tick along the top edhe are off +temp=np.empty([len(samples)-burnj]) +temp[0]=samples[burnj,0] +for i in range(burnj+1,len(samples)): + temp[i-burnj]=np.mean(samples[burnj:i,0]) +plt.plot(temp, color="#3513B6", lw=1) +plt.xlabel('Chain number') +plt.ylabel('Temperature [K]') +plt.title('Check mixing',color= "#302B2B", fontweight="bold") +plt.savefig(dir_path+"\\6B Check mixing, Temperature via mean.png") +#plt.show() +plt.close() + +# check mixing of temperature values using the mean +fig, ax = plt.subplots() + +ax.spines['top'].set_visible(False) +ax.spines['bottom'].set_visible(False) +ax.spines['right'].set_visible(False) +ax.spines['left'].set_visible(False) +ax.tick_params(colors='#302B2B',top="off",bottom="off") +ax.yaxis.label.set_color('#302B2B') +ax.xaxis.label.set_color('#302B2B') +ax.grid(color='959595', linestyle='-', linewidth=.3) +plt.tick_params( + axis='both', # changes apply to the x-axis + which='both', # both major and minor ticks are affected + left='off', # ticks along the bottom edge are off + right='off', # ticks along the top edge are off + bottom= 'off', # ticks along the bottom edge are off + top= 'off') # tick along the top edhe are off +temp=np.empty([len(samples)-burnj]) +temp[0]=samples[burnj,1] +for i in range(burnj+1,len(samples)): + temp[i-burnj]=np.mean(samples[burnj:i,1]) +plt.plot(temp, color="#3513B6", lw=1) +plt.xlabel('Chain number') +plt.ylabel('log10(factor)') +plt.title('Check mixing',color= "#302B2B", fontweight="bold") +plt.savefig(dir_path+"\\7B Check mixing, log10(factor) via mean.png") +#plt.show() +plt.close() + +# check mixing for temperature and log factor usign mean +fig, ax = plt.subplots() + +ax.spines['top'].set_visible(False) +ax.spines['bottom'].set_visible(False) +ax.spines['right'].set_visible(False) +ax.spines['left'].set_visible(False) +ax.tick_params(colors='#302B2B',top="off",bottom="off") +ax.yaxis.label.set_color('#302B2B') +ax.xaxis.label.set_color('#302B2B') +ax.grid(color='959595', linestyle='-', linewidth=.3) +plt.tick_params( + axis='both', # changes apply to the x-axis + which='both', # both major and minor ticks are affected + left='off', # ticks along the bottom edge are off + right='off', # ticks along the top edge are off + bottom= 'off', # ticks along the bottom edge are off + top= 'off') # tick along the top edhe are off + +jlist=np.arange(len(samples)) +plt.scatter(samples[burnj:,0], samples[burnj:,1], c=jlist[burnj:], cmap='coolwarm',alpha=0.5) +plt.xlabel('Temperature [K]') +plt.ylabel('log10(factor)') +plt.title('Check mixing',color= "#302B2B", fontweight="bold") +plt.colorbar().ax.set_title("Chain Number") +plt.savefig(dir_path+"\\8B Temperature vs log10(factor) with burn point.png") +plt.close() + + +fig = corner.corner(samples, labels=["$Temperature$", "$\ln\,f$"]) +fig.savefig(dir_path+"\\Line-Triangle.png") + +#Record the latest MCMC calculation into .dat file +T_mcmc_array = np.array(T_mcmc) +logfac_mcmc_array = np.array(logfac_mcmc) +ascii.write(T_mcmc_array, "results_temperature.dat", names= ("Temperature", "+", "-"), overwrite= True) +ascii.write(logfac_mcmc_array, "results_logfactor.dat", names= ("Log Factor", "+", "-"), overwrite= True) diff --git a/mcmc_test/mcmc_clone_emceee_class.py b/mcmc_test/mcmc_clone_emceee_class.py new file mode 100644 index 0000000..47cd62c --- /dev/null +++ b/mcmc_test/mcmc_clone_emceee_class.py @@ -0,0 +1,463 @@ +import sys +import numpy as np +import matplotlib.pyplot as plt +from astropy.io import ascii +import scipy.constants as con +import emcee +import corner +import scipy.optimize as op +import random +import os + +# Get the data using the astropy ascii +data = ascii.read("SED.dat", data_start=6) + +x = data[0][:] # Wavelength column +y = data[1][:] # log10(flux) +yerr = data[2][:] # Error on log10(flux) + +h = 6.626e-34 +c = 3.0e+8 +k = 1.38e-23 + +Teffmin = 10.0 #effective temperature minimum +Teffmax = 1000.0 #effective temperature maximum +logfacmin = -100.0 #log factor minimum +logfacmax = 0.0 #log factor maximum +#theatshape is 2 X 2 array +thetashape=np.array([[Teffmin,Teffmax],[logfacmin,logfacmax]]) + + +class MCMCSetup(object): + + def __init__(self): + pass + + def model(self,x, T,logfactor): + + #takes in the wavelength array approximate Temp and the log factor and returns and array of logflux + wav = x * 1.0e-6 + flux = np.empty([len(wav)]) + logflux = np.empty([len(wav)]) + + a = 2.0*h*c**2 + b = h*c/(wav*k*T) + for i in range(len(wav)): + a = 2.0*h*c**2 + b = h*c/(wav[i]*k*T) + flux[i] = a/ ( (wav[i]**5) * (np.exp(b) - 1.0) ) + logflux[i] = logfactor + np.log10(flux[i]) + return logflux + + def log_like(self,x,logf,errlogf,theta): + residuals = logf - self.model(x,theta[0],theta[1]) + loglike=0.0 + for i in range(len(x)): + loglike = loglike - np.log(errlogf[i]) - 0.5*(residuals[i]/errlogf[i])**2 + loglike = loglike - 0.5*len(x)*np.log(2.0*np.pi) + return loglike + + def log_prior(self,theta,thetashape): + + logpriors=np.empty([len(theta)]) + #logprior=0.0 + + # Prior for theta[0]: Teff~logU[Teffmin,Teffmax] + Teff = theta[0] + Teffmin = thetashape[0][0] + Teffmax = thetashape[0][1] + if Teffmin < Teff < Teffmax: + logpriors[0] = ( 1.0/(np.log(Teffmax) - np.log(Teffmin)) )/Teff + else: + logpriors[0] = -1.0e99 # -infinity + + # Prior for theta[1]: logfac~U[logfacmin,logfacmax] + logfac = theta[1] + logfacmin = thetashape[1][0] + logfacmax = thetashape[1][1] + if logfacmin < logfac < logfacmax: + logpriors[1] = 1.0/(logfacmax - logfacmin) + else: + logpriors[1] = -1.0e99 # -infinity + + #logprior = np.sum(logpriors) + + return np.sum(logpriors) + + def lnprob(self,theta, x, y, yerr): + lp = self.log_prior(theta,thetashape) + + if not np.isfinite(lp): + return -np.inf + + return lp + self.log_like(x,y,yerr,theta) #loglikechain[0] + +MCMC = MCMCSetup() + +# Initialize the MCMC from a random point drawn from the prior +Teffinitial = np.exp( np.random.uniform(np.log(thetashape[0][0]),np.log(thetashape[0][1])) ) +logfacinitial=np.random.uniform(thetashape[1][0],thetashape[1][1]) +thetachain=np.array([[Teffinitial,logfacinitial]]) + +#Set the number of dimensions the MCMC algorithm will look for and the number of walkers +ndim, nwalkers = 2, 5 +#Conversion Matrix required for the MHSampler to run +neg_lnprob = lambda *args: -MCMC.lnprob(*args) +#!!!! +res = op.minimize(neg_lnprob, x0=[200,-20], args=(x, y, yerr)) +cov = res.hess_inv +#identify the initial position for MCMC algorithm +pos = [[Teffinitial,logfacinitial] + 1e-4*np.random.randn(ndim) for i in range(nwalkers)] +#Set up the sampler function +sampler = emcee.MHSampler(cov, dim = ndim, lnprobfn = MCMC.lnprob, args=(x, y, yerr)) +# Clear and run the production chain. +number_of_samples = 12500 + +# Clear and run the production chain. +print("Running MCMC...") +sampler.run_mcmc(pos[0], 5000,rstate0=np.random.get_state()) +print("Done.") + +# Make the triangle plot. +burnin = 500 +samples = sampler.chain[burnin:,:]#.reshape((-1, 2)) + +# Compute the quantiles. +samples[:] #= np.exp(samples[:]) +T_mcmc, logfac_mcmc = list(map(lambda v: (v[1], v[2]-v[1], v[1]-v[0]), + zip(*np.percentile(samples, [16, 50, 84], + axis=0)))) + +print("""MCMC result: + T = {0[0]} +{0[1]} -{0[2]} + Log Factor = {1[0]} +{1[1]} -{1[2]} +""".format(T_mcmc, logfac_mcmc)) + + +loglikeburn=np.median(samples[:,1]) +j=-1 +while True: + j=j+1 + if samples[:,1][j] > loglikeburn: + break +burnj=j +print( 'Burn point = ',burnj) + +samples = sampler.chain[burnj:,:].reshape((-1, 2)) + +# Compute the quantiles. +samples[:] #= np.exp(samples[:]) +T_mcmc, logfac_mcmc = list(map(lambda v: (v[1], v[2]-v[1], v[1]-v[0]), + zip(*np.percentile(samples, [16, 50, 84], + axis=0)))) + +print("""MCMC result with calculated burn point: + T = {0[0]} +{0[1]} -{0[2]} + Log Factor = {1[0]} +{1[1]} -{1[2]} +""".format(T_mcmc, logfac_mcmc)) + + + + +################################################################################ + + + + +dir_path = os.path.dirname(os.path.realpath(__file__)) + "\\emcee_model_graphs" +os.makedirs(dir_path, exist_ok=True) + +# Ploting MCMC +plotting_wavelength = np.arange(x[0], 25.0, 0.01) + +# Plot the initial guess results. +fig, ax = plt.subplots() + +ax.spines['top'].set_visible(False) +ax.spines['bottom'].set_visible(False) +ax.spines['right'].set_visible(False) +ax.spines['left'].set_visible(False) +ax.tick_params(colors='#302B2B',top="off",bottom="off") +ax.yaxis.label.set_color('#302B2B') +ax.xaxis.label.set_color('#302B2B') +ax.grid(color='959595', linestyle='-', linewidth=.3) +plt.tick_params( + axis='both', # changes apply to the x-axis + which='both', # both major and minor ticks are affected + left='off', # ticks along the bottom edge are off + right='off', # ticks along the top edge are off + bottom= 'off', # ticks along the bottom edge are off + top= 'off') # tick along the top edhe are off + +data_1 = plt.errorbar(x, y, yerr=yerr, fmt=".r",color="#C80013") +line_1, = plt.plot(plotting_wavelength, MCMC.model(plotting_wavelength,samples[0][0],samples[0][1]), "--",color="#0A40AB", lw=1) +plt.ylabel('log10(fulx[erg s^-1 cm^-1 A^-1] )') +plt.xlabel("wavelength [um]") +plt.title('Initial Guess Result',color= "#302B2B", fontweight="bold") +plt.legend([data_1, line_1],['Available data','Curve with temperature from the initial guess']) +plt.savefig(dir_path+"\Initial Guess Result.png") +plt.close() + +# Plot the MCMC results. +fig, ax = plt.subplots() + +ax.spines['top'].set_visible(False) +ax.spines['bottom'].set_visible(False) +ax.spines['right'].set_visible(False) +ax.spines['left'].set_visible(False) +ax.tick_params(colors='#302B2B',top="off",bottom="off") +ax.yaxis.label.set_color('#302B2B') +ax.xaxis.label.set_color('#302B2B') +ax.grid(color='959595', linestyle='-', linewidth=.3) +plt.tick_params( + axis='both', # changes apply to the x-axis + which='both', # both major and minor ticks are affected + left='off', # ticks along the bottom edge are off + right='off', # ticks along the top edge are off + bottom= 'off', # ticks along the bottom edge are off + top= 'off') # tick along the top edhe are off + +data_2 = plt.errorbar(x, y, yerr=yerr,fmt='.',color="#C80013",ms="6") +line_2, = plt.plot(plotting_wavelength, MCMC.model(plotting_wavelength,T_mcmc[0],logfac_mcmc[0]), "--",color="#0A40AB", lw=1) +plt.ylabel('log10(fulx[erg s^-1 cm^-1 A^-1] )') +plt.xlabel("wavelength [um]") +plt.title('MCMC Result',color= "#302B2B", fontweight="bold") +plt.legend([data_2, line_2],['Available data','Curve with temperature from MCMC']) +plt.savefig(dir_path+"\MCMC results.png") +plt.close() + +# Plot the path toward the MCMC results as vaules of logfactor and temperature without the burn point +fig, ax = plt.subplots() + +ax.spines['top'].set_visible(False) +ax.spines['bottom'].set_visible(False) +ax.spines['right'].set_visible(False) +ax.spines['left'].set_visible(False) +ax.tick_params(colors='#302B2B',top="off",bottom="off") +ax.yaxis.label.set_color('#302B2B') +ax.xaxis.label.set_color('#302B2B') +ax.grid(color='959595', linestyle='-', linewidth=.3) +plt.tick_params( + axis='both', # changes apply to the x-axis + which='both', # both major and minor ticks are affected + left='off', # ticks along the bottom edge are off + right='off', # ticks along the top edge are off + bottom= 'off', # ticks along the bottom edge are off + top= 'off') # tick along the top edhe are off + +jlist=np.arange(len(samples)) +plt.scatter(samples[:,0], samples[:,1], c=jlist, cmap='coolwarm') +plt.xlabel('Temperature [K]') +plt.ylabel('log10(factor)') +plt.title('Temperature vs log10(factor)',color= "#302B2B", fontweight="bold") +plt.colorbar().ax.set_title("Chain Number") +plt.savefig(dir_path+"\\1B Temperature vs logfactor.png") +plt.close() + +np.max(samples[:,1]) + +#plotting log of likelyhood versus the chain number +fig, ax = plt.subplots() + +ax.spines['top'].set_visible(False) +ax.spines['bottom'].set_visible(False) +ax.spines['right'].set_visible(False) +ax.spines['left'].set_visible(False) +ax.tick_params(colors='#302B2B',top="off",bottom="off") +ax.yaxis.label.set_color('#302B2B') +ax.xaxis.label.set_color('#302B2B') +ax.grid(color='959595', linestyle='-', linewidth=.3) +plt.tick_params( + axis='both', # changes apply to the x-axis + which='both', # both major and minor ticks are affected + left='off', # ticks along the bottom edge are off + right='off', # ticks along the top edge are off + bottom= 'off', # ticks along the bottom edge are off + top= 'off') # tick along the top edhe are off + +plt.plot(samples[:,1],color="#3513B6", lw=1) +plt.xlabel('Chain number') +plt.ylabel('loglike') +plt.title('Chain number vs loglike',color= "#302B2B", fontweight="bold") +plt.savefig(dir_path+"\\2B Chain number vs loglike.png") +#plt.show() +plt.close() + +# Plot the path toward the MCMC results as vaules of logfactor and temperature with the burn point +fig, ax = plt.subplots() + +ax.spines['top'].set_visible(False) +ax.spines['bottom'].set_visible(False) +ax.spines['right'].set_visible(False) +ax.spines['left'].set_visible(False) +ax.tick_params(colors='#302B2B',top="off",bottom="off") +ax.yaxis.label.set_color('#302B2B') +ax.xaxis.label.set_color('#302B2B') +ax.grid(color='959595', linestyle='-', linewidth=.3) +plt.tick_params( + axis='both', # changes apply to the x-axis + which='both', # both major and minor ticks are affected + left='off', # ticks along the bottom edge are off + right='off', # ticks along the top edge are off + bottom= 'off', # ticks along the bottom edge are off + top= 'off') # tick along the top edhe are off + +jlist=np.arange(len(samples)) +plt.scatter(samples[burnj:,0], samples[burnj:,1], c=jlist[burnj:], cmap='coolwarm',alpha=0.5) +plt.xlabel('Temperature [K]') +plt.ylabel('log10(factor)') +plt.title('Temperature vs log10(factor)',color= "#302B2B", fontweight="bold") +plt.colorbar().ax.set_title("Chain Number") +plt.savefig(dir_path+"\\3B Temperature vs log10(factor).png") +#plt.show() +plt.close() + +ascii.write(samples[burnj:,:], "chains.dat", overwrite= True) + +# check mixing of temperature values +fig, ax = plt.subplots() + +ax.spines['top'].set_visible(False) +ax.spines['bottom'].set_visible(False) +ax.spines['right'].set_visible(False) +ax.spines['left'].set_visible(False) +ax.tick_params(colors='#302B2B',top="off",bottom="off") +ax.yaxis.label.set_color('#302B2B') +ax.xaxis.label.set_color('#302B2B') +ax.grid(color='959595', linestyle='-', linewidth=.3) +plt.tick_params( + axis='both', # changes apply to the x-axis + which='both', # both major and minor ticks are affected + left='off', # ticks along the bottom edge are off + right='off', # ticks along the top edge are off + bottom= 'off', # ticks along the bottom edge are off + top= 'off') # tick along the top edhe are off +plt.plot(samples[burnj:,0], color="#3513B6", lw=1) +plt.xlabel('Chain number') +plt.ylabel('Temperature [K]') +plt.title('Check mixing',color= "#302B2B", fontweight="bold") +plt.savefig(dir_path+"\\4B Check mixing, Temperature.png") +#plt.show() +plt.close() + +# check mixing of log factor values +fig, ax = plt.subplots() + +ax.spines['top'].set_visible(False) +ax.spines['bottom'].set_visible(False) +ax.spines['right'].set_visible(False) +ax.spines['left'].set_visible(False) +ax.tick_params(colors='#302B2B',top="off",bottom="off") +ax.yaxis.label.set_color('#302B2B') +ax.xaxis.label.set_color('#302B2B') +ax.grid(color='959595', linestyle='-', linewidth=.3) +plt.tick_params( + axis='both', # changes apply to the x-axis + which='both', # both major and minor ticks are affected + left='off', # ticks along the bottom edge are off + right='off', # ticks along the top edge are off + bottom= 'off', # ticks along the bottom edge are off + top= 'off') # tick along the top edhe are off +plt.plot(samples[burnj:,1], color="#3513B6", lw=1) +plt.xlabel('Chain number') +plt.ylabel('log10(factor)') +plt.title('Check mixing',color= "#302B2B", fontweight="bold") +plt.savefig(dir_path+"\\5B Check mixing, log10(factor).png") +#plt.show() +plt.close() + +# check mixing of log factor values using the mean +fig, ax = plt.subplots() + +ax.spines['top'].set_visible(False) +ax.spines['bottom'].set_visible(False) +ax.spines['right'].set_visible(False) +ax.spines['left'].set_visible(False) +ax.tick_params(colors='#302B2B',top="off",bottom="off") +ax.yaxis.label.set_color('#302B2B') +ax.xaxis.label.set_color('#302B2B') +ax.grid(color='959595', linestyle='-', linewidth=.3) +plt.tick_params( + axis='both', # changes apply to the x-axis + which='both', # both major and minor ticks are affected + left='off', # ticks along the bottom edge are off + right='off', # ticks along the top edge are off + bottom= 'off', # ticks along the bottom edge are off + top= 'off') # tick along the top edhe are off +temp=np.empty([len(samples)-burnj]) +temp[0]=samples[burnj,0] +for i in range(burnj+1,len(samples)): + temp[i-burnj]=np.mean(samples[burnj:i,0]) +plt.plot(temp, color="#3513B6", lw=1) +plt.xlabel('Chain number') +plt.ylabel('Temperature [K]') +plt.title('Check mixing',color= "#302B2B", fontweight="bold") +plt.savefig(dir_path+"\\6B Check mixing, Temperature via mean.png") +#plt.show() +plt.close() + +# check mixing of temperature values using the mean +fig, ax = plt.subplots() + +ax.spines['top'].set_visible(False) +ax.spines['bottom'].set_visible(False) +ax.spines['right'].set_visible(False) +ax.spines['left'].set_visible(False) +ax.tick_params(colors='#302B2B',top="off",bottom="off") +ax.yaxis.label.set_color('#302B2B') +ax.xaxis.label.set_color('#302B2B') +ax.grid(color='959595', linestyle='-', linewidth=.3) +plt.tick_params( + axis='both', # changes apply to the x-axis + which='both', # both major and minor ticks are affected + left='off', # ticks along the bottom edge are off + right='off', # ticks along the top edge are off + bottom= 'off', # ticks along the bottom edge are off + top= 'off') # tick along the top edhe are off +temp=np.empty([len(samples)-burnj]) +temp[0]=samples[burnj,1] +for i in range(burnj+1,len(samples)): + temp[i-burnj]=np.mean(samples[burnj:i,1]) +plt.plot(temp, color="#3513B6", lw=1) +plt.xlabel('Chain number') +plt.ylabel('log10(factor)') +plt.title('Check mixing',color= "#302B2B", fontweight="bold") +plt.savefig(dir_path+"\\7B Check mixing, log10(factor) via mean.png") +#plt.show() +plt.close() + +# check mixing for temperature and log factor usign mean +fig, ax = plt.subplots() + +ax.spines['top'].set_visible(False) +ax.spines['bottom'].set_visible(False) +ax.spines['right'].set_visible(False) +ax.spines['left'].set_visible(False) +ax.tick_params(colors='#302B2B',top="off",bottom="off") +ax.yaxis.label.set_color('#302B2B') +ax.xaxis.label.set_color('#302B2B') +ax.grid(color='959595', linestyle='-', linewidth=.3) +plt.tick_params( + axis='both', # changes apply to the x-axis + which='both', # both major and minor ticks are affected + left='off', # ticks along the bottom edge are off + right='off', # ticks along the top edge are off + bottom= 'off', # ticks along the bottom edge are off + top= 'off') # tick along the top edhe are off + +jlist=np.arange(len(samples)) +plt.scatter(samples[burnj:,0], samples[burnj:,1], c=jlist[burnj:], cmap='coolwarm',alpha=0.5) +plt.xlabel('Temperature [K]') +plt.ylabel('log10(factor)') +plt.title('Check mixing',color= "#302B2B", fontweight="bold") +plt.colorbar().ax.set_title("Chain Number") +plt.savefig(dir_path+"\\8B Temperature vs log10(factor) with burn point.png") +plt.close() + + +fig = corner.corner(samples, labels=["$Temperature$", "$\ln\,f$"]) +fig.savefig(dir_path+"\\Line-Triangle.png") + +#Record the latest MCMC calculation into .dat file +T_mcmc_array = np.array(T_mcmc) +ascii.write(T_mcmc_array, "results.dat", names= ("Temperature", "+", "-"), overwrite= True) diff --git a/mcmc_test/mcmc_clone_emceee_with_progress_bar.py b/mcmc_test/mcmc_clone_emceee_with_progress_bar.py new file mode 100644 index 0000000..7bd811f --- /dev/null +++ b/mcmc_test/mcmc_clone_emceee_with_progress_bar.py @@ -0,0 +1,484 @@ +import sys +import numpy as np +import matplotlib.pyplot as plt +from astropy.io import ascii +import scipy.constants as con +import emcee +import corner +import scipy.optimize as op +import random +import os + +# Get the data using the astropy ascii +data = ascii.read(os.path.dirname(os.path.realpath(__file__))+"\\SED.dat", data_start=6) + +x = data[0][:] # Wavelength column +y = data[1][:] # log10(flux) +yerr = data[2][:] # Error on log10(flux) + +#Constants +h = 6.626e-34 +c = 3.0e+8 +k = 1.38e-23 + +Teffmin = 10.0 #effective temperature minimum +Teffmax = 1000.0 #effective temperature maximum +logfacmin = -100.0 #log factor minimum +logfacmax = 0.0 #log factor maximum + +#theatshape is 2 X 2 array +thetashape=np.array([[Teffmin,Teffmax],[logfacmin,logfacmax]]) + + +#Model for the log of the Spectral Radiance +def model(x, T,logfactor): + + #takes in the wavelength array approximate Temp and the log factor and returns and array of logflux + wav = x * 1.0e-6 + flux = np.empty([len(wav)]) + logflux = np.empty([len(wav)]) + + a = 2.0*h*c**2 + b = h*c/(wav*k*T) + for i in range(len(wav)): + a = 2.0*h*c**2 + b = h*c/(wav[i]*k*T) + flux[i] = a/ ( (wav[i]**5) * (np.exp(b) - 1.0) ) + logflux[i] = logfactor + np.log10(flux[i]) + return logflux + + +#log of likelyhood function +def log_like(x,logf,errlogf,theta): + residuals = logf - model(x,theta[0],theta[1]) + loglike=0.0 + for i in range(len(x)): + loglike = loglike - np.log(errlogf[i]) - 0.5*(residuals[i]/errlogf[i])**2 + loglike = loglike - 0.5*len(x)*np.log(2.0*np.pi) + return loglike + +#log of the priors +def log_prior(theta,thetashape): + + logpriors=np.empty([len(theta)]) + #logprior=0.0 + + # Prior for theta[0]: Teff~logU[Teffmin,Teffmax] + Teff = theta[0] + Teffmin = thetashape[0][0] + Teffmax = thetashape[0][1] + if Teffmin < Teff < Teffmax: + logpriors[0] = ( 1.0/(np.log(Teffmax) - np.log(Teffmin)) )/Teff + else: + logpriors[0] = -1.0e99 # -infinity + + # Prior for theta[1]: logfac~U[logfacmin,logfacmax] + logfac = theta[1] + logfacmin = thetashape[1][0] + logfacmax = thetashape[1][1] + if logfacmin < logfac < logfacmax: + logpriors[1] = 1.0/(logfacmax - logfacmin) + else: + logpriors[1] = -1.0e99 # -infinity + + #logprior = np.sum(logpriors) + + return np.sum(logpriors) + +# Initialize the MCMC from a random point drawn from the prior +Teffinitial = np.exp( np.random.uniform(np.log(thetashape[0][0]),np.log(thetashape[0][1])) ) +logfacinitial=np.random.uniform(thetashape[1][0],thetashape[1][1]) +samples=np.array([[Teffinitial,logfacinitial]]) +# Calculate the associated modified loglike +loglikechain=np.empty([1]) +loglikechain[0]=log_prior(samples[0],thetashape) + log_like(x,y,yerr,samples[0]) + +#log of the probability function +def lnprob(theta, x, y, yerr): + lp = log_prior(theta,thetashape) + + loglikechain=np.empty([1]) + loglikechain[0]=log_prior(samples[0],thetashape) + log_like(x,y,yerr,samples[0]) + if not np.isfinite(lp): + return -np.inf + + return lp + log_like(x,y,yerr,theta) #loglikechain[0] + +#Set the number of dimensions the MCMC algorithm will look for and the number of walkers +ndim, nwalkers = 2, 5 +#Conversion Matrix required for the MHSampler to run +neg_lnprob = lambda *args: -lnprob(*args) +#!!!! +res = op.minimize(neg_lnprob, x0=[200,-20], args=(x, y, yerr)) +cov = res.hess_inv +#identify the initial position for MCMC algorithm +pos = [[Teffinitial,logfacinitial] + 1e-4*np.random.randn(ndim) for i in range(nwalkers)] +#Set up the sampler function +sampler = emcee.MHSampler(cov, dim = ndim, lnprobfn = lnprob, args=(x, y, yerr)) +# Clear and run the production chain. +number_of_samples = 12500 +print("Running MCMC...") +width = 30 +for i, result in enumerate(sampler.sample(pos[0], iterations=number_of_samples)): + n = int((width+1) * float(i) / number_of_samples) + sys.stdout.write("\r[{0}{1}]".format('|' * n, ' ' * (width - n))) +sys.stdout.write("\n") +print("Done.") + +acceptfrac = sampler.acceptance_fraction +print("Acceptance Fraction: " + str(acceptfrac)) + +# Give a generic burning point and choose the sample points used and identify the final result +burnin = 500 +samples = sampler.chain[burnin:,:].reshape((-1, 2)) + +# Compute the quantiles. +samples[:] #= np.exp(samples[:]) +T_mcmc, logfac_mcmc = list(map(lambda v: (v[1], v[2]-v[1], v[1]-v[0]), + zip(*np.percentile(samples, [16, 50, 84], + axis=0)))) + +print("""MCMC result: + T = {0[0]} +{0[1]} -{0[2]} + Log Factor = {1[0]} +{1[1]} -{1[2]} +""".format(T_mcmc, logfac_mcmc)) + +# Calculate the bruning point and use it to calculate the final result once again +loglikeburn=np.median(samples[:,1]) +j=-1 +while True: + j=j+1 + if samples[:,1][j] > loglikeburn: + break +burnj=j +print( 'Burn point = ',burnj) + +samples = sampler.chain[burnj:,:].reshape((-1, 2)) + +# Compute the quantiles. +samples[:] #= np.exp(samples[:]) +T_mcmc, logfac_mcmc = list(map(lambda v: (v[1], v[2]-v[1], v[1]-v[0]), + zip(*np.percentile(samples, [16, 50, 84], + axis=0)))) + +print("""MCMC result with calculated burn point: + T = {0[0]} +{0[1]} -{0[2]} + Log Factor = {1[0]} +{1[1]} -{1[2]} +""".format(T_mcmc, logfac_mcmc)) + + + + + + + + + + + + + + + + + +# ------------------------------------------------------------------------------ +dir_path = os.path.dirname(os.path.realpath(__file__)) + "\\emcee_model_graphs" +os.makedirs(dir_path, exist_ok=True) + +# Ploting MCMC +plotting_wavelength = np.arange(x[0], 25.0, 0.01) + +# Plot the initial guess results. +fig, ax = plt.subplots() + +ax.spines['top'].set_visible(False) +ax.spines['bottom'].set_visible(False) +ax.spines['right'].set_visible(False) +ax.spines['left'].set_visible(False) +ax.tick_params(colors='#302B2B',top="off",bottom="off") +ax.yaxis.label.set_color('#302B2B') +ax.xaxis.label.set_color('#302B2B') +ax.grid(color='959595', linestyle='-', linewidth=.3) +plt.tick_params( + axis='both', # changes apply to the x-axis + which='both', # both major and minor ticks are affected + left='off', # ticks along the bottom edge are off + right='off', # ticks along the top edge are off + bottom= 'off', # ticks along the bottom edge are off + top= 'off') # tick along the top edhe are off + +data_1 = plt.errorbar(x, y, yerr=yerr, fmt=".r",color="#C80013") +line_1, = plt.plot(plotting_wavelength, model(plotting_wavelength,samples[0][0],samples[0][1]), "--",color="#0A40AB", lw=1) +plt.ylabel('log10(fulx[erg s^-1 cm^-1 A^-1] )') +plt.xlabel("wavelength [um]") +plt.title('Initial Guess Result',color= "#302B2B", fontweight="bold") +plt.legend([data_1, line_1],['Available data','Curve with temperature from the initial guess']) +plt.savefig(dir_path+"\Initial Guess Result.png") +plt.close() + +# Plot the MCMC results. +fig, ax = plt.subplots() + +ax.spines['top'].set_visible(False) +ax.spines['bottom'].set_visible(False) +ax.spines['right'].set_visible(False) +ax.spines['left'].set_visible(False) +ax.tick_params(colors='#302B2B',top="off",bottom="off") +ax.yaxis.label.set_color('#302B2B') +ax.xaxis.label.set_color('#302B2B') +ax.grid(color='959595', linestyle='-', linewidth=.3) +plt.tick_params( + axis='both', # changes apply to the x-axis + which='both', # both major and minor ticks are affected + left='off', # ticks along the bottom edge are off + right='off', # ticks along the top edge are off + bottom= 'off', # ticks along the bottom edge are off + top= 'off') # tick along the top edhe are off + +data_2 = plt.errorbar(x, y, yerr=yerr,fmt='.',color="#C80013",ms="6") +line_2, = plt.plot(plotting_wavelength, model(plotting_wavelength,T_mcmc[0],logfac_mcmc[0]), "--",color="#0A40AB", lw=1) +plt.ylabel('log10(fulx[erg s^-1 cm^-1 A^-1] )') +plt.xlabel("wavelength [um]") +plt.title('MCMC Result',color= "#302B2B", fontweight="bold") +plt.legend([data_2, line_2],['Available data','Curve with temperature from MCMC']) +plt.savefig(dir_path+"\MCMC results.png") +plt.close() + +# Plot the path toward the MCMC results as vaules of logfactor and temperature without the burn point +fig, ax = plt.subplots() + +ax.spines['top'].set_visible(False) +ax.spines['bottom'].set_visible(False) +ax.spines['right'].set_visible(False) +ax.spines['left'].set_visible(False) +ax.tick_params(colors='#302B2B',top="off",bottom="off") +ax.yaxis.label.set_color('#302B2B') +ax.xaxis.label.set_color('#302B2B') +ax.grid(color='959595', linestyle='-', linewidth=.3) +plt.tick_params( + axis='both', # changes apply to the x-axis + which='both', # both major and minor ticks are affected + left='off', # ticks along the bottom edge are off + right='off', # ticks along the top edge are off + bottom= 'off', # ticks along the bottom edge are off + top= 'off') # tick along the top edhe are off + +jlist=np.arange(len(samples)) +plt.scatter(samples[:,0], samples[:,1], c=jlist, cmap='coolwarm') +plt.xlabel('Temperature [K]') +plt.ylabel('log10(factor)') +plt.title('Temperature vs log10(factor)',color= "#302B2B", fontweight="bold") +plt.colorbar().ax.set_title("Chain Number") +plt.savefig(dir_path+"\\1B Temperature vs logfactor.png") +plt.close() + +np.max(samples[:,1]) + +#plotting log of likelyhood versus the chain number +fig, ax = plt.subplots() + +ax.spines['top'].set_visible(False) +ax.spines['bottom'].set_visible(False) +ax.spines['right'].set_visible(False) +ax.spines['left'].set_visible(False) +ax.tick_params(colors='#302B2B',top="off",bottom="off") +ax.yaxis.label.set_color('#302B2B') +ax.xaxis.label.set_color('#302B2B') +ax.grid(color='959595', linestyle='-', linewidth=.3) +plt.tick_params( + axis='both', # changes apply to the x-axis + which='both', # both major and minor ticks are affected + left='off', # ticks along the bottom edge are off + right='off', # ticks along the top edge are off + bottom= 'off', # ticks along the bottom edge are off + top= 'off') # tick along the top edhe are off + +plt.plot(samples[:,1],color="#3513B6", lw=1) +plt.xlabel('Chain number') +plt.ylabel('loglike') +plt.title('Chain number vs loglike',color= "#302B2B", fontweight="bold") +plt.savefig(dir_path+"\\2B Chain number vs loglike.png") +#plt.show() +plt.close() + +# Plot the path toward the MCMC results as vaules of logfactor and temperature with the burn point +fig, ax = plt.subplots() + +ax.spines['top'].set_visible(False) +ax.spines['bottom'].set_visible(False) +ax.spines['right'].set_visible(False) +ax.spines['left'].set_visible(False) +ax.tick_params(colors='#302B2B',top="off",bottom="off") +ax.yaxis.label.set_color('#302B2B') +ax.xaxis.label.set_color('#302B2B') +ax.grid(color='959595', linestyle='-', linewidth=.3) +plt.tick_params( + axis='both', # changes apply to the x-axis + which='both', # both major and minor ticks are affected + left='off', # ticks along the bottom edge are off + right='off', # ticks along the top edge are off + bottom= 'off', # ticks along the bottom edge are off + top= 'off') # tick along the top edhe are off + +jlist=np.arange(len(samples)) +plt.scatter(samples[burnj:,0], samples[burnj:,1], c=jlist[burnj:], cmap='coolwarm',alpha=0.5) +plt.xlabel('Temperature [K]') +plt.ylabel('log10(factor)') +plt.title('Temperature vs log10(factor)',color= "#302B2B", fontweight="bold") +plt.colorbar().ax.set_title("Chain Number") +plt.savefig(dir_path+"\\3B Temperature vs log10(factor).png") +#plt.show() +plt.close() + +ascii.write(samples[burnj:,:], "chains.dat", overwrite= True) + +# check mixing of temperature values +fig, ax = plt.subplots() + +ax.spines['top'].set_visible(False) +ax.spines['bottom'].set_visible(False) +ax.spines['right'].set_visible(False) +ax.spines['left'].set_visible(False) +ax.tick_params(colors='#302B2B',top="off",bottom="off") +ax.yaxis.label.set_color('#302B2B') +ax.xaxis.label.set_color('#302B2B') +ax.grid(color='959595', linestyle='-', linewidth=.3) +plt.tick_params( + axis='both', # changes apply to the x-axis + which='both', # both major and minor ticks are affected + left='off', # ticks along the bottom edge are off + right='off', # ticks along the top edge are off + bottom= 'off', # ticks along the bottom edge are off + top= 'off') # tick along the top edhe are off +plt.plot(samples[burnj:,0], color="#3513B6", lw=1) +plt.xlabel('Chain number') +plt.ylabel('Temperature [K]') +plt.title('Check mixing',color= "#302B2B", fontweight="bold") +plt.savefig(dir_path+"\\4B Check mixing, Temperature.png") +#plt.show() +plt.close() + +# check mixing of log factor values +fig, ax = plt.subplots() + +ax.spines['top'].set_visible(False) +ax.spines['bottom'].set_visible(False) +ax.spines['right'].set_visible(False) +ax.spines['left'].set_visible(False) +ax.tick_params(colors='#302B2B',top="off",bottom="off") +ax.yaxis.label.set_color('#302B2B') +ax.xaxis.label.set_color('#302B2B') +ax.grid(color='959595', linestyle='-', linewidth=.3) +plt.tick_params( + axis='both', # changes apply to the x-axis + which='both', # both major and minor ticks are affected + left='off', # ticks along the bottom edge are off + right='off', # ticks along the top edge are off + bottom= 'off', # ticks along the bottom edge are off + top= 'off') # tick along the top edhe are off +plt.plot(samples[burnj:,1], color="#3513B6", lw=1) +plt.xlabel('Chain number') +plt.ylabel('log10(factor)') +plt.title('Check mixing',color= "#302B2B", fontweight="bold") +plt.savefig(dir_path+"\\5B Check mixing, log10(factor).png") +#plt.show() +plt.close() + +# check mixing of log factor values using the mean +fig, ax = plt.subplots() + +ax.spines['top'].set_visible(False) +ax.spines['bottom'].set_visible(False) +ax.spines['right'].set_visible(False) +ax.spines['left'].set_visible(False) +ax.tick_params(colors='#302B2B',top="off",bottom="off") +ax.yaxis.label.set_color('#302B2B') +ax.xaxis.label.set_color('#302B2B') +ax.grid(color='959595', linestyle='-', linewidth=.3) +plt.tick_params( + axis='both', # changes apply to the x-axis + which='both', # both major and minor ticks are affected + left='off', # ticks along the bottom edge are off + right='off', # ticks along the top edge are off + bottom= 'off', # ticks along the bottom edge are off + top= 'off') # tick along the top edhe are off +temp=np.empty([len(samples)-burnj]) +temp[0]=samples[burnj,0] +for i in range(burnj+1,len(samples)): + temp[i-burnj]=np.mean(samples[burnj:i,0]) +plt.plot(temp, color="#3513B6", lw=1) +plt.xlabel('Chain number') +plt.ylabel('Temperature [K]') +plt.title('Check mixing',color= "#302B2B", fontweight="bold") +plt.savefig(dir_path+"\\6B Check mixing, Temperature via mean.png") +#plt.show() +plt.close() + +# check mixing of temperature values using the mean +fig, ax = plt.subplots() + +ax.spines['top'].set_visible(False) +ax.spines['bottom'].set_visible(False) +ax.spines['right'].set_visible(False) +ax.spines['left'].set_visible(False) +ax.tick_params(colors='#302B2B',top="off",bottom="off") +ax.yaxis.label.set_color('#302B2B') +ax.xaxis.label.set_color('#302B2B') +ax.grid(color='959595', linestyle='-', linewidth=.3) +plt.tick_params( + axis='both', # changes apply to the x-axis + which='both', # both major and minor ticks are affected + left='off', # ticks along the bottom edge are off + right='off', # ticks along the top edge are off + bottom= 'off', # ticks along the bottom edge are off + top= 'off') # tick along the top edhe are off +temp=np.empty([len(samples)-burnj]) +temp[0]=samples[burnj,1] +for i in range(burnj+1,len(samples)): + temp[i-burnj]=np.mean(samples[burnj:i,1]) +plt.plot(temp, color="#3513B6", lw=1) +plt.xlabel('Chain number') +plt.ylabel('log10(factor)') +plt.title('Check mixing',color= "#302B2B", fontweight="bold") +plt.savefig(dir_path+"\\7B Check mixing, log10(factor) via mean.png") +#plt.show() +plt.close() + +# check mixing for temperature and log factor usign mean +fig, ax = plt.subplots() + +ax.spines['top'].set_visible(False) +ax.spines['bottom'].set_visible(False) +ax.spines['right'].set_visible(False) +ax.spines['left'].set_visible(False) +ax.tick_params(colors='#302B2B',top="off",bottom="off") +ax.yaxis.label.set_color('#302B2B') +ax.xaxis.label.set_color('#302B2B') +ax.grid(color='959595', linestyle='-', linewidth=.3) +plt.tick_params( + axis='both', # changes apply to the x-axis + which='both', # both major and minor ticks are affected + left='off', # ticks along the bottom edge are off + right='off', # ticks along the top edge are off + bottom= 'off', # ticks along the bottom edge are off + top= 'off') # tick along the top edhe are off + +jlist=np.arange(len(samples)) +plt.scatter(samples[burnj:,0], samples[burnj:,1], c=jlist[burnj:], cmap='coolwarm',alpha=0.5) +plt.xlabel('Temperature [K]') +plt.ylabel('log10(factor)') +plt.title('Check mixing',color= "#302B2B", fontweight="bold") +plt.colorbar().ax.set_title("Chain Number") +plt.savefig(dir_path+"\\8B Temperature vs log10(factor) with burn point.png") +plt.close() + + +fig = corner.corner(samples, labels=["$Temperature$", "$\ln\,f$"]) +fig.savefig(dir_path+"\\Line-Triangle.png") + +#Record the latest MCMC calculation into .dat file +T_mcmc_array = np.array(T_mcmc) +logfac_mcmc_array = np.array(logfac_mcmc) +ascii.write(T_mcmc_array, "results_temperature.dat", names= ("Temperature", "+", "-"), overwrite= True) +ascii.write(logfac_mcmc_array, "results_logfactor.dat", names= ("Log Factor", "+", "-"), overwrite= True) diff --git a/mcmc_test/results.dat b/mcmc_test/results.dat new file mode 100644 index 0000000..60c9a2f --- /dev/null +++ b/mcmc_test/results.dat @@ -0,0 +1,2 @@ +"Log factor" + - +-22.44612980064596 3.1812872378006247 0.08911318261189649 diff --git a/mcmc_test/results_logfactor.dat b/mcmc_test/results_logfactor.dat new file mode 100644 index 0000000..443b54b --- /dev/null +++ b/mcmc_test/results_logfactor.dat @@ -0,0 +1,2 @@ +"Log Factor" + - +-22.462552663499967 0.08814246117211155 0.07956792278165992 diff --git a/mcmc_test/results_temperature.dat b/mcmc_test/results_temperature.dat new file mode 100644 index 0000000..60e2742 --- /dev/null +++ b/mcmc_test/results_temperature.dat @@ -0,0 +1,2 @@ +Temperature + - +252.14662439750836 3.638148384722257 3.798699671175683 diff --git a/mcmc_test/timeit_analysis.py b/mcmc_test/timeit_analysis.py new file mode 100644 index 0000000..4c66df7 --- /dev/null +++ b/mcmc_test/timeit_analysis.py @@ -0,0 +1,49 @@ +import mcmc_clone_emceee +import time +import runpy +import os +import subprocess +import timeit +import numpy as np +from timeit import Timer + + +def fun(): + proc = subprocess.Popen(["python","mcmc_clone_emceee0"], shell = True) + proc.terminate() + +def fun2(): + proc = subprocess.Popen(["python","mcmc_clone_emceee"], shell = True) + proc.terminate() + +t = Timer(lambda: fun()) + +t2 = Timer(lambda: fun2()) +t_list = [] +t2_list = [] +for i in range(1000): + t2_list.append(int(t2.timeit(number=1)*10**10)) + t_list.append(int(t.timeit(number=1)*10**10)) + +t_list_B = [] +t2_list_B = [] +for a in t_list: + t_list_B.append(a/10**10) + +for b in t2_list: + t2_list_B.append(b/10**10) + +# for x in t_list_B: +# print(x) +print("----------------------------------------------------") +print(np.average((t_list_B)),"MCMC process bar included") +print(" ") + +#for x in t2_list_B: +# print(x) +print("----------------------------------------------------") +print(np.average((t2_list_B)),"MCMC standard") +print(" ") + +print("----------------------------------------------------") +print("Implementating classes on average,increases the runtime by",np.average((t2_list_B))-np.average((t_list_B)),"ms") diff --git a/reqs.txt b/reqs.txt new file mode 100644 index 0000000..1c0d650 --- /dev/null +++ b/reqs.txt @@ -0,0 +1,9 @@ +visualization --> with modification, in the code review as well +using github for discussion +add into part of the repo visualizations +readability of the code + doc strings + comments + + +Due date: Friday May 19th diff --git a/temp.py b/temp.py new file mode 100644 index 0000000..9eebad1 --- /dev/null +++ b/temp.py @@ -0,0 +1,8 @@ +import os + + +print(results[0]) +x = "mcmc_clone_emceee.py" +path = os.path.dirname(os.path.dirname(os.path.realpath(__file__))) + "\\MCMC\\mcmc_test\\emcee_model_graphs" + +print(len(os.listdir(path))) diff --git a/test/__init__.py b/test/__init__.py new file mode 100644 index 0000000..e69de29 diff --git a/test/test_mcmc_clone_emcee.py b/test/test_mcmc_clone_emcee.py new file mode 100644 index 0000000..b399450 --- /dev/null +++ b/test/test_mcmc_clone_emcee.py @@ -0,0 +1,33 @@ +from mcmc_test.mcmc_clone_emceee import model +from mccm_test.mcmc_clone_emceee import acceptfrac + +import pytest +import numpy as np +import matplotlib.pyplot as plt +from astropy.io import ascii +import scipy.constants as con +import os +import emcee +import corner +import scipy.optimize as op +import random + +from inspect import signature + +#determine if the function recieves correct number of arguments +def test_model_format(): + sig = signature(model) + params = sig.parameters + print(len(params)) + assert len(params) == 3 + +#Determines if the MCMC results are within the acceptable range +def test_mcmc_clone_emceee_output(): + path = os.path.dirname(os.path.dirname(os.path.realpath(__file__))) + "\\mcmc_test" + results = ascii.read(path+"\\results.dat") + assert 225 <= results[0][0] <= 260 and 225 <= results[0][0]+results[0][1] <= 260 and 225 <= results[0][0]+results[0][2] <= 260 + +#Test to determine if mcmc_clone_emceee outputs the right amount of graphs into the proper directory +def test_mcmc_clone_emceee_output_number(): + path = os.path.dirname(os.path.dirname(os.path.realpath(__file__))) + "\\mcmc_test\\emcee_model_graphs" + assert len(os.listdir(path)) == 9