{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Figures" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook prepares figures for documenting the package." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Initialization" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "%pylab inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Error Estimation Models" ] }, { "cell_type": "code", "execution_count": 174, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def error_model_plot(label=None,var='sky',fit='snr',flux=[100.,100.],x0=[1.,1.5],sigma=[0.25,0.5],sky=100):\n", " # Build the source models.\n", " x = np.linspace(0.,3.,100)\n", " xx = np.vstack([x,x]).T\n", " sig = np.array(sigma)\n", " root2pi = np.sqrt(2*np.pi)\n", " y = (np.exp(-(xx-x0)**2/(2*sig**2))*flux/(root2pi*sig)).T\n", " # Plot the source models.\n", " plt.plot(x,y[0]+sky,'b-')\n", " plt.plot(x,y[1]+sky,'r--')\n", " # Set the vertical plot range.\n", " ymin = sky - 2.5*np.sqrt(sky)\n", " ymax = y[0]+y[1]+sky\n", " ymax = np.max(ymax + 1.5*np.sqrt(ymax))\n", " plt.ylim((ymin,ymax))\n", " # Draw the variance band.\n", " if var == 'sky':\n", " y_var = np.zeros_like(x) + sky\n", " elif var == 'iso':\n", " y_var = y[0]+sky\n", " elif var == 'grp':\n", " y_var = y[0]+y[1]+sky\n", " y_lo = y_var - np.sqrt(y_var)\n", " y_hi = y_var + np.sqrt(y_var)\n", " plt.fill_between(x,y_lo,y_hi,color='green',alpha=0.25)\n", " # Show fit models as vertical and horizontal double-headed arrows.\n", " x_arrow = x0\n", " y_arrow = sky + flux/(root2pi*sig)\n", " dx = 0.30\n", " dy = 35.\n", " if fit in ('snr','iso','grp'):\n", " plt.annotate('',xy=(x_arrow[0],y_arrow[0]-dy),xytext=(x_arrow[0],y_arrow[0]+dy),\n", " xycoords='data',textcoords='data',arrowprops={'arrowstyle':'<->','color':'black'})\n", " if fit in ('iso','grp'):\n", " plt.annotate('',xy=(x_arrow[0]-dx,y_arrow[0]),xytext=(x_arrow[0]+dx,y_arrow[0]),\n", " xycoords='data',textcoords='data',arrowprops={'arrowstyle':'<->','color':'black'})\n", " if fit in ('grp'):\n", " plt.annotate('',xy=(x_arrow[1],y_arrow[1]-dy),xytext=(x_arrow[1],y_arrow[1]+dy),\n", " xycoords='data',textcoords='data',arrowprops={'arrowstyle':'<->','color':'black'})\n", " plt.annotate('',xy=(x_arrow[1]-dx,y_arrow[1]),xytext=(x_arrow[1]+dx,y_arrow[1]),\n", " xycoords='data',textcoords='data',arrowprops={'arrowstyle':'<->','color':'black'})\n", " # Add optional figure label.\n", " if label:\n", " plt.annotate(label,xy=(0.95,0.95),xytext=(0.95,0.95),\n", " xycoords='axes fraction',textcoords='axes fraction',\n", " horizontalalignment='right',verticalalignment='top',fontsize='x-large')\n", " # Hide axis labels.\n", " plt.gca().get_xaxis().set_visible(False)\n", " plt.gca().get_yaxis().set_visible(False)" ] }, { "cell_type": "code", "execution_count": 175, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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LFaVmxpzmoDZYS1ZCVpemV9TJtmUTUSOAVs1iw4oM6aon+qwqbxWq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\nhnBDr11yVKuFg//1d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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def error_models(name):\n", " fig = plt.figure(figsize=(10,5))\n", " plt.subplot(2,3,1)\n", " error_model_plot(label='(a) sky',var='sky',fit='snr')\n", " plt.subplot(2,3,2)\n", " error_model_plot(label='(b) iso',var='iso',fit='snr')\n", " plt.subplot(2,3,3)\n", " error_model_plot(label='(c) grp',var='grp',fit='snr')\n", " plt.subplot(2,3,5)\n", " error_model_plot(label='(d) isof',var='iso',fit='iso')\n", " plt.subplot(2,3,6)\n", " error_model_plot(label='(e) grpf',var='grp',fit='grp')\n", " fig.tight_layout()\n", " if name:\n", " fig.savefig(name+'.pdf')\n", " fig.savefig(name+'.png')\n", "error_models('output/error_models')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Blending Contamination and Systematics" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def blending_plot(alpha=0.5,flux=[100.,140.,10.],x0=[1.2,2.2,0.3],sigma=[0.4,0.25,0.1],save=None):\n", " # Build the source models.\n", " nsrc = len(flux)\n", " x = np.linspace(0.,3.,200)\n", " xx = np.vstack([x]*nsrc).T\n", " sig = np.array(sigma)\n", " root2pi = np.sqrt(2*np.pi)\n", " y = (np.exp(-(xx-x0)**2/(2*sig**2))*flux/(root2pi*sig)).T\n", " # Calculate the total signal.\n", " ytot = np.sum(y,axis=0)\n", " # Sort sources by decreasing flux.\n", " order = np.argsort(flux)[::-1]\n", " # Calculate the overlap matrix.\n", " matrix = np.einsum('ip,jp->ijp',y,y)/ytot\n", " overlap = np.sum(matrix,axis=1) - y**2/ytot\n", " ##overlap2 = (ytot[np.newaxis,:]-y)*y/ytot[np.newaxis,:]\n", " ##assert np.allclose(overlap,overlap2)\n", " purity = 1.-np.sum(overlap*y,axis=1)/np.sum(y**2,axis=1)\n", " purity2 = np.sum(y*y,axis=1)/np.sum(y*ytot[np.newaxis,:],axis=1)\n", " print 'purities:'\n", " print np.vstack([purity[order],purity2[order]])\n", " #\n", " fig = plt.figure(figsize=(6,4))\n", " #\n", " plt.subplot(1,1,1)\n", " plt.plot(x,ytot,color='black')\n", " colors = ('r','b','g')\n", " ytot2 = np.zeros_like(ytot)\n", " for i,src1 in enumerate(order):\n", " plt.plot(x,y[src1],colors[i])\n", " y2 = np.copy(y[src1])\n", " for j,src2 in enumerate(order):\n", " if i < j:\n", " plt.fill_between(x,matrix[src1,src2],facecolor='0.9',edgecolor='0.8')\n", " y2 += alpha*matrix[src1,src2]*np.sign(j-i)\n", " plt.fill_between(x,overlap[src1],y[src1],facecolor=colors[i],edgecolor='',alpha=0.1)\n", " plt.plot(x,y2,colors[i]+'--')\n", " plt.ylim(0,None)\n", " #\n", " # Hide axis labels.\n", " plt.gca().get_xaxis().set_visible(False)\n", " plt.gca().get_yaxis().set_visible(False)\n", " fig.tight_layout()\n", " if save:\n", " fig.savefig(save)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "purities:\n", "[[ 0.95816932 0.9495006 0.78887296]\n", " [ 0.94644317 0.84024683 0.75949159]]\n" ] }, { "data": { "image/png": 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pHccsataEVavg9m1wdHQmKWkrHh71qFu3Lnv37lU73jPRarVMnDiR2bNnPzpy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\n8vkVeL3eUWVMF9LaKvP442m8847OunVRVq3qxes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