ipython notebook investigating the effects of subtracting means shot-by-shot vs. over an entire dataset

subtracting shot-by-shot vs. avg over shots.ipynb

{
 "metadata": {
  "name": "subtracting shot-by-shot vs. avg over shots"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from odin import xray\n",
      "from odin import structure\n",
      "\n",
      "xray.logger.propagate = False\n",
      "xray.scatter.logger.propagate = False\n",
      "\n",
      "gold = structure.load_coor('fcc_sphere_5.0nm.coor')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 62
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "r = xray.Rings.simulate(gold, 1, [2.67], 360, 100)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 63
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# add a random mask -- each px has a 10% chance of being \"bad\"\n",
      "polar_mask = random.binomial(1, 0.9, size=(1, 360))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 64
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# compute correlators, both subtracting shot-by-shot means\n",
      "# and total means\n",
      "\n",
      "# will do this for the first ring (q=2.67) only\n",
      "\n",
      "# shot-by-shot\n",
      "x_bar = r.polar_intensities[:,0,:] - r.polar_intensities[:,0,:].mean(1)[:,None]\n",
      "\n",
      "sbs_corr = np.zeros(r.num_phi)\n",
      "for delta in range(r.num_phi):\n",
      "    for i in range(r.num_phi):\n",
      "        \n",
      "        i_shifted = (i+delta) % r.num_phi\n",
      "        if polar_mask[0,i] and polar_mask[0,i_shifted]:\n",
      "            sbs_corr[delta] += mean( x_bar[:,i] * x_bar[:,i_shifted] ) # avg over shots\n",
      "            \n",
      "# total\n",
      "x_bar = r.polar_intensities[:,0,:] - mean( r.polar_intensities[:,0,:] )\n",
      "\n",
      "ttl_corr = np.zeros(r.num_phi)\n",
      "for delta in range(r.num_phi):\n",
      "    for i in range(r.num_phi):\n",
      "        \n",
      "        i_shifted = (i+delta) % r.num_phi\n",
      "        if polar_mask[0,i] and polar_mask[0,i_shifted]:\n",
      "            ttl_corr[delta] += mean( x_bar[:,i] * x_bar[:,i_shifted] ) # avg over shots\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 65
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# plot the resulting correlation functions against the correlation w/o a mask\n",
      "\n",
      "sbs_true_corr = r.correlate_intra(2.67, 2.67, 4, mean_only=True)\n",
      "\n",
      "# total\n",
      "x_bar = r.polar_intensities[:,0,:] - mean( r.polar_intensities[:,0,:] )\n",
      "\n",
      "ttl_true_corr = np.zeros(r.num_phi)\n",
      "for delta in range(r.num_phi):\n",
      "    for i in range(r.num_phi):\n",
      "        i_shifted = (i+delta) % r.num_phi\n",
      "        ttl_true_corr[delta] += mean( x_bar[:,i] * x_bar[:,i_shifted] ) # avg over shots\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "figure(figsize=(15,8))\n",
      "\n",
      "subplot(121)\n",
      "plot(sbs_corr / sbs_corr[0], lw=2)\n",
      "plot(sbs_true_corr / true_corr[0], lw=2)\n",
      "legend(['subtracted shot-by-shot', 'true correlator'])\n",
      "\n",
      "xlim([0, r.num_phi])\n",
      "ylim([-0.1, 0.1])\n",
      "\n",
      "subplot(122)\n",
      "plot(ttl_corr / ttl_corr[0], lw=2)\n",
      "plot(ttl_true_corr / true_corr[0], lw=2)\n",
      "legend(['subtracted total mean', 'true correlator'])\n",
      "\n",
      "xlim([0, r.num_phi])\n",
      "ylim([-0.1, 0.1])\n",
      "\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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REcnNoeollyYN6PTpO1lySUQkN1GHdXbowpihIyIyB6fZM3R6ySXXoSMiMgdO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\nU0JcQhV/yRUjoBwc5hcAHB4OuL2vgdM6vzf1vHil7NjhOn+QzK680l2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       "text": [
        "<matplotlib.figure.Figure at 0x10e45bc90>"
       ]
      }
     ],
     "prompt_number": 69
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}