phy-4660/lag/data/clag_analysis-origbins-noLFerrors-4775A.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Container object of 3 artists>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f64bc2a5d10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import sys\n",
    "import getopt\n",
    "sys.path.insert(1,\"/usr/local/science/clag/\")\n",
    "import clag\n",
    "%pylab inline\n",
    "\n",
    "from scipy.stats import norm\n",
    "from scipy.stats import lognorm\n",
    "from scipy.optimize import curve_fit\n",
    "import numpy.fft\n",
    "\n",
    "ref_file=\"lc/1367A.lc\"\n",
    "echo_file=\"lc/4775A.lc\"\n",
    "\n",
    "dt = 0.01\n",
    "t1, l1, l1e = np.loadtxt(ref_file).T\n",
    "errorbar(t1, l1, yerr=l1e, fmt='o')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.005     ,  0.01861938,  0.04473305,  0.06933623,  0.10747115,\n",
       "        0.16658029,  0.25819945,  0.40020915,  0.62032418])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "\n",
    "fqL = np.array([0.0049999999, 0.018619375, 0.044733049, 0.069336227, 0.10747115, 0.16658029, \n",
    "                0.25819945, 0.40020915, 0.62032418])\n",
    "# fqL = np.logspace(np.log10(0.0006),np.log10(1.2),11)\n",
    "nfq = len(fqL) - 1\n",
    "fqd = 10**(np.log10( (fqL[:-1]*fqL[1:]) )/2.)\n",
    "\n",
    "\n",
    "fqL\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   1 4.342e-01 5.077e+01 inf -- -5.530e+02 -- 1 1 1 1 1 1 1 1\n",
      "   2 7.674e-01 5.065e+01 8.300e+01 -- -4.700e+02 -- 0.653018 0.587019 0.568277 0.567457 0.566281 0.566085 0.565773 0.566163\n",
      "   3 3.298e+00 5.043e+01 8.075e+01 -- -3.893e+02 -- 0.414806 0.209135 0.141159 0.13784 0.133393 0.132728 0.131612 0.132761\n",
      "   4 1.572e+00 5.010e+01 7.754e+01 -- -3.117e+02 -- 0.322539 -0.0834456 -0.273066 -0.284295 -0.297612 -0.299435 -0.302479 -0.300412\n",
      "   5 5.908e-01 4.964e+01 7.386e+01 -- -2.379e+02 -- 0.302357 -0.214604 -0.654658 -0.688754 -0.723838 -0.729279 -0.736418 -0.733888\n",
      "   6 3.713e-01 4.877e+01 6.953e+01 -- -1.683e+02 -- 0.284419 -0.200357 -0.96379 -1.05472 -1.13798 -1.15477 -1.17031 -1.16748\n",
      "   7 2.709e-01 4.671e+01 6.269e+01 -- -1.056e+02 -- 0.277768 -0.185001 -1.13047 -1.34026 -1.52128 -1.56845 -1.6043 -1.60101\n",
      "   8 2.135e-01 4.361e+01 5.281e+01 -- -5.282e+01 -- 0.277012 -0.185189 -1.16375 -1.49463 -1.83211 -1.9477 -2.03737 -2.03476\n",
      "   9 1.764e-01 3.767e+01 4.019e+01 -- -1.264e+01 -- 0.282161 -0.184207 -1.17891 -1.53049 -2.01851 -2.24569 -2.46562 -2.46922\n",
      "  10 1.508e-01 2.738e+01 2.645e+01 -- 1.382e+01 -- 0.289545 -0.182463 -1.18795 -1.52893 -2.08812 -2.41103 -2.87498 -2.90486\n",
      "  11 1.349e-01 1.468e+01 1.390e+01 -- 2.772e+01 -- 0.293547 -0.180898 -1.1897 -1.52803 -2.10944 -2.46526 -3.22702 -3.34288\n",
      "  12 1.358e-01 5.365e+00 5.378e+00 -- 3.309e+01 -- 0.295456 -0.179941 -1.19052 -1.52801 -2.11928 -2.48294 -3.46233 -3.79368\n",
      "  13 1.868e-01 1.338e+00 1.633e+00 -- 3.473e+01 -- 0.297315 -0.17923 -1.19104 -1.52666 -2.12491 -2.48975 -3.55567 -4.30889\n",
      "  14 6.248e-01 2.604e-01 4.517e-01 -- 3.518e+01 -- 0.299091 -0.178645 -1.191 -1.52463 -2.12805 -2.4915 -3.5672 -5.11363\n",
      "  15 2.744e+02 2.611e-01 7.022e-02 -- 3.525e+01 -- 0.300248 -0.178286 -1.19075 -1.52307 -2.12961 -2.49161 -3.56337 -8\n",
      "  16 2.745e+02 2.782e-01 4.368e-04 -- 3.525e+01 -- 0.300566 -0.178158 -1.19062 -1.52252 -2.13009 -2.49151 -3.5617 -8\n",
      "  17 2.745e+02 2.805e-01 6.410e-05 -- 3.525e+01 -- 0.300599 -0.178134 -1.19059 -1.52242 -2.13017 -2.49148 -3.56148 -8\n",
      "********************\n",
      "0.300599 -0.178134 -1.19059 -1.52242 -2.13017 -2.49148 -3.56148 -8\n",
      "0.238931 0.202434 0.232634 0.177249 0.153039 0.132988 0.297259 3285.23\n",
      "-0.000915535 -0.00131061 -0.00195128 -0.00497899 -0.0226059 -0.0776175 -0.280541 -0.000206646\n",
      "********************\n"
     ]
    }
   ],
   "source": [
    "P1 = clag.clag('psd10r', [t1], [l1], [l1e], dt, fqL)\n",
    "p1 = np.ones(nfq)\n",
    "p1, p1e = clag.optimize(P1, p1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t### errors for param 0 ###\n",
      "+++ 3.525e+01 3.480e+01 3.006e-01 5.395e-01 0.891 +++\n",
      "+++ 3.525e+01 3.431e+01 3.006e-01 6.590e-01 1.87 +++\n",
      "+++ 3.525e+01 3.458e+01 3.006e-01 5.993e-01 1.34 +++\n",
      "+++ 3.525e+01 3.469e+01 3.006e-01 5.694e-01 1.11 +++\n",
      "+++ 3.525e+01 3.475e+01 3.006e-01 5.545e-01 0.997 +++\n",
      "\t### errors for param 1 ###\n",
      "+++ 3.525e+01 3.476e+01 -1.781e-01 2.430e-02 0.973 +++\n",
      "+++ 3.525e+01 3.421e+01 -1.781e-01 1.255e-01 2.07 +++\n",
      "+++ 3.525e+01 3.451e+01 -1.781e-01 7.491e-02 1.48 +++\n",
      "+++ 3.525e+01 3.464e+01 -1.781e-01 4.961e-02 1.21 +++\n",
      "+++ 3.525e+01 3.470e+01 -1.781e-01 3.696e-02 1.09 +++\n",
      "+++ 3.525e+01 3.473e+01 -1.781e-01 3.063e-02 1.03 +++\n",
      "+++ 3.525e+01 3.475e+01 -1.781e-01 2.747e-02   1 +++\n",
      "\t### errors for param 2 ###\n",
      "+++ 3.525e+01 3.511e+01 -1.191e+00 -1.074e+00 0.276 +++\n",
      "+++ 3.525e+01 3.495e+01 -1.191e+00 -1.016e+00 0.598 +++\n",
      "+++ 3.525e+01 3.485e+01 -1.191e+00 -9.870e-01 0.8 +++\n",
      "+++ 3.525e+01 3.479e+01 -1.191e+00 -9.725e-01 0.91 +++\n",
      "+++ 3.525e+01 3.476e+01 -1.191e+00 -9.652e-01 0.968 +++\n",
      "+++ 3.525e+01 3.475e+01 -1.191e+00 -9.616e-01 0.997 +++\n",
      "\t### errors for param 3 ###\n",
      "+++ 3.525e+01 3.482e+01 -1.522e+00 -1.345e+00 0.865 +++\n",
      "+++ 3.525e+01 3.432e+01 -1.522e+00 -1.257e+00 1.86 +++\n",
      "+++ 3.525e+01 3.459e+01 -1.522e+00 -1.301e+00 1.32 +++\n",
      "+++ 3.525e+01 3.471e+01 -1.522e+00 -1.323e+00 1.08 +++\n",
      "+++ 3.525e+01 3.476e+01 -1.522e+00 -1.334e+00 0.97 +++\n",
      "+++ 3.525e+01 3.473e+01 -1.522e+00 -1.329e+00 1.03 +++\n",
      "+++ 3.525e+01 3.475e+01 -1.522e+00 -1.331e+00 0.998 +++\n",
      "\t### errors for param 4 ###\n",
      "+++ 3.525e+01 3.481e+01 -2.130e+00 -1.977e+00 0.874 +++\n",
      "+++ 3.525e+01 3.429e+01 -2.130e+00 -1.901e+00 1.91 +++\n",
      "+++ 3.525e+01 3.457e+01 -2.130e+00 -1.939e+00 1.35 +++\n",
      "+++ 3.525e+01 3.470e+01 -2.130e+00 -1.958e+00 1.1 +++\n",
      "+++ 3.525e+01 3.476e+01 -2.130e+00 -1.968e+00 0.983 +++\n",
      "+++ 3.525e+01 3.473e+01 -2.130e+00 -1.963e+00 1.04 +++\n",
      "+++ 3.525e+01 3.474e+01 -2.130e+00 -1.965e+00 1.01 +++\n",
      "+++ 3.525e+01 3.475e+01 -2.130e+00 -1.966e+00 0.997 +++\n",
      "\t### errors for param 5 ###\n",
      "+++ 3.525e+01 3.474e+01 -2.491e+00 -2.358e+00 1.01 +++\n",
      "+++ 3.525e+01 3.512e+01 -2.491e+00 -2.425e+00 0.263 +++\n",
      "+++ 3.525e+01 3.496e+01 -2.491e+00 -2.392e+00 0.579 +++\n",
      "+++ 3.525e+01 3.486e+01 -2.491e+00 -2.375e+00 0.781 +++\n",
      "+++ 3.525e+01 3.480e+01 -2.491e+00 -2.367e+00 0.893 +++\n",
      "+++ 3.525e+01 3.477e+01 -2.491e+00 -2.363e+00 0.952 +++\n",
      "+++ 3.525e+01 3.476e+01 -2.491e+00 -2.361e+00 0.982 +++\n",
      "+++ 3.525e+01 3.475e+01 -2.491e+00 -2.360e+00 0.997 +++\n",
      "\t### errors for param 6 ###\n",
      "+++ 3.525e+01 3.507e+01 -3.561e+00 -3.413e+00 0.363 +++\n",
      "+++ 3.525e+01 3.484e+01 -3.561e+00 -3.339e+00 0.814 +++\n",
      "+++ 3.525e+01 3.468e+01 -3.561e+00 -3.301e+00 1.13 +++\n",
      "+++ 3.525e+01 3.477e+01 -3.561e+00 -3.320e+00 0.962 +++\n",
      "+++ 3.525e+01 3.473e+01 -3.561e+00 -3.311e+00 1.04 +++\n",
      "+++ 3.525e+01 3.475e+01 -3.561e+00 -3.315e+00   1 +++\n",
      "\t### errors for param 7 ###\n",
      "+++ 3.525e+01 3.524e+01 -8.000e+00 -6.000e+00 0.0178 +++\n",
      "+++ 3.525e+01 3.515e+01 -8.000e+00 -5.000e+00 0.187 +++\n",
      "+++ 3.525e+01 3.494e+01 -8.000e+00 -4.500e+00 0.618 +++\n",
      "+++ 3.525e+01 3.466e+01 -8.000e+00 -4.250e+00 1.18 +++\n",
      "+++ 3.525e+01 3.482e+01 -8.000e+00 -4.375e+00 0.851 +++\n",
      "+++ 3.525e+01 3.475e+01 -8.000e+00 -4.312e+00   1 +++\n",
      "********************\n",
      "0.300605 -0.178131 -1.19059 -1.52241 -2.13019 -2.49148 -3.56144 -8\n",
      "0.253864 0.205597 0.228999 0.191096 0.1638 0.131949 0.246154 3.6875\n",
      "********************\n"
     ]
    }
   ],
   "source": [
    "p1, p1e = clag.errors(P1, p1, p1e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Container object of 3 artists>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgkAAAFrCAYAAABbtho0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n1Wpt9anVaq5RkDrAkCC
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f64cbfba0d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xscale('log'); ylim(-4,2)\n",
    "errorbar(fqd, p1, yerr=p1e, fmt='o', ms=10, color=\"black\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Container object of 3 artists>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAg8AAAFkCAYAAACn/timAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTeT6GH+ycrVb3q51KbQ
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f64bbe07d10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t2, l2, l2e = np.loadtxt(echo_file).T\n",
    "errorbar(t1, l1, yerr=l1e, fmt='o', color=\"green\")\n",
    "errorbar(t2, l2, yerr=l2e, fmt='o', color=\"black\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   1 4.348e-01 6.523e+01 inf -- -3.028e+02 -- 1 1 1 1 1 1 1 1\n",
      "   2 7.699e-01 6.427e+01 8.100e+01 -- -2.218e+02 -- 0.580653 0.565804 0.565201 0.565214 0.565618 0.565947 0.565564 0.568603\n",
      "   3 3.354e+00 6.351e+01 8.006e+01 -- -1.417e+02 -- 0.182695 0.132486 0.130058 0.130216 0.131744 0.132399 0.131339 0.138486\n",
      "   4 1.556e+00 6.272e+01 7.903e+01 -- -6.268e+01 -- -0.16907 -0.296462 -0.306097 -0.304877 -0.301753 -0.300835 -0.302915 -0.292641\n",
      "   5 5.969e-01 6.132e+01 7.726e+01 -- 1.458e+01 -- -0.432204 -0.709149 -0.744405 -0.7396 -0.734995 -0.733546 -0.736839 -0.725614\n",
      "   6 3.744e-01 5.885e+01 7.418e+01 -- 8.877e+01 -- -0.574318 -1.06985 -1.18591 -1.17296 -1.16819 -1.16502 -1.16974 -1.15872\n",
      "   7 2.704e-01 5.526e+01 6.977e+01 -- 1.585e+02 -- -0.632315 -1.30174 -1.62986 -1.60311 -1.60167 -1.59376 -1.60104 -1.58978\n",
      "   8 2.118e-01 5.083e+01 6.476e+01 -- 2.233e+02 -- -0.652594 -1.36692 -2.06821 -2.02717 -2.03482 -2.01697 -2.03052 -2.01815\n",
      "   9 1.754e-01 4.545e+01 5.869e+01 -- 2.820e+02 -- -0.636309 -1.38302 -2.45398 -2.43781 -2.46343 -2.42984 -2.45896 -2.44563\n",
      "  10 1.490e-01 3.871e+01 4.984e+01 -- 3.318e+02 -- -0.605808 -1.40775 -2.67391 -2.81453 -2.87421 -2.81781 -2.88685 -2.87465\n",
      "  11 1.236e-01 3.039e+01 3.772e+01 -- 3.696e+02 -- -0.57763 -1.42753 -2.69296 -3.11171 -3.23381 -3.14653 -3.31141 -3.30288\n",
      "  12 9.229e-02 2.069e+01 2.286e+01 -- 3.924e+02 -- -0.556681 -1.44088 -2.69001 -3.27817 -3.48572 -3.34948 -3.71554 -3.7112\n",
      "  13 5.640e-02 1.099e+01 9.621e+00 -- 4.020e+02 -- -0.542063 -1.44901 -2.6978 -3.33497 -3.57555 -3.3977 -4.04347 -4.0537\n",
      "  14 2.620e-02 4.040e+00 2.310e+00 -- 4.043e+02 -- -0.533703 -1.45096 -2.69258 -3.36521 -3.54261 -3.39935 -4.19655 -4.28234\n",
      "  15 9.422e-03 1.233e+00 3.575e-01 -- 4.047e+02 -- -0.531223 -1.44814 -2.69847 -3.37914 -3.48828 -3.41313 -4.19651 -4.39454\n",
      "  16 5.169e-03 4.540e-01 5.788e-02 -- 4.048e+02 -- -0.532521 -1.44581 -2.70748 -3.37398 -3.45542 -3.42428 -4.19558 -4.43406\n",
      "  17 2.718e-03 2.442e-01 1.172e-02 -- 4.048e+02 -- -0.533779 -1.44399 -2.71046 -3.36898 -3.43756 -3.43204 -4.19666 -4.4455\n",
      "  18 1.439e-03 1.307e-01 3.039e-03 -- 4.048e+02 -- -0.534412 -1.44278 -2.71234 -3.36531 -3.42821 -3.43643 -4.19795 -4.44912\n",
      "  19 7.592e-04 6.935e-02 8.433e-04 -- 4.048e+02 -- -0.534752 -1.44211 -2.71311 -3.36323 -3.42328 -3.43886 -4.19871 -4.45056\n",
      "  20 4.030e-04 3.692e-02 2.371e-04 -- 4.048e+02 -- -0.534926 -1.44173 -2.71356 -3.36205 -3.42068 -3.44015 -4.19914 -4.45124\n",
      "  21 2.137e-04 1.961e-02 6.686e-05 -- 4.048e+02 -- -0.53502 -1.44153 -2.71378 -3.36142 -3.4193 -3.44084 -4.19936 -4.45158\n",
      "********************\n",
      "-0.53502 -1.44153 -2.71378 -3.36142 -3.4193 -3.44084 -4.19936 -4.45158\n",
      "0.23132 0.206392 0.257293 0.247733 0.190033 0.14318 0.192361 0.189515\n",
      "-0.000780421 0.00249097 -0.00128998 0.00612834 0.0196141 -0.0166488 -0.00464909 -0.00601261\n",
      "********************\n"
     ]
    }
   ],
   "source": [
    "P2 = clag.clag('psd10r', [t2], [l2], [l2e], dt, fqL)\n",
    "p2 = np.ones(nfq)\n",
    "p2, p2e = clag.optimize(P2, p2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t### errors for param 0 ###\n",
      "+++ 4.048e+02 4.043e+02 -5.351e-01 -3.037e-01 0.864 +++\n",
      "+++ 4.048e+02 4.039e+02 -5.351e-01 -1.881e-01 1.82 +++\n",
      "+++ 4.048e+02 4.041e+02 -5.351e-01 -2.459e-01 1.3 +++\n",
      "+++ 4.048e+02 4.042e+02 -5.351e-01 -2.748e-01 1.07 +++\n",
      "+++ 4.048e+02 4.043e+02 -5.351e-01 -2.893e-01 0.967 +++\n",
      "+++ 4.048e+02 4.043e+02 -5.351e-01 -2.821e-01 1.02 +++\n",
      "+++ 4.048e+02 4.043e+02 -5.351e-01 -2.857e-01 0.993 +++\n",
      "\t### errors for param 1 ###\n",
      "+++ 4.048e+02 4.043e+02 -1.441e+00 -1.235e+00 0.928 +++\n",
      "+++ 4.048e+02 4.038e+02 -1.441e+00 -1.132e+00 1.97 +++\n",
      "+++ 4.048e+02 4.041e+02 -1.441e+00 -1.183e+00 1.41 +++\n",
      "+++ 4.048e+02 4.042e+02 -1.441e+00 -1.209e+00 1.16 +++\n",
      "+++ 4.048e+02 4.043e+02 -1.441e+00 -1.222e+00 1.04 +++\n",
      "+++ 4.048e+02 4.043e+02 -1.441e+00 -1.229e+00 0.983 +++\n",
      "+++ 4.048e+02 4.043e+02 -1.441e+00 -1.225e+00 1.01 +++\n",
      "+++ 4.048e+02 4.043e+02 -1.441e+00 -1.227e+00 0.997 +++\n",
      "\t### errors for param 2 ###\n",
      "+++ 4.048e+02 4.046e+02 -2.714e+00 -2.585e+00 0.296 +++\n",
      "+++ 4.048e+02 4.045e+02 -2.714e+00 -2.521e+00 0.647 +++\n",
      "+++ 4.048e+02 4.043e+02 -2.714e+00 -2.489e+00 0.868 +++\n",
      "+++ 4.048e+02 4.043e+02 -2.714e+00 -2.473e+00 0.989 +++\n",
      "+++ 4.048e+02 4.042e+02 -2.714e+00 -2.465e+00 1.05 +++\n",
      "+++ 4.048e+02 4.043e+02 -2.714e+00 -2.469e+00 1.02 +++\n",
      "+++ 4.048e+02 4.043e+02 -2.714e+00 -2.471e+00 1.01 +++\n",
      "\t### errors for param 3 ###\n",
      "+++ 4.048e+02 4.043e+02 -3.361e+00 -3.113e+00 0.873 +++\n",
      "+++ 4.048e+02 4.038e+02 -3.361e+00 -2.990e+00 1.95 +++\n",
      "+++ 4.048e+02 4.041e+02 -3.361e+00 -3.051e+00 1.36 +++\n",
      "+++ 4.048e+02 4.042e+02 -3.361e+00 -3.082e+00 1.1 +++\n",
      "+++ 4.048e+02 4.043e+02 -3.361e+00 -3.098e+00 0.985 +++\n",
      "+++ 4.048e+02 4.043e+02 -3.361e+00 -3.090e+00 1.04 +++\n",
      "+++ 4.048e+02 4.043e+02 -3.361e+00 -3.094e+00 1.01 +++\n",
      "+++ 4.048e+02 4.043e+02 -3.361e+00 -3.096e+00   1 +++\n",
      "\t### errors for param 4 ###\n",
      "+++ 4.048e+02 4.045e+02 -3.419e+00 -3.229e+00 0.635 +++\n",
      "+++ 4.048e+02 4.040e+02 -3.419e+00 -3.134e+00 1.47 +++\n",
      "+++ 4.048e+02 4.043e+02 -3.419e+00 -3.181e+00 1.01 +++\n",
      "\t### errors for param 5 ###\n",
      "+++ 4.048e+02 4.044e+02 -3.441e+00 -3.298e+00 0.824 +++\n",
      "+++ 4.048e+02 4.039e+02 -3.441e+00 -3.226e+00 1.85 +++\n",
      "+++ 4.048e+02 4.041e+02 -3.441e+00 -3.262e+00 1.29 +++\n",
      "+++ 4.048e+02 4.043e+02 -3.441e+00 -3.280e+00 1.04 +++\n",
      "+++ 4.048e+02 4.043e+02 -3.441e+00 -3.289e+00 0.93 +++\n",
      "+++ 4.048e+02 4.043e+02 -3.441e+00 -3.285e+00 0.985 +++\n",
      "+++ 4.048e+02 4.043e+02 -3.441e+00 -3.282e+00 1.01 +++\n",
      "+++ 4.048e+02 4.043e+02 -3.441e+00 -3.283e+00 0.999 +++\n",
      "\t### errors for param 6 ###\n",
      "+++ 4.048e+02 4.046e+02 -4.199e+00 -4.103e+00 0.303 +++\n",
      "+++ 4.048e+02 4.044e+02 -4.199e+00 -4.055e+00 0.684 +++\n",
      "+++ 4.048e+02 4.043e+02 -4.199e+00 -4.031e+00 0.933 +++\n",
      "+++ 4.048e+02 4.043e+02 -4.199e+00 -4.019e+00 0.966 +++\n",
      "+++ 4.048e+02 4.043e+02 -4.199e+00 -4.013e+00 1.03 +++\n",
      "+++ 4.048e+02 4.043e+02 -4.199e+00 -4.016e+00 0.999 +++\n",
      "\t### errors for param 7 ###\n",
      "+++ 4.048e+02 4.043e+02 -4.452e+00 -4.262e+00 0.879 +++\n",
      "+++ 4.048e+02 4.038e+02 -4.452e+00 -4.167e+00 2.03 +++\n",
      "+++ 4.048e+02 4.041e+02 -4.452e+00 -4.215e+00 1.39 +++\n",
      "+++ 4.048e+02 4.042e+02 -4.452e+00 -4.239e+00 1.12 +++\n",
      "+++ 4.048e+02 4.043e+02 -4.452e+00 -4.250e+00 0.996 +++\n",
      "********************\n",
      "-0.535069 -1.44142 -2.7139 -3.36108 -3.41857 -3.44121 -4.19949 -4.45176\n",
      "0.249396 0.214451 0.243242 0.265109 0.23744 0.157753 0.183354 0.201379\n",
      "********************\n"
     ]
    }
   ],
   "source": [
    "p2, p2e = clag.errors(P2, p2, p2e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Container object of 3 artists>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgkAAAFrCAYAAABbtho0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\no4vujSRdRvr5NOnj07e
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f64bb850750>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xscale('log'); ylim(-6,2)\n",
    "errorbar(fqd, p1, yerr=p1e, fmt='o', ms=10, color=\"green\")\n",
    "errorbar(fqd, p2, yerr=p2e, fmt='o', ms=10, color=\"black\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   1 1.165e+02 1.119e+01 inf -- 4.615e+02 -- -0.417232 -1.10978 -2.25224 -2.74174 -3.07438 -3.26634 -4.18046 -6.52588 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1\n",
      "   3 7.488e+01 1.326e+01 2.469e+00 -- 4.640e+02 -- -0.379546 -1.07024 -2.2349 -2.70308 -3.05386 -3.26052 -4.19422 -6.22588 0.0594438 0.143922 0.211494 0.183563 0.124903 0.187977 0.0382351 -1.06488\n",
      "   5 3.958e+01 1.546e+01 2.253e+00 -- 4.663e+02 -- -0.347917 -1.03742 -2.21505 -2.66882 -3.03593 -3.25222 -4.20507 -5.92588 0.0292929 0.176748 0.302165 0.24639 0.145443 0.263839 -0.0201518 0.625425\n",
      "   7 2.952e+01 1.780e+01 1.997e+00 -- 4.683e+02 -- -0.321166 -1.00987 -2.19485 -2.63901 -3.02019 -3.2426 -4.21334 -5.62588 0.00616037 0.202118 0.375333 0.294616 0.162597 0.328567 -0.0750795 -1.84997\n",
      "   9 3.498e+01 2.030e+01 1.927e+00 -- 4.702e+02 -- -0.298358 -0.986546 -2.1755 -2.61326 -3.00636 -3.23255 -4.21943 -5.92588 -0.0120242 0.222305 0.43445 0.33256 0.177047 0.383459 -0.125124 0.240961\n",
      "  11 2.323e+01 2.295e+01 1.750e+00 -- 4.719e+02 -- -0.278794 -0.966621 -2.15757 -2.59104 -2.99413 -3.22256 -4.22358 -5.62588 -0.0266225 0.238634 0.482619 0.362829 0.189318 0.429938 -0.171714 -0.602008\n",
      "  13 9.908e+00 2.576e+01 1.642e+00 -- 4.736e+02 -- -0.261904 -0.949487 -2.14126 -2.57185 -2.98327 -3.21301 -4.22619 -5.32588 -0.0385241 0.252101 0.522228 0.387431 0.199792 0.469237 -0.213944 0.796178\n",
      "  15 5.329e+01 2.871e+01 1.637e+00 -- 4.752e+02 -- -0.247262 -0.934659 -2.12658 -2.55525 -2.97361 -3.20401 -4.22742 -5.02588 -0.0483821 0.263296 0.555178 0.407636 0.208732 0.502656 -0.25301 0.00733246\n",
      "  17 2.560e+00 3.181e+01 1.529e+00 -- 4.767e+02 -- -0.234505 -0.921766 -2.11346 -2.54086 -2.96485 -3.19577 -4.22761 -4.804 -0.056605 0.27274 0.582856 0.424353 0.216437 0.5308 -0.288552 0.0464091\n",
      "  19 1.172e+00 3.504e+01 1.400e+00 -- 4.781e+02 -- -0.223355 -0.910503 -2.10178 -2.52834 -2.9569 -3.18826 -4.2269 -4.68017 -0.0635434 0.28074 0.606367 0.438267 0.223049 0.554643 -0.321322 0.0582901\n",
      "  21 7.724e-01 3.838e+01 1.293e+00 -- 4.794e+02 -- -0.21358 -0.900628 -2.09139 -2.51744 -2.94968 -3.18148 -4.22551 -4.59311 -0.0694486 0.287569 0.626536 0.449937 0.228692 0.574921 -0.351228 0.0651221\n",
      "  23 6.475e-01 4.182e+01 1.196e+00 -- 4.806e+02 -- -0.204987 -0.891941 -2.08217 -2.5079 -2.94312 -3.17538 -4.22361 -4.5264 -0.0745103 0.293433 0.644002 0.459774 0.233469 0.59222 -0.378357 0.0697841\n",
      "  24 6.033e-01 4.904e+02 9.259e+00 -- 4.899e+02 -- -0.129265 -0.815314 -2.00033 -2.42441 -2.88331 -3.12077 -4.20108 -3.99042 -0.118156 0.344039 0.796617 0.542976 0.273449 0.74018 -0.62334 0.104006\n",
      "  25 1.633e+00 2.416e+01 2.127e+00 -- 4.920e+02 -- -0.136332 -0.820492 -2.00326 -2.42953 -2.86836 -3.13063 -4.19803 -4.0221 -0.107855 0.34592 0.942222 0.436475 0.11856 0.656515 -0.24726 0.0760793\n",
      "  26 2.297e-01 1.685e+01 3.223e-01 -- 4.923e+02 -- -0.136021 -0.81967 -2.01733 -2.4291 -2.86411 -3.12575 -4.28732 -4.0298 -0.106863 0.340823 0.802305 0.502205 0.115029 0.705918 -0.651119 0.0904933\n",
      "  27 2.114e-01 1.002e+01 6.323e-02 -- 4.924e+02 -- -0.136189 -0.820198 -2.00806 -2.43011 -2.86374 -3.13176 -4.15965 -4.03428 -0.10583 0.344597 0.86383 0.461694 0.102618 0.695825 -0.501555 0.0943452\n",
      "  28 7.282e-02 6.910e+00 4.695e-02 -- 4.925e+02 -- -0.136116 -0.819859 -2.01221 -2.42953 -2.86299 -3.12599 -4.24062 -4.03499 -0.106121 0.343076 0.828348 0.490418 0.10121 0.697346 -0.60756 0.0921811\n",
      "  29 6.355e-02 4.447e+00 1.251e-02 -- 4.925e+02 -- -0.136164 -0.820085 -2.00914 -2.42964 -2.86356 -3.12997 -4.19174 -4.03653 -0.106059 0.34408 0.850084 0.472121 0.0987163 0.695127 -0.563315 0.0960744\n",
      "  30 3.208e-02 2.630e+00 6.361e-03 -- 4.925e+02 -- -0.136149 -0.819937 -2.01076 -2.4294 -2.86326 -3.12717 -4.2269 -4.03604 -0.106248 0.343798 0.836239 0.482367 0.0971931 0.696096 -0.599112 0.0951975\n",
      "  31 2.383e-02 1.888e+00 2.157e-03 -- 4.925e+02 -- -0.136169 -0.820025 -2.00964 -2.42939 -2.86343 -3.12896 -4.20665 -4.03645 -0.106249 0.344186 0.84463 0.475064 0.0961482 0.695566 -0.579893 0.0964022\n",
      "  32 1.323e-02 1.058e+00 9.738e-04 -- 4.925e+02 -- -0.136163 -0.819962 -2.01029 -2.42931 -2.86326 -3.12779 -4.22134 -4.03608 -0.106327 0.344123 0.839179 0.479109 0.0951898 0.696016 -0.593714 0.0963018\n",
      "  33 9.243e-03 7.911e-01 3.707e-04 -- 4.925e+02 -- -0.136171 -0.819998 -2.00986 -2.4293 -2.86331 -3.12857 -4.21272 -4.03621 -0.106324 0.344261 0.842547 0.476174 0.0946849 0.695851 -0.58586 0.0965931\n",
      "  34 5.341e-03 4.358e-01 1.598e-04 -- 4.925e+02 -- -0.136168 -0.819972 -2.01013 -2.42927 -2.86323 -3.12808 -4.21887 -4.03601 -0.106356 0.344247 0.840355 0.477825 0.0941922 0.69603 -0.591275 0.0966528\n",
      "  35 3.654e-03 3.303e-01 6.407e-05 -- 4.925e+02 -- -0.136172 -0.819986 -2.00996 -2.42926 -2.86324 -3.12842 -4.2152 -4.03606 -0.106352 0.344296 0.84173 0.476631 0.0939684 0.695975 -0.588117 0.0967043\n",
      "********************\n",
      "-0.136172 -0.819986 -2.00996 -2.42926 -2.86324 -3.12842 -4.2152 -4.03606 -0.106352 0.344296 0.84173 0.476631 0.0939684 0.695975 -0.588117 0.0967043\n",
      "0.0115263 0.0058258 0.0387362 0.00846868 0.0539018 0.0780724 0.334539 0.108003 0.121876 0.0805411 0.223567 0.102776 0.222423 0.256036 0.800481 0.273811\n",
      "0.0127444 0.33028 -0.0607609 0.127486 0.0143628 0.0331918 -0.0227012 0.00709893 -0.000657376 -0.00220005 -0.0168474 0.0629554 -0.0038883 0.00145515 -0.00332533 0.000655605\n",
      "********************\n"
     ]
    }
   ],
   "source": [
    "Cx = clag.clag('cxd10r', [[t1,t2]], [[l1,l2]], [[l1e,l2e]], dt, fqL, p1, p2)\n",
    "p  = np.concatenate( ((p1+p2)*0.5-0.3,p1*0+0.1) ) # a  good starting point generally\n",
    "p, pe = clag.optimize(Cx, p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "phi, phie = p[nfq:], pe[nfq:]\n",
    "lag, lage = phi/(2*np.pi*fqd), phie/(2*np.pi*fqd)    \n",
    "cx, cxe   = p[:nfq], pe[:nfq]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.75428512,  1.89869772,  2.40546134,  0.87877231,  0.11177487,\n",
       "        0.53410247, -0.29118093,  0.03088965])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAhIAAAFrCAYAAACE+GArAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nf74t/y5tuiqPSHwwybu
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f64bb3b7550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "\n",
    "xscale('log'); ylim(-10,10)\n",
    "errorbar(fqd, lag, yerr=lage, fmt='o', ms=10,color=\"black\")\n",
    "\n",
    "lag"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f64bbde9d50>]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAhIAAAFrCAYAAACE+GArAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAAPYQAAD2EBqD+naQAAIABJREFUeJzt3X98XXWd5/FXgdIKOrYVSLBA04YfqdKVSabFtgykrvhA\nxqXjrgOJOg9IHcUZZ5nqOqsPZ4hQxJ2Hrlp10LXjtOiDB7dl2dVRd+swqy26pUhtmBlrSdG0RWmb\nlBaKK9hSTfaPc2OTNElzT86P77n39Xw87iPJueec+833cXvz7vd8vt8DkiRJkiRJkiRJkiRJkiRJ\nkiRJkiRJkiRJkiRJkiRJkiRJUtW4GvgmsA/oB5aPeP7e8vahj0cybJ8kSZqk01I891nA48D7yj8P\njHh+ANgI1A95XJ9ieyRJUsLOSPHc3y4/xjIFeAk4mGIbJElSitIckTiVAaAV6AN2AWuAc3NsjyRJ\nClQ/cMOIbTcCbwZeA7yF6DLIj4Azs22aJEmKK81LG6fywJDvdwI/BPYCfwB8bZT9zy8/JElSZQ6U\nH4nLM0iM1Av8DLh4lOfOf/WrX71///79GTdJkqSqsA9YSAphIqQgcQ5wIaP/kufv37+f++67j/nz\n52fSmJUrV7J69erMzjGRfU+1z1jPj7Z9ItuS6INK2Of2+UT2qaU+37cPbrgBvvhFWLRoYuc4dgyW\nLIG77oLrr7fPk3q9Ir/Pn3jiCd75znfOJhrVL1SQOBu4ZMjP84ArgMPAs8CdwINEIxENwMeBZxj9\nsgYA8+fPp7m5OaXmDjdjxoxJv1Yl55jIvqfaZ6znR9s+kW1J9EEl7HP7fCL71FKfv/KV0dfLLoOh\nh4x3jpdeir7OmRMdY5/7Pk/b6SmeeynRAlO3Es3QuK78/UzgW8BtwPuBvwTeCGwD3kEUNEY6H7j1\n1ltv5fzzsyuTWLBgQabnmMi+p9pnrOdH236qbaVSifb29lO2KUn2uX0+kX1qpc8PH4bPfx46OqCh\nYWLnGBiIRiOWL4crrpj469nnyZ4jpD4/cOAAa9asgWh2ZOIjElOSPmFKmoHt27dvzzTF1robbriB\nb3zjG3k3o6bY59kLuc937YKmJnj4Ybj66okd098Pp58Oa9dGASREIfd5Nerq6qKlpQWgBehK+vx5\nriMhSRrHQHk94NMq+KSeUv7vYX9/8u2RRmOQ0JiyHnqUfZ6HkPt8MAxUGiSmTAk7SITc56qcQUJj\n8h979uzz7IXc53GCxOD+BgllxSAhSYEaDANTKqxmCz1IqLoYJCQpUHFqJAb3N0goKwYJSQpUtV7a\nUHUxSEhSoAwSKgKDhCQFyiChIjBISFKgBmskLLZUyAwSkhQoRyRUBAYJSQqUQUJFYJCQpEAZJFQE\nBglJCpQLUqkIDBKSFCgXpFIRGCQkKVBe2lARGCQkKVBxg0Tod/9UdTFISFKgrJFQERgkJClQk6mR\nGDxWSptBQpICZY2EisAgIUmBMkioCAwSkhQog4SKwCAhSYHypl0qAoOEJAXKEQkVgUFCkgJlkFAR\nGCQkKVAGCRWBQUKSAmWNhIrAICFJgXJEQkVgkJCkQBkkVAQGCUkKlEFCRWCQkKRAedMuFYFBQpIC\nNZmbdhkklBWDhCQFyksbKgKDhCQFyiChIjBISFKgDBIqAoOEJAXKBalUBAYJSQpUf3/lIQIMEsqW\nQUKSAtXfX/llDYjCh0FCWTFISFKg4gYJRySUJYOEJAVqYCD+pY3B+gopbQYJSQqUIxIqAoOEJAXK\nIKEiMEhIUqAMEioCg4QkBcrpnyoCg4QkBWpgwBEJhc8gIUmB8tKGisAgIUmBMkioCAwSkhQog4SK\nwCAhSYGazIJUBgllxSAhSYFyREJFYJCQpEAZJFQEBglJCpRBQkWQZpC4GvgmsA/oB5aPss8d5edf\nBDYBr0mxPZJUKNZIqAjSDBJnAY8D7yv/PPJedB8CVpafXwj0Av8EvDzFNklSYTgioSI4I8Vzf7v8\nGM0UohBxN/D18rabgT7g7cCaFNslSYVgkFAR5FUjMReoAx4asu0l4GFgSS4tkqTAGCRUBHkFifry\n174R2w8OeU6Sapo1EiqCEGdtjKylkKSa5IiEiiDNGonx9Ja/1g35frSfh1m5ciUzZswYtq29vZ32\n9vbEGyhJeYsbJKZMMUjUqlKpRKlUGrbtyJEjqb5mXkFiD1FgeBPwL+VtZwLXAH851kGrV6+mubk5\n/dZJUgAckVClRvvPdVdXFy0tLam9ZppB4mzgkiE/zwOuAA4DPwdWAx8BfgL8tPz9L4H7U2yTJBWG\nQUJFkGaQWAh8t/z9APDp8vf3AiuATwAvA74AzAQeJRqheCHFNklSYUym2HLAajNlJM0gsZlTF3Pe\nWX5IkkZwREJFEOKsDUkSBgkVg0FCkgJlkFARGCQkKVAuSKUiMEhIUqAckVARGCQkKVAGCRWBQUKS\nAmWQUBEYJCQpUNZIqAgMEpIUKEckVAQGCUkKlEFCRWCQkKRAGSRUBAYJSQrUwIBBQuEzSEhSoPr7\nLbZU+AwSkhQoL22oCAwSkhSouEHizDPh2DHDhLJhkJCkQMUNEhddBL/+Nezbl3ybpJEMEpIUqLgL\nUjU2Rl97epJtjzQag4QkBSruiMTcuVEAMUgoCwYJSQpU3CAxbRpccIFBQtkwSEhSoOIGCYgubxgk\nlAWDhCQFKu6CVBAFid27k22PNBqDhCQFKu6CVADz5jkioWwYJCQpUJO9tPHcc9FDSpNBQpICNdkg\nAY5KKH0GCUkK1GRrJMAgofQZJCQpUJOpkZg5M3oYJJQ2g4QkBWoylzbAKaDKhkFCkgJlkFARGCQk\nKVBJBAnXklDaDBKSFKi4N+0a1NgITz8d3VJcSotBQpICNdkRiXnzojCyZ09ybZJGMkhIUqCSuLQB\n1kkoXQYJSQrUZIPE7NnRnUANEkqTQUKSAjWZBakgOnbuXIOE0mWQkKRATWZBqkFOAVXaDBKSFKjJ\nXtoAp4AqfQYJSQpUkkGivz+ZNkkjGSQkKVCTrZGAKEgcOwb79yfTJmkkg4QkBSqpGgmwTkLpMUhI\nUqCSuLTR0BCFEYOE0mKQkKRAJREkpk+P1pMwSCgtBglJClQSNRLgFFClyyAhSYFKokYCDBJKl0FC\nkgKVxKUNcC0JpcsgIUmBSjJIPPssHDky+XNJIxkkJClQSQYJ8PKG0mGQkKRAJVlsCQYJpcMgIUmB\nSqrYcubM6GGQUBoMEpIUqKQubQDMm2eQUDoMEpIUqCSDhFNAlRaDhCQFKqkaCTBIKD0GCUkKVFI1\nEhAFiaefju4EKiUpzyBxB9A/4uGNbiWpLOlLGwMDsHdvMueTBuU9IrEDqB/yWJBvcyQpHEkHCfDy\nhpJ3Rs6v/xvgYM5tkKQgJVkjMXs2TJtmkFDy8h6RuATYB+wGSsDcfJsjSeFIskbitNNg7lyDhJKX\nZ5B4FPhj4E3Au4kubTwCzMqxTZIUjCQvbYBrSSgdeQaJbwNfA34MfAf4g/L2m3NrkSQFJOkg4RRQ\npSHvGomhXgR+BFw81g4rV65kxowZw7a1t7fT3t6ectMkKXtpBIk1a5I/r8JRKpUolUrDth1J+bav\nIQWJacBrgO+NtcPq1atpbm7OrkWSlKMkiy0hChLHjsGBA1HxparPaP+57urqoqWlJbXXzDOT/lfg\naqICyyuBB4GXA1/JsU2SFIwkiy3BKaBKR55BYjbRTI1u4H8AR4HXAz/PsU2SFISBgeRHJObOjYKJ\nQUJJyvPShoUNkjSGgYHoa5JBYvr06JKGQUJJstxGkgKURpAAZ24oeQYJSQpQf3/0NckaCTBIKHkG\nCUkK0GCQSHpEwkWplDSDhCQFKK0g0dgIzz4LKS8toBpikJCkAKVZIwGwe3ey51XtMkhIUoDSrJEA\nL28oOQYJSQpQWpc2Zs2Cujr4wQ+SPa9ql0FCkgKUVpAAuOkmuO8+OH48+XOr9hgkJClAadVIAKxY\nAX19sHFj8udW7TFISFK
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f64bb1a8b90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s, loc, scale = lognorm.fit(lag,loc=.008)\n",
    "\n",
    "xscale('log'); ylim(-10,15)\n",
    "errorbar(fqd, lag, yerr=lage, fmt='o', ms=10,color=\"black\")\n",
    "plot(np.logspace(np.log(fqd[0]),np.log(fqd[-1])),lognorm.pdf(np.logspace(np.log(fqd[0]),np.log(fqd[-1])),s,loc,scale))\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.47677903915219444, 1.214804919002201)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAhIAAAFrCAYAAACE+GArAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ntqeqg8Q/TPLvkpxYfv0
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f64b94d0850>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "loc, scale = norm.fit(lag,loc=.01)\n",
    "\n",
    "xscale('log'); ylim(-10,10)\n",
    "errorbar(fqd, lag, yerr=lage, fmt='o', ms=10,color=\"black\")\n",
    "plot(np.logspace(np.log(fqd[3]),np.log(fqd[-1])),norm.pdf(np.logspace(np.log(fqd[0]),np.log(fqd[-1])),loc,scale))\n",
    "\n",
    "norm.fit(lag,loc=.01,scale=.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f64bb3ec6d0>]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAhEAAAFkCAYAAACemWn9AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n5lR/rIiIyLRp1iV+7LG
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f64b95531d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(irfft(lag))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}