{
 "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"
     ]
    }
   ],
   "source": [
    "%pylab inline --no-import-all\n",
    "from scipy.stats import chi2, norm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import george\n",
    "from george.kernels import ExpSquaredKernel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "n_scan_points = 100\n",
    "x = np.linspace(0,100,n_scan_points)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n_dist = 10\n",
    "width = 5\n",
    "mixture_means = np.random.uniform(3*width,100-3*width,n_dist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def pdf(x):\n",
    "    ret = 0*x\n",
    "    for i,xx in enumerate(x):\n",
    "        ret[i] = np.sum(norm.pdf(xx,mixture_means, width))\n",
    "    return ret/n_dist\n",
    "\n",
    "def cdf(x):\n",
    "    ret = 0*x\n",
    "    for i,xx in enumerate(x):\n",
    "        ret[i] = np.sum(norm.cdf(xx,mixture_means, width))\n",
    "    return ret/n_dist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def generate(n):\n",
    "    n_ceil = np.ceil(1.*n/n_dist)\n",
    "    ret = np.zeros(n_ceil*n_dist)\n",
    "    for i, mu in enumerate(mixture_means):\n",
    "        ret[i*n_ceil : (i+1)*n_ceil] = norm.rvs(loc=mu, scale=width,size=n_ceil)\n",
    "    return ret[0:n]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "points = np.sort(generate(500))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x11388fb10>]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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       "WoBtfne0UNB1XGdgz/gXYs9ka/sgpurAVo79UOKDmO7gWHPOCdi/vl3H9IkX0wKOXWKt6JhKmyv/\n",
       "gG3NswLoW86xiYiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIhISf4/RmW0kqG65KwAAAAASUVORK5C\n",
       "YII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113870e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bins, edges, _ = plt.hist(points, bins=100, normed=True, alpha=.5)\n",
    "plt.plot(edges,pdf(edges))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "y = np.linspace(0,1,points.size)\n",
    "#binomial errors for the emperical cdf\n",
    "yerr = np.sqrt(y*(1.-y)/y.size) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1103c2250>]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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       "/tn/RcTS+3DwgJ5pSimllFJKKaWUUkoppZRSSimllFJKKaWUUkoppZRSSin1xv8HLs4xq3IyQ6wA\n",
       "AAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113c5bc90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plt.scatter(points,y,alpha=0.3)\n",
    "plt.errorbar(points, y, yerr, alpha=0.5,fmt=\".k\")\n",
    "plt.plot(x,cdf(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "dy = (y-np.roll(y,1))/(points-np.roll(points,1))\n",
    "dy[0]=0.\n",
    "dyerr = np.sqrt(yerr**2 + np.roll(yerr,1)**2)/(points-np.roll(points,1)) #neglects correlations\n",
    "dyerr = yerr/(points-np.roll(points,1)) #needs more thought\n",
    "dyerr[0]=0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "temp = cdf(points)\n",
    "tempdy = (temp-np.roll(temp,1))/(points-np.roll(points,1))\n",
    "tempdy[0]=0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "problem... want to do log-Gaussian process for positivity, but noise makes observations go negative.\n",
    "\n",
    "want ln_pred ~GP, pred ~ exp(GP) + noise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Library/Python/2.7/site-packages/IPython/kernel/__main__.py:1: RuntimeWarning: divide by zero encountered in log\n",
      "  if __name__ == '__main__':\n",
      "/Library/Python/2.7/site-packages/IPython/kernel/__main__.py:4: RuntimeWarning: divide by zero encountered in log\n",
      "/Library/Python/2.7/site-packages/IPython/kernel/__main__.py:9: RuntimeWarning: divide by zero encountered in log\n"
     ]
    }
   ],
   "source": [
    "log_dy = np.log(dy)\n",
    "log_dy[0]=log_dy[1]\n",
    "\n",
    "log_dyerr = np.log(dyerr)\n",
    "log_dyerr[0]=log_dyerr[1]\n",
    "log_dyerr[-1]=log_dyerr[-2]\n",
    "\n",
    "\n",
    "log_true_dy = np.log(np.abs(tempdy))\n",
    "log_true_dy[0]=log_true_dy[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-3.49017600035 -1.38750894045\n"
     ]
    }
   ],
   "source": [
    "length_scale_of_correaltion=50.\n",
    "kernel_d = ExpSquaredKernel(length_scale_of_correaltion, ndim=1)\n",
    "gp_d = george.GP(kernel_d, mean=np.mean(log_dy), solver=george.HODLRSolver) #faster\n",
    "#gp_d.compute(points,log_dyerr)\n",
    "#gp_d.compute(points, yerr=np.mean(log_dyerr))\n",
    "gp_d.compute(points, yerr=.1)\n",
    "pred_log_dy, _ = gp_d.predict(log_dy,x)\n",
    "print np.mean(log_dy), np.mean(log_dyerr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1171b1610>]"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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       "rsY+OYacfy02/nAOG3+7i47zhlZ3ivMvoTrqpoiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIhIvP4H\n",
       "iXllHv28LwkAAAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116a27350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plt.errorbar(points,log_dy, log_dyerr, fmt=\".k\", alpha=0.2)\n",
    "plt.scatter(points,log_dy,alpha=0.2)\n",
    "plt.plot(points,log_true_dy, c='g')\n",
    "plt.plot(x,pred_log_dy, c='r')\n",
    "#plt.ylim(-15,0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x116f7e790>]"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "AElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116f7e710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pred_d = np.exp(pred_log_dy)\n",
    "#plt.plot(points,dy)\n",
    "#plt.plot(points,tempdy)\n",
    "plt.plot(points,log_true_dy, c='g')\n",
    "plt.plot(x,pred_log_dy, c='r')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x11774ebd0>"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "QR+rz8UErAe/Cuu19iB2n4tb8E+T/Cv2rTdWnosXsLGHauxD/9sc+m+/A4ulG7AtQEVERERERERE\n",
       "REREREREREREREREREREREREwtv/B4QkNGep3c7sAAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117086990>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pred = np.cumsum(pred_d)\n",
    "#now rescale and shift\n",
    "#pred = (curve(x[-1])-curve(x[0]))*(pred[-1]-pred[0]) + curve(x[0])\n",
    "pred = pred*(y[-1]-y[0])/(pred[-1]-pred[0]) + y[0]\n",
    "\n",
    "plt.plot(x,cdf(x), c='g', label='true')\n",
    "#plt.scatter(points,y)\n",
    "plt.errorbar(points,y, yerr, fmt=\".k\", alpha=0.2)\n",
    "plt.plot(x,pred,c='r', label='isotonic gp')\n",
    "plt.legend(('true', 'data', 'isotonic gp'), loc='upper left')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "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": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}