Testing_dp4gp.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Testing\n",
    "\n",
    "- Check DP bounds not exceeded (move a point and look for its detection probability)\n",
    "- Check changing standard deviation/outputs of training data doesn't affect anything\n",
    "- Check scaling lengthscale and input locations simultaneously doesn't affect anything"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Calculating covariance between test inputs\n",
      "Calculating covariance between training inputs and test inputs\n",
      "Calculating K_NM\n",
      "Calculating K_MM\n",
      "Calculating K_NN diagonals\n",
      "Calculating K_star\n",
      "Maximum k* 1.00\n",
      "Calculating K_NN\n",
      "Calculating lambda\n",
      "THING\n",
      "(4, 2)\n",
      "[[ 0.50245576  0.50245576]\n",
      " [-0.48760599  1.47281594]\n",
      " [ 0.99746236  0.00248715]\n",
      " [ 0.00248715  0.99746236]]\n",
      "7.99532794434\n",
      "[ 0.50245576  1.47281594  0.99746236  0.99746236]\n",
      "25.376440343\n",
      "NORMAL MU\n",
      "[-1.00491152 -0.00499899 -1.49743711 -0.5024619 ]\n",
      "COVARIANCE USED:\n",
      "[[ 6.78184623  6.64755668  6.74802163  6.74802163]\n",
      " [ 6.64755668  6.78184623  6.48342792  6.74802163]\n",
      " [ 6.74802163  6.48342792  6.78184623  6.64755668]\n",
      " [ 6.74802163  6.74802163  6.64755668  6.78184623]]\n",
      "Calculating covariance between test inputs\n",
      "Calculating covariance between training inputs and test inputs\n",
      "Calculating K_NM\n",
      "Calculating K_MM\n",
      "Calculating K_NN diagonals\n",
      "Calculating K_star\n",
      "Maximum k* 1.00\n",
      "Calculating K_NN\n",
      "Calculating lambda\n",
      "THING\n",
      "(4, 2)\n",
      "[[ 0.50245576  0.50245576]\n",
      " [-0.48760599  1.47281594]\n",
      " [ 0.99746236  0.00248715]\n",
      " [ 0.00248715  0.99746236]]\n",
      "7.99532794434\n",
      "[ 0.50245576  1.47281594  0.99746236  0.99746236]\n",
      "25.376440343\n",
      "NORMAL MU\n",
      "[-0.50245576  1.46781696 -1.49494996  0.49500046]\n",
      "COVARIANCE USED:\n",
      "[[ 6.78184623  6.64755668  6.74802163  6.74802163]\n",
      " [ 6.64755668  6.78184623  6.48342792  6.74802163]\n",
      " [ 6.74802163  6.48342792  6.78184623  6.64755668]\n",
      " [ 6.74802163  6.74802163  6.64755668  6.78184623]]\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "import dp4gp\n",
    "\n",
    "Y = np.array([0.0,1.0])\n",
    "test_inputs = np.array([1.0,3.0])\n",
    "X = np.array([0.0,2.0])\n",
    "pseudo_inputs = np.array([0.0,2.0])\n",
    "lengthscales = 10.0\n",
    "sigma = 0.01\n",
    "calc_normal=True\n",
    "sens = 1.0\n",
    "delta = 0.01\n",
    "eps = 10.0\n",
    "\n",
    "def get_peroutput_samples(Y,test_inputs,X,pseudo_inputs,lengthscales,sigma,calc_normal,sens,delta,eps,Nsamples):\n",
    "    test_inputs = np.hstack([test_inputs,X])\n",
    "    test_cov, normal_msense, pseudo_msense, normal_peroutput_msense, pseudo_peroutput_msense, normal_mu, pseudo_mu, K_normal, K_pseudo, normal_covars = dp4gp.get_noise_scale(Y,test_inputs,X,pseudo_inputs,lengthscales,sigma,calc_normal=True)\n",
    "    scalings = {}\n",
    "    for i,o in zip(test_inputs,normal_peroutput_msense):\n",
    "        scalings[i] = o\n",
    "    new_test_cov, new_normal_msense, new_pseudo_msense, new_normal_peroutput_msense, new_pseudo_peroutput_msense, new_normal_mu, new_pseudo_mu, new_K_normal, new_K_pseudo, new_normal_covars = dp4gp.get_noise_scale(Y,test_inputs,X,pseudo_inputs,lengthscales,sigma,scale=scalings,calc_normal=True)\n",
    "    msense = np.max(new_normal_peroutput_msense) #new_normal_msense # \n",
    "    samps = []\n",
    "    for it in range(Nsamples):\n",
    "        samp = dp4gp.draw_sample(new_test_cov, test_inputs, new_normal_mu, msense, sens, delta, eps)\n",
    "        samps.append(samp)\n",
    "    return np.array(samps)\n",
    "\n",
    "def get_normal_samples(Y,test_inputs,X,pseudo_inputs,lengthscales,sigma,calc_normal,sens,delta,eps,Nsamples):\n",
    "    test_inputs = np.hstack([test_inputs,X])\n",
    "    test_cov, normal_msense, pseudo_msense, normal_peroutput_msense, pseudo_peroutput_msense, normal_mu, pseudo_mu, K_normal, K_pseudo, normal_covars = dp4gp.get_noise_scale(Y,test_inputs,X,pseudo_inputs,lengthscales,sigma,calc_normal=True)\n",
    "    print normal_peroutput_msense\n",
    "    print normal_msense\n",
    "    print \"NORMAL MU\"\n",
    "    print normal_mu\n",
    "    msense = 8 #normal_msense #np.max(normal_peroutput_msense) #normal_msense\n",
    "    #   the 8 comes from tot = np.dot(test_cov**-.5,np.max(np.dot(K_Nstar.T, invCov),1))\n",
    "    #   np.sqrt(np.sum(tot**2))\n",
    "    samps = []\n",
    "    \n",
    "    print \"COVARIANCE USED:\"\n",
    "    covused = test_cov*(msense*sens*np.sqrt(2*np.log(2/delta))/eps)**2\n",
    "    print covused\n",
    "    for it in range(Nsamples):\n",
    "        samp = dp4gp.draw_sample(test_cov, test_inputs, normal_mu, msense, sens, delta, eps)\n",
    "        samps.append(samp)\n",
    "    return np.array(samps), covused, normal_mu\n",
    " \n",
    "fn = get_normal_samples #get_peroutput_samples # # \n",
    "ymean = 1.5\n",
    "ystd = 1.0\n",
    "Ytransformed = dp4gp.transform(Y.copy(),ymean,ystd)\n",
    "sigmatransformed = sigma / ystd\n",
    "Nsamples = 10000\n",
    "samples, covused, mu = fn(Ytransformed,test_inputs,X,pseudo_inputs,lengthscales,sigmatransformed,calc_normal,sens,delta,eps,Nsamples)\n",
    "samples = dp4gp.untransform(samples.copy(),ymean,ystd)\n",
    "\n",
    "Y[1]+=1.0\n",
    "Ytransformed = dp4gp.transform(Y.copy(),ymean,ystd)\n",
    "sigmatransformed = sigma / ystd\n",
    "samples_prime, covused, mu_prime = fn(Ytransformed,test_inputs,X,pseudo_inputs,lengthscales,sigmatransformed,calc_normal,sens,delta,eps,Nsamples)\n",
    "samples_prime = dp4gp.untransform(samples_prime.copy(),ymean,ystd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.,  3.,  0.,  2.])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.hstack([test_inputs,X])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#plt.plot(np.hstack([test_inputs,X]),samples.T,'.k',markersize=10,alpha=0.1);\n",
    "#plt.plot(np.hstack([test_inputs,X])+0.2,samples_prime.T,'.b',markersize=10,alpha=0.1);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f0874cd4150>]"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYEAAAEACAYAAABVtcpZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nwxQCIiI5TCEgIpLD/h+nd3obzgSkFQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0874cd4190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.hstack([test_inputs,X]),mu_prime,'x-')\n",
    "plt.plot(np.hstack([test_inputs,X]),mu,'r-+')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.43089855, -1.40621886,  0.06864245, -0.9273975 ])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(samples,0) - np.mean(samples_prime,0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the plot you can see that more noise has been added to the locations where the means differ more."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 6.83202157,  6.69519646,  6.79699198,  6.79769817],\n",
       "       [ 6.69519646,  6.82711388,  6.53015963,  6.79511421],\n",
       "       [ 6.79699198,  6.53015963,  6.82934673,  6.69621955],\n",
       "       [ 6.79769817,  6.79511421,  6.69621955,  6.8309415 ]])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.cov(samples.T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Why does the sample mean not move in the direction the covariances would make us expect?!\n",
    "\n",
    "I.e. As mean[2] has changed by -0.54, I'd expect mean[3] to move by about this too."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INDEX 0\n",
      "1.56580016069\n",
      "0.993329821659\n",
      "22026.4657948\n",
      "INDEX 1\n",
      "3.90877968755\n",
      "0.985754494877\n",
      "22026.4657948\n",
      "INDEX 2\n",
      "1.07601584514\n",
      "0.994749321012\n",
      "22026.4657948\n",
      "INDEX 3\n",
      "2.53655337159\n",
      "0.990270281382\n",
      "22026.4657948\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import multivariate_normal\n",
    "stepsize = 0.1\n",
    "x, y = np.mgrid[-10:10:stepsize, -10:10:stepsize]\n",
    "pos = np.empty(x.shape + (2,))\n",
    "pos[:, :, 0] = x; pos[:, :, 1] = y\n",
    "for index in range(4):\n",
    "    rv_sample = multivariate_normal(np.mean(samples,0)[index], np.cov(samples.T)[index,index])\n",
    "\n",
    "    rv_sample_prime = multivariate_normal(np.mean(samples_prime,0)[index], np.cov(samples.T)[index,index]) #np.cov(samples_prime.T)[index,index])\n",
    "\n",
    "    stepsize = 0.01\n",
    "    histwidth = 1000\n",
    "    p = rv_sample.pdf(np.arange(-histwidth,histwidth,stepsize))\n",
    "    q = rv_sample_prime.pdf(np.arange(-histwidth,histwidth,stepsize))\n",
    "    threshold = 0.003\n",
    "    #threshold = 0.0027\n",
    "    inc = (p>threshold) & (q>threshold)\n",
    "    print \"INDEX %d\" % index\n",
    "    print np.max(p[inc]/q[inc])\n",
    "    print np.sum(p[inc])*stepsize**1\n",
    "    print np.exp(eps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f0874924390>]"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYQAAAEACAYAAACznAEdAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAPtkd+wAAAAGSURBVP8fW3c1KOy0LmUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0874ba67d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot(2,1,1)\n",
    "plt.plot(p[inc])\n",
    "plt.plot(q[inc])\n",
    "plt.subplot(2,1,2)\n",
    "plt.plot((p[inc]/q[inc]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Can we use logic such as:\n",
    " - we can have an arbitrary number of test points, so DP should be assured independently for each one.\n",
    " - but combining them might help, but we just test the one closest to the training point being adjusted."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Multivariate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-10.0, 10.0, -10.0, 10.0)"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAssAAAK/CAYAAACfu4AMAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0874844d90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "plt.figure(figsize=[12,12])\n",
    "from scipy.stats import multivariate_normal\n",
    "stepsize = 0.05\n",
    "histwidth = 10\n",
    "x, y = np.mgrid[-histwidth:histwidth:stepsize, -histwidth:histwidth:stepsize]\n",
    "pos = np.empty(x.shape + (2,))\n",
    "pos[:, :, 0] = x; pos[:, :, 1] = y\n",
    "samp_cov = np.cov(samples.T)\n",
    "samp_prime_cov = np.cov(samples_prime.T)\n",
    "rv_sample = multivariate_normal(np.mean(samples,0)[2:4], covused[2:4,2:4])# samp_cov[2:4,2:4])\n",
    "p = rv_sample.pdf(pos)\n",
    "plt.contourf(x, y, p)\n",
    "plt.axis('equal')\n",
    "rv_sample_prime = multivariate_normal(np.mean(samples_prime,0)[2:4], covused[2:4,2:4])#samp_cov[2:4,2:4])\n",
    "q = rv_sample_prime.pdf(pos)\n",
    "plt.contour(x, y, q)\n",
    "plt.axis('equal')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 168.48754869  165.08211406  167.70600031  167.60483331]\n",
      " [ 165.08211406  168.3290801   161.07500201  167.52527147]\n",
      " [ 167.70600031  161.07500201  168.59760997  165.1739652 ]\n",
      " [ 167.60483331  167.52527147  165.1739652   168.39733567]]\n",
      "[[ 172.94954266  169.27333463  172.22034414  171.95560422]\n",
      " [ 169.27333463  172.35138337  165.2637803   171.65792311]\n",
      " [ 172.22034414  165.2637803   173.19626996  169.54794221]\n",
      " [ 171.95560422  171.65792311  169.54794221  172.66437279]]\n"
     ]
    }
   ],
   "source": [
    "print samp_cov\n",
    "print samp_prime_cov\n",
    "#New\n",
    "#array([[ 1223.61180407,  2743.23937924,  2021.51874817,  2019.47229901],\n",
    "#       [ 2743.23937924,  6405.81067345,  4440.25416485,  4620.79860445],\n",
    "#       [ 2021.51874817,  4440.25416485,  3374.22530665,  3302.33679849],\n",
    "#       [ 2019.47229901,  4620.79860445,  3302.33679849,  3367.19571123]])\n",
    "\n",
    "#Normal\n",
    "#array([[ 3092.6585145 ,  3025.36943166,  3079.50103014,  3074.46465502],\n",
    "#       [ 3025.36943166,  3084.45772257,  2951.02929042,  3070.32581593],\n",
    "#       [ 3079.50103014,  2951.02929042,  3098.0204724 ,  3030.04319949],\n",
    "#       [ 3074.46465502,  3070.32581593,  3030.04319949,  3088.06106818]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.10761475855\n",
      "0.990295144354\n",
      "1.0\n",
      "7.38905609893\n"
     ]
    }
   ],
   "source": [
    "threshold = 0.000028\n",
    "#threshold = 0.0027\n",
    "inc = (p>threshold) & (q>threshold)\n",
    "print np.max(p[inc]/q[inc])\n",
    "print np.sum(p[inc])*(stepsize**2)\n",
    "print np.sum(p)*(stepsize**2)\n",
    "print np.exp(eps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXwAAAEACAYAAACwB81wAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAD9tJREFUeJzt3W+s5Fddx/H3py27Cg1NRbvXtNAlqUJrYgrGVYMJ14il\n9QFLjKlFovwJCZEQeERoiXEXY6gYNEEND4yFrAgphQR2DQqFlPsADV2kNK1sqUviLmXDXhL5YwpK\nCvv1wcy2t/fOvTN3/tz5zZz3K5kw98xvZr57Uj5z7rnnnElVIUlafpfMuwBJ0t4w8CWpEQa+JDXC\nwJekRhj4ktQIA1+SGjE08JNck+S+JF9J8nCSt/Tbr0xyb5JHk3w6yRUbnnNHktNJHkly0yz/AZKk\n0WTYOvwkK8BKVT2Y5HLgS8Bh4HXAf1fVXyR5O3BlVd2e5AbgQ8AvA9cAnwV+rlzwL0lzNXSEX1Xn\nq+rB/v3HgUfoBflh4Fj/smPAK/v3XwHcXVU/qqozwGng0JTrliTt0q7m8JMcBG4EvgAcqKp16H0o\nAFf1L7saeGzD08712yRJczRy4Pencz4GvLU/0t88ReOUjSR12GWjXJTkMnph/8GqOt5vXk9yoKrW\n+/P83+q3nwOeu+Hp1/TbNr+mHxCSNIaqyjjPG3WE/37gVFW9d0PbCeC1/fuvAY5vaL8tyb4kzweu\nA04OetGqWtjbkSNH5l6D9c+/jhbrX+Tal6H+SQwd4Sd5CfBq4OEkX6Y3dfMO4N3APUleD5wFbu2H\n+Kkk9wCngCeAN9WkVUqSJjY08KvqX4FLt3n4Zds8507gzgnqWjgrKwdZXz+7pf3AgWs5f/7M3hck\nSZuMNIevrVZXV5/2cy/st/4is74+1lTbzG2uf9FY//wscu2w+PVPYujGq5m9cbIQMz2DRu6DRu1J\nGLxQKRPPu0nSRUmoMf9oa+APMTjIt4a4gS9pL0wS+B6eJkmNMPAlqREGviQ1wsCXpEYY+JLUCANf\nkhrhxqux7O8vw5SkxWHgj+WHDFqbL0ld5pRO38rKQZJsuUnSsnCnbd9OO2UHj+ZHaeu1d+nfKWmx\nudNWkjSUgS9JjTDwJakRBr4kNcLAl6RGGPiS1AgDf+b2b1nbv7JycN5FSWqQ6/D7ZrkOf5RvzJKk\nUbgOX5I0lIEvSY0w8CWpEQa+JDXCwJekRhj4ktQIA1+SGmHgS1IjDHxJaoSBL0mNMPAlqREG/lx4\noJqkvefhaX17fXiaB6pJGoeHp0mShjLwJakRBr4kNcLAl6RGGPiS1AgDX5IaYeB3xta1+a7PlzRN\nrsPv68I6/O2e36V+kjRfrsOXJA1l4EtSIwx8SWqEgS9JjTDwO8+TNSVNx9DAT3JXkvUkD21oO5Lk\nG0ke6N9u3vDYHUlOJ3kkyU2zKrwdP6S3euep2/r62fmWJGkhjTLC/wDw8gHtf1VVL+7fPgWQ5Hrg\nVuB64Bbgfemtd5QkzdnQwK+qzwPfGfDQoCA/DNxdVT+qqjPAaeDQRBVKkqZikjn8Nyd5MMnfJ7mi\n33Y18NiGa8712yRJc3bZmM97H/CnVVVJ/gz4S+ANu32Ro0ePPnl/dXWV1dXVMcuRpOW0trbG2tra\nVF5rpKMVklwL/FNV/eJOjyW5Haiqenf/sU8BR6rq/gHP82iFCZ7fpb6TtHf24miFsGHOPsnKhsd+\nB/iP/v0TwG1J9iV5PnAdcHKcwiRJ0zV0SifJh4FV4DlJvg4cAX4jyY3ABeAM8EaAqjqV5B7gFPAE\n8KZODeMlqWHNnZZ58uRJ3vWuv9nSfvz4P+KUjqSum2RKZ9w/2i6sj3704xw//n/AKza0nplTNZK0\nd5oL/J4XA3+w4ecHgD+ZUy3j2M/m/WwHDlzL+fNn5lOOpIXQaOAvuovHLTxlfd0NzZJ25uFpktQI\nA1+SGmHgS1IjDHxJaoSBL0mNMPAlqREGviQ1wsCXpEYY+JLUCANfkhph4EtSIwz8pdE7UG3zbWXl\n4LwLk9QRHp62NLYeqAYeqibpKY7wJakRBr4kNcLAl6RGGPiS1AgDf+ltXb3jyh2pTa7SWXp+HaKk\nHkf4ktQIA18ArKwcdOOWtOSc0hEA6+tnceOWtNwc4UtSIwx8SWqEgS9JjTDwJakRBr4kNcJVOk3q\n7b6V1BYDv0mDzs73A0Badk7pSFIjDHxJaoSBL0mNMPAlqREGviQ1wsCXpEYY+JLUCANfkhph4EtS\nIwx8SWqEga+p8CsSpe7zLB1NhV+RKHWfI3xJaoSBL0mNMPA1xH7n5aUlMTTwk9yVZD3JQxvarkxy\nb5JHk3w6yRUbHrsjyekkjyS5aVaFa69cPDv/qVtvvl7SohllhP8B4OWb2m4HPltVLwDuA+4ASHID\ncCtwPXAL8L741UqS1AlDA7+qPg98Z1PzYeBY//4x4JX9+68A7q6qH1XVGeA0cGg6pUqSJjHuHP5V\nVbUOUFXngav67VcDj2247ly/TZI0Z9Nah791AfYIjh49+uT91dVVVldXp1SOJC2HtbU11tbWpvJa\n4wb+epIDVbWeZAX4Vr/9HPDcDddd028baGPgS5K22jwYfuc73zn2a406pZP+7aITwGv7918DHN/Q\nfluSfUmeD1wHnBy7OknS1Awd4Sf5MLAKPCfJ14EjwJ8DH03yeuAsvZU5VNWpJPcAp4AngDdV1VjT\nPZKk6Roa+FX1+9s89LJtrr8TuHOSotR1vc1YkhaLO201hq2bsXZj0Mma7t6VZs/TMrXnBp2s6ama\n0uw5wpekRhj4ktQIA1+SGmHgS1IjDHxJaoSBL0mNMPAlqREGviQ1wsCXpEa401Yz5rk7UlcY+Jqx\ni+fubOQHgDQPTulIUiMMfHWaJ2tK0+OUjjrNkzWl6XGEL0mNMPAlqREGviQ1wsCXpEYY+FoKg1bz\nuKJHejpX6WgpDFrN02t3RY90kSN8dcT+gSP0WXBtv1rlCF8dMegIBpjFMQyu7VerHOFLUiMMfElq\nhIEvSY0w8CWpEQa+JDXCVTpaQH6LljQOA18LyG/RksbhlI60AzdpaZk4wpd24CYtLRNH+JLUCANf\nkhph4EtSIwx8SWqEgS9JjTDwJakRBr4kNcLAl6RGuPFKS85zd6SLDHwtOc/dkS5ySkeSGmHgSzPk\n4WvqEqd0pBny8DV1iSN8SWrERCP8JGeA7wEXgCeq6lCSK4GPANcCZ4Bbq+p7E9YpSZrQpCP8C8Bq\nVb2oqg71224HPltVLwDuA+6Y8D0kSVMwaeBnwGscBo717x8DXjnhe0iSpmDSwC/gM0m+mOQN/bYD\nVbUOUFXngasmfA9pD+zfsppm+w1bW6915Y0WwaSrdF5SVd9M8jPAvUkeZesul80/P+no0aNP3l9d\nXWV1dXXCcqRxDdqgBYM3aW29dn39J9zRq5lYW1tjbW1tKq+Vqm3zeHcvlBwBHgfeQG9efz3JCvC5\nqrp+wPU1rffejbe97Q7e855n8/Q/LTwA/BLb/x9+0E7NUdp8vs8ffO08/tvXckhCVY01uhh7SifJ\nM5Nc3r//LOAm4GHgBPDa/mWvAY6P+x5SKwZt0HKqSNM2yZTOAeDjSar/Oh+qqnuT/DtwT5LXA2eB\nW6dQp7TUBm3Q6rU7TaTpGTvwq+q/gBsHtH8beNkkRUmSps+dtpLUCANfkhrh4WnSnvNLWTQfjvCl\nPXdxHf/G23bc5KXpcYQvddqgTV7+dqDxOMKXFo6jfo3HEb60cBz1azyO8KUl5lcsaiMDX1piT+3g\nfeq2vn7eD4FGOaUjNccpoVY5wpekRjjCl5aCm7k0nCN8aSkM2sw1mzP3/UPw4nKEL2lXBh3l7N8A\nFoMjfElqhIEvSY0w8CWpEQa+JDXCwJfEoAPZXH2zfFylI4lBu2/B1TfLxhG+pB1sHfnPwqC1/f6G\nMX0GvqQdjPrtXKNPCQ0K90GHvPUOejs7i39Us5zSkTQFo08JDdq4BU4d7QVH+JLUCANfkhph4EtS\nIwx8SWqEgS9JjTDwJakRBr4kNcLAl6RGGPiS1Ah32kqaIb9cvUsc4UuaoVHP4tnO1jN6Lr30WR6y\nNiYDX1KHbf3AuHDhB1vatjtkbdBBbYM+MAa1LeMHiVM6kpbATlNHT/+t4sKFjNQGy/d9AAa+pCUw\n+LROT+F8Oqd0JKkRBr4kNcLAl6RGGPiS1AgDX5IaYeBLUiMMfElqhIEvSY0w8CWpETML/CQ3J/lq\nkv9M8vZZvY8kaTQzCfwklwB/C7wc+AXgVUleOIv3mp+1eRcwobV5FzChtXkXMKG1eRegBs1qhH8I\nOF1VZ6vqCeBu4PCM3mtO1uZdwITW5l3AhNbmXcCE1uZdgBo0q8C/Gnhsw8/f6LdJkuakudMy9+17\nBvv3H2P//n97su3HP/4u3//+HIuSpD2Qqt1+A80IL5r8KnC0qm7u/3w7UFX17g3XTP+NJakBVTXW\nuc+zCvxLgUeB3wS+CZwEXlVVj0z9zSRJI5nJlE5V/TjJm4F76f2d4C7DXpLmayYjfElS98x8p+0o\nG7CS/HWS00keTHLjrGvajWH1J3lpku8meaB/++N51DlIkruSrCd5aIdrutz3O9bf8b6/Jsl9Sb6S\n5OEkb9nmuk72/yj1d7z/9ye5P8mX+/Uf2ea6rvb/0PrH6v+qmtmN3gfK14BrgWcADwIv3HTNLcAn\n+/d/BfjCLGuaQf0vBU7Mu9Zt6v914EbgoW0e72zfj1h/l/t+Bbixf/9yen/TWqT/9kepv7P936/v\nmf3/vRT4AnBoUfp/xPp33f+zHuGPsgHrMPAPAFV1P3BFkgMzrmtUo24g6+Q3JVfV54Hv7HBJl/t+\nlPqhu31/vqoe7N9/HHiErXtROtv/I9YPHe1/gKr6Qf/ufnp/r9w8f93Z/oeR6odd9v+sA3+UDVib\nrzk34Jp5GXUD2a/1fyX8ZJIb9qa0qehy34+q832f5CC931Tu3/TQQvT/DvVDh/s/ySVJvgycBz5T\nVV/cdEmn+3+E+mGX/d/cxqsZ+BLwvKr6QZJbgE8APz/nmlrR+b5PcjnwMeCt/ZHyQhlSf6f7v6ou\nAC9K8mzgE0luqKpT865rVCPUv+v+n/UI/xzwvA0/X9Nv23zNc4dcMy9D66+qxy/+6lVV/wI8I8lP\n7V2JE+ly3w/V9b5Pchm9sPxgVR0fcEmn+39Y/V3v/4uq6n+AzwE3b3qo0/1/0Xb1j9P/sw78LwLX\nJbk2yT7gNuDEpmtOAH8IT+7Q/W5Vrc+4rlENrX/jnF+SQ/SWun57b8vcUdh+nq/LfX/RtvUvQN+/\nHzhVVe/d5vGu9/+O9Xe5/5P8dJIr+vd/Evgt4KubLuts/49S/zj9P9MpndpmA1aSN/Yerr+rqn9O\n8ttJvgZ8H3jdLGvajVHqB343yR8BTwD/C/ze/Cp+uiQfBlaB5yT5OnAE2McC9D0Mr59u9/1LgFcD\nD/fnYQt4B70VX53v/1Hqp8P9D/wscCy9o9ovAT7S7++FyB5GqJ8x+t+NV5LUCL/iUJIaYeBLUiMM\nfElqhIEvSY0w8CWpEQa+JDXCwJekRhj4ktSI/wdWfxL4AuINlQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1a1c7aca10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(p[inc]/q[inc],50);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Idea for future DP reduction...\n",
    "\n",
    "If we know inputs lie at least $d$ apart, then in calculation of $K^{-1}$ infinity norm:\n",
    "\n",
    "1. Find largest value in column, scale by $k(0)$\n",
    "2. Find next largest value, scale by $k(\\frac{d}{2})$\n",
    "3. Find next largest ... scale by $k(\\frac{2d}{2})$\n",
    "4. Find next largest ... scale by $k(\\frac{3d}{2})$\n",
    "5. Find next largest ... scale by $k(\\frac{4d}{2})$\n",
    "6. ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "dp4gp.k(0,2,lengthscales,None,dp4gp.rbf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Also just remove from the test set all those columns that are causing problems!...no: the normal bound doesn't use the test locations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Other..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.array([])"
   ]
  }
 ],
 "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": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}