I switched the weight gain guess back to 1 (the corrct value - of

course the filter would find the right answer. Leaving at -1 shows
that the filter works well even when the initial estimate is incorrect.

01-g-h-filter.ipynb

@@ -377,7 +377,7 @@
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1cc09cd2400>"
+       "<matplotlib.figure.Figure at 0x15b57b83390>"
       ]
      },
      "metadata": {},
@@ -414,7 +414,7 @@
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1cc09cd2470>"
+       "<matplotlib.figure.Figure at 0x15b57b83400>"
       ]
      },
      "metadata": {},
@@ -447,7 +447,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1cc0a141b00>"
+       "<matplotlib.figure.Figure at 0x15b57f804e0>"
       ]
      },
      "metadata": {},
@@ -484,7 +484,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Average of measurements is 164.9692\n"
+      "Average of measurements is 165.0241\n"
      ]
     }
    ],
@@ -517,7 +517,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Average of measurements is 165.0343\n"
+      "Average of measurements is 164.9138\n"
      ]
     }
    ],
@@ -552,7 +552,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1cc07e9f860>"
+       "<matplotlib.figure.Figure at 0x15b55d50208>"
       ]
      },
      "metadata": {},
@@ -584,7 +584,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1cc0a6912b0>"
+       "<matplotlib.figure.Figure at 0x15b585abbe0>"
       ]
      },
      "metadata": {},
@@ -613,7 +613,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1cc0a7a0c88>"
+       "<matplotlib.figure.Figure at 0x15b585f2080>"
       ]
      },
      "metadata": {},
@@ -644,7 +644,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1cc0a80db70>"
+       "<matplotlib.figure.Figure at 0x15b586af240>"
       ]
      },
      "metadata": {},
@@ -675,7 +675,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1cc0b86bb00>"
+       "<matplotlib.figure.Figure at 0x15b5970fc18>"
       ]
      },
      "metadata": {},
@@ -710,7 +710,7 @@
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1cc0ba2b860>"
+       "<matplotlib.figure.Figure at 0x15b598ddb00>"
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      },
      "metadata": {},
@@ -739,7 +739,7 @@
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1cc0ba660f0>"
+       "<matplotlib.figure.Figure at 0x15b59918240>"
       ]
      },
      "metadata": {},
@@ -781,7 +781,7 @@
      "data": {
       "image/png": 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       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1cc0bc56908>"
+       "<matplotlib.figure.Figure at 0x15b59936dd8>"
       ]
      },
      "metadata": {},
@@ -839,7 +839,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1cc0b87b3c8>"
+       "<matplotlib.figure.Figure at 0x15b59723b00>"
       ]
      },
      "metadata": {},
@@ -1681,7 +1681,7 @@
    "source": [
     "%matplotlib notebook\n",
     "predict_using_gain_guess(weight=initial_guess, gain_rate=1, do_print=False, sim_rate=.4)\n",
-    "%matplotlib inline #reset"
+    "%matplotlib inline"
    ]
   },
   {
@@ -1702,7 +1702,7 @@
     "\n",
     "to return to the static form of plotting. You can remove this line if you want. I always do it because the plot must be in static form to be converted to PDF format, which I do for the printed version of this book.\n",
     "\n",
-    "If you are reading this in a PDF than you will see the interactive code commented out. I wrote a batch file that does this automatically. You can see that I added the comment `#reset` to the end of the `%matplotlib inline #reset`. That is used by the batch file so it knows to comment out this line; it is not a normal part of the `%matplotlib` magic.\n",
+    "If you are reading this in a PDF than you will see the interactive code commented out. I wrote a batch file that does this automatically. \n",
     "\n",
     "To get the animation to work you have to call `plt.gcf().canvas.draw()` each time you want an update, and call `time.sleep()` to slow down the animation. If you look at the code in `gh.plot_gh_results()` you'll see it using this to create the animation. For example, the following code draws a line once a second:"
    ]
@@ -2497,7 +2497,7 @@
     "    plt.gcf().canvas.draw()\n",
     "    time.sleep(1)\n",
     "\n",
-    "%matplotlib inline #reset"
+    "%matplotlib inline "
    ]
   },
   {
@@ -2518,7 +2518,7 @@
      "data": {
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-       "<matplotlib.figure.Figure at 0x1cc0bbf84e0>"
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      "metadata": {},
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+       "<img src=\"data:image/png;base64,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       ],
       "text/plain": [
        "<IPython.core.display.HTML object>"
@@ -3332,7 +3332,7 @@
    ],
    "source": [
     "weight = 160  # initial guess\n",
-    "gain_rate = 1.0 # initial guess\n",
+    "gain_rate = -1.0 # initial guess\n",
     "\n",
     "time_step = 1\n",
     "weight_scale = 4/10\n",
@@ -3356,14 +3356,14 @@
     "\n",
     "%matplotlib notebook\n",
     "gh.plot_gh_results(weights, estimates, predictions, time_step=0.1)\n",
-    "%matplotlib inline #reset"
+    "%matplotlib inline"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "I think this is starting to look really good. We used no methodology for choosing our scaling factors of $\\frac{4}{10}$ and $\\frac{1}{3}$ (actually, they are poor choices for this problem), and we 'luckily' choose 1 lb/day as our initial guess for the weight gain, but otherwise all of the reasoning followed from very reasonable assumptions. Recall that you can change the value of the parameter `time_step` to a larger value and re-run the cell if you want to see the plot drawn step-by-step.\n",
+    "I think this is starting to look really good. Because of the poor initial guess of the weight gain it takes the filter several days to accurately predict the weight, but once it does that it starts to accurately track the weight. We used no methodology for choosing our scaling factors of $\\frac{4}{10}$ and $\\frac{1}{3}$ (actually, they are poor choices for this problem), but otherwise all of the reasoning followed from very reasonable assumptions. Recall that you can change the value of the parameter `time_step` to a larger value and re-run the cell if you want to see the plot drawn step-by-step.\n",
     "\n",
     "One final point before we go on. In the prediction step I wrote the line\n",
     "```python\n",
@@ -3413,7 +3413,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1cc0bc56a58>"
+       "<matplotlib.figure.Figure at 0x15b5865fe80>"
       ]
      },
      "metadata": {},
@@ -3966,7 +3966,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1cc0a632da0>"
+       "<matplotlib.figure.Figure at 0x15b59ad0e80>"
       ]
      },
      "metadata": {},
@@ -4058,9 +4058,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAj4AAAFdCAYAAAADumfFAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1cc0bc519b0>"
+       "<matplotlib.figure.Figure at 0x15b59d055c0>"
       ]
      },
      "metadata": {},
@@ -4095,9 +4095,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAkkAAAFkCAYAAAA0Wq9BAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAkkAAAFkCAYAAAA0Wq9BAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAAPYQAAD2EBqD+naQAAIABJREFUeJzsnXec3MTZx3/a273zudu4V1zBGHO00Ak9pBAChBISINQE\nAqEFEgghwBtIgFBiaugYQm+mGlMNxmAMGJ977+dyZ/t8vWzR+8eudlVG0kgalb17vvk43KrMPBpN\nefTMM89IsiyDIAiCIAiC0BILWwCCIAiCIIgoQkoSQRAEQRAEA1KSCIIgCIIgGJCSRBAEQRAEwYCU\nJIIgCIIgCAakJBEEQRAEQTAgJYkgCIIgCIIBKUkEQRAEQRAMSEkiCIIgCIJgQEoSQRAEQRAEA1+V\nJEmSbpIkKaP7t9jPPAmCIAiCIEQQDyCPhQCOASDlfqcCyJMgCIIgCMITQShJKVmWa6wuqKurKwEw\nTnd4BwDafZcgCIIgCAlAX92xFb169Ur7mWkQStI4SZKqALQC+ArA9bIsb9BfA2BJALIQBEEQBNEx\nmABgqZ8Z+O24PRvAuQCOB3AxgFEAPpckqZvP+RIEQRAEQXjCV0uSLMvTVT8XSpI0B8A6AKcDeMrP\nvAmCIAiCILwQaAgAWZbrACwHMDbIfAmCIAiCIJwShE9SHkmSuiOrID2jO7VDf223bt0Qi1EYJ1Es\nWrQIqVQK8XgcEydODFucDgWVrX9Q2foHla1/UNmKJ5PJoKmpSX/YoDuIxlclSZKkfwN4G9kptqEA\nbgGQBPCC7lLDKrZYLEZKkkAymQzS6TSVqw9Q2foHla1/UNn6B5VtYPi+At5vS9IwAM8D2AVADYAv\nABwky/J2n/MlCIIgCILwhN+O22f6mT5BEARBEIRfkB2QIAiCIAiCASlJBEEQBEEQDEhJIgiCIAiC\nYEBKEkEQBEEQBANSkgiCIAiCIBiQkkQQBEEQBMGAlCSCIAiCIAgGpCQRBEEQBEEwICWJIAiCIAiC\nASlJBEEQBEEQDEhJIgiCIAiCYEBKEkEQBEEQBANSkgiCIAiCIBiQkkQQBEEQBMGAlCSCIAiCIAgG\npCQRBEEQBEEwICWJIAiCIAiCASlJBEEQBEEQDEhJIgiCIAiCYEBKEkEQBEEQBANSkgiCIAiCIBiQ\nkkQQBEEQBMGAlCSCIAiCIAgGgSlJkiRdJ0lSRpKke4LKkyAIgiAIwi2BKEmSJP0AwO8AVAaRH0EQ\nBEEQhFd8V5IkSeoO4H8ALgSw0+/8CIIgWMiyDFmWwxaDIIgiIghL0oMA3pZl+ZMA8iIIgmBy27OX\n4cbHzw9bDIIgioi4n4lLkvQrAHsD2N/PfAiCIOyorq0KWwSCIIoM35QkSZKGAfgPgGNlWU46vX/R\nokXIZDLiBeukJJPJ/H8rK8k1TCRUtv7hR9nSO8pC9dY/qGzFE4vFMGLEiMDz9dOStB+A/gDmSpIk\n5Y6VAPihJEmXASiTLRwEUqkU0um0j+J1XpQGTIiHytY/RJUtvSMjVCb+QWUrhpKSklDy9VNJ+gjA\nJN2xpwEsAXC7lYIEAPF4HLEYhXEShbqhJhKJECXpeFDZ+ocfZUvvKAvVW/+gshVPWPqAb0qSLMtN\nABarj0mS1ARguyzLS+zunzhxIilJAqmsrEQymUQikUBFRUXY4nQoqGz9Q2jZzsj+h95RFqq3/kFl\nK55MJoOGhobA8w1aC6H1twRBEARBFAW+rm7TI8vy0UHmRxAEQRAE4RaazyIIgiAIgmBAShJBEARB\nEAQDUpIIgiAIgiAYkJJEEARBEATBgJQkgiAIgiAIBqQkEQRBEARBMCAliSAIgiAIggEpSQRBEARB\nEAxISSIIgiAIgmBAShJBEARBEAQDUpIIgiAIgiAYkJJEEARBEATBgJQkgiAIgiAIBqQkEQRBEARB\nMCAliSAIgiAIggEpSQRBEARBEAxISSIIgiAIgmBAShJBEARBEAQDUpIIgiAIogiQZRnJVDJsMToV\npCQRBEEQRBEwY97b+NODpyGVJkUpKEhJIgiCIIgiYNHqbwAA6Uw6ZEk6D6QkEQRBEEQxIcthS9Bp\nICWJIAiCIAiCASlJBEEQBEEQDHxVkiRJuliSpEpJkupy/76UJOnHfuZJEARBEAQhAr8tSRsA/AXA\nvgD2A/AJgDclSZrgc76EimQqidb2prDFIAiCIIiiwlclSZbld2VZfl+W5VWyLK+UZflvABoBHORn\nvoSWx9/5F5778s6wxSAIgiCIoiIeVEaSJMUAnA6gK4CvgsqXAJasmxu2CARBEARRdPiuJEmStCey\nSlEXAA0ATpZleandfYsWLUImk/FbvE5HMplEZWVl2GJ0KJLJZP6/VLZi8aNs6R1loXrrH36VbWNj\n1m1iwYIFSMTLhKVbDMRiMYwYMSLwfIOwJC0FUAGgF4BTATwjSdIP7RSlVCqFdJoCZvmB0oAJ8XSW\nsm1orcWamoXYa/jhgeUpqmw7yztyApWJf4gs24ycNRwkUylA7lyL00tKSkLJ13clSZblFIDVuZ/f\nS5J0AIArAFxiKVg8jlisc1WCoEgkEmGL0KFQd4KdpWy/mP8maho2Yr/RR/uajx9l21nekR2dsd4G\nhV9lG5OyY2IiHkci3rneWVj6QGA+SSpiAGzthBMnTiQlSRQzCn8mEglUVFSEJkpHpLKyEslkslOV\n7UdLyoEG+P68Qst2RvY/neUd2dEZ621Q+FW2M1d1B3YCkyZNQllpubB0i4FMJoOGhobA8/VVSZIk\n6Z8ApgFYD6AHgN8AOALAj/zMlyAIf6FNEQiC6Az4baoZAGAKsn5JHyEbK+lHsix/4nO+hA/c9+oN\nmL9qdthiEARBdGroIyU4fLUkybJ8oZ/pE8GysmoRqms3Ya8xFOaKIAiC6PiQ008Ho7W9BW3J1rDF\nIDoJMu1GThCBQ+0uOEhJ6mD8+eEzcdMTZMAjCILoaEiQwhah00FKUgekua1R85saFkEQREeCLElB\nQUpSZ0AiJYkQTM7cL1NnTRBEByaySlJre0vYIhARYUP1aqzZvCxsMQiCICIBfZwER2SVpCnT7gpb\nBCIi/PuFq3Hvy38JWwyCIAiikxFZJWlDzRqh6VXXVuG7ZTOFplks0GQb4Ru0yoYgAADb67bi1mcu\nRUtbk/+ZUbMLjMgqSaI733+/eA2mvH+30DRF09TagMsnn4RFa74Vm7BInyTSuAiCIAzMXvwxqmur\nsHbL8rBFsSSVTqKppT7wfGsbavDJ3KmB5+uVyCpJohXltiLwcdrZsB0AMH/V147vrW+qxZJ133vK\nP51J44l3bkfNzs2e0iEIguh8BGfe8eKT9PS0u3H9o+cIlIaPZ96/F1NnPo2MnAk8by+EscEtH53Y\njO/G8PPgGzdh8/b17PQ4zT/b67agctVsJBJlOOf4q5wLQXQalE6687ZSb8iyDIlWnXZIoh5yZeGa\nb0LJN51Jh5KvVyJsSaLu1wk7G7ebn3TYZqPeyAmimFmzeSmuuO9kbNmxIWxRCIEE8l2vdM3FaEQo\n0mElskpS58S84q/bsgLXPHiG6bShlWLDq/QUYbMjfKa1vQV3Pn81ttdv1RwnRdo9azYvBQBs2rYu\nZEkIPyALoQ1FpuB1eiXp2od+hc8r3wtbDB3GRvblwg/QnmozDFb5OwQ2TNGNfPWmJbj6gdPQnmoT\nmi7hP2s2L8XGmtWYvegjzfG8pbfIOrxoQIOoHU2tDZg+55Ui26MsSJ+k4qXYZO/0SlJbshWvzngU\n7cniHsAlScCr9KFDysgZTJ/zClLpJOoadwhPvzMhwjmfIIqBN2c+jXe/eq6oFpEUjUIXkpzFan3u\n9EqSwn/f+kfYIuT5cuEHaGlrdnSPlfUnzMr50bevY8m6uaHl35F4etpdeHjqLUinU2GLQnRCXvr4\nYTzw+t8DyUtx8i1G39QgptuKRiFjUWSyk5KUY+XGhZrfdU07sGLjgkBlUHcIi9c6i5UkQhFSvtpE\nKlUrNhTKsKgbdgTYnHP0DWfgYNeJYhzEwqZYv6hnLZyO5Rvm44HX/47H37nd17yK0a8nzJbQ0taM\naV+/VHTL64sBUpJM+M8r1+P+124MNE+tDuGsk7DsVDiTevTt2+zzKdIOPkyaWxuxbssKz+nIGeoA\nix1ZlvH+nJfyf/tJY0s96prET3Ev3zAf81fNFp4uk2L6sMrJGoyCpy2XD755GdNmvyCkn/GbYvuw\nIiXJhB31NaHm77ihiZxu862RF1fjEMWjb92Gu1+61nM6cu4rMYxxg5RjMWzatk61bYW/L/Kvj56D\nGx8/39c8/EKpb5liUpLyBN9W0mklBlF0y0t5pzvqa1C58quQpeGHlKQOgmWzLELTdUdCVDycTAgd\noJm1Ix9MkkOkhau/QUPzTpFiFTHRHcQiRRH2WUFaSPTtriisM7lXet+rN+CJd+8IVxYHkJIUUZxa\nkoSsblPSEpYSoae+aSfe/eo5V1MthXtCMSW55tG3b8Ojb/9TnCwRoL6p1tV9ZoNZRs6Ebr12ysz5\n0/DuV8/5knahuomr62/NehZVgjdOZxGuP1X0e+/G1uD3jfNC0SlJre0tmDrzaSErfKLnSKyWR9Kd\nsZbVenUbERXe+PwJTJ/zCmobtjm+NxyfpJyfhcdaFKYlaUd9jdC2vmjNt/jb4+dhQ/VqT+moZfpg\nziu4+amLimKPSYVXPn0E0+e84k/iuf5MFuiI/NG3r+Hxd/10OPd/PCm0w6iNXQ6I3LhrTeSVpDWb\nl2LKtLvzvz+b9w4+mTsVS9fP85y2yAYoAi8dubXjtnifpO+WfY5P577lKNkPvnk1H9ogI2cMKzEu\nn3wSPv7uDUdpFhsy4y9elPLasmOjp53Gv1r0EZatr3R9vxbjc8xf9TXXPk1NLfXYtLine truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1cc0b868c88>"
+       "<matplotlib.figure.Figure at 0x15b59abf400>"
       ]
      },
      "metadata": {},
@@ -4149,9 +4149,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAksAAAFdCAYAAAAT2ikZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAAPYQAAD2EBqD+naQAAIABJREFUeJzs3Xd8T9cfx/HXzZaIhCDE3nvGaH9FkKhRW+3WaKyqXVqr\ntEaV1qZqxahRLdIaFbVHUXtTeyVWIiIk4pt8z++Pr1z5SqjIV/LF5/l45NGbc8+993xzS97OOfdc\nTSmFEEIIIYRImk1aN0AIIYQQwppJWBJCCCGEeA4JS0IIIYQQzyFhSQghhBDiOSQsCSGEEEI8h11a\nN+B5IiIibIFCTxXfAeQRPiGEEEJoQKanys66ubnFWfIiVh2WMAWlU2ndCCGEEEK8NooBpy15QhmG\nE0IIIYR4DglLQgghhBDPIWFJCCGEEOI5rH3O0p2nC1xcXLCxkYxnbU6cOEFsbCx2dnaUKFEirZsj\nniL3x7rJ/bF+co+sk9Fo5MGDB08XJ8oOKWXtYSnRU282NjYSlqyQ0WgkLi5O7o+Vkvtj3eT+WD+5\nR68Viz8xL3dcCCGEEOI5JCwJIYQQQjyHhCUhhBBCiOeQsCSEEEII8RwSloQQQgghnkPCkhBCCCHE\nc0hYEkIIIYR4DglLQgghhBDPYe2LUgohhBBCAHDo0CG2bduGjY0Nfn5+FC1aNFWuK2FJCCGEEFYt\nPDyc1q1bs379erPyDh06MGnSpFd+fRmGE0IIIYTVUkrRrFmzREEJYPXq1anSBglLQgghhLBau3bt\nYsuWLQB4eHgwefJkxo0bh6ura6q1QYbhhBBCCGG1Nm7cqG+PHTsWf39/AOLi4vjhhx9SpQ0SloQQ\nQghhVR49esSqVas4evQoe/bs0cvt7OyS3H7VJCwJIYQQwmocOHCApk2bcuXKlUT7Bg4cSGxsLDEx\nMYwePRpbW9tUaZOEJSGEEEJYhdu3b1OnTh1CQ0OT3H/jxg06deqkf+/h4ZEq7ZIJ3kIIIYR4IWfO\nnOGLL76gUaNG+Pv7s3HjRpRSFjv/nDlz9KBUoUIFli9fzvDhw59Zv2bNmha79vNIz5IQQggh/tNP\nP/3EZ599htFo1MsCAgJo2bIlixYtssgcoq1bt+rbixcvpnDhwjRr1ozjx4+zYsUKALp160auXLmo\nVasW3t7eREZGpvi6/0XCkhBCCPGGCg0N5eTJk2TIkIHSpUtjY/NyA0p79+6le/fuSfYiLVu2jFKl\nSjFkyJCUNtesfQaDIcntzp07U758eQCz4PYqyTCcEEII8YaJiIigQ4cOeHl54ePjQ7ly5ShcuDCB\ngYEvdb6pU6fqQalr166cP3+egIAANE3T98fFxaW43X5+fvp2ixYtmDt3Ln369GHVqlUAeHp6UrJk\nyRRfJ7mSFZY0TRukadpeTdPuaZp2U9O0QE3TCidRb4SmaSGapkVpmrZB07SCT+131DRtuqZpoZqm\nRWqatlzTtKwp/TBCCCHE285gMFC3bl0WLFhg1iNz/vx5mjVr9lKB6cCBAwDY29szadIk8ufPT8eO\nHalVqxYAN2/eJDg4OMVt9/f3x8vLC4CTJ0/SqVMnJk+erO/v2H0sDg4OKb5OciW3Z6kqMBWoDPgB\n9sBfmqali6+gadqXQA+gC1AJeACs1zQt4aebBHwANAOqAV7Aipf8DEIIIYR4bMWKFezevRsAV1dX\nunbtStWqVQHTq0MGDBiQ7OGr9OnTA6YgFv9If2xsLBcuXEhUJzmio6P57rvvKFy4ME5OTnh7e9Os\nWTOKFCliVs/e3p66Hdcy7q92zFtruQnlLypZc5aUUvUSfq9pWgfgFuAN7Hxc3BsYqZRa87hOO+Am\n0Bj4VdO0DMAnQCul1LbHdToCpzRNq6SU2vvyH0cIIYR4u8VPhAb49ddfqVOnDkopfHx82LFjB+fP\nn+fo0aOULVv2hc/ZuHFj9u3bB0CNGjVo1aoVO3fu5Ny5cwBUq1aNTJkyJaud0dHR1K5dmx07duhl\nFy5cYOrUqVSoUIHVq1fz77//kiGDG+cetuL7X1wA6PwduLkomlbXknW9lEjpnCV3QAF3ADRNywdk\nAzbFV1BK3QP+Ad59XFQBU0hLWOdf4EqCOkIIIYR4CQmfDitevDgAmqZRrFixJOu8iO7du5MvXz4A\nQkJCmDBhAnv3mvo27O3tGT16dLLbOWXKFD0oaZpGoUKF9Ane+/fvZ9++ffTt24+TUf56UAIwGqHN\n13DmSur1ML10WNJMs7omATuVUicfF2fDFJ5uPlX95uN9AJ7Ao8ch6ll1hBBCCPESypUrp28PGDCA\ny5cvs27dOpYuXQqYwk18iHpR7u7ubNu2jTp16piVFy1alHXr1lGlSpVkt3PevHmAKSht376dM2fO\n8M8//+ircs8NWECnMTD518THDusIhXIl+5IvTXvZxaQ0TZsB1AbeU0pdf1z2LqbhOC+l1M0EdZcB\nRqVUa03TWgMBSql0T53vH2CzUmpQfFlEREQWTMN8uitXrqTao4LixSWcRGhvb5+GLRFJkftj3eT+\nWL/X6R4FBwfTuHFjszYn1LBhQ0aMGJGi81+5cgV3d3eKFi2qPxGXXJUrVyYmJoZcuXKxevVqvbxF\nixacOXsZCi9G82hqdoymKQa2CKGFTxhgWmogd+7cT586q5ub2+2XatQzvNQ6S5qmTQPqAVXjg9Jj\nNwANU+9Rwt4lT+BQgjoOmqZleKp3yfPxvueKjY21yOOJ4tV51h9QYR3k/lg3uT/Wz9rvUdasWRk5\nciRfffVVoraWKVOGvn37pugzZM2alaxZTQ+wx8bGvvR5PD09uXLlCteuXePw4cOUKFGCM2fOcO5S\nKBQPQnPzMatva6MY3vYidSqEE998q3033OOg1AjwUUqZveVOKXVR07QbgC9w9HH9DJienpv+uNoB\nIPZxncDHdYoAuYHd/9lgO7uXXlRLvDqv07+63kZyf6yb3B/rZ8l7FBoayurVq7l06RJubm7Url2b\nEiVKpLSJZurUqUOpUqVYsWIF//77L87Ozvj5+eHr62uRlbYtoWHDhkybNg2lFJ988gn58+fnwrVo\njMU2obmUMavraG9kXKfLVCt1H9OD+CaplQeSNQynadqPQGugIXAmwa4IpdTDx3W+AL4EOgCXgJFA\nCaCEUupRgvPUBToCkcAUTMN0VRNeL6lhOFdXVwlLVujIkSMYDAbs7e0pU6bMfx8gUpXcH+sm98f6\nWeoe/fbbb7Rv357o6Giz8s6dOzNjxoxU6ymxBlFRUfj6+rJnzx5TgVMhU4+SUz6zehlc4I+x4FMu\n8XCf0WhMarK6xYfhkps6ugEZgK1ASIKvFvEVlFLjMK3FNBPTU3DpgLrxQemxvsAaYHmCczV7mQ8g\nhBBCvA5OnjxJmzZtEgUlgNmzZzN+/Pg0aFXacXZ2ZuPGjXz99dd4FqiPVmpnoqCUzQO2TU86KKWm\nZIUlpZSNUso2ia+FT9X7WinlpZRyVkrVVkqde2p/jFKqp1Iqs1LKVSnVXCl1CyGEEOINNWXKFH2O\nz4cffsi+ffuYOHGivn/SpElv3ZxcFxcXCr07jAd5V4F9FrN9BXPC3z9BmUJpG5RAXqQrhBBCpIr4\n4SYbGxsCAgJwdXWlQoUKBAUFsX79eq5fv87ly5fJnz9/Grc0dTyMUfSZDLP+SLzPuwisHQ9ZM6Z9\nUAJ5ka4QQgiRKpycnADTPJtbt0yDKUoprl+/nqjOm+78NcV73ZIOSrUqwuap1hOUQHqWhBBCiFRR\nv359/vnnHwBq165Nhw4d2LVrF0ePHgVMi0lmz549LZuYLEaj4vINOHYejl+AM1fAOZ2pV6hiMSie\nF+zsngSe2FjFxeuw4wj0mwL3HiQ+p38DmP45ONhbT1ACCUtCCCFEqvj000/56aefCA4O5vz583z1\n1Vf6Pk3TGDVq1Esv8Jia5q9VzF5lCkn3E89V1zk7QbnCCo8McOYqnA8GwzOWZXJ2gh/7Q7u61vn5\nJSwJIYQQqcDDw4OtW7fSrl07du9+sqxgtmzZmDJlCvXq1XvO0dZhzipFl7EvVjfqIfx99L/rFcsL\nv46EEvmtMyiBhCUhhBAi1RQsWJBdu3Zx5MgRTp8+TaZMmfDx8cHBwSGtm/afdh1TfGbh1Q0+qm3q\nUUrvbL1BCSQsCSGEEKmuTJkyr9UCpMG3FR8OSXoYLVMGKFXA1EMUFgH7TsGl64nrxcvspiie10jX\nJra08uO1GHqUsCSEEEKIZ3oYo2g6CG6EmZd/1gwGt4N0dvdYtOhn9uzZQ3pHR8a3rc87VRtw+Kwt\nB/6F6BjTmkmutiH8unAUa35fwLboaK6uz09I9+707t3bal7B8izW3TohhBBCpBmlFJ9+b+otSqhW\nRZjYCw4e3McHH3xAaGiovi8gIIB33nmHtWvXUvfdTAD8+++/vPfee4SFPUlcFy5coH///uzevZtf\nf/3Vql9lZr0tE0IIIUSaCA8P58svv8S92DAWrDPfl98Llo6A6Oj7NGjQwCwoxduzZw/+/v769336\n9NGDkru7OxUqVND3rVixgj/+SGLBJSsiPUtCCCHEG+p2uOKPHRAaAXFGiIsz/Tc2DrK4Q7WyUKYg\n2No+mTd061YY3n6DuWaoD5nqkXBGkS3R/DbKjkwZHPjpp8X64prvvPMOkydP5saNG3zyySeEhYXx\n+++/c/HiRZydnQkKCgIgZ86cHD16lIwZM7J06VLatGkDwMKFC2nSpEmq/VySS8KSEEII8Qa6Ha54\npwtcDHl+vYyuUKO8ooa3ad2kMXON3HP9iaSmXceebsvuTbUoV6Q7+/bt08t/+OEHKlWqBJjWkxo1\nahQA+/bto0iRInq96tWrkzFjRgCaNm2qlydcxdwayTCcEEII8QbqMeG/gxJAeCSs3Line truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAksAAAFdCAYAAAAT2ikZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1cc0bbdf0f0>"
+       "<matplotlib.figure.Figure at 0x15b59d05b38>"
       ]
      },
      "metadata": {},
@@ -4212,9 +4212,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlcAAAFdCAYAAAAuSEh/AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1cc0a1202b0>"
+       "<matplotlib.figure.Figure at 0x15b59d60c50>"
       ]
      },
      "metadata": {},
@@ -4279,7 +4279,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1cc0bbeb5f8>"
+       "<matplotlib.figure.Figure at 0x15b598defd0>"
       ]
      },
      "metadata": {},
@@ -4357,7 +4357,7 @@
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1cc0bc4b710>"
+       "<matplotlib.figure.Figure at 0x15b59d2d710>"
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1cc0b9dbd68>"
+       "<matplotlib.figure.Figure at 0x15b597501d0>"
       ]
      },
      "metadata": {},
@@ -4453,7 +4453,7 @@
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1cc0a833e10>"
+       "<matplotlib.figure.Figure at 0x15b59d031d0>"
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      "metadata": {},
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1cc0a754668>"
+       "<matplotlib.figure.Figure at 0x15b585195c0>"
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      },
      "metadata": {},
@@ -4546,7 +4546,7 @@
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1cc0a6f7390>"
+       "<matplotlib.figure.Figure at 0x15b59da65f8>"
       ]
      },
      "metadata": {},
@@ -4595,7 +4595,7 @@
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1cc0a6ec5f8>"
+       "<matplotlib.figure.Figure at 0x15b59d82ef0>"
       ]
      },
      "metadata": {},
@@ -4631,7 +4631,7 @@
      "data": {
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       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1cc0a6ba9e8>"
+       "<matplotlib.figure.Figure at 0x15b59d03dd8>"
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      "metadata": {},
@@ -4696,7 +4696,7 @@
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1cc09ebf3c8>"
+       "<matplotlib.figure.Figure at 0x15b5992e6d8>"
       ]
      },
      "metadata": {},
@@ -4748,7 +4748,7 @@
      "data": {
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       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1cc0bbebe10>"
+       "<matplotlib.figure.Figure at 0x15b59905470>"
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      "metadata": {},
@@ -4780,7 +4780,7 @@
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       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1cc0b876780>"
+       "<matplotlib.figure.Figure at 0x15b584a6b38>"
       ]
      },
      "metadata": {},
@@ -4813,7 +4813,7 @@
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1cc0bedf8d0>"
+       "<matplotlib.figure.Figure at 0x15b59da0eb8>"
       ]
      },
      "metadata": {},
@@ -4863,7 +4863,7 @@
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1cc0a7c6f60>"
+       "<matplotlib.figure.Figure at 0x15b59b296a0>"
       ]
      },
      "metadata": {},
@@ -4894,7 +4894,7 @@
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1cc0a60c668>"
+       "<matplotlib.figure.Figure at 0x15b586daa20>"
       ]
      },
      "metadata": {},
@@ -5141,6 +5141,18 @@
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
    "version": "3.5.2"
+  },
+  "widgets": {
+   "state": {
+    "93f4411da7ea42738e12c0ac83448a20": {
+     "views": [
+      {
+       "cell_index": 121
+      }
+     ]
+    }
+   },
+   "version": "1.2.0"
   }
  },
  "nbformat": 4,