Making book work in Python 2.7

2016-03-06 08:18:27 -08:00
1 parent f62fb8bbe8
commit fb21cf6313
@@ -1107,7 +1107,7 @@
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      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
@@ -1120,6 +1120,7 @@
   "source": [
    "from book_format import set_figsize, figsize\n",
    "from book_plots import interactive_plot\n",
+    "import matplotlib.pyplot as plt\n",
    "\n",
    "import filterpy.stats as stats\n",
    "with interactive_plot():\n",
@@ -1910,7 +1911,7 @@
    {
     "data": {
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      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
@@ -1923,7 +1924,7 @@
     "name": "stdout",
     "output_type": "stream",
     "text": [
-      "Mean of readings is 10.003\n"
+      "Mean of readings is 9.957\n"
     ]
    }
   ],
@@ -1935,7 +1936,8 @@
    "xs = range(500)\n",
    "ys = randn(500)*1 + 10.\n",
    "with interactive_plot():\n",
-    "    bp.plot_track(xs, ys)\n",
+    "    #_ = bp.plot_track(xs, ys)\n",
+    "    plt.plot(xs, ys)\n",
    "print('Mean of readings is {:.3f}'.format(np.mean(ys)))"
   ]
  },
@@ -2742,7 +2744,7 @@
    {
     "data": {
      "text/html": [
-       "<img 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      "text/plain": [
       "<IPython.core.display.HTML object>"
@@ -2762,9 +2764,9 @@
   "cell_type": "markdown",
   "metadata": {},
   "source": [
-    "I hope you see the power of this. We can replace hundreds to thousands of numbers with a single pair of numbers $x = \\mathcal N(\\mu, \\sigma^2)$. \n",
+    "I hope you see the power of this. We can replace hundreds to thousands of numbers with a single pair of numbers: $x = \\mathcal N(\\mu, \\sigma^2)$. \n",
    "\n",
-    "The tails of the Gaussian extend to infinity on both sides, so it incorporates arbitrarily many bars in the histogram. If this represents our belief in the position of the dog in the hallway, this one Gaussian covers the entire hallway. We think that it is likely the dog is at 10, but he could be at 8, 14, or, with infinitesimally small probability, at 10$^{80}$. \n",
+    "The tails of the Gaussian extend to infinity on both sides, so it incorporates arbitrarily many bars in the histogram. If this represents our belief in the position of the dog in the hallway, this one Gaussian covers the entire hallway (and the entire universe in one direction). We think that it is likely the dog is at 10, but he could be at 8, 14, or, with infinitesimally small probability, at 10$^{80}$. \n",
    "\n",
    "In this chapter we replace histograms with Gaussians:\n",
    "\n",
@@ -2772,14 +2774,14 @@
    "\\text{discrete Bayes} & \\text{Gaussian} & \\text{Step}\\\\\n",
    "\\hline\n",
    "\\bar {\\mathbf x} = \\mathbf x \\ast f(\\mathbf x) & \n",
-    "\\bar {x_\\mathcal{N}} =  x_\\mathcal{N} \\, \\oplus \\, f_{x_\\mathcal{N}}(\\bullet) &\n",
+    "\\bar {x}_\\mathcal{N} =  x_\\mathcal{N} \\, \\oplus \\, f_{x_\\mathcal{N}}(\\bullet) &\n",
    "\\text{Predict} \\\\\n",
    "\\mathbf x = \\|\\mathcal L \\bar{\\mathbf x}\\| & x_\\mathcal{N} = L \\, \\otimes \\, \\bar{x}_\\mathcal{N} & \\text{Update} \n",
    "\\end{array}$$\n",
    "\n",
    "where $\\oplus$ and $\\otimes$ is meant to express some unknown operator on Gaussians. I won't do it in the rest of the book, but the subscript indicates that $x_\\mathcal{N}$ is a Gaussian. \n",
    "\n",
-    "The discrete Bayes filter used convolution for the prediction. We showed that it used the *total probabability theorem*, computed as a sum, so maybe we can add the Gaussians. It uses multiplications to incorporate the measurement into the prior, so maybe we can multiply the Gaussians. Could it be this easy:\n",
+    "The discrete Bayes filter used convolution for the prediction. We showed that it used the *total probabability theorem*, computed as a sum, so maybe we can add the Gaussians. It used multiplications to incorporate the measurement into the prior, so maybe we can multiply the Gaussians. Could it be this easy:\n",
    "\n",
    "$$\\begin{aligned} \n",
    "\\bar x &\\stackrel{?}{=} x + f_x(\\bullet) \\\\\n",
@@ -2801,6 +2803,7 @@
    " &= x_{k-1} + f_x\\end{aligned}$$\n",
    "\n",
    "I've dropped the notation $f_x(\\bullet)$ in favor of $f_x$ to keep the equations uncluttered. \n",
+    "\n",
    "If the dog is at 10 m, his velocity is 15 m/s, and the epoch is 2 seconds long, we have\n",
    "\n",
    "$$ \\begin{aligned} f_x &= v\\Delta t = 15\\cdot 2\\\\\n",
@@ -2871,7 +2874,7 @@
    {
     "data": {
      "text/plain": [
-       "(25, 49.040)"
+       "(25, 0.530)"
      ]
     },
     "execution_count": 6,
@@ -2881,7 +2884,7 @@
   ],
   "source": [
    "%precision 3\n",
-    "predict((10, .2**2), (15, 7**2))"
+    "predict((10, .2**2), (15, .7**2))"
   ]
  },
  {
@@ -2982,7 +2985,7 @@
   "source": [
    "### Understanding Gaussian Multiplication\n",
    "\n",
-    "Let's plot the pdf of $\\mathcal{N}(10,\\, 1) \\cdot \\mathcal{N}(10,\\, 1)$. Can you determine its shape without looking at the result? What should the new mean be? Will the curve be wider, narrower, or the same as $\\mathcal{N}(10,\\, 1)$?"
+    "Let's plot the pdf of $\\mathcal{N}(10,\\, 1) \\times \\mathcal{N}(10,\\, 1)$. Can you determine its shape without looking at the result? What should the new mean be? Will the curve be wider, narrower, or the same as $\\mathcal{N}(10,\\, 1)$?"
   ]
  },
  {
@@ -3760,7 +3763,7 @@
    {
     "data": {
      "text/html": [
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truncated
+       "<img src=\"data:image/png;base64,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 truncated
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
@@ -3792,8 +3795,8 @@
    "    plt.plot(xs, ys, label='$\\mathcal{N}(10,1)$')\n",
    "\n",
    "    ys = [stats.gaussian(x, product[0], product[1]) for x in xs]\n",
-    "    plt.plot(xs, ys, label='$\\mathcal{N}(10,1) \\cdot \\mathcal{N}(10,1)$', ls='--')\n",
-    "    bp.show_legend()\n",
+    "    plt.plot(xs, ys, label='$\\mathcal{N}(10,1) \\\\times \\mathcal{N}(10,1)$', ls='--')\n",
+    "    plt.legend()\n",
    "print(product)"
   ]
  },
@@ -3807,7 +3810,7 @@
    "\n",
    "\"Measure twice, cut once\" is a well known saying. Gaussian multiplication is a mathematical model of this physical fact. \n",
    "\n",
-    "I'm unlikely to get the same measurement twice in a row. Now let's plot the pdf of $\\mathcal{N}(10.2,\\, 1) \\cdot \\mathcal{N}(9.7,\\, 1)$. What do you think the result will be? Think about it, and then look at the graph."
+    "I'm unlikely to get the same measurement twice in a row. Now let's plot the pdf of $\\mathcal{N}(10.2,\\, 1) \\times \\mathcal{N}(9.7,\\, 1)$. What do you think the result will be? Think about it, and then look at the graph."
   ]
  },
  {
@@ -4584,7 +4587,7 @@
    {
     "data": {
      "text/html": [
-       "<img 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      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
@@ -4614,7 +4617,7 @@
    "z1 = (10.2, 1)\n",
    "z2 = (9.7, 1)\n",
    " \n",
-    "plot_products(*z1, *z2)"
+    "plot_products(z1[0], z1[1], z2[0], z2[1])"
   ]
  },
  {
@@ -4629,7 +4632,7 @@
    "\n",
    "In the update step we are combining two measurements, but one measurement and the prior, our estimate before incorporating the measurement. We went through this logic for the g-h filter. It doesn't matter if we are incorporating information from two measurements, or a measurement and a prediction, the math is the same. \n",
    "\n",
-    "Let's look at that. I'll create a fairly inaccurate prior of $\\mathcal N(8.5, 1.5)$ and a more accurate measurement of $\\mathcal N(10.2, 0.5)$. By \"accurate\" I mean the sensor variance is smaller than the prior's variance, not that I somehow know that the dog is closer to 10.2 than 8.5. Beside that I'll plot the reverse relationship: an accurate prior of $\\mathcal N(8.5, 0.5)$ and a inaccurate measurement of $\\mathcal N(10.2, 1.5)$."
+    "Let's look at that. I'll create a fairly inaccurate prior of $\\mathcal N(8.5, 1.5)$ and a more accurate measurement of $\\mathcal N(10.2, 0.5).$ By \"accurate\" I mean the sensor variance is smaller than the prior's variance, not that I somehow know that the dog is closer to 10.2 than 8.5. Next I'll plot the reverse relationship: an accurate prior of $\\mathcal N(8.5, 0.5)$ and a inaccurate measurement of $\\mathcal N(10.2, 1.5)$."
   ]
  },
  {
@@ -5406,7 +5409,7 @@
    {
     "data": {
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+       "<img 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      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
@@ -6194,9 +6197,9 @@
   ],
   "source": [
    "prior, z = (8.5, 1.5), (10.2, 0.5)\n",
-    "plot_products(*prior, *z, False)\n",
+    "plot_products(prior[0], prior[1], z[0], z[1], True)\n",
    "prior, z = (8.5, 0.5), (10.2, 1.5)\n",
-    "plot_products(*prior, *z, False)"
+    "plot_products(prior[0], prior[1], z[0], z[1], True)"
   ]
  },
  {
@@ -6205,7 +6208,7 @@
   "source": [
    "The result is a Gaussian that is taller than either input. This makes sense - we have incorporated information, so our variance should have been reduced. And notice how the result is far closer to the the input with the smaller variance. We have more confidence in that value, so it makes sense to weight it more heavily.\n",
    "\n",
-    "It *seems* to work, but it is really correct? There is more to say about this, but I want to get a working filter going so you can it in concrete terms. After that we will revisit Gaussian multiplication and determine why it is correct."
+    "It *seems* to work, but it is really correct? There is more to say about this, but I want to get a working filter going so you can it experience it in concrete terms. After that we will revisit Gaussian multiplication and determine why it is correct."
   ]
  },
  {
@@ -6992,7 +6995,7 @@
    {
     "data": {
      "text/html": [
-       "<img 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truncated
+       "<img src=\"data:image/png;base64,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 truncated
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
@@ -7088,6 +7091,13 @@
    "print('actual final position: {:10.3f}'.format(dog.x))"
   ]
  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Here is an animation of the filter. Predictions are plotted with a red triangle. After the prediction, the filter receives the next measurement, plotted as a black circle. The filter then forms an estimate part way between the two. "
+   ]
+  },
  {
   "cell_type": "code",
   "execution_count": 13,
@@ -7862,7 +7872,7 @@
    {
     "data": {
      "text/html": [
-       "<img 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      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
@@ -7873,12 +7883,32 @@
    }
   ],
   "source": [
-    "# plot the results\n",
-    "with interactive_plot():\n",
-    "    bp.plot_filter(xs)\n",
-    "    bp.plot_measurements(zs)\n",
-    "    bp.plot_predictions(predictions)\n",
-    "    bp.show_legend()"
+    "import time\n",
+    "fig = plt.figure()\n",
+    "canvas = fig.canvas\n",
+    "time_step = .25\n",
+    "for i in range(2, len(xs)+1):\n",
+    "\n",
+    "    bp.plot_predictions(predictions[:i])  \n",
+    "    plt.xlim(-1, 10)\n",
+    "    plt.ylim(0,20)\n",
+    "    fig.canvas.draw()\n",
+    "    time.sleep(time_step)\n",
+    "\n",
+    "    bp.plot_measurements(zs[:i])\n",
+    "    plt.xlim(-1, 10)\n",
+    "    plt.ylim(0,20)\n",
+    "    fig.canvas.draw()\n",
+    "    time.sleep(time_step)\n",
+    "\n",
+    "    bp.plot_filter(xs[:i])\n",
+    "    plt.xlim(-1, 10)\n",
+    "    plt.ylim(0,20)\n",
+    "    fig.canvas.draw()\n",
+    "    time.sleep(time_step)\n",
+    "    \n",
+    "    if i == 2:\n",
+    "        plt.legend(loc=4);"
   ]
  },
  {
@@ -8860,7 +8890,7 @@
    {
     "data": {
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@@ -19073,21 +19103,21 @@
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  "kernelspec": {
-   "display_name": "Python 3",
+   "display_name": "Python 2",
   "language": "python",
-   "name": "python3"
+   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
-    "version": 3
+    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.5.1"
+   "pygments_lexer": "ipython2",
+   "version": "2.7.11"
  }
 },
 "nbformat": 4,
@@ -1136,7 +1136,7 @@
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     "data": {
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     "name": "stdout",
     "output_type": "stream",
     "text": [
-      "[[ 10.4337   2.8677]\n",
-      " [  2.8677   2.3027]]\n"
+      "[[ 11.1303   3.0208]\n",
+      " [  3.0208   2.2891]]\n"
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     "name": "stdout",
     "output_type": "stream",
     "text": [
-      "[[ 0.9956 -0.0028]\n",
-      " [-0.0028  0.9964]]\n"
+      "[[ 0.9972  0.0024]\n",
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truncated
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
@@ -26599,21 +26599,21 @@
 ],
 "metadata": {
  "kernelspec": {
-   "display_name": "Python 3",
+   "display_name": "Python 2",
   "language": "python",
-   "name": "python3"
+   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
-    "version": 3
+    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.5.1"
+   "pygments_lexer": "ipython2",
+   "version": "2.7.11"
  }
 },
 "nbformat": 4,
@@ -1302,9 +1302,9 @@
   "outputs": [
    {
     "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
      "text/plain": [
-       "<matplotlib.figure.Figure at 0x1b5cdedb550>"
+       "<matplotlib.figure.Figure at 0x6eebf60>"
      ]
     },
     "metadata": {},
@@ -1336,9 +1336,9 @@
   "outputs": [
    {
     "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
      "text/plain": [
-       "<matplotlib.figure.Figure at 0x1b5cdedb470>"
+       "<matplotlib.figure.Figure at 0x6bf4320>"
      ]
     },
     "metadata": {},
@@ -1417,9 +1417,9 @@
   "outputs": [
    {
     "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
      "text/plain": [
-       "<matplotlib.figure.Figure at 0x1b5d09777b8>"
+       "<matplotlib.figure.Figure at 0x6f25128>"
      ]
     },
     "metadata": {},
@@ -1449,7 +1449,7 @@
     "output_type": "stream",
     "text": [
      "exact answer= 54.5981500331\n",
-      "euler answer= 54.59705808834125\n",
+      "euler answer= 54.5970580883\n",
      "difference = 0.00109194480299\n",
      "iterations = 400000\n"
     ]
@@ -1569,14 +1569,14 @@
     "name": "stdout",
     "output_type": "stream",
     "text": [
-      "max error 5.206970035942504e-05\n"
+      "max error 5.20697002457e-05\n"
     ]
    },
    {
     "data": {
-      "image/png": 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-       "<matplotlib.figure.Figure at 0x1b5d1359198>"
+       "<matplotlib.figure.Figure at 0x93f1588>"
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     "metadata": {},
@@ -1754,21 +1754,21 @@
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 "metadata": {
  "kernelspec": {
-   "display_name": "Python 3",
+   "display_name": "Python 2",
   "language": "python",
-   "name": "python3"
+   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
-    "version": 3
+    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.5.1"
+   "pygments_lexer": "ipython2",
+   "version": "2.7.11"
  }
 },
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       "<IPython.core.display.HTML object>"
@@ -39075,21 +39075,21 @@
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 "metadata": {
  "kernelspec": {
-   "display_name": "Python 3",
+   "display_name": "Python 2",
   "language": "python",
-   "name": "python3"
+   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
-    "version": 3
+    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.5.1"
+   "pygments_lexer": "ipython2",
+   "version": "2.7.11"
  }
 },
 "nbformat": 4,
@@ -1112,7 +1112,7 @@
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     "data": {
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      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
@@ -6937,7 +6937,7 @@
     "name": "stdout",
     "output_type": "stream",
     "text": [
-      "Final P: [ 0.0249  0.0397  0.00219]\n"
+      "Final P: [ 0.0237  0.0429  0.00223]\n"
     ]
    }
   ],
@@ -7737,7 +7737,7 @@
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@@ -7750,7 +7750,7 @@
     "name": "stdout",
     "output_type": "stream",
     "text": [
-      "Final P: [ 0.0199  0.0207  0.00154]\n"
+      "Final P: [ 0.0207  0.02  0.00153]\n"
     ]
    }
   ],
@@ -8546,7 +8546,7 @@
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      "text/plain": [
       "<IPython.core.display.HTML object>"
@@ -8559,7 +8559,7 @@
     "name": "stdout",
     "output_type": "stream",
     "text": [
-      "Final P: [ 0.0195  0.0453  0.000224]\n"
+      "Final P: [ 0.0209  0.0449  0.000225]\n"
     ]
    }
   ],
@@ -9352,7 +9352,7 @@
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      "text/plain": [
       "<IPython.core.display.HTML object>"
@@ -9365,7 +9365,7 @@
     "name": "stdout",
     "output_type": "stream",
     "text": [
-      "Final P: [ 0.263  0.795  0.00351]\n"
+      "Final P: [ 0.294  0.814  0.00366]\n"
     ]
    }
   ],
@@ -10158,7 +10158,7 @@
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@@ -10171,7 +10171,7 @@
     "name": "stdout",
     "output_type": "stream",
     "text": [
-      "Final P: [ 0.0087  0.00855  0.000765]\n"
+      "Final P: [ 0.00852  0.00868  0.000762]\n"
     ]
    }
   ],
@@ -10988,7 +10988,7 @@
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      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
@@ -11001,7 +11001,7 @@
     "name": "stdout",
     "output_type": "stream",
     "text": [
-      "actual mean=1.30, std=1.13\n",
+      "actual mean=1.30, std=1.12\n",
      "EKF    mean=1.00, std=0.95\n"
     ]
    }
@@ -11793,7 +11793,7 @@
    {
     "data": {
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      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
@@ -11826,21 +11826,21 @@
 ],
 "metadata": {
  "kernelspec": {
-   "display_name": "Python 3",
+   "display_name": "Python 2",
   "language": "python",
-   "name": "python3"
+   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
-    "version": 3
+    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.5.1"
+   "pygments_lexer": "ipython2",
+   "version": "2.7.11"
  }
 },
 "nbformat": 4,
@@ -64,12 +64,6 @@ test_filterpy_version()
 pylab.rcParams['figure.max_open_warning'] = 50


-def end_interactive(fig):
-    """ end interaction in a plot created with %matplotlib notebook """
-    import time
-    plt.gcf().canvas.draw()
-    time.sleep(0.1)
-    plt.close(fig)

 def equal_axis():
    pylab.rcParams['figure.figsize'] = 10,10
@@ -37,7 +37,7 @@ sys.path.insert(0, '..')
 def end_interactive(fig):
    """ end interaction in a plot created with %matplotlib notebook """
    plt.gcf().canvas.draw()
-    time.sleep(0.2)
+    time.sleep(1.)
    plt.close(fig)


@@ -436,11 +436,11 @@ def set_limits(x, y):
    plt.gca().set_xlim(x)
    plt.gca().set_ylim(y)

-def plot_predictions(p, rng=None):
+def plot_predictions(p, rng=None, label='Prediction'):
    if rng is None:
        rng = range(len(p))
    plt.scatter(rng, p, marker='v', s=40, edgecolor='r',
-                facecolor='None', lw=2, label='prediction')
+                facecolor='None', lw=2, label=label)