daviddoji/Kalman-and-Bayesian-Filters-in-Python
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PEP-8 compliance.

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Roger Labbe committed 2014-11-28 11:14:47 -08:00
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commit bf14f2fbc4
1 file changed
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06_Multivariate_Kalman_filter/Multivariate_Kalman_Filters.ipynb
+95 -122
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@@ -1,7 +1,7 @@
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@@ -261,7 +261,7 @@
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@@ -395,7 +395,7 @@
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"text": [
"<matplotlib.figure.Figure at 0x7f7422d85ef0>"
"<matplotlib.figure.Figure at 0x7f7daa91cf28>"
]
}
],
@@ -455,9 +455,9 @@
"source": [
"Let's use it to compute a few values just to make sure we know how to call and use the function, and then move on to more interesting things.\n",
"\n",
"First, let's find the probability density for our dog being at (2.5, 7.3) if we believe he is at (2,7) with a variance of 8 for $x$ and a variance of 10 for $y$.\n",
"First, let's find the probability density for our dog being at (2.5, 7.3) if we believe he is at (2, 7) with a variance of 8 for $x$ and a variance of 10 for $y$.\n",
"\n",
"Start by setting $x$ to (2.5,7.3):"
"Start by setting $x$ to (2.5, 7.3):"
]
},
{
@@ -563,7 +563,7 @@
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truncated
"text": [
"<matplotlib.figure.Figure at 0x7f73febd1978>"
"<matplotlib.figure.Figure at 0x7f7d8677ffd0>"
]
}
],
@@ -617,7 +617,7 @@
"output_type": "display_data",
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"text": [
"<matplotlib.figure.Figure at 0x7f73fec2e240>"
"<matplotlib.figure.Figure at 0x7f7d86525630>"
]
}
],
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"text": [
"<matplotlib.figure.Figure at 0x7f73feba3710>"
"<matplotlib.figure.Figure at 0x7f7d865294a8>"
]
}
],
@@ -742,7 +742,7 @@
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"text": [
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}
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"text": [
"<matplotlib.figure.Figure at 0x7f73fe719128>"
"<matplotlib.figure.Figure at 0x7f7d863083c8>"
]
}
],
@@ -800,7 +800,7 @@
"output_type": "display_data",
"png": 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truncated
"text": [
"<matplotlib.figure.Figure at 0x7f73fe761a20>"
"<matplotlib.figure.Figure at 0x7f7d8674d390>"
]
}
],
@@ -865,7 +865,7 @@
"output_type": "display_data",
"png": 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truncated
"text": [
"<matplotlib.figure.Figure at 0x7f73feaed630>"
"<matplotlib.figure.Figure at 0x7f7d8656edd8>"
]
}
],
@@ -979,7 +979,7 @@
"collapsed": false,
"input": [
"import numpy as np\n",
"x = np.array([1,2,3])\n",
"x = np.array([1, 2, 3])\n",
"print(x)\n",
"print(type(x))"
],
@@ -1008,8 +1008,8 @@
"cell_type": "code",
"collapsed": false,
"input": [
"x = np.array([[1,2,3],\n",
" [4,5,6]])\n",
"x = np.array([[1, 2 ,3],\n",
" [4, 5, 6]])\n",
"print(x)"
],
"language": "python",
@@ -1039,7 +1039,7 @@
"cell_type": "code",
"collapsed": false,
"input": [
"x = np.array([1,2,3],dtype=float)\n",
"x = np.array([1, 2, 3], dtype=float)\n",
"print(x)"
],
"language": "python",
@@ -1066,7 +1066,8 @@
"cell_type": "code",
"collapsed": false,
"input": [
"x = np.array([[1,2],[3,4]], dtype=float)\n",
"x = np.array([[1, 2],\n",
" [3, 4]], dtype=float)\n",
"print('addition:\\n', x+x)\n",
"print('\\nelement-wise multiplication\\n', x*x)\n",
"print('\\nmultiplication\\n', np.dot(x,x))\n",
@@ -1143,7 +1144,7 @@
"cell_type": "code",
"collapsed": false,
"input": [
"print('zeros\\n', np.zeros((3,2)))\n",
"print('zeros\\n', np.zeros((3, 2)))\n",
"print('\\neye\\n', np.eye(3))"
],
"language": "python",
@@ -1687,8 +1688,8 @@
" Model. dim may be either 2 or 3, dt is the time step, and sigma is the\n",
" variance in the noise.\n",
" \n",
" Paramaeters\n",
" -----------\n",
" **Paramaeters**\n",
" \n",
" dim : int (2 or 3)\n",
" dimension for Q, where the final dimension is (dim x dim)\n",
" \n",
@@ -1765,8 +1766,7 @@
" various state variables to reasonable values; the defaults below will\n",
" not give you a functional filter.\n",
" \n",
" Parameters\n",
" ----------\n",
" **Parameters**\n",
" \n",
" dim_x : int\n",
" Number of state variables for the Kalman filter. For example, if\n",
@@ -1782,33 +1782,6 @@
" dim_u : int (optional)\n",
" size of the control input, if it is being used.\n",
" Default value of 0 indicates it is not used.\n",
" \n",
" \n",
" Instance Variables\n",
" ------------------\n",
" You will have to assign reasonable values to all of these before\n",
" running the filter. All must have dtype of float\n",
" \n",
" x : ndarray (dim_x, 1), default = [0,0,0...0]\n",
" state of the filter\n",
" \n",
" P : ndarray (dim_x, dim_x), default identity matrix\n",
" covariance matrix\n",
" \n",
" Q : ndarray (dim_x, dim_x), default identity matrix\n",
" Process uncertainty matrix\n",
" \n",
" R : ndarray (dim_z, dim_z), default identity matrix\n",
" measurement uncertainty\n",
" \n",
" H : ndarray (dim_z, dim_x)\n",
" measurement function\n",
" \n",
" F : ndarray (dim_x, dim_x)\n",
" state transistion matrix\n",
" \n",
" B : ndarray (dim_x, dim_u), default 0\n",
" control transition matrix\n",
"\n"
]
}
@@ -1969,27 +1942,27 @@
" ps, zs, cov = filter_dog(noise_var=noise_var, data=data, count=count,\n",
" R=R_var, Q=Q_var, P=P, initial_x=initial_x)\n",
" \n",
" p0, = plt.plot([0,count],[0,count])\n",
" p1, = plt.plot(range(1,count+1),zs, linestyle='dashed')\n",
" p2, = plt.plot(range(1,count+1),ps)\n",
" plt.legend([p0,p1,p2], ['actual','measurement', 'filter'], loc=2)\n",
" plt.ylim((0-10,count+10))\n",
" plt.plot([0, count],[0, count], label='actual')\n",
" plt.plot(range(1, count+1), zs, linestyle='dashed', label='measurement')\n",
" plt.plot(range(1, count+1), ps, label='filter')\n",
" plt.legend(loc=2)\n",
" plt.ylim((0-10, count+10))\n",
" plt.title(title)\n",
" plt.show()\n",
" \n",
" if plot_P:\n",
" ax = plt.subplot(121)\n",
" ax.set_title(\"$\\sigma^2_x$\")\n",
" plot_covariance(cov, (0,0))\n",
" plot_covariance(cov, (0, 0))\n",
" ax = plt.subplot(122)\n",
" ax.set_title(\"$\\sigma^2_y$\")\n",
" plot_covariance(cov, (1,1)) \n",
" plot_covariance(cov, (1, 1)) \n",
" plt.show()\n",
" \n",
"def plot_covariance(P, index=(0,0)):\n",
"def plot_covariance(P, index=(0, 0)):\n",
" ps = []\n",
" for p in P:\n",
" ps.append(p[index[0],index[1]])\n",
" ps.append(p[index[0], index[1]])\n",
" plt.plot(ps)"
],
"language": "python",
@@ -2016,9 +1989,9 @@
{
"metadata": {},
"output_type": "display_data",
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truncated
"png": 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truncated
"text": [
"<matplotlib.figure.Figure at 0x7f73fe74f5c0>"
"<matplotlib.figure.Figure at 0x7f7d866b5e80>"
]
},
{
@@ -2026,7 +1999,7 @@
"output_type": "display_data",
"png": 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truncated
"text": [
"<matplotlib.figure.Figure at 0x7f740a323f28>"
"<matplotlib.figure.Figure at 0x7f7d866ca6d8>"
]
}
],
@@ -2158,8 +2131,8 @@
"\n",
" # initialize the filters\n",
" f = mkf_filter(R, Q)\n",
" f.x[0,0] = 0.\n",
" f.P[0,0] = p0\n",
" f.x[0, 0] = 0.\n",
" f.P[0, 0] = p0\n",
" pos = (x0, p0)\n",
" for i in range(50):\n",
" z = i*move + randn()\n",
@@ -2193,9 +2166,9 @@
{
"metadata": {},
"output_type": "display_data",
"png": 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"png": "iVBORw0KGgoAAAANSUhEUgAAAsoAAAGDCAYAAAAyKTZ5AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
"text": [
"<matplotlib.figure.Figure at 0x7f73fead7860>"
"<matplotlib.figure.Figure at 0x7f7d866e2390>"
]
},
{
@@ -2203,7 +2176,7 @@
"output_type": "display_data",
"png": 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truncated
"text": [
"<matplotlib.figure.Figure at 0x7f73feb15438>"
"<matplotlib.figure.Figure at 0x7f7d866cacf8>"
]
}
],
@@ -2391,9 +2364,9 @@
" f.R = R\n",
" f.Q = Q_discrete_white_noise(dim=2, dt=0.1, var=Q)\n",
" \n",
" f.F = np.array([[1,1],\n",
" [0,1]]) # state transition matrix\n",
" f.H = np.array([[1,0]]) # Measurement function\n",
" f.F = np.array([[1, 1],\n",
" [0, 1]]) # state transition matrix\n",
" f.H = np.array([[1, 0]]) # Measurement function\n",
" return f\n",
"\n",
"def plot_compare_pos_vel(x0, p0, R, Q, move):\n",
@@ -2403,12 +2376,12 @@
"\n",
" # initialize the filters\n",
" f1 = mkf_filter(R, Q)\n",
" f1.x[0,0] = 0.\n",
" f1.P[0,0] = p0\n",
" f1.x[0, 0] = 0.\n",
" f1.P[0, 0] = p0\n",
" \n",
" f2 = pos_vel_filter(R, Q)\n",
" f2.x[0,0] = 0.\n",
" f2.x[1,0] = 1.\n",
" f2.x[0, 0] = 0.\n",
" f2.x[1, 0] = 1.\n",
" f2.P *= p0\n",
" \n",
" for i in range(50):\n",
@@ -2420,8 +2393,8 @@
" f1.update(z)\n",
" f2.update(z)\n",
" \n",
" x1.append(f1.x[0,0])\n",
" x2.append(f2.x[0,0])\n",
" x1.append(f1.x[0, 0])\n",
" x2.append(f2.x[0, 0])\n",
"\n",
" plt.plot(x1, label='1D Filter')\n",
" plt.scatter(range(len(x2)), x2, c='r', label='2D Filter')\n",
@@ -2437,9 +2410,9 @@
{
"metadata": {},
"output_type": "display_data",
"png": 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"text": [
"<matplotlib.figure.Figure at 0x7f73fe7591d0>"
"<matplotlib.figure.Figure at 0x7f7d8684a828>"
]
}
],
@@ -2495,10 +2468,10 @@
" 40.77, 32.95, 38.20, 40.93, 39.42, 35.49, 36.31, 31.56,\n",
" 50.29, 40.20, 54.49, 50.38, 42.79, 37.89, 56.69, 41.47, 53.66]\n",
" \n",
"plot_track(data=zs, R_var=50, Q_var=20,count=50, plot_P=False, \n",
"plot_track(data=zs, R_var=50, Q_var=20, count=50, plot_P=False, \n",
" title='R_var = 50 m, Q_var = 20 m')\n",
"\n",
"plot_track(data=zs, R_var=50, Q_var=.02,count=50, plot_P=False, \n",
"plot_track(data=zs, R_var=50, Q_var=.02, count=50, plot_P=False, \n",
" title='R_var = 50 m, Q_var = 0.02 m')"
],
"language": "python",
@@ -2509,7 +2482,7 @@
"output_type": "display_data",
"png": 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"text": [
"<matplotlib.figure.Figure at 0x7f73fe88b710>"
"<matplotlib.figure.Figure at 0x7f7d91f1e828>"
]
},
{
@@ -2517,7 +2490,7 @@
"output_type": "display_data",
"png": 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truncated
"text": [
"<matplotlib.figure.Figure at 0x7f73feb57e10>"
"<matplotlib.figure.Figure at 0x7f7d867589b0>"
]
}
],
@@ -2549,7 +2522,7 @@
"cell_type": "code",
"collapsed": false,
"input": [
"plot_track(data=zs, R_var=10000., Q_var=.2,count=50, plot_P=False, \n",
"plot_track(data=zs, R_var=10000., Q_var=.2, count=50, plot_P=False, \n",
" title='R_var = 10000 m, Q_var = 0.2 m')"
],
"language": "python",
@@ -2560,7 +2533,7 @@
"output_type": "display_data",
"png": 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truncated
"text": [
"<matplotlib.figure.Figure at 0x7f73fe769e48>"
"<matplotlib.figure.Figure at 0x7f7d864949b0>"
]
}
],
@@ -2577,8 +2550,8 @@
"cell_type": "code",
"collapsed": false,
"input": [
"plot_track(data=zs, R_var=10000., Q_var=.2,count=50, \n",
" initial_x=np.array([[20],[1]]),plot_P=False, \n",
"plot_track(data=zs, R_var=10000., Q_var=.2, count=50, \n",
" initial_x=np.array([[20], [1]]), plot_P=False, \n",
" title='R_var = 10000 m, Q_var = 0.2 m')"
],
"language": "python",
@@ -2589,7 +2562,7 @@
"output_type": "display_data",
"png": 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truncated
"text": [
"<matplotlib.figure.Figure at 0x7f7408038a20>"
"<matplotlib.figure.Figure at 0x7f7d86703898>"
]
}
],
@@ -2606,8 +2579,8 @@
"cell_type": "code",
"collapsed": false,
"input": [
"plot_track(data=zs, R_var=30, Q_var=.2,count=50, \n",
" initial_x=np.array([[20],[1]]),plot_P=False, \n",
"plot_track(data=zs, R_var=30, Q_var=.2, count=50, \n",
" initial_x=np.array([[20], [1]]), plot_P=False, \n",
" title='R_var = 30 m, Q_var = 0.2 m')"
],
"language": "python",
@@ -2618,7 +2591,7 @@
"output_type": "display_data",
"png": 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"text": [
"<matplotlib.figure.Figure at 0x7f73fe976780>"
"<matplotlib.figure.Figure at 0x7f7d86709dd8>"
]
}
],
@@ -2674,8 +2647,9 @@
"cell_type": "code",
"collapsed": false,
"input": [
"P = np.array([[2,0],[0,6]])\n",
"stats.plot_covariance_ellipse((0,0), P, facecolor='g', alpha=0.2,\n",
"P = np.array([[2, 0], \n",
" [0, 6]])\n",
"stats.plot_covariance_ellipse((0, 0), P, facecolor='g', alpha=0.2,\n",
" title='|2 0|\\n|0 6|')"
],
"language": "python",
@@ -2686,7 +2660,7 @@
"output_type": "display_data",
"png": 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truncated
"text": [
"<matplotlib.figure.Figure at 0x7f73fe769a20>"
"<matplotlib.figure.Figure at 0x7f7d86404cf8>"
]
}
],
@@ -2703,8 +2677,9 @@
"cell_type": "code",
"collapsed": false,
"input": [
"P = np.array([[2,2.4],[2.4,6]])\n",
"stats.plot_covariance_ellipse((0,0), P, facecolor='g', alpha=0.2, \n",
"P = np.array([[2, 2.4],\n",
" [2.4, 6]])\n",
"stats.plot_covariance_ellipse((0, 0), P, facecolor='g', alpha=0.2, \n",
" title='|2.0 2.4|\\n|2.4 6.0|')"
],
"language": "python",
@@ -2715,7 +2690,7 @@
"output_type": "display_data",
"png": 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"text": [
"<matplotlib.figure.Figure at 0x7f73feb18208>"
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}
],
@@ -2787,7 +2762,7 @@
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truncated
"text": [
"<matplotlib.figure.Figure at 0x7f73feb666d8>"
"<matplotlib.figure.Figure at 0x7f7d8644a438>"
]
},
{
@@ -2795,7 +2770,7 @@
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"text": [
"<matplotlib.figure.Figure at 0x7f73fea06f60>"
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}
],
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"text": [
"<matplotlib.figure.Figure at 0x7f73fe9fd400>"
"<matplotlib.figure.Figure at 0x7f7d91f1eda0>"
]
},
{
@@ -2833,7 +2808,7 @@
"output_type": "display_data",
"png": 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truncated
"text": [
"<matplotlib.figure.Figure at 0x7f73feb02358>"
"<matplotlib.figure.Figure at 0x7f7d86685710>"
]
}
],
@@ -2854,9 +2829,9 @@
"cell_type": "code",
"collapsed": false,
"input": [
"x = np.array([[100.,0.]]).T\n",
"plot_track(data=zs, R_var=50., Q_var=.2, P=1., initial_x=x,count=len(zs),\n",
" plot_P=False, title='P=1 m')"
"x = np.array([[100., 0.]]).T\n",
"plot_track(data=zs, R_var=50., Q_var=.2, P=1., initial_x=x,\n",
" count=len(zs), plot_P=False, title='P=1 m')"
],
"language": "python",
"metadata": {},
@@ -2866,7 +2841,7 @@
"output_type": "display_data",
"png": 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truncated
"text": [
"<matplotlib.figure.Figure at 0x7f73fe72f5c0>"
"<matplotlib.figure.Figure at 0x7f7d86519940>"
]
}
],
@@ -2885,9 +2860,9 @@
"cell_type": "code",
"collapsed": false,
"input": [
"x = np.array([[100,0]]).T\n",
"plot_track(data=zs, R_var=50, Q_var=.02, P=500., initial_x=x,count=len(zs),\n",
" plot_P=False, title='P=500')"
"x = np.array([[100, 0]]).T\n",
"plot_track(data=zs, R_var=50, Q_var=.02, P=500., initial_x=x,\n",
" count=len(zs), plot_P=False, title='P=500')"
],
"language": "python",
"metadata": {},
@@ -2897,7 +2872,7 @@
"output_type": "display_data",
"png": 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truncated
"text": [
"<matplotlib.figure.Figure at 0x7f73fe9fd358>"
"<matplotlib.figure.Figure at 0x7f7d865e87f0>"
]
}
],
@@ -2933,16 +2908,16 @@
" cov = []\n",
" for t in range (count):\n",
" z = dog.sense()\n",
" f.update (z)\n",
" ps.append (f.x[0,0])\n",
" f.update(z)\n",
" ps.append(f.x[0, 0])\n",
" cov.append(f.P)\n",
" zs.append(z)\n",
" f.predict()\n",
"\n",
" p0, = plt.plot([0,count],[0,count],'g', label='actual')\n",
" p1, = plt.plot(range(1,count+1),zs,c='r', linestyle='dashed', \n",
" label='measurement')\n",
" p2, = plt.plot(range(1,count+1),ps, c='b', label='filter')\n",
" plt.plot([0, count], [0, count], 'g', label='actual')\n",
" plt.plot(range(1,count+1), zs, c='r', linestyle='dashed', \n",
" label='measurement')\n",
" plt.plot(range(1,count+1), ps, c='b', label='filter')\n",
" plt.legend(loc='best')\n",
" plt.title(title)\n",
"\n",
@@ -2953,11 +2928,9 @@
"\n",
" if i == len(cov)-1:\n",
" s = ('$\\sigma^2_{pos} = %.2f$' % p[0,0])\n",
" plt.text (20,10,s,fontsize=18)\n",
" plt.text (20, 10, s, fontsize=18)\n",
" s = ('$\\sigma^2_{vel} = %.2f$' % p[1,1])\n",
" plt.text (20,5,s,fontsize=18)\n",
" #plt.xlim((-10,30))\n",
" #plt.ylim((-10,40))\n",
" plt.text (20, 5, s, fontsize=18)\n",
" plt.show()\n",
"\n",
"\n",
@@ -2970,17 +2943,17 @@
{
"metadata": {},
"output_type": "display_data",
"png": 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truncated
"png": 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truncated
"text": [
"<matplotlib.figure.Figure at 0x7f73fe885080>"
"<matplotlib.figure.Figure at 0x7f7d8675a470>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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truncated
"png": 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truncated
"text": [
"<matplotlib.figure.Figure at 0x7f73fec100b8>"
"<matplotlib.figure.Figure at 0x7f7d865e6a58>"
]
}
],
@@ -3055,7 +3028,7 @@
"output_type": "display_data",
"png": 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truncated
"text": [
"<matplotlib.figure.Figure at 0x7f73feb68be0>"
"<matplotlib.figure.Figure at 0x7f7d8662c860>"
]
}
],