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@slinderman
Last active October 24, 2017 22:17
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Using an switching linear model to approximate a nonlinear dynamical system
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import os\n",
"os.chdir(os.path.expanduser(os.path.join(\"~\", \"Projects\", \"pyhsmm-slds\")))\n",
"\n",
"import seaborn as sns\n",
"color_names = [\"windows blue\",\n",
" \"red\",\n",
" \"amber\",\n",
" \"faded green\",\n",
" \"dusty purple\",\n",
" \"crimson\",\n",
" \"greyish\"]\n",
"colors = sns.xkcd_palette(color_names)\n",
"sns.set_style(\"white\")"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import numpy as np\n",
"np.random.seed(1)\n",
"\n",
"from scipy.integrate import odeint\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# Lorenz attractor parameters\n",
"mu = np.array([-2.5, -2.5, 24])\n",
"std = 15.\n",
"standardize = lambda state: (state - mu) / std\n",
"unstandardize = lambda stdstate: std * stdstate + mu\n",
"\n",
"sigma = 10.0\n",
"rho = 28.0\n",
"beta = 8.0/3.0\n",
"\n",
"# Observation noise\n",
"eta = 1e-3\n",
"\n",
"def lorenz(stdstate, t):\n",
" # unpack the state vector\n",
" state = unstandardize(stdstate)\n",
" x = state[0]\n",
" y = state[1]\n",
" z = state[2]\n",
"\n",
" # compute state derivatives\n",
" xd = sigma * (y-x)\n",
" yd = (rho-z)*x - y\n",
" zd = x*y - beta*z\n",
" \n",
" # standardize the derivatives \n",
" # dxs / dt = dxs / dx * dx /dt\n",
" # = 1/std * dx / dt\n",
" dstate = np.array([xd, yd, zd]) / std\n",
"\n",
" # return the state derivatives\n",
" return dstate\n",
"\n",
"x0 = standardize(np.array([2.0, 3.0, 4.0]))\n",
"t = np.arange(0.0, 30.0, 0.01)\n",
"T = t.size\n",
"\n",
"xfull = odeint(lorenz, x0, t)\n",
"yfull = xfull + eta * np.random.randn(*xfull.shape)\n",
"\n",
"# Downsample\n",
"ds = 1\n",
"x = xfull[::ds]\n",
"y = yfull[::ds]"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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YMmUKoaGhvUwep9PJ1atX2bt3L2fPnmX+/PnExsZKjWT+/Pls3bqVhIQEQkNDPe7pbkla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\n2oV3dGTNHP8f9E7B6Moq8lkAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x116c4b0f0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# do some fancy 3D plotting\n",
"from mpl_toolkits.mplot3d import Axes3D\n",
"fig = plt.figure(figsize=(4,4))\n",
"ax = fig.gca(projection='3d')\n",
"ax.plot(y[:,0], y[:,1], y[:,2], lw=1, color=\"k\", alpha=0.5)\n",
" \n",
"ax.set_xlabel('$x_1$', fontsize=12, labelpad=10)\n",
"ax.set_ylabel('$x_2$', fontsize=12, labelpad=10)\n",
"ax.set_zlabel('$x_3$', fontsize=12, labelpad=10)\n",
"ax.set_xlim(-1.5, 1.5)\n",
"ax.set_ylim(-1.5, 1.5)\n",
"ax.set_zlim(-1.5, 1.5)\n",
"fig.savefig(\"lorenz_trajectory.pdf\")"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"......."
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/scott/Projects/pybasicbayes/pybasicbayes/util/stats.py:191: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
" x = np.random.randn(nu,n)\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
".................. [ 25/500, 0.03sec avg, ETA 11.90 ]\n",
"......................... [ 50/500, 0.03sec avg, ETA 13.79 ]\n",
"......................... [ 75/500, 0.03sec avg, ETA 13.23 ]\n",
"......................... [ 100/500, 0.03sec avg, ETA 11.65 ]\n",
"......................... [ 125/500, 0.03sec avg, ETA 10.41 ]\n",
"......................... [ 150/500, 0.03sec avg, ETA 9.39 ]\n",
"......................... [ 175/500, 0.03sec avg, ETA 8.47 ]\n",
"......................... [ 200/500, 0.03sec avg, ETA 7.70 ]\n",
"......................... [ 225/500, 0.03sec avg, ETA 7.32 ]\n",
"......................... [ 250/500, 0.03sec avg, ETA 6.89 ]\n",
"......................... [ 275/500, 0.03sec avg, ETA 6.35 ]\n",
"......................... [ 300/500, 0.03sec avg, ETA 5.69 ]\n",
"......................... [ 325/500, 0.03sec avg, ETA 4.99 ]\n",
"......................... [ 350/500, 0.03sec avg, ETA 4.28 ]\n",
"......................... [ 375/500, 0.03sec avg, ETA 3.56 ]\n",
"......................... [ 400/500, 0.03sec avg, ETA 2.95 ]\n",
"......................... [ 425/500, 0.03sec avg, ETA 2.22 ]\n",
"......................... [ 450/500, 0.03sec avg, ETA 1.47 ]\n",
"......................... [ 475/500, 0.03sec avg, ETA 0.73 ]\n",
"......................... [ 500/500, 0.03sec avg, ETA 0.00 ]\n",
"\n",
" 0.03sec avg, 14.65 total\n",
"\n"
]
}
],
"source": [
"# Fit the data with a linear dynamical system\n",
"from pybasicbayes.distributions import Regression, Gaussian, AutoRegression\n",
"from pyhsmm.util.text import progprint_xrange\n",
"from autoregressive.models import ARWeakLimitStickyHDPHMM\n",
"\n",
"Nmax = 20 # number of latnt discrete states\n",
"D = y.shape[1] # data dimension\n",
"affine = False\n",
"\n",
"from pyslds.util import get_empirical_ar_params\n",
"dynamics_hypparams = \\\n",
" dict(nu_0=D+2, \n",
" S_0=np.eye(D), \n",
" M_0=np.zeros((D,D+affine)), \n",
" K_0=np.eye(D+affine), \n",
" affine=affine)\n",
"dynamics_hypparams = get_empirical_ar_params([y], dynamics_hypparams)\n",
"\n",
"dynamics_distns = [\n",
" AutoRegression(\n",
" A=np.column_stack((0.99*np.eye(D), np.zeros((D,int(affine))))), \n",
" sigma=np.eye(D),\n",
" **dynamics_hypparams)\n",
" for _ in range(Nmax)]\n",
"\n",
"\n",
"init_distn = \\\n",
" Gaussian(nu_0=D+2,sigma_0=np.eye(D),mu_0=np.zeros(D),kappa_0=1.0)\n",
"\n",
"\n",
"model = ARWeakLimitStickyHDPHMM(\n",
" init_state_distn='uniform',\n",
" init_emission_distn=init_distn,\n",
" obs_distns=dynamics_distns,\n",
" kappa=1.,alpha=3.,gamma=3.)\n",
"\n",
"model.add_data(y)\n",
"\n",
"for itr in progprint_xrange(500):\n",
" # Resample everything except the emission distribution\n",
" model.resample_model()\n",
" \n",
"from pyhsmm.util.general import relabel_by_usage, relabel_by_permutation\n",
"\n",
"zhat = model.states_list[0].stateseq\n",
"zhat, newlabels = relabel_by_usage(model.stateseqs[0], return_mapping=True)\n",
"z_cps = np.concatenate(([0], np.where(np.diff(zhat))[0]+1, [zhat.size]))\n",
"N_used = zhat.max()+1\n",
"perm_dynamics_distns = [dynamics_distns[i] for i in np.argsort(newlabels)]\n"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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vvIO5d69N1q98BSQJq6UF68ABRF8f8uzZyDNmIC9dCsEg2jCTR5gm1pkz6Js2YR04gLVm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8xTTkJdxFbOzs7G2rVr0b9/f5/HGsJoGaSlUVFRgW3btmHr1q1gGAY5OTl45JFHOM8lASmzCUhb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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11a0c7438>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(4,4))\n",
"ax = fig.gca(projection='3d')\n",
"for start, stop in zip(z_cps[:-1], z_cps[1:]):\n",
" ax.plot(y[start:stop+1,0], \n",
" y[start:stop+1,1], \n",
" y[start:stop+1,2], \n",
" lw=1,\n",
" color=colors[zhat[start]],\n",
" alpha=0.5)\n",
" \n",
"ax.set_xlabel('$x_1$', fontsize=12, labelpad=10)\n",
"ax.set_ylabel('$x_2$', fontsize=12, labelpad=10)\n",
"ax.set_zlabel('$x_3$', fontsize=12, labelpad=10)\n",
"ax.set_xlim(-1.5, 1.5)\n",
"ax.set_ylim(-1.5, 1.5)\n",
"ax.set_zlim(-1.5, 1.5)\n",
"fig.savefig(\"lorenz_arhmm.pdf\")"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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/kFKOTDnns6ho4tzOxVdJKWe9i3HHuhqe6Rjn5kub2Ht8jPe8RvCl33Sg6waH\nusNcuraKdFbn6RPjXLe5lqFwkg9csYF/vVfFIBw+HeEl2xo4ORTj2VNh2uqDVIc8bF1dwU+fVEmb\nuofjvOryJtY1Kdnvcmq0VPvxe5zUlXvoHonTM5qgqdpHY5WPwYmk6cdJUVuuBkd9hZehiSRjk2mq\npjgnq0IeRidTxJJL5xMAlMLoVzPliX4VV1ERcHOkJ78hcHVdAIdDY3QyRc9onJYaP6tqA9w9rJyT\nA+OKYEYnfTx4YJDRSF49+D1OPC4H4VjGVCBnJoiWGj+HDgwyNJG0YoM8LgcBj5NI/NzXN1T6eLpj\nfJp5BFAZdDMWTRFNZJe0vdc0BDg5HEPXDfrGErxsu4+sbvDwc8MMhdVE5HY5qDOJZHQyVaR+q4Ju\nOgdjVAbSlJ1ngpmrgnm7EOJKACHE1UIIt5Sy91wXzQJ3An+UUr4A+B4qYncqdgA3FaTMnNMW6R1r\nKnm6Y5xEKkvnYJQXXlRH0OvkeP8kB0+F2byynEtWV7K/a5yjfZO0N4bY0FLG6ZE4sWSGo72TiOYy\n1jWFON4X5UT/JGsbg6yuD9I7miCZznJqOMaq2gDrmoIc75ukdzS/ArKqLkD3cFwNtmo/HpeDqpCH\nwXCSoXB+cNSWeRmOpJTEnTJzV4c8DEdSJNJ60Ux7vlEd8uByagyFk3QMRFnbGLLMmpPDyrmoaRpt\n9QE6BmL0jCRYUe1jZa2f7uEY0USGrG5Q7neZZkhyms+pvsLLYDjJeCxdpOSmoqXaT89InJEpDtrq\nMg/DkSThszh5AZqqlBlUuIKUQ2XQzUQsTSy1tIQe8Loo97von0iYJpJqy56ROMPhJHVmhHd9uSKY\nqZNTVcjDeDRtmkjLm2CeA46Y/38SKNVmRyvIDvg1KmLXgrmNYB3wdSHEo0KIN8/1AStr/WR1g98+\nO8iahiBet5NL2irZ3zXBoW61U3ZbWwX7OieQPRFEi5qJ2+qD7O9S/oXmKp9l/hzvj9LeqM5ZUevn\nwMkJsrpBVdDN2oYgHYNRi0wAVph+gd7RBM3VinSaq3wc7Z3E6dCsZdCaMg9D4STj0ekDqzropm8s\ngc/twOFY2n1VaxtzRBtlbWOQtQ1BOgejnByKsapWfedVtcokOm0qmHK/G5/byaHTYcsB2VDhZXAi\nwchkiuqy/PfNKT7DMPC5z9xNm6t99I4lihQQQG2Zhx7TKX6269XzzVk/VNzelQG3MpESWQLnefVl\nKlrrAnTLvu8zAAAgAElEQVT0Ry3nbX25l9HJFP3jCYsYa8vV5DQSSVr+F4CqkFJi4SXwwcy11VqB\n7wohfgc8BlTO9YFCiL8E3o75gjXUmxz7yQfSRSiOeQEIAp9HbRdwAf8jhNgrpTw42+dqmsb2NZXc\n9dApdq1Xr2XYtrqC3+wfoHc0QXtjEIemEYmnefTICC/eqvKSipYQv9k3QFt9EIdDo70xyNceiIIB\nL9qqNr+tbQjy0MFhVtb6zZk7aC0TXrZW7ftYUePn5FCM3rE4zVVqADZW+jjUHS7aV1RX7qV7OI7T\noU3bLV0ecNM7mlhSf0AO7Y1Bnjg2itOhUR3yEPQ66RlJ0NGvIm8BU7HE6S0g2pZqP/s6JqivULOu\nz+PE73Fyon+ymCDKvZzon6Qi4D5r3Ea5341DU47lwkFVHfLQORilPHD2uI/KoJt4KkvvWGJadHR5\nwM1kQvnEgkuoGEERzJ7jY9SUeXA5FWHWlXs51B2x+o/H5aDM5+LEQJSqYIGaC3oYnUwTjqfPmeKj\n1JirgukC/go4DfwlMOcEU1LK/5BSXiSlvNj8dxHFQXYzBdHFgM9LKRNSykng96hNkXPCjrWVnBqO\nc3Gr8ktvbavgyWNjbFpZjsupVMElqyt56sQ4G1eo6ojmMh44MEhbgzloavwMhZP88dQE7eaP1d4Y\n5KFDQ9Z2/qDPRWXQzd7jY7SYsSwrqv0c65skmshaHaKh0stz3ZEiaV5T5uG4ObCmojLopm88sWRL\n1IVobwxx//4BK0rW63bSUOnl0SMjFsGsqPHzx5MTeFwOQqYCaKnxsa9z3CIYgIYKH0d6phKMh+P9\n0bOaRzk0Vfk41B0pGlQ1ZR5O9EfPah6Bmnjqy73Insg0H0xOWfaPJwgusYJZVRvgiaOjRUGHzdU+\nnj01UVTvugovsre4LavMxYHIEjh550owMSArpbwH+AQqfWUpYAXZmX8fmXJ8PbDb3JrgRplUz8z1\nIVdvqOXlOxq5eqN670tTpY+Wah83bMnvm8wlFcqFp29eqYhmfZNK3uRyOqgOqdWFXCBce2OI0YLP\n6vogo5NpWkxzSA22MI1VXsu8UQMjXNQZ6iq8ZxwYFQE3faOJJV2izmFtY5CJWIZ1TfmkVmsagvSP\nJ1ldlyfj505HitqlpdrP/q6JonQT9ZVenjsdLiLa2rIzt8NUNFf5OdwTKTJxasqUgpnN9XUVXp47\nHZkx4rci4KJvLLGkPhhArRANFwdfNlf7TQVTSNaKLAvVXLlfhTiMR9PLe5naTI3ZZH6sQJkupcBX\ngC1CiEdQycU/DCCEeLsQ4mYp5RHgLpTf53+A70opD5/xbmdATZmHD7xug7V8p2kaP3nXLl53RT63\nyeuvaOHef9plydB1TSH+/uVri7buv/GalfzplS35c5rVIMuREWDN0LkfPzfzNFXlO0hDhZdEWi8a\nWHXlHnrHEjMuzVaYPphlQTANQcr9Lq5Yn38LYG4TnWUO1eT9TznkjjUXzMQNFV7GJtOWsxKUgjk9\nEp8VQeTattCxqUyk2Kyub6jw0TeWmObkBWUm9Y0lltwHs6qAtHPItWFhvdWSdKqoLRwOjXK/i9Mj\n8fPu5J3z03J+DynlAWDum1Jmvmcc+JMZyj9T8P9PoyJ8FxU+j5PGAhNE0zTecPXKonMKCQmULfy9\nt11atA3+xovrqQy6LbWS2yhXOMvm8osUDqx68/8zBYdVBFxEEksbk5GD2+Xg/g9cVeTf+JMrW9i+\nptL6zj63k6YqH9va8q66lhpT0dUWEy0ocs0hR8xTl+pnQs5pXrjqVhPykMkaZ42hySE3GcykYMoD\nbp47HVlyH0yujQo3bjZbk1YBWZvKsHrK964KuekYiC37OBgbZ0ChqQBwWXsVl7UXJ/b55p3baazM\nk0muYxQSUy6p1EzRq7mypZbrOUx1ntaWe6365/DTd+0sOm/LynL+4rpVbF6R9+PnFE7hQMkt208d\nKDMh98zm6jxp5fwSs0lrkSOYQr9QDrkBuZSRvKBUyC/ee0XRZJRTzjmTFPJENJUsK4MeILb8FYyN\n+WNq0mif28nP37OrqNPkstbP5FTMyf2ldjjOBVNJyOV0cOdNa4rKrhA1vPe1681BoJAjhtkokO1t\nFfz5tauKMv7nBthMZs9U5NTiTGSUa/PloBrrppB3W32Qxz9+bVEbrzEXHlbWFieuyi3Vn+/4qaVv\ntQIIIV4DvE5K+cYZjr0FeCsqZebHSriLe0lRXzE9FcEn/2wzW1ZN34GR7+zLQ8GUCn6Pk1dd1lxU\nljMpZ5N9rTLo4W9esmZKmWqr2RDMzvXVfOB1G2aMLcq1eWiZkvpUAm9vDPHw/3eN5R/MIbeP93zn\npV42rWZuBXgxsH+GYw3A3wHbgQDwqBDiATO73QWHazfPnA3USni0NK8lOu949KMvmDZQZgunQ+O/\n/2nXjGbPVJT73bx8x8yvL8ntPj7fvouFYKa3TbTWBXj86Nxfl7tQnP8UXWfGbqa/FymHy4FHpZQZ\n8yVsx4CLz1vNlhn0JXrx2fnGfMklh4ZK34Jn7NyKo/cs0cDPB7zlRau5959m9waFUuK80/KUSF7N\n/PtmKeV/CSGuPcNlU1NmTvI82MW9WGip9p/7JBslQc4cfb6/8ibodS1JVr7z/kQp5X8A/zHHyxaU\nMvNCwq//+cpZRbfaKA1u2FLHr/75yqWuxvMWzxfDcg/wUTNdph/YAMx6H9KFhNnEhdgoHRzmXisb\n88OyJhghxNtRryv5pRDi86jXlWjA+6SUqaWtnQ0bNs6FZUUwUsqHgYcLPhdG8n4L+NZS1MuGDRvz\nw/PbNW7Dho1ljWWlYM4RaLeglJk2bNg4/1g2BHO2QDsTuZSZ5z9ayIYNG/PCcjKRzhhoV4qUmTZs\n2Dj/eL4E2s01ZaYToH+Zv/Deho3liIJxs+BNb8+XQDsrZSaAECKXMvNMBNME8MY3TnPl2LBhY/Zo\nAhb0Uvdl44M5B9YDPxZCXIKq89XAd85y/l7gGqAPyC567WzYuLDgRJHL3oXeaFkTzJRAu1zKzBTn\nSJkppUyigvJs2LAxPyxIueSgGf9LdubasGHj/GM5rSLZsGHjAoNNMDZs2Fg02ARjw4aNRYNNMDZs\n2Fg02ARjw4aNRYNNMDZs2Fg02ARjw4aNRYNNMDZs2Fg02ARjw4aNRYNNMDZs2Fg02ARjw4aNRYNN\nMDZs2Fg0LKvd1EKIncAnpJTXTyn/B+B2YNAsukNKeex818+GDRtzw7IhGCHEu4A3oV4LOxU7gDdJ\nKfed31rZsGFjIVhOJtJx4DVnOLYDeK8Q4hEhxHvOY51s2LCxACwbBSOl/JkQovUMh+8GvoR6R/W9\nQoiXSSl/daZ7CSG8wGXYGe1s2JgPrIx2ZvK2eWPZEMw58DkpZRhACHEfsA04I8GgyOWR81ExGzYu\nYFzDAjNDLkeC0Qo/CCHKgYNCiA1AHLiBc79Ctg/g86dO0djeTs2vf70oFb3QkDl0CEdzM46qqmnH\nBoWAVIr6zs4lqFkeY69/Pemnnpp3PQbb2vBccw2Vd91V4prNHYZhoPf24mxpmXZssK0N3xveQPnH\nP35e6xT//vfp2bePO/bvB3M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IA1LKOHBMCPGnUsofl7RGJcbz1UQ6ORRjOJJkx5riDP/p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\nwYOHdcP/BYwWfe6r+SzwAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11bf712e8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Look at the inferred segmentation in 2D \n",
"# here it's harder to see the transition\n",
"import matplotlib.gridspec as gridspec\n",
"from hips.plotting.colormaps import gradient_cmap\n",
"fig = plt.figure(figsize=(4,4))\n",
"gs = gridspec.GridSpec(10,1)\n",
"\n",
"# Plot the discrete state sequence\n",
"ax0 = fig.add_subplot(gs[0])\n",
"ax0.matshow(zhat[None,:], aspect='auto', cmap=gradient_cmap(colors[:2]), vmin=0, vmax=1)\n",
"ax0.set_xticks([])\n",
"ax0.set_yticks([])\n",
"ax0.set_ylabel(\"$z_t$\", labelpad=30)\n",
"\n",
"for i in range(3):\n",
" ax = fig.add_subplot(gs[1+i*3:1+(i+1)*3])\n",
" for start, stop in zip(z_cps[:-1], z_cps[1:]):\n",
" stop = min(zhat.size, stop+1)\n",
" ax.plot(np.arange(start, stop), \n",
" y[start:stop,i], \n",
" lw=1,\n",
" color=colors[zhat[start]])\n",
"\n",
" ax.set_ylim(-1.5, 1.5)\n",
" ax.set_ylabel(\"$x_{}(t)$\".format(i+1))\n",
" if i < 2:\n",
" ax.set_xticklabels([])\n",
"\n",
"ax.set_xlabel(\"Time\")\n",
"plt.tight_layout()\n",
"plt.savefig(\"lorenz_arhmm_2d.pdf\")"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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mcPrppzN37lwuvvhiqqqqCt7HueeeS1NTU6av/xP4F8APvODz+S5oaGj448DP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\nzj///KKHZOVC5uXLl8f/PRQKcfbZZ/PMM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V8I85///CeBQIDly5ezdu1alixZEi9kDoVC\n3HnnnTzzzDMYjUYWLFjAqaeeGncBGUb/YHgup8fPfvYzzGZzvN+rMEe48cYbcblcXHXVVZx44olA\notAmVScVuaVWsXQN4sQKMXX77Nmzqaqqor29nVdeeYUbbrihXwjzqzCfB4QwZ82axWmnncaTTz7Z\n57VoNMqOHTu49dZbaW9v5+KLL+aiiy4aiGENCTgcjj5h2AkTJnD77bfzm9/8hg8++IAHHniANWvW\ncPHFF3PBBRdgs9mSytoVRSlqI1oB4Skp/vuKK67gvvvuY+bMmQT+//bOPiaqK43DDwgoH9Uohm1q\nGj8Qbhe/KnTZ1lodEtmN0SpWKIOWaWgBq0G3W79XaKRJSzUa66Y1NLothBoB3baxFHZbNlpru7RI\nLMTanrjgkkYE+TArwsLUevcPnLszwwCKM8Nw5zzJ/DH3DHAOh999uee85/eazS5x8AGoqanRbi7z\n5s3jwoULWlt9fT1Tp07Vnl5iYmKorq5265EWb0RqeXAsf68Wxo0bR1JSEklJSZo5wtq1awkLCyMj\nI4M5c+bYHDmzXkUym8309va6LMs2ICCA4uJiGhsbKSwsBPoye51137BHD3p26p3uxIkT2i/eQl5e\nHkuXLuXbb791+DXd3d2kpqaSlpbGrVu3MJlMzJkzxyal2FuxmCMsWLAAs9lMRUUFO3fupLW1lRdf\nfJG4uDj8/Py0SioW/P39nfZH/8svv2g+lX5+fphMJnJzc5k/fz6AS4vHDnSQ2dfXt19bcHAwnZ2d\nLuuLtyG17Hws5ggbNmygvr6eo0ePkp2dTWxsLM8//zwPP/ywzSqShaCgIKcFS8sREz8/P06dOsWn\nn37Kxx9/rD25uipYgj707NSAmZiYSGJi4j19TWBgIKmpqdoT0eOPP86PP/4oRWZHQEAAK1euZOXK\nlZo5QlpaGsHBwaSnpxMYGEhkZKRmGm35D3I4Nl4WrI0Jxo0bx7p16zCZTC5ZfnXEYAeZQ0JCtKQm\n6EtEGj9+vFv65Q1ILbuW8PBwXn31VXJycqiurqagoIBvvvmGhIQEFi9eTGBgoFacubu7+57r8TrC\nei/04sWLHDx4kIqKCo8wJhgteh5x44LLly+TkpKiZXDV1NTIw+VDYG+O8M4777BhwwZ2795NY2Nj\nP3OE4Vhm2e+F5ubmEh0dTWpqqgtHZstgB5nDw8NpbGzkxo0bmM1mqqurefTRR93WN0l/pJbvHXtz\nBEv5rNTUVCoqKmzMEbq6ujRzhHu1s7TeC21qamLbtm0cP37crQlZetDziFnjFRQUMHXqVOLi4khI\nSCApKQl/f39WrVrVr27iYFl5paWllJSU4O/vz0svvYTBYHDTCDyDMWPG0NDQwPz588nMzKS0tJQv\nv/ySpUuXkpycTGho6D1bZlk7Do0dO5bDhw9z69Yttm/f7s6hER8fz1dffaXt8ebl5VFWVqYdZN65\ncycvvPACqqqSlJREWFiYW/sn6UNq2Tn4+/vT0NAAwBtvvMH169fJyMjAz8+PzMxMYmNjuX379j3b\nWVo7DnV1dbFu3TqKiop48MEH3TU0QB969vhzmNZZefYia2trIy0tjY8++oienh5SUlL48MMP3bbE\n4CmcO3eOqKgozfjA3hzhueeeY9myZYwdO9amkoqjtHb7A9Ll5eWcPHmSkpISbzcmGAp5DnMIpJaH\n5tq1a3R0dNi47FibI0RERJCenk5EREQ/Ry5HR86sj48AJCcns2fPHp544gn3DGj0MjqrlURHR7N7\n926HbXV1dcTExODn50dISAjTpk3TbJW8iccee0wLltD31LlkyRIKCwuprKxk4sSJZGVlYTKZ+Prr\nr4G+wNjb22tTScWyjGupVnDu3DkKCwv54IMPZLCU3DdSy0MTFhbWz5JuypQpbNmyhbNnz7J582ZO\nnjzJ8uXLOXjwIO3t7Q4rqVhWlayLI6Snp7NlyxYZLO8Dj6lWMpysPPvMqqCgII/MrBpJgoKCSElJ\nISUlhWvXrlFcXIzRaGTKlClkZGQwa9YszRgB+pZv6urqmDBhArm5uZSVlTmlYorEe5Badh2zZ89m\nz5493L59mzNnznDgwAEuXryI0WhkxYoVNuYI0LevPGbMGA4dOsTTTz/NihUrRngEoxuPCZjDycob\nLZlVnkJYWBibNm1i06ZNmjnCjh07WLBgAQaDgQceeIDLly+zd+9efH19WbRoEe3t7YSGhrq0X729\nvWzdupX29nZCQkJ48803mThxos1nvNlBZrQhtex6fH19MRgMGAyGfuYIJpOJgIAAYmNj2bp1K21t\nbYwfP564uLh+JbNcgZ717DEBczjMnTuXt956Szvg29DQQEREBKDvSXMG1uYI+fn5bNu2jeDgYJ55\n5hliYmJoamri9OnTBAUFceDAAZf25dixY0RGRpKVlUV5eTmHDh1i165dNp/xdgcZvTOYlkHqeTCs\nzRGam5sxGo1cvXoVg8HAU089xfnz57ly5Qp5eXksXryY6dOnu7Q/etbzqAyY1ll5qamprFmzBlVV\neeWVV7SD9HqeNGfi4+PDhQsXCAwM5PDhw9TV1REeHo7RaEQI4ZZMtZqaGjIyMgBYtGiRZpdlQTrI\n6Je70TJIPd8tHR0dXL16lWXLlrF+/Xry8/MpKyuju7ubK1euuDxYgr717PFZssNl48aNZGRkMHfu\nXG7evInRaKSsrExrV1WVhQsXEhMTM+omzdlcv36dnp4e7aC0K3G0vzV58mRycnKYMWMGqqoSFxfH\n6dOntfauri6KiopsHGTy8vI87UC8zJJ1IVLPd4eqqly6dInw8HC3JOp5m55H5ROmPQNNmmU5Jjg4\n2GZ/BKSNlzX2S1uuxNH+1saNG7Vsvq6urn5V3qWDjHch9Tx8fHx83Dpmb9Ozxx8ruRsSExP55JNP\nbF7WNkxDTVpwcLA2aRL3Y+0A8sUXX2iVHiw4y0Gmu7ubjo4Op/RZ4jqknkc3etazLgKmI9w1aZL7\nJyUlhUuXLrFmzRqOHz9OVlYW0Le/derUKcLDwzUHGZPJ5NBBZihqa2s5duwY+/bto7Ky0hXDkLgQ\nqefRg571rNs9zJ6eHrZv305raysBAQHs37+f0NBQmySD9957j/Lycvz9/UlISCA5OVkXRU4l/+fs\n2bNERkbyww8/8Mgjj2A2m6mqqnLFvMk9TBcyHD0/++yzUss6Y8T1rKrqYC+v47PPPlN37Nihqqqq\nfvfdd+r69eu1tp9//lmNj49XOzs7VbPZrK5evVptb28fqa5KhqC2tlbdtWuXeubMGfX9999X6+vr\n1fb2djU/P1/t7OxUz58/78wfN5SWPOHlVUgt6wtP0LMukn6ciR6KnEpACEFlZSUvv/wykydPZtKk\nScyYMQOAJUuWUFVVRVVVFVFRUS6t6SkZOaSW9YOn6Fm3e5jDZaAip47aPLXIqbfT3NxMS0sL3d3d\nZGdnA33OKJYbZnV1NW+//TZr166VwVLHSC3rA0/SswyYduihyKkn8vnnn7N582aHbaWlpaxevRqj\n0WhzXmu43Lx5k4ceeojs7GwUReHo0aM0NTVpTxMzZ85k3759TJ9Q15cbAAACxElEQVQ+XbuBSvSH\n1LLr8FY9y4Bphx6KnHoar7/++oD2em1tbRQVFVFSUsKRI0fYv3+/Zhw9XMLCwpgwYQLQN58tLS30\n9vYybdo0oG/5bebMmQAu99WUjBxSy67Bm/Us9zDtuN8ip+oQWbYFBQWcOHGCSZMmAfDaa69pE69X\noqOjiY+Pp6SkpF/bQGWdZs+ePeyfZ3lSaGlp4aeffiI2NpaFCxcCffMzUOFsib6QWnYN3qxnGTDt\n8PHxITc31+aatf+ipULAQFRWVmI2mykuLqa2tpa8vDwbL8Xvv/+evXv3EhUV5fS+jzSeVtapubkZ\ngCeffBKQwdLbkFq+P6Se+yMDppMZLDMP+kT27rvv0traisFgIDMzcyS66RI8razTvHnzmDVrFj4+\nPjJYSu4Zb9YySD07YijjAsk9oijKYeCEEOLvd97/G5ghhLh9530O8A5wA/gYOCSEKB+Z3roPRVEW\nA+uEEGvsrv8K+Az4DRAI/BN4VAhhdn8vJZL/I7U8MN6qZ5nx4HxuANZGl74Wgd3hoBCiQwhxC/gU\nmO/W3nkIiqL8UVGU5UKIFuDPwFmgEviTXsQlGfVILd8l3qJn+YTpZBRFeQZYLoR4QVGUx4EcIcSy\nO23jgQvAI8B/gVLgL0KIv41YhyUSiUOkliX2yIDpZBRF8QEOAXPvXEoDYoBgIcQRRVHWAn8AeoB/\nCCFyB/g+vwXeFELE2V1/GsgBfgbeF0Iccc1IJBLvRmpZYo8MmB6IoihbgVTgphBigdV1P+AH+kT7\nX+ArYJkQonVEOiqRSAZFallfyCxZz+RfwCqgyO76r4FLQogbAIqinAUWAX91b/f6oyjKKiBRCLHW\nQdtbwJOAJb98pRBC+pBJvAGpZR0hA6YHIoT4SFGUqQ6axgP/sXrfCUxwT68G5o6Ifgd8N8BHYoDf\nCyFk9WaJVyG1rC/+B/YvfWd/irdKAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x116ecc898>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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f/vSnP+XCCy/kySef5KSTTuK9997jnXfeOSSiZUd7I/yAozAbhV//+tfMnTuX8847j9LS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\nYqwzz8SYO5fGlStxCgrw3Hkn1NTgVFai9O4Nhw7hvecetK5dxfWdPx/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f/xi1aScZef11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\nf8PRy7eGPxmyAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11c719c88>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Look at the projected dynamics under each model\n",
"for ii in range(N_used):\n",
" ini = np.where(zhat == ii)[0]\n",
" # Subsample accordingly\n",
" if ini.size > 500:\n",
" ini_inds = np.random.choice(ini.size, replace=False, size=500)\n",
" ini = ini[ini_inds]\n",
" \n",
" dydt_l = np.row_stack((np.zeros(D),\n",
" np.diff(y, axis=0)))\n",
"\n",
" Ai = perm_dynamics_distns[ii].A[:,:D]\n",
" bi = perm_dynamics_distns[ii].A[:,D] if affine else 0\n",
" dydt_m = y.dot(Ai.T) + bi - y\n",
"\n",
" fig = plt.figure(figsize=(8,4))\n",
" ax = fig.add_subplot(121, projection='3d')\n",
" ax.quiver(y[ini,0], y[ini,1], y[ini,2],\n",
" dydt_l[ini,0], dydt_l[ini,1], dydt_l[ini,2],\n",
" color=colors[ii], alpha=0.35,\n",
" arrow_length_ratio=0.25,\n",
" length=0.1) \n",
" ax.set_xlabel('$x_1$', fontsize=12, labelpad=10)\n",
" ax.set_ylabel('$x_2$', fontsize=12, labelpad=10)\n",
" ax.set_zlabel('$x_3$', fontsize=12, labelpad=10)\n",
" ax.set_xlim(-1.5, 1.5)\n",
" ax.set_ylim(-1.5, 1.5)\n",
" ax.set_zlim(-1.5, 1.5)\n",
" ax.set_title(\"True dynamics\", fontsize=14)\n",
" \n",
" ax = fig.add_subplot(122, projection='3d')\n",
" ax.quiver(y[ini,0], y[ini,1], y[ini,2],\n",
" dydt_m[ini,0], dydt_m[ini,1], dydt_m[ini,2],\n",
" color=colors[ii], alpha=0.35,\n",
" arrow_length_ratio=0.25,\n",
" length=0.1) \n",
" ax.set_xlabel('$x_1$', fontsize=12, labelpad=10)\n",
" ax.set_ylabel('$x_2$', fontsize=12, labelpad=10)\n",
" ax.set_zlabel('$x_3$', fontsize=12, labelpad=10)\n",
" ax.set_xlim(-1.5, 1.5)\n",
" ax.set_ylim(-1.5, 1.5)\n",
" ax.set_zlim(-1.5, 1.5)\n",
" ax.set_title(\"Linear approximation\", fontsize=14)\n",
"\n",
" \n",
" fig.savefig(\"lorenz_dynamics_{}.pdf\".format(ii))"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"(-1.5, 1.5)"
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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7ndLacozBQbSXXmL06Ek8TTtYtayEQ+dCDIyn+ESTn8OdYW5tKWF1jSud4NGy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\nbC/R1AAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11c7d8898>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"xgen, zgen = model.generate(3000)\n",
"zgen = relabel_by_usage(zgen)\n",
"zgen[0] = 0\n",
"zgen_cps = np.concatenate(([0], np.where(np.diff(zgen))[0]+1, [zgen.size]))\n",
"\n",
"fig = plt.figure(figsize=(4,4))\n",
"ax = fig.gca(projection='3d')\n",
"for start, stop in zip(zgen_cps[:-1], zgen_cps[1:]):\n",
" ax.plot(xgen[start:stop+1,0], \n",
" xgen[start:stop+1,1], \n",
" xgen[start:stop+1,2], \n",
" lw=1,\n",
" color=colors[zgen[start]],\n",
" alpha=0.5)\n",
" \n",
"ax.set_xlabel('$x_1$', fontsize=12, labelpad=10)\n",
"ax.set_ylabel('$x_2$', fontsize=12, labelpad=10)\n",
"ax.set_zlabel('$x_3$', fontsize=12, labelpad=10)\n",
"ax.set_xlim(-1.5, 1.5)\n",
"ax.set_ylim(-1.5, 1.5)\n",
"ax.set_zlim(-1.5, 1.5)"
]
}
],
"metadata": {
"anaconda-cloud": {},
"kernelspec": {
"display_name": "Python [Root]",
"language": "python",
"name": "Python [Root]"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.5.2"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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