study_ode.ipynb

{
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  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "vscode": {}
   },
   "outputs": [],
   "source": [
    "%autoreload 2\n",
    "import ajcs\n",
    "import sqra\n",
    "import optim\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import ode "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "nx = 5\n",
    "ny = 5\n",
    "\n",
    "\n",
    "U = np.zeros((ny,nx))\n",
    "s = sqra.sqra2d(U)\n",
    "s.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [],
   "source": [
    "nt = 3\n",
    "dt = 1\n",
    "ts = ([dt] * nt)\n",
    "\n",
    "o=optim.SqraOptimNonaut(s, ts, penalty = 0.001)\n",
    "j=o.j\n",
    "\n",
    "Qs = [Q.toarray() for Q in j.Q]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "80.5 ms ± 5.06 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n60.7 ms ± 6.08 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n170 ms ± 24.2 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
    }
   ],
   "source": [
    "Qs = [Q.toarray() for Q in j.Q] \n",
    "%timeit ode.finite_time_hitting_probs(j.Q, j.dt)# ode sparse\n",
    "%timeit ode.finite_time_hitting_probs(Qs, j.dt) # ode dense\n",
    "%timeit j.finite_time_hitting_probs() # galerkin"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "0.6026131922163003"
     },
     "metadata": {},
     "execution_count": 154
    }
   ],
   "source": [
    "def error(nt, dt):\n",
    "    ts = ([dt]*nt)\n",
    "    o = optim.SqraOptimNonaut(s, ts)\n",
    "    j = o.j\n",
    "\n",
    "    hpo = ode.finite_time_hitting_probs(j.Q, j.dt)\n",
    "    hpj = j.finite_time_hitting_probs()\n",
    "    return np.linalg.norm(hpo-hpj), hpo, hpj, j\n",
    "\n",
    "error(3,1)[0]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "[<matplotlib.lines.Line2D at 0x1282acd90>]"
     },
     "metadata": {},
     "execution_count": 165
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "dts = np.logspace(0.1, 2, 5)\n",
    "plt.plot(dts, [error(10,dt)[0] for dt in dts])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Text(0.5, 0, 'n')"
     },
     "metadata": {},
     "execution_count": 171
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "nt = np.arange(1,20)\n",
    "plt.plot(nt, [error(n, 1/n)[0] for n in nt])\n",
    "plt.xlabel(\"n\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {},
   "outputs": [],
   "source": [
    "e, hpo, hpj, j = error(30, 1/30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "<matplotlib.colorbar.Colorbar at 0x127359100>"
     },
     "metadata": {},
     "execution_count": 173
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 2 Axes>",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.imshow(hpo - hpj)\n",
    "plt.colorbar()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.8.5 64-bit",
   "name": "python_defaultSpec_1600700162263"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5-final"
  },
  "orig_nbformat": 2
 },
 "nbformat": 4,
 "nbformat_minor": 2
}