ToyModel_LambdaDynamics.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook is designed to run lambda dynamics for the toy model where\n",
    "$$ R = e^{-\\lambda_1 n - \\lambda_2 f(n)}/Z $$\n",
    "and\n",
    "$$ f(n) = b_0 n - d_0 N/N_c n^2. $$\n",
    "\n",
    "The idea is to eventually test my derivation from information geometry against this lambda dynamics iteration. Note that the f function I've written I actually have changed a few times. This notebook has been run with N/N_c present and without it. Without it I think I can show lambda dynamics and the information geometry approach are the same, however with the N/N_c included I can't get it to work."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import lambda_dynamics_ToyModel as ld\n",
    "import DynaMETE_Rfunctions_ToyModel as rf\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Non exact parameters\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "b0        0.030000\n",
       "d0        0.000075\n",
       "Nc    10000.000000\n",
       "dtype: float64"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "dS    0.00000\n",
       "dN   -0.00012\n",
       "dtype: float64"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Exact parameters\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "b0        0.030000\n",
       "d0        0.000075\n",
       "Nc    10000.000000\n",
       "dtype: float64"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "dS    0.000000e+00\n",
       "dN    3.650018e-15\n",
       "dtype: float64"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Set up unperturbed parameters\n",
    "\n",
    "# state variables\n",
    "s = pd.Series(np.array([50, 10000]), index=['S','N']) #'S' = array.item(0), 'N' is array.item(1)\n",
    "\n",
    "# parameters. We will derive the precise ones below\n",
    "p_d = np.array([0.03,0.000075188,s['N']]) #s['N'] gives us array.item(1) (array is the first argument to pd.Series)\n",
    "p = pd.Series(p_d,index=['b0','d0','Nc']) #to assign the birth rate, unperturbed death rate, and carrying capacity\n",
    "\n",
    "# To get precise parameters\n",
    "pp = ld.get_ss_params(s,p)\n",
    "\n",
    "# Initial lambdas\n",
    "li = rf.lambda_i(s)\n",
    "# Display parameters and show derivatives are close enough to zero. (-900/2.5*10^5 is still small)\n",
    "print(\"Non exact parameters\")\n",
    "display(p)\n",
    "display(rf.get_dXdt(li,s,p))\n",
    "print(\"Exact parameters\")\n",
    "display(pp)\n",
    "display(rf.get_dXdt(li,s,pp))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lambda dynamics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#keep perturbing and unperturbing, then the steady state keeps increasing. \n",
    "#https://www.google.com/search?q=hysteresis&rlz=1C1CHBF_enUS926US926&oq=historesis\n",
    "#&aqs=chrome.1.69i57j0i10i433j0i10l8.3819j0j7&sourceid=chrome&ie=UTF-8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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   ],
   "source": [
    "# Test stability in steady state\n",
    "l_ss,s_ss,ds_ss = ld.iterate(1000,s,pp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ds_ss.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x17818a3bd00>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(l_ss[:,0],label='L1')\n",
    "plt.plot(l_ss[:,1],label='L2')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Perturbations\n",
    "Let's try $d_0 \\to 1.25 d_0$.\n",
    "Let's try going out to about $t = 10$ or 20 with a relatively small (maybe 0.1 or 0.05) iteration step. I used 0.2 above just to see roughly what happens, but with the perturbation I think a smaller step size would be more appropriate.\n",
    "\n",
    "I changed the perturbed $d_0$ to $0.00008$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "perturb = pp.copy()\n",
    "pdeathrate = (0.00008)/(0.000075188)\n",
    "perturb['d0'] = perturb['d0']*pdeathrate #setting new rate such that the death rate is 0.00008 in the first iteration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 1/200\n",
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      "Iteration 200/200\n"
     ]
    }
   ],
   "source": [
    "l_d0,s_d0,ds_d0 = ld.iterate(200,s,perturb, dt=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plotting the N-independent transition function\n",
    "s_d0['N'].plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ds_d0.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1781b916e50>"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(l_d0[:,0],label='L1')\n",
    "plt.plot(l_d0[:,1],label='L2')\n",
    "plt.legend()\n",
    "#Closest to figure 2 of entropic dynamics paper"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1781cbb3b50>]"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# I expected l2 to be < 0 because of the n^2 term. What does R look like?\n",
    "nr = np.arange(s['N'])+1\n",
    "plt.plot(nr,rf.R(nr,l_d0[200],s_d0.iloc[200],perturb))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1781b465280>]"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Setting up the simple logistic model - parameters\n",
    "\n",
    "big_n = s['N']/s['S'] \n",
    "big_n_copy = s['N']/s['S']\n",
    "f_n = 2*(big_n ** 2) - (big_n)\n",
    "birth_rate = pp['b0']\n",
    "array_of_ns = [50 * big_n]\n",
    "perturbation = 0.00008\n",
    "\n",
    "#iterations\n",
    "\n",
    "for i in np.arange(200):\n",
    "    f_n = 2 * (big_n ** 2) - (big_n)\n",
    "    growth = big_n * birth_rate\n",
    "    decline = perturbation * f_n * big_n/big_n_copy\n",
    "    big_n = big_n + growth - decline\n",
    "    true_big_n = 50 * big_n\n",
    "    array_of_ns = np.append(array_of_ns, true_big_n)\n",
    "    perturbation = perturbation * pdeathrate\n",
    "    \n",
    "plt.plot(array_of_ns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [],
   "source": [
    "#plotting the N-independent transition function(without N/Nc term)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(9000.0, 10000.0)"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plotting both the logistic function and the N-independent transition functions together:\n",
    "plt.plot(array_of_ns,label='Logistic Function')\n",
    "plt.plot(s_d0['N'],label='N-dependent transition function')\n",
    "plt.legend()\n",
    "plt.ylim([9000, 10000])\n",
    "\n",
    "#Compared with Figure 1 of Entropic Dynamics and Updating of Lagrange Multipliers Paper"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Geometry part\n",
    "Now import the geometry iteration and see if it's the same"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "import geometry_ToyModel as gtm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 1/10\n",
      "Iteration 2/10\n",
      "Iteration 3/10\n",
      "Iteration 4/10\n",
      "Iteration 5/10\n",
      "Iteration 6/10\n",
      "Iteration 7/10\n",
      "Iteration 8/10\n",
      "Iteration 9/10\n",
      "Iteration 10/10\n"
     ]
    }
   ],
   "source": [
    "# Test stability in steady state\n",
    "l_ssg,s_ssg,ds_ssg = gtm.iterate(10,s,pp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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nmWWvBc5N8igTp87OSPKvgx1p1o0D41W18zutTzMR9vlsFfD9qtpSVU8DNwGvGfBMc+VnSQ4H6P25uYtFWwr5t4DjkixL8jwmfjjy+QHPNKuShIlzpw9U1T8Mep7ZVlXvraqRqlrKxN/v16pqXh+pVdVPgR8lOb636Uzg/gGONBd+CLw6yaLev/Ezmec/4N3F54E1vctrgM91seiCLhaZC1W1I8k7gNuY+Cn3hqq6b8BjzbbXAm8D7kny7d62y6rqS4MbSbPgncANvQOUR4C/GvA8s6qqvpnk08BdTLwy627m4Vv1k3wKOB04JMk4cAVwNbAxyduZ+IL2pk725Vv0JaltLZ1akSRNwpBLUuMMuSQ1zpBLUuMMuSQ1zpBLUuMMuSQ17v8B30aRREqj3ooAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ds_ssg.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x152359d128>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(l_ssg[:,0],label='L1')\n",
    "plt.plot(l_ssg[:,1],label='L2')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "Iteration 958/1000\n",
      "Iteration 959/1000\n",
      "Iteration 960/1000\n",
      "Iteration 961/1000\n",
      "Iteration 962/1000\n",
      "Iteration 963/1000\n",
      "Iteration 964/1000\n",
      "Iteration 965/1000\n",
      "Iteration 966/1000\n",
      "Iteration 967/1000\n",
      "Iteration 968/1000\n",
      "Iteration 969/1000\n",
      "Iteration 970/1000\n",
      "Iteration 971/1000\n",
      "Iteration 972/1000\n",
      "Iteration 973/1000\n",
      "Iteration 974/1000\n",
      "Iteration 975/1000\n",
      "Iteration 976/1000\n",
      "Iteration 977/1000\n",
      "Iteration 978/1000\n",
      "Iteration 979/1000\n",
      "Iteration 980/1000\n",
      "Iteration 981/1000\n",
      "Iteration 982/1000\n",
      "Iteration 983/1000\n",
      "Iteration 984/1000\n",
      "Iteration 985/1000\n",
      "Iteration 986/1000\n",
      "Iteration 987/1000\n",
      "Iteration 988/1000\n",
      "Iteration 989/1000\n",
      "Iteration 990/1000\n",
      "Iteration 991/1000\n",
      "Iteration 992/1000\n",
      "Iteration 993/1000\n",
      "Iteration 994/1000\n",
      "Iteration 995/1000\n",
      "Iteration 996/1000\n",
      "Iteration 997/1000\n",
      "Iteration 998/1000\n",
      "Iteration 999/1000\n",
      "Iteration 1000/1000\n"
     ]
    }
   ],
   "source": [
    "l_d0g,s_d0g,ds_d0g = gtm.iterate(1000,s,perturb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ds_d0g.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1523601f98>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(l_d0g[:,0],label='L1')\n",
    "plt.plot(l_d0g[:,1],label='L2')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "s_d0g.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This isn't quite the same, but this was either ignoring d^2 N/dt^2 or approximating it badly as <df/dt>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Now check Brute Force"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "import brute_force_ToyModel as bf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 1/10\n",
      "Iteration 2/10\n",
      "Iteration 3/10\n",
      "Iteration 4/10\n",
      "Iteration 5/10\n",
      "Iteration 6/10\n",
      "Iteration 7/10\n",
      "Iteration 8/10\n",
      "Iteration 9/10\n",
      "Iteration 10/10\n"
     ]
    }
   ],
   "source": [
    "# Test stability in steady state\n",
    "l_ssbf,s_ssbf,ds_ssbf = bf.iterate(10,s,pp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x15239266d8>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(l_ssbf[:,0],label='L1')\n",
    "plt.plot(l_ssbf[:,1],label='L2')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "Iteration 957/1000\n",
      "Iteration 958/1000\n",
      "Iteration 959/1000\n",
      "Iteration 960/1000\n",
      "Iteration 961/1000\n",
      "Iteration 962/1000\n",
      "Iteration 963/1000\n",
      "Iteration 964/1000\n",
      "Iteration 965/1000\n",
      "Iteration 966/1000\n",
      "Iteration 967/1000\n",
      "Iteration 968/1000\n",
      "Iteration 969/1000\n",
      "Iteration 970/1000\n",
      "Iteration 971/1000\n",
      "Iteration 972/1000\n",
      "Iteration 973/1000\n",
      "Iteration 974/1000\n",
      "Iteration 975/1000\n",
      "Iteration 976/1000\n",
      "Iteration 977/1000\n",
      "Iteration 978/1000\n",
      "Iteration 979/1000\n",
      "Iteration 980/1000\n",
      "Iteration 981/1000\n",
      "Iteration 982/1000\n",
      "Iteration 983/1000\n",
      "Iteration 984/1000\n",
      "Iteration 985/1000\n",
      "Iteration 986/1000\n",
      "Iteration 987/1000\n",
      "Iteration 988/1000\n",
      "Iteration 989/1000\n",
      "Iteration 990/1000\n",
      "Iteration 991/1000\n",
      "Iteration 992/1000\n",
      "Iteration 993/1000\n",
      "Iteration 994/1000\n",
      "Iteration 995/1000\n",
      "Iteration 996/1000\n",
      "Iteration 997/1000\n",
      "Iteration 998/1000\n",
      "Iteration 999/1000\n",
      "Iteration 1000/1000\n"
     ]
    }
   ],
   "source": [
    "l_d0bf,s_d0bf,ds_d0bf = bf.iterate(1000,s,perturb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ds_d0bf.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1523a4c128>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(l_d0bf[:,0],label='L1')\n",
    "plt.plot(l_d0bf[:,1],label='L2')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "s_d0bf.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Discussion\n",
    "So in the end lambda dynamics is still approximating the brute force iteration, and the information geometry approach is not the same.\n",
    "\n",
    "However, it's still unclear to me that we know that lambda dynamics is the correct iteration scheme over the information geometry approach at all. I was just really hoping they would be the same."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1523cbd780>]"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Look at all three dN plots\n",
    "plt.plot(ds_d0['dN'])\n",
    "plt.plot(ds_d0g['dN'])\n",
    "plt.plot(ds_d0bf['dN'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1523d472b0>]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Let's try to look at d^2N/dt^2, since that may be where the difference is coming.\n",
    "plt.plot(np.gradient(ds_d0bf['dN']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Now calculate cov(f,f) dl2/dt + cov(n,f) dl1/dt at each time step\n",
    "dn2t = []#np.zeros([len(ds_d0bf['dN'])])\n",
    "dl1t = np.gradient(l_d0bf[:,0])\n",
    "dl2t = np.gradient(l_d0bf[:,1])\n",
    "for lt,st,dst,dl1tt,dl2tt in zip(l_d0bf,s_d0bf.iterrows(),ds_d0bf.iterrows(),dl1t,dl2t):\n",
    "    zt = rf.mean_pow(0,lt,st[1],perturb)\n",
    "    covff = rf.cov(rf.f,rf.f,lt,st[1],perturb,zt)\n",
    "    covnf = rf.cov(lambda n,s,p: n,rf.f,lt,st[1],perturb,zt)\n",
    "    mdfdt = rf.mean(rf.dfdt,lt,st[1],perturb,dst[1],z=zt)\n",
    "    covfdf = rf.cov(lambda n,s,p,ds: rf.f(n,s,p),rf.dfdt,lt,st[1],perturb,zt,dst[1])\n",
    "    #dn2t.append(-covnf*dl1tt-covff*dl2tt - covfdf*lt[1] + mdfdt)\n",
    "    dn2t.append(-covnf*dl1tt-covff*dl2tt)# - covfdf*lt[1] + mdfdt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x15240643c8>]"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(dn2t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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     ]
    }
   ],
   "source": [
    "# What about a finer iteration?\n",
    "l_d0f,s_d0f,ds_d0f = ld.iterate(5000,s,perturb,dt=0.01)\n",
    "l_d0gf,s_d0gf,ds_d0gf = gtm.iterate(5000,s,perturb,dt=0.01)\n",
    "l_d0bff,s_d0bff,ds_d0bff = bf.iterate(5000,s,perturb,dt=0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1524843400>"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# These are the same! The error in lambda dynamics is just because I forgot to redo dfdt there.\n",
    "plt.plot(np.arange(5001)*0.01,ds_d0f['dN'],label='lambda')\n",
    "plt.plot(np.arange(5001)*0.01,ds_d0gf['dN'],label='geom.')\n",
    "plt.plot(np.arange(5001)*0.01,ds_d0bff['dN'],label='brute')\n",
    "plt.plot(np.arange(251)*0.2,ds_d0g['dN'][0:251],label='geom. large')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#NOTES\n",
    "#d = 0.03/10000, perturbed d = 0.03/10000 (0.00008/0.000075188)\n",
    "#pranavm@berkeley.edu\n",
    "#0.03 * 200 / (2 * (200 ** 2) - 200)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}