{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import os.path\n",
    "import scipy.linalg\n",
    "import scipy.integrate\n",
    "import scipy.signal\n",
    "import matplotlib.cm"
   ]
  },
  {
   "attachments": {
    "lec21_Goodwin.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Goodwin's Oscillator\n",
    "\n",
    "We will examine how the amplitude and period are affected by each parameter in the system. Each state is produced at a rate proportional to $\\alpha_{1,2,3}$ and destroyed at a rate proportional to $\\gamma_{1,2,3}$. Z down-regulates X with activation threshold $K$ and Hill coefficient $n$.\n",
    "\n",
    "<div style=\"max-width:200px;margin-left: auto; margin-right: auto;\">\n",
    "    \n",
    "![lec21_Goodwin.png](attachment:lec21_Goodwin.png)\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Copy code from Lecture 22.\n",
    "\n",
    "Copy-paste the model code, get_period, simulate_goodwin, and goodwin_period."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Write code here."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Write a function to compute the amplitude of the Goodwin oscillator\n",
    "\n",
    "The input should be the paras and which_state. which_state should be the index of the state for which we want to compute the amplitude. If which_state is -1, then compute the amplitude of all the states, and return the sum."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def goodwin_amplitude( params, which_state=-1 ):\n",
    "    \"\"\" Return the amplitude of the given state or of the sum of all three states\n",
    "        If which_state  == -1, then return the sum of all 3.\n",
    "        Otherwise, which_state should be 0 (for M), 1 (for P), or 2 (for I)\n",
    "    \"\"\"\n",
    "    pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compute the period and amplitude of the Goodwin oscillator with published parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha_1 = 1\n",
    "K = 0.61\n",
    "n = 11\n",
    "gamma_1 = 0.15\n",
    "alpha_2 = 1\n",
    "gamma_2 = 0.15\n",
    "alpha_3 = 1\n",
    "gamma_3 = 0.25\n",
    "\n",
    "pub_params = [alpha_1,K,n,gamma_1,alpha_2,gamma_2,alpha_3,gamma_3]\n",
    "param_names = ['alpha_1','K','n','gamma_1','alpha_2','gamma_2','alpha _3','gamma_3']\n",
    "\n",
    "per = goodwin_period( pub_params )\n",
    "print(\"period\", per)\n",
    "amp1 = goodwin_amplitude( pub_params, which_state = 0 )\n",
    "print( \"amplitude of X\", amp1)\n",
    "amp2 = goodwin_amplitude( pub_params, which_state = 1 )\n",
    "print( \"amplitude of Y\", amp2)\n",
    "amp3 = goodwin_amplitude( pub_params, which_state = 2 )\n",
    "print( \"amplitude of Z\", amp3)\n",
    "ampTot = goodwin_amplitude( pub_params, which_state = -1 )\n",
    "print( \"amplitude of X+Y+Z\", ampTot)\n",
    "\n",
    "sol = simulate_goodwin( pub_params, tStop=4*24)\n",
    "plt.plot( sol.t, sol.y.T );\n",
    "plt.legend( [\"X\",\"Y\",\"Z\"]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Copy your sensitivity function here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sensitivity( fcn, ref_params, frac_change ):\n",
    "    \"\"\"\n",
    "    fcn should be a handle to a function that takes a parameter set as input\n",
    "        and returns a scalar as output.\n",
    "    ref_params should be a 1D ndarray with the parameter set\n",
    "    frac_change is the perturbation size, as a scale (i.e. the fraction by which you want to adjust the parameter by)\n",
    "    \"\"\"\n",
    "    pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compute the sensitivity of the amplitude of the first state \n",
    "\n",
    "Compute the sensitivity of X's amplitude to 5% perturbations in each of the parameters.\n",
    "\n",
    "To which parameters is the amplitude sensitive? To which parameters is it insensitive?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Write code here."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And plot it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "plt.figure(figsize=(12,4))\n",
    "plt.plot( np.arange(len(pub_params)), Srel, '*')\n",
    "plt.plot( plt.xlim(), [0, 0], 'k');\n",
    "plt.xticks( ticks=np.arange(len(param_names)), labels=param_names);\n",
    "plt.title( \"Sensitivity of X's amplitude to parametric perturbation\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulate the model to visualize\n",
    "\n",
    "The sensitivity measure tells us that increasing the rate of degradation of X, we should see an increase in X's amplitude. Let's verify that nothing funky is going on. We will use a perturbation size of 10% (which is still small, but will reveal the changes more clearly than 5% would)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha_1 = 1\n",
    "K = 0.61\n",
    "n = 11\n",
    "gamma_1 = 0.15\n",
    "alpha_2 = 1\n",
    "gamma_2 = 0.15\n",
    "alpha_3 = 1\n",
    "gamma_3 = 0.25\n",
    "\n",
    "params = [alpha_1,K,n,gamma_1,alpha_2,gamma_2,alpha_3,gamma_3]\n",
    "sol = simulate_goodwin( params, tStop=24*4 )\n",
    "plt.plot( sol.t, sol.y.T );\n",
    "plt.gca().set_prop_cycle(None)\n",
    "\n",
    "\n",
    "params = [alpha_1*1.1,K,n,gamma_1,alpha_2,gamma_2,alpha_3,gamma_3]\n",
    "sol = simulate_goodwin( params, tStop=24*4 )\n",
    "plt.plot( sol.t, sol.y.T, '--' );\n",
    "plt.gca().set_prop_cycle(None)\n",
    "\n",
    "\n",
    "params = [alpha_1,K,n,gamma_1*1.1,alpha_2,gamma_2,alpha_3,gamma_3]\n",
    "sol = simulate_goodwin( params, tStop=24*4 )\n",
    "plt.plot( sol.t, sol.y.T, ':' );\n",
    "\n",
    "plt.legend( ['X (ref)','Y (ref)','Z (ref)',\n",
    "             'X (larger alpha 1)','Y (larger alpha 1)','Z (larger alpha 1)',\n",
    "             'X (larger gamma 1)','Y (larger gamma 1)','Z (larger gamma 1)']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Visualize the effects of perturbing the Hill coefficient n by 10%."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Write code here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compare amplitude sensitivities across the three states\n",
    "\n",
    "Compute and plot amplitude sensitivities for each state."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "state_names = ['X','Y','Z']\n",
    "plt.figure(figsize=(12,4))\n",
    "legs = []\n",
    "\n",
    "for i in range(len(state_names)):\n",
    "    Srel = sensitivity( lambda p: goodwin_amplitude( p, which_state = i), np.array(pub_params), 0.05 )\n",
    "    plt.plot( np.arange(len(pub_params)), Srel, '*')\n",
    "    plt.xticks( ticks=np.arange(len(param_names)), labels=param_names);\n",
    "    plt.title( \"Sensitivity of amplitude to parametric perturbation\" );\n",
    "    legs.append( \"Sensitivity of %s amp\" % state_names[i])\n",
    "plt.plot( plt.xlim(), [0, 0], 'k');\n",
    "plt.legend( legs );"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compare the amplitude sensitivities to the period sensitivities\n",
    "\n",
    "Ok, I really just mean plot the period sensitivities so that we can look at the two in close proximity. What are the similarities and differences?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Srel = sensitivity( goodwin_period, np.array(pub_params), 0.05 )\n",
    "plt.figure(figsize=(12,4))\n",
    "plt.plot( np.arange(len(pub_params)), Srel, '*')\n",
    "plt.plot( plt.xlim(), [0, 0], 'k');\n",
    "plt.xticks( ticks=np.arange(len(param_names)), labels=param_names);\n",
    "plt.title( \"Sensitivity of Period to Parametric Perturbation\");"
   ]
  }
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