pwchs param fitting diff time intervals.ipynb

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 "cells": [
  {
   "cell_type": "markdown",
   "id": "15a95e58-e03e-447f-b1c7-bb56215db822",
   "metadata": {},
   "source": [
    "## Imports and Needed functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "0490082b-0f22-423f-b1f9-8baa2f528a7a",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "#!/usr/bin/env python3\n",
    "# -*- coding: utf-8 -*-\n",
    "\"\"\"\n",
    "Created on Dec 6, 2023\n",
    "\n",
    "@author: Jamiree Harrison\n",
    "         https://github.com/Jamiree\n",
    "         jamiree@ucsb.edu\n",
    "\n",
    "Purpose of script: \n",
    "Simulates hybrid promoter data. \n",
    "Produces hybrid promoter model parameters that fit the simulated data. \n",
    "The assumed model is that of protein synthesis, we simply fit the parameters \n",
    "of this model at different time intervals. \n",
    "\n",
    "\"\"\"\n",
    "\n",
    "# Imports\n",
    "import numpy as np\n",
    "from numpy import linalg as LA\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "import random\n",
    "import ruptures as rpt\n",
    "from scipy.signal import savgol_filter\n",
    "from mpl_toolkits import mplot3d\n",
    "from random import gauss\n",
    "from scipy.integrate import odeint\n",
    "from scipy.integrate import solve_ivp\n",
    "from scipy.optimize import curve_fit\n",
    "from scipy.optimize import minimize\n",
    "import os"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1967d225-ea9a-4828-8d51-8dd2decab51a",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Backend Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "2c306c16-c10f-4479-9548-0fdd05f7b591",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "############################################################ \n",
    "\n",
    "''' Uses binary segmentation to detect when a signal switches\n",
    "    \n",
    "    Documentation: \n",
    "    https://centre-borelli.github.io/ruptures-docs/user-guide/detection/binseg/\n",
    "\n",
    "'''\n",
    "def bkpt_binseg(signal, model, sigma): \n",
    "    \n",
    "    n = len(signal)\n",
    "    \n",
    "    # Point Detection:\n",
    "    # here we choose the Least-squares estimate for changes in autoregressive (ar) coefficients\n",
    "    algo = rpt.Binseg(model=model).fit(signal)\n",
    "    \n",
    "    # manually select how many breakpoints to select\n",
    "    if type(sigma) == str:\n",
    "        sigma = int(sigma)\n",
    "        my_bkps = algo.predict(n_bkps=sigma)\n",
    "        \n",
    "        # show results\n",
    "        # rpt.show.display(signal, my_bkps, figsize=(10, 6))\n",
    "        # plt.show()\n",
    "        \n",
    "    else:\n",
    "    \n",
    "        ## if we want to treat the number of change points as unknown, use\n",
    "        ## one of the following (note: sigma is the standard deviation of the noise. ) : \n",
    "\n",
    "        ## specify a penalty using the pen parameter\n",
    "        # sigma = 0.1\n",
    "        # dim = 1\n",
    "        # my_bkps = algo.predict(pen=np.log(n) * sigma**2)\n",
    "\n",
    "        ## specify a threshold on the residual norm using epsilon\n",
    "        ## note that sigma needs to be small for non-noisy data\n",
    "        my_bkps = algo.predict(epsilon = n * sigma**2)\n",
    "\n",
    "        # show results\n",
    "        # rpt.show.display(signal, my_bkps, figsize=(10, 6))\n",
    "        # plt.show()\n",
    "\n",
    "    return my_bkps\n",
    "\n",
    "\n",
    "############################################################ \n",
    "\n",
    "''' Detects the times that a signal \"switches\"\n",
    "\n",
    "inputs:  data                            | array of size (num_time_pts, num_states)\n",
    "             - each column of the data array is the evolution of that state in time\n",
    "         t                               | array of size (num_time_pts, 1)\n",
    "             - time vector\n",
    "             \n",
    "         switch_gap                      | integer\n",
    "             - must define the number of indices that is allowable\n",
    "                between switches.  If switch_gap is zero, then you \n",
    "                cannot have consecutive time points being switch times\n",
    "        \n",
    "         ls_model                           | str\n",
    "            - pick from the following least-squares estimates:\n",
    "                \"l1\", \"l2\", \"rbf\", \"linear\", \"normal\", \"ar\",...\n",
    "        \n",
    "         \\\\sigma   (type determined)     | float \n",
    "                                 | (if the number of switches is\n",
    "                                 | to be determined by algorithm)\n",
    "            - standard deviation of the noise in the data\n",
    "         \\\\sigma   (type determined)     | str \n",
    "                                | (if the number of switches is\n",
    "                                | to be input by the user)\n",
    "            - standard deviation of the noise in the data\n",
    "                \n",
    "outputs: t_switch_index         | array of size (num_switches, 0) \n",
    "         num_switches           | integer\n",
    "         num_time_intervals     | integer\n",
    "         time_of_switch         | array of size (num_switches, 0) \n",
    "'''\n",
    "def switch_time_detect(data, t, switch_gap, ls_model, sigma):\n",
    "    \n",
    "    num_time_pts, num_states = np.shape(data)\n",
    "    \n",
    "    true_t_switch_index = np.array([], dtype=int)\n",
    "    \n",
    "    # iterate over all states of system\n",
    "    for j in range(num_states):\n",
    "        \n",
    "        # detects switch time using binary segmentation \n",
    "        t_switch_index = bkpt_binseg(data[:,j], ls_model, sigma)\n",
    "\n",
    "        # the following code removes switch indices that are too close for each state\n",
    "        result = [t_switch_index[0]]\n",
    "        for i in range(1, len(t_switch_index)):\n",
    "            # makes it so that consecutive switches are not too close\n",
    "            if t_switch_index[i] > t_switch_index[i - 1] + switch_gap:\n",
    "                # Remove the current indexed entry\n",
    "                result = np.append(result, t_switch_index[i])\n",
    "\n",
    "        # makes it so that the last time point cannot be a switch time\n",
    "        if result[-1] == len(t):\n",
    "            result = np.delete(result, -1)\n",
    "            \n",
    "        \n",
    "        # indices of t where state switching occurs in the j-th state\n",
    "        t_switch_index = result \n",
    "        \n",
    "        # print('switches = ',t_switch_index)\n",
    "        \n",
    "        # only takes switches not already detected from previous states\n",
    "        for entry in t_switch_index:\n",
    "            if entry not in true_t_switch_index:\n",
    "                true_t_switch_index = np.append(true_t_switch_index, entry)\n",
    "        true_t_switch_index = np.sort(true_t_switch_index)\n",
    "\n",
    "        # print('time indices of switches: ', true_t_switch_index)\n",
    "        \n",
    "    # checks if there are no switches\n",
    "    if len(true_t_switch_index) == 0:\n",
    "\n",
    "        num_switches = 0\n",
    "        time_of_switch = np.zeros((num_switches,))\n",
    "        num_time_intervals = num_switches + 1\n",
    "        print('no switches detected in signal given chosen parameters')\n",
    "        \n",
    "        return true_t_switch_index, num_switches, num_time_intervals, time_of_switch\n",
    "            \n",
    "    else:\n",
    "        result = [true_t_switch_index[0]]\n",
    "        for i in range(1, len(true_t_switch_index)):\n",
    "            # makes it so that consecutive switches are not too close\n",
    "            if true_t_switch_index[i] > true_t_switch_index[i - 1] + switch_gap:\n",
    "                # Remove the current indexed entry\n",
    "                result = np.append(result, true_t_switch_index[i])\n",
    "                \n",
    "        # makes it so that the last time point cannot be a switch time            \n",
    "        if result[-1] == len(t):\n",
    "            result = np.delete(result, -1)\n",
    "\n",
    "        true_t_switch_index = result\n",
    "               \n",
    "    num_switches = len(true_t_switch_index)\n",
    "    \n",
    "    if isinstance(sigma, str) and int(sigma) != num_switches:\n",
    "        print('expected switch number not equal to detected number of switches')\n",
    "\n",
    "\n",
    "    # gets times of switches\n",
    "    time_of_switch = np.zeros((num_switches,))\n",
    "    for i in range(num_switches):\n",
    "        time_of_switch[i] = t[true_t_switch_index[i]]\n",
    "\n",
    "    print('times_of_switches = ', time_of_switch)\n",
    "\n",
    "    \n",
    "    # plt.figure()\n",
    "    # plt.plot(t, data[:,num_states//2], 'g', label='x(t)')\n",
    "    # plt.plot(t[true_t_switch_index], data[true_t_switch_index, num_states//2], 'ro')\n",
    "    # plt.xlabel('time')\n",
    "    # plt.ylabel('cross section of u(t,x) for some x')\n",
    "    # plt.title('switch times found')\n",
    "    # plt.savefig(os.path.join(os.getcwd(), 'switch times.svg'), format='svg')\n",
    "    # plt.show()\n",
    "        \n",
    "    num_time_intervals = num_switches + 1\n",
    "    \n",
    "#     print('num_switches =', num_switches)\n",
    "#     print('num_time_intervals =', num_time_intervals)\n",
    "    \n",
    "    return true_t_switch_index, num_switches, num_time_intervals, time_of_switch\n",
    "\n",
    "    \n",
    "############################################################ \n",
    "\n",
    "''' Breaks data up into sections based on the \n",
    "    times of the switches\n",
    "\n",
    "inputs:  data                   | array of size (num_time_pts, num_states)\n",
    "             - each column of the data array is the evolution of that state in time\n",
    "             \n",
    "         t                      | array of size (num_time_pts, 1)\n",
    "             - time vector\n",
    "        \n",
    "         num_switches           | integer\n",
    "        \n",
    "         t_switch_index         | array of size (num_switches, 0) \n",
    "                     \n",
    "outputs: data_intervals_dict    | dictionary of data over time intervals\n",
    "            - example: data_intervals_dict['data_t0']\n",
    "                       gives the data over the first time interval\n",
    "                       \n",
    "         time_intervals_dict    | dictionary of time intervals\n",
    "            - example: time_intervals_dict['t0']\n",
    "                       gives the first time interval\n",
    "'''\n",
    "def data_segementation(data, t, num_switches, t_switch_index):\n",
    "    \n",
    "    # instantiate dictionary of data over the time intervals\n",
    "    data_intervals_dict = {}\n",
    "\n",
    "    # instantiate dictionary of the time intervals\n",
    "    time_intervals_dict = {}\n",
    "\n",
    "    # used to iterate through every time point\n",
    "    temp_index = 0  \n",
    "\n",
    "    # iterates through time up to the last switch time\n",
    "    for i in range(num_switches):\n",
    "        \n",
    "        key = f\"t{i}\"\n",
    "        \n",
    "        # data over the i-th time interval\n",
    "        data_intervals_dict[key] = data[temp_index:t_switch_index[i] , :]\n",
    "\n",
    "        # the i-th time interval\n",
    "        time_intervals_dict[key] = t[temp_index:t_switch_index[i]]\n",
    "\n",
    "        # updtate the index of the current time point\n",
    "        temp_index = t_switch_index[i]\n",
    "\n",
    "    # data over the last time interval\n",
    "    key = f\"t{num_switches}\"\n",
    "    data_intervals_dict[key] = data[temp_index: , :]\n",
    "\n",
    "    # last time interval\n",
    "    time_intervals_dict[key] = t[temp_index:]\n",
    "    \n",
    "    return data_intervals_dict, time_intervals_dict\n",
    "\n",
    "############################################################ \n",
    "\n",
    "''' Fits the params of the model over each time interval\n",
    "\n",
    "inputs:  data_intervals_dict    | dictionary of semented data\n",
    "             \n",
    "         time_intervals_dict    | dictionary of semented time vector\n",
    "             - time vector\n",
    "        \n",
    "         dt                     | float\n",
    "             - sampling time, i.e. difference between time points\n",
    "             \n",
    "         params_init            | array of size (num_model_params, )\n",
    "         bounds                 | see documentation for scipy optimize\n",
    "          https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html\n",
    "         \n",
    "         num_time_intervals.    | float\n",
    "                     \n",
    "outputs: params_dict            | dictionary of parameter values over \n",
    "                                | each time interval\n",
    "\n",
    "         param_matrix           | array of size (num_model_params, num_time_intervals)\n",
    "         param_time             | dictionary of parameter values for each point in time\n",
    "\n",
    "'''\n",
    "def fit_params(data_intervals_dict, time_intervals_dict, dt, params_init, bounds, \n",
    "               num_time_intervals, num_static_params):\n",
    "    \n",
    "    num_model_params = len(params_init)\n",
    "    \n",
    "    # matrix of params\n",
    "    param_matrix = np.zeros((num_model_params, num_time_intervals))\n",
    "\n",
    "    # dictionary of params\n",
    "    params_dict = {}\n",
    "\n",
    "    for i in range(num_time_intervals):\n",
    "\n",
    "        # Minimize the objective function over each time domain\n",
    "\n",
    "        key = f\"t{i}\"\n",
    "        \n",
    "        result = minimize(objective, \n",
    "                         params_init, \n",
    "                         args=(data_intervals_dict[key], \n",
    "                               dt, time_intervals_dict[key]), \n",
    "                         method='Nelder-Mead', \n",
    "                         bounds = bounds)\n",
    "        \n",
    "        params_approx = result.x\n",
    "\n",
    "        params_dict[key] = params_approx\n",
    "        param_matrix[:,i] = params_approx\n",
    "\n",
    "        # Print the estimated parameters\n",
    "        # print(\"Estimated parameters for the \" + str(i+1)  +\"th time interval:\")\n",
    "\n",
    "        # Sets initial parameter value guesses for next time interval\n",
    "        # Note that we use the results from the first time domain fit as our new\n",
    "        # initial guesses\n",
    "        params_init = result.x\n",
    "        \n",
    "        if i == 0: \n",
    "            # first set of params found over first time interval\n",
    "            first_params = result.x\n",
    "            \n",
    "            num_vary_params = num_model_params - num_static_params\n",
    "            \n",
    "            # if no bounds are selected for the params, then make it so that\n",
    "            # the time-varying params are able to vary, while the static\n",
    "            # params must stay the same.\n",
    "            if bounds == None:\n",
    "                bounds = []\n",
    "                # set bounds for params in the form of : (lower, upper)\n",
    "                for j in range(num_vary_params):\n",
    "                    bounds.append((-np.inf , np.inf)) \n",
    "                \n",
    "                # makes it so that the static params do not change\n",
    "                for j in range(num_static_params):\n",
    "                    bounds.append((first_params[j + num_vary_params], first_params[j + num_vary_params]))\n",
    "                    \n",
    "            else: \n",
    "                \n",
    "                # if bounds are selected for the params, then make it so that\n",
    "                # the time-varying params are able to vary within the pre-set bounds\n",
    "                # while the static params must stay the same.\n",
    "                bounds = bounds[:num_vary_params]     # keeps initialized bounds\n",
    "                for j in range(num_static_params):\n",
    "                    # makes it so that the static params do not change\n",
    "                    bounds.append((first_params[j + num_vary_params], first_params[j + num_vary_params]))\n",
    "                \n",
    "            print('bounds=',bounds)\n",
    "\n",
    "    # dictionary containing arrays of each parameter at each time point\n",
    "    param_time = {}\n",
    "\n",
    "    for k in range(num_model_params):\n",
    "\n",
    "        # initialize array\n",
    "        param_time[f\"p{k}\"] = []\n",
    "        for i in range(num_time_intervals):\n",
    "\n",
    "            # iterates through time intervals and stitches together the parameter arrays\n",
    "            param_time[f\"p{k}\"] = np.append(param_time[f\"p{k}\"] , \n",
    "                                   param_matrix[k,i]*np.ones(len(time_intervals_dict[f't{i}'])))\n",
    "        \n",
    "    return params_dict, param_matrix, param_time\n",
    "\n",
    "############################################################ \n",
    "\n",
    "''' Generate approx trajectory using estimated params\n",
    "\n",
    "inputs:  params_dict            | dictionary of parameters for each time interval\n",
    "\n",
    "         data_intervals_dict    | dictionary of semented data\n",
    "             \n",
    "         time_intervals_dict    | dictionary of semented time vector\n",
    "             - time vector\n",
    "         \n",
    "         num_time_intervals.    | float\n",
    "                     \n",
    "outputs: traj_dict              | dictionary of trajectories over each time interval\n",
    "                               \n",
    "'''\n",
    "def predicted_trajectories(params_dict, data_intervals_dict, time_intervals_dict, num_time_intervals):\n",
    "\n",
    "    traj_dict = {}\n",
    "\n",
    "    for i in range(num_time_intervals):\n",
    "\n",
    "        key= f\"t{i}\"\n",
    "   \n",
    "\n",
    "\n",
    "        tspan = time_intervals_dict[key]\n",
    "\n",
    "        y0 = data_intervals_dict[key][0,:]\n",
    "\n",
    "        traj_dict[key] = odeint(pend, y0, tspan, \n",
    "                                          args =  tuple(params_dict[key]))\n",
    "        \n",
    "        # puts all trajectories into one array\n",
    "        if i==0:\n",
    "            traj = traj_dict[key]\n",
    "        else:\n",
    "            traj = np.append(traj , traj_dict[key], axis = 0)\n",
    "\n",
    "            \n",
    "    return traj_dict, traj\n",
    "\n",
    "\n",
    "############################################################ \n",
    "\n",
    "\n",
    "''' Computs the error of the found trajectory\n",
    "\n",
    "inputs:  data_intervals_dict    | dictionary of semented data\n",
    "\n",
    "         traj_dict              | dictionary of trajectories over each time interval\n",
    "         \n",
    "         num_time_intervals     | integer\n",
    "                     \n",
    "outputs: err_dict               | dictionary of approximation error over each time interval\n",
    "    \n",
    "         err_arry               | array of size (num_time_pts, num_states)\n",
    "\n",
    "         total_err              | float \n",
    "             - norm of error array\n",
    "\n",
    "'''\n",
    "def traj_err(data_intervals_dict, traj_dict, num_time_intervals):\n",
    "    \n",
    "    err_dict = {}\n",
    "    \n",
    "    for i in range(num_time_intervals):\n",
    "\n",
    "        key = f\"t{i}\"\n",
    "        \n",
    "        err_dict[key] = (traj_dict[key] - data_intervals_dict[key])\n",
    "        \n",
    "        # puts all errors into one array\n",
    "        if i==0:\n",
    "            err_array = err_dict[key]\n",
    "        else:\n",
    "            err_array = np.append(err_array , err_dict[key], axis=0)\n",
    "                            \n",
    "    total_err = LA.norm((err_array),2)/len(err_array)\n",
    "\n",
    "    return err_dict, err_array, total_err\n",
    "\n",
    "############################################################ \n",
    "\n",
    "''' continuous piecewise time-varying model identification\n",
    "\n",
    "inputs:  data                   | array of size (num_time_pts, num_states)\n",
    "             - each column of the data array is the evolution of that state in time\n",
    "             \n",
    "         switch_gap             | integer\n",
    "             - must define the number of indices that is allowable\n",
    "                between switches.  If switch_gap is zero, then you \n",
    "                cannot have consecutive time points being switch times\n",
    "        \n",
    "         model                   | str\n",
    "            - pick from the following least-squares estimates:\n",
    "                \"l1\", \"l2\", \"rbf\", \"linear\", \"normal\", \"ar\",...\n",
    "        \n",
    "         sigma                   | float\n",
    "            - standard deviation of the noise in the data\n",
    "                \n",
    "outputs: result                  | dictionary of identified model results\n",
    "            - print(result.keys()) \n",
    "            - run the above line of code for outputs\n",
    "'''\n",
    "def cont_pw_tv_model_ID(data, t, switch_gap, ls_model, sigma, params_init, bounds, num_static_params):\n",
    "    \n",
    "    num_time_pts, num_states = np.shape(data)\n",
    "\n",
    "    # time step\n",
    "    dt = t[1] - t[0]\n",
    "\n",
    "    ## Switch time detection\n",
    "\n",
    "    # define data signal which contains switches\n",
    "    switch_signal = data\n",
    "\n",
    "    t_switch_index, num_switches, num_time_intervals, time_of_switch = switch_time_detect(switch_signal, \n",
    "                                                                                          t,\n",
    "                                                                                          switch_gap, \n",
    "                                                                                          ls_model, \n",
    "                                                                                          sigma)\n",
    "\n",
    "\n",
    "    # breaks data up into sections based on the \n",
    "    # times of the switches\n",
    "    data_intervals_dict, time_intervals_dict = data_segementation(data, t, num_switches, t_switch_index)\n",
    "\n",
    "    ## Estimate the parameters of the genetic mybrid promoter model using SciPy optimization\n",
    "    ## over each time interval\n",
    "\n",
    "    params_dict, param_matrix, param_time = fit_params(data_intervals_dict, time_intervals_dict, dt, params_init, \n",
    "                                           model_param_bounds, num_time_intervals, num_static_params)\n",
    "\n",
    "    # generate approx trajectory based on estimated params\n",
    "\n",
    "    traj_dict, traj = predicted_trajectories(params_dict, \n",
    "                                       data_intervals_dict, \n",
    "                                       time_intervals_dict, \n",
    "                                       num_time_intervals)\n",
    "    \n",
    "    err_dict, err_array, total_err = traj_err(data_intervals_dict, traj_dict, num_time_intervals)\n",
    "        \n",
    "    # results form fitting params to the model\n",
    "    result = {'params_dict': params_dict, \n",
    "               'param_matrix':param_matrix, \n",
    "               'traj_dict':traj_dict, \n",
    "               'traj':traj,\n",
    "               'data_intervals_dict':data_intervals_dict, \n",
    "               'time_intervals_dict':time_intervals_dict, \n",
    "               't_switch_index':t_switch_index, \n",
    "               'num_switches':num_switches, \n",
    "               'num_time_intervals':num_time_intervals,\n",
    "               'time_of_switch':time_of_switch,\n",
    "               'err_dict':err_dict,\n",
    "               'err_array':err_array,\n",
    "               'total_err':total_err,\n",
    "               'param_time':param_time}\n",
    "    \n",
    "    return result\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "912a22af-286c-412a-8da1-d57d7d5d5a82",
   "metadata": {
    "tags": []
   },
   "source": [
    "## USER INPUT: Must define parametrized system and objective function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "a75f9c1c-d416-4d49-ba4d-72854bc101c9",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "''' Dynamics for simulation\n",
    "inputs:  y                       | array of size (num_states, )\n",
    "             - state at current time point\n",
    "             \n",
    "         ti                      | float\n",
    "             - current time, i.e. the i-th index of time vector\n",
    "        \n",
    "         param_1                 | float\n",
    "         param_2\n",
    "         .\n",
    "         .\n",
    "         .\n",
    "         param_n\n",
    "                \n",
    "outputs: dydt                    | array of size (num_states, ) \n",
    "'''\n",
    "# dynamics for simulation\n",
    "def pend(y, ti, alpha, beta, bm, bp):\n",
    "    \n",
    "    # 2 state system \n",
    "    m, p = y\n",
    "    \n",
    "    dydt = [ (alpha - bm*m) , \n",
    "            (beta*m  - bp*p) ]\n",
    "    \n",
    "    # Return the rates of change of the concentrations as a NumPy array\n",
    "    return dydt\n",
    "\n",
    "############################################################ \n",
    "''' Dynamics for objective function\n",
    "inputs:  y                       | array of size (num_states, )\n",
    "             - state at current time point\n",
    "             \n",
    "         ti                      | float\n",
    "             - current time, i.e. the i-th index of time vector\n",
    "        \n",
    "         params                  | array of size (num_params, )\n",
    "             - must be coordinated with the params in pend\n",
    "                \n",
    "outputs: dydt                    | array of size (num_states, ) \n",
    "'''\n",
    "# dynamics for objective function\n",
    "def obj_dynamics(y, ti, params):\n",
    "\n",
    "    alpha, beta, bm, bp = params\n",
    "    \n",
    "    # 2 state system \n",
    "    m = y[0]\n",
    "    p = y[1]\n",
    "    \n",
    "    dmdt = (alpha - bm*m) \n",
    "\n",
    "    dpdt = (beta*m  - bp*p)\n",
    "\n",
    "    # Return the rates of change of the concentrations as a NumPy array\n",
    "    return np.array([dmdt, dpdt])\n",
    "\n",
    "############################################################ \n",
    "''' Objective function to minimize\n",
    "inputs:  params                  | array of size (num_params, )\n",
    "             - must be coordinated with the params in pend\n",
    "         \n",
    "         data                    | array of size (num_time_pts, 1)\n",
    "             - each column of the data array is the evolution of that state in time\n",
    "             \n",
    "         dt                      | float\n",
    "             - sampling time, i.e. difference between time points\n",
    "         \n",
    "         t                       | array of size (num_time_pts, )\n",
    "             - time vector\n",
    "                \n",
    "outputs: err                     | float\n",
    "'''\n",
    "# Define the objective function to minimize\n",
    "def objective(params, data, dt, t):\n",
    "    \n",
    "    m,n = np.shape(data)\n",
    "    \n",
    "    # initialize array for predicted data.\n",
    "    # we leave off the initial condition because that is given to us\n",
    "    x_pred = np.zeros((m-1,n))\n",
    "    x_data = data[1:,:]\n",
    "    \n",
    "    # use euler's method to solve ODE with set of params\n",
    "    for i in range(len(data)-1):\n",
    "        x0 = data[i,:]\n",
    "        x_pred[i,:] = x0 + obj_dynamics(x0, t[i], params)*dt\n",
    "    \n",
    "    # distance between the predicted data and the real data\n",
    "    err = LA.norm(x_data - x_pred)\n",
    "    \n",
    "    return err"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "572114cd-b4cc-424f-8cce-0adbe44f1ee6",
   "metadata": {
    "tags": []
   },
   "source": [
    "##  simulates data for hybrid promoter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "fbfae195-6f92-4386-8f7c-b922c1d4b711",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def sim_hybrid_promoter():\n",
    "    \n",
    "    # initial condition for simulation\n",
    "    y0 = [1., 2.]\n",
    "\n",
    "    ti = 0      # start time\n",
    "\n",
    "    tf = 25     # end time\n",
    "    \n",
    "    # define time vector\n",
    "    num_time_grid_points = 700\n",
    "    t = np.linspace(ti, tf, num_time_grid_points)\n",
    "    \n",
    "    dt = t[1] - t[0]\n",
    "\n",
    "    ########################################################  \n",
    "    ## parameters\n",
    "    am = 4. \n",
    "    ap = 4.\n",
    "    \n",
    "    bm = 1.\n",
    "    bp = 1.\n",
    "\n",
    "    ######################################################## \n",
    "    ## Simulate trajectories\n",
    "\n",
    "    num_time_ints = 5\n",
    "\n",
    "    break_len = len(t)//num_time_ints\n",
    "\n",
    "\n",
    "    # used to iterate through every time point\n",
    "    temp_index = 0  \n",
    "\n",
    "    # true solution over first time interval\n",
    "    u_true = odeint(pend, y0, t[temp_index : temp_index + break_len], args = (am,ap,bm,bp))\n",
    "\n",
    "\n",
    "    for i in range(num_time_ints):\n",
    "\n",
    "        # update params\n",
    "        \n",
    "        # only updates am every other time interval\n",
    "        if i%2==0:\n",
    "            am = am + 1.\n",
    "            \n",
    "        ap = ap + 1.\n",
    "\n",
    "        u0 = u_true[-1,:]\n",
    "\n",
    "        # updtate the index of the current time point\n",
    "        temp_index = temp_index + break_len\n",
    "\n",
    "        # true solution over next time interval\n",
    "        u_new = odeint(pend, u0, t[temp_index : temp_index + break_len ], args = (am,ap,bm,bp))\n",
    "        u_true = np.append(u_true, u_new, axis=0)\n",
    "\n",
    "    # true solution over last time interval\n",
    "    u0 = u_true[-1,:]\n",
    "    u_new = odeint(pend, u0, t[temp_index:], args = (am,ap,bm,bp))\n",
    "    u_true = np.append(u_true, u_new, axis=0)\n",
    "    \n",
    "    data = u_true\n",
    "    \n",
    "    return data , t"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab975410-ae08-454b-826d-2dcd19931782",
   "metadata": {},
   "source": [
    "## Main code to run"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "b3c7bc77-fa61-4639-8fde-fbf70bb3c39b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "times_of_switches =  [ 5.00715308 10.01430615 15.02145923 20.0286123 ]\n",
      "bounds= [(-inf, inf), (-inf, inf), (0.9823265458531373, 0.9823265458531373), (1.0056574513979601, 1.0056574513979601)]\n"
     ]
    }
   ],
   "source": [
    "## runs the algorithm to fit parameter estimates \n",
    "\n",
    "# Gets simulated data\n",
    "data , t = sim_hybrid_promoter()\n",
    "\n",
    "# gets shape of data\n",
    "m,n = np.shape(data)\n",
    "\n",
    "# switch detection parameters\n",
    "switch_gap = 10\n",
    "ls_model = \"ar\"\n",
    "\n",
    "# noise_level*1.1 seems to work well for some noise levels\n",
    "# sigma = noise_level*1.1\n",
    "\n",
    "# number of switches\n",
    "sigma=0.00001\n",
    "\n",
    "\n",
    "# Sets initial parameter value guesses for first time domain \n",
    "#           [alpha, beta, bm,  bp]\n",
    "params_init = [1.5, 1.5, 1.5, 1.5 ]\n",
    "\n",
    "# set bounds for paramsin the form of : (lower, upper)\n",
    "#         [alpha,    beta,     bm,     bp]\n",
    "# bounds = [(0, 10), (0, 10), (1, 10), (1, 10)]\n",
    "model_param_bounds = None\n",
    "\n",
    "switch_state = 1\n",
    "\n",
    "# amplifies signal\n",
    "noise_level = 0.\n",
    "\n",
    "# static params must be the last params defined in\n",
    "# pend and the objective function\n",
    "num_static_params = 2\n",
    "\n",
    "for i in range(1):\n",
    "    # adds noise to data\n",
    "    np.random.seed(0)    # seed value for repeatable results\n",
    "    noise = np.random.randn(m,n)\n",
    "    data = data + noise_level * noise\n",
    "\n",
    "    result = cont_pw_tv_model_ID(data, t, switch_gap, \n",
    "                                 ls_model, \n",
    "                                 sigma, params_init,\n",
    "                                 model_param_bounds, \n",
    "                                 num_static_params)\n",
    "    \n",
    "    param_matrix = result['param_matrix']\n",
    "    # print('total_error = ', result['total_err'])\n",
    "    \n",
    "    noise_level = noise_level + .0\n",
    "    \n",
    "# note that for troubleshooting, all of the results which are dictionaries have keys \n",
    "# which can be analyzed as below\n",
    "\n",
    "# print(result.keys())\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6d69e84b-64cc-4f7b-a71a-abe0eb8b5bbf",
   "metadata": {},
   "source": [
    "## Plotting "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "d459842b-a49c-46c4-bd2b-c3aaa9bed3b3",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total_error =  0.0011928334239460524\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# results needed for plotting\n",
    "\n",
    "num_switches = result['num_switches']\n",
    "time_intervals_dict = result['time_intervals_dict']\n",
    "traj_dict = result['traj_dict']\n",
    "traj = result['traj']\n",
    "param_matrix = result['param_matrix']\n",
    "num_time_intervals = result['num_time_intervals']\n",
    "params_dict = result['params_dict']\n",
    "err_array = result['err_array']\n",
    "param_time = result['param_time']\n",
    "switch_times = result['time_of_switch']\n",
    "\n",
    "print('total_error = ', result['total_err'])\n",
    "\n",
    "num_model_params = np.shape(param_matrix)[0]\n",
    "\n",
    "# trajectory plot\n",
    "plt.figure(1)\n",
    "plt.plot(t, data[:, 0], 'r--o', alpha = 1, label='mRNA')\n",
    "plt.plot(t, data[:, 1], 'g--o', alpha = 1, label='GFP')\n",
    "for each in switch_times:\n",
    "    plt.axvline(x=each, color='gray', linestyle='--', linewidth=1.5, alpha=0.5)\n",
    "plt.plot(t, traj[:, 0], 'k--', label='approx mRNA')\n",
    "plt.plot(t, traj[:,1], 'k--', label='approx GFP')\n",
    "plt.xlabel('time (hours)')\n",
    "plt.ylabel('relative concentration')\n",
    "plt.title('hybrid promoter trajectory')\n",
    "plt.legend()\n",
    "plt.savefig(os.path.join(os.getcwd(), 'trajectory.svg'), format='svg')\n",
    "# plt.grid()\n",
    "\n",
    "\n",
    "# Plot of param values over time intervals\n",
    "fig, ax = plt.subplots()\n",
    "im = ax.imshow(param_matrix, cmap = 'jet')\n",
    "\n",
    "x_ticks_str = [str(item) for item in np.arange(1, num_time_intervals + 1 , step=1)]\n",
    "y_ticks_str = [str(item) for item in np.arange(1, num_model_params + 1 , step=1)]\n",
    "\n",
    "# Show all ticks and label them with the respective list entries\n",
    "ax.set_xticks(np.arange(num_time_intervals), labels = x_ticks_str)\n",
    "ax.set_yticks(np.arange(num_model_params), labels = y_ticks_str)\n",
    "plt.xlabel('time interval')\n",
    "plt.ylabel('parameter number')\n",
    "plt.title('parameter values over time intervals')\n",
    "cbar = plt.colorbar(im, ax=ax)\n",
    "cbar.set_label('value')\n",
    "# Loop over data dimensions and create text annotations.\n",
    "for k in range(num_model_params):\n",
    "    for i in range(num_time_intervals):\n",
    "        text = ax.text(i, k, round(param_matrix[k, i],2),\n",
    "                       ha=\"center\", va=\"center\", color=\"w\")\n",
    "plt.savefig(os.path.join(os.getcwd(), 'params.svg'), format='svg')\n",
    "\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2ac85cbf-2183-4ba7-be89-8bf16959eb9f",
   "metadata": {},
   "source": [
    "## Plot param error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "c9324a96-191f-4152-8f6b-2e71376ce354",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "param_err =  0.05537238778948222\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "param_true_arr = np.array([[4, 5, 5, 6, 6], \n",
    "                          [4, 5, 6, 7, 8], \n",
    "                          [1, 1, 1, 1, 1], \n",
    "                          [1, 1, 1, 1, 1]])\n",
    "\n",
    "param_err_arr= LA.norm(param_true_arr - param_matrix, 2)/4\n",
    "print('param_err = ', param_err_arr)\n",
    "\n",
    "for k in range(num_model_params):\n",
    "    plt.figure()\n",
    "    plt.plot(t,param_time[f\"p{k}\"], label = 'param '+str(k))\n",
    "    plt.xlabel('time intervals')\n",
    "    plt.ylabel('param values')\n",
    "    plt.title('param value over time')\n",
    "    plt.legend()\n",
    "    plt.grid()\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a5da2827-0b62-4f80-9676-3169a67f46a4",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.8.18"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}