ODE example.ipynb

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   "source": [
    "########################################################\n",
    "### This file is used to generate Table 4-6, Fig 2-3 ###\n",
    "########################################################\n",
    "\n",
    "- [Forward Problem](#Forward-Problem)\n",
    "    - [Verify Assumption 1](#Verify-Assumption-1)\n",
    "        - [Table 4](#Table-4)\n",
    "        - [Table 5](#Table-5)\n",
    "    - [Verify Lemma 1](#Verify-Lemma-1)\n",
    "        - [Left plot in Figure 2](#Left-plot-in-Figure-2)\n",
    "    - [Verify Theorem 3.1](#Verify-Theorem-3.1)\n",
    "        - [Right plot in Figure 2](#Right-plot-in-Figure-2)\n",
    "- [Inverse Problem](#Inverse-Problem)\n",
    "    - [Verify Assumption 2](#Verify-Assumption-2)\n",
    "        - [Table 6](#Table-6)\n",
    "    - [Verify Theorem 4.2](#Verify-Theorem-4.2)\n",
    "        - [Figure 3](#Figure-3)"
   ]
  },
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   "source": [
    "import os\n",
    "import numpy as np\n",
    "import numpy.polynomial.legendre as leg\n",
    "from scipy.stats import beta\n",
    "from scipy.stats import uniform\n",
    "from scipy.integrate import odeint\n",
    "from scipy.stats import gaussian_kde as kde\n",
    "from ipywidgets import interact, interactive, fixed, interact_manual\n",
    "import ipywidgets as widgets\n",
    "\n",
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
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   "source": [
    "####### Plot Formatting ######\n",
    "plt.rc('lines', linewidth = 1.5)\n",
    "plt.rc('xtick', labelsize = 14)\n",
    "plt.rc('ytick', labelsize = 14)\n",
    "plt.rc('legend',fontsize=14)\n",
    "# plt.rcParams[\"font.family\"] = \"serif\"\n",
    "plt.rcParams['axes.labelsize'] = 20\n",
    "plt.rcParams['axes.titlesize'] = 12\n",
    "plt.rcParams['lines.markersize'] = 6\n",
    "plt.rcParams['figure.figsize'] = (8.0, 6.0)"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Modified version of Example from Xiu2002\n",
    "\n",
    "$$ \\frac{dy(t)}{dt} = -\\lambda y, \\ \\  y(0)=1 $$\n",
    "$$ y(t) = e^{-\\lambda t} $$\n",
    "$$QoI = y(0.5)$$\n",
    "\n",
    "$\\lambda\\sim U[-1,1]$, $t\\in[0,1]$\n",
    "\n",
    "$\\Lambda = [-1,1]$, $\\mathcal{D}=[e^{-0.5},e^{0.5}]$"
   ]
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   "outputs": [],
   "source": [
    "def Phi(n):\n",
    "    '''Define L_n'''\n",
    "    coeffs = [0]*(n+1)\n",
    "    coeffs[n] = 1\n",
    "    return coeffs\n",
    "\n",
    "def inner2_leg(n):       \n",
    "    return 2/(2*n+1)\n",
    "\n",
    "def product3_leg(i,j,l):\n",
    "    #compute \\Phi_i*\\Phi_j*\\Phi_l\n",
    "    return lambda x: leg.legval(x, leg.legmul(leg.legmul(Phi(i),Phi(j)),Phi(l))) \n",
    "\n",
    "def inner3_leg(i,j,l):\n",
    "    '''\n",
    "    compute <\\Phi_i\\Phi_j\\Phi_l>    \n",
    "    Set up Gauss-Legendra quadrature\n",
    "    '''\n",
    "\n",
    "    x, w=leg.leggauss(20) \n",
    "    inner=sum([product3_leg(i,j,l)(x[idx]) * w[idx] for idx in range(20)])         \n",
    "    \n",
    "    return inner  "
   ]
  },
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   "execution_count": 4,
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   "source": [
    "def ode_system_leg(y, t, P):   \n",
    "    '''P indicates highest order of Polynomial we use'''\n",
    "    dydt = np.zeros(P+1) \n",
    "    for l in range(len(dydt)):\n",
    "        dydt[l] = -(sum(sum(inner3_leg(i,j,l)*ki_leg[i]*y[j] for j in range(P+1)) for i in range(P+1)))/inner2_leg(l)\n",
    "    return dydt"
   ]
  },
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   "execution_count": 5,
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    "ExecuteTime": {
     "end_time": "2021-07-01T02:54:20.867929Z",
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   "outputs": [],
   "source": [
    "P=5\n",
    "ki_leg = [0,1]+[0]*(P-1)\n",
    "sol_leg = odeint(ode_system_leg, [1.0]+[0.0]*P, np.linspace(0,1,101), args=(P,)) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
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     "end_time": "2021-07-01T02:54:20.882384Z",
     "start_time": "2021-07-01T02:54:20.871119Z"
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   "outputs": [],
   "source": [
    "def a(i):\n",
    "    return sol_leg[:,i][50]\n",
    "coef = np.array([a(0), a(1), a(2), a(3), a(4), a(5)])   #fixed\n",
    "\n",
    "def Q(i,x):\n",
    "    return leg.legval(x,coef[:(i+1)])\n",
    "\n",
    "def Qexact(x):\n",
    "    return np.exp(-x*0.5)"
   ]
  },
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   "cell_type": "code",
   "execution_count": 7,
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   "outputs": [
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       "<Figure size 576x432 with 0 Axes>"
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      "text/plain": [
       "interactive(children=(IntSlider(value=1, description='n', max=5, min=1), Output()), _dom_classes=('widget-inte…"
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     "data": {
      "text/plain": [
       "<function __main__.plot_Qn(n)>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#### Use plot to show the difference between the exact and approximate map #####\n",
    "fig = plt.figure()\n",
    "\n",
    "def plot_Qn(n):\n",
    "    fig.clear()\n",
    "    x = np.linspace(-3,3,100)\n",
    "    y = Qexact(x)\n",
    "    yn = Q(n, x)\n",
    "    plt.plot(x,y,linestyle='-.',linewidth=4,label=\"$Q(\\lambda)$\")\n",
    "    plt.plot(x,yn,label='Q_'+str(n)+'$(\\lambda)$')\n",
    "    plt.xlabel('$\\Lambda$')\n",
    "    plt.legend();\n",
    "    \n",
    "interact(plot_Qn, \n",
    "         n = widgets.IntSlider(value=1,min=1,max=5,step=1))  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Forward Problem"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\lambda\\sim U([-1,1])$, QOI is the value at $t=0.5$ ($y(0.5)$). $Q_n$ defines the Polynomial Chaos expansion with degree $n$.\n",
    "\n",
    "$$\n",
    "Q(\\lambda)=y(0.5)=\\sum\\limits_{i=0}^{\\infty} y_i(0.5)\\Phi_i\n",
    "$$\n",
    "$$\n",
    "Q_n(\\lambda)=\\sum\\limits_{i=0}^n y_i(0.5)\\Phi_i\n",
    "$$\n",
    "\n",
    "Verify Result of Lemma 2:\n",
    "\n",
    "$Q_n(\\lambda)\\to Q(\\lambda)$ in $L^p(\\Lambda)$, if Assumptions 1 holds and $D_c\\subset\\mathcal{D}$ being compact, then \n",
    "\\begin{equation}\n",
    "\t\\pi_{\\mathcal{D}}^{Q_n}(q) \\to \\pi_{\\mathcal{D}}^{Q}(q) \\text{ almost in} {L^r(D_c)}   \n",
    "\\end{equation}\n",
    "\n",
    "Since $\\mathcal{D}$ is compact in this problem, we choose $D_c=\\mathcal{D}$.\n",
    "\n",
    "Verify Result of Theorem 3.1:\n",
    "\n",
    "$Q_n(\\lambda)\\to Q(\\lambda)$ in $L^p(\\Lambda)$, if Assumptions 1 holds, $\\{\\pi_{\\mathcal{D}}^{Q_n}\\}$ are uniformly integrable in $L^p(\\mathcal{D})$, $\\mathcal{D}$ is compact, then \n",
    "\\begin{equation}\n",
    "        \\pi_{\\mathcal{D}}^{Q_n}(Q_n(\\lambda)) \\to \\pi_{\\mathcal{D}}^{Q}(Q(\\lambda)) \\text{ in } L^p(\\Lambda) \n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Verify Assumption 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
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   "outputs": [],
   "source": [
    "##### Generate data in Table 4 and 5 #####\n",
    "def assumption1(n,J):\n",
    "    np.random.seed(123456)\n",
    "    initial_sample = np.random.uniform(-1,1,size = J)\n",
    "    pfprior_sample_n = Q(n,initial_sample)\n",
    "    pfprior_dens_n = kde(pfprior_sample_n)\n",
    "    x = np.linspace(-1,3,1000)\n",
    "    return np.round(np.max(np.abs(np.gradient(pfprior_dens_n(x), x))), 2), np.round(np.max(pfprior_dens_n(x)),2)\n",
    "\n",
    "size_J = [int(1E3), int(1E4), int(1E5)]\n",
    "degree_n = [1, 2, 3, 4, 5]\n",
    "Bound_matrix, Lip_Bound_matrix = np.zeros((3,5)), np.zeros((3,5))\n",
    "for i in range(3):\n",
    "    for j in range(5):\n",
    "        n, J = degree_n[j], size_J[i]\n",
    "        Lip_Bound_matrix[i,j] = assumption1(n, J)[0]\n",
    "        Bound_matrix[i,j] = assumption1(n, J)[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Table 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-01T02:55:11.499740Z",
     "start_time": "2021-07-01T02:55:11.484312Z"
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Table 4\n",
      "Bound under certain n and J values\n",
      "[[1.06 1.28 1.24 1.24 1.24]\n",
      " [1.03 1.49 1.42 1.42 1.42]\n",
      " [1.   1.61 1.49 1.5  1.5 ]]\n"
     ]
    }
   ],
   "source": [
    "###########################################\n",
    "################ Table 4 ##################\n",
    "###########################################\n",
    "print('Table 4')\n",
    "print('Bound under certain n and J values')\n",
    "print(Bound_matrix)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Table 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-01T02:55:11.515334Z",
     "start_time": "2021-07-01T02:55:11.505630Z"
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Table 5\n",
      "Lipschitz bound under certain n and J values\n",
      "[[ 5.58  8.18  7.73  7.76  7.76]\n",
      " [ 8.4  14.18 12.97 13.05 13.05]\n",
      " [13.45 23.43 21.   21.22 21.21]]\n"
     ]
    }
   ],
   "source": [
    "###########################################\n",
    "################ Table 5 ##################\n",
    "###########################################\n",
    "print('Table 5')\n",
    "print('Lipschitz bound under certain n and J values')\n",
    "print(Lip_Bound_matrix)"
   ]
  },
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   "cell_type": "code",
   "execution_count": 11,
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     "end_time": "2021-07-01T02:55:12.087646Z",
     "start_time": "2021-07-01T02:55:11.519679Z"
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       "<Figure size 576x432 with 0 Axes>"
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       "interactive(children=(IntSlider(value=1, description='n', max=5, min=1), IntSlider(value=1000, description='J'…"
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     "metadata": {},
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    {
     "data": {
      "text/plain": [
       "<function __main__.plot_pushforward(n, J)>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#### Use plot to show the difference between the exact pushforward and approximate pushforward #####\n",
    "fig=plt.figure()\n",
    "\n",
    "def plot_pushforward(n,J):\n",
    "    fig.clear()\n",
    "    np.random.seed(123456)\n",
    "    initial_sample = np.random.uniform(-1,1,size = J)\n",
    "    \n",
    "    pfprior_sample = Qexact(initial_sample)\n",
    "    pfprior_dens = kde(pfprior_sample)\n",
    "    \n",
    "    pfprior_sample_n = Q(n,initial_sample)\n",
    "    pfprior_dens_n = kde(pfprior_sample_n)\n",
    "    \n",
    "    fig.clear()\n",
    "    x = np.linspace(-1,3,1000)\n",
    "    y = pfprior_dens(x)\n",
    "    yn = pfprior_dens_n(x)\n",
    "    plt.plot(x,y,color='r', linestyle='-.', linewidth=4, label=\"$\\pi_{\\mathcal{D}}^Q$\")\n",
    "    plt.plot(x,yn,linewidth=2,label=\"$\\pi_{\\mathcal{D}}^{Q_{n}}$\")\n",
    "    plt.title('Lipschitz const. = %4.2f and Bound = %2.2f' %(np.max(np.abs(np.gradient(pfprior_dens_n(x), x))),\n",
    "                                                                             np.max(pfprior_dens_n(x))))\n",
    "    plt.xlabel(\"$\\mathcal{D}$\")\n",
    "    plt.legend()\n",
    "        \n",
    "interact(plot_pushforward, \n",
    "         n = widgets.IntSlider(value=1,min=1,max=5,step=1),\n",
    "         J = widgets.IntSlider(value=int(1E3),min=int(1E3),max=int(1E5),step=int(1E3)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Verify Lemma 1\n",
    "**Print out Monte Carlo Approximation of $\t\\|\\pi_{\\mathcal{D}}^Q(q)-\\pi_{\\mathcal{D}}^{Q_n}(q)\\|_{L^r(\\mathcal{D_c})} $ where $r>0$ and $D_c=\\mathcal{D}$ because $\\mathcal{D}$ is compact.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-01T02:55:12.108259Z",
     "start_time": "2021-07-01T02:55:12.096545Z"
    }
   },
   "outputs": [],
   "source": [
    "#Build $\\pi_D^Q$ and $\\pi_D^{Q,n}$, use 10,000 samples\n",
    "N_kde = int(1E4)\n",
    "N_mc = int(1E4)\n",
    "\n",
    "np.random.seed(123456)\n",
    "initial_sample = np.random.uniform(-1,1,size = N_kde)\n",
    "pfprior_sample = Qexact(initial_sample)\n",
    "pfprior_dens = kde(pfprior_sample)\n",
    "\n",
    "def pfprior_dens_n(n,x):\n",
    "    pfprior_sample_n = Q(n,initial_sample)\n",
    "    pdf = kde(pfprior_sample_n)\n",
    "    return pdf(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-01T02:56:38.326826Z",
     "start_time": "2021-07-01T02:55:12.112284Z"
    }
   },
   "outputs": [],
   "source": [
    "error_r_D = np.zeros((5,5))\n",
    "np.random.seed(123456)            \n",
    "qsample = np.random.uniform(np.exp(-0.5),np.exp(0.5),N_mc)\n",
    "\n",
    "for i in range(5):\n",
    "    for j in range(5):\n",
    "        error_r_D[i,j] = (np.mean((np.abs(pfprior_dens(qsample) - pfprior_dens_n(j+1,qsample)))**(i+1)))**(1/(i+1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-01T02:56:38.339927Z",
     "start_time": "2021-07-01T02:56:38.329660Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "L^r error on data space for Forward Problem\n",
      "\n",
      "[[1.94238726e-01 2.05042717e-02 1.47356406e-03 7.87288538e-05 3.59183884e-06]\n",
      " [2.22506150e-01 2.49390997e-02 1.76945246e-03 9.32066906e-05 4.07528839e-06]\n",
      " [2.44870659e-01 2.96231360e-02 2.02466852e-03 1.04710022e-04 4.44179886e-06]\n",
      " [2.63194738e-01 3.41497229e-02 2.25659747e-03 1.14385798e-04 4.75561998e-06]\n",
      " [2.78426119e-01 3.81183280e-02 2.46559182e-03 1.22601045e-04 5.03864501e-06]]\n"
     ]
    }
   ],
   "source": [
    "np.set_printoptions(linewidth=110)  \n",
    "print('L^r error on data space for Forward Problem',end='\\n\\n')\n",
    "print(error_r_D)        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-01T02:56:38.355427Z",
     "start_time": "2021-07-01T02:56:38.346026Z"
    }
   },
   "outputs": [],
   "source": [
    "#### To make it cleaner, create Directory \"images\" to store all the figures ####\n",
    "imagepath = os.path.join(os.getcwd(),\"images\")\n",
    "os.makedirs(imagepath,exist_ok=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Left plot in Figure 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-01T03:00:34.527277Z",
     "start_time": "2021-07-01T03:00:33.390922Z"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "###########################################\n",
    "######### The left plot of Fig 2 ##########\n",
    "###########################################\n",
    "fig = plt.figure()\n",
    "plt.xlim([0,6])\n",
    "marker = ['-D', '-o', '-v', '-s', '-.']\n",
    "for i in range(5):\n",
    "    plt.semilogy([1,2,3,4,5],error_r_D[i,:],marker[i],label='r = ' + np.str(i+1))    \n",
    "plt.xlabel('Order of PCE (n)')\n",
    "plt.ylabel('$L^r$'+' Error in Push-Forward on '+'$\\mathcal{D}$')\n",
    "plt.legend();\n",
    "# fig.savefig(\"images/1forward_D_uniform.png\")\n",
    "fig.savefig(\"images/Fig2(Left).png\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Verify Theorem 3.1\n",
    "**Print out Monte Carlo Approximation of $\t\\|\\pi_{\\mathcal{D}}^Q(Q(\\lambda))-\\pi_{\\mathcal{D}}^{Q_n}(Q_n(\\lambda))\\|_{L^2(\\Lambda)} $**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-01T02:56:55.255380Z",
     "start_time": "2021-07-01T02:56:39.055331Z"
    }
   },
   "outputs": [],
   "source": [
    "##### Generate data for the right plot of Fig 2 #####\n",
    "np.random.seed(123456)       \n",
    "lamsample = np.random.uniform(-1,1,size = N_mc)\n",
    "\n",
    "error_2 = np.zeros(5)\n",
    "for i in range(5):\n",
    "    error_2[i] = (np.mean((np.abs(pfprior_dens(Qexact(lamsample)) - pfprior_dens_n(i+1,Q(i+1,lamsample))))**2))**(1/2)     "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-01T02:56:55.268830Z",
     "start_time": "2021-07-01T02:56:55.258297Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "L^2 error on parameter space for Forward Problem\n",
      "\n",
      "[2.42452472e-01 3.51921960e-02 2.34712105e-03 1.20430887e-04 4.89385277e-06]\n"
     ]
    }
   ],
   "source": [
    "np.set_printoptions(linewidth=110)   \n",
    "print('L^2 error on parameter space for Forward Problem',end='\\n\\n')\n",
    "print(error_2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Right plot in Figure 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-01T02:56:56.074871Z",
     "start_time": "2021-07-01T02:56:55.274698Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "############################################\n",
    "######### The right plot of Fig 2 ##########\n",
    "############################################\n",
    "fig = plt.figure()\n",
    "plt.xlim([0,6])\n",
    "plt.semilogy([1,2,3,4,5],error_2,'-s')   \n",
    "plt.xlabel('Order of PCE (n)')\n",
    "plt.ylabel('$L^2$'+' Error in Push-Forward on '+'$\\Lambda$');\n",
    "# fig.savefig(\"images/1forward_Lam_uniform.png\")\n",
    "fig.savefig(\"images/Fig2(Right).png\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Inverse Problem"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Initial guess is $\\lambda\\sim U([-1,1])$. \n",
    "\n",
    "Observation is $\\pi_{\\mathcal{D}}\\sim Beta(4,4)$ with location and scale parameters chosen to be on $[1,1.25]$.\n",
    "\n",
    "Verify Result of Theorem 4.2:\n",
    "\n",
    "$Q_n(\\lambda)\\to Q(\\lambda)$ in $L^p(\\Lambda)$, $\\pi_{\\Lambda}^i\\in L^p(\\mathcal{D})$. If Assumptions 1, 2 hold, $\\{\\pi_{\\mathcal{D}}^{Q_n}\\}$ are uniformly integrable in $L^p(\\mathcal{D})$, then \n",
    "\\begin{equation}\n",
    "        \\pi_{\\Lambda}^{u,n}(\\lambda) \\to \\pi_{\\Lambda}^{u}(\\lambda) \\text{ in } L^p(\\Lambda) \n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-01T02:56:56.092364Z",
     "start_time": "2021-07-01T02:56:56.083357Z"
    }
   },
   "outputs": [],
   "source": [
    "def pdf_obs(x):\n",
    "    return beta.pdf(x, a=4, b=4, loc=1, scale=0.25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-01T02:56:56.927823Z",
     "start_time": "2021-07-01T02:56:56.101179Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#### Use plot to show the difference between the pushforward of the init and the observed #####\n",
    "fig = plt.figure()\n",
    "xx = np.linspace(-1,3,1000)\n",
    "y = pdf_obs(xx)\n",
    "y_pf = pfprior_dens(xx)\n",
    "plt.plot(xx,y,label=\"$\\pi_{\\mathcal{D}}^{obs}$\")\n",
    "plt.plot(xx,y_pf, label=\"$\\pi_{\\mathcal{D}}^{Q(init)}$\")\n",
    "plt.xlabel(\"$\\mathcal{D}$\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Verify Assumption 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-01T02:57:08.488739Z",
     "start_time": "2021-07-01T02:56:56.937190Z"
    }
   },
   "outputs": [],
   "source": [
    "def Meanr(n):\n",
    "    pfprior_sample_n = Q(n,initial_sample)\n",
    "    if n==0:\n",
    "        r = pdf_obs(pfprior_sample)/pfprior_dens(pfprior_sample)\n",
    "    else:\n",
    "        r = pdf_obs(pfprior_sample_n)/pfprior_dens_n(n,pfprior_sample_n)\n",
    "    return np.mean(r)\n",
    " \n",
    "\n",
    "def pdf_update(n,x):\n",
    "    if n==0:\n",
    "        r = pdf_obs(pfprior_sample)/pfprior_dens(pfprior_sample)\n",
    "        pdf = kde(initial_sample,weights=r)\n",
    "    else:\n",
    "        pfprior_sample_n = Q(n,initial_sample)\n",
    "#         pfprior_dens_n = kde(pfprior_sample_n)\n",
    "        r = pdf_obs(pfprior_sample_n)/pfprior_dens_n(n,pfprior_sample_n)\n",
    "        pdf = kde(initial_sample,weights=r)\n",
    "    return pdf(x)\n",
    "\n",
    "Expect_r = np.zeros(6)\n",
    "for i in range(6):\n",
    "    Expect_r[i] = Meanr(i)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Table 6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-01T02:57:08.504749Z",
     "start_time": "2021-07-01T02:57:08.497702Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Table 6\n",
      "Expected ratio for verifying Assumption 2\n",
      "[1.00342642 0.97855489 0.97788712 0.97809176 0.97809595]\n"
     ]
    }
   ],
   "source": [
    "###########################################\n",
    "################ Table 6 ##################\n",
    "###########################################\n",
    "print('Table 6')\n",
    "print('Expected ratio for verifying Assumption 2')\n",
    "print(Expect_r[1:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-01T02:57:12.383809Z",
     "start_time": "2021-07-01T02:57:08.511097Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 576x432 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "30ebfe2f829c4006965a488344a9e0a4",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=1, description='n', max=5, min=1), Output()), _dom_classes=('widget-inte…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<function __main__.plot_update(n)>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#### Use plot to show the difference between the initial, updated, approximate updated #####\n",
    "fig=plt.figure()\n",
    "\n",
    "def plot_update(n):\n",
    "    fig.clear()\n",
    "    xx = np.linspace(-1.1,1.1,100)\n",
    "    plt.plot(xx, uniform.pdf(xx, loc=-1, scale=2), label=\"Initial Density\")\n",
    "    plt.plot(xx, pdf_update(0,xx), label=\"$\\pi_{\\Lambda}^u$\")\n",
    "    plt.plot(xx, pdf_update(n,xx), label=\"$\\pi_{\\Lambda}^{u,n}$, n=\"+str(n))\n",
    "    plt.legend()\n",
    "    plt.xlabel(\"$\\Lambda$\")\n",
    "    plt.title('$\\mathbb{E}(r) =$ %3.2f' %(Expect_r[n]));\n",
    "    \n",
    "interact(plot_update, \n",
    "         n = widgets.IntSlider(value=int(1),min=int(1),max=int(5),step=1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-01T02:57:20.401431Z",
     "start_time": "2021-07-01T02:57:12.389456Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#### Use plot to show the difference between the observed and the pushforward of the approximate updated pdf #####\n",
    "def update_pushforward(n,x):\n",
    "    pfprior_sample_n = Q(n,initial_sample)\n",
    "    r = pdf_obs(pfprior_sample_n)/pfprior_dens_n(n,pfprior_sample_n)\n",
    "    pdf = kde(pfprior_sample_n,weights=r)\n",
    "    return pdf(x)\n",
    "\n",
    "fig = plt.figure()\n",
    "xx = np.linspace(-1,3,100)\n",
    "y = pdf_obs(xx)\n",
    "plt.plot(xx,y,label=\"$\\pi_{\\mathcal{D}}^{obs}$\")\n",
    "for i in range(1,6,1):\n",
    "    y_pf = update_pushforward(i,xx)\n",
    "    plt.plot(xx,y_pf, label=\"n=\"+str(i))\n",
    "plt.xlabel(\"$\\mathcal{D}$\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Verify Theorem 4.2\n",
    "\n",
    "Print out Monte Carlo Approximation of $\\|\\pi_{\\Lambda}^{u,n}(\\lambda)-\\pi_{\\Lambda}^u(\\lambda)\\|_{L^2(\\Lambda)} $ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-01T02:58:02.721388Z",
     "start_time": "2021-07-01T02:57:20.406280Z"
    }
   },
   "outputs": [],
   "source": [
    "##### Generate data for Fig 3 #####\n",
    "np.random.seed(123456)     \n",
    "lamsample = np.random.uniform(-1,1,size = N_mc)\n",
    "\n",
    "error_update = np.zeros(5)\n",
    "for i in range(5):\n",
    "    error_update[i] = (np.mean((np.abs(pdf_update(0,lamsample) - pdf_update(i+1,lamsample)))**2))**(1/2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-01T02:58:02.736017Z",
     "start_time": "2021-07-01T02:58:02.724969Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "L^2 Error for Inverse Problem\n",
      "\n",
      "[7.93989864e-01 6.16431006e-02 3.38614091e-03 2.52824991e-04 6.91016768e-06]\n"
     ]
    }
   ],
   "source": [
    "np.set_printoptions(linewidth=110)\n",
    "print('L^2 Error for Inverse Problem',end='\\n\\n')\n",
    "print(error_update)      "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Figure 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-01T02:58:03.532534Z",
     "start_time": "2021-07-01T02:58:02.741261Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "###########################################\n",
    "################ Figure 3 #################\n",
    "###########################################\n",
    "fig = plt.figure()\n",
    "plt.xlim([0,6])\n",
    "plt.semilogy([1,2,3,4,5],error_update,'-s')   \n",
    "plt.xlabel('Order of PCE (n)')\n",
    "plt.ylabel('$L^2$'+' Error in Update');\n",
    "# fig.savefig(\"images/1inverse_error_uniform.png\")\n",
    "fig.savefig(\"images/Fig3.png\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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   "current_citInitial": 1,
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   "eqNumInitial": 1,
   "hotkeys": {
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  "toc": {
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   "toc_position": {},
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  "varInspector": {
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   "kernels_config": {
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