{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Building up tools to analyse a 1-D problem"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Code for a 1-D problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from dolfin import *\n",
    "import numpy as np\n",
    "from scipy.interpolate import interp1d\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import matplotlib.cm as cm\n",
    "plt.rcParams['figure.figsize'] = (10,6)\n",
    "import sympy; sympy.init_printing()\n",
    "# code for displaying matrices nicely\n",
    "def display_matrix(m):\n",
    "    display(sympy.Matrix(m))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1 dimensional case (ODE)\n",
    "\n",
    "We consider the following 1-D problem:\n",
    "\n",
    "$$-\\frac{d}{dx}\\left(p(x)\\frac{du(x)}{dx}\\right)=f(x) \\hspace{0.5cm}\\forall x\\in[0,1]$$\n",
    "\n",
    "$$u(0)=u(1)=0$$\n",
    "\n",
    "where here $f$ is a random forcing term, assumed to be a GP in this work. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "### Variational formulation\n",
    "\n",
    "The variational formulation is given by:\n",
    "\n",
    "$$a(u,v)=L(v)$$\n",
    "\n",
    "where:\n",
    "\n",
    "$$a(u,v)=\\int_{0}^{1}pu^{\\prime}v^{\\prime}dx$$\n",
    "\n",
    "and\n",
    "\n",
    "$$L(v)=\\int_{0}^{1}fvdx$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will make the following choices for $p,f$:\n",
    "\n",
    "$$p(x)=1$$\n",
    "\n",
    "$$f\\sim\\mathcal{G}\\mathcal{P}(\\bar{f},k_{f})$$\n",
    "\n",
    "$$\\bar{f}(x)=1$$\n",
    "\n",
    "$$ k_{f}(x,y) = \\sigma_f^{2}\\exp\\left(-\\frac{|x-y|^2}{2l_f^2}\\right)$$\n",
    "\n",
    "$$ \\sigma_{f} = 0.1$$\n",
    "\n",
    "$$ l_f = 0.4 $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Difference between true prior mean and statFEM prior mean\n",
    "\n",
    "Since the mean of $f$ is $\\bar{f}(x)=1$ we have that the true mean of the solution $u$ is the solution of the ODE with forcing term set to the constant function 1. This has the exact analytic solution:\n",
    "\n",
    "$$u(x)=\\frac{1}{2}x(1-x)$$\n",
    "\n",
    "as can be directly verified.\n",
    "\n",
    "The FEM approximation to the solution distribution has mean $\\boldsymbol{\\Phi}(x)^{*}A^{-1}\\bar{F}$ which is the solution to the approximate variational problem obtained by replacing $f$ with $\\bar{f}$ in the linear form $L$. \n",
    "\n",
    "We will utilise FEniCS to compute the error between these two as a function of $h$ the mesh size. To do this we first create a function [mean_assembler()](statFEM_analysis.rst#statFEM_analysis.oneDim.mean_assembler) which will assemble the mean for the statFEM prior."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statFEM_analysis.oneDim import mean_assembler"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`mean_assembler` takes in the mesh size `h` and the mean function `f_bar` for the forcing and computes the mean of the approximate statFEM prior, returning this as a FEniCS function."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-warning\">\n",
    "    \n",
    "Important:\n",
    "    \n",
    "`mean_assembler` requires `f_bar` to be represented as a FEniCS function/expression/constant.\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's check that this is working:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Coefficient(FunctionSpace(Mesh(VectorElement(FiniteElement('Lagrange', interval, 1), dim=1), 1), FiniteElement('Lagrange', interval, 1)), 9)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h = 0.15\n",
    "f_bar = Constant(1.0)\n",
    "μ = mean_assembler(h,f_bar)\n",
    "μ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# check the type of μ\n",
    "assert type(μ) == function.function.Function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As explained above the true mean is the function $u(x)=\\frac{1}{2}x(1-x)$. Let's check that the approximate mean resembles this by plotting both:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# use FEniCS to plot μ\n",
    "x = np.linspace(0,1,100)\n",
    "μ_true = 0.5*x*(1-x)\n",
    "plt.plot(x,μ_true,label='true mean',color='red')\n",
    "plot(μ,label='FEM approximation',color='blue')\n",
    "plt.legend()\n",
    "plt.xlabel(r'$x$')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the FEM approximation does indeed resemble the true mean!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Difference between true prior covariance and statFEM prior covariance\n",
    "\n",
    "The solution $u$ has covariance function $c_u(x,y)$ given by the following expression:\n",
    "\n",
    "$$c_u(x,y)=\\int_{0}^{1}\\int_{0}^{1}G(x,w)k_f(w,t)G(t,y)dtdw$$\n",
    "\n",
    "Where $G(x,y)$ is the Green's function for our problem:\n",
    "\n",
    "$$G(x,y) = x(1-y)\\Theta(y-x) + (1-x)y\\Theta(x-y) \\quad \\forall x,y\\in[0,1]$$\n",
    "\n",
    "(note: $\\Theta(x)$ is the Heaviside Step function)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The statFEM covariance can be approximated as follows:\n",
    "\n",
    "$$c_u^{\\text{FEM}}(x,y)\\approx\\sum_{i,j=1}^{J}\\varphi_{i}(x)Q_{ij}\\varphi_{j}(y)$$\n",
    "\n",
    "where $Q=A^{-1}MC_{f}M^{T}A^{-T}$ and where the $\\{\\varphi_{i}\\}_{i=1}^{J}$ are the FE basis functions corresponding to the interior nodes of our domain. $C_f$ is the kernel matrix of $f$ (evaluated on the FEM grid)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The difference between the covariance operators we are interested in computing is the following contribution to the 2-Wasserstein distance between the true solution GP and the approximate FEM GP:\n",
    "\n",
    "$$d_W(C_1,C_2) = \\operatorname{tr} C_1 +\\operatorname{tr} C_2-2\\operatorname{tr}\\sqrt{C_{1}^{1/2}C_{2}C_{1}^{1/2}}$$\n",
    "\n",
    "where $C_1, C_2$ are the covariance operators corresponding to $c_u$ and $c_u^{\\text{FEM}}$ respectively.\n",
    "\n",
    "The above quantity will be approximated by fixing a fine grid and computing the cov matrices $\\Sigma_1, \\Sigma_2$ for the cov operators $C_1, C_2$, respectively, on this grid. We will then utilise the approximation:\n",
    "\n",
    "$d_W(C_1,C_2)\\approx \\operatorname{tr} \\Sigma_1 +\\operatorname{tr} \\Sigma_2-2\\operatorname{tr}\\sqrt{\\Sigma_{1}^{1/2}\\Sigma_{2}\\Sigma_{1}^{1/2}}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thus, it will be necessary to write code to form the matrices $\\Sigma_1,\\Sigma_2$ above. The structure of the approximate $c_u^{\\text{FEM}}$ will allow us to compute $\\Sigma_2$ in a very efficient manner using FEniCS. This is achieved by noting that we can write:\n",
    "\n",
    "$$c_u^{\\text{FEM}}(x,y)\\approx\\boldsymbol{\\phi}(x)^{T}Q\\boldsymbol{\\phi}(y)$$\n",
    "\n",
    "where $\\boldsymbol{\\phi}(x):=\\left(\\varphi_1(x),\\cdots,\\varphi_J(x)\\right)^{T}$\n",
    "\n",
    "Written in this form, it is now easy to see that $\\Sigma_2$, whose $ij$-th entry is given by $(\\Sigma_2)_{ij}=\\boldsymbol{\\phi}(x_i)^{T}Q\\boldsymbol{\\phi}(x_j)$, can be expressed as follows:\n",
    "\n",
    "$$\\Sigma_2=\\boldsymbol{\\Phi}^{T}Q\\boldsymbol{\\Phi}$$\n",
    "\n",
    "where $\\boldsymbol{\\Phi}$ is a $J\\times N$ matrix whose $i$th column is given by $\\boldsymbol{\\phi}(x_i)$ where $\\{x_i\\}_{i=1}^{N}$ are the grid points.\n",
    "\n",
    "Thus, provided we can efficiently compute the matrices $\\boldsymbol{\\Phi}$ and $Q$ with FEniCS we can efficiently compute the differene between the covariances required."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to compute $\\Sigma_1$ and the matrix $C_f$ needed for $Q$ we will need to be able to construct a covariance matrix on a grid for a given cov function. We thus will first create a function [kernMat()](statFEM_analysis.rst#statFEM_analysis.oneDim.kernMat) which assembles the covariance matrix corresponding to the covariance function `k` on a grid `grid`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statFEM_analysis.oneDim import kernMat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-info\">\n",
    "\n",
    "Note:\n",
    "\n",
    "This function takes in two optional boolean arguments `parallel` and `translation_inv`. The first of these specifies whether or not the cov matrix should be computed in parallel and the second specifies whether or not the cov kernel is translation invariant. If it is, the covariance matrix is computed more efficiently using the `cdist` function from scipy.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's quickly test if this function is working, by computing the cov matrix for white noise, which has kernel function $k(x,y)=\\delta(x-y)$. For a grid of length $N$ this should be the $N\\times N$ identity matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# set up the kernel function\n",
    "# set up tolerance for comparison\n",
    "tol = 1e-16\n",
    "def k(x,y):\n",
    "    if np.abs(x-y) < tol:\n",
    "        # x == y within the tolerance\n",
    "        return 1.0\n",
    "    else:\n",
    "        # x != y within the tolerance\n",
    "        return 0.0\n",
    "\n",
    "# set up grid\n",
    "N = 21\n",
    "grid = np.linspace(0,1,N)\n",
    "K = kernMat(k,grid,True,False) # parallel mode\n",
    "\n",
    "# check that this is the N x N identity matrix\n",
    "assert (K == np.eye(N)).all()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now create a function [BigPhiMat()](statFEM_analysis.rst#statFEM_analysis.oneDim.BigPhiMat) to utilise FEniCS to efficiently compute the matrix $\\boldsymbol{\\Phi}$ defined above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statFEM_analysis.oneDim import BigPhiMat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`BigPhiMat` takes in two arguments: `J`, which controls the FE mesh size ($h=1/J$), and `grid` which is the grid in the definition of $\\boldsymbol{\\Phi}$. `BigPhiMat` returns $\\boldsymbol{\\Phi}$ as a sparse `csr_matrix` for memory efficiency."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-info\">\n",
    "\n",
    "Note:\n",
    "\n",
    "Since FEniCS works with the FE functions corresponding to all the FE dofs and our matrix $\\Sigma_2$ only uses the FE functions corresponding to non-boundary dofs we need to account for this in the code. See the source code for `BigPhiMat` to see how this is done.\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now create a function [cov_asssembler()](statFEM_analysis.rst#statFEM_analysis.oneDim.cov_assembler) which assembles the approximate FEM covariance matrix on the grid."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statFEM_analysis.oneDim import cov_assembler"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`cov_assembler` takes in several arguments which are explained below:\n",
    "\n",
    "- `J`: controls the FE mesh size ($h=1/J)$\n",
    "- `k_f`: the covariance function for the forcing $f$\n",
    "- `grid`: the reference grid where the FEM cov matrix should be computed on\n",
    "- `parallel`: boolean argument indicating whether the intermediate computation of $C_f$ should be done in parallel \n",
    "- `translation_inv`: boolean argument indicating whether the intermediate computation of $C_f$ should be computed assuming `k_f` is translation invariant or not"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As a quick demonstration that the code is working, we will compute the true and approximate covariance matrices for a relatively coarse grid. We first set up functions to compute the true covariance matrix $\\Sigma_1$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# set up kernel functions for f\n",
    "l_f = 0.4\n",
    "σ_f = 0.1\n",
    "\n",
    "def c_f(x,y):\n",
    "    return (σ_f**2)*np.exp(-(x-y)**2/(2*(l_f**2)))\n",
    "\n",
    "# translation invariant form of c_f\n",
    "def k_f(x):\n",
    "    return (σ_f**2)*np.exp(-(x**2)/(2*(l_f**2)))\n",
    "\n",
    "# use quadrature for the true cov function\n",
    "from scipy import integrate\n",
    "# compute inner integral over t\n",
    "def η(w,y):\n",
    "    I_1 = integrate.quad(lambda t: t*c_f(w,t),0.0,y)[0]\n",
    "    I_2 = integrate.quad(lambda t: (1-t)*c_f(w,t),y,1.0)[0]\n",
    "    return (1-y)*I_1 + y*I_2\n",
    "\n",
    "# use this function η and compute the outer integral over w\n",
    "def c_u(x,y):\n",
    "    I_1 = integrate.quad(lambda w: (1-w)*η(w,y),x,1.0)[0]\n",
    "    I_2 = integrate.quad(lambda w: w*η(w,y),0.0,x)[0]\n",
    "    return x*I_1 + (1-x)*I_2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With these functions we can now compute $\\Sigma_1$ as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# set up a reference grid\n",
    "N = 21\n",
    "grid = np.linspace(0,1,N)\n",
    "\n",
    "# compute Σ_1 using c_u\n",
    "Σ_1 = kernMat(c_u,grid,True,False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now use our function `cov_assembler` to compute $\\Sigma_2$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "J = 20 # choose a FE mesh size\n",
    "Σ_2 = cov_assembler(J,k_f,grid,False,True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot heatmaps of both $\\Sigma_1, \\Sigma_2$ to compare:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "vmin = min(Σ_1.min(), Σ_2.min())\n",
    "vmax = max(Σ_1.max(), Σ_2.max())\n",
    "plt.rcParams['figure.figsize'] = (12,6)\n",
    "fig, axs = plt.subplots(ncols=3, gridspec_kw=dict(width_ratios=[4,4,0.2]))\n",
    "sns.heatmap(Σ_1,cbar=False,\n",
    "                annot=False,\n",
    "                xticklabels=False,\n",
    "                yticklabels=False,\n",
    "                cmap=cm.viridis,\n",
    "                ax=axs[0])\n",
    "axs[0].title.set_text(r'$\\Sigma_1$')\n",
    "sns.heatmap(Σ_2,cbar=False,\n",
    "                annot=False,\n",
    "                xticklabels=False,\n",
    "                yticklabels=False,\n",
    "                cmap=cm.viridis,\n",
    "                ax=axs[1])\n",
    "axs[1].title.set_text(r'$\\Sigma_2$')\n",
    "fig.colorbar(axs[np.argmax([Σ_1.max(), Σ_2.max()])].collections[0], cax=axs[2])\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Even with a relatively coarse reference grid and a relatively coarse FE space it looks as if the approximate FEM covariance is quite similar to the true covariance matrix as can be seen from the heatmaps above. Let's also check how similar they are by utilising `np.linalg.norm` to compute the relative percentage difference:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Relative percentage difference is: 0.68%\n"
     ]
    }
   ],
   "source": [
    "print(\"Relative percentage difference is: %.2f\" %(100*np.linalg.norm(Σ_1-Σ_2)/np.linalg.norm(Σ_1)) + \"%\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Posterior from incorporating sensor readings\n",
    "\n",
    "Denote by $\\nu_{i}=\\mathcal{N}(m_{i},\\Sigma_{i})$, where $i$ is either the symbol $\\star$ or $h$, the true and statFEM prior respectively. When we take $u\\sim\\nu_{i}$ as our prior, the resulting posterior after incorporating the noisy sensor readings $\\mathbf{v}$ at the locations $\\{y_{j}\\}_{j=1}^{s}$ is given by:\n",
    "\n",
    "$$u|\\mathbf{v}\\sim\\mathcal{N}\\left(m_{u|\\mathbf{v}}^{(i)},\\Sigma_{u|\\mathbf{v}}^{(i)}\\right)$$\n",
    "\n",
    "where we have:\n",
    "\n",
    "$$m_{u|\\mathbf{v}}^{(i)}=m_{i} + \\Sigma_{i}S^{\\dagger}(\\epsilon^{2}I+S\\Sigma_{i}S^{\\dagger})^{-1}(\\mathbf{v}-Sm_{i})$$\n",
    "\n",
    "$$\\Sigma_{u|\\mathbf{v}}^{(i)}=\\Sigma_{i} - \\Sigma_{i}S^{\\dagger}(\\epsilon^{2}I+S\\Sigma_{i}S^{\\dagger})^{-1}S\\Sigma_{i}$$\n",
    "\n",
    "where $S$ is the operator which maps a function $g$ to the vector $\\left(g(y_1),\\cdots,g(y_s)\\right)^{T}$.\n",
    "\n",
    "For brevity we will denote the $s\\times s$ matrix which appears above as $B_{\\epsilon,i}:=\\epsilon^{2}I+S\\Sigma_{i}S^{\\dagger}=\\epsilon^{2}I+C_{Y,i}$ where we have also defined $C_{Y,i}:=S\\Sigma_{i}S^{\\dagger}$. This matrix has $pq$*-th* entry $c^{(i)}(y_{p},y_{q})$ where $c^{(i)}$ is the covariance function associated with the covariance operator $\\Sigma_{i}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Posterior mean\n",
    "\n",
    "Thus, our posterior mean in both cases has the form:\n",
    "\n",
    "$$m^{(i)}_{u|\\mathbf{v}}(x)=m_{i}(x)+\\sum_{p,q=1}^{s}c^{(i)}(x,y_{p})\\left(B_{\\epsilon,i}^{-1}\\right)_{pq}(v_{q}-m_{i}(y_{q}))$$\n",
    "\n",
    "Note that this can be expressed as:\n",
    "\n",
    "$$m^{(i)}_{u|\\mathbf{v}}(x)=m_{i}(x) - \\mathbf{c}^{(i)}(x)^{T}B_{\\epsilon,i}^{-1}(\\mathbf{m}^{(i)}-\\mathbf{v})$$\n",
    "\n",
    "where $\\mathbf{m}^{(i)}:=Sm_{i}=(m_{i}(y_1),\\cdots,m_{i}(y_s))^{T}$ and $\\mathbf{c}^{(i)}(x):=(c^{(i)}(x,y_1),\\cdots,c^{(i)}(x,y_s))^{T}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thus, we require a function to evaluate the posterior means. We will thus create a function [m_post()](statFEM_analysis.rst#statFEM_analysis.oneDim.m_post) which evaluates the posterior means. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statFEM_analysis.oneDim import m_post"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`m_post` takes in several arguments which are explained below:\n",
    "\n",
    "- `x`: point where the posterior mean will be evaluated\n",
    "- `m`: function which computes the prior mean at a given point y\n",
    "- `c`: function which returns the vector (c(x,y)) for y in Y (note: c is the prior covariance function)\n",
    "- `v`: vector of noisy sensor readings\n",
    "- `Y`: vector of sensor locations\n",
    "- `B`: the matrix $\\epsilon^{2}I+C_Y$ to be inverted in order to obtain the posterior"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As a quick test to see if the code is working, note that if we choose $\\mathbf{c}$ above to be constant at the $j$*-th* standard basis vector and if we take $B$ to be the identity matrix then we should obtain the function $m(x)-m(y_j)+v_j$. This will give us the $v_j$ when evaluated at $y_j$. We will test that this is indeed what we get:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# choose several prior mean functions to try\n",
    "m_list = [lambda x: 1.0, lambda x: 0.5*x*(1.0-x), lambda x: np.sin(2*np.pi*x)]\n",
    "\n",
    "# set up Y and B and v:\n",
    "Y = np.linspace(0.01,0.99,11)\n",
    "s = len(Y)\n",
    "B = np.eye(s)\n",
    "np.random.seed(42)\n",
    "v = np.random.randn(s)\n",
    "\n",
    "# test that we get v_j when evaluated at y_j (and when c is set to be j-th basis vector)\n",
    "for j in range(s):\n",
    "    # define c to be j-th basis vector for all x\n",
    "    def c(x):\n",
    "        c_vect = np.zeros(s)\n",
    "        c_vect[j] = 1.0\n",
    "        return c_vect\n",
    "    \n",
    "    # evaluate the posterior mean at jth sensor location and check that this is v_j\n",
    "    # (this check is done up to a tolerance tol)\n",
    "    tol = 1e-15\n",
    "    for m in m_list:\n",
    "        assert np.abs(m_post(Y[j],m,c,v,Y,B) - v[j]) < tol"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Difference between posterior means\n",
    "\n",
    "In order to compute the difference between the posterior means we require some more code."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Firstly, we will need code to generate samples from a GP with mean $m$ and cov function $k$ on a grid. We write the function [sample_gp()](statFEM_analysis.rst#statFEM_analysis.oneDim.sample_gp) for this purpose."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statFEM_analysis.oneDim import sample_gp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`sample_gp` takes in several arguments which are explained below:\n",
    "\n",
    "- `n_sim`: number of trajectories to be sampled\n",
    "- `m`: mean function for the GP\n",
    "- `k`: cov function for the GP\n",
    "- `grid`: grid of points on which to sample the GP\n",
    "- `par`: boolean argument indicating whether the computation of the cov matrix should be done in parallel\n",
    "- `trans`: boolean argument indicating whether the computation of the cov matrix should be computed assuming `k` is translation invariant or not\n",
    "- `tol`: controls the size of the tiny diagonal perturbation added to cov matrix to ensure it is strictly positive definite (defaults to `1e-9`)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As a quick demonstration that the code is working lets generate 10 trajectories of white noise, using the kernel `k` from one of the previous tests:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# set up grid to sample on\n",
    "N = 51\n",
    "grid = np.linspace(0,1,N)\n",
    "\n",
    "# set up mean\n",
    "def m(x):\n",
    "    return 0.0\n",
    "\n",
    "# sample the GP\n",
    "n_sim = 10\n",
    "np.random.seed(235)\n",
    "samples = sample_gp(n_sim,m,k,grid,True,False)\n",
    "plt.plot(grid,samples)\n",
    "plt.grid()\n",
    "plt.xlabel(r'$x$')\n",
    "plt.title('White noise trajectories')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next bit of code we require is code to generate noisy sensor readings from our system. We write the function [gen_sensor()](statFEM_analysis.rst#statFEM_analysis.oneDim.gen_sensor) for this purpose."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statFEM_analysis.oneDim import gen_sensor"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`gen_sensor` takes in several arguments which are explained below:\n",
    "\n",
    "- `ϵ`: controls the amount of sensor noise\n",
    "- `m`: mean function for the forcing f\n",
    "- `k`: cov function for the forcing f\n",
    "- `Y`: vector of sensor locations\n",
    "- `u_quad`: function to accurately compute the solution u given a realisation of the forcing f\n",
    "- `grid`: grid where forcing f is sampled on\n",
    "- `par`: boolean argument indicating whether the computation of the forcing cov matrix should be done in parallel\n",
    "- `trans`: boolean argument indicating whether the computation of the forcing cov matrix should be computed assuming `k` is translation invariant or not\n",
    "- `tol`: controls the size of the tiny diagonal perturbation added to forcing cov matrix to ensure it is strictly positive definite (defaults to `1e-9`)\n",
    "- `maxiter`: parameter which controls the accuracy of the quadrature used in u_quad (defaults to `50`)\n",
    "- `require_f` : boolean argument indicating whether or not to also return the realisation of the forcing f (defaults to `False`)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-warning\">\n",
    "\n",
    "Important:\n",
    "\n",
    "The function `u_quad` which is passed to `gen_sensor` is assumed to compute the solution using quadrature. This must be done in a particular way and will be demonstrated below. It is also important to choose a fine enough grid for the argument `grid` passed to `gen_sensor` as this affects the solution accuracy.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's demonstrate that this code is working. To start we note that due to the form of the Green's function for our problem, we can express the solution $u$ in terms of the forcing $f$ as follows:\n",
    "\n",
    "$$u(x)=\\int_{0}^{1}G(x,y)f(y)\\mathrm{d}y=(1-x)\\int_{0}^{x}yf(y)\\mathrm{d}y+x\\int_{x}^{1}(1-y)f(y)\\mathrm{d}y$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will use this observation when setting up `u_quad` below. We now generate $s=20$ sensor observations with the sensors equally spaced in the interval $(0.01,0.99)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# set up mean and kernel functions for the forcing f\n",
    "l_f = 0.4\n",
    "σ_f = 0.1\n",
    "\n",
    "def m_f(x):\n",
    "    return 1.0\n",
    " \n",
    "def k_f(x):\n",
    "    return (σ_f**2)*np.exp(-(x**2)/(2*(l_f**2)))\n",
    "\n",
    "# set up sensor grid and sensor noise level\n",
    "s = 20\n",
    "Y = np.linspace(0.01,0.99,s)\n",
    "ϵ = 0.1\n",
    "\n",
    "# set up grid to simulate f on\n",
    "N = 40\n",
    "grid = np.linspace(0,1,N+1)\n",
    "\n",
    "# set up u_quad\n",
    "def u_quad(x,f,maxiter=50):\n",
    "    I_1 = integrate.quadrature(lambda w: w*f(w), 0.0, x,maxiter=maxiter)[0]\n",
    "    I_2 = integrate.quadrature(lambda w: (1-w)*f(w),x, 1.0,maxiter=maxiter)[0]\n",
    "    return (1-x)*I_1 + x*I_2\n",
    "\n",
    "# generate the sensor observations\n",
    "np.random.seed(534)\n",
    "v_dat,f_sim = gen_sensor(ϵ,m_f,k_f,Y,u_quad,grid,maxiter=200,require_f=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting these sensor observations with the solution for this particular realisation of the forcing gives:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the sensor readings as well as the true mean\n",
    "x_range = np.linspace(0,1,100)\n",
    "f = interp1d(grid,f_sim.flatten(),kind='cubic')\n",
    "def u(x):\n",
    "    return u_quad(x,f,maxiter=200)\n",
    "res = np.array([u(x) for x in x_range])\n",
    "plt.scatter(Y,v_dat,c='r',label='noisy sensor observations')\n",
    "plt.plot(x_range,res,c='b',label='solution')\n",
    "plt.xlabel(r'$x$')\n",
    "plt.ylim(-0.2,0.3)\n",
    "plt.title('Noisy sensor observations')\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next bit of code needed in order to compute the difference between the posterior means is a way of comparing the two different mean functions. One possible solution is to overload the `UserExpression` class in FEniCS to create custom FEniCS expressions from user defined functions. This will allow us to use our function `m_post` together with `errornorm` from FEniCS to compute the L2 norm of the difference. We thus, create a class called [MyExpression()](statFEM_analysis.rst#statFEM_analysis.oneDim.MyExpression)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statFEM_analysis.oneDim import MyExpression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will now demonstrate how this works, building on the sensor observation example above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Coefficient(FunctionSpace(None, FiniteElement('Lagrange', None, 2)), 44)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# set up the true prior mean and the true prior cov needed for the true posterior \n",
    "μ_true = Expression('0.5*x[0]*(1-x[0])',degree=2)\n",
    "C_true_s = kernMat(c_u,Y.flatten())\n",
    "def c_u_vect(x):\n",
    "    return np.array([c_u(x,y_i) for y_i in Y])\n",
    "# set up matrix B for posterior\n",
    "B_true = (ϵ**2)*np.eye(s) + C_true_s\n",
    "\n",
    "# compute the true posterior mean\n",
    "def true_post_mean(x):\n",
    "        return m_post(x,μ_true,c_u_vect,v_dat,Y,B_true)\n",
    "    \n",
    "# set up MyExpression object\n",
    "μ_true_post = MyExpression()\n",
    "μ_true_post.f = true_post_mean\n",
    "μ_true_post"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`μ_true_post` now works like a usual FEniCS expression/function. We can evaluate it at a point:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$0.10740217262611212$$"
      ],
      "text/plain": [
       "0.10740217262611212"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "μ_true_post(0.3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or even evaluate it on the nodes of a FEniCS mesh:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.        , 0.08179325, 0.12278251, 0.12279555, 0.08181789,\n",
       "       0.        ])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "μ_true_post.compute_vertex_values(mesh=UnitIntervalMesh(5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-warning\">\n",
    "\n",
    "Warning:\n",
    "    \n",
    "A mesh needs to be passed when using `MyExpression` objects with certain FEniCS methods\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now require code which will create the matrix $C_Y,h$ and the function $\\mathbf{c}^{(h)}$ required for the statFEM posterior mean. We will create the function [fem_cov_assembler_post()](statFEM_analysis.rst#statFEM_analysis.oneDim.fem_cov_assembler_post) for this purpose. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statFEM_analysis.oneDim import fem_cov_assembler_post"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`fem_cov_assembler_post` takes in several arguments which are explained below:\n",
    "\n",
    "- `J`: controls the FE mesh size ($h=1/J$)\n",
    "- `k_f`: the covariance function for the forcing $f$\n",
    "- `Y`: vector of sensor locations\n",
    "- `parallel`: boolean argument indicating whether the computation of the forcing cov mat should be done in parallel\n",
    "- `translation_inv`: boolean argument indicating whether the computation of the forcing cov mat should be computed assuming `k_f` is translation invariant or not"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With all of this code in place we can now finally write the function [m_post_fem_assembler()](statFEM_analysis.rst#statFEM_analysis.oneDim.m_post_fem_assembler) which will assemble the statFEM posterior mean function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statFEM_analysis.oneDim import m_post_fem_assembler"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`m_post_fem_assembler` takes in several arguments which are explained below:\n",
    "\n",
    "- `J`: controls the FE mesh size ($h=1/J$)\n",
    "- `f_bar`: the mean function for the forcing $f$\n",
    "- `k_f`: the covariance function for the forcing $f$\n",
    "- `ϵ`: controls the amount of sensor noise\n",
    "- `Y`: vector of sensor locations\n",
    "- `v_dat`: vector of noisy sensor observations\n",
    "- `par`: boolean argument passed to `fem_cov_assembler_post`'s argument `parallel` (defaults to `False`)\n",
    "- `trans`: boolean argument passed to `fem_cov_assembler_post`'s argument `translation_inv` (defaults to `True`)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-warning\">\n",
    "\n",
    "Important:\n",
    "\n",
    "`m_post_fem_assembler` requires `f_bar` to be represented as a FEniCS function/expression/constant.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's quickly check that this function is working."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$0.10741625985588846$$"
      ],
      "text/plain": [
       "0.10741625985588846"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "J = 20\n",
    "f_bar = Constant(1.0)\n",
    "m_post_fem = m_post_fem_assembler(J,f_bar,k_f,ϵ,Y,v_dat)\n",
    "# compute posterior mean at a location x in [0,1]\n",
    "x = 0.3\n",
    "m_post_fem(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's also plot the statFEM posterior mean together with the corresponding statFEM prior mean:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "h = 1/J\n",
    "m_prior = mean_assembler(h,f_bar)\n",
    "x_range = np.linspace(0,1,100)\n",
    "y_range = np.array([m_post_fem(x) for x in x_range])\n",
    "plot(m_prior,label='prior')\n",
    "plt.plot(x_range,y_range,label='posterior',c='r')\n",
    "plt.grid()\n",
    "plt.xlabel(r'$x$')\n",
    "plt.title('statFEM prior and posterior means')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Posterior covariance\n",
    "\n",
    "From the form of the posterior covariance operators $\\Sigma_{u|\\mathbf{v}}^{(i)}$ given in the section **\"Posterior from incorporating sensor readings\"** we can see that the posterior covariance functions both have the form:\n",
    "\n",
    "$$c_{u|\\mathbf{v}}^{(i)}(x,y) = c^{(i)}(x,y) - \\sum_{p,q=1}^{s}c^{(i)}(x,y_p)(B_{\\epsilon,i}^{-1})_{pq}c^{(i)}(y_q,y)$$\n",
    "\n",
    "Note that this can be expressed as:\n",
    "\n",
    "$$c_{u|\\mathbf{v}}^{(i)}(x,y) = c^{(i)}(x,y) - \\mathbf{c}^{(i)}(x)^{T}B_{\\epsilon,i}^{-1}\\mathbf{c}^{(i)}(y)$$\n",
    "\n",
    "where we have utilised the fact that $c^{(i)}$ are covariance functions and are hence symmetric which allows us to put $\\mathbf{c}^{(i)}(y)=(c^{(i)}(y,y_1),\\cdots,c^{(i)}(y,y_s))^{T}=(c^{(i)}(y_1,y),\\cdots,c^{(i)}(y_s,y))^{T}$.\n",
    "\n",
    "Thus, we require a function to evalute the posterior covarainces. We will thus create a function [c_post()](statFEM_analysis.rst#statFEM_analysis.oneDim.c_post) which evalutes the posterior covariances."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statFEM_analysis.oneDim import c_post"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`c_post` takes in several arguments which are explained below:\n",
    "\n",
    "- `x`,`y`: points to evaluate the covariance at\n",
    "- `c`: function which returns the prior covariance at any given pair $(x,y)$\n",
    "- `Y`: vector of sensor locations\n",
    "- `B`: the matrix $\\epsilon^{2}I+C_{Y}$ to be inverted in order to obtain the posterior"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-info\">\n",
    "\n",
    "Note:\n",
    "\n",
    "The function `c_post` will only be used for the true posterior covariances.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Difference between posterior covariances\n",
    "\n",
    "In order to compute the difference between the posterior covariances we require some more code. Since we will be comparing the posterior covariances on a fixed reference grid $\\{x_{i}\\}_{i=1}^{N}$ we will need to assemble the cov matrices on this grid. I.e. we will require the matrices $\\tilde{C}_{X,i}$ with $pq$*-th* entry $c_{u|\\mathbf{v}}^{(i)}(x_{p},x_{q})$ for $p,q=1,\\cdots N$. For statFEM this matrix can be efficiently assembled by exploiting the form of the statFEM prior and posterior covariance functions, i.e. by noting that we have:\n",
    "\n",
    "$$\\tilde{C}_{X,h} = \\Sigma_{X} - \\Sigma_{XY}B_{\\epsilon,h}^{-1}\\Sigma_{XY}^{T}$$\n",
    "\n",
    "where $\\Sigma_{X}:=\\Phi_{X}^{T}Q\\Phi_{X}$, $\\Sigma_{XY}=\\Phi_{X}^{T}Q\\Phi_{Y}$ and where $\\Phi_{X}$ is a $J\\times N$ matrix whose $i$*-th* column is given by $\\phi(x_{i})$ and similarly $\\Phi_{Y}$ is a $J\\times s$ matrix whose $i$*-th* column is given by $\\phi(y_{i})$ and $Q$ is the matrix defined in the section **\"Difference between the true prior covariance and the statFEM prior covariance\"**. \n",
    "\n",
    "Thus, we can use our function `BigPhiMat` to compute $\\tilde{C}_{X,h}$ efficiently. We start by creating the function [post_fem_cov_assembler()](statFEM_analysis.rst#statFEM_analysis.oneDim.post_fem_cov_assembler) which assembles the matrices $\\Sigma_{X}, \\Sigma_{XY}$, and $\\Sigma_{Y}:=\\Phi_{Y}^{T}Q\\Phi_{Y}$ required for the statFEM posterior covariance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statFEM_analysis.oneDim import post_fem_cov_assembler"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`post_fem_cov_assembler` takes in several arguments which are explained below:\n",
    "\n",
    "- `J`: controls the FE mesh size ($h=1/J$)\n",
    "- `k_f`: the covariance function for the forcing $f$\n",
    "- `grid`: the fixed reference grid $\\{x_{i}\\}_{i=1}^{N}$ on which to assemble the posterior cov mat\n",
    "- `Y`: vector of sensor locations.\n",
    "- `parallel`: boolean argument indicating whether the computation of the forcing cov mat should be done in parallel\n",
    "- `translation_inv`: boolean argument indicating whether the computation of the forcing cov mat should be computed assuming `k_f` is translation invariant or not"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we create the function [c_post_fem_assembler()](statFEM_analysis.rst#statFEM_analysis.oneDim.c_post_fem_assembler) which assembles the statFEM posterior cov mat on the reference grid using the matrices `post_fem_cov_assembler` returns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statFEM_analysis.oneDim import c_post_fem_assembler"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's quickly demonstrate that this code is working by computing the statFEM posterior covariance matrix on a reference grid and comparing this to the corresponding statFEM prior."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "# set up reference grid and J\n",
    "N = 21\n",
    "grid = np.linspace(0,1,N)\n",
    "J = 20\n",
    "\n",
    "# get statFEM prior cov mat on this grid\n",
    "Σ_prior = cov_assembler(J,k_f,grid,False,True)\n",
    "\n",
    "# get statFEM posterior cov mat on this grid\n",
    "Σ_posterior = c_post_fem_assembler(J,k_f,grid,Y,ϵ,False,True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "vmin = min(Σ_prior.min(), Σ_posterior.min())\n",
    "vmax = max(Σ_prior.max(), Σ_posterior.max())\n",
    "plt.rcParams['figure.figsize'] = (12,6)\n",
    "fig, axs = plt.subplots(ncols=3, gridspec_kw=dict(width_ratios=[4,4,0.2]))\n",
    "sns.heatmap(Σ_prior,cbar=False,\n",
    "                annot=False,\n",
    "                xticklabels=False,\n",
    "                yticklabels=False,\n",
    "                cmap=cm.viridis,\n",
    "                ax=axs[0])\n",
    "axs[0].title.set_text('statFEM prior covariance')\n",
    "sns.heatmap(Σ_posterior,cbar=False,\n",
    "                annot=False,\n",
    "                xticklabels=False,\n",
    "                yticklabels=False,\n",
    "                cmap=cm.viridis,\n",
    "                ax=axs[1])\n",
    "axs[1].title.set_text('statFEM posterior covariance')\n",
    "fig.colorbar(axs[np.argmax([Σ_prior.max(), Σ_posterior.max()])].collections[0], cax=axs[2])\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.6.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}