{ "cells": [ { "cell_type": "markdown", "id": "96d38bf4-221b-480a-848b-d4ee15b34070", "metadata": {}, "source": [ "# Building up tools to analyse a 2-D problem" ] }, { "cell_type": "markdown", "id": "15549864-62f9-4b92-ac98-e2645dfe2273", "metadata": {}, "source": [ "> Code for a 2-D problem." ] }, { "cell_type": "code", "execution_count": 1, "id": "32cc5716-a252-467d-907f-0fea8a97b7e0", "metadata": {}, "outputs": [], "source": [ "from dolfin import *\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "import matplotlib.cm as cm\n", "import matplotlib.colors as colors\n", "import matplotlib.colorbar as colorbar\n", "import matplotlib.tri as tri\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", "id": "52998acf-499d-4f22-8282-c3938709fcfc", "metadata": {}, "source": [ "## 2 dimensional case (PDE)\n", "\n", "We consider the following 2-D problem:\n", "\n", "$$\\nabla\\cdot\\left(\\kappa(x)\\nabla u(x)\\right)=f(x) \\quad\\forall x\\in D=[0,1]^{2}$$\n", "\n", "$$u(x)=0\\quad\\forall x\\in\\partial D$$\n", "\n", "where here $f$ is again a random forcing term, assumed to be a GP in this work." ] }, { "cell_type": "markdown", "id": "bdbf1fc6-1887-49d3-941e-1b05cd3ea95d", "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", "$$a(u,v)=\\int_{D}\\nabla u\\cdot\\left(\\kappa\\nabla u\\right)dx$$\n", "\n", "and\n", "\n", "$$L(v)=\\int_{D}fvdx$$" ] }, { "cell_type": "markdown", "id": "c82313d9-47b6-4f25-a5cc-b88c1b36e2cf", "metadata": {}, "source": [ "We will make the following choices for $\\kappa,f$:\n", "\n", "$$\\kappa(x)=1$$\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", "$$ l_f = 0.4 $$\n", "\n", "where $\\|\\cdot\\|$ is the usual Euclidean norm." ] }, { "cell_type": "markdown", "id": "a4659450-d579-49e8-a1d8-7eb42e01d39b", "metadata": {}, "source": [ "Since we do not have access to a suitable Green's function for this problem, we will have to estimate the rate of convergence of the statFEM prior and posterior by comparing them on a sequence of refined meshes. More details on this will follow later. Thus, we need similar code as for the 1-D problem." ] }, { "cell_type": "markdown", "id": "39f5bd38-7a22-4167-8cdc-7232e142730d", "metadata": {}, "source": [ "### statFEM prior mean\n", "\n", "We will again utilise FEniCS to obtain the statFEM prior mean. For this purpose, we create a function [mean_assembler()](statFEM_analysis.rst#statFEM_analysis.twoDim.mean_assembler) which will assemble the mean for the statFEM prior." ] }, { "cell_type": "code", "execution_count": 2, "id": "310df957-b312-41d3-a908-4a260257e61a", "metadata": {}, "outputs": [], "source": [ "from statFEM_analysis.twoDim import mean_assembler" ] }, { "cell_type": "markdown", "id": "4a3330e1-8a52-4273-a7a5-d05aeb892f8b", "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", "id": "e5d34a07-91fe-40b4-b0b6-d6114146dbce", "metadata": {}, "source": [ "
\n", " \n", "Important:\n", " \n", "`mean_assembler` requires `f_bar` to be represented as a FEniCS function/expression/constant.\n", " \n", "
" ] }, { "cell_type": "markdown", "id": "5151eb44-29ad-40e8-9a7a-3fb9214e6b1b", "metadata": {}, "source": [ "Let's check that this is working:" ] }, { "cell_type": "code", "execution_count": 3, "id": "f8b75bfa-e565-4b0b-ac1c-b9df04770174", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Coefficient(FunctionSpace(Mesh(VectorElement(FiniteElement('Lagrange', triangle, 1), dim=2), 1), FiniteElement('Lagrange', triangle, 1)), 9)" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "h = 0.1\n", "f_bar = Constant(1.0)\n", "μ = mean_assembler(h,f_bar)\n", "μ" ] }, { "cell_type": "code", "execution_count": 4, "id": "d8a9288b-caa8-4cdc-ac4d-bbd1df140889", "metadata": {}, "outputs": [], "source": [ "# check the type of μ\n", "assert type(μ) == function.function.Function" ] }, { "cell_type": "markdown", "id": "690a326d-5b56-490c-b6f8-357744e81a78", "metadata": {}, "source": [ "Let's plot $\\mu$:" ] }, { "cell_type": "code", "execution_count": 5, "id": "0b904489-95f0-4b2a-9278-a705dc01148a", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# use FEniCS to plot μ\n", "plot(μ)\n", "plt.xlabel(r'$x$')\n", "plt.ylabel(r'$y$')\n", "plt.title(r'Plot of statFEM mean for $h=%.2f$'%h)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "3cf6dc84-883f-48b3-bd5f-09cce80a0de5", "metadata": {}, "source": [ "### statFEM prior covariance\n", "\n", "We will also utilise FEniCS again to obtain an approximation of our statFEM covariance function.\n", "\n", "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.\n", "\n", "with $C_f$ being the kernel matrix of $f$ (evaluated on the FEM grid).\n", "\n", "As we will be comparing the statFEM covariance functions for finer and finer FE mesh sizes we will need to be able to assemble the statFEM covariance function on a grid. As discussed in oneDim, we can assemble such covariance matrices in a very efficient manner. The code remains largely the same as in the 1-D case and so we do not go into as much detail here." ] }, { "cell_type": "markdown", "id": "51472abe-33d1-4238-b509-bfa70fadf4d4", "metadata": {}, "source": [ "We start by creating a function [kernMat()](statFEM_analysis.rst#statFEM_analysis.twoDim.kernMat) which assembles the covariance matrix corresponding to a covariance function `k` on a grid `grid`." ] }, { "cell_type": "code", "execution_count": 6, "id": "6faf8e07-8e5e-4551-a7a8-634f5b397ffc", "metadata": {}, "outputs": [], "source": [ "from statFEM_analysis.twoDim import kernMat" ] }, { "cell_type": "markdown", "id": "c5c7bc08-bdb6-41d7-9f57-8eb6a67ef56b", "metadata": {}, "source": [ "
\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", "
" ] }, { "cell_type": "markdown", "id": "2799f8a7-98a2-4b6c-bf9f-441219253219", "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, "id": "7326a81a-b7ce-432f-b2b2-17e01514df74", "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).all():\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", "x_range = np.linspace(0,1,n)\n", "grid = np.array([[x,y] for x in x_range for y in x_range])\n", "N = len(grid) # get length of grid (N=n^2)\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", "id": "ea9bb1a5-c2b8-455f-902d-69b5e951c00d", "metadata": {}, "source": [ "We now create a function [BigPhiMat()](statFEM_analysis.rst#statFEM_analysis.twoDim.BigPhiMat) to utilise FEniCS to efficiently compute the matrix $\\boldsymbol{\\Phi}$ defined above." ] }, { "cell_type": "code", "execution_count": 8, "id": "fb59e13d-dc81-490b-8a8a-5970fb6930a6", "metadata": {}, "outputs": [], "source": [ "from statFEM_analysis.twoDim import BigPhiMat" ] }, { "cell_type": "markdown", "id": "6a2dbcc4-c8d6-445e-b30b-afb85a0029f7", "metadata": {}, "source": [ "`BigPhiMat` takes in two arguments: `J`, which controls the FE mesh size ($h=1/J^{2}$), 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", "id": "cebdf937-d521-49c6-8867-6644c96289ee", "metadata": {}, "source": [ "
\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", "
" ] }, { "cell_type": "markdown", "id": "fbaecfa5-fe03-40a9-946e-a53399ea2a0c", "metadata": {}, "source": [ "We now create a function [cov_asssembler()](statFEM_analysis.rst#statFEM_analysis.twoDim.cov_assembler) which assembles the approximate FEM covariance matrix on the grid." ] }, { "cell_type": "code", "execution_count": 9, "id": "3bcfc60a-80aa-4cd4-9a0e-c288abcfb082", "metadata": {}, "outputs": [], "source": [ "from statFEM_analysis.twoDim import cov_assembler" ] }, { "cell_type": "markdown", "id": "fdbb30b7-31eb-477c-ac27-6459551317fd", "metadata": {}, "source": [ "`cov_assembler` takes in several arguments which are explained below:\n", "\n", "- `J`: controls the FE mesh size ($h=1/J^{2})$\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", "id": "44b57279-0e48-4ec6-8085-ad80db8f582f", "metadata": {}, "source": [ "As a quick demonstration that the code is working, we will the statFEM cov matrix for a relatively coarse grid." ] }, { "cell_type": "code", "execution_count": 10, "id": "c48bb73f-4dc8-47df-bba5-f6b27822dd00", "metadata": {}, "outputs": [], "source": [ "# set up kernel function for forcing\n", "f_bar = Constant(1.0)\n", "\n", "l_f = 0.4\n", "σ_f = 0.1\n", "\n", "def k_f(x):\n", " return (σ_f**2)*np.exp(-(x**2)/(2*(l_f**2)))\n", "\n", "# set up grid\n", "n = 21\n", "x_range = np.linspace(0,1,n)\n", "grid = np.array([[x,y] for x in x_range for y in x_range])\n", "\n", "# get the statFEM grid for a particular choice of J\n", "J = 10\n", "Σ = cov_assembler(J,k_f,grid,False,True)" ] }, { "cell_type": "markdown", "id": "ad8c6971-dc84-48fa-984e-4e550efe2505", "metadata": {}, "source": [ "Let's plot a heatmap of the statFEM cov matrix:" ] }, { "cell_type": "code", "execution_count": 11, "id": "ab91cdf3-0eb0-481a-b856-2f372545ace6", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "sns.heatmap(Σ,cbar=True,\n", " annot=False,\n", " xticklabels=False,\n", " yticklabels=False,\n", " cmap=cm.viridis)\n", "plt.title('Heat map of statFEM covariance matrix')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "8532e9ed-76d8-4e09-a452-16a63f62a3fa", "metadata": {}, "source": [ "
\n", " \n", "Note:\n", " \n", "The banded structure in the above statFEM covariance matrix is due to the internal ordering of the FE grid in FEniCS.\n", "\n", "
" ] }, { "cell_type": "markdown", "id": "1ebbf3f3-c00d-4f85-8ecf-6e9004065d92", "metadata": {}, "source": [ "### statFEM posterior mean\n", "\n", "The statFEM posterior from incorporating sensor readings has the same form as given in [oneDim](00_oneDim.ipynb#Posterior-from-incorporating-sensor-readings). We will thus require very similar code as to the 1-D case. We start by creating a function [m_post()](statFEM_analysis.rst#statFEM_analysis.twoDim.m_post) which evaluates the posterior mean at a given point." ] }, { "cell_type": "code", "execution_count": 12, "id": "988c2876-59f9-45a1-bb38-b2bf99cd70b7", "metadata": {}, "outputs": [], "source": [ "from statFEM_analysis.twoDim import m_post" ] }, { "cell_type": "markdown", "id": "04df2f04-a1f4-470d-835f-7c88105d08f8", "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", "id": "9a237f93-452e-4b99-a77e-4ddd37da61f6", "metadata": {}, "source": [ "We now require 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.twoDim.sample_gp) for this purpose." ] }, { "cell_type": "code", "execution_count": 13, "id": "12b04355-1c17-4052-92e1-98319e249028", "metadata": {}, "outputs": [], "source": [ "from statFEM_analysis.twoDim import sample_gp" ] }, { "cell_type": "markdown", "id": "24776ca1-8ab6-40c3-9398-e41b37478014", "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", "id": "eafbafed-cb80-410d-b4b0-eafb78b668d4", "metadata": {}, "source": [ "As a quick demonstration that the code is working lets generate 2 realisations of white noise, using the kernel `k` from one of the previous tests and plot a heatmap of these random fields side-by-side." ] }, { "cell_type": "code", "execution_count": 14, "id": "a7108081-5946-43da-a208-8326e7fc5347", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "n = 41\n", "x_range = np.linspace(0,1,n)\n", "grid = np.array([[x,y] for x in x_range for y in x_range])\n", "\n", "# set up mean\n", "def m(x):\n", " return 0.0\n", "\n", "np.random.seed(23534)\n", "samples = sample_gp(2,m,k,grid,True,False)\n", "\n", "sample_1 = samples[:,0].flatten()\n", "sample_2 = samples[:,1].flatten()\n", "\n", "vmin = min(sample_1.min(),sample_2.min())\n", "vmax = max(sample_1.max(),sample_2.max())\n", "cmap = cm.jet\n", "norm = colors.Normalize(vmin=vmin,vmax=vmax)\n", "\n", "x = grid[:,0].flatten()\n", "y = grid[:,1].flatten()\n", "triang = tri.Triangulation(x,y)\n", "\n", "plt.rcParams['figure.figsize'] = (12,6)\n", "fig, axs = plt.subplots(ncols=3, gridspec_kw=dict(width_ratios=[4,4,0.2]))\n", "axs[0].tricontourf(triang,sample_1.flatten(),cmap=cmap)\n", "axs[1].tricontourf(triang,sample_2.flatten(),cmap=cmap)\n", "cb = colorbar.ColorbarBase(axs[2],cmap=cmap,norm=norm)\n", "fig.suptitle('Realisations of white-noise fields')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "df7d6846-efee-440b-9ab0-8cd9f8ec4fbb", "metadata": {}, "source": [ "Let's also quickly generate 2 realisations for the kernel `k_f` above:" ] }, { "cell_type": "code", "execution_count": 15, "id": "8ab2b1b5-cec1-47b8-a6eb-b28fd58a3bdf", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "np.random.seed(534)\n", "samples = sample_gp(2,m,k_f,grid,False,True)\n", "\n", "sample_1 = samples[:,0].flatten()\n", "sample_2 = samples[:,1].flatten()\n", "\n", "vmin = min(sample_1.min(),sample_2.min())\n", "vmax = max(sample_1.max(),sample_2.max())\n", "cmap = cm.jet\n", "norm = colors.Normalize(vmin=vmin,vmax=vmax)\n", "\n", "x = grid[:,0].flatten()\n", "y = grid[:,1].flatten()\n", "triang = tri.Triangulation(x,y)\n", "\n", "plt.rcParams['figure.figsize'] = (12,6)\n", "fig, axs = plt.subplots(ncols=3, gridspec_kw=dict(width_ratios=[4,4,0.2]))\n", "axs[0].tricontourf(triang,sample_1.flatten(),cmap=cmap)\n", "axs[1].tricontourf(triang,sample_2.flatten(),cmap=cmap)\n", "cb = colorbar.ColorbarBase(axs[2],cmap=cmap,norm=norm)\n", "fig.suptitle(r'Realisations of random fields with covariance $k_f$')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "413268bd-d717-4a0d-8469-38d036662d39", "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.twoDim.gen_sensor) for this purpose." ] }, { "cell_type": "code", "execution_count": 16, "id": "4421c4d7-73e1-4f57-b1b2-aee46f8f587a", "metadata": {}, "outputs": [], "source": [ "from statFEM_analysis.twoDim import gen_sensor" ] }, { "cell_type": "markdown", "id": "be3c7abe-5867-4b04-a98d-80dcd994fdb2", "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", "- `J`: controls the FE mesh size ($h=1/J^{2}$)\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", "- `require` : boolean argument indicating whether or not to also return the realisation of the forcing `f_sim` and the FEniCS solution `u_sol` (defaults to `False`)" ] }, { "cell_type": "markdown", "id": "4ab8ea67-c8c0-4786-b3bd-0ac6ff5ec8bc", "metadata": {}, "source": [ "
\n", "\n", "Warning:\n", "\n", "Since we do not have access to the true solution we must use FEniCS to get the solution for our system. Thus, one must choose a small enough `J` in `gen_sensor` above to ensure we get realistic noisy sensor readings.\n", " \n", "
" ] }, { "cell_type": "markdown", "id": "341106a6-5c92-4317-84cb-70fd2a12bc4a", "metadata": {}, "source": [ "Let's demonstrate that this code is working, by generating $s=25$ sensor observations with the sensors equally space in the domain $D$." ] }, { "cell_type": "code", "execution_count": 17, "id": "77518817-0ada-4ddc-85a5-ec7f95c29dba", "metadata": {}, "outputs": [], "source": [ "# set up mean function for forcing\n", "def m_f(x):\n", " return 1.0\n", "\n", "# set up sensor grid and sensor noise level\n", "ϵ = 0.2\n", "s = 25\n", "s_sqrt = int(np.round(np.sqrt(s)))\n", "Y_range = np.linspace(0.01,0.99,s_sqrt)\n", "Y = np.array([[x,y] for x in Y_range for y in Y_range])\n", "J_fine = 100 # FE mesh size to compute solution on\n", "\n", "# generate the sensor observations\n", "np.random.seed(235)\n", "v_dat = gen_sensor(ϵ,m_f,k_f,Y,J_fine,False,True)" ] }, { "cell_type": "markdown", "id": "b8afde8b-1b7c-4721-8b9a-5de7d3c5bc9b", "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.twoDim.MyExpression)." ] }, { "cell_type": "code", "execution_count": 18, "id": "6b6744ad-0b68-4bf5-a6c3-c30b7148c26b", "metadata": {}, "outputs": [], "source": [ "from statFEM_analysis.twoDim import MyExpression" ] }, { "cell_type": "markdown", "id": "6fb52e2a-7c49-4dcb-b01c-4c4b9a89c231", "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.twoDim.fem_cov_assembler_post) for this purpose. " ] }, { "cell_type": "code", "execution_count": 19, "id": "07e4059d-8d4c-4f59-b4c4-7e2a3368fb7d", "metadata": {}, "outputs": [], "source": [ "from statFEM_analysis.twoDim import fem_cov_assembler_post" ] }, { "cell_type": "markdown", "id": "1be22835-770b-4ea1-9b1d-f67bd36c01c2", "metadata": {}, "source": [ "`fem_cov_assembler_post` takes in several arguments which are explained below:\n", "\n", "- `J`: controls the FE mesh size ($h=1/J^2$)\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", "id": "b4ff6c97-10ee-4fe4-bce5-7ca2072fdeb8", "metadata": {}, "source": [ "With all of this code in place we can now finally write the function [m_post_fem_assmebler()](statFEM_analysis.rst#statFEM_analysis.twoDim.m_post_fem_assembler) which will assemble the statFEM posterior mean function." ] }, { "cell_type": "code", "execution_count": 20, "id": "6f07a525-7016-4690-9dca-76e96c359fb1", "metadata": {}, "outputs": [], "source": [ "from statFEM_analysis.twoDim import m_post_fem_assembler" ] }, { "cell_type": "markdown", "id": "56c2ff4c-7b37-45a0-9e9d-b7fe50b60860", "metadata": {}, "source": [ "`m_post_fem_assembler` takes in several arguments which are explained below:\n", "\n", "- `J`: controls the FE mesh size ($h=1/J^{2}$)\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", "id": "6310c331-5937-4cdb-88cb-2e6aaae2bc1a", "metadata": {}, "source": [ "Let's quickly check that this function is working." ] }, { "cell_type": "code", "execution_count": 21, "id": "e9aec6c5-e66e-4719-9937-e1a1ef20a8c7", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$$0.025478333034320278$$" ], "text/plain": [ "0.025478333034320278" ] }, "execution_count": 21, "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 D\n", "x = np.array([0.3,0.1])\n", "m_post_fem(x)" ] }, { "cell_type": "markdown", "id": "a95dc6dc-8c74-4924-a2b1-6f78d7705330", "metadata": {}, "source": [ "### statFEM posterior covariance\n", "\n", "The form of the statFEM posterior covariance remains the same as given in [oneDim](00_oneDim.ipynb#Posterior-covariance). Thus, we require very similar code as to the 1-D case. We start by creating a function [c_post()](statFEM_analysis.rst#statFEM_analysis.twoDim.c_post) which evaluates the posterior covariance at a given point." ] }, { "cell_type": "code", "execution_count": 22, "id": "e295e3d9-20d8-4676-b31d-83295cda0d57", "metadata": {}, "outputs": [], "source": [ "from statFEM_analysis.twoDim import c_post" ] }, { "cell_type": "markdown", "id": "de18ee29-c26f-4184-9388-ce8385f16511", "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", "id": "11f0759a-ca42-4a73-92f2-14ae9c7fd84c", "metadata": {}, "source": [ "To compare the statFEM covariance matrices for finer and finer FE mesh sizes we will require some more code. First we create a function [post_fem_cov_assembler()](statFEM_analysis.rst#statFEM_analysis.twoDim.post_fem_cov_assembler) which helps us to quickly assemble the statFEM posterior covariance matrix as explained in [oneDim](00_oneDim.ipynb#Difference-between-posterior-covariances)." ] }, { "cell_type": "code", "execution_count": 23, "id": "d35ab80c-84e8-4332-a592-5b6d7b56e684", "metadata": {}, "outputs": [], "source": [ "from statFEM_analysis.twoDim import post_fem_cov_assembler" ] }, { "cell_type": "markdown", "id": "705a1d20-45c9-4207-a904-c09a665c1fca", "metadata": {}, "source": [ "`post_fem_cov_assembler` takes in several arguments which are explained below:\n", "\n", "- `J`: controls the FE mesh size ($h=1/J^2$)\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", "id": "38a301c5-0d96-4b3e-9cb6-cafa5c321a8d", "metadata": {}, "source": [ "Finally, we create the function [c_post_fem_assembler()](statFEM_analysis.rst#statFEM_analysis.twoDim.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": 24, "id": "737e1b24-866d-4dd1-b6ab-61b38df9b609", "metadata": {}, "outputs": [], "source": [ "from statFEM_analysis.twoDim import c_post_fem_assembler" ] } ], "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": 5 }