poisson1D-parametric-study.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from fenics import *\n",
    "import mshr\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from egfcore import *\n",
    "from utils import *\n",
    "\n",
    "set_log_level(30)\n",
    "%matplotlib widget"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "class Simulator:\n",
    "    \n",
    "    def __init__(self, meshDensity):\n",
    "        self.mesh = IntervalMesh(meshDensity,0,1) # (meshDensity = N_sensors) =  # of positions at which the problem is discretized on a unit interval\n",
    "        mesh_dict = {\"X\": self.mesh.coordinates()}\n",
    "        scipy.io.savemat(\"mesh.mat\", mesh_dict)\n",
    "        self.V = FunctionSpace(self.mesh, 'P', 2)\n",
    "        \n",
    "        # Define the function space and store the meshweights for computation.\n",
    "        V = FunctionSpace(self.mesh,'P',1)\n",
    "        u = TestFunction(V)\n",
    "        temp = assemble(u*dx)\n",
    "        self.meshweights = (temp.get_local()[vertex_to_dof_map(V)]).reshape(-1,1)\n",
    "        \n",
    "        mesh_dict = {\"X\": self.mesh.coordinates()}\n",
    "        scipy.io.savemat(\"mesh2D.mat\", mesh_dict)\n",
    "        \n",
    "        # Create variational form for the problem\n",
    "        self.bc = self.boundaryConditions()\n",
    "        u = TrialFunction(self.V)\n",
    "        v = TestFunction(self.V)\n",
    "        self.f = Function(V)\n",
    "        self.param = Constant(0)\n",
    "        self.d2v = dof_to_vertex_map(V)\n",
    "        self.a = dot(grad(u), grad(v))* dx\n",
    "        self.L = self.f*v*dx\n",
    "        self.u = Function(self.V)\n",
    "        \n",
    "    def boundaryConditions(self):\n",
    "        \"\"\"\n",
    "        Define homogeneous Dirichlet Boundary conditions for the problem.\n",
    "        \"\"\"\n",
    "        def boundary(x, on_boundary):\n",
    "            return on_boundary\n",
    "        \n",
    "        u_D = Constant(0)\n",
    "        bc = DirichletBC(self.V, u_D, boundary)\n",
    "        \n",
    "        return bc\n",
    "    \n",
    "    def solve(self, forcing, noise_level = None, param=None):\n",
    "        \"\"\"\n",
    "        Given a (N_sensors x 1) forcing vector, solve the a 1D Poisson problem on a unit interval.\n",
    "        \"\"\"\n",
    "        \n",
    "        self.f.vector()[:] = forcing[self.d2v] # Instantiate the source term in the variational form by interpolating the sampled sourcing term.\n",
    "        if param is not None:\n",
    "            self.param.assign(param) # Define the parameter for the problem\n",
    "        solve(self.a == self.L, self.u, self.bc) # Solve the variation form\n",
    "\n",
    "        # Sample the solution at the nodes of the mesh.\n",
    "        solution = self.u.compute_vertex_values(self.mesh)\n",
    "        \n",
    "        # As specified, add IID Gaussian white noise.\n",
    "        if noise_level is not None:\n",
    "            noise =  noise_level*np.random.normal(0,np.abs(solution.mean()),solution.shape)\n",
    "            solution += noise\n",
    "        \n",
    "        return solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def exactGreen(domain, param):\n",
    "    x, s = np.meshgrid(domain,domain)\n",
    "    G = np.empty(np.shape(x))\n",
    "    for i in range(x.shape[0]):\n",
    "        for j in range(x.shape[0]):\n",
    "            xx, ss = x[i,j], s[i,j]\n",
    "            if xx <= ss:\n",
    "                G[i,j] = xx * (1-ss)\n",
    "            else:\n",
    "                G[i,j] = ss * (1-xx)\n",
    "    return G"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Run 0:\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 100, rank: 100, Noise: False\n",
      "(2001, 100)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 250, rank: 100, Noise: False\n",
      "(2001, 250)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 500, rank: 100, Noise: False\n",
      "(2001, 500)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 750, rank: 100, Noise: False\n",
      "(2001, 750)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 1000, rank: 100, Noise: False\n",
      "(2001, 1000)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 1250, rank: 100, Noise: False\n",
      "(2001, 1250)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 1500, rank: 100, Noise: False\n",
      "(2001, 1500)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 1750, rank: 100, Noise: False\n",
      "(2001, 1750)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "(2001, 2000)\n",
      "Run 1:\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 100, rank: 100, Noise: False\n",
      "(2001, 100)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 250, rank: 100, Noise: False\n",
      "(2001, 250)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 500, rank: 100, Noise: False\n",
      "(2001, 500)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 750, rank: 100, Noise: False\n",
      "(2001, 750)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 1000, rank: 100, Noise: False\n",
      "(2001, 1000)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 1250, rank: 100, Noise: False\n",
      "(2001, 1250)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 1500, rank: 100, Noise: False\n",
      "(2001, 1500)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 1750, rank: 100, Noise: False\n",
      "(2001, 1750)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "(2001, 2000)\n",
      "Run 2:\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 100, rank: 100, Noise: False\n",
      "(2001, 100)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 250, rank: 100, Noise: False\n",
      "(2001, 250)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 500, rank: 100, Noise: False\n",
      "(2001, 500)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 750, rank: 100, Noise: False\n",
      "(2001, 750)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 1000, rank: 100, Noise: False\n",
      "(2001, 1000)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 1250, rank: 100, Noise: False\n",
      "(2001, 1250)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 1500, rank: 100, Noise: False\n",
      "(2001, 1500)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 1750, rank: 100, Noise: False\n",
      "(2001, 1750)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "(2001, 2000)\n",
      "Run 3:\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 100, rank: 100, Noise: False\n",
      "(2001, 100)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 250, rank: 100, Noise: False\n",
      "(2001, 250)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 500, rank: 100, Noise: False\n",
      "(2001, 500)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 750, rank: 100, Noise: False\n",
      "(2001, 750)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 1000, rank: 100, Noise: False\n",
      "(2001, 1000)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 1250, rank: 100, Noise: False\n",
      "(2001, 1250)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 1500, rank: 100, Noise: False\n",
      "(2001, 1500)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 1750, rank: 100, Noise: False\n",
      "(2001, 1750)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "(2001, 2000)\n",
      "Run 4:\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 100, rank: 100, Noise: False\n",
      "(2001, 100)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 250, rank: 100, Noise: False\n",
      "(2001, 250)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 500, rank: 100, Noise: False\n",
      "(2001, 500)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 750, rank: 100, Noise: False\n",
      "(2001, 750)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 1000, rank: 100, Noise: False\n",
      "(2001, 1000)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 1250, rank: 100, Noise: False\n",
      "(2001, 1250)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 1500, rank: 100, Noise: False\n",
      "(2001, 1500)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 1750, rank: 100, Noise: False\n",
      "(2001, 1750)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "(2001, 2000)\n",
      "Run 5:\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 100, rank: 100, Noise: False\n",
      "(2001, 100)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 250, rank: 100, Noise: False\n",
      "(2001, 250)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 500, rank: 100, Noise: False\n",
      "(2001, 500)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 750, rank: 100, Noise: False\n",
      "(2001, 750)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 1000, rank: 100, Noise: False\n",
      "(2001, 1000)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 1250, rank: 100, Noise: False\n",
      "(2001, 1250)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 1500, rank: 100, Noise: False\n",
      "(2001, 1500)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 1750, rank: 100, Noise: False\n",
      "(2001, 1750)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "(2001, 2000)\n",
      "Run 6:\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 100, rank: 100, Noise: False\n",
      "(2001, 100)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 250, rank: 100, Noise: False\n",
      "(2001, 250)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 500, rank: 100, Noise: False\n",
      "(2001, 500)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 750, rank: 100, Noise: False\n",
      "(2001, 750)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 1000, rank: 100, Noise: False\n",
      "(2001, 1000)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 1250, rank: 100, Noise: False\n",
      "(2001, 1250)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 1500, rank: 100, Noise: False\n",
      "(2001, 1500)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 1750, rank: 100, Noise: False\n",
      "(2001, 1750)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "(2001, 2000)\n",
      "Run 7:\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 100, rank: 100, Noise: False\n",
      "(2001, 100)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 250, rank: 100, Noise: False\n",
      "(2001, 250)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 500, rank: 100, Noise: False\n",
      "(2001, 500)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 750, rank: 100, Noise: False\n",
      "(2001, 750)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 1000, rank: 100, Noise: False\n",
      "(2001, 1000)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 1250, rank: 100, Noise: False\n",
      "(2001, 1250)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 1500, rank: 100, Noise: False\n",
      "(2001, 1500)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 1750, rank: 100, Noise: False\n",
      "(2001, 1750)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "(2001, 2000)\n",
      "Run 8:\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 100, rank: 100, Noise: False\n",
      "(2001, 100)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 250, rank: 100, Noise: False\n",
      "(2001, 250)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 500, rank: 100, Noise: False\n",
      "(2001, 500)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 750, rank: 100, Noise: False\n",
      "(2001, 750)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 1000, rank: 100, Noise: False\n",
      "(2001, 1000)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 1250, rank: 100, Noise: False\n",
      "(2001, 1250)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 1500, rank: 100, Noise: False\n",
      "(2001, 1500)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 1750, rank: 100, Noise: False\n",
      "(2001, 1750)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "(2001, 2000)\n",
      "Run 9:\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 100, rank: 100, Noise: False\n",
      "(2001, 100)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 250, rank: 100, Noise: False\n",
      "(2001, 250)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 500, rank: 100, Noise: False\n",
      "(2001, 500)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 750, rank: 100, Noise: False\n",
      "(2001, 750)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 1000, rank: 100, Noise: False\n",
      "(2001, 1000)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 1250, rank: 100, Noise: False\n",
      "(2001, 1250)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 1500, rank: 100, Noise: False\n",
      "(2001, 1500)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 1750, rank: 100, Noise: False\n",
      "(2001, 1750)\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "(2001, 2000)\n",
      "CPU times: user 10h 58min 4s, sys: 1d 11h 28min 8s, total: 1d 22h 26min 12s\n",
      "Wall time: 4h 27min 35s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "add_noise = False\n",
    "noise_level = 0.1\n",
    "params = np.array([0])\n",
    "verbose = False\n",
    "\n",
    "# np.random.seed(42)\n",
    "\n",
    "\n",
    "meshDensitySpace = np.array([2000]) #np.linspace(50, 500, 9)\n",
    "# meshDensitySpace = np.array([200]) #np.linspace(50, 500, 9)\n",
    "sigmaSpace = np.array([0.0025])  # np.logspace(-2, -1, 10) \n",
    "nSamplesSpace = np.array([100, 250, 500, 750, 1000, 1250, 1500, 1750, 2000]) #np.array([100, 200, 300, 400, 500, 600]) # np.linspace(50, 200, 16, dtype = 'I') \n",
    "rankSpace = np.array([100]) #np.linspace(5, 50, 46, dtype = 'I') #np.array([20])\n",
    "\n",
    "runs = 10\n",
    "errors = np.empty((runs, meshDensitySpace.shape[0], sigmaSpace.shape[0], nSamplesSpace.shape[0], rankSpace.shape[0]))\n",
    "models = np.empty((runs, meshDensitySpace.shape[0], sigmaSpace.shape[0], nSamplesSpace.shape[0], rankSpace.shape[0]), dtype = 'O')\n",
    "\n",
    "for run in range(runs):\n",
    "    print(f\"Run {run}:\")\n",
    "    for i, meshDensity in enumerate(meshDensitySpace):\n",
    "        for j, sigma in enumerate(sigmaSpace):\n",
    "            Forcing = sampleforcing(sigma, nSamplesSpace[-1], np.random.randint(1,1000));\n",
    "            for k, nSamples in enumerate(nSamplesSpace):\n",
    "                for l, rank in enumerate(rankSpace):\n",
    "                    print(f\"Method: Coefficient fit | meshDensity: {meshDensity}, sigma: {sigma}, nSamples: {nSamples}, rank: {rank}, Noise: {add_noise}\")\n",
    "                    Sim = Simulator(meshDensity)\n",
    "                    forcing = Forcing[:,:nSamples]\n",
    "                    print(forcing.shape)\n",
    "                    solution = np.zeros(forcing.shape)\n",
    "                    for s in range(solution.shape[1]):\n",
    "                        if verbose:\n",
    "                            print(\"i = %d / %d\"%(s+1, solution.shape[1]))\n",
    "                        if add_noise:\n",
    "                            solution[:,s] = Sim.solve(forcing[:,s], noise_level)\n",
    "                        else:\n",
    "                            solution[:,s] = Sim.solve(forcing[:,s])\n",
    "                    models[run, i,j,k,l] = EGF(\"coefficient-fit\", params, rank, Sim.mesh, forcing, solution, None, None, None, None, verbose = verbose)\n",
    "\n",
    "                    G_reconstruction = reconstructEGF1D(models[run, i,j,k,l])\n",
    "                    G = exactGreen(models[run, i,j,k,l].mesh.coordinates(), models[run, i,j,k,l].params[0])\n",
    "                    errors[run, i,j,k,l] = errorL2(G_reconstruction, G, models[run, i,j,k,l].meshweights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import matplotlib.ticker as mticker\n",
    "\n",
    "# My axis should display 10⁻¹ but you can switch to e-notation 1.00e+01\n",
    "def log_tick_formatter(val, pos=None):\n",
    "    return f\"$10^{{{int(val)}}}$\"  # remove int() if you don't use MaxNLocator\n",
    "    # return f\"{10**val:.2e}\"      # e-Notation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "errorsamples = np.hstack([nSamplesSpace.reshape((-1,1)), np.mean(errors, axis = 0)[0,0,:,0].reshape((-1,1))])\n",
    "np.savetxt('errorsamples.csv', errorsamples, delimiter=',') "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.0, 1.0, 'A')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "7d1f3b2a72f94336b34bd1d3b9e85141",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
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       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=800.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "meshDensitySpace = np.array([2000]) #np.linspace(50, 500, 9)\n",
    "sigmaSpace = np.array([0.0025])  # np.logspace(-2, -1, 10) \n",
    "nSamplesSpace = np.array([100, 250, 500, 750, 1000, 1250, 1500, 1750, 2000]) #np.array([100, 200, 300, 400, 500, 600]) # np.linspace(50, 200, 16, dtype = 'I') \n",
    "rankSpace = np.array([100]) #np.linspace(5, 50, 46, dtype = 'I') #np.array([20])\n",
    "\n",
    "plt.figure(figsize = (8,6))\n",
    "plt.semilogy(nSamplesSpace,np.mean(errors, axis = 0)[0,0,:,0],'b.')\n",
    "plt.xlabel('$N_{samples}$')\n",
    "plt.ylabel('Error $\\epsilon$')\n",
    "plt.xlim([0,2000])\n",
    "plt.title('A',loc ='left', weight = 'bold', size = 12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Run 0:\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 1.0, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.5, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.3, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.2, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.1, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.05, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.025, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.01, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0075, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.005, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Run 1:\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 1.0, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.5, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.3, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.2, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.1, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.05, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.025, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.01, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0075, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.005, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Run 2:\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 1.0, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.5, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.3, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.2, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.1, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.05, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.025, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.01, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0075, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.005, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Run 3:\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 1.0, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.5, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.3, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.2, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.1, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.05, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.025, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.01, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0075, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.005, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Run 4:\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 1.0, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.5, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.3, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.2, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.1, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.05, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.025, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.01, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0075, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.005, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Run 5:\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 1.0, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.5, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.3, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.2, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.1, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.05, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.025, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.01, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0075, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.005, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Run 6:\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 1.0, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.5, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.3, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.2, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.1, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.05, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.025, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.01, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0075, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.005, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Run 7:\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 1.0, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.5, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.3, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.2, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.1, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.05, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.025, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.01, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0075, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.005, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Run 8:\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 1.0, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.5, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.3, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.2, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.1, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.05, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.025, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.01, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0075, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.005, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Run 9:\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 1.0, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.5, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.3, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.2, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.1, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.05, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.025, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.01, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0075, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.005, nSamples: 2000, rank: 100, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "CPU times: user 1d 2h 34min 15s, sys: 3d 13h 1min 39s, total: 4d 15h 35min 54s\n",
      "Wall time: 8h 32min 37s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "add_noise = False\n",
    "noise_level = 0.1\n",
    "params = np.array([0])\n",
    "verbose = False\n",
    "\n",
    "np.random.seed(42)\n",
    "\n",
    "runs = 10\n",
    "meshDensitySpace = np.array([2000]) #np.linspace(50, 500, 9)\n",
    "sigmaSpace = np.array([1, 0.5, 0.3, 0.2, 0.1, 0.05, 0.025, 0.01, 0.0075, 0.005, 0.0025])  # np.logspace(-2, -1, 10)\n",
    "nSamplesSpace = np.array([2000]) #np.array([100, 200, 300, 400, 500, 600]) # np.linspace(50, 200, 16, dtype = 'I') \n",
    "rankSpace = np.array([100]) #np.linspace(5, 50, 46, dtype = 'I') #np.array([20])\n",
    "\n",
    "errors2 = np.empty((runs, meshDensitySpace.shape[0], sigmaSpace.shape[0], nSamplesSpace.shape[0], rankSpace.shape[0]))\n",
    "models2 = np.empty((runs, meshDensitySpace.shape[0], sigmaSpace.shape[0], nSamplesSpace.shape[0], rankSpace.shape[0]), dtype = 'O')\n",
    "\n",
    "for run in range(runs):\n",
    "    print(f\"Run {run}:\")\n",
    "    for i, meshDensity in enumerate(meshDensitySpace):\n",
    "        for j, sigma in enumerate(sigmaSpace):\n",
    "            seed = np.random.randint(1,1000)\n",
    "            for k, nSamples in enumerate(nSamplesSpace):\n",
    "                for l, rank in enumerate(rankSpace):\n",
    "                    print(f\"Method: Coefficient fit | meshDensity: {meshDensity}, sigma: {sigma}, nSamples: {nSamples}, rank: {rank}, Noise: {add_noise}\")\n",
    "                    Sim = Simulator(meshDensity)\n",
    "                    forcing = sampleforcing(sigma, nSamples, seed)\n",
    "                    solution = np.zeros(forcing.shape)\n",
    "                    for s in range(solution.shape[1]):\n",
    "                        if verbose:\n",
    "                            print(\"i = %d / %d\"%(s+1, solution.shape[1]))\n",
    "                        if add_noise:\n",
    "                            solution[:,s] = Sim.solve(forcing[:,s], noise_level)\n",
    "                        else:\n",
    "                            solution[:,s] = Sim.solve(forcing[:,s])\n",
    "                    models2[run, i,j,k,l] = EGF(\"coefficient-fit\", params, rank, Sim.mesh, forcing, solution, None, None, None, None, verbose = verbose)\n",
    "\n",
    "                    G_reconstruction = reconstructEGF1D(models2[run, i,j,k,l])\n",
    "                    G = exactGreen(models2[run, i,j,k,l].mesh.coordinates(), models2[run, i,j,k,l].params[0])\n",
    "                    errors2[run, i,j,k,l] = errorL2(G_reconstruction, G, models2[run, i,j,k,l].meshweights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "errorsigma = np.hstack([sigmaSpace.reshape((-1,1)), np.mean(errors2, axis = 0)[0,:,0,0].reshape((-1,1))])\n",
    "np.savetxt('errorsigma.csv', errorsigma, delimiter=',') "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.0, 1.0, 'B')"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "873e378ccf854fd3bec4428c879cb6d3",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
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       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img src='data:image/png;base64,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' 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      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "meshDensitySpace = np.array([2000]) #np.linspace(50, 500, 9)\n",
    "sigmaSpace = np.array([1, 0.5, 0.3, 0.2, 0.1, 0.05, 0.025, 0.01, 0.0075, 0.005, 0.0025])  # np.logspace(-2, -1, 10) \n",
    "nSamplesSpace = np.array([2000]) #np.array([100, 200, 300, 400, 500, 600]) # np.linspace(50, 200, 16, dtype = 'I') \n",
    "rankSpace = np.array([100]) #np.linspace(5, 50, 46, dtype = 'I') #np.array([20])\n",
    "\n",
    "plt.figure(figsize = (8,6))\n",
    "plt.loglog(sigmaSpace,np.mean(errors2, axis = 0)[0,:,0,0],'b.-')\n",
    "plt.xlabel('$\\\\sigma$')\n",
    "plt.ylabel('Error $\\epsilon$')\n",
    "plt.xlim(right = 1)\n",
    "plt.title('B',loc ='left', weight = 'bold', size = 12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Run 0:\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 10, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 11, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 12, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 13, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 15, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 18, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 25, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 50, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 75, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "\n",
      "Run 1:\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 10, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 11, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 12, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 13, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 15, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 18, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 25, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 50, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 75, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "\n",
      "Run 2:\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 10, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 11, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 12, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 13, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 15, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 18, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 25, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 50, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 75, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "\n",
      "Run 3:\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 10, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 11, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 12, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 13, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 15, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 18, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 25, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 50, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 75, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "\n",
      "Run 4:\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 10, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 11, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 12, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 13, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 15, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 18, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 25, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 50, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 75, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "\n",
      "Run 5:\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 10, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 11, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 12, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 13, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 15, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 18, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 25, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 50, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 75, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "\n",
      "Run 6:\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 10, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 11, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 12, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 13, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 15, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 18, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 25, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 50, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 75, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "\n",
      "Run 7:\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 10, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 11, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 12, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 13, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 15, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 18, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 25, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 50, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 75, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "\n",
      "Run 8:\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 10, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 11, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 12, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 13, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 15, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 18, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 25, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 50, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 75, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "\n",
      "Run 9:\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 10, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 11, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 12, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 13, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 15, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 18, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 25, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 50, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 75, Noise: False\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "CPU times: user 10h 16min 9s, sys: 1d 9h 15min 40s, total: 1d 19h 31min 49s\n",
      "Wall time: 3h 58min 4s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "add_noise = False\n",
    "noise_level = 0.1\n",
    "params = np.array([0])\n",
    "verbose = False\n",
    "\n",
    "np.random.seed(42)\n",
    "\n",
    "runs = 10\n",
    "meshDensitySpace = np.array([2000]) #np.linspace(50, 500, 9)\n",
    "sigmaSpace = np.array([0.0025])  # np.logspace(-2, -1, 10) \n",
    "nSamplesSpace = np.array([2000]) #np.array([100, 200, 300, 400, 500, 600]) # np.linspace(50, 200, 16, dtype = 'I') \n",
    "rankSpace = np.array([10, 11, 12, 13, 15, 18, 25, 50, 75, 100]) #np.linspace(5, 50, 46, dtype = 'I') #np.array([20])\n",
    "\n",
    "errors3 = np.empty((runs, meshDensitySpace.shape[0], sigmaSpace.shape[0], nSamplesSpace.shape[0], rankSpace.shape[0]))\n",
    "models3 = np.empty((runs, meshDensitySpace.shape[0], sigmaSpace.shape[0], nSamplesSpace.shape[0], rankSpace.shape[0]), dtype = 'O')\n",
    "\n",
    "for run in range(runs):\n",
    "    print(f'\\nRun {run}:')\n",
    "    for i, meshDensity in enumerate(meshDensitySpace):\n",
    "        for j, sigma in enumerate(sigmaSpace):\n",
    "            for k, nSamples in enumerate(nSamplesSpace):\n",
    "                Sim = Simulator(meshDensity)\n",
    "                forcing = sampleforcing(sigma, nSamples, np.random.randint(1,1000))\n",
    "                solution = np.zeros(forcing.shape)\n",
    "                for s in range(solution.shape[1]):\n",
    "                    if verbose:\n",
    "                        print(\"i = %d / %d\"%(s+1, solution.shape[1]))\n",
    "                    if add_noise:\n",
    "                        solution[:,s] = Sim.solve(forcing[:,s], noise_level)\n",
    "                    else:\n",
    "                        solution[:,s] = Sim.solve(forcing[:,s])\n",
    "                for l, rank in enumerate(rankSpace):\n",
    "                    print(f\"Method: Coefficient fit | meshDensity: {meshDensity}, sigma: {sigma}, nSamples: {nSamples}, rank: {rank}, Noise: {add_noise}\")\n",
    "                    \n",
    "                    models3[run, i,j,k,l] = EGF(\"coefficient-fit\", params, rank, Sim.mesh, forcing, solution, None, None, None, None, verbose = verbose)\n",
    "\n",
    "                    G_reconstruction = reconstructEGF1D(models3[run, i,j,k,l])\n",
    "                    G = exactGreen(models3[run, i,j,k,l].mesh.coordinates(), models3[run, i,j,k,l].params[0])\n",
    "                    errors3[run, i,j,k,l] = errorL2(G_reconstruction, G, models3[run, i,j,k,l].meshweights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.01858819, 0.0167877 , 0.01538474, 0.01427669, 0.01266972,\n",
       "       0.0111978 , 0.00968112, 0.00872979, 0.00862337, 0.00859684])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(errors3, axis = 0)[0,0,0,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "errorrank = np.hstack([rankSpace.reshape((-1,1)), np.mean(errors3, axis = 0)[0,0,0,:].reshape((-1,1))])\n",
    "np.savetxt('errorrank.csv', errorrank, delimiter=',') "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.0, 1.0, 'C')"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "efda29f4f2764f5aa98cf88f3df6e403",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=640.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "meshDensitySpace = np.array([2000]) #np.linspace(50, 500, 9)\n",
    "sigmaSpace = np.array([0.0025])  # np.logspace(-2, -1, 10) \n",
    "nSamplesSpace = np.array([2000]) #np.array([100, 200, 300, 400, 500, 600]) # np.linspace(50, 200, 16, dtype = 'I') \n",
    "rankSpace = np.array([10, 11, 12, 13, 15, 18, 25, 50, 75, 100]) #np.linspace(5, 50, 46, dtype = 'I') #np.array([20])\n",
    "\n",
    "plt.figure()\n",
    "plt.semilogy(rankSpace, np.mean(errors3, axis = 0)[0,0,0,:],'b.-')\n",
    "plt.xlabel('Rank $K$')\n",
    "plt.ylabel('$\\epsilon$', rotation='horizontal', labelpad=15)\n",
    "plt.xlim([0,100])\n",
    "plt.title('C',loc ='left', weight = 'bold', size = 12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Run 0:\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 4000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 8000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 16000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Run 1:\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 4000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 8000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 16000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Run 2:\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 4000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 8000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 16000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Run 3:\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 4000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 8000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 16000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Run 4:\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 4000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 8000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 16000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Run 5:\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 4000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 8000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 16000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Run 6:\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 4000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 8000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 16000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Run 7:\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 4000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 8000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 16000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Run 8:\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 4000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 8000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 16000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Run 9:\n",
      "Method: Coefficient fit | meshDensity: 2000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 4000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 8000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "Method: Coefficient fit | meshDensity: 16000, sigma: 0.0025, nSamples: 2000, rank: 100, Noise: False\n",
      "Warning: Not a low-rank function. \n",
      "> In chebfun2/constructor (line 121)\n",
      "In chebfun2 (line 82)\n",
      "In sample1D (line 13)\n",
      "In run (line 91) \n",
      "CPU times: user 13h 6min 9s, sys: 1d 9h 12min 53s, total: 1d 22h 19min 2s\n",
      "Wall time: 13h 55min 31s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "add_noise = False\n",
    "noise_level = 0.1\n",
    "params = np.array([0])\n",
    "verbose = False\n",
    "\n",
    "# np.random.seed(42)\n",
    "\n",
    "\n",
    "meshDensitySpace = np.array([2000, 4000, 8000, 16000]) #np.linspace(50, 500, 9)\n",
    "# meshDensitySpace = np.array([200]) #np.linspace(50, 500, 9)\n",
    "sigmaSpace = np.array([0.0025])  # np.logspace(-2, -1, 10) \n",
    "nSamplesSpace = np.array([2000]) #np.array([100, 200, 300, 400, 500, 600]) # np.linspace(50, 200, 16, dtype = 'I') \n",
    "rankSpace = np.array([100]) #np.linspace(5, 50, 46, dtype = 'I') #np.array([20])\n",
    "\n",
    "runs = 10\n",
    "\n",
    "errors4 = np.empty((runs, meshDensitySpace.shape[0], sigmaSpace.shape[0], nSamplesSpace.shape[0], rankSpace.shape[0]))\n",
    "models4 = np.empty((runs, meshDensitySpace.shape[0], sigmaSpace.shape[0], nSamplesSpace.shape[0], rankSpace.shape[0]), dtype = 'O')\n",
    "\n",
    "for run in range(runs):\n",
    "    print(f\"Run {run}:\")\n",
    "    seed = np.random.randint(1,1000)\n",
    "    for i, meshDensity in enumerate(meshDensitySpace):\n",
    "        for j, sigma in enumerate(sigmaSpace):\n",
    "            for k, nSamples in enumerate(nSamplesSpace):\n",
    "                for l, rank in enumerate(rankSpace):\n",
    "                    print(f\"Method: Coefficient fit | meshDensity: {meshDensity}, sigma: {sigma}, nSamples: {nSamples}, rank: {rank}, Noise: {add_noise}\")\n",
    "                    Sim = Simulator(meshDensity)\n",
    "                    forcing = sampleforcing(sigma, nSamples, seed)\n",
    "                    solution = np.zeros(forcing.shape)\n",
    "                    for s in range(solution.shape[1]):\n",
    "                        if verbose:\n",
    "                            print(\"i = %d / %d\"%(s+1, solution.shape[1]))\n",
    "                        if add_noise:\n",
    "                            solution[:,s] = Sim.solve(forcing[:,s], noise_level)\n",
    "                        else:\n",
    "                            solution[:,s] = Sim.solve(forcing[:,s])\n",
    "                    models4[run, i,j,k,l] = EGF(\"coefficient-fit\", params, rank, Sim.mesh, forcing, solution, None, None, None, None, verbose = verbose)\n",
    "\n",
    "                    G_reconstruction = reconstructEGF1D(models4[run, i,j,k,l])\n",
    "                    G = exactGreen(models4[run, i,j,k,l].mesh.coordinates(), models4[run, i,j,k,l].params[0])\n",
    "                    errors4[run, i,j,k,l] = errorL2(G_reconstruction, G, models4[run, i,j,k,l].meshweights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "errordisc = np.hstack([meshDensitySpace.reshape((-1,1)), np.mean(errors4, axis = 0)[:,0,0,0].reshape((-1,1))])\n",
    "np.savetxt('errordisc.csv', errordisc, delimiter=',') "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2.00000000e+03, 8.58745733e-03],\n",
       "       [4.00000000e+03, 8.58720367e-03],\n",
       "       [8.00000000e+03, 8.58714017e-03],\n",
       "       [1.60000000e+04, 8.58712246e-03]])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "errordisc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.0, 1.0, 'C')"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "7374537dfbfe400594df6f82e245c6fe",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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AgAAGAZAiAAAIBlCIAAAACWIQACAABYhgAIAABgGQIgAACAZQiAAAAAliEAAgAAWKZJBMD58+crPj5eISEhSkpK0vr16+utz8/PV1JSkkJCQpSQkKAFCxbUqsnNzVXPnj0VHBysnj17asWKFbVq9u3bp5tuukkRERE666yz1KdPHxUUFDRYXwAAAE2R3wPgsmXLlJGRoVmzZqmoqEiDBg3SyJEjVVJSUmf9nj17NGrUKA0aNEhFRUWaOXOmpkyZotzcXG+Ny+VSWlqa0tPTtXXrVqWnp+uGG27Qpk2bvDWHDh3SJZdcosDAQK1atUo7d+7UE088oXbt2p3plgEAAPzKYYwx/lxA//791a9fP2VnZ3vHevToodGjRysrK6tW/YwZM7Ry5Urt2rXLOzZx4kRt3bpVLpdLkpSWliaPx6NVq1Z5a0aMGKH27dtryZIlkqR7771XH3zwwUnPNtbH4/EoPDxcbrdbYWFh//U8AACg8fD+7eczgJWVlSooKFBqaqrPeGpqqjZu3FjnY1wuV6364cOHa8uWLaqqqqq35udzrly5UsnJybr++usVFRWlvn376vnnn2+ItgAAAJo0vwbA8vJyHTlyRNHR0T7j0dHRKisrq/MxZWVlddZXV1ervLy83pqfz/nFF18oOztb55xzjt59911NnDhRU6ZM0eLFi0+43oqKCnk8Hp8bAABAc+P09wIkyeFw+Nw3xtQaO1n98eMnm7OmpkbJycl65JFHJEl9+/bVjh07lJ2drZtvvrnO/WZlZenBBx88hY4AAACaLr+eAYyMjFRAQECts3379++vdQbvmJiYmDrrnU6nIiIi6q35+ZwdO3ZUz549fWp69OhxwotPJOm+++6T2+323vbu3XvyJgEAAJoYvwbAoKAgJSUlKS8vz2c8Ly9PAwYMqPMxKSkptepXr16t5ORkBQYG1lvz8zkvueQSffLJJz41n376qeLi4k643uDgYIWFhfncAAAAmh3jZ0uXLjWBgYFm4cKFZufOnSYjI8O0adPGfPnll8YYY+69916Tnp7urf/iiy/MWWedZaZNm2Z27txpFi5caAIDA81rr73mrfnggw9MQECAmTNnjtm1a5eZM2eOcTqd5sMPP/TWbN682TidTvPwww+b3bt3m5dfftmcddZZ5qWXXjrltbvdbiPJuN3uBjgSAACgMfD+bYzfA6Axxjz77LMmLi7OBAUFmX79+pn8/HzvtvHjx5shQ4b41K9bt8707dvXBAUFma5du5rs7Oxac7766qvmvPPOM4GBgaZ79+4mNze3Vs2bb75pEhMTTXBwsOnevbvJyck5rXXzBAIAoPnh/dsYv/8OYHPG7wgBAND88P7dBP4lEAAAADQuAiAAAIBlCIAAAACWIQACAABYhgAIAABgGQIgAACAZQiAAAAAliEAAgAAWIYACAAAYBkCIAAAgGUIgAAAAJYhAAIAAFiGAAgAAGAZAiAAAIBlCIAAAACWIQACAABYhgAIAABgGQIgAACAZQiAAAAAljlpAFywYIF69eql1q1bKzw8XMOGDWuMdQEAAOAMcda3MTc3V/fee69ycnJ08cUX6/Dhw/ryyy8baWkAAAA4E+oNgJ9++qm6dOmi1NRUtWvXTpJ0/vnnN8a6AAAAcIbU+xHwhAkTFBAQoA4dOqht27b6/PPPG2tdAAAAOENOGACrqqp044036sILL9TmzZtVXFyshISExlwbAAAAzoATfgS8YsUKffbZZ1qzZk1jrgcAAABn2AnPAFZWVqq0tFR/+9vf9OWXX2r79u167rnnVFVV1ZjrAwAAQAM74RnAG2+8UUVFRZo5c6b+/e9/q0OHDrr00kt15513Nub6AAAA0MAcxhjj70U0Vx6PR+Hh4XK73QoLC/P3cgAAwCng/Zt/CQQAAMA6BEAAAADLEAABAAAsQwAEAACwDAEQAADAMgRAAAAAyxAAAQAALEMABAAAsAwBEAAAwDIEQAAAAMsQAAEAACxDAAQAALAMARAAAMAyBEAAAADLEAABAAAsQwAEAACwDAEQAADAMgRAAAAAyxAAAQAALEMABAAAsAwBEAAAwDIEQAAAAMsQAAEAACxDAAQAALAMARAAAMAyBEAAAADLEAABAAAsQwAEAACwDAEQAADAMgRAAAAAyxAAAQAALEMABAAAsAwBEAAAwDIEQAAAAMsQAAEAACzTJALg/PnzFR8fr5CQECUlJWn9+vX11ufn5yspKUkhISFKSEjQggULatXk5uaqZ8+eCg4OVs+ePbVixYoTzpeVlSWHw6GMjIxf2goAAECT5/cAuGzZMmVkZGjWrFkqKirSoEGDNHLkSJWUlNRZv2fPHo0aNUqDBg1SUVGRZs6cqSlTpig3N9db43K5lJaWpvT0dG3dulXp6em64YYbtGnTplrzffTRR8rJydEFF1xwxnoEAABoShzGGOPPBfTv31/9+vVTdna2d6xHjx4aPXq0srKyatXPmDFDK1eu1K5du7xjEydO1NatW+VyuSRJaWlp8ng8WrVqlbdmxIgRat++vZYsWeId+/7779WvXz/Nnz9ff/rTn9SnTx899dRTp7x2j8ej8PBwud1uhYWFnU7bAADAT3j/9vMZwMrKShUUFCg1NdVnPDU1VRs3bqzzMS6Xq1b98OHDtWXLFlVVVdVbc/ycd999t6644gpddtllv7QVAACAZsPpz52Xl5fryJEjio6O9hmPjo5WWVlZnY8pKyurs766ulrl5eXq2LHjCWt+PufSpUtVWFiojz766JTXW1FRoYqKCu99j8dzyo8FAABoKvz+HUBJcjgcPveNMbXGTlZ//Hh9c+7du1dTp07VSy+9pJCQkFNeZ1ZWlsLDw723zp07n/JjAQAAmgq/BsDIyEgFBATUOtu3f//+WmfwjomJiamz3ul0KiIiot6aY3MWFBRo//79SkpKktPplNPpVH5+vp5++mk5nU4dOXKkzn3fd999crvd3tvevXv/q74BAAD8ya8BMCgoSElJScrLy/MZz8vL04ABA+p8TEpKSq361atXKzk5WYGBgfXWHJvz0ksv1bZt21RcXOy9JScna9y4cSouLlZAQECd+w4ODlZYWJjPDQAAoLnx63cAJSkzM1Pp6elKTk5WSkqKcnJyVFJSookTJ0o6etZt3759Wrx4saSjV/w+88wzyszM1IQJE+RyubRw4UKfq3unTp2qwYMHa+7cubrmmmv0xhtvaM2aNdqwYYMkKTQ0VImJiT7raNOmjSIiImqNAwAAtDR+D4BpaWk6ePCgZs+erdLSUiUmJuqdd95RXFycJKm0tNTnNwHj4+P1zjvvaNq0aXr22WcVGxurp59+WmPGjPHWDBgwQEuXLtX999+vP/zhD/rVr36lZcuWqX///o3eHwAAQFPj998BbM74HSEAAJof3r+byFXAAAAAaDwEQAAAAMsQAAEAACxDAAQAALAMARAAAMAyBEAAAADLEAABAAAsQwAEAACwDAEQAADAMgRAAAAAyxAAAQAALEMABAAAsAwBEAAAwDIEQAAAAMsQAAEAACxDAAQAALAMARAAAMAyBEAAAADLEAABAAAsQwAEAACwDAEQAADAMgRAAAAAyxAAAQAALEMABAAAsAwBEAAAwDIEQAAAAMsQAAEAACxDAAQAALAMARAAAMAyBEAAAADLEAABAAAsQwAEAACwDAEQAADAMgRAAAAAyxAAAQAALEMABAAAsAwBEAAAwDIEQAAAAMsQAAEAACxDAAQAALAMARAAAMAyBEAAAADLEAABAAAsQwAEAACwDAEQAADAMgRAAAAAyxAAAQAALEMABAAAsAwBEAAAwDIEQAAAAMsQAAEAACxDAAQAALAMARAAAMAyBEAAAADLEAABAAAsQwAEAACwDAEQAADAMgRAAAAAyxAAAQAALEMABAAAsAwBEAAAwDIEQAAAAMsQAAEAACzTJALg/PnzFR8fr5CQECUlJWn9+vX11ufn5yspKUkhISFKSEjQggULatXk5uaqZ8+eCg4OVs+ePbVixQqf7VlZWbrwwgsVGhqqqKgojR49Wp988kmD9gUAANAU+T0ALlu2TBkZGZo1a5aKioo0aNAgjRw5UiUlJXXW79mzR6NGjdKgQYNUVFSkmTNnasqUKcrNzfXWuFwupaWlKT09XVu3blV6erpuuOEGbdq0yVuTn5+vu+++Wx9++KHy8vJUXV2t1NRU/fDDD2e8ZwAAAH9yGGOMPxfQv39/9evXT9nZ2d6xHj16aPTo0crKyqpVP2PGDK1cuVK7du3yjk2cOFFbt26Vy+WSJKWlpcnj8WjVqlXemhEjRqh9+/ZasmRJnes4cOCAoqKilJ+fr8GDB5/S2j0ej8LDw+V2uxUWFnZKjwEAAP7F+7efzwBWVlaqoKBAqampPuOpqanauHFjnY9xuVy16ocPH64tW7aoqqqq3poTzSlJbrdbktShQ4fT7gMAAKA5cfpz5+Xl5Tpy5Iiio6N9xqOjo1VWVlbnY8rKyuqsr66uVnl5uTp27HjCmhPNaYxRZmamBg4cqMTExBOut6KiQhUVFd77Ho+n3v4AAACaIr9/B1CSHA6Hz31jTK2xk9UfP346c06aNEkff/zxCT8ePiYrK0vh4eHeW+fOneutBwAAaIr8GgAjIyMVEBBQ68zc/v37a53BOyYmJqbOeqfTqYiIiHpr6ppz8uTJWrlypdauXatOnTrVu9777rtPbrfbe9u7d+9JewQAAGhq/BoAg4KClJSUpLy8PJ/xvLw8DRgwoM7HpKSk1KpfvXq1kpOTFRgYWG/Nz+c0xmjSpElavny5/vnPfyo+Pv6k6w0ODlZYWJjPDQAAoLnx63cAJSkzM1Pp6elKTk5WSkqKcnJyVFJSookTJ0o6etZt3759Wrx4saSjV/w+88wzyszM1IQJE+RyubRw4UKfj2+nTp2qwYMHa+7cubrmmmv0xhtvaM2aNdqwYYO35u6779Yrr7yiN954Q6Ghod4zhuHh4WrdunUjHgEAAIBGZpqAZ5991sTFxZmgoCDTr18/k5+f7902fvx4M2TIEJ/6devWmb59+5qgoCDTtWtXk52dXWvOV1991Zx33nkmMDDQdO/e3eTm5vpsl1Tn7YUXXjjldbvdbiPJuN3u0+oXAAD4D+/fxvj9dwCbM35HCACA5of37yZyFTAAAAAaDwEQAADAMgRAAAAAyxAAAQAALEMABAAAsAwBEAAAwDIEQAAAAMsQAAEAACxDAAQAALAMARAAAMAyBEAAAADLEAABAAAsQwAEAACwDAEQAADAMgRAAAAAyxAAAQAALEMABAAAsAwBEAAAwDIEQAAAAMsQAAEAACxDAAQAALAMARAAAMAyBEAAAADLEAABAAAsQwAEAACwDAEQAADAMgRAAAAAyxAAAQAALEMABAAAsAwBEAAAwDIEQAAAAMsQAAEAACxDAAQAALAMARAAAMAyBEAAAADLEAABAAAsQwAEAACwDAEQAADAMgRAAAAAyxAAAQAALEMABAAAsAwBEAAAwDIEQAAAAMsQAAEAACxDAAQAALAMARAAAMAyBEAAAADLEAABAAAsQwAEAACwDAEQAADAMgRAAAAAyxAAAQAALEMABAAAsAwBEAAAwDIEQAAAAMsQAAEAACxDAAQAALAMARAAAMAyBEAAAADLEAABAAAsQwAEAACwDAEQAADAMgRAAAAAyxAAAQAALEMABAAAsAwBEAAAwDJOfy+gOTPGSJI8Ho+fVwIAAE7VsfftY+/jNiIA/gKHDx+WJHXu3NnPKwEAAKfr8OHDCg8P9/cy/MJhbI6/v1BNTY2++eYbhYaGyuFwNOjcHo9HnTt31t69exUWFtagczcH9G93/xLHwPb+JY4B/Z+5/o0xOnz4sGJjY9WqlZ3fhuMM4C/QqlUrderU6YzuIywszMo/+MfQv939SxwD2/uXOAb0f2b6t/XM3zF2xl4AAACLEQABAAAsQwBsooKDg/XAAw8oODjY30vxC/q3u3+JY2B7/xLHgP7t7v9M4yIQAAAAy3AGEAAAwDIEQAAAAMsQAAEAACxDAAQAALAMAfAMycrK0oUXXqjQ0FBFRUVp9OjR+uSTT3xqjDH64x//qNjYWLVu3VpDhw7Vjh07fGoqKio0efJkRUZGqk2bNrr66qv19ddf+9QcOnRI6enpCg8PV3h4uNLT0/Xdd9+d6RZPS1ZWlhwOhzIyMrxjNvS/b98+3XTTTYqIiNBZZ52lPn36qKCgwLu9JR+D6upq3X///YqPj1fr1q2VkJCg2bNnq6amxlvT0vp///33ddVVVyk2NlYOh0Ovv/66z/bG7LekpERXXXWV2rRpo8jISE2ZMkWVlZVnom2v+vqvqqrSjBkz1KtXL7Vp00axsbG6+eab9c033/jM0VL7P96dd94ph8Ohp556yme8Ofcvndox2LVrl66++mqFh4crNDRUF198sUpKSrzbm/sxaDYMzojhw4ebF154wWzfvt0UFxebK664wnTp0sV8//333po5c+aY0NBQk5uba7Zt22bS0tJMx44djcfj8dZMnDjRnH322SYvL88UFhaaX//616Z3796murraWzNixAiTmJhoNm7caDZu3GgSExPNlVde2aj91mfz5s2ma9eu5oILLjBTp071jrf0/r/99lsTFxdnbrnlFrNp0yazZ88es2bNGvPZZ595a1ryMfjTn/5kIiIizFtvvWX27NljXn31VdO2bVvz1FNPeWtaWv/vvPOOmTVrlsnNzTWSzIoVK3y2N1a/1dXVJjEx0fz61782hYWFJi8vz8TGxppJkyb5rf/vvvvOXHbZZWbZsmXmX//6l3G5XKZ///4mKSnJZ46W2v/PrVixwvTu3dvExsaaJ5980mdbc+7fmJMfg88++8x06NDBTJ8+3RQWFprPP//cvPXWW+bf//53izkGzQUBsJHs37/fSDL5+fnGGGNqampMTEyMmTNnjrfmp59+MuHh4WbBggXGmKMvmIGBgWbp0qXemn379plWrVqZf/zjH8YYY3bu3GkkmQ8//NBb43K5jCTzr3/9qzFaq9fhw4fNOeecY/Ly8syQIUO8AdCG/mfMmGEGDhx4wu0t/RhcccUV5rbbbvMZu+6668xNN91kjGn5/R//5teY/b7zzjumVatWZt++fd6aJUuWmODgYON2u89Iv8erLwAds3nzZiPJfPXVV8YYO/r/+uuvzdlnn222b99u4uLifAJgS+rfmLqPQVpamvc1oC4t7Rg0ZXwE3EjcbrckqUOHDpKkPXv2qKysTKmpqd6a4OBgDRkyRBs3bpQkFRQUqKqqyqcmNjZWiYmJ3hqXy6Xw8HD179/fW3PxxRcrPDzcW+NPd999t6644gpddtllPuM29L9y5UolJyfr+uuvV1RUlPr27avnn3/eu72lH4OBAwfqvffe06effipJ2rp1qzZs2KBRo0ZJavn9H68x+3W5XEpMTFRsbKy3Zvjw4aqoqPD5CoK/ud1uORwOtWvXTlLL77+mpkbp6emaPn26zj///Frbbej/7bff1rnnnqvhw4crKipK/fv39/mYuKUfg6aEANgIjDHKzMzUwIEDlZiYKEkqKyuTJEVHR/vURkdHe7eVlZUpKChI7du3r7cmKiqq1j6joqK8Nf6ydOlSFRYWKisrq9Y2G/r/4osvlJ2drXPOOUfvvvuuJk6cqClTpmjx4sWSWv4xmDFjhsaOHavu3bsrMDBQffv2VUZGhsaOHSup5fd/vMbst6ysrNZ+2rdvr6CgoCZzTH766Sfde++9+u1vf6uwsDBJLb//uXPnyul0asqUKXVub+n979+/X99//73mzJmjESNGaPXq1br22mt13XXXKT8/X1LLPwZNidPfC7DBpEmT9PHHH2vDhg21tjkcDp/7xphaY8c7vqau+lOZ50zau3evpk6dqtWrVyskJOSEdS21f+no33aTk5P1yCOPSJL69u2rHTt2KDs7WzfffLO3rqUeg2XLlumll17SK6+8ovPPP1/FxcXKyMhQbGysxo8f761rqf2fSGP125SPSVVVlW688UbV1NRo/vz5J61vCf0XFBToL3/5iwoLC097DS2hf0neC8CuueYaTZs2TZLUp08fbdy4UQsWLNCQIUNO+NiWcgyaEs4AnmGTJ0/WypUrtXbtWnXq1Mk7HhMTI0m1/iayf/9+799aYmJiVFlZqUOHDtVb8+9//7vWfg8cOFDrbz+NqaCgQPv371dSUpKcTqecTqfy8/P19NNPy+l0etfWUvuXpI4dO6pnz54+Yz169PBe7dbSnwPTp0/XvffeqxtvvFG9evVSenq6pk2b5j0j3NL7P15j9hsTE1NrP4cOHVJVVZXfj0lVVZVuuOEG7dmzR3l5ed6zf1LL7n/9+vXav3+/unTp4n1N/Oqrr/S///u/6tq1q6SW3b8kRUZGyul0nvR1sSUfg6aEAHiGGGM0adIkLV++XP/85z8VHx/vsz0+Pl4xMTHKy8vzjlVWVio/P18DBgyQJCUlJSkwMNCnprS0VNu3b/fWpKSkyO12a/Pmzd6aTZs2ye12e2v84dJLL9W2bdtUXFzsvSUnJ2vcuHEqLi5WQkJCi+5fki655JJaP/3z6aefKi4uTlLLfw78+OOPatXK9yUmICDAexagpfd/vMbsNyUlRdu3b1dpaam3ZvXq1QoODlZSUtIZ7bM+x8Lf7t27tWbNGkVERPhsb8n9p6en6+OPP/Z5TYyNjdX06dP17rvvSmrZ/UtSUFCQLrzwwnpfF1v6MWhSGuliE+vcddddJjw83Kxbt86UlpZ6bz/++KO3Zs6cOSY8PNwsX77cbNu2zYwdO7bOn4To1KmTWbNmjSksLDTDhg2r83L4Cy64wLhcLuNyuUyvXr38/hMgdfn5VcDGtPz+N2/ebJxOp3n44YfN7t27zcsvv2zOOuss89JLL3lrWvIxGD9+vDn77LO9PwOzfPlyExkZae655x5vTUvr//Dhw6aoqMgUFRUZSebPf/6zKSoq8l7l2lj9HvsJjEsvvdQUFhaaNWvWmE6dOp3xn8Cor/+qqipz9dVXm06dOpni4mKf18WKiooW339djr8K2Jjm3b8xJz8Gy5cvN4GBgSYnJ8fs3r3bzJs3zwQEBJj169e3mGPQXBAAzxBJdd5eeOEFb01NTY154IEHTExMjAkODjaDBw8227Zt85nnP//5j5k0aZLp0KGDad26tbnyyitNSUmJT83BgwfNuHHjTGhoqAkNDTXjxo0zhw4daoQuT8/xAdCG/t98802TmJhogoODTffu3U1OTo7P9pZ8DDwej5k6darp0qWLCQkJMQkJCWbWrFk+b/Ytrf+1a9fW+ed+/PjxxpjG7ferr74yV1xxhWndurXp0KGDmTRpkvnpp5/OZPv19r9nz54Tvi6uXbu2xfdfl7oCYHPu35hTOwYLFy403bp1MyEhIaZ3797m9ddf95mjuR+D5sJhjDFn9hwjAAAAmhK+AwgAAGAZAiAAAIBlCIAAAACWIQACAABYhgAIAABgGQIgAACAZQiAAAAAliEAAgAAWIYACAAAYBkCIIDTMnToUGVkZPh7GV7GGN1xxx3q0KGDHA6HiouL/b0kAGjyCIBAM3PLLbfI4XBozpw5PuOvv/66HA6Hn1blP//4xz/04osv6q233lJpaakSExP9vSS/Gjx4sBwOh5YsWeIzPn/+fEVFRflpVQCaGgIg0AyFhIRo7ty5OnTokL+X0mAqKyv/q8d9/vnn6tixowYMGKCYmBg5nc4GXpl//DfHwxij4uJidezYUbm5uT7bCgsL1a9fv4ZaHoBmjgAINEOXXXaZYmJilJWVdcKarl276qmnnvIZ69Onj/74xz967w8dOlSTJ09WRkaG2rdvr+joaOXk5OiHH37QrbfeqtDQUP3qV7/SqlWrfOaprq7WpEmT1K5dO0VEROj++++XMca73RijRx99VAkJCWrdurV69+6t1157zWeOoUOHatKkScrMzFRkZKQuv/zyOvuoqKjQlClTFBUVpZCQEA0cOFAfffSRpKNnQydPnqySkhI5HA517dr1hMfjtddeU69evdS6dWtFRETosssu0w8//HBK6x06dKimTJmie+65Rx06dFBMTIzPcTzZ/PX1cLLjUd+8x9u9e7cOHz6s+++/X6tWrdKPP/7o3VZQUKCkpKQTHh8AdiEAAs1QQECAHnnkEc2bN09ff/31L5pr0aJFioyM1ObNmzV58mTddddduv766zVgwAAVFhZq+PDhSk9P9wkTixYtktPp1KZNm/T000/rySef1F//+lfv9vvvv18vvPCCsrOztWPHDk2bNk033XST8vPza+3b6XTqgw8+0HPPPVfn+u655x7l5uZq0aJFKiwsVLdu3TR8+HB9++23+stf/qLZs2erU6dOKi0trRWqjiktLdXYsWN12223adeuXVq3bp2uu+46b2g9lfUuWrRIbdq00aZNm/Too49q9uzZysvLO6X56+uhvuNxsnmPV1BQoJCQEP3ud79TWFiYN7hXVFRox44dnAEE8P8MgGZl/Pjx5pprrjHGGHPxxReb2267zRhjzIoVK8zP/0jHxcWZJ5980uexvXv3Ng888ID3/pAhQ8zAgQO996urq02bNm1Menq6d6y0tNRIMi6Xy/uYHj16mJqaGm/NjBkzTI8ePYwxxnz//fcmJCTEbNy40Wfft99+uxk7dqzPvvv06VNvr99//70JDAw0L7/8snessrLSxMbGmkcffdQYY8yTTz5p4uLi6p2noKDASDJffvllnfs42XqPP07GGHPhhReaGTNmnNL8J+vh2D6OPx71zVuX3//+9+aiiy4yxhhz1113mRtvvNEYY8zmzZuNJLNnz55TmgdAy8cZQKAZmzt3rhYtWqSdO3f+13NccMEF3v8OCAhQRESEevXq5R2Ljo6WJO3fv987dvHFF/tccJKSkqLdu3fryJEj2rlzp3766Sddfvnlatu2rfe2ePFiff755z77Tk5Orndtn3/+uaqqqnTJJZd4xwIDA3XRRRdp165dp9xj7969demll6pXr166/vrr9fzzz3u/P3mq6/35cZKkjh07eo9JffOfTg/HH4/65q1LQUGB9yzfddddp7ffflsVFRUqKChQhw4d6v2IvDEdOXLE30sArEcABJqxwYMHa/jw4Zo5c2atba1atar1UWFVVVWtusDAQJ/7DofDZ+xY0KupqTmlNR2re/vtt1VcXOy97dy5s9b3ANu0aVPvXMfWf/zVzcaY07riOSAgQHl5eVq1apV69uypefPm6bzzztOePXtOeb11Hadjj61v/tPp4fjjUd+8dSkqKvJ+z2/o0KEKCgrSu+++q8LCQvXt29en9rnnnlO/fv2UmJio3/72t5KkTz75RKNGjVJSUpKGDh2q8vJySdLIkSP1wAMP6OKLL1ZcXJz3Lxx1zbFt2zalpKQoMTFRY8aM8V7MMnLkSN1zzz0aPHiwFi9eXOdjATQeAiDQzM2ZM0dvvvmmNm7c6DP+P//zPyotLfXe93g8JwwOp+vDDz+sdf+cc85RQECAevbsqeDgYJWUlKhbt24+t86dO5/Wfrp166agoCBt2LDBO1ZVVaUtW7aoR48epzWXw+HQJZdcogcffFBFRUUKCgrSihUrGmy9J5r/l/ZwonmP98UXX+i7777zngF0Op266qqrlJubW+sCkEOHDiknJ0cfffSRtm/frvnz56uiokJ33323cnJyVFBQoN/85jfe73Vu375d8fHx+vDDDzVhwgS9+eabdc7x008/aezYsVq0aJG2b9+uyMhILV261DvH2Wefrffff1+jR4+u9VgAjatl/F4CYLFevXpp3Lhxmjdvns/4sGHD9OKLL+qqq65S+/bt9Yc//EEBAQENss+9e/cqMzNTd955pwoLCzVv3jw98cQTkqTQ0FD9/ve/17Rp01RTU6OBAwfK4/Fo48aNatu2rcaPH3/K+2nTpo3uuusuTZ8+XR06dFCXLl306KOP6scff9Ttt99+yvNs2rRJ7733nlJTUxUVFaVNmzbpwIED6tGjR4Ost775f0kP9c17vIKCAgUFBfn8DuKYMWO8F/Dcc8893nGn06mDBw9qxowZuvXWW3X++edr2bJl2rlzp6688kpJRy8c+d3vfie3263AwEDdcsstkqSgoCCFh4fXOcfSpUs1YsQInXvuuZKk7t2768CBA3K73XI4HJo6deoJ9w+gcREAgRbgoYce0t///nefsfvuu09ffPGFrrzySoWHh+uhhx5qsDOAN998s/7zn//ooosuUkBAgCZPnqw77rjDZz1RUVHKysrSF198oXbt2qlfv351flR9MnPmzFFNTY3S09N1+PBhJScn691331X79u1PeY6wsDC9//77euqpp+TxeBQXF6cnnnhCI0eObJD1nmz+/7aHk837c4WFhUpMTFRQUJB37PLLL9eRI0dUWVnpcwVwaGiotm3bptdff12/+c1v9Nhjj2nbtm164oknNHbsWJ95P/jgA1100UXe+9u3b9cdd9xR5xy7du3yCac7duzQmDFjtH37dg0YMKDe/R8LngAah8Mc/yUhAECLtnv3bp1zzjmSpDvuuEPDhw9XaWmptmzZohdffFHS0e/y9erVS88995zKy8s1a9YsSVLfvn21du1aHThwoNYcBw4c0Oeff67HHntMhYWFuuWWW1RUVKS//vWvPnPUtf8xY8Y08lEA7MZ3AAHAMg899JDOO+889e3bVyEhIbr22mt166236rvvvlP37t3Vu3dvvfLKK5KOnsU7dlV4dXW1vv/+e7Vr167OOdLT07Vz50716tVLGRkZ+vvf/66AgACfOU60fwCNizOAAAAAluEMIAAAgGUIgAAAAJYhAAIAAFiGAAgAAGAZAiAAAIBlCIAAAACWIQACAABYhgAIAABgmf8D8VNnVl6L5t0AAAAASUVORK5CYII=' width=640.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "meshDensitySpace = np.array([2000, 4000, 8000, 16000]) #np.linspace(50, 500, 9)\n",
    "# meshDensitySpace = np.array([200]) #np.linspace(50, 500, 9)\n",
    "sigmaSpace = np.array([0.0025])  # np.logspace(-2, -1, 10) \n",
    "nSamplesSpace = np.array([2000]) #np.array([100, 200, 300, 400, 500, 600]) # np.linspace(50, 200, 16, dtype = 'I') \n",
    "rankSpace = np.array([100]) #np.linspace(5, 50, 46, dtype = 'I') #np.array([20])\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(meshDensitySpace, np.mean(errors4, axis = 0)[:,0,0,0],'b.-')\n",
    "plt.xlabel('Number of sensors $N_{sensors}$')\n",
    "plt.ylabel('$\\epsilon$', rotation='horizontal', labelpad=15)\n",
    "plt.ylim([1e-5,1e-2])\n",
    "plt.title('C',loc ='left', weight = 'bold', size = 12)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}