{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multiple sensors and correlations\n",
    "## Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "# Problem definition\n",
    "from probeye.definition.inverse_problem import InverseProblem\n",
    "from probeye.definition.forward_model import ForwardModelBase\n",
    "from probeye.definition.distribution import Normal\n",
    "from probeye.definition.sensor import Sensor\n",
    "from probeye.definition.likelihood_model import GaussianLikelihoodModel\n",
    "from probeye.definition.correlation_model import ExpModel\n",
    "\n",
    "# Inference\n",
    "from probeye.inference.emcee.solver import EmceeSolver\n",
    "\n",
    "# Postprocessing\n",
    "from probeye.postprocessing.sampling_plots import create_posterior_plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Fixed parameters\n",
    "I = 1e9  # mm^4\n",
    "L = 10_000  # mm\n",
    "Q = 100  # kN\n",
    "\n",
    "# Measurements\n",
    "x_sensors = [2500, 5000]  # mm  (always from lower to higher, bug in inv_cov_vec_1D in tripy)\n",
    "d_sensors = [35, 50]  # mm\n",
    "sigma_model = 10  # mm\n",
    "pearson = 0.5\n",
    "l_corr = ...  # mm (calculate using an exponential correlation function)\n",
    "\n",
    "# Prior\n",
    "E_mean = 60  # GPa\n",
    "E_std = 20  # GPa"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define forward model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def beam_deflection(E, x):  # x is sensor position\n",
    "    return Q * x * (3 * L ** 2 - 4 * x ** 2) / (48 * E * I)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "class BeamModel(ForwardModelBase):\n",
    "    def interface(self):\n",
    "        self.parameters = ...\n",
    "        self.input_sensors = ...\n",
    "        self.output_sensors = ...\n",
    "\n",
    "    def response(self, inp: dict) -> dict:\n",
    "        E = ...\n",
    "        x = ...\n",
    "        return {...}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define inverse problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Instantiate the inverse problem\n",
    "problem = InverseProblem(...)\n",
    "\n",
    "# Add latent parameters\n",
    "problem.add_parameter(...)\n",
    "\n",
    "# Add fixed parameters\n",
    "problem.add_parameter(...)\n",
    "problem.add_parameter(...)  # Correlation length parameter\n",
    "\n",
    "# Add measurement data\n",
    "problem.add_experiment(...)\n",
    "                 \n",
    "# Add forward model\n",
    "problem.add_forward_model(...)\n",
    "\n",
    "# Add likelihood model\n",
    "likelihood_model = GaussianLikelihoodModel(...)  # Include correlation model\n",
    "problem.add_likelihood_model(likelihood_model)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solve with MCMC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "emcee_solver = EmceeSolver(problem, show_progress=True)\n",
    "inference_data = emcee_solver.run(n_steps=2000, n_initial_steps=2000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_plot_array = create_posterior_plot(\n",
    "    inference_data,\n",
    "    emcee_solver.problem,\n",
    "    kind=\"kde\",\n",
    "    title=\"Kernel density estimate of the posterior distribution\",\n",
    ")"
   ]
  }
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