{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Basic use of Probeye\n",
    "## Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 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",
    "\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_meas = 5000  # mm\n",
    "d_meas = 50  # mm\n",
    "sigma_meas = 10  # mm\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 midspan_deflection(E):\n",
    "    return Q * L ** 3 / (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",
    "        return {...}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define inverse problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Instantiate the inverse problem\n",
    "problem = ...\n",
    "\n",
    "# Add latent parameters\n",
    "problem.add_parameter(...)\n",
    "\n",
    "# Add fixed parameters\n",
    "problem.add_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",
    "problem.add_likelihood_model(...)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solve with MCMC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "emcee_solver = EmceeSolver(...)\n",
    "inference_data = emcee_solver.run(...)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "post_plot_array = create_posterior_plot(...)"
   ]
  }
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