{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "8ef12ff3",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "statistics"
    ]
   },
   "source": [
    "# Conversion functions\n",
    "\n",
    "In this example, we will demonstrate how to use conversion functions. These functions allow to convert failure probabilities into reliability indices and return periods, and vice versa.\n",
    "\n",
    "First, let's import the necessary class:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "4989b056",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "from probabilistic_library import StandardNormal"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "25d37ea3",
   "metadata": {},
   "source": [
    "We will consider the following list of failure probabilities:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a7faa405",
   "metadata": {},
   "outputs": [],
   "source": [
    "p = [0.9, 0.5, 0.1, 0.01, 0.001, 0.0001, 0.00001]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b16cb2ec",
   "metadata": {},
   "source": [
    "The failure probabilities can be converted to reliability indices:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "16a53a22",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-1.2815515655446008, -0.0, 1.2815515655446008, 2.3263478740408408, 3.090232306167813, 3.71901648545568, 4.2648907939228256]\n"
     ]
    }
   ],
   "source": [
    "reliability_index = [-StandardNormal.get_u_from_p(val) for val in p]\n",
    "print(reliability_index)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "06e63fdb",
   "metadata": {},
   "source": [
    "The reliability indices can be converted to return periods:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "abad4055",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.43429448190325176, 1.4426950408889634, 9.491221581029905, 99.49916247342207, 999.4999166249727, 9999.499991667351, 99999.49999851154]\n"
     ]
    }
   ],
   "source": [
    "return_period =  [StandardNormal.get_t_from_u(val) for val in reliability_index]\n",
    "print(return_period)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2a97d355",
   "metadata": {},
   "source": [
    "The frequency of a failure event can be obtained as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "411a93b8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2.302585092994046, 0.6931471805599453, 0.10536051565782628, 0.01005033585350145, 0.0010005003335835344, 0.00010000500033334732, 1.0000050000398848e-05]\n"
     ]
    }
   ],
   "source": [
    "freq = [1/val for val in return_period]\n",
    "print(freq)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3cac0c26",
   "metadata": {},
   "source": [
    "The return periods can be converted back to reliability indices:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "fd5c346c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-1.2815515655446008, 0.0, 1.2815515655446008, 2.3263478740408408, 3.090232306167813, 3.7190164854557084, 4.264890793921361]\n"
     ]
    }
   ],
   "source": [
    "calculated_reliability_index = [StandardNormal.get_u_from_t(val) for val in return_period]\n",
    "print(calculated_reliability_index)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8d4ab40e",
   "metadata": {},
   "source": [
    "And the reliability indices can be converted back to failure probabilities. The obtained failure probabilities should match the original list of failure probabilities:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "7cb2a66c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.9, 0.5, 0.09999999999999998, 0.010000000000000009, 0.0010000000000000009, 9.999999999998899e-05, 1.0000000000065512e-05]\n"
     ]
    }
   ],
   "source": [
    "calculated_p = [1-StandardNormal.get_p_from_u(val) for val in calculated_reliability_index]\n",
    "print(calculated_p)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b640a472",
   "metadata": {},
   "source": [
    "Let’s plot the relationship between the reliability index (`beta`) and the failure probability:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e38dc0f6",
   "metadata": {
    "tags": [
     "gallery",
     "statistics"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Failure probability (-)')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "beta = np.arange(-8.0, 8.0, 0.1)\n",
    "prob = [StandardNormal.get_p_from_u(val) for val in beta]\n",
    "plt.plot(beta, prob)\n",
    "plt.grid()\n",
    "plt.xlabel('Reliability index (-)')\n",
    "plt.ylabel('Failure probability (-)')\n",
    "plt.show()\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "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": "3.12.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}