{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Configuring the Hoffman failure criterion by fitting to experimental data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sigmaepsilon.solid.material import HoffmanFailureCriterion\n",
    "import numpy as np\n",
    "\n",
    "inputs = [\n",
    "    [-1, 0, 0, 0, 0, 0],\n",
    "    [0, 1, 0, 0, 0, 0],\n",
    "    [0, 0, -1, 0, 0, 0],\n",
    "    [0, 0, 0, 1, 0, 0],\n",
    "    [0, 0, 0, 0, -1, 0],\n",
    "    [0, 0, 0, 0, 0, 1],\n",
    "    [-1, 0.2, 0, 0, 0, 0],\n",
    "    [0.2, 1, 0, 0, 0, 0],\n",
    "    [-1, 0, 0.2, 0, 0, 0],\n",
    "]\n",
    "inputs = np.array(inputs, dtype=float)\n",
    "outputs = np.ones(len(inputs))\n",
    "\n",
    "failure_obj = HoffmanFailureCriterion()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Parameter fitting with a Binary Genetic Algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.9694749694749696,\n",
       " -3.0647130647130645,\n",
       " 0.808302808302809,\n",
       " 8.686202686202687,\n",
       " -4.378510378510379,\n",
       " -4.349206349206349,\n",
       " 1.2380952380952372,\n",
       " -2.5274725274725274,\n",
       " 1.0378510378510377)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "params = failure_obj.fit(\n",
    "    inputs,\n",
    "    outputs,\n",
    "    solver_params=dict(nPop=100, length=12),\n",
    "    penalty=1e12,\n",
    "    tol=0.1,\n",
    "    n_iter=100,\n",
    "    ranges=[[-10, 10] for _ in range(9)],\n",
    "    method=\"bga\",\n",
    ")\n",
    "failure_obj.params = params\n",
    "params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.6043478260869566, 1.9910851099808313)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prediction = failure_obj.utilization(stresses=inputs)\n",
    "max_error = np.max(np.abs(prediction - outputs))\n",
    "total_error = np.sum(np.sqrt((prediction - outputs) ** 2))\n",
    "max_error, total_error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.02121238, 1.20985704, 0.40580257, 0.80769231, 0.39565217,\n",
       "       0.96352941, 1.20067546, 1.01013493, 0.87811824])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prediction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Parameter fitting with Scipy's Nelder-Mead method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1.007322989181017,\n",
       " 2.1576353611607075,\n",
       " -0.1541917498510884,\n",
       " 0.9728903373271577,\n",
       " -0.9949634593134442,\n",
       " 0.30283382032188944,\n",
       " 0.35151153576340144,\n",
       " 0.4327118607825844,\n",
       " 0.44137317208707544)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "params = failure_obj.fit(\n",
    "    inputs,\n",
    "    outputs,\n",
    "    penalty=1e12,\n",
    "    tol=0.1,\n",
    "    method=\"Nelder-Mead\",\n",
    "    x0=[-1.0, 1.0, -1.0, 1.0, -1.0, 1.0, 0.2, 0.2, 0.2],\n",
    ")\n",
    "failure_obj.params = params\n",
    "params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3.311006678188673, 7.380983890058536)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prediction = failure_obj.utilization(stresses=inputs)\n",
    "max_error = np.max(np.abs(prediction - outputs))\n",
    "total_error = np.sum(np.sqrt((prediction - outputs) ** 2))\n",
    "max_error, total_error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.98936093,  1.20858211,  1.02177759,  2.84485685, -2.31100668,\n",
       "        2.26565651,  0.92597216,  0.35965563,  1.00409288])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prediction"
   ]
  }
 ],
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   "display_name": ".solid.material",
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