{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "262a5ec8-2553-4237-ab62-319b6ca22089",
   "metadata": {},
   "source": [
    "# Example-59: Matrix (element)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "a70494a3-5f9f-44c4-8d98-bfbf92ed8163",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Can be used to model 4x4 linear elements\n",
    "# Transport matrix is constructed given elements of the symmetric matrix\n",
    "# M = exp(S A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "2003aa98-76f1-4a84-9e2a-9c4ad1fbdb87",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "from model.library.drift import Drift\n",
    "from model.library.matrix import Matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "035e68e0-235c-4607-81a7-966f60189ef0",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set state\n",
    "\n",
    "state = torch.tensor([0.01, -0.05, -0.01, 0.05], dtype=torch.float64)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "eab9b355-261d-4ba9-9701-0060252207d6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([-0.0650, -0.0500,  0.0650,  0.0500], dtype=torch.float64)\n",
      "\n",
      "tensor([[1.0000, 1.5000, 0.0000, 0.0000],\n",
      "        [0.0000, 1.0000, 0.0000, 0.0000],\n",
      "        [0.0000, 0.0000, 1.0000, 1.5000],\n",
      "        [0.0000, 0.0000, 0.0000, 1.0000]], dtype=torch.float64)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Drift (forward)\n",
    "\n",
    "D = Drift('D', length=1.5)\n",
    "\n",
    "print(D(state))\n",
    "print()\n",
    "\n",
    "print(torch.func.jacrev(D)(state))\n",
    "print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "78150170-966c-49ff-bd57-da4507141185",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([ 0.0850, -0.0500, -0.0850,  0.0500], dtype=torch.float64)\n",
      "\n",
      "tensor([[ 1.0000, -1.5000,  0.0000,  0.0000],\n",
      "        [ 0.0000,  1.0000,  0.0000,  0.0000],\n",
      "        [ 0.0000,  0.0000,  1.0000, -1.5000],\n",
      "        [ 0.0000,  0.0000,  0.0000,  1.0000]], dtype=torch.float64)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Drift (inverse)\n",
    "\n",
    "D = Drift('D', length=1.5).inverse()\n",
    "\n",
    "print(D(state))\n",
    "print()\n",
    "\n",
    "print(torch.func.jacrev(D)(state))\n",
    "print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "0ab134e4-1b2d-4dc1-ba0f-f678a52463d3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([-0.0650, -0.0500,  0.0650,  0.0500], dtype=torch.float64)\n",
      "\n",
      "tensor([[1.0000, 1.5000, 0.0000, 0.0000],\n",
      "        [0.0000, 1.0000, 0.0000, 0.0000],\n",
      "        [0.0000, 0.0000, 1.0000, 1.5000],\n",
      "        [0.0000, 0.0000, 0.0000, 1.0000]], dtype=torch.float64)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Matrix (forward)\n",
    "\n",
    "[a11, a12, a13, a14, a22, a23, a24, a33, a34, a44] = [0.0, 0.0, 0.0, 0.0, 1.5, 0.0, 0.0, 0.0, 0.0, 1.5]\n",
    "\n",
    "M = Matrix('M', length=1.5, A=[a11, a12, a13, a14, a22, a23, a24, a33, a34, a44])\n",
    "\n",
    "print(M(state))\n",
    "print()\n",
    "\n",
    "print(torch.func.jacrev(M)(state))\n",
    "print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "cb33c9a4-87bd-475e-a910-6009a3548913",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([ 0.0850, -0.0500, -0.0850,  0.0500], dtype=torch.float64)\n",
      "\n",
      "tensor([[ 1.0000, -1.5000,  0.0000,  0.0000],\n",
      "        [ 0.0000,  1.0000,  0.0000,  0.0000],\n",
      "        [ 0.0000,  0.0000,  1.0000, -1.5000],\n",
      "        [ 0.0000,  0.0000,  0.0000,  1.0000]], dtype=torch.float64)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Matrix (inverse)\n",
    "\n",
    "[a11, a12, a13, a14, a22, a23, a24, a33, a34, a44] = [0.0, 0.0, 0.0, 0.0, 1.5, 0.0, 0.0, 0.0, 0.0, 1.5]\n",
    "\n",
    "M = Matrix('M', length=1.5, A=[a11, a12, a13, a14, a22, a23, a24, a33, a34, a44]).inverse()\n",
    "\n",
    "print(M(state))\n",
    "print()\n",
    "\n",
    "print(torch.func.jacrev(M)(state))\n",
    "print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f8c8fd1c-de33-44df-8f83-3a93ffec164e",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [
    "myt0_gMIOq7b",
    "5d97819c"
   ],
   "name": "03_frequency.ipynb",
   "provenance": []
  },
  "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": "3.14.0"
  },
  "latex_envs": {
   "LaTeX_envs_menu_present": true,
   "autoclose": false,
   "autocomplete": true,
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 1,
   "hotkeys": {
    "equation": "Ctrl-E",
    "itemize": "Ctrl-I"
   },
   "labels_anchors": false,
   "latex_user_defs": false,
   "report_style_numbering": false,
   "user_envs_cfg": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}