{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "inappropriate-technician",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "from torch.autograd.functional import jacobian\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "rubber-accreditation",
   "metadata": {},
   "outputs": [],
   "source": [
    "a = torch.tensor([2., 3.], requires_grad=True)\n",
    "b = torch.tensor([6., 4.], requires_grad=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "adverse-efficiency",
   "metadata": {},
   "outputs": [],
   "source": [
    "def C(a,b):\n",
    "    return a*torch.exp(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "biblical-finance",
   "metadata": {},
   "outputs": [],
   "source": [
    "def D(a,b):\n",
    "    return a@b *  jacobian(C,(a,b))[0].inverse()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "native-congress",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[0.0025, -0.0000],\n",
       "        [0.0000, 0.0183]])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "jacobian(C,(a,b))[0].inverse()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "residential-sight",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([[[0.0149, 0.0099],\n",
       "          [0.0000, 0.0000]],\n",
       " \n",
       "         [[0.0000, 0.0000],\n",
       "          [0.1099, 0.0733]]]),\n",
       " tensor([[[0.0050, 0.0074],\n",
       "          [0.0000, 0.0000]],\n",
       " \n",
       "         [[0.0000, 0.0000],\n",
       "          [0.0366, 0.0549]]]))"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "jacobian(D,(a,b))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "still-province",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}