Tested incorporating the jacobian as part of a funciton

Code/test_double.ipynb

@@ -0,0 +1,130 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "4104cbdc-87e8-4be6-b2aa-064a5c0d1bde",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import torch\n",
+    "from torch.autograd.functional import jacobian\n",
+    "import numpy as np"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "bf266b6c-e071-45e4-8001-69fe4a70517a",
+   "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": "ad508a39-9690-45e0-af0b-c2c9f6819ad3",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def C(a,b):\n",
+    "    return a*torch.exp(b)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 35,
+   "id": "baabba71-6bcd-46cb-8d31-336087eb6e9f",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def D(a,b):\n",
+    "    return a@b *  jacobian(C,(a,b))[0].inverse()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 36,
+   "id": "3f098bbe-6ed9-48e7-ae9a-a88992a72541",
+   "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": "f6dd665f-2965-4e7f-9d3b-2c1ce3ff522e",
+   "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": "8ca4b6a4-1a13-4ad4-8856-a38ac69d96a6",
+   "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": "3.9.5"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}