sync

explore.ipynb

@@ -2,20 +2,13 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "import sympy as sym\n",
-    "from sympy import *"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {},
-   "outputs": [],
-   "source": [
+    "from sympy import *\n",
+    "\n",
     "def symbolize_matrix(matrix_prefix=\"k\"):\n",
     "    \"\"\"Symbolize a matrix with the given prefix.\n",
     "    \n",
@@ -37,11 +30,32 @@
     "    return A\n",
     "\n",
     "A = symbolize_matrix(\"a\")\n",
-    "K = symbolize_matrix(\"k\")\n",
     "\n",
-    "B=A*K*(A.T)"
+    "B=A*(A.T)\n",
+    "\n",
+    "DB = symbolize_matrix(\"\\partial_B\")\n",
+    "# sum(diff(B[i,j], A[0,0]) for i in range(3) for j in range(3))\n",
+    "DB = sym.Matrix([\n",
+    "    [diff(B[0,0], A[0,0]), diff(B[0,0], A[0,1]), diff(B[0,0], A[0,2]), diff(B[0,0], A[1,0]), diff(B[0,0], A[1,1]), diff(B[0,0], A[1,2]), diff(B[0,0], A[2,0]), diff(B[0,0], A[2,1]), diff(B[0,0], A[2,2])],\n",
+    "    [diff(B[0,1], A[0,0]), diff(B[0,1], A[0,1]), diff(B[0,1], A[0,2]), diff(B[0,1], A[1,0]), diff(B[0,1], A[1,1]), diff(B[0,1], A[1,2]), diff(B[0,1], A[2,0]), diff(B[0,1], A[2,1]), diff(B[0,1], A[2,2])],\n",
+    "    [diff(B[0,2], A[0,0]), diff(B[0,2], A[0,1]), diff(B[0,2], A[0,2]), diff(B[0,2], A[1,0]), diff(B[0,2], A[1,1]), diff(B[0,2], A[1,2]), diff(B[0,2], A[2,0]), diff(B[0,2], A[2,1]), diff(B[0,2], A[2,2])],\n",
+    "    [diff(B[1,0], A[0,0]), diff(B[1,0], A[0,1]), diff(B[1,0], A[0,2]), diff(B[1,0], A[1,0]), diff(B[1,0], A[1,1]), diff(B[1,0], A[1,2]), diff(B[1,0], A[2,0]), diff(B[1,0], A[2,1]), diff(B[1,0], A[2,2])],\n",
+    "    [diff(B[1,1], A[0,0]), diff(B[1,1], A[0,1]), diff(B[1,1], A[0,2]), diff(B[1,1], A[1,0]), diff(B[1,1], A[1,1]), diff(B[1,1], A[1,2]), diff(B[1,1], A[2,0]), diff(B[1,1], A[2,1]), diff(B[1,1], A[2,2])],\n",
+    "    [diff(B[1,2], A[0,0]), diff(B[1,2], A[0,1]), diff(B[1,2], A[0,2]), diff(B[1,2], A[1,0]), diff(B[1,2], A[1,1]), diff(B[1,2], A[1,2]), diff(B[1,2], A[2,0]), diff(B[1,2], A[2,1]), diff(B[1,2], A[2,2])],\n",
+    "    [diff(B[2,0], A[0,0]), diff(B[2,0], A[0,1]), diff(B[2,0], A[0,2]), diff(B[2,0], A[1,0]), diff(B[2,0], A[1,1]), diff(B[2,0], A[1,2]), diff(B[2,0], A[2,0]), diff(B[2,0], A[2,1]), diff(B[2,0], A[2,2])],\n",
+    "    [diff(B[2,1], A[0,0]), diff(B[2,1], A[0,1]), diff(B[2,1], A[0,2]), diff(B[2,1], A[1,0]), diff(B[2,1], A[1,1]), diff(B[2,1], A[1,2]), diff(B[2,1], A[2,0]), diff(B[2,1], A[2,1]), diff(B[2,1], A[2,2])],\n",
+    "    [diff(B[2,2], A[0,0]), diff(B[2,2], A[0,1]), diff(B[2,2], A[0,2]), diff(B[2,2], A[1,0]), diff(B[2,2], A[1,1]), diff(B[2,2], A[1,2]), diff(B[2,2], A[2,0]), diff(B[2,2], A[2,1]), diff(B[2,2], A[2,2])]\n",
+    "])\n",
+    "print(DB)"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
   {
    "cell_type": "code",
    "execution_count": 11,