Fix typos

dnguyend · Jul 21, 2024 · 9102ef7 · 9102ef7
1 parent 4b56386
commit 9102ef7
Showing 1 changed file with 12 additions and 12 deletions.
diff --git a/tests/notebooks/TestExpmAndCayleyIntegrator.ipynb b/tests/notebooks/TestExpmAndCayleyIntegrator.ipynb
@@ -4,7 +4,7 @@
   "metadata": {
     "colab": {
       "provenance": [],
-      "authorship_tag": "ABX9TyMlNlaglNMKeKmRLIRWl9bp",
+      "authorship_tag": "ABX9TyOqYilyIAPowpS6WwTskmcE",
       "include_colab_link": true
     },
     "kernelspec": {
@@ -50,7 +50,7 @@
         "id": "wpJ5PwCM-CIa",
         "outputId": "4f4f4478-905e-4535-e5c5-135b56ab8fb5"
       },
-      "execution_count": 1,
+      "execution_count": null,
       "outputs": [
         {
           "output_type": "stream",
@@ -96,7 +96,7 @@
         "where $v\\in T_xG$. We have the expansion\n",
         "$$\\fR(x, hv) = x + hv + \\frac{h^2}{2}x(x^{-1}v)^2 + O(h^3)\n",
         "$$\n",
-        "Thus, the adjustmented drift will be $\\mu_{\\fR} = \\mu - \\frac{1}{2}x(x^{-1}\\sigmam(x; E_{ij}))^2$ for the equation:\n",
+        "Thus, the adjusted drift will be $\\mu_{\\fR} = \\mu - \\frac{1}{2}x(x^{-1}\\sigmam(x; E_{ij}))^2$ for the equation:\n",
         "$$dX = \\mu dt + \\sigmam(X)dW_t.$$\n",
         "For a random move $\\Delta_W \\sim N(0, h^{\\frac{1}{2}}I_{\\R^{N\\times N}})$, the  Euler-Maruyama exponential step will be\n",
         "$$X_{i+1} = X_i\\expm(X_i^{-1}(h\\mu_r(X_i)+ \\sigmam(X)\\Delta_W ))\n",
@@ -105,7 +105,7 @@
         "\n",
         "For the group SO(N), or (more generally, for quadratic Lie group [Celledoni and Iserle]), for $a\\in \\so(N)$, we have $p(-a)^{-1}p(a)$ is in $SO(N)$ for all analytic $p$ with real coefficients. With $p(x) = 1+\\frac{x}{2}$, we have the Cayley retraction\n",
         "\n",
-        "$$\\fR_{Cayley}(x, v) = x(I-\\frac{1}{2}x^{-1}v)^{-1}(I-\\frac{1}{2}x^{-1}v),\n",
+        "$$\\fR_{Cayley}(x, v) = x(I-\\frac{1}{2}x^{-1}v)^{-1}(I+\\frac{1}{2}x^{-1}v),\n",
         "$$\n",
         "and the Euler-Maruyama Cayle steps will be\n",
         "$$X_{i+1} = X_i(I - \\frac{1}{2}X_i^{-1}(h\\mu_r(X_i)+ \\sigmam(X)\\Delta_W ))^{-1}\n",
@@ -134,7 +134,7 @@
         "id": "R50_I6ldmHMn",
         "outputId": "e64532f6-84ac-4d9b-dcec-2a06f1aff4bf"
       },
-      "execution_count": 2,
+      "execution_count": null,
       "outputs": [
         {
           "output_type": "stream",
@@ -159,7 +159,7 @@
     },
     {
       "cell_type": "code",
-      "execution_count": 3,
+      "execution_count": null,
       "metadata": {
         "id": "QYVLILrQRLLO"
       },
@@ -228,7 +228,7 @@
       "metadata": {
         "id": "mIbxYgIAvuRx"
       },
-      "execution_count": 4,
+      "execution_count": null,
       "outputs": []
     },
     {
@@ -321,7 +321,7 @@
       "metadata": {
         "id": "7A5PZbZ1msZg"
       },
-      "execution_count": 5,
+      "execution_count": null,
       "outputs": []
     },
     {
@@ -442,7 +442,7 @@
         "id": "Hp0BDZJowmDX",
         "outputId": "12419e30-f42a-495a-9039-45d7f839567a"
       },
-      "execution_count": 6,
+      "execution_count": null,
       "outputs": [
         {
           "output_type": "stream",
@@ -595,7 +595,7 @@
         "id": "TlZkYHY4uvgB",
         "outputId": "0c950e9e-e80a-4a20-addc-adaf2d280593"
       },
-      "execution_count": 7,
+      "execution_count": null,
       "outputs": [
         {
           "output_type": "stream",
@@ -658,7 +658,7 @@
       "metadata": {
         "id": "OJSr4lXWN3Sf"
       },
-      "execution_count": 8,
+      "execution_count": null,
       "outputs": []
     },
     {
@@ -775,7 +775,7 @@
         "id": "WD-SSgqMPFTq",
         "outputId": "1dce2e27-30d4-45d8-9811-cb115a861008"
       },
-      "execution_count": 9,
+      "execution_count": null,
       "outputs": [
         {
           "output_type": "stream",