Change hat to bar. (#5640)

Co-authored-by: Ubuntu <ubuntu@ip-172-31-28-63.ap-northeast-1.compute.internal>

notebooks/sparse/gcn.ipynb

@@ -63,16 +63,16 @@
         "\n",
         "Mathematically, the graph convolutional layer is defined as:\n",
         "\n",
-        "$$f(X^{(l)}, A) = \\sigma(\\hat{D}^{-\\frac{1}{2}}\\hat{A}\\hat{D}^{-\\frac{1}{2}}X^{(l)}W^{(l)})$$\n",
+        "$$f(X^{(l)}, A) = \\sigma(\\bar{D}^{-\\frac{1}{2}}\\bar{A}\\bar{D}^{-\\frac{1}{2}}X^{(l)}W^{(l)})$$\n",
         "\n",
-        "with $\\hat{A} = A + I$, where $A$ denotes the adjacency matrix and $I$ denotes the identity matrix, $\\hat{D}$ refers to the diagonal node degree matrix of $\\hat{A}$ and $W^{(l)}$ denotes a trainable weight matrix. $\\sigma$ refers to a non-linear activation (e.g. relu).\n",
+        "with $\\bar{A} = A + I$, where $A$ denotes the adjacency matrix and $I$ denotes the identity matrix, $\\bar{D}$ refers to the diagonal node degree matrix of $\\bar{A}$ and $W^{(l)}$ denotes a trainable weight matrix. $\\sigma$ refers to a non-linear activation (e.g. relu).\n",
         "\n",
         "The code below shows how to implement it using the `dgl.sparse` package. The core operations are:\n",
         "\n",
         "* `dgl.sparse.identity` creates the identity matrix $I$.\n",
-        "* The augmented adjacency matrix $\\hat{A}$ is then computed by adding the identity matrix to the adjacency matrix $A$.\n",
-        "* `A_hat.sum(0)` aggregates the augmented adjacency matrix $\\hat{A}$ along the first dimension which gives the degree vector of the augmented graph. The diagonal degree matrix $\\hat{D}$ is then created by `dgl.sparse.diag`.\n",
-        "* Compute $\\hat{D}^{-\\frac{1}{2}}$.\n",
+        "* The augmented adjacency matrix $\\bar{A}$ is then computed by adding the identity matrix to the adjacency matrix $A$.\n",
+        "* `A_hat.sum(0)` aggregates the augmented adjacency matrix $\\bar{A}$ along the first dimension which gives the degree vector of the augmented graph. The diagonal degree matrix $\\bar{D}$ is then created by `dgl.sparse.diag`.\n",
+        "* Compute $\\bar{D}^{-\\frac{1}{2}}$.\n",
         "* `D_hat_invsqrt @ A_hat @ D_hat_invsqrt` computes the convolution matrix which is then multiplied by the linearly transformed node features."
       ],
       "metadata": {

notebooks/sparse/graph_diffusion.ipynb

@@ -125,9 +125,9 @@
       "source": [
         "We use the graph convolution matrix from Graph Convolution Networks as the diffusion matrix in this example. The graph convolution matrix is defined as:\n",
         "\n",
-        "$$\\tilde{A} = \\hat{D}^{-\\frac{1}{2}}\\hat{A}\\hat{D}^{-\\frac{1}{2}}$$\n",
+        "$$\\tilde{A} = \\bar{D}^{-\\frac{1}{2}}\\bar{A}\\bar{D}^{-\\frac{1}{2}}$$\n",
         "\n",
-        "with $\\hat{A} = A + I$, where $A$ denotes the adjacency matrix and $I$ denotes the identity matrix, $\\hat{D}$ refers to the diagonal node degree matrix of $\\hat{A}$."
+        "with $\\bar{A} = A + I$, where $A$ denotes the adjacency matrix and $I$ denotes the identity matrix, $\\bar{D}$ refers to the diagonal node degree matrix of $\\bar{A}$."
       ],
       "metadata": {
         "id": "wJMT4oHOCCqJ"

notebooks/sparse/quickstart.ipynb

@@ -1219,9 +1219,9 @@
       "source": [
         "*Let's test what you've learned. Feel free to [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/dmlc/dgl/blob/master/notebooks/sparse/quickstart.ipynb).*\n",
         "\n",
-        "Given a sparse symmetrical adjacency matrix $A$, calculate its symmetrically normalized adjacency matrix: $$norm = \\hat{D}^{-\\frac{1}{2}}\\hat{A}\\hat{D}^{-\\frac{1}{2}}$$\n",
+        "Given a sparse symmetrical adjacency matrix $A$, calculate its symmetrically normalized adjacency matrix: $$norm = \\bar{D}^{-\\frac{1}{2}}\\bar{A}\\bar{D}^{-\\frac{1}{2}}$$\n",
         "\n",
-        "Where $\\hat{A} = A + I$, $I$ is the identity matrix, and $\\hat{D}$ is the diagonal node degree matrix of $\\hat{A}$."
+        "Where $\\bar{A} = A + I$, $I$ is the identity matrix, and $\\bar{D}$ is the diagonal node degree matrix of $\\bar{A}$."
       ],
       "metadata": {
         "id": "yDQ4Kmr_08St"