[Sparse] Add elementwise mul and div method, and polish the python doc. (#5142)

* add mul and div

* polish

* equivalent

* indent

* double
Co-authored-by: Steve <ubuntu@ip-172-31-34-29.ap-northeast-1.compute.internal>

python/dgl/sparse/elementwise_op.py

@@ -5,18 +5,19 @@ from typing import Union
 from .diag_matrix import DiagMatrix
 from .sparse_matrix import SparseMatrix
 
-__all__ = ["add", "power"]
+__all__ = ["add", "sub", "mul", "div", "power"]
 
 
 def add(
     A: Union[DiagMatrix, SparseMatrix], B: Union[DiagMatrix, SparseMatrix]
 ) -> Union[DiagMatrix, SparseMatrix]:
-    """Elementwise additions for `DiagMatrix` and `SparseMatrix`.
+    """Elementwise additions for ``DiagMatrix`` and ``SparseMatrix``. This is
+     equivalent to ``A + B``.
 
     The supported combinations are shown as follows.
 
     +--------------+------------+--------------+--------+
-    |     A \ B    | DiagMatrix | SparseMatrix | scalar |
+    |    A \\ B    | DiagMatrix | SparseMatrix | scalar |
     +--------------+------------+--------------+--------+
     |  DiagMatrix  |     ✅     |      ✅      |   🚫   |
     +--------------+------------+--------------+--------+
@@ -45,7 +46,7 @@ def add(
     >>> val = torch.tensor([10, 20, 30])
     >>> A = from_coo(row, col, val)
     >>> B = diag(torch.arange(1, 4))
-    >>> A + B
+    >>> add(A, B)
     SparseMatrix(indices=tensor([[0, 0, 1, 1, 2],
                                  [0, 1, 0, 1, 2]]),
                  values=tensor([ 1, 20, 10,  2, 33]),
@@ -55,12 +56,13 @@ def add(
 
 
 def sub(A: Union[DiagMatrix], B: Union[DiagMatrix]) -> Union[DiagMatrix]:
-    """Elementwise subtraction for `DiagMatrix` and `SparseMatrix`.
+    """Elementwise subtraction for ``DiagMatrix`` and ``SparseMatrix``. This is
+    equivalent to ``A - B``.
 
     The supported combinations are shown as follows.
 
     +--------------+------------+--------------+--------+
-    |     A \ B    | DiagMatrix | SparseMatrix | scalar |
+    |    A \\ B    | DiagMatrix | SparseMatrix | scalar |
     +--------------+------------+--------------+--------+
     |  DiagMatrix  |     ✅     |      🚫      |   🚫   |
     +--------------+------------+--------------+--------+
@@ -85,22 +87,125 @@ def sub(A: Union[DiagMatrix], B: Union[DiagMatrix]) -> Union[DiagMatrix]:
     --------
     >>> A = diag(torch.arange(1, 4))
     >>> B = diag(torch.arange(10, 13))
-    >>> A - B
+    >>> sub(A, B)
     DiagMatrix(val=tensor([-9, -9, -9]),
                shape=(3, 3))
     """
     return A - B
 
 
+def mul(
+    A: Union[SparseMatrix, DiagMatrix, float, int],
+    B: Union[SparseMatrix, DiagMatrix, float, int],
+) -> Union[SparseMatrix, DiagMatrix]:
+    """Elementwise multiplication for ``DiagMatrix`` and ``SparseMatrix``. This
+     is equivalent to ``A * B``.
+
+    The supported combinations are shown as follows.
+
+    +--------------+------------+--------------+--------+
+    |    A \\ B    | DiagMatrix | SparseMatrix | scalar |
+    +--------------+------------+--------------+--------+
+    |  DiagMatrix  |     ✅     |      🚫      |   ✅   |
+    +--------------+------------+--------------+--------+
+    | SparseMatrix |     🚫     |      🚫      |   ✅   |
+    +--------------+------------+--------------+--------+
+    |    scalar    |     ✅     |      ✅      |   🚫   |
+    +--------------+------------+--------------+--------+
+
+    Parameters
+    ----------
+    A : SparseMatrix or DiagMatrix or float or int
+        Sparse matrix or diagonal matrix or scalar value
+    B : SparseMatrix or DiagMatrix or float or int
+        Sparse matrix or diagonal matrix or scalar value
+
+    Returns
+    -------
+    SparseMatrix or DiagMatrix
+        Either sparse matrix or diagonal matrix
+
+    Examples
+    --------
+    >>> row = torch.tensor([1, 0, 2])
+    >>> col = torch.tensor([0, 3, 2])
+    >>> val = torch.tensor([10, 20, 30])
+    >>> A = from_coo(row, col, val)
+    >>> mul(A, 2)
+    SparseMatrix(indices=tensor([[1, 0, 2],
+                                 [0, 3, 2]]),
+                 values=tensor([20, 40, 60]),
+                 shape=(3, 4), nnz=3)
+
+    >>> D = diag(torch.arange(1, 4))
+    >>> mul(D, 2)
+    DiagMatrix(val=tensor([2, 4, 6]),
+               shape=(3, 3))
+
+    >>> D = diag(torch.arange(1, 4))
+    >>> mul(D, D)
+    DiagMatrix(val=tensor([1, 4, 9]),
+               shape=(3, 3))
+    """
+    return A * B
+
+
+def div(
+    A: Union[DiagMatrix], B: Union[DiagMatrix, float, int]
+) -> Union[DiagMatrix]:
+    """Elementwise division for ``DiagMatrix`` and ``SparseMatrix``. This is
+    equivalent to ``A / B``.
+
+    The supported combinations are shown as follows.
+
+    +--------------+------------+--------------+--------+
+    |    A \\ B    | DiagMatrix | SparseMatrix | scalar |
+    +--------------+------------+--------------+--------+
+    |  DiagMatrix  |     ✅     |      🚫      |   ✅   |
+    +--------------+------------+--------------+--------+
+    | SparseMatrix |     🚫     |      🚫      |   🚫   |
+    +--------------+------------+--------------+--------+
+    |    scalar    |     🚫     |      🚫      |   🚫   |
+    +--------------+------------+--------------+--------+
+
+    Parameters
+    ----------
+    A : DiagMatrix
+        Diagonal matrix
+    B : DiagMatrix or float or int
+        Diagonal matrix or scalar value
+
+    Returns
+    -------
+    DiagMatrix
+        Diagonal matrix
+
+    Examples
+    --------
+    >>> A = diag(torch.arange(1, 4))
+    >>> B = diag(torch.arange(10, 13))
+    >>> div(A, B)
+    DiagMatrix(val=tensor([0.1000, 0.1818, 0.2500]),
+               shape=(3, 3))
+
+    >>> A = diag(torch.arange(1, 4))
+    >>> div(A, 2)
+    DiagMatrix(val=tensor([0.5000, 1.0000, 1.5000]),
+               shape=(3, 3))
+    """
+    return A / B
+
+
 def power(
     A: Union[SparseMatrix, DiagMatrix], scalar: Union[float, int]
 ) -> Union[SparseMatrix, DiagMatrix]:
-    """Elementwise exponentiation for `DiagMatrix` and `SparseMatrix`.
+    """Elementwise exponentiation for ``DiagMatrix`` and ``SparseMatrix``. This
+     is equivalent to ``A ** scalar``.
 
     The supported combinations are shown as follows.
 
     +--------------+------------+--------------+--------+
-    |     A \ B    | DiagMatrix | SparseMatrix | scalar |
+    |    A \\ B    | DiagMatrix | SparseMatrix | scalar |
     +--------------+------------+--------------+--------+
     |  DiagMatrix  |     🚫     |      🚫      |   ✅   |
     +--------------+------------+--------------+--------+
@@ -123,7 +228,6 @@ def power(
 
     Examples
     --------
-
     >>> row = torch.tensor([1, 0, 2])
     >>> col = torch.tensor([0, 3, 2])
     >>> val = torch.tensor([10, 20, 30])