polish the dist doc, test=document_fix (#23982)

python/paddle/tensor/linalg.py

@@ -341,9 +341,32 @@ def norm(input, p='fro', axis=None, keepdim=False, out=None, name=None):
 def dist(x, y, p=2):
     """
     This OP returns the p-norm of (x - y). It is not a norm in a strict sense, only as a measure
-    of distance. The shapes of x and y must be broadcastable.
+    of distance. The shapes of x and y must be broadcastable. The definition is as follows, for
+    details, please refer to the `numpy's broadcasting <https://docs.scipy.org/doc/numpy/user/basics.broadcasting.html>`_:
 
-    Where, z = x - y,
+    - Each input has at least one dimension.
+    - Match the two input dimensions from back to front, the dimension sizes must either be equal, one of them is 1, or one of them does not exist.
+
+    Where, z = x - y, the shapes of x and y are broadcastable, then the shape of z can be
+    obtained as follows:
+
+    1. If the number of dimensions of x and y are not equal, prepend 1 to the dimensions of the
+    tensor with fewer dimensions.
+
+    For example, The shape of x is [8, 1, 6, 1], the shape of y is [7, 1, 5], prepend 1 to the
+    dimension of y.
+
+    x (4-D Tensor):  8 x 1 x 6 x 1
+
+    y (4-D Tensor):  1 x 7 x 1 x 5
+
+    2. Determine the size of each dimension of the output z: choose the maximum value from the
+    two input dimensions.
+
+    z (4-D Tensor):  8 x 7 x 6 x 5
+
+    If the number of dimensions of the two inputs are the same, the size of the output can be
+    directly determined in step 2. When p takes different values, the norm formula is as follows:
 
     When p = 0, defining $0^0=0$, the zero-norm of z is simply the number of non-zero elements of z.