udpate scatter spec

docs/ops/movement/ScatterUpdate_3.md

@@ -7,82 +7,80 @@
 **Short description**: *ScatterUpdate* creates a copy of the first input tensor with updated elements specified with second and third input tensors.
 
 **Detailed description**: *ScatterUpdate* creates a copy of the first input tensor with updated elements in positions specified with `indices` input
-and values specified with `updates` tensor starting from the dimension with index `axis`. For the `data` tensor of shape `[d_0, d_1, ..., d_n]`,
-`indices` tensor of shape `[i_0, i_1, ..., i_k]` and `updates` tensor of shape
-`[d_0, d_1, ... d_(axis - 1), i_0, i_1, ..., i_k, d_(axis + 1), ..., d_n]` the operation computes
+and values specified with `updates` tensor starting from the dimension with index `axis`. For the `data` tensor of shape \f$[d_0,\;d_1,\;\dots,\;d_n]\f$,
+`indices` tensor of shape \f$[i_0,\;i_1,\;\dots,\;i_k]\f$ and `updates` tensor of shape
+\f$[d_0,\;d_1,\;\dots,\;d_{axis - 1},\;i_0,\;i_1,\;\dots,\;i_k,\;d_{axis + 1},\;\dots, d_n]\f$ the operation computes
 for each `m, n, ..., p` of the `indices` tensor indices:
 
-```
-data[..., indices[m, n, ..., p], ...] = updates[..., m, n, ..., p, ...]
-```
 
-where first `...` in the `data` corresponds to first `axis` dimensions, last `...` in the `data` corresponds to the
+\f[data[\dots,\;indices[m,\;n,\;\dots,\;p],\;\dots] = updates[\dots,\;m,\;n,\;\dots,\;p,\;\dots]\f]
+
+where first \f$\dots\f$ in the `data` corresponds to \f$[d_0,\;\dots,\;d_{axis - 1}]\f$ dimensions, last\f$\dots\f$ in the `data` corresponds to the
 `rank(data) - (axis + 1)` dimensions.
 
 Several examples for case when `axis = 0`:
-1. `indices` is a 0D tensor: `data[indices, ...] = updates[...]`
-2. `indices` is a 1D tensor (for each `i`): `data[indices[i], ...] = updates[i, ...]`
-3. `indices` is a ND tensor (for each `i, ..., j`): `data[indices[i, ..., j], ...] = updates[i, ..., j, ...]`
-
-This operation is similar to TensorFlow* operation [ScatterUpdate](https://www.tensorflow.org/versions/r1.15/api_docs/python/tf/scatter_update)
-but allows scattering for the arbitrary axis.
+1. `indices` is a \f$0\f$D tensor: \f$data[indices,\;\dots] = updates[\dots]\f$
+2. `indices` is a \f$1\f$D tensor (\f$\forall_{i}\f$): \f$data[indices[i],\;\dots] = updates[i,\;\dots]\f$
+3. `indices` is a \f$N\f$D tensor (\f$\forall_{i,\;\dots,\;j}\f$): \f$data[indices[i],\;\dots,\;j],\;\dots] = updates[i,\;\dots,\;j,\;\dots]\f$
 
 **Attributes**: *ScatterUpdate* does not have attributes.
 
 **Inputs**:
 
-*   **1**: `data` tensor of arbitrary rank `r` and of type *T*. **Required.**
+*   **1**: `data` tensor of arbitrary rank `r` and type *T_NUMERIC*. **Required.**
 
 *   **2**: `indices` tensor with indices of type *T_IND*.
-All index values are expected to be within bounds `[0, s - 1]` along axis of size `s`. If multiple indices point to the
-same output location then the order of updating the values is undefined. If an index points to non-existing output
-tensor element or is negative then an exception is raised. **Required.**
+All index values are expected to be within bounds `[0, s - 1]` along the axis of size `s`. If multiple indices point to the
+same output location, the order of updating the values is undefined. If an index points to a non-existing output
+tensor element or is negative, then an exception is raised. **Required.**
 
-*   **3**: `updates` tensor of type *T*. **Required.**
+*   **3**: `updates` tensor of type *T_NUMERIC* and rank equal to `rank(indices) + rank(data) - 1` **Required.**
 
 *   **4**: `axis` tensor with scalar or 1D tensor with one element of type *T_AXIS* specifying axis for scatter.
-The value can be in range `[-r, r - 1]` where `r` is the rank of `data`. **Required.**
+The value can be in the range `[ -r, r - 1]`, where `r` is the rank of `data`. **Required.**
 
 **Outputs**:
 
-*   **1**: tensor with shape equal to `data` tensor of the type *T*.
+*   **1**: tensor with shape equal to `data` tensor of the type *T_NUMERIC*.
 
 **Types**
 
-* *T*: any numeric type.
+* *T_NUMERIC*: any numeric type.
 
 * *T_IND*: any supported integer types.
 
 * *T_AXIS*: any supported integer types.
 
-**Example**
+**Examples**
+
+*Example 1*
 
 ```xml
 <layer ... type="ScatterUpdate">
     <input>
-        <port id="0">
+        <port id="0">  <!-- data -->
             <dim>1000</dim>
             <dim>256</dim>
             <dim>10</dim>
             <dim>15</dim>
         </port>
-        <port id="1">
+        <port id="1">  <!-- indices -->
             <dim>125</dim>
             <dim>20</dim>
         </port>
-        <port id="2">
+        <port id="2">  <!-- udpates -->
             <dim>1000</dim>
             <dim>125</dim>
             <dim>20</dim>
             <dim>10</dim>
             <dim>15</dim>
         </port>
-        <port id="3">     <!-- value [1] -->
-            <dim>1</dim>
+        <port id="3">   <!-- axis -->
+            <dim>1</dim> <!-- value [1] -->
         </port>
     </input>
     <output>
-        <port id="4" precision="FP32">
+        <port id="4" precision="FP32"> <!-- output -->
             <dim>1000</dim>
             <dim>256</dim>
             <dim>10</dim>
@@ -91,3 +89,32 @@ The value can be in range `[-r, r - 1]` where `r` is the rank of `data`. **Requi
     </output>
 </layer>
 ```
+
+*Example 2*
+
+```xml
+<layer ... type="ScatterUpdate">
+    <input>
+        <port id="0">  <!-- data -->
+            <dim>3</dim>    <!-- {{-1.0f, 1.0f, -1.0f, 3.0f, 4.0f},  -->
+            <dim>5</dim>    <!-- {-1.0f, 6.0f, -1.0f, 8.0f, 9.0f},   -->
+        </port>             <!-- {-1.0f, 11.0f, 1.0f, 13.0f, 14.0f}} -->
+        <port id="1">  <!-- indices -->
+            <dim>2</dim> <!-- {0, 2} -->
+        </port>
+        <port id="2">  <!-- udpates -->
+            <dim>3</dim> <!-- {1.0f, 1.0f} -->
+            <dim>2</dim> <!-- {1.0f, 1.0f} -->
+        </port>          <!-- {1.0f, 2.0f} -->
+        <port id="3">   <!-- axis -->
+            <dim>1</dim> <!-- {1} -->
+        </port>
+    </input>
+    <output>
+        <port id="4">  <!-- output -->
+            <dim>3</dim>    <!-- {{1.0f, 1.0f, 1.0f, 3.0f, 4.0f},   -->
+            <dim>5</dim>    <!-- {1.0f, 6.0f, 1.0f, 8.0f, 9.0f},    -->
+        </port>             <!-- {1.0f, 11.0f, 2.0f, 13.0f, 14.0f}} -->
+    </output>
+</layer>
+```