MatMul spec update (openvinotoolkit#2765)

Aligned specification with nGraph MatMul shape inference operation. Affects description of the behavior for 1D tensors.

docs/ops/matrix/MatMul_1.md

@@ -12,29 +12,43 @@
 
 Before matrix multiplication, there is an implicit shape alignment for input arguments. It consists of the following steps:
 
-1. If rank of an input less than 2 it is unsqueezed to 2D tensor by adding axes with size 1 to the left of the shape. For example, if input has shape `[S]` it will be reshaped to `[1, S]`. It is applied for each input independently.
+1. Applying transpositions specified by optional `transpose_a` and `transpose_b` attributes. Only the two right-most dimensions are transposed, other dimensions remain the same. Transpose attributes are ignored for 1D tensors.
 
-2. Applied transpositions specified by optional `transpose_a` and `transpose_b` attributes.
+2. One-dimensional tensors unsqueezing is applied for each input independently. The axes inserted in this step are not included in the output shape.
+    * If rank of the **first** input is equal to 1, it is always unsqueezed to 2D tensor **row vector** (regardless of `transpose_a`) by adding axes with size 1 at ROW_INDEX_DIM, to the **left** of the shape. For example `[S]` will be reshaped to `[1, S]`. 
+    * If rank of the **second** input is equal to 1, it is always unsqueezed to 2D tensor **column vector** (regardless of `transpose_b`) by adding axes with size 1 at COL_INDEX_DIM, to the **right** of the shape. For example `[S]` will be reshaped to `[S, 1]`.
 
-3. If ranks of input arguments are different after steps 1 and 2, each is unsqueezed from the left side of the shape by necessary number of axes to make both shapes of the same rank.
+3. If ranks of input arguments are different after steps 1 and 2, the tensor with a smaller rank is unsqueezed from the left side of the shape by necessary number of axes to make both shapes of the same rank.
 
-3. Usual rules of the broadcasting are applied for batch dimensions.
+4. Usual rules of the broadcasting are applied for batch dimensions.
 
-Two attributes, transpose_a and transpose_b specifies embedded transposition for two right-most dimension for the first and the second input tensors correspondingly. It implies swapping of ROW_INDEX_DIM and COL_INDEX_DIM in the corresponding input tensor. Batch dimensions are not affected by these attributes.
+Temporary axes inserted in **step 2** are removed from the final output shape after multiplying.
+After vector-matrix multiplication, the temporary axis inserted at ROW_INDEX_DIM is removed. After matrix-vector multiplication, the temporary axis inserted at COL_INDEX_DIM is removed.
+Output shape of two 1D tensors multiplication `[S] x [S]` is squeezed to scalar.
+
+Output shape inference logic examples (ND here means bigger than 1D):
+
+* 1D x 1D: `[X] x [X] -> [1, X] x [X, 1] -> [1, 1] => []` (scalar)
+* 1D x ND: `[X] x [B, ..., X, Y] -> [1, X] x [B, ..., X, Y] -> [B, ..., 1, Y] => [B, ..., Y]`
+* ND x 1D: `[B, ..., X, Y] x [Y] -> [B, ..., X, Y] x [Y, 1] -> [B, ..., X, 1] => [B, ..., X]`
+* ND x ND: `[B, ..., X, Y] x [B, ..., Y, Z] => [B, ..., X, Z]`
+
+
+Two attributes, `transpose_a` and `transpose_b` specify embedded transposition for two right-most dimensions for the first and the second input tensors correspondingly. It implies swapping of ROW_INDEX_DIM and COL_INDEX_DIM in the corresponding input tensor. Batch dimensions and 1D tensors are not affected by these attributes.
 
 **Attributes**
 
 * *transpose_a*
 
-  * **Description**: transposes dimensions ROW_INDEX_DIM and COL_INDEX_DIM of the 1st input; 0 means no transpose, 1 means transpose
+  * **Description**: transposes dimensions ROW_INDEX_DIM and COL_INDEX_DIM of the 1st input; **False** means no transpose, **True** means transpose. It is ignored if first input is 1D tensor.
   * **Range of values**: False or True
   * **Type**: boolean
   * **Default value**: False
   * **Required**: *no*
 
 * *transpose_b*
 
-  * **Description**: transposes dimensions ROW_INDEX_DIM and COL_INDEX_DIM of the 2nd input; 0 means no transpose, 1 means transpose
+  * **Description**: transposes dimensions ROW_INDEX_DIM and COL_INDEX_DIM of the 2nd input; **False** means no transpose, **True** means transpose. It is ignored if second input is 1D tensor.
   * **Range of values**: False or True
   * **Type**: boolean
   * **Default value**: False
@@ -47,10 +61,14 @@ Two attributes, transpose_a and transpose_b specifies embedded transposition for
 
 *   **2**: Input batch of matrices B. Rank >= 1. Required.
 
+**Outputs**
+
+*   **1**: Tensor with results of the multiplication.
+
 
 **Example**
 
-*Vector-matric multiplication*
+*Vector-matrix multiplication*
 
 ```xml
 <layer ... type="MatMul">
@@ -65,7 +83,27 @@ Two attributes, transpose_a and transpose_b specifies embedded transposition for
     </input>
     <output>
         <port id="2">
-            <dim>1</dim>
+            <dim>1000</dim>
+        </port>
+    </output>
+</layer>
+```
+
+*Matrix-vector multiplication*
+
+```xml
+<layer ... type="MatMul">
+    <input>
+        <port id="0">
+            <dim>1000</dim>
+            <dim>1024</dim>
+        </port>
+        <port id="1">
+            <dim>1024</dim>
+        </port>
+    </input>
+    <output>
+        <port id="2">
             <dim>1000</dim>
         </port>
     </output>
@@ -95,14 +133,13 @@ Two attributes, transpose_a and transpose_b specifies embedded transposition for
 </layer>
 ```
 
-*Matrix-vector multiplication with embedded transposition of the second matrix*
+*Vector-matrix multiplication with embedded transposition of the second matrix*
 
 ```xml
 <layer ... type="MatMul">
     <data transpose_b="true"/>
     <input>
         <port id="0">
-            <dim>1</dim>
             <dim>1024</dim>
         </port>
         <port id="1">
@@ -112,7 +149,6 @@ Two attributes, transpose_a and transpose_b specifies embedded transposition for
     </input>
     <output>
         <port id="2">
-            <dim>1</dim>
             <dim>1000</dim>
         </port>
     </output>