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Power operation specification refactoring. (#4566)

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* Power operation specification refactoring.

* Add dummy broadcast_rules.md.

* Minor fixes, e.g. capitalize operation names, typos.

* Fix mathematical formula.

Co-authored-by: Szymon Durawa <szymon.durawa@intel.com>
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Jozef Daniecki 2021-03-10 07:57:06 +01:00 committed by GitHub
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33
docs/ops/arithmetic/Power_1.md
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@ -4,7 +4,14 @@
**Category**: Arithmetic binary operation
**Short description**: *Power* performs element-wise power operation with two given tensors applying multi-directional broadcast rules.
**Short description**: *Power* performs element-wise power operation with two given tensors applying broadcasting rule specified in the *auto_broadcast* attribute.
**Detailed description**
As a first step input tensors *a* and *b* are broadcasted if their shapes differ. Broadcasting is performed according to `auto_broadcast` attribute specification. As a second step *Power* operation is computed element-wise on the input tensors *a* and *b* according to the formula below:
\f[
o_{i} = {a_{i} ^ b_{i}}
\f]
**Attributes**:
@ -12,40 +19,33 @@
* **Description**: specifies rules used for auto-broadcasting of input tensors.
* **Range of values**:
* *none* - no auto-broadcasting is allowed, all input shapes should match
* *numpy* - numpy broadcasting rules, aligned with ONNX Broadcasting. Description is available in <a href="https://github.com/onnx/onnx/blob/master/docs/Broadcasting.md">ONNX docs</a>.
* *none* - no auto-broadcasting is allowed, all input shapes must match
* *numpy* - numpy broadcasting rules, description is available in [Broadcast Rules For Elementwise Operations](../broadcast_rules.md)
* **Type**: string
* **Default value**: "numpy"
* **Required**: *no*
**Inputs**
* **1**: A tensor of type T. Required.
* **2**: A tensor of type T. Required.
* **1**: A tensor of type T and arbitrary shape. Required.
* **2**: A tensor of type T and arbitrary shape. Required.
**Outputs**
* **1**: The result of element-wise power operation. A tensor of type T.
* **1**: The result of element-wise power operation. A tensor of type T with shape equal to broadcasted shape of two inputs.
**Types**
* *T*: any numeric type.
**Detailed description**
Before performing arithmetic operation, input tensors *a* and *b* are broadcasted if their shapes are different and `auto_broadcast` attributes is not `none`. Broadcasting is performed according to `auto_broadcast` value.
After broadcasting *Power* does the following with the input tensors *a* and *b*:
\f[
o_{i} = {a_{i} ^ b}_{i}
\f]
**Examples**
*Example 1*
*Example 1 - no broadcasting*
```xml
<layer ... type="Power">
<data auto_broadcast="none"/>
<input>
<port id="0">
<dim>256</dim>
@ -65,9 +65,10 @@ o_{i} = {a_{i} ^ b}_{i}
</layer>
```
*Example 2: broadcast*
*Example 2: numpy broadcasting*
```xml
<layer ... type="Power">
<data auto_broadcast="numpy"/>
<input>
<port id="0">
<dim>8</dim>