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DOCS shift to rst - Opsets C (#17112)

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docs/ops/convolution/Convolution_1.md
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# Convolution {#openvino_docs_ops_convolution_Convolution_1}
@sphinxdirective
**Versioned name**: *Convolution-1*
**Category**: *Convolution*
**Short description**: Computes 1D, 2D or 3D convolution (cross-correlation to be precise) of input and kernel tensors.
**Detailed description**: Basic building block of convolution is a dot product of input patch and kernel. Whole operation consist of multiple such computations over multiple input patches and kernels. More thorough explanation can be found in [Convolutional Neural Networks](http://cs231n.github.io/convolutional-networks/#conv) and [Convolution operation](https://medium.com/apache-mxnet/convolutions-explained-with-ms-excel-465d6649831c).
**Detailed description**: Basic building block of convolution is a dot product of input patch and kernel. Whole operation consist of multiple such computations over multiple input patches and kernels. More thorough explanation can be found in `Convolutional Neural Networks <http://cs231n.github.io/convolutional-networks/#conv>`__ and `Convolution operation <https://medium.com/apache-mxnet/convolutions-explained-with-ms-excel-465d6649831c>`__ .
For the convolutional layer, the number of output features in each dimension is calculated using the formula:
\f[
n_{out} = \left ( \frac{n_{in} + 2p - k}{s} \right ) + 1
\f]
.. math::
n_{out} = \left ( \frac{n_{in} + 2p - k}{s} \right ) + 1
The receptive field in each layer is calculated using the formulas:
* Jump in the output feature map:
\f[
j_{out} = j_{in} \cdot s
\f]
* Size of the receptive field of output feature:
\f[
r_{out} = r_{in} + ( k - 1 ) \cdot j_{in}
\f]
* Center position of the receptive field of the first output feature:
\f[
start_{out} = start_{in} + ( \frac{k - 1}{2} - p ) \cdot j_{in}
\f]
* Output is calculated using the following formula:
\f[
out = \sum_{i = 0}^{n}w_{i}x_{i} + b
\f]
* Jump in the output feature map:
.. math::
j_{out} = j_{in} \cdot s
* Size of the receptive field of output feature:
.. math::
r_{out} = r_{in} + ( k - 1 ) \cdot j_{in}
* Center position of the receptive field of the first output feature:
.. math::
start_{out} = start_{in} + ( \frac{k - 1}{2} - p ) \cdot j_{in}
* Output is calculated using the following formula:
.. math::
out = \sum_{i = 0}^{n}w_{i}x_{i} + b
**Attributes**:
* *strides*
* **Description**: *strides* is a distance (in pixels) to slide the filter on the feature map over the `(z, y, x)` axes for 3D convolutions and `(y, x)` axes for 2D convolutions. For example, *strides* equal `4,2,1` means sliding the filter 4 pixel at a time over depth dimension, 2 over height dimension and 1 over width dimension.
* **Description**: *strides* is a distance (in pixels) to slide the filter on the feature map over the ``(z, y, x)`` axes for 3D convolutions and ``(y, x)`` axes for 2D convolutions. For example, *strides* equal ``4,2,1`` means sliding the filter 4 pixel at a time over depth dimension, 2 over height dimension and 1 over width dimension.
* **Range of values**: integer values starting from 0
* **Type**: `int[]`
* **Type**: ``int[]``
* **Required**: *yes*
* *pads_begin*
* **Description**: *pads_begin* is a number of pixels to add to the beginning along each axis. For example, *pads_begin* equal `1,2` means adding 1 pixel to the top of the input and 2 to the left of the input.
* **Description**: *pads_begin* is a number of pixels to add to the beginning along each axis. For example, *pads_begin* equal ``1,2`` means adding 1 pixel to the top of the input and 2 to the left of the input.
* **Range of values**: integer values starting from 0
* **Type**: `int[]`
* **Type**: ``int[]``
* **Required**: *yes*
* **Note**: the attribute is ignored when *auto_pad* attribute is specified.
* *pads_end*
* **Description**: *pads_end* is a number of pixels to add to the ending along each axis. For example, *pads_end* equal `1,2` means adding 1 pixel to the bottom of the input and 2 to the right of the input.
* **Description**: *pads_end* is a number of pixels to add to the ending along each axis. For example, *pads_end* equal ``1,2`` means adding 1 pixel to the bottom of the input and 2 to the right of the input.
* **Range of values**: integer values starting from 0
* **Type**: `int[]`
* **Type**: ``int[]``
* **Required**: *yes*
* **Note**: the attribute is ignored when *auto_pad* attribute is specified.
* *dilations*
* **Description**: *dilations* denotes the distance in width and height between elements (weights) in the filter. For example, *dilation* equal `1,1` means that all the elements in the filter are neighbors, so it is the same as for the usual convolution. *dilation* equal `2,2` means that all the elements in the filter are matched not to adjacent elements in the input matrix, but to those that are adjacent with distance 1.
* **Description**: *dilations* denotes the distance in width and height between elements (weights) in the filter. For example, *dilation* equal ``1,1`` means that all the elements in the filter are neighbors, so it is the same as for the usual convolution. *dilation* equal ``2,2`` means that all the elements in the filter are matched not to adjacent elements in the input matrix, but to those that are adjacent with distance 1.
* **Range of values**: integer value starting from 0
* **Type**: `int[]`
* **Type**: ``int[]``
* **Required**: *yes*
* *auto_pad*
* **Description**: *auto_pad* how the padding is calculated. Possible values:
* *explicit* - use explicit padding values from *pads_begin* and *pads_end*.
* *same_upper* - the input is padded to match the output size. In case of odd padding value an extra padding is added at the end.
* *same_lower* - the input is padded to match the output size. In case of odd padding value an extra padding is added at the beginning.
* *valid* - do not use padding.
* **Type**: `string`
* **Type**: ``string``
* **Default value**: explicit
* **Required**: *no*
* **Note**: *pads_begin* and *pads_end* attributes are ignored when *auto_pad* is specified.
**Inputs**:
* **1**: Input tensor of type *T* and rank 3, 4 or 5. Layout is `[N, C_IN, Z, Y, X]` (number of batches, number of channels, spatial axes Z, Y, X). **Required.**
* **2**: Kernel tensor of type *T* and rank 3, 4 or 5. Layout is `[C_OUT, C_IN, Z, Y, X]` (number of output channels, number of input channels, spatial axes Z, Y, X). **Required.**
* **Note**: Type of the convolution (1D, 2D or 3D) is derived from the rank of the input tensors and not specified by any attribute:
* 1D convolution (input tensors rank 3) means that there is only one spatial axis X
* 2D convolution (input tensors rank 4) means that there are two spatial axes Y, X
* 3D convolution (input tensors rank 5) means that there are three spatial axes Z, Y, X
* **1**: Input tensor of type *T* and rank 3, 4 or 5. Layout is ``[N, C_IN, Z, Y, X]`` (number of batches, number of channels, spatial axes Z, Y, X). **Required.**
* **2**: Kernel tensor of type *T* and rank 3, 4 or 5. Layout is ``[C_OUT, C_IN, Z, Y, X]`` (number of output channels, number of input channels, spatial axes Z, Y, X). **Required.**
* **Note**: Type of the convolution (1D, 2D or 3D) is derived from the rank of the input tensors and not specified by any attribute:
* 1D convolution (input tensors rank 3) means that there is only one spatial axis X
* 2D convolution (input tensors rank 4) means that there are two spatial axes Y, X
* 3D convolution (input tensors rank 5) means that there are three spatial axes Z, Y, X
**Outputs**:
* **1**: Output tensor of type *T* and rank 3, 4 or 5. Layout is `[N, C_OUT, Z, Y, X]` (number of batches, number of kernel output channels, spatial axes Z, Y, X).
* **1**: Output tensor of type *T* and rank 3, 4 or 5. Layout is ``[N, C_OUT, Z, Y, X]`` (number of batches, number of kernel output channels, spatial axes Z, Y, X).
**Types**:
@@ -95,87 +108,96 @@ The receptive field in each layer is calculated using the formulas:
**Example**:
1D Convolution
```xml
<layer type="Convolution" ...>
<data dilations="1" pads_begin="0" pads_end="0" strides="2" auto_pad="valid"/>
<input>
<port id="0">
<dim>1</dim>
<dim>5</dim>
<dim>128</dim>
</port>
<port id="1">
<dim>16</dim>
<dim>5</dim>
<dim>4</dim>
</port>
</input>
<output>
<port id="2" precision="FP32">
<dim>1</dim>
<dim>16</dim>
<dim>63</dim>
</port>
</output>
</layer>
```
.. code-block:: cpp
<layer type="Convolution" ...>
<data dilations="1" pads_begin="0" pads_end="0" strides="2" auto_pad="valid"/>
<input>
<port id="0">
<dim>1</dim>
<dim>5</dim>
<dim>128</dim>
</port>
<port id="1">
<dim>16</dim>
<dim>5</dim>
<dim>4</dim>
</port>
</input>
<output>
<port id="2" precision="FP32">
<dim>1</dim>
<dim>16</dim>
<dim>63</dim>
</port>
</output>
</layer>
2D Convolution
```xml
<layer type="Convolution" ...>
<data dilations="1,1" pads_begin="2,2" pads_end="2,2" strides="1,1" auto_pad="explicit"/>
<input>
<port id="0">
<dim>1</dim>
<dim>3</dim>
<dim>224</dim>
<dim>224</dim>
</port>
<port id="1">
<dim>64</dim>
<dim>3</dim>
<dim>5</dim>
<dim>5</dim>
</port>
</input>
<output>
<port id="2" precision="FP32">
<dim>1</dim>
<dim>64</dim>
<dim>224</dim>
<dim>224</dim>
</port>
</output>
</layer>
```
.. code-block:: cpp
<layer type="Convolution" ...>
<data dilations="1,1" pads_begin="2,2" pads_end="2,2" strides="1,1" auto_pad="explicit"/>
<input>
<port id="0">
<dim>1</dim>
<dim>3</dim>
<dim>224</dim>
<dim>224</dim>
</port>
<port id="1">
<dim>64</dim>
<dim>3</dim>
<dim>5</dim>
<dim>5</dim>
</port>
</input>
<output>
<port id="2" precision="FP32">
<dim>1</dim>
<dim>64</dim>
<dim>224</dim>
<dim>224</dim>
</port>
</output>
</layer>
3D Convolution
```xml
<layer type="Convolution" ...>
<data dilations="2,2,2" pads_begin="0,0,0" pads_end="0,0,0" strides="3,3,3" auto_pad="explicit"/>
<input>
<port id="0">
<dim>1</dim>
<dim>7</dim>
<dim>320</dim>
<dim>320</dim>
<dim>320</dim>
</port>
<port id="1">
<dim>32</dim>
<dim>7</dim>
<dim>3</dim>
<dim>3</dim>
<dim>3</dim>
</port>
</input>
<output>
<port id="2" precision="FP32">
<dim>1</dim>
<dim>32</dim>
<dim>106</dim>
<dim>106</dim>
<dim>106</dim>
</port>
</output>
</layer>
```
.. code-block:: cpp
<layer type="Convolution" ...>
<data dilations="2,2,2" pads_begin="0,0,0" pads_end="0,0,0" strides="3,3,3" auto_pad="explicit"/>
<input>
<port id="0">
<dim>1</dim>
<dim>7</dim>
<dim>320</dim>
<dim>320</dim>
<dim>320</dim>
</port>
<port id="1">
<dim>32</dim>
<dim>7</dim>
<dim>3</dim>
<dim>3</dim>
<dim>3</dim>
</port>
</input>
<output>
<port id="2" precision="FP32">
<dim>1</dim>
<dim>32</dim>
<dim>106</dim>
<dim>106</dim>
<dim>106</dim>
</port>
</output>
</layer>
@endsphinxdirective