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# AvgPool3d¶

Applies a 3D average pooling over an input signal composed of several input planes.

In the simplest case, the output value of the layer with input size $(N, C, D, H, W)$, output $(N, C, D_{out}, H_{out}, W_{out})$ and kernel_size $(kD, kH, kW)$ can be precisely described as:

\begin{aligned} \text{out}(N_i, C_j, d, h, w) ={} & \sum_{k=0}^{kD-1} \sum_{m=0}^{kH-1} \sum_{n=0}^{kW-1} \\ & \frac{\text{input}(N_i, C_j, \text{stride}[0] \times d + k, \text{stride}[1] \times h + m, \text{stride}[2] \times w + n)} {kD \times kH \times kW} \end{aligned}

If padding is non-zero, then the input is implicitly zero-padded on all three sides for padding number of points.

Note

When ceil_mode=True, sliding windows are allowed to go off-bounds if they start within the left padding or the input. Sliding windows that would start in the right padded region are ignored.

The parameters kernel_size, stride can either be:

• a single int – in which case the same value is used for the depth, height and width dimension

• a tuple of three ints – in which case, the first int is used for the depth dimension, the second int for the height dimension and the third int for the width dimension

Parameters
• kernel_size (Union[int, Tuple[int, int, int]]) – the size of the window

• stride (Union[int, Tuple[int, int, int]]) – the stride of the window. Default value is kernel_size

• padding (Union[int, Tuple[int, int, int]]) – implicit zero padding to be added on all three sides

• ceil_mode (bool) – when True, will use ceil instead of floor to compute the output shape

• count_include_pad (bool) – when True, will include the zero-padding in the averaging calculation

• divisor_override (Optional[int]) – if specified, it will be used as divisor, otherwise kernel_size will be used

Shape:
• Input: $(N, C, D_{in}, H_{in}, W_{in})$ or $(C, D_{in}, H_{in}, W_{in})$.

• Output: $(N, C, D_{out}, H_{out}, W_{out})$ or $(C, D_{out}, H_{out}, W_{out})$, where

$D_{out} = \left\lfloor\frac{D_{in} + 2 \times \text{padding}[0] - \text{kernel\_size}[0]}{\text{stride}[0]} + 1\right\rfloor$
$H_{out} = \left\lfloor\frac{H_{in} + 2 \times \text{padding}[1] - \text{kernel\_size}[1]}{\text{stride}[1]} + 1\right\rfloor$
$W_{out} = \left\lfloor\frac{W_{in} + 2 \times \text{padding}[2] - \text{kernel\_size}[2]}{\text{stride}[2]} + 1\right\rfloor$

Per the note above, if ceil_mode is True and $(D_{out} - 1)\times \text{stride}[0]\geq D_{in} + \text{padding}[0]$, we skip the last window as it would start in the padded region, resulting in $D_{out}$ being reduced by one.

The same applies for $W_{out}$ and $H_{out}$.

Examples:

>>> # pool of square window of size=3, stride=2
>>> m = nn.AvgPool3d(3, stride=2)
>>> # pool of non-square window
>>> m = nn.AvgPool3d((3, 2, 2), stride=(2, 1, 2))
>>> input = torch.randn(20, 16, 50, 44, 31)
>>> output = m(input)


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