# Pooling Operator

This folder contains example for the pooling operator using ck_tile tile-programming implementation. Currently the pooling kernel only supports 2D and 3D pooling.

## Tensor Descriptor Transformations

The pooling kernel transforms the input tensor into 2D format suitable for reduction. This section explains the transformation pipeline for both 2D and 3D pooling operations.

### 3D Pooling Transformations

For 3D pooling, the input tensor has shape `(N, D, H, W, C)` where:
- `N`: batch size
- `D`: depth dimension  
- `H`: height dimension
- `W`: width dimension
- `C`: channel dimension

The transformations convert this 5D tensor into a 2D tensor where rows represent output positions (M) and columns represent pooling window elements (K).

```mermaid
graph TD
    %% Input Tensor: (N, D, H, W, C)
    Input["Input Tensor<br/>(N, D, H, W, C)"]
    style Input fill:#e1f5fe

    %% Pass-through N dimension
    PassN["Pass-through N<br/>(batch size)"]
    style PassN fill:#f3e5f5
    Input --> PassN

    %% Pad spatial dimensions
    PadD["Pad D<br/>(depth with left/right padding)"]
    style PadD fill:#fff9c4
    Input --> PadD

    PadH["Pad H<br/>(height with left/right padding)"]
    style PadH fill:#fff9c4
    Input --> PadH

    PadW["Pad W<br/>(width with left/right padding)"]
    style PadW fill:#fff9c4
    Input --> PadW

    %% Pass-through C dimension
    PassC["Pass-through C<br/>(channels)"]
    style PassC fill:#f3e5f5
    Input --> PassC

    %% Embed sliding windows
    EmbedD["Embed D<br/>window(Z) × output_positions(Dₒ)"]
    style EmbedD fill:#fff3e0
    PadD --> EmbedD

    EmbedH["Embed H<br/>window(Y) × output_positions(Hₒ)"]
    style EmbedH fill:#fff3e0
    PadH --> EmbedH

    EmbedW["Embed W<br/>window(X) × output_positions(Wₒ)"]
    style EmbedW fill:#fff3e0
    PadW --> EmbedW

    %% Merge into 2D matrix
    MergeM["Merge M<br/>(N, Dₒ, Hₒ, Wₒ, C)<br/>→ output positions"]
    style MergeM fill:#e8f5e9
    PassN --> MergeM
    EmbedD --> MergeM
    EmbedH --> MergeM
    EmbedW --> MergeM
    PassC --> MergeM

    MergeK["Merge K<br/>(Z, Y, X)<br/>→ window elements"]
    style MergeK fill:#e8f5e9
    EmbedD --> MergeK
    EmbedH --> MergeK
    EmbedW --> MergeK

    %% Final padding for block alignment
    PadM["Right-pad M<br/>(for block alignment)"]
    style PadM fill:#fff9c4
    MergeM --> PadM

    PadK["Right-pad K<br/>(for block alignment)"]
    style PadK fill:#fff9c4
    MergeK --> PadK

    %% Result
    Result["2D Matrix<br/>(M × K)"]
    style Result fill:#c8e6c9
    PadM --> Result
    PadK --> Result
```

**Transformation Steps:**
1. **Padding**: Apply left and right padding to spatial dimensions (D, H, W) to handle boundary conditions
2. **Sliding Windows**: Use embed transforms to create sliding windows across each spatial dimension, expanding each dimension into (window_size, output_positions)
3. **Reshaping**: Merge all dimensions into a 2D matrix where:
   - M dimension = N × Dₒ × Hₒ × Wₒ × C (total output positions)
   - K dimension = Z × Y × X (elements per pooling window)
4. **Block Alignment**: Apply right padding to ensure M and K dimensions are aligned to block size

### 2D Pooling Transformations

2D pooling follows the same transformation pipeline but operates on 4D tensors with shape `(N, H, W, C)`. The process is identical except:
- Only H and W dimensions are padded and embedded
- K dimension merges only (Y, X) window elements
- M dimension merges (N, Hₒ, Wₒ, C)

### Output Tensor Transformations

The output tensor transformations are simpler:
- Merge all output dimensions (N, Dₒ/Hₒ, Wₒ, C) into a single M dimension
- Apply right padding for block alignment
- The result is a 1D tensor that maps directly to the M dimension of the computation matrix

## build
```
# in the root of ck_tile
mkdir build && cd build
# you can replace <arch> with the appropriate architecture (for example gfx90a or gfx942) or leave it blank
../script/cmake-ck-dev.sh  ../ <arch>
# The 3D pooling example
make tile_example_pool3d -j`nproc`
```
This will result in an executable `build/bin/tile_example_pool3d`

## example
```
args:
          -N    batch size (default:2)
          -D    depth dimension (default:30)
          -H    height dimension (default:30)
          -W    width dimension (default:30)
          -C    channel dimension (default:32)
          -Z    pooling window depth (default:2)
          -Y    pooling window height (default:2)
          -X    pooling window width (default:2)
         -Sz    window stride depth (default:2)
         -Sy    window stride height (default:2)
         -Sx    window stride width (default:2)
         -Dz    window dilation depth (default:1)
         -Dy    window dilation height (default:1)
         -Dx    window dilation width (default:1)
     -LeftPz    left padding depth (default:1)
     -LeftPy    left padding height (default:1)
     -LeftPx    left padding width (default:1)
    -RightPz    right padding depth (default:1)
    -RightPy    right padding height (default:1)
    -RightPx    right padding width (default:1)
          -v    0: No validation, 1: CPU validation (default:1)
     -warmup    number of iterations before benchmark (default:0)
     -repeat    number of iterations to benchmark (default:1)
```