composable_kernel/client_example/04_contraction

Client Example: General Tensor Contraction

Theory

This client example demonstrates general tensor contraction operations, including bilinear and scaled contractions. Tensor contraction generalizes matrix multiplication to higher dimensions and is used in scientific computing, quantum chemistry, and advanced neural network layers.

Mathematical Formulation:

• General contraction: C_{i,j} = \sum_k A_{i,k} \cdot B_{k,j}
• Bilinear contraction: C = \alpha (A \cdot B) + \beta D
• Scale contraction: C = \text{scale}(A, B) (elementwise or broadcasted scaling)

Algorithmic Background:

• Contraction can be performed over arbitrary axes and supports broadcasting.
• Bilinear and scale contractions are used for feature fusion, gating, and scientific workloads.

How to Run

Prerequisites

Please follow the instructions in the main Build Guide section as a prerequisite to building and running this example.

Build and run

cd composable_kernel/client_example/04_contraction
mkdir build && cd build
cmake -DCMAKE_CXX_COMPILER=/opt/rocm/bin/hipcc ..
make -j

# Example run (bilinear FP32)
./contraction_bilinear_fp32

# Example run (scale FP64)
./contraction_scale_fp64

Source Code Structure

Directory Layout

client_example/04_contraction/
├── contraction_bilinear_fp32.cpp         # Bilinear contraction (FP32)
├── contraction_bilinear_fp64.cpp         # Bilinear contraction (FP64)
├── contraction_g1m2n3k1_add_xdl_fp16.cpp # Grouped contraction with addition (FP16)
├── contraction_scale_fp32.cpp            # Scale contraction (FP32)
├── contraction_scale_fp64.cpp            # Scale contraction (FP64)
├── CMakeLists.txt                        # Build configuration for the example

Key Functions

• main() (in each .cpp):
  Sets up input tensors, configures contraction parameters, launches the contraction kernel, and verifies the result.
• Contraction kernel invocation:
  Uses the Composable Kernel device API to launch the contraction operation.

This client example provides several variants to demonstrate different contraction types and data types for scientific and ML workloads.