Flexible Linear Algebra with Matrix-Empowered Synthesis (for Vitis HLS)

Developed by Wuqiong Zhao and other contributors, from LEADS, Southeast University. This is part of the AutoHDW project.

Key Features

Header-only Library (Super Easy to Install and Use)
Templated-based C++ Design:
- Mat and Tensor Classes
- MatRef and MatView for Reference and View
- (Relatively) Modern C++ Implementation (C++14/17)
Hardware-friendly Design:
- Optimized RAM Usage
- Configurable Parallelism
- Optimized Matrix Operations
Fully Open Source

Read our paper for details (open access PDF).

Example

Linear algebra algorithm implementation made easy by FLAMES! Here is the NSA algorithm and the corresponding implementation using FLAMES:

Step	Algorithm	FLAMES C++ Implementation
1	\(\mathbf{D} = \mathbf{A} \circ \mathbf{I}\)	`auto D = A.diagMat_();`
2	\(\mathbf{E} = \mathbf{A} - \mathbf{D}\)	`auto E = A.offDiag_();`
3	\(\mathbf{D}_I = \mathbf{D}^{-1}\)	`auto D_I = D.inv();`
4	\(\mathbf{P} = -\mathbf{D}_I \mathbf{E}\)	`auto P = -D_I * E;`
5	\(\mathbf{X} = \mathbf{P}\) (Iter. 1)	`auto X = P_ = P;`
6	\(\text{for } i = 2, \dots, n\)	`for (int i = 2; i <= n; ++i) {`
7	\(\quad \mathbf{P}^i = \mathbf{P}^{i-1} \mathbf{P}\)	`P_ *= P;`
8	\(\quad \mathbf{X} = \mathbf{X} + \mathbf{P}^i\)	`X += P_;`
9	\(\text{end}\)	`}`
10	\(\mathbf{A}^{-1} = \mathbf{X} \mathbf{D}_I + \mathbf{D}_I\)	`A_inv = X * D_I + D_I;`

From Table 2 in our paper, code available at examples/mat-inv-nsa.

Citation

If you find FLAMES useful, please cite our paper: Flexible High-Level Synthesis Library for Linear Transformations, IEEE TCAS-II, vol. 71, no. 7, pp. 3348-3352, Jul. 2024. [IEEE Xplore] [PDF] [DOI]

@article{zhao2024flexible,
  title     = {Flexible High-Level Synthesis Library for Linear Transformations},
  author    = {Zhao, Wuqiong and Li, Changhan and Ji, Zhenhao and Guo, Zhichen and Chen, Xuanbo and You, You and Huang, Yongming and You, Xiaohu and Zhang, Chuan},
  journal   = {{IEEE} Transactions on Circuits and Systems {II}: Express Briefs},
  volume    = {71},
  number    = {7},
  pages     = {3348--3352},
  year      = {2024},
  month     = jul,
  publisher = {IEEE}
}

Supported Versions

Since FLAMES is a modern library written using C++14 (with some C++17 features), it only supports Vitis HLS 2020 or later where the GCC compiler version is 6.2.0. Notably, Vivado HLS is not supported.