| Goal | Implementing the Covariance application for Xilinx FPGA |
| Approach | OpenCL for SDAccel |
| Benefits | Learning how to describe an application in Xilinx OpenCL |
| Credit | This work has been done under the ENPOWER project (funded by EPSRC) at University of Bristol. |
Covariance
The description of the covariance is taken from [1][2].
Covariance is one of the operator in statistics and data mining. It takes an input data as a 2D matrix and calculate the covariance of each two column. Therefore, the output is a symmetric matrix.
data: is an 
cove : is an 
where
This description can be divided into three kernels [2]: k_mean, k_reduce and k_covar as shown in the following figure.
There are three memory objects shares the data between kernels and host program: d_data, d_mean and d_covar
The k_mean kernel calculates the mean value of each column in the d_data 2D matrix. The k_mean kernel subtract the corresponding mean from each element in the d_data. Finally, d_covar calculate the covariance.
The three kernels are running sequentially one after another as shown in the figure.
The corresponding unoptimised code can be found at here.
References
[1] Tomofumi Yuki, Louis-Noel Pouchet, “PolyBench 4.2.1 (pre-release),” May 20, 2016, [online] http://web.cse.ohio-state.edu/~pouchet/software/polybench/
[2] S. Grauer-Gray, L. Xu, R. Searles, S. Ayalasomayajula and J. Cavazos, “Auto-tuning a high-level language targeted to GPU codes,” Innovative Parallel Computing (InPar), 2012, San Jose, CA, 2012, pp. 1-10. [online] https://cavazos-lab.github.io/PolyBench-ACC/