Singular Value Decomposition for general matrix (GESVJ)¶

GESVJ example resides in L2/benchmarks/gesvj directory. The tutorial provides a step-by-step guide that covers commands for building and running kernel.

Executable Usage¶

Work Directory(Step 1)

The steps for library download and environment setup can be found in Vitis Solver Library. For getting the design,

cd L2/benchmarks/gesvj

Build kernel(Step 2)

Run the following make command to build your XCLBIN and host binary targeting a specific device. Please be noticed that this process will take a long time, maybe couple of hours.

source /opt/xilinx/Vitis/2021.1/settings64.sh
source /opt/xilinx/xrt/setenv.sh
export DEVICE=/opt/xilinx/platforms/xilinx_u250_xdma_201830_2/xilinx_u250_xdma_201830_2.xpfm
export TARGET=hw
make run

Run kernel(Step 3)

To get the benchmark results, please run the following command.

./build_dir.hw.xilinx_u250_xdma_201830_2/test_gesvj.exe -xclbin build_dir.hw.xilinx_u250_xdma_201830_2/kernel_gesvj.xclbin -runs 1 -M 512 -N 512 -seed 12

GESVDJ Input Arguments:

Usage: test_gesvj.exe -[-xclbin -o -c -g]
       -xclbin     gesvj binary;
       -runs       number of runs;
       -M          size of input Matrix row;
       -N          size of input Matrix column;
       -seed       seed for generating a random number;

Note: Default arguments are set in Makefile. The default configs are: -runs 1 -M 4 -N 3 -seed 12.

Example output(Step 4)

---------------------GESVJ Test----------------
Found Platform
Platform Name: Xilinx
INFO: Found Device=xilinx_u250_xdma_201830_2
INFO: Importing build_dir.hw.xilinx_u250_xdma_201830_2/wcc_kernel.xclbin
Loading: 'build_dir.hw.xilinx_u250_xdma_201830_2/wcc_kernel.xclbin'
INFO: kernel has been created
INFO: kernel start------
INFO: kernel end------
INFO: Execution time 53.697ms
INFO: Write DDR Execution time 0.11773ms
INFO: Kernel Execution time 53.198ms
INFO: Read DDR Execution time 0.049562ms
INFO: Total Execution time 53.3653ms
============================================================

Profiling¶

The GESVJ is validated on Xilinx Alveo U250 board. The accuracy of GESVDJ implementation has been verified with Lapack dgesvd (QR based SVD) and dgesvj (Jacobi SVD) functions. The hardware resources and performance for double datatype gesvj is listed in Table 4. To describe the resource utilization, we separate the overall utilization into two parts, P stands for the resource usage in platform, that is those instantiated in static region of the FPGA card, K stands for those used in kernels(dynamic region). The Unroll factor means how many CUs are configured to calculate Matrix in parell.

Table 4 double Type GESVJ performance table¶
Matrix Size	Unroll	Frequency(MHz)	Latency(MHz)	LUT	REG	BRAM	URAM	DSP
512x512	16	248.4		146836(P)	225255(P)	283(P)	0(P)	7(P)
512x512	16	248.4		137271(K)	180145(K)	123(K)	192(K)	1801(K)

Note

The unroll factor is limited by 2 factors, the matrix size and URAM port. The maximum unroll factor should be less than half of matrix size, and \(2 \times {Unroll}^{2}\) should also be less than available URAM on board. Besides, unroll factor can only be the factorization of 2.

Matrix Size	Unroll	URAM	BRAM	DSP	Register	LUT	Kernel time (ms)	Frequency (MHz)
64x64	2	55	27	282	81753	73895	27.8	300
512x512	4	192	41	500	98763	92207	4827	230
512x512	16	192	125	1808	203666	165800	4686.5	249