Singular Value Decomposition for symmetric matrix (GESVDJ)

The hardware resources and performance for double and float datatype gesvdj are listed in Table 2 and Table 3.

Table 2 double Type GESVDJ performance table

Matrix Size	Unroll	URAM	BRAM	DSP	Register	LUT	Kernel time (ms)	Frequency(MHz)
8x8	4	20	6	216	46245	39365	0.0711	250
512x512	8	128	333	408	120837	115121	2100.833	208.3

Table 3 float Type GESVDJ performance table

Matrix Size	Unroll	URAM	BRAM	DSP	Register	LUT	Kernel time (ms)	Frequency(MHz)
8x8	4	20	4	114	23647	18529	0.0533	250
512x512	8	128	307	210	65569	65003	1687.274	208.3

Note

Board: Xilinx Alveo U250 Data Center Accelerator Card

The accuracy of GESVDJ implementation has been verified with Lapack dgesvd (QR based SVD) and dgesvj (Jacobi SVD) functions.

Caution

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