Table 2 Achieved IO advantages in the experiments*

From: I/O-efficient iterative matrix inversion with photonic integrated circuits

 

Parameters

\({{{{{{\rm{T}}}}}}}_{{{{{{\rm{save}}}}}}}\) (µs)

\({{{{{{\rm{E}}}}}}}_{{{{{{\rm{save}}}}}}}\) (nJ)

\(\frac{{{{{{{\rm{t}}}}}}}_{{{{{{\rm{total}}}}}}{\_}{{{{{\rm{PSP}}}}}}}}{{{{{{{\rm{t}}}}}}}_{{{{{{\rm{total}}}}}} {\_}{{{{{\rm{PIP}}}}}}}}\)

\(\frac{{{{{{{\rm{C}}}}}} \_{{{{{\rm{to}}}}}} \_ {{{{{\rm{IO}}}}}}}_{{{{{\rm{PIP}}}}}}} {{{{{{\rm{C}}}}}} \_ {{{{{\rm{to}}}}}} \_ {{{{{\rm{IO}}}}}}_{{{{{\rm{PSP}}}}}}}\)

\({{{{{{\bf{A}}}}}}}_{1}^{-1}\)

\(q=0\), \(N=4\), \({{{{{{\rm{t}}}}}}}_{{{{{{\rm{loop}}}}}}}=130\) ns, \(P=5\)

58.3

1.4

4.3

4.9

\({{{{{{\bf{A}}}}}}}_{2}^{-1}\)

\(q=0\), \(N=4\), \({{{{{{\rm{t}}}}}}}_{{{{{{\rm{loop}}}}}}}=130\) ns, \(P=8\)

98.3

2.4

6.1

7.6

IE

\(q=1\), \(N=4\), \({{{{{{\rm{t}}}}}}}_{{{{{{\rm{loop}}}}}}}=130\) ns, \({P}_{1}=6\), \({P}_{2}=6\)

156.7

3.8

1.7

1.75

ODE

\(q=1\), \(N=4\), \({{{{{{\rm{t}}}}}}}_{{{{{{\rm{loop}}}}}}}=130\) ns, \({P}_{1}=5\), \({P}_{2}=8\)

170.0

4.1

1.8

1.82

PDE

\(q=2\), \(N=4\), \({{{{{{\rm{t}}}}}}}_{{{{{{\rm{loop}}}}}}}=130\) ns, \({P}_{1}={P}_{3}=9\), \({P}_{2}={P}_{4}=8\)

460.0

11.0

1.2

1.2

\({{{{{{\bf{A}}}}}}}_{3}^{-1}\)

\(q=0\), \(N=2\), \({{{{{{\rm{t}}}}}}}_{{{{{{\rm{loop}}}}}}}=300\) ps, \(P=3\)

9.0

0.22

2.8

2.8

\({{{{{{\bf{A}}}}}}}_{4}^{-1}\)

\(q=0\), \(N=2\), \({{{{{{\rm{t}}}}}}}_{{{{{{\rm{loop}}}}}}}=300\) ps, \(P=2\)

5.0

0.12

2.0

2.0

\({{{{{{\bf{A}}}}}}}_{5}^{-1}\)

\(q=0\), \(N=2\), \({{{{{{\rm{t}}}}}}}_{{{{{{\rm{loop}}}}}}}=300\) ps, \(P=2\)

5.0

0.12

2.0

2.0

  1. *A resolution of 10 bit is used for experiments involving real-valued matrix inversions and a resolution of 12 bit is used for experiments involving complex-valued matrix inversions, which is mainly limited by the resolution of the oscilloscope used. A data transmission rate of 24 Mb/s is employed for the Serial Peripheral Interface (SPI communication protocol. \(q\) is the number of times a matrix is decomposed before being inverted on an \(N\times N\) PIP. \(N\) is the matrix size. \(P\) is the number of iterations for the Richardson method to converge.