Abstract

Performance and efficiency of multiple processor computers depend strongly on the network that interconnects the distinct collaborating processors. Constrained connectivity forces much of the potential computing speed to be used to compensate for the limitation in connections. The availability of a multiple parallel I/O connections allows full unrestricted connectivity and is an essential prerequisite for an interprocessor network that is able to meet the ever growing communication demands. This paper emphasizes the design, building and application of an electrooptic communication system [EOCS]. The EOCS uses dedicated free space multiple data distributors and integrated optically writable inputbuffer arrays with fully parallel access.

© 1990 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. A. Franklin, S. Dhar, “On Designing Interconnection Networks for Multi-Processors,” in Proceedings, International Conference on Parallel Processing, Chicago (1986), pp. 208–215.
  2. H. J. Siegel, Interconnection Networks for Large-Scale Parallel Processing (Lexington Books, Lexington, Massachusetts, 1985).
  3. L. Dekker, “Expendability of an MIMD Multiprocessor System to a Large Size,” in Proceedings, SCS Eastern Conference on Simulation (1985), pp. 157–162.
  4. L. Dekker, E. E. E. Frietman, W. Smit, J. C. Zuidervaart, “Optical Link in the Delft Parallel Processor, an Example of an MOMI-Connection in MIMD-Supercomputers,” in Frontiers in Computing, Elsevier Science Publishers b.v., Ed. (North-Holland, Amsterdam, 1988), pp. 141–156.
  5. L. Dekker, E. E. E. Frietman, “Optical Link and Processor Clustering in the Delft Parallel Processor,” in Proceedings, Second European Simulation Multiconference, Nice (1988).
  6. E. E. E. Frietman, A. B. Ruighaver, “An Electro-Optic Data Communication System for the Delft Parallel Processor,” Comput. Archit. News 15, No. 6, 2–7 (1987).
    [CrossRef]
  7. A. B. Ruighaver, “Design Aspects of the Delft Parallel Processor DPP84 and Its Programming System,” Comput. Archit. News 14, No. 1, 14–20 (1987).
  8. H. J. Sips, “Design Aspects of a Distributed MIMD Processor,” Ph.D. Thesis, Delft U. of Technology (1984).
  9. S. R. Forrest, “Monolithic Optoelectronic Integration: A New Component Technology for Lightwave Communication,” IEEE Trans. Electron. Devices ED-32, 2640–2655 (1985).
    [CrossRef]
  10. E. E. E. Frietman, L. Dekker, E. H. Nordholt, D. C. van Maaren, “Optical Interconnects Facilitate the Way to Massive Parallelism,” Proc. Soc. Photo-Opt. Instrum. Eng. 991, 152–161 (1988).
  11. E. E. E. Frietman, W. van Nifterick, “Opto-electronic ICs for High-Speed Parallel Processing,” Lasers Optronics 6, No. 8, 69–71 (1987).
  12. T. J. M. Jongeling, E. E. E. Frietman, K. Moddemeier, L. Dekker, “Kaleidoscopic Optical Backplane for Parallel Processing,” Proc. Soc. Photo-Opt. Instrum. Eng. 991, 22–27 (1988).
  13. P. R. S. Haugen, A. Rychnovsky, A. Husain, L. D. Hutcheson, “Optical Interconnects for High Speed Computing,” Opt. Eng. 25, 1076–1085 (1986).
    [CrossRef]
  14. S. M. Sze, Physics of Semiconductor Devices (Wiley, New York, 1981).
  15. J. B. Sondervan, E. H. Nordholt, L. P. de Jong, “Integrated PIN-Photodiode,” Internal Report, Electronic Research Laboratory, Department of Electrical Engineering, Delft U. of Technology, Delft, The Netherlands (1985).
  16. J. Wilson, J. F. B. Hawkes, Optoelectronics: An Introduction (Prentice-Hall International, London, 1983).
  17. E. E. E. Frietman, L. Dekker, “The POWERRAM,” Dutch Patent Application86.02684 (1987); European Patent Application87 202 068.0 (1988).
  18. E. E. E. Frietman, “Bitflip,” Internal Report [051547EL11 No. 46], Faculty of Electrical Engineering, Delft U. of Technology, Delft, The Netherlands (1984).
  19. J. B. F. Melein, “Realization of an Optic Sensitive Memory Element in Bipolar Process,” Internal Report, Faculty of Applied Physics, Delft U. of Technology, Delft, The Netherlands (1987).
  20. T. Kohonen, Content Addressable Memories, (Springer-Verlag, New York, 1987).
    [CrossRef]
  21. A. Ackaert, P. Demeester, D. Lootens, I. Moerman, R. Baets, “Selective and Non-Planar Growth of GaAs on Si by MOVPE,” in Second European Workshop on MOVPE, St. Andrews, Scotland (1988).
  22. C. Fernstrom, “The LUCAS Associative Array Processor and Its Programming Environment,” Ph.D. Thesis, U. Lund, Sweden (1983).

1988

E. E. E. Frietman, L. Dekker, E. H. Nordholt, D. C. van Maaren, “Optical Interconnects Facilitate the Way to Massive Parallelism,” Proc. Soc. Photo-Opt. Instrum. Eng. 991, 152–161 (1988).

T. J. M. Jongeling, E. E. E. Frietman, K. Moddemeier, L. Dekker, “Kaleidoscopic Optical Backplane for Parallel Processing,” Proc. Soc. Photo-Opt. Instrum. Eng. 991, 22–27 (1988).

1987

E. E. E. Frietman, W. van Nifterick, “Opto-electronic ICs for High-Speed Parallel Processing,” Lasers Optronics 6, No. 8, 69–71 (1987).

E. E. E. Frietman, A. B. Ruighaver, “An Electro-Optic Data Communication System for the Delft Parallel Processor,” Comput. Archit. News 15, No. 6, 2–7 (1987).
[CrossRef]

A. B. Ruighaver, “Design Aspects of the Delft Parallel Processor DPP84 and Its Programming System,” Comput. Archit. News 14, No. 1, 14–20 (1987).

1986

P. R. S. Haugen, A. Rychnovsky, A. Husain, L. D. Hutcheson, “Optical Interconnects for High Speed Computing,” Opt. Eng. 25, 1076–1085 (1986).
[CrossRef]

1985

L. Dekker, “Expendability of an MIMD Multiprocessor System to a Large Size,” in Proceedings, SCS Eastern Conference on Simulation (1985), pp. 157–162.

S. R. Forrest, “Monolithic Optoelectronic Integration: A New Component Technology for Lightwave Communication,” IEEE Trans. Electron. Devices ED-32, 2640–2655 (1985).
[CrossRef]

Ackaert, A.

A. Ackaert, P. Demeester, D. Lootens, I. Moerman, R. Baets, “Selective and Non-Planar Growth of GaAs on Si by MOVPE,” in Second European Workshop on MOVPE, St. Andrews, Scotland (1988).

Baets, R.

A. Ackaert, P. Demeester, D. Lootens, I. Moerman, R. Baets, “Selective and Non-Planar Growth of GaAs on Si by MOVPE,” in Second European Workshop on MOVPE, St. Andrews, Scotland (1988).

de Jong, L. P.

J. B. Sondervan, E. H. Nordholt, L. P. de Jong, “Integrated PIN-Photodiode,” Internal Report, Electronic Research Laboratory, Department of Electrical Engineering, Delft U. of Technology, Delft, The Netherlands (1985).

Dekker, L.

T. J. M. Jongeling, E. E. E. Frietman, K. Moddemeier, L. Dekker, “Kaleidoscopic Optical Backplane for Parallel Processing,” Proc. Soc. Photo-Opt. Instrum. Eng. 991, 22–27 (1988).

E. E. E. Frietman, L. Dekker, E. H. Nordholt, D. C. van Maaren, “Optical Interconnects Facilitate the Way to Massive Parallelism,” Proc. Soc. Photo-Opt. Instrum. Eng. 991, 152–161 (1988).

L. Dekker, “Expendability of an MIMD Multiprocessor System to a Large Size,” in Proceedings, SCS Eastern Conference on Simulation (1985), pp. 157–162.

L. Dekker, E. E. E. Frietman, W. Smit, J. C. Zuidervaart, “Optical Link in the Delft Parallel Processor, an Example of an MOMI-Connection in MIMD-Supercomputers,” in Frontiers in Computing, Elsevier Science Publishers b.v., Ed. (North-Holland, Amsterdam, 1988), pp. 141–156.

L. Dekker, E. E. E. Frietman, “Optical Link and Processor Clustering in the Delft Parallel Processor,” in Proceedings, Second European Simulation Multiconference, Nice (1988).

E. E. E. Frietman, L. Dekker, “The POWERRAM,” Dutch Patent Application86.02684 (1987); European Patent Application87 202 068.0 (1988).

Demeester, P.

A. Ackaert, P. Demeester, D. Lootens, I. Moerman, R. Baets, “Selective and Non-Planar Growth of GaAs on Si by MOVPE,” in Second European Workshop on MOVPE, St. Andrews, Scotland (1988).

Dhar, S.

M. A. Franklin, S. Dhar, “On Designing Interconnection Networks for Multi-Processors,” in Proceedings, International Conference on Parallel Processing, Chicago (1986), pp. 208–215.

Fernstrom, C.

C. Fernstrom, “The LUCAS Associative Array Processor and Its Programming Environment,” Ph.D. Thesis, U. Lund, Sweden (1983).

Forrest, S. R.

S. R. Forrest, “Monolithic Optoelectronic Integration: A New Component Technology for Lightwave Communication,” IEEE Trans. Electron. Devices ED-32, 2640–2655 (1985).
[CrossRef]

Franklin, M. A.

M. A. Franklin, S. Dhar, “On Designing Interconnection Networks for Multi-Processors,” in Proceedings, International Conference on Parallel Processing, Chicago (1986), pp. 208–215.

Frietman, E. E. E.

T. J. M. Jongeling, E. E. E. Frietman, K. Moddemeier, L. Dekker, “Kaleidoscopic Optical Backplane for Parallel Processing,” Proc. Soc. Photo-Opt. Instrum. Eng. 991, 22–27 (1988).

E. E. E. Frietman, L. Dekker, E. H. Nordholt, D. C. van Maaren, “Optical Interconnects Facilitate the Way to Massive Parallelism,” Proc. Soc. Photo-Opt. Instrum. Eng. 991, 152–161 (1988).

E. E. E. Frietman, A. B. Ruighaver, “An Electro-Optic Data Communication System for the Delft Parallel Processor,” Comput. Archit. News 15, No. 6, 2–7 (1987).
[CrossRef]

E. E. E. Frietman, W. van Nifterick, “Opto-electronic ICs for High-Speed Parallel Processing,” Lasers Optronics 6, No. 8, 69–71 (1987).

E. E. E. Frietman, L. Dekker, “The POWERRAM,” Dutch Patent Application86.02684 (1987); European Patent Application87 202 068.0 (1988).

L. Dekker, E. E. E. Frietman, “Optical Link and Processor Clustering in the Delft Parallel Processor,” in Proceedings, Second European Simulation Multiconference, Nice (1988).

L. Dekker, E. E. E. Frietman, W. Smit, J. C. Zuidervaart, “Optical Link in the Delft Parallel Processor, an Example of an MOMI-Connection in MIMD-Supercomputers,” in Frontiers in Computing, Elsevier Science Publishers b.v., Ed. (North-Holland, Amsterdam, 1988), pp. 141–156.

E. E. E. Frietman, “Bitflip,” Internal Report [051547EL11 No. 46], Faculty of Electrical Engineering, Delft U. of Technology, Delft, The Netherlands (1984).

Haugen, P. R. S.

P. R. S. Haugen, A. Rychnovsky, A. Husain, L. D. Hutcheson, “Optical Interconnects for High Speed Computing,” Opt. Eng. 25, 1076–1085 (1986).
[CrossRef]

Hawkes, J. F. B.

J. Wilson, J. F. B. Hawkes, Optoelectronics: An Introduction (Prentice-Hall International, London, 1983).

Husain, A.

P. R. S. Haugen, A. Rychnovsky, A. Husain, L. D. Hutcheson, “Optical Interconnects for High Speed Computing,” Opt. Eng. 25, 1076–1085 (1986).
[CrossRef]

Hutcheson, L. D.

P. R. S. Haugen, A. Rychnovsky, A. Husain, L. D. Hutcheson, “Optical Interconnects for High Speed Computing,” Opt. Eng. 25, 1076–1085 (1986).
[CrossRef]

Jongeling, T. J. M.

T. J. M. Jongeling, E. E. E. Frietman, K. Moddemeier, L. Dekker, “Kaleidoscopic Optical Backplane for Parallel Processing,” Proc. Soc. Photo-Opt. Instrum. Eng. 991, 22–27 (1988).

Kohonen, T.

T. Kohonen, Content Addressable Memories, (Springer-Verlag, New York, 1987).
[CrossRef]

Lootens, D.

A. Ackaert, P. Demeester, D. Lootens, I. Moerman, R. Baets, “Selective and Non-Planar Growth of GaAs on Si by MOVPE,” in Second European Workshop on MOVPE, St. Andrews, Scotland (1988).

Melein, J. B. F.

J. B. F. Melein, “Realization of an Optic Sensitive Memory Element in Bipolar Process,” Internal Report, Faculty of Applied Physics, Delft U. of Technology, Delft, The Netherlands (1987).

Moddemeier, K.

T. J. M. Jongeling, E. E. E. Frietman, K. Moddemeier, L. Dekker, “Kaleidoscopic Optical Backplane for Parallel Processing,” Proc. Soc. Photo-Opt. Instrum. Eng. 991, 22–27 (1988).

Moerman, I.

A. Ackaert, P. Demeester, D. Lootens, I. Moerman, R. Baets, “Selective and Non-Planar Growth of GaAs on Si by MOVPE,” in Second European Workshop on MOVPE, St. Andrews, Scotland (1988).

Nordholt, E. H.

E. E. E. Frietman, L. Dekker, E. H. Nordholt, D. C. van Maaren, “Optical Interconnects Facilitate the Way to Massive Parallelism,” Proc. Soc. Photo-Opt. Instrum. Eng. 991, 152–161 (1988).

J. B. Sondervan, E. H. Nordholt, L. P. de Jong, “Integrated PIN-Photodiode,” Internal Report, Electronic Research Laboratory, Department of Electrical Engineering, Delft U. of Technology, Delft, The Netherlands (1985).

Ruighaver, A. B.

E. E. E. Frietman, A. B. Ruighaver, “An Electro-Optic Data Communication System for the Delft Parallel Processor,” Comput. Archit. News 15, No. 6, 2–7 (1987).
[CrossRef]

A. B. Ruighaver, “Design Aspects of the Delft Parallel Processor DPP84 and Its Programming System,” Comput. Archit. News 14, No. 1, 14–20 (1987).

Rychnovsky, A.

P. R. S. Haugen, A. Rychnovsky, A. Husain, L. D. Hutcheson, “Optical Interconnects for High Speed Computing,” Opt. Eng. 25, 1076–1085 (1986).
[CrossRef]

Siegel, H. J.

H. J. Siegel, Interconnection Networks for Large-Scale Parallel Processing (Lexington Books, Lexington, Massachusetts, 1985).

Sips, H. J.

H. J. Sips, “Design Aspects of a Distributed MIMD Processor,” Ph.D. Thesis, Delft U. of Technology (1984).

Smit, W.

L. Dekker, E. E. E. Frietman, W. Smit, J. C. Zuidervaart, “Optical Link in the Delft Parallel Processor, an Example of an MOMI-Connection in MIMD-Supercomputers,” in Frontiers in Computing, Elsevier Science Publishers b.v., Ed. (North-Holland, Amsterdam, 1988), pp. 141–156.

Sondervan, J. B.

J. B. Sondervan, E. H. Nordholt, L. P. de Jong, “Integrated PIN-Photodiode,” Internal Report, Electronic Research Laboratory, Department of Electrical Engineering, Delft U. of Technology, Delft, The Netherlands (1985).

Sze, S. M.

S. M. Sze, Physics of Semiconductor Devices (Wiley, New York, 1981).

van Maaren, D. C.

E. E. E. Frietman, L. Dekker, E. H. Nordholt, D. C. van Maaren, “Optical Interconnects Facilitate the Way to Massive Parallelism,” Proc. Soc. Photo-Opt. Instrum. Eng. 991, 152–161 (1988).

van Nifterick, W.

E. E. E. Frietman, W. van Nifterick, “Opto-electronic ICs for High-Speed Parallel Processing,” Lasers Optronics 6, No. 8, 69–71 (1987).

Wilson, J.

J. Wilson, J. F. B. Hawkes, Optoelectronics: An Introduction (Prentice-Hall International, London, 1983).

Zuidervaart, J. C.

L. Dekker, E. E. E. Frietman, W. Smit, J. C. Zuidervaart, “Optical Link in the Delft Parallel Processor, an Example of an MOMI-Connection in MIMD-Supercomputers,” in Frontiers in Computing, Elsevier Science Publishers b.v., Ed. (North-Holland, Amsterdam, 1988), pp. 141–156.

Comput. Archit. News

E. E. E. Frietman, A. B. Ruighaver, “An Electro-Optic Data Communication System for the Delft Parallel Processor,” Comput. Archit. News 15, No. 6, 2–7 (1987).
[CrossRef]

A. B. Ruighaver, “Design Aspects of the Delft Parallel Processor DPP84 and Its Programming System,” Comput. Archit. News 14, No. 1, 14–20 (1987).

IEEE Trans. Electron. Devices

S. R. Forrest, “Monolithic Optoelectronic Integration: A New Component Technology for Lightwave Communication,” IEEE Trans. Electron. Devices ED-32, 2640–2655 (1985).
[CrossRef]

Lasers Optronics

E. E. E. Frietman, W. van Nifterick, “Opto-electronic ICs for High-Speed Parallel Processing,” Lasers Optronics 6, No. 8, 69–71 (1987).

Opt. Eng.

P. R. S. Haugen, A. Rychnovsky, A. Husain, L. D. Hutcheson, “Optical Interconnects for High Speed Computing,” Opt. Eng. 25, 1076–1085 (1986).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng.

E. E. E. Frietman, L. Dekker, E. H. Nordholt, D. C. van Maaren, “Optical Interconnects Facilitate the Way to Massive Parallelism,” Proc. Soc. Photo-Opt. Instrum. Eng. 991, 152–161 (1988).

T. J. M. Jongeling, E. E. E. Frietman, K. Moddemeier, L. Dekker, “Kaleidoscopic Optical Backplane for Parallel Processing,” Proc. Soc. Photo-Opt. Instrum. Eng. 991, 22–27 (1988).

Proceedings, SCS Eastern Conference on Simulation

L. Dekker, “Expendability of an MIMD Multiprocessor System to a Large Size,” in Proceedings, SCS Eastern Conference on Simulation (1985), pp. 157–162.

Other

L. Dekker, E. E. E. Frietman, W. Smit, J. C. Zuidervaart, “Optical Link in the Delft Parallel Processor, an Example of an MOMI-Connection in MIMD-Supercomputers,” in Frontiers in Computing, Elsevier Science Publishers b.v., Ed. (North-Holland, Amsterdam, 1988), pp. 141–156.

L. Dekker, E. E. E. Frietman, “Optical Link and Processor Clustering in the Delft Parallel Processor,” in Proceedings, Second European Simulation Multiconference, Nice (1988).

M. A. Franklin, S. Dhar, “On Designing Interconnection Networks for Multi-Processors,” in Proceedings, International Conference on Parallel Processing, Chicago (1986), pp. 208–215.

H. J. Siegel, Interconnection Networks for Large-Scale Parallel Processing (Lexington Books, Lexington, Massachusetts, 1985).

H. J. Sips, “Design Aspects of a Distributed MIMD Processor,” Ph.D. Thesis, Delft U. of Technology (1984).

S. M. Sze, Physics of Semiconductor Devices (Wiley, New York, 1981).

J. B. Sondervan, E. H. Nordholt, L. P. de Jong, “Integrated PIN-Photodiode,” Internal Report, Electronic Research Laboratory, Department of Electrical Engineering, Delft U. of Technology, Delft, The Netherlands (1985).

J. Wilson, J. F. B. Hawkes, Optoelectronics: An Introduction (Prentice-Hall International, London, 1983).

E. E. E. Frietman, L. Dekker, “The POWERRAM,” Dutch Patent Application86.02684 (1987); European Patent Application87 202 068.0 (1988).

E. E. E. Frietman, “Bitflip,” Internal Report [051547EL11 No. 46], Faculty of Electrical Engineering, Delft U. of Technology, Delft, The Netherlands (1984).

J. B. F. Melein, “Realization of an Optic Sensitive Memory Element in Bipolar Process,” Internal Report, Faculty of Applied Physics, Delft U. of Technology, Delft, The Netherlands (1987).

T. Kohonen, Content Addressable Memories, (Springer-Verlag, New York, 1987).
[CrossRef]

A. Ackaert, P. Demeester, D. Lootens, I. Moerman, R. Baets, “Selective and Non-Planar Growth of GaAs on Si by MOVPE,” in Second European Workshop on MOVPE, St. Andrews, Scotland (1988).

C. Fernstrom, “The LUCAS Associative Array Processor and Its Programming Environment,” Ph.D. Thesis, U. Lund, Sweden (1983).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (18)

Fig. 1
Fig. 1

Four-dimensional hypercube topology.

Fig. 2
Fig. 2

Multiple Broadcast topology applied to interconnect sixteen PEs.

Fig. 3
Fig. 3

Block diagram of the DPP84.

Fig. 4
Fig. 4

Block diagram of the DPP8X.

Fig. 5
Fig. 5

Wired optical iriternconnection alternative.

Fig. 6
Fig. 6

Optical parallel multiplexer scheme.

Fig. 7
Fig. 7

(a) Facet object lens; (b) multiobjective lens; (c) facet prism; (d) plane facet mirror; (e) curved facet mirror.

Fig. 8
Fig. 8

Three-dimensional drawing of the prototype.

Fig. 9
Fig. 9

Overall view of the prototype.

Fig. 10
Fig. 10

Input and output plane of the prototype.

Fig. 11
Fig. 11

Basic integrated p-ν-n photodetecting structure.

Fig. 12
Fig. 12

Contribution to the photocurrent by the distinct layers.

Fig. 13
Fig. 13

Schematic outline of a basic input/memory cell.

Fig. 14
Fig. 14

POWERRAM.

Fig. 15
Fig. 15

4 × 4 POWERRAM prototype.

Fig. 16
Fig. 16

POWERCAM OELE.

Fig. 17
Fig. 17

Improved POWERCAM.

Fig. 18
Fig. 18

POWORRAM/CAM device.

Tables (2)

Tables Icon

Table I Randomly Chosen Words and Their Numerical Values Defined by the First Two Letters

Tables Icon

Table II Partial Contents of the Memory Field Used to Store the Data of Table I

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

cube i PE { s k / k : p k - 1 , , p i + 1 , p i , , p 1 , p 0 [ PE { d j / j : p k - 1 , , p i + 1 , p i . # .. p 1 , p 0 ] ,
t - nary - broadcast [ PE { s k i k i { 1 , 2 , , N } ] [ PE { d i d i { 1 , 2 , , q } ] 1 i t i = 1 : single broadcast ; i = N & t = N : full multiple broadcast .
[ PE { s 3 } ] [ PE { d 0 } & PE { d 1 } & PE { d 15 } ] ; [ PE { s 0 } & PE { s 1 } & PE { s 15 } ] [ PE { d 0 } & PE { d 1 } & PE { d 15 } ] .
L α α - 1 = x 2 - x 1 ln [ x 2 ] - ln [ x 1 ] .
~ x 1 2 2 D n ,
I C = I CO [ exp ( V BE / V th ) - 1 ] ,
I C 1 I C 2 = exp ( V BE 1 / V th ) S exp ( V BE 2 / V th ) = exp [ ( V B 1 - V E ) / V th ] S exp [ ( V B2 - V E ) / V th ] = exp { [ V B 1 - V B 2 - V th ln ( S ) ] / V th } .
V diff = R C I 1 t p tanh [ V B 1 - V B 2 - V th ln ( S ) 2 V th ] .
V diff = R C I 1 t p { ( 1 - γ ) tanh [ V B 1 - V B 2 - V th ln ( S ) 2 V th ] + γ tanh ( V diff 2 V th ) } .
V diff = R C I 1 t p tanh ( V diff 2 V th ) .
( x y ) = ( x y ) ( x ¯ y ¯ ) .
( x y ) = ( x y ) ( x ¯ y ) .
M j i = ( a i z j i ) m i .
M ¯ j i = ( a i z j i ) m ¯ i .
M j = i = 0 n M j i .
M ¯ j = i = 0 n M ¯ j i .
R : S D , R : { s k s k S , k = 1 , 2 , , N } { d j d j D , j = 1 , 2 , , q ; q N } .

Metrics