I have following complex sparse matrices A and B (24*24). These are copied here for testing.
import Pkg
Pkg.update()
Pkg.add("Arpack")
using Arpack
A=[0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 65.7714539723253 + 0.00000000000000im 6.57712045439343 + 0.00000000000000im -3.28856022719671 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im
0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im -78.9258507738567 + 0.00000000000000im 26.3083571033780 + 0.00000000000000im -13.1543344444335 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im
0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 13.1543188551591 + 0.00000000000000im -32.8857893432605 + 0.00000000000000im 16.4428167252580 + 0.00000000000000im -1.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im
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0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 1179958.24994025 + 0.00000000000000im -9261890.35921954 + 0.00000000000000im 7929640.66701274 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im
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0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 353233.048287276 + 0.00000000000000im -2771414.99780079 + 0.00000000000000im 2341090.38738113 + 0.00000000000000im
65.7714539723253 + 0.00000000000000im -78.9258507738567 + 0.00000000000000im 13.1543188551591 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im
6.57712045439343 + 0.00000000000000im 26.3083571033780 + 0.00000000000000im -32.8857893432605 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im
-3.28856022719671 + 0.00000000000000im -13.1543344444335 + 0.00000000000000im 16.4428167252580 + 0.00000000000000im -1.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im
0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im -1.00000000000000 + 0.00000000000000im 7981894.33571940 + 0.00000000000000im -9268625.58382269 + 0.00000000000000im 1179958.24994025 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 44.0345380647197im 0.00000000000000 + 401.669338090628im 0.00000000000000 - 100.417334522657im
0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im -8909066.58814057 + 0.00000000000000im 18184639.8436103 + 0.00000000000000im -9261890.35921954 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 - 401.669338090628im 0.00000000000000 - 4.88881580381847e-15im 0.00000000000000 + 401.669338090628im
0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 1091752.33584926 + 0.00000000000000im -8916014.29858941 + 0.00000000000000im 7929640.66701274 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 100.417334522657im 0.00000000000000 - 401.669338090628im 0.00000000000000 - 44.0345380647197im
0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 2503418.11900378 + 0.00000000000000im -2773050.96381355 + 0.00000000000000im 353027.620990499 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im 0.00000000000000 + 0.00000000000000im
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B=[65.7714539723253 6.57712045439343 -3.28856022719671 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-78.9258507738567 26.3083571033780 -13.1543344444335 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13.1543188551591 -32.8857893432605 16.4428167252580 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 -1 7981894.33571940 -8909066.58814057 1091752.33584926 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 -9268625.58382269 18184639.8436103 -8916014.29858941 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1179958.24994025 -9261890.35921954 7929640.66701274 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 2503418.11900378 -2665475.59607924 326637.560503545 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 -2773050.96381355 5440605.26594710 -2667554.34093531 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 353027.620990499 -2771035.95274201 2265716.88948497 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 2420260.56884197 -2665918.26020757 326842.987800322 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 -2773493.62794188 5437333.21475780 -2667933.38599409 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 353233.048287276 -2771414.99780079 2341090.38738113 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 -1.28521008571341e-05 -6.42605042856707e-06 3.21302521428354e-06 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 -6.42605042856707e-06 -5.14084034285365e-05 -6.42605042856708e-06 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 3.21302521428354e-06 -6.42605042856708e-06 -1.28521008571341e-05 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.00865011040000004 -0.00432505520000004 0.00216252760000000 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.00432505520000004 -0.0346004416000000 -0.00432505519999997 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.00216252760000000 -0.00432505519999997 -0.00865011039999993 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.00865011040000004 -0.00432505520000004 0.00216252760000000 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.00432505520000004 -0.0346004416000000 -0.00432505519999997 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.00216252760000000 -0.00432505519999997 -0.00865011039999993 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.0289120555520194 -0.0144560277760098 0.00722801388800482
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.0144560277760098 -0.115648222208077 -0.0144560277760095
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.00722801388800482 -0.0144560277760095 -0.0289120555520190]
(orivalue,orivector)=eigs(A,B,nev=10,which=:LM,sigma=2)
julia> orivalue
10-element Array{Complex{Float64},1}:
2.0135947372124687 + 0.006540592813947718im
2.013602774904544 - 0.006631855060845525im
2.00329725379507 - 0.01581258375841256im
2.0099980754658553 - 0.013038404131823366im
1.9907633549985115 + 0.013966331979297178im
2.003644975767938 + 0.016355957893117584im
2.010245220441175 + 0.013439150803930586im
2.0133231026854173 + 0.010524733919968566im
1.9962359551442763 + 0.016655539295428314im
2.013817257648958 - 0.010462716860425962im
This solution is wrong. I have tested the same matrices and ‘eigs’ in Matlab. The Matlab eigen value solutions are:
2.48027232367581 + 1.61216262590941e-09i
0.618203230571705 - 2.47730836307454e-09i
0.999999945798074 + 7.74033894846523e-10i
etc.
The Matlab solution is correct.