[Bug-gsl] Bug in eigenvalue decomposition of a nonsymmetric matrix

[Youna Hu]

Hi, there:

I was using *gsl_eigen_nonsymmv *to get the eigenvalue decomposition of the
matrix in the attached file but found that the result is not right. Theory
says that there is an eigenvalue with value 1.0 and the corresponding
eigenvectors should be real. I've also tested this in the package R.

Could you please check? Thanks,

Youna

*Eigenvalue decompositon result from R:*

eigen(a)$values

 [1]   1.000000e+00   1.110223e-16  -2.691078e-17  -1.540744e-33
-1.022873e-48

 [6]  -3.798227e-64   9.041170e-80 -4.313994e-112  1.043900e-127
2.451083e-129

[11]   0.000000e+00   0.000000e+00   0.000000e+00   0.000000e+00
0.000000e+00

[16]   0.000000e+00   0.000000e+00   0.000000e+00   0.000000e+00
0.000000e+00

[21]   0.000000e+00   0.000000e+00   0.000000e+00   0.000000e+00
0.000000e+00

[26]   0.000000e+00   0.000000e+00   0.000000e+00   0.000000e+00
0.000000e+00

[31]   0.000000e+00

eigen(a)$vectors[,1]

 [1] -0.1796053 -0.1796053 -0.1796053 -0.1796053 -0.1796053 -0.1796053
-0.1796053

 [8] -0.1796053 -0.1796053 -0.1796053 -0.1796053 -0.1796053 -0.1796053
-0.1796053

[15] -0.1796053 -0.1796053 -0.1796053 -0.1796053 -0.1796053 -0.1796053
-0.1796053

[22] -0.1796053 -0.1796053 -0.1796053 -0.1796053 -0.1796053 -0.1796053
-0.1796053

[29] -0.1796053 -0.1796053 -0.1796053


*EigenValue decomposition from GSL:*

eigenvalue[0] = 1.00000000000000066613 + 0.00000000000000000000 i

eigenvalue[1] = -0.00000000000000003534 + 0.00000000000000000000 i

eigenvalue[2] = 0.00000000000000000413 + 0.00000000000000000000 i

eigenvalue[3] = -0.00000000000000000000 + 0.00000000000000000000 i

eigenvalue[4] = -0.00000000000000000000 + 0.00000000000000000000 i

eigenvalue[5] = -0.00000000000000000000 + 0.00000000000000000000 i

eigenvalue[6] = -0.00000000000000000000 + 0.00000000000000000000 i

eigenvalue[7] = -0.00000000000000000000 + 0.00000000000000000000 i

eigenvalue[8] = -0.00000000000000000000 + 0.00000000000000000000 i

eigenvalue[9] = -0.00000000000000000000 + 0.00000000000000000000 i

eigenvalue[10] = 0.00000000000000000000 + 0.00000000000000000000 i

eigenvalue[11] = -0.00000000000000000000 + 0.00000000000000000000 i

eigenvalue[12] = 0.00000000000000000000 + 0.00000000000000000000 i

eigenvalue[13] = 0.00000000000000000000 + 0.00000000000000000000 i

eigenvalue[14] = -0.00000000000000000000 + 0.00000000000000000000 i

eigenvalue[15] = 0.00000000000000000000 + 0.00000000000000000000 i

eigenvalue[16] = -0.00000000000000000000 + 0.00000000000000000000 i

eigenvalue[17] = 0.00000000000000000000 + 0.00000000000000000000 i

eigenvalue[18] = -0.00000000000000000000 + 0.00000000000000000000 i

eigenvalue[19] = 0.00000000000000000000 + 0.00000000000000000000 i

eigenvalue[20] = 0.00000000000000000000 + 0.00000000000000000000 i

eigenvalue[21] = 0.00000000000000000000 + 0.00000000000000000000 i

eigenvalue[22] = 0.00000000000000000000 + 0.00000000000000000000 i

eigenvalue[23] = 0.00000000000000000000 + 0.00000000000000000000 i

eigenvalue[24] = 0.00000000000000000000 + 0.00000000000000000000 i

eigenvalue[25] = 0.00000000000000000000 + 0.00000000000000000000 i

eigenvalue[26] = 0.00000000000000000000 + 0.00000000000000000000 i

eigenvalue[27] = 0.00000000000000000000 + 0.00000000000000000000 i

eigenvalue[28] = 0.00000000000000000000 + 0.00000000000000000000 i

eigenvalue[29] = 0.00000000000000000000 + 0.00000000000000000000 i

eigenvalue[30] = 0.00000000000000000000 + 0.00000000000000000000 i

*The eigenvectors:*

The eigenvector [0] = 0,0

The eigenvector [1] = 0.158848,-0.000727072

The eigenvector [2] = 2.0093e-07,-9.19685e-10

The eigenvector [3] = 1.87534e-06,-8.58373e-09

The eigenvector [4] = 1.26586e-05,-5.79402e-08

The eigenvector [5] = 6.58246e-05,-3.01289e-07

The eigenvector [6] = 0.000274269,-1.25537e-06

The eigenvector [7] = 0.000940351,-4.30413e-06

The eigenvector [8] = 0.00270351,-1.23744e-05

The eigenvector [9] = 0.00660858,-3.02484e-05

The eigenvector [10] = 0.013878,-6.35217e-05

The eigenvector [11] = 0.0252328,-0.000115494

The eigenvector [12] = 0.0399519,-0.000182866

The eigenvector [13] = 0.055318,-0.000253199

The eigenvector [14] = 0.0671718,-0.000307455

The eigenvector [15] = 0.0716499,-0.000327952

The eigenvector [16] = 0.0671718,-0.000307455

The eigenvector [17] = 0.055318,-0.000253199

The eigenvector [18] = 0.0399519,-0.000182866

The eigenvector [19] = -0.974767,-0.000115494

The eigenvector [20] = 0.013878,0.025667

The eigenvector [21] = 0.00660858,0.0349227

The eigenvector [22] = 0.00270351,-1.15514e-05

The eigenvector [23] = 0.000940351,-0.625902

The eigenvector [24] = 0.000274269,0.262268

The eigenvector [25] = 6.58244e-05,0.65909

The eigenvector [26] = 1.26585e-05,1.9919e-05

The eigenvector [27] = 1.87525e-06,0.351666

The eigenvector [28] = 2.0093e-07,-9.19685e-10

The eigenvector [29] = 1.38572e-08,-6.34266e-11

The eigenvector [30] = 4.61907e-10,-2.11422e-12

TransitionMatrix_30_nu_0_5.txt
Description: Text document