LAPACKE_zgeev - Eigenvalue - Eigenvector

apocalx · ‎10-29-2015

Bonjour,

J'ai quelques difficultés a bien comprendre les résultats de l'exemple "LAPACKE_zgeev".

Dans l'exemple, c'est écrit que A*v(j) = lambda(j)*v(j)

ou A est la matrice initial, v(j) le right Eigenvector et lambda(j) le Eigenvalue.

Sauf que si je prends la matrice de l'exemple:

( -3.84,  2.25) ( -8.94, -4.75) (  8.95, -6.53) ( -9.87,  4.82)
( -0.66,  0.83) ( -4.40, -3.82) ( -3.50, -4.26) ( -3.15,  7.36)
( -3.99, -4.73) ( -5.88, -6.60) ( -3.36, -0.40) ( -0.75,  5.23)
(  7.74,  4.18) (  3.66, -7.53) (  2.58,  3.60) (  4.59,  5.41)

Le EigenValue de l'exemple:

( -9.43,-12.98) ( -3.44, 12.69) ( 0.11, -3.40) ( 5.76, 7.13)

Et le right EigenVector de l'exemple:

(  0.43,  0.33) (  0.83,  0.00) (  0.60,  0.00) ( -0.31,  0.03)
(  0.51, -0.03) (  0.08, -0.25) ( -0.40, -0.20) (  0.04,  0.34)
(  0.62,  0.00) ( -0.25,  0.28) ( -0.09, -0.48) (  0.36,  0.06)
( -0.23,  0.11) ( -0.10, -0.32) ( -0.43,  0.13) (  0.81,  0.00)

Alors A*v(j) n'est pas égal a lambda(j)*v(j), ce qui devrait etre le cas.

De plus, le resultats (EigenValue et EigenVectors) ne correspondent pas non plus a ce que Matlab me donne avec [V,D] = eig(A)

Est-ce que il y a une subtilité que je ne comprends pas?

merci

MarcB

mecej4 · ‎10-29-2015

You have shown only two significant digits in the results, which is barely sufficient to check them. However, they agree with the results from Matlab. Please note that MKL/Lapack and Matlab may not report the eigenvalues and matching eigenvectors in the same order.

With Matlab 7.5, I obtained the following results, which agree with those that you reported (taking the altered order into account):

A=[complex( -3.84,  2.25) complex( -8.94, -4.75) complex(  8.95, -6.53) complex( -9.87,  4.82);
 complex( -0.66,  0.83) complex( -4.40, -3.82) complex( -3.50, -4.26) complex( -3.15,  7.36);
 complex( -3.99, -4.73) complex( -5.88, -6.60) complex( -3.36, -0.40) complex( -0.75,  5.23);
 complex(  7.74,  4.18) complex(  3.66, -7.53) complex(  2.58,  3.60) complex(  4.59,  5.41)];
[V,D]=eigs(A)
V =
  Columns 1 through 2
  4.3086e-001 +3.2681e-001i  8.2568e-001              
  5.0874e-001 -2.8833e-002i  7.5029e-002 -2.4873e-001i
  6.1985e-001               -2.4576e-001 +2.7887e-001i
 -2.2693e-001 +1.1044e-001i -1.0343e-001 -3.1920e-001i
  Columns 3 through 4
 -3.0543e-001 +3.3332e-002i  5.9840e-001              
  3.9783e-002 +3.4451e-001i -4.0048e-001 -2.0145e-001i
  3.5833e-001 +6.0645e-002i -9.0080e-002 -4.7526e-001i
  8.0824e-001               -4.3484e-001 +1.3372e-001i
D =
  Columns 1 through 2
 -9.4299e+000 -1.2983e+001i            0              
            0               -3.4418e+000 +1.2690e+001i
            0                          0              
            0                          0              
  Columns 3 through 4
            0                          0              
            0                          0              
  5.7562e+000 +7.1286e+000i            0              
            0                1.0555e-001 -3.3950e+000i

mecej4 · ‎10-29-2015

Please show the source code/Matlab scripts that you used. Neither the Matlab results nor the Lapack results in #3 are correct. Here is what I see in Matlab:

A =
  -2.0336e-03 + 3.9531e-03i  -1.8461e-04 - 1.3929e-05i  -1.8461e-04 - 1.3929e-05i
  -1.8461e-04 - 1.3929e-05i  -2.0336e-03 + 3.9531e-03i  -1.8461e-04 - 1.3929e-05i
  -1.8461e-04 - 1.3929e-05i  -1.8461e-04 - 1.3929e-05i  -2.0336e-03 + 3.9531e-03i
>> [V,D]=eigs(A)
V =
   5.7735e-01 + 2.0269e-08i  -1.3900e-02 + 1.0195e-01i   8.0542e-01              
   5.7735e-01 + 3.8170e-10i  -6.9267e-01 - 1.0195e-01i  -4.0995e-01 + 1.1584e-01i
   5.7735e-01                 7.0657e-01                -3.9547e-01 - 1.1584e-01i
D =
  -2.4028e-03 + 3.9252e-03i            0                          0              
            0                -1.8490e-03 + 3.9670e-03i            0              
            0                          0                -1.8490e-03 + 3.9670e-03i

Similarly, from Lapack using code adapted from geev.f90 in the MKL examples directory:

  VR on exit :
( 0.5773503E+00 ,  0.2026919E-07) ( 0.8054216E+00 ,  0.0000000E+00) (-0.1390000E-01 ,  0.1019502E+00)
( 0.5773503E+00 ,  0.3817009E-09) (-0.4099496E+00 ,  0.1158433E+00) (-0.6926651E+00 , -0.1019502E+00)
( 0.5773503E+00 ,  0.0000000E+00) (-0.3954719E+00 , -0.1158434E+00) ( 0.7065651E+00 ,  0.0000000E+00)

which agrees with the Matlab results after you interchange the second and third right eigenvectors.