LAPACK Archives

[Lapack] Invalid (?) output from DGGEV for some matrices

Dear Lapack authors,

DGGEV returns for some matrices an ALPHAI vector such that ALPHAI(i) = 0
but ALPHAI(i+1) < 0. The DGGEV documentation does not mention such
outputs. Does this imply that the i, i+1 entries describe a complex
eigenvalue pair, or does this indicate a bug in LAPACK or in the
compiler?

The problematic matrix pairs are of the form

        [  1  0  0  0 ]    [  0  0  1   0 ]    c1 = omega^2 - 9
        [  0  1  0  0 ]    [  0  0  0   1 ]    c2 = 2 omega
        [  0  0 c1  0 ]    [  1  0  0 -c2 ]
        [  0  0  0 c1 ]    [  0  1 c2   0 ]

A test program `2dof.f` illustrating this is attached. However, what it
outputs appears to depend on compiler, compiler version, and
optimization flags:

* LAPACK 3.2, compiled with gfortran 4.3.2-1ubuntu11, OPTS = -O0:
  No problematic outputs.

  BLAS provided by Atlas 3.6.0.

* LAPACK 3.2, compiled with gfortran 4.3.2-1ubuntu11, OPTS = -O1 (2/3):

         Missing (?) complex pair for omega =   1.5656565656565657     
         Info:           0
         I / ALPHAR(I) / ALPHAI(I) / BETA(I):
                   1   0.0000000000000000        1.7080358288156292       
0.37410519259457370     
                   2   0.0000000000000000       -1.7080358288156292       
0.37410519259457370     
                   3   0.0000000000000000        0.0000000000000000        
0.0000000000000000     
                   4   0.0000000000000000      -2.62037428091521910E-016  
1.82688066063807497E-016
         Missing (?) complex pair for omega =   1.9191919191919191     
         Info:           0
         I / ALPHAR(I) / ALPHAI(I) / BETA(I):
                   1   0.0000000000000000        0.0000000000000000        
0.0000000000000000     
                   2   0.0000000000000000      -1.46001785734970358E-017  
2.96800344717906839E-018
                   3   0.0000000000000000        3.6846073726768025        
3.4091227092990981     
                   4   0.0000000000000000       -3.6846073726768025        
3.4091227092990981     

  BLAS provided by Atlas 3.6.0.

* LAPACK 3.2, compiled with gfortran 4.1.2 20061115, OPTS = -O0:
  Missing (?) complex pair for omega =   1.86868686868687

  BLAS provided by Atlas 3.6.0; same with Netlib BLAS.

* LAPACK 3.1.1, compiled with g77 3.4.6, OPTS = -O0/O1/O2/O3:
  Missing (?) complex pair for omega =  1.86868687

  BLAS provided by Atlas 3.6.0; same with Netlib BLAS.

What appears to matter for gfortran 4.3.2 is which optimization flags
were used to compile the file `dhgeqz.f`; recompiling this file can make
the problem appear (-O1) and disappear (-O0).

Output from LAPACK double eigenvalue tests, `dgd-O0/O1.out` is also
attached. It corresponds to gfortran 4.3.2-1ubuntu11, for -O0 and -O1.
There are some failures, but they are the same for both flags.

This issue is present at least in LAPACK libraries shipped by Ubuntu and
Debian. It may be that also other Linux distributions are affected.

    ***

We ran into this problem while wrapping DGGEV for use in the
higher-level language Python: the ambiguity in the return value caused
an error in repacking the complex eigenvectors in our code. [1]  (Cc'd
to the developer list.)

If this is a LAPACK or compiler bug, suggestions on how the DGGEV return
values should be interpreted are appreciated: should we treat this as an
error condition, or should we attempt to treat the result as a complex
eigenvalue pair?

Best regards,
Pauli Virtanen

.. [1] http://scipy.org/scipy/scipy/ticket/709

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 Tests of the Generalized Nonsymmetric Eigenvalue Problem Driver DGGES

 LAPACK VERSION 3.2.0

 The following parameter values will be used:
    M:         2     6    10    12    20
    N:         2     6    10    12    20
    NB:        1
    NBMIN:     1
    NX:        1
    NS:        2
    MAXB:      1

 Relative machine underflow is taken to be    0.222507-307
 Relative machine overflow  is taken to be    0.179769+309
 Relative machine precision is taken to be    0.111022D-15

 Routines pass computational tests if test ratio is less than   10.00


 DGS routines passed the tests of the error exits ( 87 tests done)

 All tests for DGS drivers  passed the threshold (  1560 tests run)

 -----------------------------------------------------------------------

 Tests of the Generalized Nonsymmetric Eigenvalue Problem Driver DGGEV

 LAPACK VERSION 3.2.0

 The following parameter values will be used:
    M:         2     6     8    10    15    20
    N:         2     6     8    10    15    20
    NB:        1
    NBMIN:     1
    NX:        1
    NS:        2
    MAXB:      1

 Relative machine underflow is taken to be    0.222507-307
 Relative machine overflow  is taken to be    0.179769+309
 Relative machine precision is taken to be    0.111022D-15

 Routines pass computational tests if test ratio is less than   10.00


 DGV routines passed the tests of the error exits ( 87 tests done)

 All tests for DGV drivers  passed the threshold (  1092 tests run)

 -----------------------------------------------------------------------

 Tests of the Generalized Nonsymmetric Eigenvalue Problem Expert Driver DGGESX

 LAPACK VERSION 3.2.0

 The following parameter values will be used:
    N:         2
    NB:        1
    NBMIN:     1
    NX:        1
    NS:        2
    MAXB:      1

 Relative machine underflow is taken to be    0.222507-307
 Relative machine overflow  is taken to be    0.179769+309
 Relative machine precision is taken to be    0.111022D-15

 Routines pass computational tests if test ratio is less than   10.00


 DGX routines passed the tests of the error exits ( 87 tests done)

 All tests for SGX drivers  passed the threshold (   150 tests run)

 -----------------------------------------------------------------------

 Tests of the Generalized Nonsymmetric Eigenvalue Problem Expert Driver DGGESX

 LAPACK VERSION 3.2.0

 The following parameter values will be used:
    N:         0
    NB:        1
    NBMIN:     1
    NX:        1
    NS:        2
    MAXB:      1

 Relative machine underflow is taken to be    0.222507-307
 Relative machine overflow  is taken to be    0.179769+309
 Relative machine precision is taken to be    0.111022D-15

 Routines pass computational tests if test ratio is less than   10.00


 DGX routines passed the tests of the error exits ( 87 tests done)

 All tests for SGX drivers  passed the threshold (    20 tests run)

 -----------------------------------------------------------------------

 Tests of the Generalized Nonsymmetric Eigenvalue Problem Expert Driver DGGEVX

 LAPACK VERSION 3.2.0

 The following parameter values will be used:
    N:         5
    NB:        1
    NBMIN:     1
    NX:        1
    NS:        2
    MAXB:      1

 Relative machine underflow is taken to be    0.222507-307
 Relative machine overflow  is taken to be    0.179769+309
 Relative machine precision is taken to be    0.111022D-15

 Routines pass computational tests if test ratio is less than   10.00


 DXV routines passed the tests of the error exits ( 87 tests done)

 DXV -- Real Expert Eigenvalue/vector problem driver
 Matrix types: 

 TYPE 1: Da is diagonal, Db is identity, 
     A = Y^(-H) Da X^(-1), B = Y^(-H) Db X^(-1) 
     YH and X are left and right eigenvectors. 

 TYPE 2: Da is quasi-diagonal, Db is identity, 
     A = Y^(-H) Da X^(-1), B = Y^(-H) Db X^(-1) 
     YH and X are left and right eigenvectors. 


 Tests performed:  
     a is alpha, b is beta, l is a left eigenvector, 
     r is a right eigenvector and ' means transpose.
 1 = max | ( b A - a B )' l | / const.
 2 = max | ( b A - a B ) r | / const.
 3 = max ( Sest/Stru, Stru/Sest )  over all eigenvalues
 4 = max( DIFest/DIFtru, DIFtru/DIFest )  over the 1st and 5th eigenvectors

 Type= 2, IWA= 1, IWB= 1, IWX= 5, IWY= 1, result  4 is 3766.18
 Type= 2, IWA= 1, IWB= 1, IWX= 5, IWY= 2, result  4 is 3930.80
 Type= 2, IWA= 1, IWB= 1, IWX= 5, IWY= 3, result  4 is 3540.26
 Type= 2, IWA= 1, IWB= 1, IWX= 5, IWY= 4, result  4 is 3327.88
 Type= 2, IWA= 1, IWB= 1, IWX= 5, IWY= 5, result  4 is 1648.31
 Type= 2, IWA= 1, IWB= 2, IWX= 5, IWY= 5, result  4 is 2269.35
 Type= 2, IWA= 1, IWB= 3, IWX= 5, IWY= 5, result  4 is 1325.15
 Type= 2, IWA= 1, IWB= 4, IWX= 5, IWY= 5, result  4 is  476.00
 Type= 2, IWA= 1, IWB= 5, IWX= 1, IWY= 1, result  4 is 4096.29
 Type= 2, IWA= 1, IWB= 5, IWX= 1, IWY= 2, result  4 is 3817.53
 Type= 2, IWA= 1, IWB= 5, IWX= 1, IWY= 3, result  4 is 2120.76
 Type= 2, IWA= 1, IWB= 5, IWX= 1, IWY= 4, result  4 is  288.27
 Type= 2, IWA= 1, IWB= 5, IWX= 2, IWY= 1, result  4 is 3817.53
 Type= 2, IWA= 1, IWB= 5, IWX= 2, IWY= 2, result  4 is 3707.73
 Type= 2, IWA= 1, IWB= 5, IWX= 2, IWY= 3, result  4 is 2114.67
 Type= 2, IWA= 1, IWB= 5, IWX= 2, IWY= 4, result  4 is  288.25
 Type= 2, IWA= 1, IWB= 5, IWX= 3, IWY= 1, result  4 is 2120.76
 Type= 2, IWA= 1, IWB= 5, IWX= 3, IWY= 2, result  4 is 2114.67
 Type= 2, IWA= 1, IWB= 5, IWX= 3, IWY= 3, result  4 is 1697.03
 Type= 2, IWA= 1, IWB= 5, IWX= 3, IWY= 4, result  4 is  286.85
 Type= 2, IWA= 1, IWB= 5, IWX= 4, IWY= 1, result  4 is  288.27
 Type= 2, IWA= 1, IWB= 5, IWX= 4, IWY= 2, result  4 is  288.25
 Type= 2, IWA= 1, IWB= 5, IWX= 4, IWY= 3, result  4 is  286.85
 Type= 2, IWA= 1, IWB= 5, IWX= 4, IWY= 4, result  4 is  204.34
 Type= 2, IWA= 2, IWB= 1, IWX= 5, IWY= 5, result  4 is 4540.57
 Type= 2, IWA= 2, IWB= 2, IWX= 5, IWY= 5, result  4 is 3644.74
 Type= 2, IWA= 2, IWB= 3, IWX= 5, IWY= 5, result  4 is 1633.45
 Type= 2, IWA= 2, IWB= 4, IWX= 5, IWY= 5, result  4 is  481.28
 Type= 2, IWA= 2, IWB= 5, IWX= 1, IWY= 1, result  4 is 4096.34
 Type= 2, IWA= 2, IWB= 5, IWX= 1, IWY= 2, result  4 is 3817.57
 Type= 2, IWA= 2, IWB= 5, IWX= 1, IWY= 3, result  4 is 2120.79
 Type= 2, IWA= 2, IWB= 5, IWX= 1, IWY= 4, result  4 is  288.27
 Type= 2, IWA= 2, IWB= 5, IWX= 2, IWY= 1, result  4 is 3817.57
 Type= 2, IWA= 2, IWB= 5, IWX= 2, IWY= 2, result  4 is 3707.78
 Type= 2, IWA= 2, IWB= 5, IWX= 2, IWY= 3, result  4 is 2114.70
 Type= 2, IWA= 2, IWB= 5, IWX= 2, IWY= 4, result  4 is  288.26
 Type= 2, IWA= 2, IWB= 5, IWX= 3, IWY= 1, result  4 is 2120.79
 Type= 2, IWA= 2, IWB= 5, IWX= 3, IWY= 2, result  4 is 2114.70
 Type= 2, IWA= 2, IWB= 5, IWX= 3, IWY= 3, result  4 is 1697.05
 Type= 2, IWA= 2, IWB= 5, IWX= 3, IWY= 4, result  4 is  286.85
 Type= 2, IWA= 2, IWB= 5, IWX= 4, IWY= 1, result  4 is  288.27
 Type= 2, IWA= 2, IWB= 5, IWX= 4, IWY= 2, result  4 is  288.26
 Type= 2, IWA= 2, IWB= 5, IWX= 4, IWY= 3, result  4 is  286.85
 Type= 2, IWA= 2, IWB= 5, IWX= 4, IWY= 4, result  4 is  204.34
 Type= 2, IWA= 3, IWB= 1, IWX= 5, IWY= 5, result  4 is 4780.11
 Type= 2, IWA= 3, IWB= 2, IWX= 5, IWY= 5, result  4 is 4729.74
 Type= 2, IWA= 3, IWB= 3, IWX= 5, IWY= 5, result  4 is 3176.28
 Type= 2, IWA= 3, IWB= 4, IWX= 5, IWY= 5, result  4 is  524.84
 Type= 2, IWA= 3, IWB= 5, IWX= 1, IWY= 1, result  4 is 4096.79
 Type= 2, IWA= 3, IWB= 5, IWX= 1, IWY= 2, result  4 is 3817.99
 Type= 2, IWA= 3, IWB= 5, IWX= 1, IWY= 3, result  4 is 2121.02
 Type= 2, IWA= 3, IWB= 5, IWX= 1, IWY= 4, result  4 is  288.30
 Type= 2, IWA= 3, IWB= 5, IWX= 2, IWY= 1, result  4 is 3817.99
 Type= 2, IWA= 3, IWB= 5, IWX= 2, IWY= 2, result  4 is 3708.19
 Type= 2, IWA= 3, IWB= 5, IWX= 2, IWY= 3, result  4 is 2114.93
 Type= 2, IWA= 3, IWB= 5, IWX= 2, IWY= 4, result  4 is  288.29
 Type= 2, IWA= 3, IWB= 5, IWX= 3, IWY= 1, result  4 is 2121.02
 Type= 2, IWA= 3, IWB= 5, IWX= 3, IWY= 2, result  4 is 2114.93
 Type= 2, IWA= 3, IWB= 5, IWX= 3, IWY= 3, result  4 is 1697.24
 Type= 2, IWA= 3, IWB= 5, IWX= 3, IWY= 4, result  4 is  286.89
 Type= 2, IWA= 3, IWB= 5, IWX= 4, IWY= 1, result  4 is  288.30
 Type= 2, IWA= 3, IWB= 5, IWX= 4, IWY= 2, result  4 is  288.29
 Type= 2, IWA= 3, IWB= 5, IWX= 4, IWY= 3, result  4 is  286.89
 Type= 2, IWA= 3, IWB= 5, IWX= 4, IWY= 4, result  4 is  204.37
 Type= 2, IWA= 4, IWB= 1, IWX= 5, IWY= 5, result  4 is  638.62
 Type= 2, IWA= 4, IWB= 2, IWX= 5, IWY= 5, result  4 is  643.29
 Type= 2, IWA= 4, IWB= 3, IWX= 5, IWY= 5, result  4 is  678.13
 Type= 2, IWA= 4, IWB= 4, IWX= 5, IWY= 5, result  4 is  547.38
 Type= 2, IWA= 4, IWB= 5, IWX= 1, IWY= 1, result  4 is 4101.29
 Type= 2, IWA= 4, IWB= 5, IWX= 1, IWY= 2, result  4 is 3822.19
 Type= 2, IWA= 4, IWB= 5, IWX= 1, IWY= 3, result  4 is 2123.35
 Type= 2, IWA= 4, IWB= 5, IWX= 1, IWY= 4, result  4 is  288.62
 Type= 2, IWA= 4, IWB= 5, IWX= 2, IWY= 1, result  4 is 3822.19
 Type= 2, IWA= 4, IWB= 5, IWX= 2, IWY= 2, result  4 is 3712.26
 Type= 2, IWA= 4, IWB= 5, IWX= 2, IWY= 3, result  4 is 2117.25
 Type= 2, IWA= 4, IWB= 5, IWX= 2, IWY= 4, result  4 is  288.61
 Type= 2, IWA= 4, IWB= 5, IWX= 3, IWY= 1, result  4 is 2123.35
 Type= 2, IWA= 4, IWB= 5, IWX= 3, IWY= 2, result  4 is 2117.25
 Type= 2, IWA= 4, IWB= 5, IWX= 3, IWY= 3, result  4 is 1699.11
 Type= 2, IWA= 4, IWB= 5, IWX= 3, IWY= 4, result  4 is  287.20
 Type= 2, IWA= 4, IWB= 5, IWX= 4, IWY= 1, result  4 is  288.62
 Type= 2, IWA= 4, IWB= 5, IWX= 4, IWY= 2, result  4 is  288.61
 Type= 2, IWA= 4, IWB= 5, IWX= 4, IWY= 3, result  4 is  287.20
 Type= 2, IWA= 4, IWB= 5, IWX= 4, IWY= 4, result  4 is  204.59
 Type= 2, IWA= 5, IWB= 1, IWX= 1, IWY= 1, result  4 is 3.355D+07
 Type= 2, IWA= 5, IWB= 1, IWX= 1, IWY= 2, result  4 is 3.127D+07
 Type= 2, IWA= 5, IWB= 1, IWX= 1, IWY= 3, result  4 is 1.737D+07
 Type= 2, IWA= 5, IWB= 1, IWX= 1, IWY= 4, result  4 is 2.361D+06
 Type= 2, IWA= 5, IWB= 1, IWX= 1, IWY= 5, result  4 is 2896.66
 Type= 2, IWA= 5, IWB= 1, IWX= 2, IWY= 1, result  4 is 3.127D+07
 Type= 2, IWA= 5, IWB= 1, IWX= 2, IWY= 2, result  4 is 3.037D+07
 Type= 2, IWA= 5, IWB= 1, IWX= 2, IWY= 3, result  4 is 1.732D+07
 Type= 2, IWA= 5, IWB= 1, IWX= 2, IWY= 4, result  4 is 2.361D+06
 Type= 2, IWA= 5, IWB= 1, IWX= 2, IWY= 5, result  4 is 2896.66
 Type= 2, IWA= 5, IWB= 1, IWX= 3, IWY= 1, result  4 is 1.737D+07
 Type= 2, IWA= 5, IWB= 1, IWX= 3, IWY= 2, result  4 is 1.732D+07
 Type= 2, IWA= 5, IWB= 1, IWX= 3, IWY= 3, result  4 is 1.390D+07
 Type= 2, IWA= 5, IWB= 1, IWX= 3, IWY= 4, result  4 is 2.350D+06
 Type= 2, IWA= 5, IWB= 1, IWX= 3, IWY= 5, result  4 is 2896.66
 Type= 2, IWA= 5, IWB= 1, IWX= 4, IWY= 1, result  4 is 2.361D+06
 Type= 2, IWA= 5, IWB= 1, IWX= 4, IWY= 2, result  4 is 2.361D+06
 Type= 2, IWA= 5, IWB= 1, IWX= 4, IWY= 3, result  4 is 2.350D+06
 Type= 2, IWA= 5, IWB= 1, IWX= 4, IWY= 4, result  4 is 1.674D+06
 Type= 2, IWA= 5, IWB= 1, IWX= 4, IWY= 5, result  4 is 2896.66
 Type= 2, IWA= 5, IWB= 1, IWX= 5, IWY= 1, result  4 is 2896.66
 Type= 2, IWA= 5, IWB= 1, IWX= 5, IWY= 2, result  4 is 2896.66
 Type= 2, IWA= 5, IWB= 1, IWX= 5, IWY= 3, result  4 is 2896.66
 Type= 2, IWA= 5, IWB= 1, IWX= 5, IWY= 4, result  4 is 2896.66
 Type= 2, IWA= 5, IWB= 1, IWX= 5, IWY= 5, result  4 is 2048.38
 Type= 2, IWA= 5, IWB= 2, IWX= 1, IWY= 1, result  4 is 3.051D+07
 Type= 2, IWA= 5, IWB= 2, IWX= 1, IWY= 2, result  4 is 2.843D+07
 Type= 2, IWA= 5, IWB= 2, IWX= 1, IWY= 3, result  4 is 1.579D+07
 Type= 2, IWA= 5, IWB= 2, IWX= 1, IWY= 4, result  4 is 2.147D+06
 Type= 2, IWA= 5, IWB= 2, IWX= 1, IWY= 5, result  4 is 2633.68
 Type= 2, IWA= 5, IWB= 2, IWX= 2, IWY= 1, result  4 is 2.843D+07
 Type= 2, IWA= 5, IWB= 2, IWX= 2, IWY= 2, result  4 is 2.761D+07
 Type= 2, IWA= 5, IWB= 2, IWX= 2, IWY= 3, result  4 is 1.575D+07
 Type= 2, IWA= 5, IWB= 2, IWX= 2, IWY= 4, result  4 is 2.147D+06
 Type= 2, IWA= 5, IWB= 2, IWX= 2, IWY= 5, result  4 is 2633.68
 Type= 2, IWA= 5, IWB= 2, IWX= 3, IWY= 1, result  4 is 1.579D+07
 Type= 2, IWA= 5, IWB= 2, IWX= 3, IWY= 2, result  4 is 1.575D+07
 Type= 2, IWA= 5, IWB= 2, IWX= 3, IWY= 3, result  4 is 1.264D+07
 Type= 2, IWA= 5, IWB= 2, IWX= 3, IWY= 4, result  4 is 2.136D+06
 Type= 2, IWA= 5, IWB= 2, IWX= 3, IWY= 5, result  4 is 2633.68
 Type= 2, IWA= 5, IWB= 2, IWX= 4, IWY= 1, result  4 is 2.147D+06
 Type= 2, IWA= 5, IWB= 2, IWX= 4, IWY= 2, result  4 is 2.147D+06
 Type= 2, IWA= 5, IWB= 2, IWX= 4, IWY= 3, result  4 is 2.136D+06
 Type= 2, IWA= 5, IWB= 2, IWX= 4, IWY= 4, result  4 is 1.522D+06
 Type= 2, IWA= 5, IWB= 2, IWX= 4, IWY= 5, result  4 is 2633.68
 Type= 2, IWA= 5, IWB= 2, IWX= 5, IWY= 1, result  4 is 2633.68
 Type= 2, IWA= 5, IWB= 2, IWX= 5, IWY= 2, result  4 is 2633.68
 Type= 2, IWA= 5, IWB= 2, IWX= 5, IWY= 3, result  4 is 2633.68
 Type= 2, IWA= 5, IWB= 2, IWX= 5, IWY= 4, result  4 is 2633.68
 Type= 2, IWA= 5, IWB= 2, IWX= 5, IWY= 5, result  4 is 1862.41
 Type= 2, IWA= 5, IWB= 3, IWX= 1, IWY= 1, result  4 is 1.678D+07
 Type= 2, IWA= 5, IWB= 3, IWX= 1, IWY= 2, result  4 is 1.564D+07
 Type= 2, IWA= 5, IWB= 3, IWX= 1, IWY= 3, result  4 is 8.688D+06
 Type= 2, IWA= 5, IWB= 3, IWX= 1, IWY= 4, result  4 is 1.181D+06
 Type= 2, IWA= 5, IWB= 3, IWX= 1, IWY= 5, result  4 is 1448.69
 Type= 2, IWA= 5, IWB= 3, IWX= 2, IWY= 1, result  4 is 1.564D+07
 Type= 2, IWA= 5, IWB= 3, IWX= 2, IWY= 2, result  4 is 1.519D+07
 Type= 2, IWA= 5, IWB= 3, IWX= 2, IWY= 3, result  4 is 8.663D+06
 Type= 2, IWA= 5, IWB= 3, IWX= 2, IWY= 4, result  4 is 1.181D+06
 Type= 2, IWA= 5, IWB= 3, IWX= 2, IWY= 5, result  4 is 1448.69
 Type= 2, IWA= 5, IWB= 3, IWX= 3, IWY= 1, result  4 is 8.688D+06
 Type= 2, IWA= 5, IWB= 3, IWX= 3, IWY= 2, result  4 is 8.663D+06
 Type= 2, IWA= 5, IWB= 3, IWX= 3, IWY= 3, result  4 is 6.952D+06
 Type= 2, IWA= 5, IWB= 3, IWX= 3, IWY= 4, result  4 is 1.175D+06
 Type= 2, IWA= 5, IWB= 3, IWX= 3, IWY= 5, result  4 is 1448.69
 Type= 2, IWA= 5, IWB= 3, IWX= 4, IWY= 1, result  4 is 1.181D+06
 Type= 2, IWA= 5, IWB= 3, IWX= 4, IWY= 2, result  4 is 1.181D+06
 Type= 2, IWA= 5, IWB= 3, IWX= 4, IWY= 3, result  4 is 1.175D+06
 Type= 2, IWA= 5, IWB= 3, IWX= 4, IWY= 4, result  4 is 8.371D+05
 Type= 2, IWA= 5, IWB= 3, IWX= 4, IWY= 5, result  4 is 1448.68
 Type= 2, IWA= 5, IWB= 3, IWX= 5, IWY= 1, result  4 is 1448.69
 Type= 2, IWA= 5, IWB= 3, IWX= 5, IWY= 2, result  4 is 1448.69
 Type= 2, IWA= 5, IWB= 3, IWX= 5, IWY= 3, result  4 is 1448.69
 Type= 2, IWA= 5, IWB= 3, IWX= 5, IWY= 4, result  4 is 1448.68
 Type= 2, IWA= 5, IWB= 3, IWX= 5, IWY= 5, result  4 is 1024.44
 Type= 2, IWA= 5, IWB= 4, IWX= 1, IWY= 1, result  4 is 3.055D+06
 Type= 2, IWA= 5, IWB= 4, IWX= 1, IWY= 2, result  4 is 2.846D+06
 Type= 2, IWA= 5, IWB= 4, IWX= 1, IWY= 3, result  4 is 1.581D+06
 Type= 2, IWA= 5, IWB= 4, IWX= 1, IWY= 4, result  4 is 2.149D+05
 Type= 2, IWA= 5, IWB= 4, IWX= 1, IWY= 5, result  4 is  263.69
 Type= 2, IWA= 5, IWB= 4, IWX= 2, IWY= 1, result  4 is 2.846D+06
 Type= 2, IWA= 5, IWB= 4, IWX= 2, IWY= 2, result  4 is 2.765D+06
 Type= 2, IWA= 5, IWB= 4, IWX= 2, IWY= 3, result  4 is 1.577D+06
 Type= 2, IWA= 5, IWB= 4, IWX= 2, IWY= 4, result  4 is 2.149D+05
 Type= 2, IWA= 5, IWB= 4, IWX= 2, IWY= 5, result  4 is  263.69
 Type= 2, IWA= 5, IWB= 4, IWX= 3, IWY= 1, result  4 is 1.581D+06
 Type= 2, IWA= 5, IWB= 4, IWX= 3, IWY= 2, result  4 is 1.577D+06
 Type= 2, IWA= 5, IWB= 4, IWX= 3, IWY= 3, result  4 is 1.265D+06
 Type= 2, IWA= 5, IWB= 4, IWX= 3, IWY= 4, result  4 is 2.139D+05
 Type= 2, IWA= 5, IWB= 4, IWX= 3, IWY= 5, result  4 is  263.69
 Type= 2, IWA= 5, IWB= 4, IWX= 4, IWY= 1, result  4 is 2.149D+05
 Type= 2, IWA= 5, IWB= 4, IWX= 4, IWY= 2, result  4 is 2.149D+05
 Type= 2, IWA= 5, IWB= 4, IWX= 4, IWY= 3, result  4 is 2.139D+05
 Type= 2, IWA= 5, IWB= 4, IWX= 4, IWY= 4, result  4 is 1.524D+05
 Type= 2, IWA= 5, IWB= 4, IWX= 4, IWY= 5, result  4 is  263.69
 Type= 2, IWA= 5, IWB= 4, IWX= 5, IWY= 1, result  4 is  263.69
 Type= 2, IWA= 5, IWB= 4, IWX= 5, IWY= 2, result  4 is  263.69
 Type= 2, IWA= 5, IWB= 4, IWX= 5, IWY= 3, result  4 is  263.69
 Type= 2, IWA= 5, IWB= 4, IWX= 5, IWY= 4, result  4 is  263.69
 Type= 2, IWA= 5, IWB= 4, IWX= 5, IWY= 5, result  4 is  186.47
 Type= 2, IWA= 5, IWB= 5, IWX= 1, IWY= 1, result  4 is 1.158D+04
 Type= 2, IWA= 5, IWB= 5, IWX= 1, IWY= 2, result  4 is 1.080D+04
 Type= 2, IWA= 5, IWB= 5, IWX= 1, IWY= 3, result  4 is 5997.33
 Type= 2, IWA= 5, IWB= 5, IWX= 1, IWY= 4, result  4 is  815.19
 Type= 2, IWA= 5, IWB= 5, IWX= 2, IWY= 1, result  4 is 1.080D+04
 Type= 2, IWA= 5, IWB= 5, IWX= 2, IWY= 2, result  4 is 1.049D+04
 Type= 2, IWA= 5, IWB= 5, IWX= 2, IWY= 3, result  4 is 5980.12
 Type= 2, IWA= 5, IWB= 5, IWX= 2, IWY= 4, result  4 is  815.15
 Type= 2, IWA= 5, IWB= 5, IWX= 3, IWY= 1, result  4 is 5997.33
 Type= 2, IWA= 5, IWB= 5, IWX= 3, IWY= 2, result  4 is 5980.12
 Type= 2, IWA= 5, IWB= 5, IWX= 3, IWY= 3, result  4 is 4799.16
 Type= 2, IWA= 5, IWB= 5, IWX= 3, IWY= 4, result  4 is  811.19
 Type= 2, IWA= 5, IWB= 5, IWX= 4, IWY= 1, result  4 is  815.19
 Type= 2, IWA= 5, IWB= 5, IWX= 4, IWY= 2, result  4 is  815.15
 Type= 2, IWA= 5, IWB= 5, IWX= 4, IWY= 3, result  4 is  811.19
 Type= 2, IWA= 5, IWB= 5, IWX= 4, IWY= 4, result  4 is  577.87
 DXV drivers:    200 out of   5000 tests failed to pass the threshold

 -----------------------------------------------------------------------

 Tests of the Generalized Nonsymmetric Eigenvalue Problem Expert Driver DGGEVX

 LAPACK VERSION 3.2.0

 The following parameter values will be used:
    N:         0
    NB:        1
    NBMIN:     1
    NX:        1
    NS:        2
    MAXB:      1

 Relative machine underflow is taken to be    0.222507-307
 Relative machine overflow  is taken to be    0.179769+309
 Relative machine precision is taken to be    0.111022D-15

 Routines pass computational tests if test ratio is less than   10.00


 DXV routines passed the tests of the error exits ( 87 tests done)

 All tests for DXV drivers  passed the threshold (     8 tests run)

 -----------------------------------------------------------------------


 End of tests
 Total time used =         1.11 seconds

-------------- next part --------------

 Tests of the Generalized Nonsymmetric Eigenvalue Problem Driver DGGES

 LAPACK VERSION 3.2.0

 The following parameter values will be used:
    M:         2     6    10    12    20
    N:         2     6    10    12    20
    NB:        1
    NBMIN:     1
    NX:        1
    NS:        2
    MAXB:      1

 Relative machine underflow is taken to be    0.222507-307
 Relative machine overflow  is taken to be    0.179769+309
 Relative machine precision is taken to be    0.111022D-15

 Routines pass computational tests if test ratio is less than   10.00


 DGS routines passed the tests of the error exits ( 87 tests done)

 All tests for DGS drivers  passed the threshold (  1560 tests run)

 -----------------------------------------------------------------------

 Tests of the Generalized Nonsymmetric Eigenvalue Problem Driver DGGEV

 LAPACK VERSION 3.2.0

 The following parameter values will be used:
    M:         2     6     8    10    15    20
    N:         2     6     8    10    15    20
    NB:        1
    NBMIN:     1
    NX:        1
    NS:        2
    MAXB:      1

 Relative machine underflow is taken to be    0.222507-307
 Relative machine overflow  is taken to be    0.179769+309
 Relative machine precision is taken to be    0.111022D-15

 Routines pass computational tests if test ratio is less than   10.00


 DGV routines passed the tests of the error exits ( 87 tests done)

 All tests for DGV drivers  passed the threshold (  1092 tests run)

 -----------------------------------------------------------------------

 Tests of the Generalized Nonsymmetric Eigenvalue Problem Expert Driver DGGESX

 LAPACK VERSION 3.2.0

 The following parameter values will be used:
    N:         2
    NB:        1
    NBMIN:     1
    NX:        1
    NS:        2
    MAXB:      1

 Relative machine underflow is taken to be    0.222507-307
 Relative machine overflow  is taken to be    0.179769+309
 Relative machine precision is taken to be    0.111022D-15

 Routines pass computational tests if test ratio is less than   10.00


 DGX routines passed the tests of the error exits ( 87 tests done)

 All tests for SGX drivers  passed the threshold (   150 tests run)

 -----------------------------------------------------------------------

 Tests of the Generalized Nonsymmetric Eigenvalue Problem Expert Driver DGGESX

 LAPACK VERSION 3.2.0

 The following parameter values will be used:
    N:         0
    NB:        1
    NBMIN:     1
    NX:        1
    NS:        2
    MAXB:      1

 Relative machine underflow is taken to be    0.222507-307
 Relative machine overflow  is taken to be    0.179769+309
 Relative machine precision is taken to be    0.111022D-15

 Routines pass computational tests if test ratio is less than   10.00


 DGX routines passed the tests of the error exits ( 87 tests done)

 All tests for SGX drivers  passed the threshold (    20 tests run)

 -----------------------------------------------------------------------

 Tests of the Generalized Nonsymmetric Eigenvalue Problem Expert Driver DGGEVX

 LAPACK VERSION 3.2.0

 The following parameter values will be used:
    N:         5
    NB:        1
    NBMIN:     1
    NX:        1
    NS:        2
    MAXB:      1

 Relative machine underflow is taken to be    0.222507-307
 Relative machine overflow  is taken to be    0.179769+309
 Relative machine precision is taken to be    0.111022D-15

 Routines pass computational tests if test ratio is less than   10.00


 DXV routines passed the tests of the error exits ( 87 tests done)

 DXV -- Real Expert Eigenvalue/vector problem driver
 Matrix types: 

 TYPE 1: Da is diagonal, Db is identity, 
     A = Y^(-H) Da X^(-1), B = Y^(-H) Db X^(-1) 
     YH and X are left and right eigenvectors. 

 TYPE 2: Da is quasi-diagonal, Db is identity, 
     A = Y^(-H) Da X^(-1), B = Y^(-H) Db X^(-1) 
     YH and X are left and right eigenvectors. 


 Tests performed:  
     a is alpha, b is beta, l is a left eigenvector, 
     r is a right eigenvector and ' means transpose.
 1 = max | ( b A - a B )' l | / const.
 2 = max | ( b A - a B ) r | / const.
 3 = max ( Sest/Stru, Stru/Sest )  over all eigenvalues
 4 = max( DIFest/DIFtru, DIFtru/DIFest )  over the 1st and 5th eigenvectors

 Type= 2, IWA= 1, IWB= 1, IWX= 5, IWY= 1, result  4 is 3766.18
 Type= 2, IWA= 1, IWB= 1, IWX= 5, IWY= 2, result  4 is 3930.80
 Type= 2, IWA= 1, IWB= 1, IWX= 5, IWY= 3, result  4 is 4742.40
 Type= 2, IWA= 1, IWB= 1, IWX= 5, IWY= 4, result  4 is 3327.01
 Type= 2, IWA= 1, IWB= 1, IWX= 5, IWY= 5, result  4 is 1648.19
 Type= 2, IWA= 1, IWB= 2, IWX= 5, IWY= 5, result  4 is 2269.53
 Type= 2, IWA= 1, IWB= 3, IWX= 5, IWY= 5, result  4 is 1325.15
 Type= 2, IWA= 1, IWB= 4, IWX= 5, IWY= 5, result  4 is  476.04
 Type= 2, IWA= 1, IWB= 5, IWX= 1, IWY= 1, result  4 is 4096.29
 Type= 2, IWA= 1, IWB= 5, IWX= 1, IWY= 2, result  4 is 3817.53
 Type= 2, IWA= 1, IWB= 5, IWX= 1, IWY= 3, result  4 is 2120.76
 Type= 2, IWA= 1, IWB= 5, IWX= 1, IWY= 4, result  4 is  288.27
 Type= 2, IWA= 1, IWB= 5, IWX= 2, IWY= 1, result  4 is 3817.53
 Type= 2, IWA= 1, IWB= 5, IWX= 2, IWY= 2, result  4 is 3707.73
 Type= 2, IWA= 1, IWB= 5, IWX= 2, IWY= 3, result  4 is 2114.67
 Type= 2, IWA= 1, IWB= 5, IWX= 2, IWY= 4, result  4 is  288.25
 Type= 2, IWA= 1, IWB= 5, IWX= 3, IWY= 1, result  4 is 2120.76
 Type= 2, IWA= 1, IWB= 5, IWX= 3, IWY= 2, result  4 is 2114.67
 Type= 2, IWA= 1, IWB= 5, IWX= 3, IWY= 3, result  4 is 1697.03
 Type= 2, IWA= 1, IWB= 5, IWX= 3, IWY= 4, result  4 is  286.85
 Type= 2, IWA= 1, IWB= 5, IWX= 4, IWY= 1, result  4 is  288.27
 Type= 2, IWA= 1, IWB= 5, IWX= 4, IWY= 2, result  4 is  288.25
 Type= 2, IWA= 1, IWB= 5, IWX= 4, IWY= 3, result  4 is  286.85
 Type= 2, IWA= 1, IWB= 5, IWX= 4, IWY= 4, result  4 is  204.34
 Type= 2, IWA= 2, IWB= 1, IWX= 5, IWY= 5, result  4 is 4540.57
 Type= 2, IWA= 2, IWB= 2, IWX= 5, IWY= 5, result  4 is 3645.08
 Type= 2, IWA= 2, IWB= 3, IWX= 5, IWY= 5, result  4 is 1633.21
 Type= 2, IWA= 2, IWB= 4, IWX= 5, IWY= 5, result  4 is  481.28
 Type= 2, IWA= 2, IWB= 5, IWX= 1, IWY= 1, result  4 is 4096.34
 Type= 2, IWA= 2, IWB= 5, IWX= 1, IWY= 2, result  4 is 3817.57
 Type= 2, IWA= 2, IWB= 5, IWX= 1, IWY= 3, result  4 is 2120.79
 Type= 2, IWA= 2, IWB= 5, IWX= 1, IWY= 4, result  4 is  288.27
 Type= 2, IWA= 2, IWB= 5, IWX= 2, IWY= 1, result  4 is 3817.57
 Type= 2, IWA= 2, IWB= 5, IWX= 2, IWY= 2, result  4 is 3707.78
 Type= 2, IWA= 2, IWB= 5, IWX= 2, IWY= 3, result  4 is 2114.70
 Type= 2, IWA= 2, IWB= 5, IWX= 2, IWY= 4, result  4 is  288.26
 Type= 2, IWA= 2, IWB= 5, IWX= 3, IWY= 1, result  4 is 2120.79
 Type= 2, IWA= 2, IWB= 5, IWX= 3, IWY= 2, result  4 is 2114.70
 Type= 2, IWA= 2, IWB= 5, IWX= 3, IWY= 3, result  4 is 1697.05
 Type= 2, IWA= 2, IWB= 5, IWX= 3, IWY= 4, result  4 is  286.85
 Type= 2, IWA= 2, IWB= 5, IWX= 4, IWY= 1, result  4 is  288.27
 Type= 2, IWA= 2, IWB= 5, IWX= 4, IWY= 2, result  4 is  288.26
 Type= 2, IWA= 2, IWB= 5, IWX= 4, IWY= 3, result  4 is  286.85
 Type= 2, IWA= 2, IWB= 5, IWX= 4, IWY= 4, result  4 is  204.34
 Type= 2, IWA= 3, IWB= 1, IWX= 5, IWY= 5, result  4 is 4780.11
 Type= 2, IWA= 3, IWB= 2, IWX= 5, IWY= 5, result  4 is 4729.52
 Type= 2, IWA= 3, IWB= 3, IWX= 5, IWY= 5, result  4 is 3176.28
 Type= 2, IWA= 3, IWB= 4, IWX= 5, IWY= 5, result  4 is  524.84
 Type= 2, IWA= 3, IWB= 5, IWX= 1, IWY= 1, result  4 is 4096.79
 Type= 2, IWA= 3, IWB= 5, IWX= 1, IWY= 2, result  4 is 3817.99
 Type= 2, IWA= 3, IWB= 5, IWX= 1, IWY= 3, result  4 is 2121.02
 Type= 2, IWA= 3, IWB= 5, IWX= 1, IWY= 4, result  4 is  288.30
 Type= 2, IWA= 3, IWB= 5, IWX= 2, IWY= 1, result  4 is 3817.99
 Type= 2, IWA= 3, IWB= 5, IWX= 2, IWY= 2, result  4 is 3708.19
 Type= 2, IWA= 3, IWB= 5, IWX= 2, IWY= 3, result  4 is 2114.93
 Type= 2, IWA= 3, IWB= 5, IWX= 2, IWY= 4, result  4 is  288.29
 Type= 2, IWA= 3, IWB= 5, IWX= 3, IWY= 1, result  4 is 2121.02
 Type= 2, IWA= 3, IWB= 5, IWX= 3, IWY= 2, result  4 is 2114.93
 Type= 2, IWA= 3, IWB= 5, IWX= 3, IWY= 3, result  4 is 1697.24
 Type= 2, IWA= 3, IWB= 5, IWX= 3, IWY= 4, result  4 is  286.89
 Type= 2, IWA= 3, IWB= 5, IWX= 4, IWY= 1, result  4 is  288.30
 Type= 2, IWA= 3, IWB= 5, IWX= 4, IWY= 2, result  4 is  288.29
 Type= 2, IWA= 3, IWB= 5, IWX= 4, IWY= 3, result  4 is  286.89
 Type= 2, IWA= 3, IWB= 5, IWX= 4, IWY= 4, result  4 is  204.37
 Type= 2, IWA= 4, IWB= 1, IWX= 5, IWY= 5, result  4 is  638.70
 Type= 2, IWA= 4, IWB= 2, IWX= 5, IWY= 5, result  4 is  643.37
 Type= 2, IWA= 4, IWB= 3, IWX= 5, IWY= 5, result  4 is  678.08
 Type= 2, IWA= 4, IWB= 4, IWX= 5, IWY= 5, result  4 is  547.42
 Type= 2, IWA= 4, IWB= 5, IWX= 1, IWY= 1, result  4 is 4101.29
 Type= 2, IWA= 4, IWB= 5, IWX= 1, IWY= 2, result  4 is 3822.19
 Type= 2, IWA= 4, IWB= 5, IWX= 1, IWY= 3, result  4 is 2123.35
 Type= 2, IWA= 4, IWB= 5, IWX= 1, IWY= 4, result  4 is  288.62
 Type= 2, IWA= 4, IWB= 5, IWX= 2, IWY= 1, result  4 is 3822.19
 Type= 2, IWA= 4, IWB= 5, IWX= 2, IWY= 2, result  4 is 3712.26
 Type= 2, IWA= 4, IWB= 5, IWX= 2, IWY= 3, result  4 is 2117.25
 Type= 2, IWA= 4, IWB= 5, IWX= 2, IWY= 4, result  4 is  288.61
 Type= 2, IWA= 4, IWB= 5, IWX= 3, IWY= 1, result  4 is 2123.35
 Type= 2, IWA= 4, IWB= 5, IWX= 3, IWY= 2, result  4 is 2117.25
 Type= 2, IWA= 4, IWB= 5, IWX= 3, IWY= 3, result  4 is 1699.11
 Type= 2, IWA= 4, IWB= 5, IWX= 3, IWY= 4, result  4 is  287.20
 Type= 2, IWA= 4, IWB= 5, IWX= 4, IWY= 1, result  4 is  288.62
 Type= 2, IWA= 4, IWB= 5, IWX= 4, IWY= 2, result  4 is  288.61
 Type= 2, IWA= 4, IWB= 5, IWX= 4, IWY= 3, result  4 is  287.20
 Type= 2, IWA= 4, IWB= 5, IWX= 4, IWY= 4, result  4 is  204.59
 Type= 2, IWA= 5, IWB= 1, IWX= 1, IWY= 1, result  4 is 3.355D+07
 Type= 2, IWA= 5, IWB= 1, IWX= 1, IWY= 2, result  4 is 3.127D+07
 Type= 2, IWA= 5, IWB= 1, IWX= 1, IWY= 3, result  4 is 1.737D+07
 Type= 2, IWA= 5, IWB= 1, IWX= 1, IWY= 4, result  4 is 2.361D+06
 Type= 2, IWA= 5, IWB= 1, IWX= 1, IWY= 5, result  4 is 2896.66
 Type= 2, IWA= 5, IWB= 1, IWX= 2, IWY= 1, result  4 is 3.127D+07
 Type= 2, IWA= 5, IWB= 1, IWX= 2, IWY= 2, result  4 is 3.037D+07
 Type= 2, IWA= 5, IWB= 1, IWX= 2, IWY= 3, result  4 is 1.732D+07
 Type= 2, IWA= 5, IWB= 1, IWX= 2, IWY= 4, result  4 is 2.361D+06
 Type= 2, IWA= 5, IWB= 1, IWX= 2, IWY= 5, result  4 is 2896.66
 Type= 2, IWA= 5, IWB= 1, IWX= 3, IWY= 1, result  4 is 1.737D+07
 Type= 2, IWA= 5, IWB= 1, IWX= 3, IWY= 2, result  4 is 1.732D+07
 Type= 2, IWA= 5, IWB= 1, IWX= 3, IWY= 3, result  4 is 1.390D+07
 Type= 2, IWA= 5, IWB= 1, IWX= 3, IWY= 4, result  4 is 2.350D+06
 Type= 2, IWA= 5, IWB= 1, IWX= 3, IWY= 5, result  4 is 2896.66
 Type= 2, IWA= 5, IWB= 1, IWX= 4, IWY= 1, result  4 is 2.361D+06
 Type= 2, IWA= 5, IWB= 1, IWX= 4, IWY= 2, result  4 is 2.361D+06
 Type= 2, IWA= 5, IWB= 1, IWX= 4, IWY= 3, result  4 is 2.350D+06
 Type= 2, IWA= 5, IWB= 1, IWX= 4, IWY= 4, result  4 is 1.674D+06
 Type= 2, IWA= 5, IWB= 1, IWX= 4, IWY= 5, result  4 is 2896.66
 Type= 2, IWA= 5, IWB= 1, IWX= 5, IWY= 1, result  4 is 2896.66
 Type= 2, IWA= 5, IWB= 1, IWX= 5, IWY= 2, result  4 is 2896.66
 Type= 2, IWA= 5, IWB= 1, IWX= 5, IWY= 3, result  4 is 2896.66
 Type= 2, IWA= 5, IWB= 1, IWX= 5, IWY= 4, result  4 is 2896.66
 Type= 2, IWA= 5, IWB= 1, IWX= 5, IWY= 5, result  4 is 2048.38
 Type= 2, IWA= 5, IWB= 2, IWX= 1, IWY= 1, result  4 is 3.051D+07
 Type= 2, IWA= 5, IWB= 2, IWX= 1, IWY= 2, result  4 is 2.843D+07
 Type= 2, IWA= 5, IWB= 2, IWX= 1, IWY= 3, result  4 is 1.579D+07
 Type= 2, IWA= 5, IWB= 2, IWX= 1, IWY= 4, result  4 is 2.147D+06
 Type= 2, IWA= 5, IWB= 2, IWX= 1, IWY= 5, result  4 is 2633.68
 Type= 2, IWA= 5, IWB= 2, IWX= 2, IWY= 1, result  4 is 2.843D+07
 Type= 2, IWA= 5, IWB= 2, IWX= 2, IWY= 2, result  4 is 2.761D+07
 Type= 2, IWA= 5, IWB= 2, IWX= 2, IWY= 3, result  4 is 1.575D+07
 Type= 2, IWA= 5, IWB= 2, IWX= 2, IWY= 4, result  4 is 2.147D+06
 Type= 2, IWA= 5, IWB= 2, IWX= 2, IWY= 5, result  4 is 2633.68
 Type= 2, IWA= 5, IWB= 2, IWX= 3, IWY= 1, result  4 is 1.579D+07
 Type= 2, IWA= 5, IWB= 2, IWX= 3, IWY= 2, result  4 is 1.575D+07
 Type= 2, IWA= 5, IWB= 2, IWX= 3, IWY= 3, result  4 is 1.264D+07
 Type= 2, IWA= 5, IWB= 2, IWX= 3, IWY= 4, result  4 is 2.136D+06
 Type= 2, IWA= 5, IWB= 2, IWX= 3, IWY= 5, result  4 is 2633.68
 Type= 2, IWA= 5, IWB= 2, IWX= 4, IWY= 1, result  4 is 2.147D+06
 Type= 2, IWA= 5, IWB= 2, IWX= 4, IWY= 2, result  4 is 2.147D+06
 Type= 2, IWA= 5, IWB= 2, IWX= 4, IWY= 3, result  4 is 2.136D+06
 Type= 2, IWA= 5, IWB= 2, IWX= 4, IWY= 4, result  4 is 1.522D+06
 Type= 2, IWA= 5, IWB= 2, IWX= 4, IWY= 5, result  4 is 2633.68
 Type= 2, IWA= 5, IWB= 2, IWX= 5, IWY= 1, result  4 is 2633.68
 Type= 2, IWA= 5, IWB= 2, IWX= 5, IWY= 2, result  4 is 2633.68
 Type= 2, IWA= 5, IWB= 2, IWX= 5, IWY= 3, result  4 is 2633.68
 Type= 2, IWA= 5, IWB= 2, IWX= 5, IWY= 4, result  4 is 2633.68
 Type= 2, IWA= 5, IWB= 2, IWX= 5, IWY= 5, result  4 is 1862.41
 Type= 2, IWA= 5, IWB= 3, IWX= 1, IWY= 1, result  4 is 1.678D+07
 Type= 2, IWA= 5, IWB= 3, IWX= 1, IWY= 2, result  4 is 1.564D+07
 Type= 2, IWA= 5, IWB= 3, IWX= 1, IWY= 3, result  4 is 8.688D+06
 Type= 2, IWA= 5, IWB= 3, IWX= 1, IWY= 4, result  4 is 1.181D+06
 Type= 2, IWA= 5, IWB= 3, IWX= 1, IWY= 5, result  4 is 1448.69
 Type= 2, IWA= 5, IWB= 3, IWX= 2, IWY= 1, result  4 is 1.564D+07
 Type= 2, IWA= 5, IWB= 3, IWX= 2, IWY= 2, result  4 is 1.519D+07
 Type= 2, IWA= 5, IWB= 3, IWX= 2, IWY= 3, result  4 is 8.663D+06
 Type= 2, IWA= 5, IWB= 3, IWX= 2, IWY= 4, result  4 is 1.181D+06
 Type= 2, IWA= 5, IWB= 3, IWX= 2, IWY= 5, result  4 is 1448.69
 Type= 2, IWA= 5, IWB= 3, IWX= 3, IWY= 1, result  4 is 8.688D+06
 Type= 2, IWA= 5, IWB= 3, IWX= 3, IWY= 2, result  4 is 8.663D+06
 Type= 2, IWA= 5, IWB= 3, IWX= 3, IWY= 3, result  4 is 6.952D+06
 Type= 2, IWA= 5, IWB= 3, IWX= 3, IWY= 4, result  4 is 1.175D+06
 Type= 2, IWA= 5, IWB= 3, IWX= 3, IWY= 5, result  4 is 1448.69
 Type= 2, IWA= 5, IWB= 3, IWX= 4, IWY= 1, result  4 is 1.181D+06
 Type= 2, IWA= 5, IWB= 3, IWX= 4, IWY= 2, result  4 is 1.181D+06
 Type= 2, IWA= 5, IWB= 3, IWX= 4, IWY= 3, result  4 is 1.175D+06
 Type= 2, IWA= 5, IWB= 3, IWX= 4, IWY= 4, result  4 is 8.371D+05
 Type= 2, IWA= 5, IWB= 3, IWX= 4, IWY= 5, result  4 is 1448.68
 Type= 2, IWA= 5, IWB= 3, IWX= 5, IWY= 1, result  4 is 1448.69
 Type= 2, IWA= 5, IWB= 3, IWX= 5, IWY= 2, result  4 is 1448.69
 Type= 2, IWA= 5, IWB= 3, IWX= 5, IWY= 3, result  4 is 1448.69
 Type= 2, IWA= 5, IWB= 3, IWX= 5, IWY= 4, result  4 is 1448.68
 Type= 2, IWA= 5, IWB= 3, IWX= 5, IWY= 5, result  4 is 1024.44
 Type= 2, IWA= 5, IWB= 4, IWX= 1, IWY= 1, result  4 is 3.055D+06
 Type= 2, IWA= 5, IWB= 4, IWX= 1, IWY= 2, result  4 is 2.846D+06
 Type= 2, IWA= 5, IWB= 4, IWX= 1, IWY= 3, result  4 is 1.581D+06
 Type= 2, IWA= 5, IWB= 4, IWX= 1, IWY= 4, result  4 is 2.149D+05
 Type= 2, IWA= 5, IWB= 4, IWX= 1, IWY= 5, result  4 is  263.69
 Type= 2, IWA= 5, IWB= 4, IWX= 2, IWY= 1, result  4 is 2.846D+06
 Type= 2, IWA= 5, IWB= 4, IWX= 2, IWY= 2, result  4 is 2.765D+06
 Type= 2, IWA= 5, IWB= 4, IWX= 2, IWY= 3, result  4 is 1.577D+06
 Type= 2, IWA= 5, IWB= 4, IWX= 2, IWY= 4, result  4 is 2.149D+05
 Type= 2, IWA= 5, IWB= 4, IWX= 2, IWY= 5, result  4 is  263.69
 Type= 2, IWA= 5, IWB= 4, IWX= 3, IWY= 1, result  4 is 1.581D+06
 Type= 2, IWA= 5, IWB= 4, IWX= 3, IWY= 2, result  4 is 1.577D+06
 Type= 2, IWA= 5, IWB= 4, IWX= 3, IWY= 3, result  4 is 1.265D+06
 Type= 2, IWA= 5, IWB= 4, IWX= 3, IWY= 4, result  4 is 2.139D+05
 Type= 2, IWA= 5, IWB= 4, IWX= 3, IWY= 5, result  4 is  263.69
 Type= 2, IWA= 5, IWB= 4, IWX= 4, IWY= 1, result  4 is 2.149D+05
 Type= 2, IWA= 5, IWB= 4, IWX= 4, IWY= 2, result  4 is 2.149D+05
 Type= 2, IWA= 5, IWB= 4, IWX= 4, IWY= 3, result  4 is 2.139D+05
 Type= 2, IWA= 5, IWB= 4, IWX= 4, IWY= 4, result  4 is 1.524D+05
 Type= 2, IWA= 5, IWB= 4, IWX= 4, IWY= 5, result  4 is  263.69
 Type= 2, IWA= 5, IWB= 4, IWX= 5, IWY= 1, result  4 is  263.69
 Type= 2, IWA= 5, IWB= 4, IWX= 5, IWY= 2, result  4 is  263.69
 Type= 2, IWA= 5, IWB= 4, IWX= 5, IWY= 3, result  4 is  263.69
 Type= 2, IWA= 5, IWB= 4, IWX= 5, IWY= 4, result  4 is  263.69
 Type= 2, IWA= 5, IWB= 4, IWX= 5, IWY= 5, result  4 is  186.47
 Type= 2, IWA= 5, IWB= 5, IWX= 1, IWY= 1, result  4 is 1.158D+04
 Type= 2, IWA= 5, IWB= 5, IWX= 1, IWY= 2, result  4 is 1.080D+04
 Type= 2, IWA= 5, IWB= 5, IWX= 1, IWY= 3, result  4 is 5997.33
 Type= 2, IWA= 5, IWB= 5, IWX= 1, IWY= 4, result  4 is  815.19
 Type= 2, IWA= 5, IWB= 5, IWX= 2, IWY= 1, result  4 is 1.080D+04
 Type= 2, IWA= 5, IWB= 5, IWX= 2, IWY= 2, result  4 is 1.049D+04
 Type= 2, IWA= 5, IWB= 5, IWX= 2, IWY= 3, result  4 is 5980.12
 Type= 2, IWA= 5, IWB= 5, IWX= 2, IWY= 4, result  4 is  815.15
 Type= 2, IWA= 5, IWB= 5, IWX= 3, IWY= 1, result  4 is 5997.33
 Type= 2, IWA= 5, IWB= 5, IWX= 3, IWY= 2, result  4 is 5980.12
 Type= 2, IWA= 5, IWB= 5, IWX= 3, IWY= 3, result  4 is 4799.16
 Type= 2, IWA= 5, IWB= 5, IWX= 3, IWY= 4, result  4 is  811.19
 Type= 2, IWA= 5, IWB= 5, IWX= 4, IWY= 1, result  4 is  815.19
 Type= 2, IWA= 5, IWB= 5, IWX= 4, IWY= 2, result  4 is  815.15
 Type= 2, IWA= 5, IWB= 5, IWX= 4, IWY= 3, result  4 is  811.19
 Type= 2, IWA= 5, IWB= 5, IWX= 4, IWY= 4, result  4 is  577.87
 DXV drivers:    200 out of   5000 tests failed to pass the threshold

 -----------------------------------------------------------------------

 Tests of the Generalized Nonsymmetric Eigenvalue Problem Expert Driver DGGEVX

 LAPACK VERSION 3.2.0

 The following parameter values will be used:
    N:         0
    NB:        1
    NBMIN:     1
    NX:        1
    NS:        2
    MAXB:      1

 Relative machine underflow is taken to be    0.222507-307
 Relative machine overflow  is taken to be    0.179769+309
 Relative machine precision is taken to be    0.111022D-15

 Routines pass computational tests if test ratio is less than   10.00


 DXV routines passed the tests of the error exits ( 87 tests done)

 All tests for DXV drivers  passed the threshold (     8 tests run)

 -----------------------------------------------------------------------


 End of tests
 Total time used =         0.80 seconds


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