Tests of the Generalized Nonsymmetric Eigenvalue Problem Driver CGGEV LAPACK VERSION 3.0, released June 30, 1999 The following parameter values will be used: M: 2 6 8 10 12 20 N: 2 6 8 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 0.222045E-15 Routines pass computational tests if test ratio is less than 10.00 CGV routines passed the tests of the error exits ( 85 tests done) All tests for CGV drivers passed the threshold ( 1092 tests run) ----------------------------------------------------------------------- Tests of the Generalized Nonsymmetric Eigenvalue Problem Driver CGGES LAPACK VERSION 3.0, released June 30, 1999 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 0.222045E-15 Routines pass computational tests if test ratio is less than 10.00 CGS routines passed the tests of the error exits ( 85 tests done) All tests for CGS drivers passed the threshold ( 1560 tests run) ----------------------------------------------------------------------- Tests of the Generalized Nonsymmetric Eigenvalue Problem Expert Driver CGGESX LAPACK VERSION 3.0, released June 30, 1999 The following parameter values will be used: N: 6 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 0.222045E-15 Routines pass computational tests if test ratio is less than 10.00 CGX routines passed the tests of the error exits ( 85 tests done) CGX -- Complex Expert Generalized Schur form problem driver Matrix types: 1: A is a block diagonal matrix of Jordan blocks and B is the identity matrix, 2: A and B are upper triangular matrices, 3: A and B are as type 2, but each second diagonal block in A_11 and each third diaongal block in A_22 are 2x2 blocks, 4: A and B are block diagonal matrices, 5: (A,B) has potentially close or common eigenvalues. Tests performed: (S is Schur, T is triangular, Q and Z are unitary, a is alpha, b is beta, and ' means transpose.) 1 = | A - Q S Z' | / ( |A| n ulp ) 2 = | B - Q T Z' | / ( |B| n ulp ) 3 = | I - QQ' | / ( n ulp ) 4 = | I - ZZ' | / ( n ulp ) 5 = 1/ULP if A is not in Schur form S 6 = difference between (alpha,beta) and diagonals of (S,T) 7 = 1/ULP if SDIM is not the correct number of selected eigenvalues 8 = 1/ULP if DIFEST/DIFTRU > 10*THRESH or DIFTRU/DIFEST > 10*THRESH 9 = 1/ULP if DIFEST <> 0 or DIFTRU > ULP*norm(A,B) when reordering fails 10 = 1/ULP if PLEST/PLTRU > THRESH or PLTRU/PLEST > THRESH ( Test 10 is only for input examples ) Matrix order= 5, type= 1, a=0.2107E-07, order(A_11)= 2, result 8 is 0.5788E+06 Matrix order= 4, type= 1, a=0.2107E-07, order(A_11)= 3, result 8 is 873.82 Matrix order= 6, type= 1, a=0.2107E-07, order(A_11)= 3, result 8 is 0.7443E+08 Matrix order= 6, type= 1, a=0.2107E-07, order(A_11)= 4, result 8 is 0.7345E+09 Matrix order= 6, type= 1, a=0.2107E-07, order(A_11)= 1, result 8 is 0.4737E+06 Matrix order= 6, type= 1, a=0.2107E-07, order(A_11)= 2, result 8 is 0.2435E+09 Matrix order= 5, type= 1, a=0.2107E-07, order(A_11)= 4, result 8 is 137.18 Matrix order= 6, type= 1, a=0.2107E-07, order(A_11)= 5, result 8 is 0.2860E+06 Matrix order= 3, type= 5, a=0.4745E+08, order(A_11)= 1, result 8 is 0.1238E+07 Matrix order= 5, type= 5, a=0.4745E+08, order(A_11)= 1, result 8 is 0.1448E+07 CGX drivers: 10 out of 2250 tests failed to pass the threshold ----------------------------------------------------------------------- Tests of the Generalized Nonsymmetric Eigenvalue Problem Expert Driver CGGEVX LAPACK VERSION 3.0, released June 30, 1999 The following parameter values will be used: N: 6 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 0.222045E-15 Routines pass computational tests if test ratio is less than 10.00 CXV routines passed the tests of the error exits ( 85 tests done) CXV -- Complex 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= 1, IWY= 5, result 4 is 1988.72 Type= 2, IWA= 1, IWB= 1, IWX= 2, IWY= 5, result 4 is 1916.95 Type= 2, IWA= 1, IWB= 1, IWX= 3, IWY= 5, result 4 is 1274.32 Type= 2, IWA= 1, IWB= 1, IWX= 4, IWY= 5, result 4 is 215.22 Type= 2, IWA= 1, IWB= 1, IWX= 5, IWY= 1, result 4 is 2038.01 Type= 2, IWA= 1, IWB= 1, IWX= 5, IWY= 2, result 4 is 2098.67 Type= 2, IWA= 1, IWB= 1, IWX= 5, IWY= 3, result 4 is 1817.24 Type= 2, IWA= 1, IWB= 1, IWX= 5, IWY= 4, result 4 is 209.88 Type= 2, IWA= 5, IWB= 1, IWX= 1, IWY= 5, result 4 is 4302.03 Type= 2, IWA= 5, IWB= 1, IWX= 2, IWY= 5, result 4 is 4343.48 Type= 2, IWA= 5, IWB= 1, IWX= 3, IWY= 5, result 4 is 4656.13 Type= 2, IWA= 5, IWB= 1, IWX= 4, IWY= 5, result 4 is 2171.24 Type= 2, IWA= 5, IWB= 2, IWX= 1, IWY= 5, result 4 is 3919.79 Type= 2, IWA= 5, IWB= 2, IWX= 2, IWY= 5, result 4 is 3954.31 Type= 2, IWA= 5, IWB= 2, IWX= 3, IWY= 5, result 4 is 4221.04 Type= 2, IWA= 5, IWB= 2, IWX= 4, IWY= 5, result 4 is 2168.55 Type= 2, IWA= 5, IWB= 3, IWX= 1, IWY= 5, result 4 is 2171.26 Type= 2, IWA= 5, IWB= 3, IWX= 2, IWY= 5, result 4 is 2181.97 Type= 2, IWA= 5, IWB= 3, IWX= 3, IWY= 5, result 4 is 2272.29 Type= 2, IWA= 5, IWB= 3, IWX= 4, IWY= 5, result 4 is 1943.22 Type= 2, IWA= 5, IWB= 4, IWX= 1, IWY= 5, result 4 is 395.97 Type= 2, IWA= 5, IWB= 4, IWX= 2, IWY= 5, result 4 is 396.32 Type= 2, IWA= 5, IWB= 4, IWX= 3, IWY= 5, result 4 is 399.53 Type= 2, IWA= 5, IWB= 4, IWX= 4, IWY= 5, result 4 is 427.10 CXV drivers: 24 out of 5000 tests failed to pass the threshold ----------------------------------------------------------------------- Tests of the Generalized Nonsymmetric Eigenvalue Problem Expert Driver CGGESX LAPACK VERSION 3.0, released June 30, 1999 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 0.222045E-15 Routines pass computational tests if test ratio is less than 10.00 CGX routines passed the tests of the error exits ( 85 tests done) All tests for CGX drivers passed the threshold ( 20 tests run) ----------------------------------------------------------------------- Tests of the Generalized Nonsymmetric Eigenvalue Problem Expert Driver CGGEVX LAPACK VERSION 3.0, released June 30, 1999 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 0.222045E-15 Routines pass computational tests if test ratio is less than 10.00 CXV routines passed the tests of the error exits ( 85 tests done) All tests for CXV drivers passed the threshold ( 8 tests run) ----------------------------------------------------------------------- End of tests Total time used = 3.93 seconds