cget243

!>
!>    CGET24 checks the nonsymmetric eigenvalue (Schur form) problem
!>    expert driver CGEESX.
!>
!>    If COMP = .FALSE., the first 13 of the following tests will be
!>    be performed on the input matrix A, and also tests 14 and 15
!>    if LWORK is sufficiently large.
!>    If COMP = .TRUE., all 17 test will be performed.
!>
!>    (1)     0 if T is in Schur form, 1/ulp otherwise
!>           (no sorting of eigenvalues)
!>
!>    (2)     | A - VS T VS' | / ( n |A| ulp )
!>
!>      Here VS is the matrix of Schur eigenvectors, and T is in Schur
!>      form  (no sorting of eigenvalues).
!>
!>    (3)     | I - VS VS' | / ( n ulp ) (no sorting of eigenvalues).
!>
!>    (4)     0     if W are eigenvalues of T
!>            1/ulp otherwise
!>            (no sorting of eigenvalues)
!>
!>    (5)     0     if T(with VS) = T(without VS),
!>            1/ulp otherwise
!>            (no sorting of eigenvalues)
!>
!>    (6)     0     if eigenvalues(with VS) = eigenvalues(without VS),
!>            1/ulp otherwise
!>            (no sorting of eigenvalues)
!>
!>    (7)     0 if T is in Schur form, 1/ulp otherwise
!>            (with sorting of eigenvalues)
!>
!>    (8)     | A - VS T VS' | / ( n |A| ulp )
!>
!>      Here VS is the matrix of Schur eigenvectors, and T is in Schur
!>      form  (with sorting of eigenvalues).
!>
!>    (9)     | I - VS VS' | / ( n ulp ) (with sorting of eigenvalues).
!>
!>    (10)    0     if W are eigenvalues of T
!>            1/ulp otherwise
!>            If workspace sufficient, also compare W with and
!>            without reciprocal condition numbers
!>            (with sorting of eigenvalues)
!>
!>    (11)    0     if T(with VS) = T(without VS),
!>            1/ulp otherwise
!>            If workspace sufficient, also compare T with and without
!>            reciprocal condition numbers
!>            (with sorting of eigenvalues)
!>
!>    (12)    0     if eigenvalues(with VS) = eigenvalues(without VS),
!>            1/ulp otherwise
!>            If workspace sufficient, also compare VS with and without
!>            reciprocal condition numbers
!>            (with sorting of eigenvalues)
!>
!>    (13)    if sorting worked and SDIM is the number of
!>            eigenvalues which were SELECTed
!>            If workspace sufficient, also compare SDIM with and
!>            without reciprocal condition numbers
!>
!>    (14)    if RCONDE the same no matter if VS and/or RCONDV computed
!>
!>    (15)    if RCONDV the same no matter if VS and/or RCONDE computed
!>
!>    (16)  |RCONDE - RCDEIN| / cond(RCONDE)
!>
!>       RCONDE is the reciprocal average eigenvalue condition number
!>       computed by CGEESX and RCDEIN (the precomputed true value)
!>       is supplied as input.  cond(RCONDE) is the condition number
!>       of RCONDE, and takes errors in computing RCONDE into account,
!>       so that the resulting quantity should be O(ULP). cond(RCONDE)
!>       is essentially given by norm(A)/RCONDV.
!>
!>    (17)  |RCONDV - RCDVIN| / cond(RCONDV)
!>
!>       RCONDV is the reciprocal right invariant subspace condition
!>       number computed by CGEESX and RCDVIN (the precomputed true
!>       value) is supplied as input. cond(RCONDV) is the condition
!>       number of RCONDV, and takes errors in computing RCONDV into
!>       account, so that the resulting quantity should be O(ULP).
!>       cond(RCONDV) is essentially given by norm(A)/RCONDE.
!> 

COMP

!>          COMP is LOGICAL
!>          COMP describes which input tests to perform:
!>            = .FALSE. if the computed condition numbers are not to
!>                      be tested against RCDVIN and RCDEIN
!>            = .TRUE.  if they are to be compared
!> 

JTYPE

!>          JTYPE is INTEGER
!>          Type of input matrix. Used to label output if error occurs.
!> 

ISEED

!>          ISEED is INTEGER array, dimension (4)
!>          If COMP = .FALSE., the random number generator seed
!>          used to produce matrix.
!>          If COMP = .TRUE., ISEED(1) = the number of the example.
!>          Used to label output if error occurs.
!> 

THRESH

!>          THRESH is REAL
!>          A test will count as  if the , computed as
!>          described above, exceeds THRESH.  Note that the error
!>          is scaled to be O(1), so THRESH should be a reasonably
!>          small multiple of 1, e.g., 10 or 100.  In particular,
!>          it should not depend on the precision (single vs. double)
!>          or the size of the matrix.  It must be at least zero.
!> 

NOUNIT

!>          NOUNIT is INTEGER
!>          The FORTRAN unit number for printing out error messages
!>          (e.g., if a routine returns INFO not equal to 0.)
!> 

N

!>          N is INTEGER
!>          The dimension of A. N must be at least 0.
!> 

A

!>          A is COMPLEX array, dimension (LDA, N)
!>          Used to hold the matrix whose eigenvalues are to be
!>          computed.
!> 

LDA

!>          LDA is INTEGER
!>          The leading dimension of A, and H. LDA must be at
!>          least 1 and at least N.
!> 

H

!>          H is COMPLEX array, dimension (LDA, N)
!>          Another copy of the test matrix A, modified by CGEESX.
!> 

HT

!>          HT is COMPLEX array, dimension (LDA, N)
!>          Yet another copy of the test matrix A, modified by CGEESX.
!> 

W

!>          W is COMPLEX array, dimension (N)
!>          The computed eigenvalues of A.
!> 

WT

!>          WT is COMPLEX array, dimension (N)
!>          Like W, this array contains the eigenvalues of A,
!>          but those computed when CGEESX only computes a partial
!>          eigendecomposition, i.e. not Schur vectors
!> 

WTMP

!>          WTMP is COMPLEX array, dimension (N)
!>          Like W, this array contains the eigenvalues of A,
!>          but sorted by increasing real or imaginary part.
!> 

VS

!>          VS is COMPLEX array, dimension (LDVS, N)
!>          VS holds the computed Schur vectors.
!> 

LDVS

!>          LDVS is INTEGER
!>          Leading dimension of VS. Must be at least max(1, N).
!> 

VS1

!>          VS1 is COMPLEX array, dimension (LDVS, N)
!>          VS1 holds another copy of the computed Schur vectors.
!> 

RCDEIN

!>          RCDEIN is REAL
!>          When COMP = .TRUE. RCDEIN holds the precomputed reciprocal
!>          condition number for the average of selected eigenvalues.
!> 

RCDVIN

!>          RCDVIN is REAL
!>          When COMP = .TRUE. RCDVIN holds the precomputed reciprocal
!>          condition number for the selected right invariant subspace.
!> 

NSLCT

!>          NSLCT is INTEGER
!>          When COMP = .TRUE. the number of selected eigenvalues
!>          corresponding to the precomputed values RCDEIN and RCDVIN.
!> 

ISLCT

!>          ISLCT is INTEGER array, dimension (NSLCT)
!>          When COMP = .TRUE. ISLCT selects the eigenvalues of the
!>          input matrix corresponding to the precomputed values RCDEIN
!>          and RCDVIN. For I=1, ... ,NSLCT, if ISLCT(I) = J, then the
!>          eigenvalue with the J-th largest real or imaginary part is
!>          selected. The real part is used if ISRT = 0, and the
!>          imaginary part if ISRT = 1.
!>          Not referenced if COMP = .FALSE.
!> 

ISRT

!>          ISRT is INTEGER
!>          When COMP = .TRUE., ISRT describes how ISLCT is used to
!>          choose a subset of the spectrum.
!>          Not referenced if COMP = .FALSE.
!> 

RESULT

!>          RESULT is REAL array, dimension (17)
!>          The values computed by the 17 tests described above.
!>          The values are currently limited to 1/ulp, to avoid
!>          overflow.
!> 

WORK

!>          WORK is COMPLEX array, dimension (2*N*N)
!> 

LWORK

!>          LWORK is INTEGER
!>          The number of entries in WORK to be passed to CGEESX. This
!>          must be at least 2*N, and N*(N+1)/2 if tests 14--16 are to
!>          be performed.
!> 

RWORK

!>          RWORK is REAL array, dimension (N)
!> 

BWORK

!>          BWORK is LOGICAL array, dimension (N)
!> 

INFO

!>          INFO is INTEGER
!>          If 0,  successful exit.
!>          If <0, input parameter -INFO had an incorrect value.
!>          If >0, CGEESX returned an error code, the absolute
!>                 value of which is returned.
!> 

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.