cget233

!>
!>    CGET23  checks the nonsymmetric eigenvalue problem driver CGEEVX.
!>    If COMP = .FALSE., the first 8 of the following tests will be
!>    performed on the input matrix A, and also test 9 if LWORK is
!>    sufficiently large.
!>    if COMP is .TRUE. all 11 tests will be performed.
!>
!>    (1)     | A * VR - VR * W | / ( n |A| ulp )
!>
!>      Here VR is the matrix of unit right eigenvectors.
!>      W is a diagonal matrix with diagonal entries W(j).
!>
!>    (2)     | A**H * VL - VL * W**H | / ( n |A| ulp )
!>
!>      Here VL is the matrix of unit left eigenvectors, A**H is the
!>      conjugate transpose of A, and W is as above.
!>
!>    (3)     | |VR(i)| - 1 | / ulp and largest component real
!>
!>      VR(i) denotes the i-th column of VR.
!>
!>    (4)     | |VL(i)| - 1 | / ulp and largest component real
!>
!>      VL(i) denotes the i-th column of VL.
!>
!>    (5)     0 if W(full) = W(partial), 1/ulp otherwise
!>
!>      W(full) denotes the eigenvalues computed when VR, VL, RCONDV
!>      and RCONDE are also computed, and W(partial) denotes the
!>      eigenvalues computed when only some of VR, VL, RCONDV, and
!>      RCONDE are computed.
!>
!>    (6)     0 if VR(full) = VR(partial), 1/ulp otherwise
!>
!>      VR(full) denotes the right eigenvectors computed when VL, RCONDV
!>      and RCONDE are computed, and VR(partial) denotes the result
!>      when only some of VL and RCONDV are computed.
!>
!>    (7)     0 if VL(full) = VL(partial), 1/ulp otherwise
!>
!>      VL(full) denotes the left eigenvectors computed when VR, RCONDV
!>      and RCONDE are computed, and VL(partial) denotes the result
!>      when only some of VR and RCONDV are computed.
!>
!>    (8)     0 if SCALE, ILO, IHI, ABNRM (full) =
!>                 SCALE, ILO, IHI, ABNRM (partial)
!>            1/ulp otherwise
!>
!>      SCALE, ILO, IHI and ABNRM describe how the matrix is balanced.
!>      (full) is when VR, VL, RCONDE and RCONDV are also computed, and
!>      (partial) is when some are not computed.
!>
!>    (9)     0 if RCONDV(full) = RCONDV(partial), 1/ulp otherwise
!>
!>      RCONDV(full) denotes the reciprocal condition numbers of the
!>      right eigenvectors computed when VR, VL and RCONDE are also
!>      computed. RCONDV(partial) denotes the reciprocal condition
!>      numbers when only some of VR, VL and RCONDE are computed.
!>
!>   (10)     |RCONDV - RCDVIN| / cond(RCONDV)
!>
!>      RCONDV is the reciprocal right eigenvector condition number
!>      computed by CGEEVX 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.
!>
!>   (11)     |RCONDE - RCDEIN| / cond(RCONDE)
!>
!>      RCONDE is the reciprocal eigenvalue condition number
!>      computed by CGEEVX 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.
!> 

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
!> 

ISRT

!>          ISRT is INTEGER
!>          If COMP = .TRUE., ISRT indicates in how the eigenvalues
!>          corresponding to values in RCDVIN and RCDEIN are ordered:
!>            = 0 means the eigenvalues are sorted by
!>                increasing real part
!>            = 1 means the eigenvalues are sorted by
!>                increasing imaginary part
!>          If COMP = .FALSE., ISRT is not referenced.
!> 

BALANC

!>          BALANC is CHARACTER
!>          Describes the balancing option to be tested.
!>            = 'N' for no permuting or diagonal scaling
!>            = 'P' for permuting but no diagonal scaling
!>            = 'S' for no permuting but diagonal scaling
!>            = 'B' for permuting and diagonal scaling
!> 

JTYPE

!>          JTYPE is INTEGER
!>          Type of input matrix. 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.
!> 

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.
!> 

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 CGEEVX.
!> 

W

!>          W is COMPLEX array, dimension (N)
!>          Contains the eigenvalues of A.
!> 

W1

!>          W1 is COMPLEX array, dimension (N)
!>          Like W, this array contains the eigenvalues of A,
!>          but those computed when CGEEVX only computes a partial
!>          eigendecomposition, i.e. not the eigenvalues and left
!>          and right eigenvectors.
!> 

VL

!>          VL is COMPLEX array, dimension (LDVL,N)
!>          VL holds the computed left eigenvectors.
!> 

LDVL

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

VR

!>          VR is COMPLEX array, dimension (LDVR,N)
!>          VR holds the computed right eigenvectors.
!> 

LDVR

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

LRE

!>          LRE is COMPLEX array, dimension (LDLRE,N)
!>          LRE holds the computed right or left eigenvectors.
!> 

LDLRE

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

RCONDV

!>          RCONDV is REAL array, dimension (N)
!>          RCONDV holds the computed reciprocal condition numbers
!>          for eigenvectors.
!> 

RCNDV1

!>          RCNDV1 is REAL array, dimension (N)
!>          RCNDV1 holds more computed reciprocal condition numbers
!>          for eigenvectors.
!> 

RCDVIN

!>          RCDVIN is REAL array, dimension (N)
!>          When COMP = .TRUE. RCDVIN holds the precomputed reciprocal
!>          condition numbers for eigenvectors to be compared with
!>          RCONDV.
!> 

RCONDE

!>          RCONDE is REAL array, dimension (N)
!>          RCONDE holds the computed reciprocal condition numbers
!>          for eigenvalues.
!> 

RCNDE1

!>          RCNDE1 is REAL array, dimension (N)
!>          RCNDE1 holds more computed reciprocal condition numbers
!>          for eigenvalues.
!> 

RCDEIN

!>          RCDEIN is REAL array, dimension (N)
!>          When COMP = .TRUE. RCDEIN holds the precomputed reciprocal
!>          condition numbers for eigenvalues to be compared with
!>          RCONDE.
!> 

SCALE

!>          SCALE is REAL array, dimension (N)
!>          Holds information describing balancing of matrix.
!> 

SCALE1

!>          SCALE1 is REAL array, dimension (N)
!>          Holds information describing balancing of matrix.
!> 

RESULT

!>          RESULT is REAL array, dimension (11)
!>          The values computed by the 11 tests described above.
!>          The values are currently limited to 1/ulp, to avoid
!>          overflow.
!> 

WORK

!>          WORK is COMPLEX array, dimension (LWORK)
!> 

LWORK

!>          LWORK is INTEGER
!>          The number of entries in WORK.  This must be at least
!>          2*N, and 2*N+N**2 if tests 9, 10 or 11 are to be performed.
!> 

RWORK

!>          RWORK is REAL array, dimension (2*N)
!> 

INFO

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

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