ZGET23  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 ZGEEVX 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 ZGEEVX 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 DOUBLE PRECISION


          A test will count as 'failed' if the 'error', 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*16 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*16 array, dimension (LDA,N)


          Another copy of the test matrix A, modified by ZGEEVX.

W

          W is COMPLEX*16 array, dimension (N)


          Contains the eigenvalues of A.

W1

          W1 is COMPLEX*16 array, dimension (N)


          Like W, this array contains the eigenvalues of A,


          but those computed when ZGEEVX only computes a partial


          eigendecomposition, i.e. not the eigenvalues and left


          and right eigenvectors.

VL

          VL is COMPLEX*16 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*16 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*16 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 DOUBLE PRECISION array, dimension (N)


          RCONDV holds the computed reciprocal condition numbers


          for eigenvectors.

RCNDV1

          RCNDV1 is DOUBLE PRECISION array, dimension (N)


          RCNDV1 holds more computed reciprocal condition numbers


          for eigenvectors.

RCDVIN

          RCDVIN is DOUBLE PRECISION array, dimension (N)


          When COMP = .TRUE. RCDVIN holds the precomputed reciprocal


          condition numbers for eigenvectors to be compared with


          RCONDV.

RCONDE

          RCONDE is DOUBLE PRECISION array, dimension (N)


          RCONDE holds the computed reciprocal condition numbers


          for eigenvalues.

RCNDE1

          RCNDE1 is DOUBLE PRECISION array, dimension (N)


          RCNDE1 holds more computed reciprocal condition numbers


          for eigenvalues.

RCDEIN

          RCDEIN is DOUBLE PRECISION array, dimension (N)


          When COMP = .TRUE. RCDEIN holds the precomputed reciprocal


          condition numbers for eigenvalues to be compared with


          RCONDE.

SCALE

          SCALE is DOUBLE PRECISION array, dimension (N)


          Holds information describing balancing of matrix.

SCALE1

          SCALE1 is DOUBLE PRECISION array, dimension (N)


          Holds information describing balancing of matrix.

RESULT

          RESULT is DOUBLE PRECISION 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*16 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 DOUBLE PRECISION array, dimension (2*N)

INFO

          INFO is INTEGER


          If 0,  successful exit.


          If <0, input parameter -INFO had an incorrect value.


          If >0, ZGEEVX returned an error code, the absolute


                 value of which is returned.

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