DGET24 checks the nonsymmetric eigenvalue (Schur form) problem


    expert driver DGEESX.


    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 WR+sqrt(-1)*WI 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 WR+sqrt(-1)*WI are eigenvalues of T


            1/ulp otherwise


            If workspace sufficient, also compare WR, WI 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 DGEESX 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 DGEESX 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 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.

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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDA, N)


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

HT

          HT is DOUBLE PRECISION array, dimension (LDA, N)


          Yet another copy of the test matrix A, modified by DGEESX.

WR

          WR is DOUBLE PRECISION array, dimension (N)

WI

          WI is DOUBLE PRECISION array, dimension (N)


          The real and imaginary parts of the eigenvalues of A.


          On exit, WR + WI*i are the eigenvalues of the matrix in A.

WRT

          WRT is DOUBLE PRECISION array, dimension (N)

WIT

          WIT is DOUBLE PRECISION array, dimension (N)


          Like WR, WI, these arrays contain the eigenvalues of A,


          but those computed when DGEESX only computes a partial


          eigendecomposition, i.e. not Schur vectors

WRTMP

          WRTMP is DOUBLE PRECISION array, dimension (N)

WITMP

          WITMP is DOUBLE PRECISION array, dimension (N)


          Like WR, WI, these arrays contain the eigenvalues of A,


          but sorted by increasing real part.

VS

          VS is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDVS, N)


          VS1 holds another copy of the computed Schur vectors.

RCDEIN

          RCDEIN is DOUBLE PRECISION


          When COMP = .TRUE. RCDEIN holds the precomputed reciprocal


          condition number for the average of selected eigenvalues.

RCDVIN

          RCDVIN is DOUBLE PRECISION


          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 part is selected.


          Not referenced if COMP = .FALSE.

RESULT

          RESULT is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LWORK)

LWORK

          LWORK is INTEGER


          The number of entries in WORK to be passed to DGEESX. This


          must be at least 3*N, and N+N**2 if tests 14--16 are to


          be performed.

IWORK

          IWORK is INTEGER array, dimension (N*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, DGEESX returned an error code, the absolute


                 value of which is returned.

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