zget24.f - Man Page

subroutine zget24 (comp, jtype, thresh, iseed, nounit, n, a, lda, h, ht, w, wt, wtmp, vs, ldvs, vs1, rcdein, rcdvin, nslct, islct, isrt, result, work, lwork, rwork, bwork, info)
ZGET24

ZGET24

Purpose:

    ZGET24 checks the nonsymmetric eigenvalue (Schur form) problem
    expert driver ZGEESX.

    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 ZGEESX 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 ZGEESX 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.

Parameters

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 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 ZGEESX.

HT

          HT is COMPLEX*16 array, dimension (LDA, N)
          Yet another copy of the test matrix A, modified by ZGEESX.

W

          W is COMPLEX*16 array, dimension (N)
          The computed eigenvalues of A.

WT

          WT is COMPLEX*16 array, dimension (N)
          Like W, this array contains the eigenvalues of A,
          but those computed when ZGEESX only computes a partial
          eigendecomposition, i.e. not Schur vectors

WTMP

          WTMP is COMPLEX*16 array, dimension (N)
          Like W, this array contains the eigenvalues of A,
          but sorted by increasing real or imaginary part.

VS

          VS is COMPLEX*16 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*16 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 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 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 COMPLEX*16 array, dimension (2*N*N)

LWORK

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

RWORK

          RWORK is DOUBLE PRECISION 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, ZGEESX returned an error code, the absolute
                 value of which is returned.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 331 of file zget24.f.