TESTING/EIG/dget24.f(3)

NAME
TESTING/EIG/dget24.f

SYNOPSIS

  Functions/Subroutines
subroutine dget24 (comp, jtype, thresh, iseed, nounit, n, a, lda, h, ht, wr, wi, wrt, wit, wrtmp, witmp, vs, ldvs, vs1, rcdein, rcdvin, nslct, islct, result, work, lwork, iwork, bwork, info)
DGET24

Function/Subroutine Documentation

  subroutine dget24 (logical comp, integer jtype, double precision thresh, integer, dimension( 4 ) iseed, integer nounit, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( lda, * ) h, double precision, dimension( lda, * ) ht, double precision, dimension( * ) wr, double precision, dimension( * ) wi, double precision, dimension( * ) wrt, double precision, dimension( * ) wit, double precision, dimension( * ) wrtmp, double precision, dimension( * ) witmp, double precision, dimension( ldvs, * ) vs, integer ldvs, double precision, dimension( ldvs, * ) vs1, double precision rcdein, double precision rcdvin, integer nslct, integer, dimension( * ) islct, double precision, dimension( 17 ) result, double precision, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, logical, dimension( * ) bwork, integer info)

DGET24

Purpose:

    !>
    !>    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.
    !>

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  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 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.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 339 of file dget24.f.

Author

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