TESTING/EIG/sget24.f(3)

NAME
TESTING/EIG/sget24.f

SYNOPSIS

  Functions/Subroutines
subroutine sget24 (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)
SGET24

Function/Subroutine Documentation

  subroutine sget24 (logical comp, integer jtype, real thresh, integer, dimension( 4 ) iseed, integer nounit, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( lda, * ) h, real, dimension( lda, * ) ht, real, dimension( * ) wr, real, dimension( * ) wi, real, dimension( * ) wrt, real, dimension( * ) wit, real, dimension( * ) wrtmp, real, dimension( * ) witmp, real, dimension( ldvs, * ) vs, integer ldvs, real, dimension( ldvs, * ) vs1, real rcdein, real rcdvin, integer nslct, integer, dimension( * ) islct, real, dimension( 17 ) result, real, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, logical, dimension( * ) bwork, integer info)

SGET24

Purpose:

        SGET24 checks the nonsymmetric eigenvalue (Schur form) problem
        expert driver SGEESX.
        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 SGEESX 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 SGEESX 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 REAL
              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 REAL 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 REAL array, dimension (LDA, N)
              Another copy of the test matrix A, modified by SGEESX.

    HT

              HT is REAL array, dimension (LDA, N)
              Yet another copy of the test matrix A, modified by SGEESX.

    WR

              WR is REAL array, dimension (N)

    WI

              WI is REAL 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 REAL array, dimension (N)

    WIT

              WIT is REAL array, dimension (N)
              Like WR, WI, these arrays contain the eigenvalues of A,
              but those computed when SGEESX only computes a partial
              eigendecomposition, i.e. not Schur vectors

    WRTMP

              WRTMP is REAL array, dimension (N)

    WITMP

              WITMP is REAL array, dimension (N)
              Like WR, WI, these arrays contain the eigenvalues of A,
              but sorted by increasing real part.

    VS

              VS is REAL 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 REAL array, dimension (LDVS, N)
              VS1 holds another copy of the computed Schur vectors.

    RCDEIN

              RCDEIN is REAL
              When COMP = .TRUE. RCDEIN holds the precomputed reciprocal
              condition number for the average of selected eigenvalues.

    RCDVIN

              RCDVIN is REAL
              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 REAL 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 REAL array, dimension (LWORK)

    LWORK

              LWORK is INTEGER
              The number of entries in WORK to be passed to SGEESX. 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, SGEESX 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 sget24.f.

Author

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