TESTING/EIG/zdrvsx.f(3)

NAME
TESTING/EIG/zdrvsx.f

SYNOPSIS

  Functions/Subroutines
subroutine zdrvsx (nsizes, nn, ntypes, dotype, iseed, thresh, niunit, nounit, a, lda, h, ht, w, wt, wtmp, vs, ldvs, vs1, result, work, lwork, rwork, bwork, info)
ZDRVSX

Function/Subroutine Documentation

  subroutine zdrvsx (integer nsizes, integer, dimension( * ) nn, integer ntypes, logical, dimension( * ) dotype, integer, dimension( 4 ) iseed, double precision thresh, integer niunit, integer nounit, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( lda, * ) h, complex*16, dimension( lda, * ) ht, complex*16, dimension( * ) w, complex*16, dimension( * ) wt, complex*16, dimension( * ) wtmp, complex*16, dimension( ldvs, * ) vs, integer ldvs, complex*16, dimension( ldvs, * ) vs1, double precision, dimension( 17 ) result, complex*16, dimension( * ) work, integer lwork, double precision, dimension( * ) rwork, logical, dimension( * ) bwork, integer info)

ZDRVSX

Purpose:

    !>
    !>    ZDRVSX checks the nonsymmetric eigenvalue (Schur form) problem
    !>    expert driver ZGEESX.
    !>
    !>    ZDRVSX uses both test matrices generated randomly depending on
    !>    data supplied in the calling sequence, as well as on data
    !>    read from an input file and including precomputed condition
    !>    numbers to which it compares the ones it computes.
    !>
    !>    When ZDRVSX is called, a number of matrix  () and a
    !>    number of matrix  are specified.  For each size ()
    !>    and each type of matrix, one matrix will be generated and used
    !>    to test the nonsymmetric eigenroutines.  For each matrix, 15
    !>    tests 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
    !>
    !>    The  are specified by an array NN(1:NSIZES); the value of
    !>    each element NN(j) specifies one size.
    !>    The  are specified by a logical array DOTYPE( 1:NTYPES );
    !>    if DOTYPE(j) is .TRUE., then matrix type  will be generated.
    !>    Currently, the list of possible types is:
    !>
    !>    (1)  The zero matrix.
    !>    (2)  The identity matrix.
    !>    (3)  A (transposed) Jordan block, with 1's on the diagonal.
    !>
    !>    (4)  A diagonal matrix with evenly spaced entries
    !>         1, ..., ULP  and random complex angles.
    !>         (ULP = (first number larger than 1) - 1 )
    !>    (5)  A diagonal matrix with geometrically spaced entries
    !>         1, ..., ULP  and random complex angles.
    !>    (6)  A diagonal matrix with  entries 1, ULP, ..., ULP
    !>         and random complex angles.
    !>
    !>    (7)  Same as (4), but multiplied by a constant near
    !>         the overflow threshold
    !>    (8)  Same as (4), but multiplied by a constant near
    !>         the underflow threshold
    !>
    !>    (9)  A matrix of the form  U' T U, where U is unitary and
    !>         T has evenly spaced entries 1, ..., ULP with random
    !>         complex angles on the diagonal and random O(1) entries in
    !>         the upper triangle.
    !>
    !>    (10) A matrix of the form  U' T U, where U is unitary and
    !>         T has geometrically spaced entries 1, ..., ULP with random
    !>         complex angles on the diagonal and random O(1) entries in
    !>         the upper triangle.
    !>
    !>    (11) A matrix of the form  U' T U, where U is orthogonal and
    !>         T has  entries 1, ULP,..., ULP with random
    !>         complex angles on the diagonal and random O(1) entries in
    !>         the upper triangle.
    !>
    !>    (12) A matrix of the form  U' T U, where U is unitary and
    !>         T has complex eigenvalues randomly chosen from
    !>         ULP < |z| < 1   and random O(1) entries in the upper
    !>         triangle.
    !>
    !>    (13) A matrix of the form  X' T X, where X has condition
    !>         SQRT( ULP ) and T has evenly spaced entries 1, ..., ULP
    !>         with random complex angles on the diagonal and random O(1)
    !>         entries in the upper triangle.
    !>
    !>    (14) A matrix of the form  X' T X, where X has condition
    !>         SQRT( ULP ) and T has geometrically spaced entries
    !>         1, ..., ULP with random complex angles on the diagonal
    !>         and random O(1) entries in the upper triangle.
    !>
    !>    (15) A matrix of the form  X' T X, where X has condition
    !>         SQRT( ULP ) and T has  entries 1, ULP,..., ULP
    !>         with random complex angles on the diagonal and random O(1)
    !>         entries in the upper triangle.
    !>
    !>    (16) A matrix of the form  X' T X, where X has condition
    !>         SQRT( ULP ) and T has complex eigenvalues randomly chosen
    !>         from ULP < |z| < 1 and random O(1) entries in the upper
    !>         triangle.
    !>
    !>    (17) Same as (16), but multiplied by a constant
    !>         near the overflow threshold
    !>    (18) Same as (16), but multiplied by a constant
    !>         near the underflow threshold
    !>
    !>    (19) Nonsymmetric matrix with random entries chosen from (-1,1).
    !>         If N is at least 4, all entries in first two rows and last
    !>         row, and first column and last two columns are zero.
    !>    (20) Same as (19), but multiplied by a constant
    !>         near the overflow threshold
    !>    (21) Same as (19), but multiplied by a constant
    !>         near the underflow threshold
    !>
    !>    In addition, an input file will be read from logical unit number
    !>    NIUNIT. The file contains matrices along with precomputed
    !>    eigenvalues and reciprocal condition numbers for the eigenvalue
    !>    average and right invariant subspace. For these matrices, in
    !>    addition to tests (1) to (15) we will compute the following two
    !>    tests:
    !>
    !>   (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
    NSIZES

    !>          NSIZES is INTEGER
    !>          The number of sizes of matrices to use.  NSIZES must be at
    !>          least zero. If it is zero, no randomly generated matrices
    !>          are tested, but any test matrices read from NIUNIT will be
    !>          tested.
    !>

    NN

    !>          NN is INTEGER array, dimension (NSIZES)
    !>          An array containing the sizes to be used for the matrices.
    !>          Zero values will be skipped.  The values must be at least
    !>          zero.
    !>

    NTYPES

    !>          NTYPES is INTEGER
    !>          The number of elements in DOTYPE. NTYPES must be at least
    !>          zero. If it is zero, no randomly generated test matrices
    !>          are tested, but and test matrices read from NIUNIT will be
    !>          tested. If it is MAXTYP+1 and NSIZES is 1, then an
    !>          additional type, MAXTYP+1 is defined, which is to use
    !>          whatever matrix is in A.  This is only useful if
    !>          DOTYPE(1:MAXTYP) is .FALSE. and DOTYPE(MAXTYP+1) is .TRUE. .
    !>

    DOTYPE

    !>          DOTYPE is LOGICAL array, dimension (NTYPES)
    !>          If DOTYPE(j) is .TRUE., then for each size in NN a
    !>          matrix of that size and of type j will be generated.
    !>          If NTYPES is smaller than the maximum number of types
    !>          defined (PARAMETER MAXTYP), then types NTYPES+1 through
    !>          MAXTYP will not be generated.  If NTYPES is larger
    !>          than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES)
    !>          will be ignored.
    !>

    ISEED

    !>          ISEED is INTEGER array, dimension (4)
    !>          On entry ISEED specifies the seed of the random number
    !>          generator. The array elements should be between 0 and 4095;
    !>          if not they will be reduced mod 4096.  Also, ISEED(4) must
    !>          be odd.  The random number generator uses a linear
    !>          congruential sequence limited to small integers, and so
    !>          should produce machine independent random numbers. The
    !>          values of ISEED are changed on exit, and can be used in the
    !>          next call to ZDRVSX to continue the same random number
    !>          sequence.
    !>

    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.
    !>

    NIUNIT

    !>          NIUNIT is INTEGER
    !>          The FORTRAN unit number for reading in the data file of
    !>          problems to solve.
    !>

    NOUNIT

    !>          NOUNIT is INTEGER
    !>          The FORTRAN unit number for printing out error messages
    !>          (e.g., if a routine returns INFO not equal to 0.)
    !>

    A

    !>          A is COMPLEX*16 array, dimension (LDA, max(NN))
    !>          Used to hold the matrix whose eigenvalues are to be
    !>          computed.  On exit, A contains the last matrix actually used.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of A, and H. LDA must be at
    !>          least 1 and at least max( NN ).
    !>

    H

    !>          H is COMPLEX*16 array, dimension (LDA, max(NN))
    !>          Another copy of the test matrix A, modified by ZGEESX.
    !>

    HT

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

    W

    !>          W is COMPLEX*16 array, dimension (max(NN))
    !>          The computed eigenvalues of A.
    !>

    WT

    !>          WT is COMPLEX*16 array, dimension (max(NN))
    !>          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 (max(NN))
    !>          More temporary storage for eigenvalues.
    !>

    VS

    !>          VS is COMPLEX*16 array, dimension (LDVS, max(NN))
    !>          VS holds the computed Schur vectors.
    !>

    LDVS

    !>          LDVS is INTEGER
    !>          Leading dimension of VS. Must be at least max(1,max(NN)).
    !>

    VS1

    !>          VS1 is COMPLEX*16 array, dimension (LDVS, max(NN))
    !>          VS1 holds another copy of the computed Schur vectors.
    !>

    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 (LWORK)
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The number of entries in WORK.  This must be at least
    !>          max(1,2*NN(j)**2) for all j.
    !>

    RWORK

    !>          RWORK is DOUBLE PRECISION array, dimension (max(NN))
    !>

    BWORK

    !>          BWORK is LOGICAL array, dimension (max(NN))
    !>

    INFO

    !>          INFO is INTEGER
    !>          If 0,  successful exit.
    !>            <0,  input parameter -INFO is incorrect
    !>            >0,  ZLATMR, CLATMS, CLATME or ZGET24 returned an error
    !>                 code and INFO is its absolute value
    !>
    !>-----------------------------------------------------------------------
    !>
    !>     Some Local Variables and Parameters:
    !>     ---- ----- --------- --- ----------
    !>     ZERO, ONE       Real 0 and 1.
    !>     MAXTYP          The number of types defined.
    !>     NMAX            Largest value in NN.
    !>     NERRS           The number of tests which have exceeded THRESH
    !>     COND, CONDS,
    !>     IMODE           Values to be passed to the matrix generators.
    !>     ANORM           Norm of A; passed to matrix generators.
    !>
    !>     OVFL, UNFL      Overflow and underflow thresholds.
    !>     ULP, ULPINV     Finest relative precision and its inverse.
    !>     RTULP, RTULPI   Square roots of the previous 4 values.
    !>             The following four arrays decode JTYPE:
    !>     KTYPE(j)        The general type (1-10) for type .
    !>     KMODE(j)        The MODE value to be passed to the matrix
    !>                     generator for type .
    !>     KMAGN(j)        The order of magnitude ( O(1),
    !>                     O(overflow^(1/2) ), O(underflow^(1/2) )
    !>     KCONDS(j)       Selectw whether CONDS is to be 1 or
    !>                     1/sqrt(ulp).  (0 means irrelevant.)
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 431 of file zdrvsx.f.

Author

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