TESTING/EIG/zdrves.f(3)

NAME
TESTING/EIG/zdrves.f

SYNOPSIS

  Functions/Subroutines
subroutine zdrves (nsizes, nn, ntypes, dotype, iseed, thresh, nounit, a, lda, h, ht, w, wt, vs, ldvs, result, work, nwork, rwork, iwork, bwork, info)
ZDRVES

Function/Subroutine Documentation

  subroutine zdrves (integer nsizes, integer, dimension( * ) nn, integer ntypes, logical, dimension( * ) dotype, integer, dimension( 4 ) iseed, double precision thresh, 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( ldvs, * ) vs, integer ldvs, double precision, dimension( 13 ) result, complex*16, dimension( * ) work, integer nwork, double precision, dimension( * ) rwork, integer, dimension( * ) iwork, logical, dimension( * ) bwork, integer info)

ZDRVES

Purpose:

    !>
    !>    ZDRVES checks the nonsymmetric eigenvalue (Schur form) problem
    !>    driver ZGEES.
    !>
    !>    When ZDRVES 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, 13
    !>    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
    !>            (with sorting of eigenvalues)
    !>
    !>    (11)    0     if T(with VS) = T(without VS),
    !>            1/ulp otherwise
    !>            (with sorting of eigenvalues)
    !>
    !>    (12)    0     if eigenvalues(with VS) = eigenvalues(without VS),
    !>            1/ulp otherwise
    !>            (with sorting of eigenvalues)
    !>
    !>    (13)    if sorting worked and SDIM is the number of
    !>            eigenvalues which were SELECTed
    !>
    !>    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
    !>

Parameters
    NSIZES

    !>          NSIZES is INTEGER
    !>          The number of sizes of matrices to use.  If it is zero,
    !>          ZDRVES does nothing.  It must be at least zero.
    !>

    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.   If it is zero, ZDRVES
    !>          does nothing.  It must be at least zero.  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 ZDRVES 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.
    !>

    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 ZGEES.
    !>

    HT

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

    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 ZGEES only computes a partial
    !>          eigendecomposition, i.e. not Schur vectors
    !>

    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)).
    !>

    RESULT

    !>          RESULT is DOUBLE PRECISION array, dimension (13)
    !>          The values computed by the 13 tests described above.
    !>          The values are currently limited to 1/ulp, to avoid overflow.
    !>

    WORK

    !>          WORK is COMPLEX*16 array, dimension (NWORK)
    !>

    NWORK

    !>          NWORK is INTEGER
    !>          The number of entries in WORK.  This must be at least
    !>          5*NN(j)+2*NN(j)**2 for all j.
    !>

    RWORK

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

    IWORK

    !>          IWORK is INTEGER array, dimension (max(NN))
    !>

    BWORK

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

    INFO

    !>          INFO is INTEGER
    !>          If 0, then everything ran OK.
    !>           -1: NSIZES < 0
    !>           -2: Some NN(j) < 0
    !>           -3: NTYPES < 0
    !>           -6: THRESH < 0
    !>           -9: LDA < 1 or LDA < NMAX, where NMAX is max( NN(j) ).
    !>          -15: LDVS < 1 or LDVS < NMAX, where NMAX is max( NN(j) ).
    !>          -18: NWORK too small.
    !>          If  ZLATMR, CLATMS, CLATME or ZGEES returns an error code,
    !>              the absolute value of it is returned.
    !>
    !>-----------------------------------------------------------------------
    !>
    !>     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)       Select 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 375 of file zdrves.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.