ddrvsx.f - Man Page

subroutine ddrvsx (nsizes, nn, ntypes, dotype, iseed, thresh, niunit, nounit, a, lda, h, ht, wr, wi, wrt, wit, wrtmp, witmp, vs, ldvs, vs1, result, work, lwork, iwork, bwork, info)
DDRVSX

DDRVSX

Purpose:

    DDRVSX checks the nonsymmetric eigenvalue (Schur form) problem
    expert driver DGEESX.

    DDRVSX 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 DDRVSX is called, a number of matrix 'sizes' ('n's') and a
    number of matrix 'types' are specified.  For each size ('n')
    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 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

    The 'sizes' are specified by an array NN(1:NSIZES); the value of
    each element NN(j) specifies one size.
    The 'types' are specified by a logical array DOTYPE( 1:NTYPES );
    if DOTYPE(j) is .TRUE., then matrix type 'j' 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 signs.
         (ULP = (first number larger than 1) - 1 )
    (5)  A diagonal matrix with geometrically spaced entries
         1, ..., ULP  and random signs.
    (6)  A diagonal matrix with 'clustered' entries 1, ULP, ..., ULP
         and random signs.

    (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 orthogonal and
         T has evenly spaced entries 1, ..., ULP with random signs
         on the diagonal and random O(1) entries in the upper
         triangle.

    (10) A matrix of the form  U' T U, where U is orthogonal and
         T has geometrically spaced entries 1, ..., ULP with random
         signs 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 'clustered' entries 1, ULP,..., ULP with random
         signs on the diagonal and random O(1) entries in the upper
         triangle.

    (12) A matrix of the form  U' T U, where U is orthogonal and
         T has real or complex conjugate paired eigenvalues randomly
         chosen from ( ULP, 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 signs 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 signs 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 'clustered' entries 1, ULP,..., ULP
         with random signs 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 real or complex conjugate paired
         eigenvalues randomly chosen from ( ULP, 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 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

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 DDRVSX to continue the same random number
          sequence.

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.

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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDA, max(NN))
          Another copy of the test matrix A, modified by DGEESX.

HT

          HT is DOUBLE PRECISION array, dimension (LDA, max(NN))
          Yet another copy of the test matrix A, modified by DGEESX.

WR

          WR is DOUBLE PRECISION array, dimension (max(NN))

WI

          WI is DOUBLE PRECISION array, dimension (max(NN))

          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 (max(NN))

WIT

          WIT is DOUBLE PRECISION array, dimension (max(NN))

          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 (max(NN))

WITMP

          WITMP is DOUBLE PRECISION array, dimension (max(NN))

          More temporary storage for eigenvalues.

VS

          VS is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LWORK)

LWORK

          LWORK is INTEGER
          The number of entries in WORK.  This must be at least
          max(3*NN(j),2*NN(j)**2) for all j.

IWORK

          IWORK is INTEGER array, dimension (max(NN)*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,  DLATMR, SLATMS, SLATME or DGET24 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 'j'.
     KMODE(j)        The MODE value to be passed to the matrix
                     generator for type 'j'.
     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 450 of file ddrvsx.f.