TESTING/EIG/ddrvsx.f(3)

NAME
TESTING/EIG/ddrvsx.f

SYNOPSIS

  Functions/Subroutines
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

Function/Subroutine Documentation

  subroutine ddrvsx (integer nsizes, integer, dimension( * ) nn, integer ntypes, logical, dimension( * ) dotype, integer, dimension( 4 ) iseed, double precision thresh, integer niunit, integer nounit, 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, dimension( 17 ) result, double precision, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, logical, dimension( * ) bwork, integer info)

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.

Author

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