TESTING/EIG/sdrvsx.f(3)

NAME
TESTING/EIG/sdrvsx.f

SYNOPSIS

  Functions/Subroutines
subroutine sdrvsx (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)
SDRVSX

Function/Subroutine Documentation

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

SDRVSX

Purpose:

    !>
    !>    SDRVSX checks the nonsymmetric eigenvalue (Schur form) problem
    !>    expert driver SGEESX.
    !>
    !>    SDRVSX 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 SDRVSX 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 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  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 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  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  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  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 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
    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 SDRVSX to continue the same random number
    !>          sequence.
    !>

    THRESH

    !>          THRESH is REAL
    !>          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 REAL 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 REAL array, dimension (LDA, max(NN))
    !>          Another copy of the test matrix A, modified by SGEESX.
    !>

    HT

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

    WR

    !>          WR is REAL array, dimension (max(NN))
    !>

    WI

    !>          WI is REAL 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 REAL array, dimension (max(NN))
    !>

    WIT

    !>          WIT is REAL array, dimension (max(NN))
    !>
    !>          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 (max(NN))
    !>

    WITMP

    !>          WITMP is REAL array, dimension (max(NN))
    !>
    !>          More temporary storage for eigenvalues.
    !>

    VS

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

    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.  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,  SLATMR, SLATMS, SLATME or SGET24 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 450 of file sdrvsx.f.

Author

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