TESTING/EIG/ddrvev.f(3)

NAME
TESTING/EIG/ddrvev.f

SYNOPSIS

  Functions/Subroutines
subroutine ddrvev (nsizes, nn, ntypes, dotype, iseed, thresh, nounit, a, lda, h, wr, wi, wr1, wi1, vl, ldvl, vr, ldvr, lre, ldlre, result, work, nwork, iwork, info)
DDRVEV

Function/Subroutine Documentation

  subroutine ddrvev (integer nsizes, integer, dimension( * ) nn, integer ntypes, logical, dimension( * ) dotype, integer, dimension( 4 ) iseed, double precision thresh, integer nounit, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( lda, * ) h, double precision, dimension( * ) wr, double precision, dimension( * ) wi, double precision, dimension( * ) wr1, double precision, dimension( * ) wi1, double precision, dimension( ldvl, * ) vl, integer ldvl, double precision, dimension( ldvr, * ) vr, integer ldvr, double precision, dimension( ldlre, * ) lre, integer ldlre, double precision, dimension( 7 ) result, double precision, dimension( * ) work, integer nwork, integer, dimension( * ) iwork, integer info)

DDRVEV

Purpose:

    !>
    !>    DDRVEV  checks the nonsymmetric eigenvalue problem driver DGEEV.
    !>
    !>    When DDRVEV 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, 7
    !>    tests will be performed:
    !>
    !>    (1)     | A * VR - VR * W | / ( n |A| ulp )
    !>
    !>      Here VR is the matrix of unit right eigenvectors.
    !>      W is a block diagonal matrix, with a 1x1 block for each
    !>      real eigenvalue and a 2x2 block for each complex conjugate
    !>      pair.  If eigenvalues j and j+1 are a complex conjugate pair,
    !>      so WR(j) = WR(j+1) = wr and WI(j) = - WI(j+1) = wi, then the
    !>      2 x 2 block corresponding to the pair will be:
    !>
    !>              (  wr  wi  )
    !>              ( -wi  wr  )
    !>
    !>      Such a block multiplying an n x 2 matrix  ( ur ui ) on the
    !>      right will be the same as multiplying  ur + i*ui  by  wr + i*wi.
    !>
    !>    (2)     | A**H * VL - VL * W**H | / ( n |A| ulp )
    !>
    !>      Here VL is the matrix of unit left eigenvectors, A**H is the
    !>      conjugate transpose of A, and W is as above.
    !>
    !>    (3)     | |VR(i)| - 1 | / ulp and whether largest component real
    !>
    !>      VR(i) denotes the i-th column of VR.
    !>
    !>    (4)     | |VL(i)| - 1 | / ulp and whether largest component real
    !>
    !>      VL(i) denotes the i-th column of VL.
    !>
    !>    (5)     W(full) = W(partial)
    !>
    !>      W(full) denotes the eigenvalues computed when both VR and VL
    !>      are also computed, and W(partial) denotes the eigenvalues
    !>      computed when only W, only W and VR, or only W and VL are
    !>      computed.
    !>
    !>    (6)     VR(full) = VR(partial)
    !>
    !>      VR(full) denotes the right eigenvectors computed when both VR
    !>      and VL are computed, and VR(partial) denotes the result
    !>      when only VR is computed.
    !>
    !>     (7)     VL(full) = VL(partial)
    !>
    !>      VL(full) denotes the left eigenvectors computed when both VR
    !>      and VL are also computed, and VL(partial) denotes the result
    !>      when only VL is 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
    !>

Parameters
    NSIZES

    !>          NSIZES is INTEGER
    !>          The number of sizes of matrices to use.  If it is zero,
    !>          DDRVEV 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, DDRVEV
    !>          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 DDRVEV 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 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 DGEEV.
    !>

    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.
    !>

    WR1

    !>          WR1 is DOUBLE PRECISION array, dimension (max(NN))
    !>

    WI1

    !>          WI1 is DOUBLE PRECISION array, dimension (max(NN))
    !>
    !>          Like WR, WI, these arrays contain the eigenvalues of A,
    !>          but those computed when DGEEV only computes a partial
    !>          eigendecomposition, i.e. not the eigenvalues and left
    !>          and right eigenvectors.
    !>

    VL

    !>          VL is DOUBLE PRECISION array, dimension (LDVL, max(NN))
    !>          VL holds the computed left eigenvectors.
    !>

    LDVL

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

    VR

    !>          VR is DOUBLE PRECISION array, dimension (LDVR, max(NN))
    !>          VR holds the computed right eigenvectors.
    !>

    LDVR

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

    LRE

    !>          LRE is DOUBLE PRECISION array, dimension (LDLRE,max(NN))
    !>          LRE holds the computed right or left eigenvectors.
    !>

    LDLRE

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

    RESULT

    !>          RESULT is DOUBLE PRECISION array, dimension (7)
    !>          The values computed by the seven tests described above.
    !>          The values are currently limited to 1/ulp, to avoid overflow.
    !>

    WORK

    !>          WORK is DOUBLE PRECISION 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.
    !>

    IWORK

    !>          IWORK is INTEGER 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) ).
    !>          -16: LDVL < 1 or LDVL < NMAX, where NMAX is max( NN(j) ).
    !>          -18: LDVR < 1 or LDVR < NMAX, where NMAX is max( NN(j) ).
    !>          -20: LDLRE < 1 or LDLRE < NMAX, where NMAX is max( NN(j) ).
    !>          -23: NWORK too small.
    !>          If  DLATMR, SLATMS, SLATME or DGEEV 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)       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 402 of file ddrvev.f.

Author

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