TESTING/EIG/ddrvvx.f(3)

NAME
TESTING/EIG/ddrvvx.f

SYNOPSIS

  Functions/Subroutines
subroutine ddrvvx (nsizes, nn, ntypes, dotype, iseed, thresh, niunit, nounit, a, lda, h, wr, wi, wr1, wi1, vl, ldvl, vr, ldvr, lre, ldlre, rcondv, rcndv1, rcdvin, rconde, rcnde1, rcdein, scale, scale1, result, work, nwork, iwork, info)
DDRVVX

Function/Subroutine Documentation

  subroutine ddrvvx (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( * ) 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( * ) rcondv, double precision, dimension( * ) rcndv1, double precision, dimension( * ) rcdvin, double precision, dimension( * ) rconde, double precision, dimension( * ) rcnde1, double precision, dimension( * ) rcdein, double precision, dimension( * ) scale, double precision, dimension( * ) scale1, double precision, dimension( 11 ) result, double precision, dimension( * ) work, integer nwork, integer, dimension( * ) iwork, integer info)

DDRVVX

Purpose:

    !>
    !>    DDRVVX  checks the nonsymmetric eigenvalue problem expert driver
    !>    DGEEVX.
    !>
    !>    DDRVVX 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 DDRVVX is called, a number of matrix  () and a
    !>    number of matrix  are specified in the calling sequence.
    !>    For each size () and each type of matrix, one matrix will be
    !>    generated and used to test the nonsymmetric eigenroutines.  For
    !>    each matrix, 9 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 largest component real
    !>
    !>      VR(i) denotes the i-th column of VR.
    !>
    !>    (4)     | |VL(i)| - 1 | / ulp and largest component real
    !>
    !>      VL(i) denotes the i-th column of VL.
    !>
    !>    (5)     W(full) = W(partial)
    !>
    !>      W(full) denotes the eigenvalues computed when VR, VL, RCONDV
    !>      and RCONDE are also computed, and W(partial) denotes the
    !>      eigenvalues computed when only some of VR, VL, RCONDV, and
    !>      RCONDE are computed.
    !>
    !>    (6)     VR(full) = VR(partial)
    !>
    !>      VR(full) denotes the right eigenvectors computed when VL, RCONDV
    !>      and RCONDE are computed, and VR(partial) denotes the result
    !>      when only some of VL and RCONDV are computed.
    !>
    !>    (7)     VL(full) = VL(partial)
    !>
    !>      VL(full) denotes the left eigenvectors computed when VR, RCONDV
    !>      and RCONDE are computed, and VL(partial) denotes the result
    !>      when only some of VR and RCONDV are computed.
    !>
    !>    (8)     0 if SCALE, ILO, IHI, ABNRM (full) =
    !>                 SCALE, ILO, IHI, ABNRM (partial)
    !>            1/ulp otherwise
    !>
    !>      SCALE, ILO, IHI and ABNRM describe how the matrix is balanced.
    !>      (full) is when VR, VL, RCONDE and RCONDV are also computed, and
    !>      (partial) is when some are not computed.
    !>
    !>    (9)     RCONDV(full) = RCONDV(partial)
    !>
    !>      RCONDV(full) denotes the reciprocal condition numbers of the
    !>      right eigenvectors computed when VR, VL and RCONDE are also
    !>      computed. RCONDV(partial) denotes the reciprocal condition
    !>      numbers when only some of VR, VL and RCONDE are 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 eigenvalues
    !>    and right eigenvectors. For these matrices, in addition to tests
    !>    (1) to (9) we will compute the following two tests:
    !>
    !>   (10)  |RCONDV - RCDVIN| / cond(RCONDV)
    !>
    !>      RCONDV is the reciprocal right eigenvector condition number
    !>      computed by DGEEVX 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.
    !>
    !>   (11)  |RCONDE - RCDEIN| / cond(RCONDE)
    !>
    !>      RCONDE is the reciprocal eigenvalue condition number
    !>      computed by DGEEVX 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.
    !>

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 DDRVVX 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.
    !>

    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,12))
    !>          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 the arrays A and H.
    !>          LDA >= max(NN,12), since 12 is the dimension of the largest
    !>          matrix in the precomputed input file.
    !>

    H

    !>          H is DOUBLE PRECISION array, dimension
    !>                      (LDA, max(NN,12))
    !>          Another copy of the test matrix A, modified by DGEEVX.
    !>

    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,12))
    !>

    WI1

    !>          WI1 is DOUBLE PRECISION array, dimension (max(NN,12))
    !>
    !>          Like WR, WI, these arrays contain the eigenvalues of A,
    !>          but those computed when DGEEVX 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,12))
    !>          VL holds the computed left eigenvectors.
    !>

    LDVL

    !>          LDVL is INTEGER
    !>          Leading dimension of VL. Must be at least max(1,max(NN,12)).
    !>

    VR

    !>          VR is DOUBLE PRECISION array, dimension
    !>                      (LDVR, max(NN,12))
    !>          VR holds the computed right eigenvectors.
    !>

    LDVR

    !>          LDVR is INTEGER
    !>          Leading dimension of VR. Must be at least max(1,max(NN,12)).
    !>

    LRE

    !>          LRE is DOUBLE PRECISION array, dimension
    !>                      (LDLRE, max(NN,12))
    !>          LRE holds the computed right or left eigenvectors.
    !>

    LDLRE

    !>          LDLRE is INTEGER
    !>          Leading dimension of LRE. Must be at least max(1,max(NN,12))
    !>

    RCONDV

    !>          RCONDV is DOUBLE PRECISION array, dimension (N)
    !>          RCONDV holds the computed reciprocal condition numbers
    !>          for eigenvectors.
    !>

    RCNDV1

    !>          RCNDV1 is DOUBLE PRECISION array, dimension (N)
    !>          RCNDV1 holds more computed reciprocal condition numbers
    !>          for eigenvectors.
    !>

    RCDVIN

    !>          RCDVIN is DOUBLE PRECISION array, dimension (N)
    !>          When COMP = .TRUE. RCDVIN holds the precomputed reciprocal
    !>          condition numbers for eigenvectors to be compared with
    !>          RCONDV.
    !>

    RCONDE

    !>          RCONDE is DOUBLE PRECISION array, dimension (N)
    !>          RCONDE holds the computed reciprocal condition numbers
    !>          for eigenvalues.
    !>

    RCNDE1

    !>          RCNDE1 is DOUBLE PRECISION array, dimension (N)
    !>          RCNDE1 holds more computed reciprocal condition numbers
    !>          for eigenvalues.
    !>

    RCDEIN

    !>          RCDEIN is DOUBLE PRECISION array, dimension (N)
    !>          When COMP = .TRUE. RCDEIN holds the precomputed reciprocal
    !>          condition numbers for eigenvalues to be compared with
    !>          RCONDE.
    !>

    SCALE

    !>          SCALE is DOUBLE PRECISION array, dimension (N)
    !>          Holds information describing balancing of matrix.
    !>

    SCALE1

    !>          SCALE1 is DOUBLE PRECISION array, dimension (N)
    !>          Holds information describing balancing of matrix.
    !>

    RESULT

    !>          RESULT is DOUBLE PRECISION array, dimension (11)
    !>          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
    !>          max(6*12+2*12**2,6*NN(j)+2*NN(j)**2) =
    !>          max(    360     ,6*NN(j)+2*NN(j)**2)    for all j.
    !>

    IWORK

    !>          IWORK is INTEGER array, dimension (2*max(NN,12))
    !>

    INFO

    !>          INFO is INTEGER
    !>          If 0,  then successful exit.
    !>          If <0, then input parameter -INFO is incorrect.
    !>          If >0, DLATMR, SLATMS, SLATME or DGET23 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 or 12.
    !>     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 516 of file ddrvvx.f.

Author

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