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 'sizes' ('n's') and a
        number of matrix 'types' are specified in the calling sequence.
        For each size ('n') 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 '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 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 '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,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 '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 516 of file ddrvvx.f.

Author

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