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 '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, 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 '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

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 '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.

    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 '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 402 of file ddrvev.f.

Author

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