TESTING/EIG/cdrves.f(3)

NAME
TESTING/EIG/cdrves.f

SYNOPSIS

  Functions/Subroutines
subroutine cdrves (nsizes, nn, ntypes, dotype, iseed, thresh, nounit, a, lda, h, ht, w, wt, vs, ldvs, result, work, nwork, rwork, iwork, bwork, info)
CDRVES

Function/Subroutine Documentation

  subroutine cdrves (integer nsizes, integer, dimension( * ) nn, integer ntypes, logical, dimension( * ) dotype, integer, dimension( 4 ) iseed, real thresh, integer nounit, complex, dimension( lda, * ) a, integer lda, complex, dimension( lda, * ) h, complex, dimension( lda, * ) ht, complex, dimension( * ) w, complex, dimension( * ) wt, complex, dimension( ldvs, * ) vs, integer ldvs, real, dimension( 13 ) result, complex, dimension( * ) work, integer nwork, real, dimension( * ) rwork, integer, dimension( * ) iwork, logical, dimension( * ) bwork, integer info)

CDRVES

Purpose:

        CDRVES checks the nonsymmetric eigenvalue (Schur form) problem
        driver CGEES.
        When CDRVES 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, 13
        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 W 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 W are eigenvalues of T
                1/ulp otherwise
                (with sorting of eigenvalues)
        (11)    0     if T(with VS) = T(without VS),
                1/ulp otherwise
                (with sorting of eigenvalues)
        (12)    0     if eigenvalues(with VS) = eigenvalues(without VS),
                1/ulp otherwise
                (with sorting of eigenvalues)
        (13)    if sorting worked and SDIM is the number of
                eigenvalues which were SELECTed
        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 complex angles.
             (ULP = (first number larger than 1) - 1 )
        (5)  A diagonal matrix with geometrically spaced entries
             1, ..., ULP  and random complex angles.
        (6)  A diagonal matrix with 'clustered' entries 1, ULP, ..., ULP
             and random complex angles.
        (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 unitary and
             T has evenly spaced entries 1, ..., ULP with random
             complex angles on the diagonal and random O(1) entries in
             the upper triangle.
        (10) A matrix of the form  U' T U, where U is unitary and
             T has geometrically spaced entries 1, ..., ULP with random
             complex angles 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
             complex angles on the diagonal and random O(1) entries in
             the upper triangle.
        (12) A matrix of the form  U' T U, where U is unitary and
             T has complex eigenvalues randomly chosen from
             ULP < |z| < 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 complex angles 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 complex angles 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 complex angles 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 complex eigenvalues randomly chosen
             from ULP < |z| < 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,
              CDRVES 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, CDRVES
              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 CDRVES to continue the same random number
              sequence.

    THRESH

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

    HT

              HT is COMPLEX array, dimension (LDA, max(NN))
              Yet another copy of the test matrix A, modified by CGEES.

    W

              W is COMPLEX array, dimension (max(NN))
              The computed eigenvalues of A.

    WT

              WT is COMPLEX array, dimension (max(NN))
              Like W, this array contains the eigenvalues of A,
              but those computed when CGEES only computes a partial
              eigendecomposition, i.e. not Schur vectors

    VS

              VS is COMPLEX 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)).

    RESULT

              RESULT is REAL array, dimension (13)
              The values computed by the 13 tests described above.
              The values are currently limited to 1/ulp, to avoid overflow.

    WORK

              WORK is COMPLEX 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.

    RWORK

              RWORK is REAL array, dimension (max(NN))

    IWORK

              IWORK is INTEGER array, dimension (max(NN))

    BWORK

              BWORK is LOGICAL 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) ).
              -15: LDVS < 1 or LDVS < NMAX, where NMAX is max( NN(j) ).
              -18: NWORK too small.
              If  CLATMR, CLATMS, CLATME or CGEES 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)       Select 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 375 of file cdrves.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.