TESTING/EIG/ddrvsg.f(3)

NAME
TESTING/EIG/ddrvsg.f

SYNOPSIS

  Functions/Subroutines
subroutine ddrvsg (nsizes, nn, ntypes, dotype, iseed, thresh, nounit, a, lda, b, ldb, d, z, ldz, ab, bb, ap, bp, work, nwork, iwork, liwork, result, info)
DDRVSG

Function/Subroutine Documentation

  subroutine ddrvsg (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( ldb, * ) b, integer ldb, double precision, dimension( * ) d, double precision, dimension( ldz, * ) z, integer ldz, double precision, dimension( lda, * ) ab, double precision, dimension( ldb, * ) bb, double precision, dimension( * ) ap, double precision, dimension( * ) bp, double precision, dimension( * ) work, integer nwork, integer, dimension( * ) iwork, integer liwork, double precision, dimension( * ) result, integer info)

DDRVSG

Purpose:

    !>
    !>      DDRVSG checks the real symmetric generalized eigenproblem
    !>      drivers.
    !>
    !>              DSYGV computes all eigenvalues and, optionally,
    !>              eigenvectors of a real symmetric-definite generalized
    !>              eigenproblem.
    !>
    !>              DSYGVD computes all eigenvalues and, optionally,
    !>              eigenvectors of a real symmetric-definite generalized
    !>              eigenproblem using a divide and conquer algorithm.
    !>
    !>              DSYGVX computes selected eigenvalues and, optionally,
    !>              eigenvectors of a real symmetric-definite generalized
    !>              eigenproblem.
    !>
    !>              DSPGV computes all eigenvalues and, optionally,
    !>              eigenvectors of a real symmetric-definite generalized
    !>              eigenproblem in packed storage.
    !>
    !>              DSPGVD computes all eigenvalues and, optionally,
    !>              eigenvectors of a real symmetric-definite generalized
    !>              eigenproblem in packed storage using a divide and
    !>              conquer algorithm.
    !>
    !>              DSPGVX computes selected eigenvalues and, optionally,
    !>              eigenvectors of a real symmetric-definite generalized
    !>              eigenproblem in packed storage.
    !>
    !>              DSBGV computes all eigenvalues and, optionally,
    !>              eigenvectors of a real symmetric-definite banded
    !>              generalized eigenproblem.
    !>
    !>              DSBGVD computes all eigenvalues and, optionally,
    !>              eigenvectors of a real symmetric-definite banded
    !>              generalized eigenproblem using a divide and conquer
    !>              algorithm.
    !>
    !>              DSBGVX computes selected eigenvalues and, optionally,
    !>              eigenvectors of a real symmetric-definite banded
    !>              generalized eigenproblem.
    !>
    !>      When DDRVSG is called, a number of matrix  () and a
    !>      number of matrix  are specified.  For each size ()
    !>      and each type of matrix, one matrix A of the given type will be
    !>      generated; a random well-conditioned matrix B is also generated
    !>      and the pair (A,B) is used to test the drivers.
    !>
    !>      For each pair (A,B), the following tests are performed:
    !>
    !>      (1) DSYGV with ITYPE = 1 and UPLO ='U':
    !>
    !>              | A Z - B Z D | / ( |A| |Z| n ulp )
    !>
    !>      (2) as (1) but calling DSPGV
    !>      (3) as (1) but calling DSBGV
    !>      (4) as (1) but with UPLO = 'L'
    !>      (5) as (4) but calling DSPGV
    !>      (6) as (4) but calling DSBGV
    !>
    !>      (7) DSYGV with ITYPE = 2 and UPLO ='U':
    !>
    !>              | A B Z - Z D | / ( |A| |Z| n ulp )
    !>
    !>      (8) as (7) but calling DSPGV
    !>      (9) as (7) but with UPLO = 'L'
    !>      (10) as (9) but calling DSPGV
    !>
    !>      (11) DSYGV with ITYPE = 3 and UPLO ='U':
    !>
    !>              | B A Z - Z D | / ( |A| |Z| n ulp )
    !>
    !>      (12) as (11) but calling DSPGV
    !>      (13) as (11) but with UPLO = 'L'
    !>      (14) as (13) but calling DSPGV
    !>
    !>      DSYGVD, DSPGVD and DSBGVD performed the same 14 tests.
    !>
    !>      DSYGVX, DSPGVX and DSBGVX performed the above 14 tests with
    !>      the parameter RANGE = 'A', 'N' and 'I', respectively.
    !>
    !>      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.
    !>      This type is used for the matrix A which has half-bandwidth KA.
    !>      B is generated as a well-conditioned positive definite matrix
    !>      with half-bandwidth KB (<= KA).
    !>      Currently, the list of possible types for A is:
    !>
    !>      (1)  The zero matrix.
    !>      (2)  The identity matrix.
    !>
    !>      (3)  A diagonal matrix with evenly spaced entries
    !>           1, ..., ULP  and random signs.
    !>           (ULP = (first number larger than 1) - 1 )
    !>      (4)  A diagonal matrix with geometrically spaced entries
    !>           1, ..., ULP  and random signs.
    !>      (5)  A diagonal matrix with  entries
    !>           1, ULP, ..., ULP and random signs.
    !>
    !>      (6)  Same as (4), but multiplied by SQRT( overflow threshold )
    !>      (7)  Same as (4), but multiplied by SQRT( underflow threshold )
    !>
    !>      (8)  A matrix of the form  U* D U, where U is orthogonal and
    !>           D has evenly spaced entries 1, ..., ULP with random signs
    !>           on the diagonal.
    !>
    !>      (9)  A matrix of the form  U* D U, where U is orthogonal and
    !>           D has geometrically spaced entries 1, ..., ULP with random
    !>           signs on the diagonal.
    !>
    !>      (10) A matrix of the form  U* D U, where U is orthogonal and
    !>           D has  entries 1, ULP,..., ULP with random
    !>           signs on the diagonal.
    !>
    !>      (11) Same as (8), but multiplied by SQRT( overflow threshold )
    !>      (12) Same as (8), but multiplied by SQRT( underflow threshold )
    !>
    !>      (13) symmetric matrix with random entries chosen from (-1,1).
    !>      (14) Same as (13), but multiplied by SQRT( overflow threshold )
    !>      (15) Same as (13), but multiplied by SQRT( underflow threshold)
    !>
    !>      (16) Same as (8), but with KA = 1 and KB = 1
    !>      (17) Same as (8), but with KA = 2 and KB = 1
    !>      (18) Same as (8), but with KA = 2 and KB = 2
    !>      (19) Same as (8), but with KA = 3 and KB = 1
    !>      (20) Same as (8), but with KA = 3 and KB = 2
    !>      (21) Same as (8), but with KA = 3 and KB = 3
    !>

    !>  NSIZES  INTEGER
    !>          The number of sizes of matrices to use.  If it is zero,
    !>          DDRVSG does nothing.  It must be at least zero.
    !>          Not modified.
    !>
    !>  NN      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.
    !>          Not modified.
    !>
    !>  NTYPES  INTEGER
    !>          The number of elements in DOTYPE.   If it is zero, DDRVSG
    !>          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. .
    !>          Not modified.
    !>
    !>  DOTYPE  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.
    !>          Not modified.
    !>
    !>  ISEED   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 DDRVSG to continue the same random number
    !>          sequence.
    !>          Modified.
    !>
    !>  THRESH  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.
    !>          Not modified.
    !>
    !>  NOUNIT  INTEGER
    !>          The FORTRAN unit number for printing out error messages
    !>          (e.g., if a routine returns IINFO not equal to 0.)
    !>          Not modified.
    !>
    !>  A       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.
    !>          Modified.
    !>
    !>  LDA     INTEGER
    !>          The leading dimension of A and AB.  It must be at
    !>          least 1 and at least max( NN ).
    !>          Not modified.
    !>
    !>  B       DOUBLE PRECISION array, dimension (LDB , max(NN))
    !>          Used to hold the symmetric positive definite matrix for
    !>          the generalized problem.
    !>          On exit, B contains the last matrix actually
    !>          used.
    !>          Modified.
    !>
    !>  LDB     INTEGER
    !>          The leading dimension of B and BB.  It must be at
    !>          least 1 and at least max( NN ).
    !>          Not modified.
    !>
    !>  D       DOUBLE PRECISION array, dimension (max(NN))
    !>          The eigenvalues of A. On exit, the eigenvalues in D
    !>          correspond with the matrix in A.
    !>          Modified.
    !>
    !>  Z       DOUBLE PRECISION array, dimension (LDZ, max(NN))
    !>          The matrix of eigenvectors.
    !>          Modified.
    !>
    !>  LDZ     INTEGER
    !>          The leading dimension of Z.  It must be at least 1 and
    !>          at least max( NN ).
    !>          Not modified.
    !>
    !>  AB      DOUBLE PRECISION array, dimension (LDA, max(NN))
    !>          Workspace.
    !>          Modified.
    !>
    !>  BB      DOUBLE PRECISION array, dimension (LDB, max(NN))
    !>          Workspace.
    !>          Modified.
    !>
    !>  AP      DOUBLE PRECISION array, dimension (max(NN)**2)
    !>          Workspace.
    !>          Modified.
    !>
    !>  BP      DOUBLE PRECISION array, dimension (max(NN)**2)
    !>          Workspace.
    !>          Modified.
    !>
    !>  WORK    DOUBLE PRECISION array, dimension (NWORK)
    !>          Workspace.
    !>          Modified.
    !>
    !>  NWORK   INTEGER
    !>          The number of entries in WORK.  This must be at least
    !>          1+5*N+2*N*lg(N)+3*N**2 where N = max( NN(j) ) and
    !>          lg( N ) = smallest integer k such that 2**k >= N.
    !>          Not modified.
    !>
    !>  IWORK   INTEGER array, dimension (LIWORK)
    !>          Workspace.
    !>          Modified.
    !>
    !>  LIWORK  INTEGER
    !>          The number of entries in WORK.  This must be at least 6*N.
    !>          Not modified.
    !>
    !>  RESULT  DOUBLE PRECISION array, dimension (70)
    !>          The values computed by the 70 tests described above.
    !>          Modified.
    !>
    !>  INFO    INTEGER
    !>          If 0, then everything ran OK.
    !>           -1: NSIZES < 0
    !>           -2: Some NN(j) < 0
    !>           -3: NTYPES < 0
    !>           -5: THRESH < 0
    !>           -9: LDA < 1 or LDA < NMAX, where NMAX is max( NN(j) ).
    !>          -16: LDZ < 1 or LDZ < NMAX.
    !>          -21: NWORK too small.
    !>          -23: LIWORK too small.
    !>          If  DLATMR, SLATMS, DSYGV, DSPGV, DSBGV, SSYGVD, SSPGVD,
    !>              DSBGVD, DSYGVX, DSPGVX or SSBGVX returns an error code,
    !>              the absolute value of it is returned.
    !>          Modified.
    !>
    !> ----------------------------------------------------------------------
    !>
    !>       Some Local Variables and Parameters:
    !>       ---- ----- --------- --- ----------
    !>       ZERO, ONE       Real 0 and 1.
    !>       MAXTYP          The number of types defined.
    !>       NTEST           The number of tests that have been run
    !>                       on this matrix.
    !>       NTESTT          The total number of tests for this call.
    !>       NMAX            Largest value in NN.
    !>       NMATS           The number of matrices generated so far.
    !>       NERRS           The number of tests which have exceeded THRESH
    !>                       so far (computed by DLAFTS).
    !>       COND, 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.
    !>       RTOVFL, RTUNFL  Square roots of the previous 2 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) )
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 352 of file ddrvsg.f.

Author

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