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 'sizes' ('n's') and a
          number of matrix 'types' are specified.  For each size ('n')
          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 '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.
          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 'clustered' 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 'clustered' 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 '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.
              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 '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) )

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 352 of file ddrvsg.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.