TESTING/EIG/sdrvsg2stg.f(3)

NAME
TESTING/EIG/sdrvsg2stg.f

SYNOPSIS

  Functions/Subroutines
subroutine sdrvsg2stg (nsizes, nn, ntypes, dotype, iseed, thresh, nounit, a, lda, b, ldb, d, d2, z, ldz, ab, bb, ap, bp, work, nwork, iwork, liwork, result, info)
SDRVSG2STG

Function/Subroutine Documentation

  subroutine sdrvsg2stg (integer nsizes, integer, dimension( * ) nn, integer ntypes, logical, dimension( * ) dotype, integer, dimension( 4 ) iseed, real thresh, integer nounit, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, real, dimension( * ) d, real, dimension( * ) d2, real, dimension( ldz, * ) z, integer ldz, real, dimension( lda, * ) ab, real, dimension( ldb, * ) bb, real, dimension( * ) ap, real, dimension( * ) bp, real, dimension( * ) work, integer nwork, integer, dimension( * ) iwork, integer liwork, real, dimension( * ) result, integer info)

SDRVSG2STG

Purpose:

    !>
    !>      SDRVSG2STG checks the real symmetric generalized eigenproblem
    !>      drivers.
    !>
    !>              SSYGV computes all eigenvalues and, optionally,
    !>              eigenvectors of a real symmetric-definite generalized
    !>              eigenproblem.
    !>
    !>              SSYGVD computes all eigenvalues and, optionally,
    !>              eigenvectors of a real symmetric-definite generalized
    !>              eigenproblem using a divide and conquer algorithm.
    !>
    !>              SSYGVX computes selected eigenvalues and, optionally,
    !>              eigenvectors of a real symmetric-definite generalized
    !>              eigenproblem.
    !>
    !>              SSPGV computes all eigenvalues and, optionally,
    !>              eigenvectors of a real symmetric-definite generalized
    !>              eigenproblem in packed storage.
    !>
    !>              SSPGVD computes all eigenvalues and, optionally,
    !>              eigenvectors of a real symmetric-definite generalized
    !>              eigenproblem in packed storage using a divide and
    !>              conquer algorithm.
    !>
    !>              SSPGVX computes selected eigenvalues and, optionally,
    !>              eigenvectors of a real symmetric-definite generalized
    !>              eigenproblem in packed storage.
    !>
    !>              SSBGV computes all eigenvalues and, optionally,
    !>              eigenvectors of a real symmetric-definite banded
    !>              generalized eigenproblem.
    !>
    !>              SSBGVD computes all eigenvalues and, optionally,
    !>              eigenvectors of a real symmetric-definite banded
    !>              generalized eigenproblem using a divide and conquer
    !>              algorithm.
    !>
    !>              SSBGVX computes selected eigenvalues and, optionally,
    !>              eigenvectors of a real symmetric-definite banded
    !>              generalized eigenproblem.
    !>
    !>      When SDRVSG2STG 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) SSYGV with ITYPE = 1 and UPLO ='U':
    !>
    !>              | A Z - B Z D | / ( |A| |Z| n ulp )
    !>              | D - D2 | / ( |D| ulp )   where D is computed by
    !>                                         SSYGV and  D2 is computed by
    !>                                         SSYGV_2STAGE. This test is
    !>                                         only performed for SSYGV
    !>
    !>      (2) as (1) but calling SSPGV
    !>      (3) as (1) but calling SSBGV
    !>      (4) as (1) but with UPLO = 'L'
    !>      (5) as (4) but calling SSPGV
    !>      (6) as (4) but calling SSBGV
    !>
    !>      (7) SSYGV with ITYPE = 2 and UPLO ='U':
    !>
    !>              | A B Z - Z D | / ( |A| |Z| n ulp )
    !>
    !>      (8) as (7) but calling SSPGV
    !>      (9) as (7) but with UPLO = 'L'
    !>      (10) as (9) but calling SSPGV
    !>
    !>      (11) SSYGV with ITYPE = 3 and UPLO ='U':
    !>
    !>              | B A Z - Z D | / ( |A| |Z| n ulp )
    !>
    !>      (12) as (11) but calling SSPGV
    !>      (13) as (11) but with UPLO = 'L'
    !>      (14) as (13) but calling SSPGV
    !>
    !>      SSYGVD, SSPGVD and SSBGVD performed the same 14 tests.
    !>
    !>      SSYGVX, SSPGVX and SSBGVX 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,
    !>          SDRVSG2STG 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, SDRVSG2STG
    !>          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 SDRVSG2STG to continue the same random number
    !>          sequence.
    !>          Modified.
    !>
    !>  THRESH  REAL
    !>          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. real)
    !>          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       REAL             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       REAL             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       REAL             array, dimension (max(NN))
    !>          The eigenvalues of A. On exit, the eigenvalues in D
    !>          correspond with the matrix in A.
    !>          Modified.
    !>
    !>  Z       REAL             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      REAL             array, dimension (LDA, max(NN))
    !>          Workspace.
    !>          Modified.
    !>
    !>  BB      REAL             array, dimension (LDB, max(NN))
    !>          Workspace.
    !>          Modified.
    !>
    !>  AP      REAL             array, dimension (max(NN)**2)
    !>          Workspace.
    !>          Modified.
    !>
    !>  BP      REAL             array, dimension (max(NN)**2)
    !>          Workspace.
    !>          Modified.
    !>
    !>  WORK    REAL 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  REAL 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  SLATMR, SLATMS, SSYGV, SSPGV, SSBGV, SSYGVD, SSPGVD,
    !>              SSBGVD, SSYGVX, SSPGVX 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 SLAFTS).
    !>       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 358 of file sdrvsg2stg.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.