TESTING/EIG/zdrvsg.f(3)

NAME
TESTING/EIG/zdrvsg.f

SYNOPSIS

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

Function/Subroutine Documentation

  subroutine zdrvsg (integer nsizes, integer, dimension( * ) nn, integer ntypes, logical, dimension( * ) dotype, integer, dimension( 4 ) iseed, double precision thresh, integer nounit, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) d, complex*16, dimension( ldz, * ) z, integer ldz, complex*16, dimension( lda, * ) ab, complex*16, dimension( ldb, * ) bb, complex*16, dimension( * ) ap, complex*16, dimension( * ) bp, complex*16, dimension( * ) work, integer nwork, double precision, dimension( * ) rwork, integer lrwork, integer, dimension( * ) iwork, integer liwork, double precision, dimension( * ) result, integer info)

ZDRVSG

Purpose:

          ZDRVSG checks the complex Hermitian generalized eigenproblem
          drivers.
                  ZHEGV computes all eigenvalues and, optionally,
                  eigenvectors of a complex Hermitian-definite generalized
                  eigenproblem.
                  ZHEGVD computes all eigenvalues and, optionally,
                  eigenvectors of a complex Hermitian-definite generalized
                  eigenproblem using a divide and conquer algorithm.
                  ZHEGVX computes selected eigenvalues and, optionally,
                  eigenvectors of a complex Hermitian-definite generalized
                  eigenproblem.
                  ZHPGV computes all eigenvalues and, optionally,
                  eigenvectors of a complex Hermitian-definite generalized
                  eigenproblem in packed storage.
                  ZHPGVD computes all eigenvalues and, optionally,
                  eigenvectors of a complex Hermitian-definite generalized
                  eigenproblem in packed storage using a divide and
                  conquer algorithm.
                  ZHPGVX computes selected eigenvalues and, optionally,
                  eigenvectors of a complex Hermitian-definite generalized
                  eigenproblem in packed storage.
                  ZHBGV computes all eigenvalues and, optionally,
                  eigenvectors of a complex Hermitian-definite banded
                  generalized eigenproblem.
                  ZHBGVD computes all eigenvalues and, optionally,
                  eigenvectors of a complex Hermitian-definite banded
                  generalized eigenproblem using a divide and conquer
                  algorithm.
                  ZHBGVX computes selected eigenvalues and, optionally,
                  eigenvectors of a complex Hermitian-definite banded
                  generalized eigenproblem.
          When ZDRVSG 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) ZHEGV with ITYPE = 1 and UPLO ='U':
                  | A Z - B Z D | / ( |A| |Z| n ulp )
          (2) as (1) but calling ZHPGV
          (3) as (1) but calling ZHBGV
          (4) as (1) but with UPLO = 'L'
          (5) as (4) but calling ZHPGV
          (6) as (4) but calling ZHBGV
          (7) ZHEGV with ITYPE = 2 and UPLO ='U':
                  | A B Z - Z D | / ( |A| |Z| n ulp )
          (8) as (7) but calling ZHPGV
          (9) as (7) but with UPLO = 'L'
          (10) as (9) but calling ZHPGV
          (11) ZHEGV with ITYPE = 3 and UPLO ='U':
                  | B A Z - Z D | / ( |A| |Z| n ulp )
          (12) as (11) but calling ZHPGV
          (13) as (11) but with UPLO = 'L'
          (14) as (13) but calling ZHPGV
          ZHEGVD, ZHPGVD and ZHBGVD performed the same 14 tests.
          ZHEGVX, ZHPGVX and ZHBGVX 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 unitary 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 unitary 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 unitary 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) Hermitian 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,
              ZDRVSG 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, ZDRVSG
              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 ZDRVSG 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       COMPLEX*16 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.  It must be at
              least 1 and at least max( NN ).
              Not modified.
      B       COMPLEX*16 array, dimension (LDB , max(NN))
              Used to hold the Hermitian positive definite matrix for
              the generalized problem.
              On exit, B contains the last matrix actually
              used.
              Modified.
      LDB     INTEGER
              The leading dimension of B.  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       COMPLEX*16 array, dimension (LDZ, max(NN))
              The matrix of eigenvectors.
              Modified.
      LDZ     INTEGER
              The leading dimension of ZZ.  It must be at least 1 and
              at least max( NN ).
              Not modified.
      AB      COMPLEX*16 array, dimension (LDA, max(NN))
              Workspace.
              Modified.
      BB      COMPLEX*16 array, dimension (LDB, max(NN))
              Workspace.
              Modified.
      AP      COMPLEX*16 array, dimension (max(NN)**2)
              Workspace.
              Modified.
      BP      COMPLEX*16 array, dimension (max(NN)**2)
              Workspace.
              Modified.
      WORK    COMPLEX*16 array, dimension (NWORK)
              Workspace.
              Modified.
      NWORK   INTEGER
              The number of entries in WORK.  This must be at least
              2*N + N**2  where  N = max( NN(j), 2 ).
              Not modified.
      RWORK   DOUBLE PRECISION array, dimension (LRWORK)
              Workspace.
              Modified.
      LRWORK  INTEGER
              The number of entries in RWORK.  This must be at least
              max( 7*N, 1 + 4*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 IWORK.  This must be at least
              2 + 5*max( NN(j) ).
              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: LRWORK too small.
              -25: LIWORK too small.
              If  ZLATMR, CLATMS, ZHEGV, ZHPGV, ZHBGV, CHEGVD, CHPGVD,
                  ZHPGVD, ZHEGVX, CHPGVX, ZHBGVX 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 366 of file zdrvsg.f.

Author

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