TESTING/EIG/zchkhb2stg.f(3)

NAME
TESTING/EIG/zchkhb2stg.f

SYNOPSIS

  Functions/Subroutines
subroutine zchkhb2stg (nsizes, nn, nwdths, kk, ntypes, dotype, iseed, thresh, nounit, a, lda, sd, se, d1, d2, d3, u, ldu, work, lwork, rwork, result, info)
ZCHKHB2STG

Function/Subroutine Documentation

  subroutine zchkhb2stg (integer nsizes, integer, dimension( * ) nn, integer nwdths, integer, dimension( * ) kk, integer ntypes, logical, dimension( * ) dotype, integer, dimension( 4 ) iseed, double precision thresh, integer nounit, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) sd, double precision, dimension( * ) se, double precision, dimension( * ) d1, double precision, dimension( * ) d2, double precision, dimension( * ) d3, complex*16, dimension( ldu, * ) u, integer ldu, complex*16, dimension( * ) work, integer lwork, double precision, dimension( * ) rwork, double precision, dimension( * ) result, integer info)

ZCHKHB2STG

Purpose:

     ZCHKHB2STG tests the reduction of a Hermitian band matrix to tridiagonal
     from, used with the Hermitian eigenvalue problem.
     ZHBTRD factors a Hermitian band matrix A as  U S U* , where * means
     conjugate transpose, S is symmetric tridiagonal, and U is unitary.
     ZHBTRD can use either just the lower or just the upper triangle
     of A; ZCHKHB2STG checks both cases.
     ZHETRD_HB2ST factors a Hermitian band matrix A as  U S U* ,
     where * means conjugate transpose, S is symmetric tridiagonal, and U is
     unitary. ZHETRD_HB2ST can use either just the lower or just
     the upper triangle of A; ZCHKHB2STG checks both cases.
     DSTEQR factors S as  Z D1 Z'.
     D1 is the matrix of eigenvalues computed when Z is not computed
     and from the S resulting of DSBTRD 'U' (used as reference for DSYTRD_SB2ST)
     D2 is the matrix of eigenvalues computed when Z is not computed
     and from the S resulting of DSYTRD_SB2ST 'U'.
     D3 is the matrix of eigenvalues computed when Z is not computed
     and from the S resulting of DSYTRD_SB2ST 'L'.
     When ZCHKHB2STG is called, a number of matrix 'sizes' ('n's'), a number
     of bandwidths ('k's'), and a number of matrix 'types' are
     specified.  For each size ('n'), each bandwidth ('k') less than or
     equal to 'n', and each type of matrix, one matrix will be generated
     and used to test the hermitian banded reduction routine.  For each
     matrix, a number of tests will be performed:
     (1)     | A - V S V* | / ( |A| n ulp )  computed by ZHBTRD with
                                             UPLO='U'
     (2)     | I - UU* | / ( n ulp )
     (3)     | A - V S V* | / ( |A| n ulp )  computed by ZHBTRD with
                                             UPLO='L'
     (4)     | I - UU* | / ( n ulp )
     (5)     | D1 - D2 | / ( |D1| ulp )      where D1 is computed by
                                             DSBTRD with UPLO='U' and
                                             D2 is computed by
                                             ZHETRD_HB2ST with UPLO='U'
     (6)     | D1 - D3 | / ( |D1| ulp )      where D1 is computed by
                                             DSBTRD with UPLO='U' and
                                             D3 is computed by
                                             ZHETRD_HB2ST with UPLO='L'
     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 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 )

Parameters
    NSIZES

              NSIZES is INTEGER
              The number of sizes of matrices to use.  If it is zero,
              ZCHKHB2STG 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.

    NWDTHS

              NWDTHS is INTEGER
              The number of bandwidths to use.  If it is zero,
              ZCHKHB2STG does nothing.  It must be at least zero.

    KK

              KK is INTEGER array, dimension (NWDTHS)
              An array containing the bandwidths to be used for the band
              matrices.  The values must be at least zero.

    NTYPES

              NTYPES is INTEGER
              The number of elements in DOTYPE.   If it is zero, ZCHKHB2STG
              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 ZCHKHB2STG to continue the same random number
              sequence.

    THRESH

              THRESH is 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.

    NOUNIT

              NOUNIT is INTEGER
              The FORTRAN unit number for printing out error messages
              (e.g., if a routine returns IINFO not equal to 0.)

    A

              A is COMPLEX*16 array, dimension
                                (LDA, max(NN))
              Used to hold the matrix whose eigenvalues are to be
              computed.

    LDA

              LDA is INTEGER
              The leading dimension of A.  It must be at least 2 (not 1!)
              and at least max( KK )+1.

    SD

              SD is DOUBLE PRECISION array, dimension (max(NN))
              Used to hold the diagonal of the tridiagonal matrix computed
              by ZHBTRD.

    SE

              SE is DOUBLE PRECISION array, dimension (max(NN))
              Used to hold the off-diagonal of the tridiagonal matrix
              computed by ZHBTRD.

    D1

              D1 is DOUBLE PRECISION array, dimension (max(NN))

    D2

              D2 is DOUBLE PRECISION array, dimension (max(NN))

     *>
    D3

              D3 is DOUBLE PRECISION array, dimension (max(NN))

    U

              U is COMPLEX*16 array, dimension (LDU, max(NN))
              Used to hold the unitary matrix computed by ZHBTRD.

    LDU

              LDU is INTEGER
              The leading dimension of U.  It must be at least 1
              and at least max( NN ).

    WORK

              WORK is COMPLEX*16 array, dimension (LWORK)

    LWORK

              LWORK is INTEGER
              The number of entries in WORK.  This must be at least
              max( LDA+1, max(NN)+1 )*max(NN).

    RWORK

              RWORK is DOUBLE PRECISION array

    RESULT

              RESULT is DOUBLE PRECISION array, dimension (4)
              The values computed by the tests described above.
              The values are currently limited to 1/ulp, to avoid
              overflow.

    INFO

              INFO is INTEGER
              If 0, then everything ran OK.
    -----------------------------------------------------------------------
           Some Local Variables and Parameters:
           ---- ----- --------- --- ----------
           ZERO, ONE       Real 0 and 1.
           MAXTYP          The number of types defined.
           NTEST           The number of tests performed, or which can
                           be performed so far, for the current matrix.
           NTESTT          The total number of tests performed so far.
           NMAX            Largest value in NN.
           NMATS           The number of matrices generated so far.
           NERRS           The number of tests which have exceeded THRESH
                           so far.
           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 334 of file zchkhb2stg.f.

Author

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