TESTING/EIG/schksb2stg.f(3)

NAME
TESTING/EIG/schksb2stg.f

SYNOPSIS

  Functions/Subroutines
subroutine schksb2stg (nsizes, nn, nwdths, kk, ntypes, dotype, iseed, thresh, nounit, a, lda, sd, se, d1, d2, d3, u, ldu, work, lwork, result, info)
SCHKSB2STG

Function/Subroutine Documentation

  subroutine schksb2stg (integer nsizes, integer, dimension( * ) nn, integer nwdths, integer, dimension( * ) kk, integer ntypes, logical, dimension( * ) dotype, integer, dimension( 4 ) iseed, real thresh, integer nounit, real, dimension( lda, * ) a, integer lda, real, dimension( * ) sd, real, dimension( * ) se, real, dimension( * ) d1, real, dimension( * ) d2, real, dimension( * ) d3, real, dimension( ldu, * ) u, integer ldu, real, dimension( * ) work, integer lwork, real, dimension( * ) result, integer info)

SCHKSB2STG

Purpose:

    !>
    !> SCHKSB2STG tests the reduction of a symmetric band matrix to tridiagonal
    !> form, used with the symmetric eigenvalue problem.
    !>
    !> SSBTRD factors a symmetric band matrix A as  U S U' , where ' means
    !> transpose, S is symmetric tridiagonal, and U is orthogonal.
    !> SSBTRD can use either just the lower or just the upper triangle
    !> of A; SCHKSB2STG checks both cases.
    !>
    !> SSYTRD_SB2ST factors a symmetric band matrix A as  U S U' ,
    !> where ' means transpose, S is symmetric tridiagonal, and U is
    !> orthogonal. SSYTRD_SB2ST can use either just the lower or just
    !> the upper triangle of A; SCHKSB2STG checks both cases.
    !>
    !> SSTEQR factors S as  Z D1 Z'.
    !> D1 is the matrix of eigenvalues computed when Z is not computed
    !> and from the S resulting of SSBTRD  (used as reference for SSYTRD_SB2ST)
    !> D2 is the matrix of eigenvalues computed when Z is not computed
    !> and from the S resulting of SSYTRD_SB2ST .
    !> D3 is the matrix of eigenvalues computed when Z is not computed
    !> and from the S resulting of SSYTRD_SB2ST .
    !>
    !> When SCHKSB2STG is called, a number of matrix  (), a number
    !> of bandwidths (), and a number of matrix  are
    !> specified.  For each size (), each bandwidth () less than or
    !> equal to , and each type of matrix, one matrix will be generated
    !> and used to test the symmetric banded reduction routine.  For each
    !> matrix, a number of tests will be performed:
    !>
    !> (1)     | A - V S V' | / ( |A| n ulp )  computed by SSBTRD with
    !>                                         UPLO='U'
    !>
    !> (2)     | I - UU' | / ( n ulp )
    !>
    !> (3)     | A - V S V' | / ( |A| n ulp )  computed by SSBTRD with
    !>                                         UPLO='L'
    !>
    !> (4)     | I - UU' | / ( n ulp )
    !>
    !> (5)     | D1 - D2 | / ( |D1| ulp )      where D1 is computed by
    !>                                         SSBTRD with UPLO='U' and
    !>                                         D2 is computed by
    !>                                         SSYTRD_SB2ST with UPLO='U'
    !>
    !> (6)     | D1 - D3 | / ( |D1| ulp )      where D1 is computed by
    !>                                         SSBTRD with UPLO='U' and
    !>                                         D3 is computed by
    !>                                         SSYTRD_SB2ST with UPLO='L'
    !>
    !> 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.
    !> 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  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 )
    !>

Parameters
    NSIZES

    !>          NSIZES is INTEGER
    !>          The number of sizes of matrices to use.  If it is zero,
    !>          SCHKSB2STG 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,
    !>          SCHKSB2STG 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, SCHKSB2STG
    !>          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 SCHKSB2STG to continue the same random number
    !>          sequence.
    !>

    THRESH

    !>          THRESH is 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. 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 REAL 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 REAL array, dimension (max(NN))
    !>          Used to hold the diagonal of the tridiagonal matrix computed
    !>          by SSBTRD.
    !>

    SE

    !>          SE is REAL array, dimension (max(NN))
    !>          Used to hold the off-diagonal of the tridiagonal matrix
    !>          computed by SSBTRD.
    !>

    D1

    !>          D1 is REAL array, dimension (max(NN))
    !>

    D2

    !>          D2 is REAL array, dimension (max(NN))
    !>

    D3

    !>          D3 is REAL array, dimension (max(NN))
    !>

    U

    !>          U is REAL array, dimension (LDU, max(NN))
    !>          Used to hold the orthogonal matrix computed by SSBTRD.
    !>

    LDU

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

    WORK

    !>          WORK is REAL 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).
    !>

    RESULT

    !>          RESULT is REAL 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 .
    !>       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 329 of file schksb2stg.f.

Author

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