TESTING/EIG/cdrvst2stg.f(3)

NAME
TESTING/EIG/cdrvst2stg.f

SYNOPSIS

  Functions/Subroutines
subroutine cdrvst2stg (nsizes, nn, ntypes, dotype, iseed, thresh, nounit, a, lda, d1, d2, d3, wa1, wa2, wa3, u, ldu, v, tau, z, work, lwork, rwork, lrwork, iwork, liwork, result, info)
CDRVST2STG

Function/Subroutine Documentation

  subroutine cdrvst2stg (integer nsizes, integer, dimension( * ) nn, integer ntypes, logical, dimension( * ) dotype, integer, dimension( 4 ) iseed, real thresh, integer nounit, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) d1, real, dimension( * ) d2, real, dimension( * ) d3, real, dimension( * ) wa1, real, dimension( * ) wa2, real, dimension( * ) wa3, complex, dimension( ldu, * ) u, integer ldu, complex, dimension( ldu, * ) v, complex, dimension( * ) tau, complex, dimension( ldu, * ) z, complex, dimension( * ) work, integer lwork, real, dimension( * ) rwork, integer lrwork, integer, dimension( * ) iwork, integer liwork, real, dimension( * ) result, integer info)

CDRVST2STG

Purpose:

    !>
    !>      CDRVST2STG  checks the Hermitian eigenvalue problem drivers.
    !>
    !>              CHEEVD computes all eigenvalues and, optionally,
    !>              eigenvectors of a complex Hermitian matrix,
    !>              using a divide-and-conquer algorithm.
    !>
    !>              CHEEVX computes selected eigenvalues and, optionally,
    !>              eigenvectors of a complex Hermitian matrix.
    !>
    !>              CHEEVR computes selected eigenvalues and, optionally,
    !>              eigenvectors of a complex Hermitian matrix
    !>              using the Relatively Robust Representation where it can.
    !>
    !>              CHPEVD computes all eigenvalues and, optionally,
    !>              eigenvectors of a complex Hermitian matrix in packed
    !>              storage, using a divide-and-conquer algorithm.
    !>
    !>              CHPEVX computes selected eigenvalues and, optionally,
    !>              eigenvectors of a complex Hermitian matrix in packed
    !>              storage.
    !>
    !>              CHBEVD computes all eigenvalues and, optionally,
    !>              eigenvectors of a complex Hermitian band matrix,
    !>              using a divide-and-conquer algorithm.
    !>
    !>              CHBEVX computes selected eigenvalues and, optionally,
    !>              eigenvectors of a complex Hermitian band matrix.
    !>
    !>              CHEEV computes all eigenvalues and, optionally,
    !>              eigenvectors of a complex Hermitian matrix.
    !>
    !>              CHPEV computes all eigenvalues and, optionally,
    !>              eigenvectors of a complex Hermitian matrix in packed
    !>              storage.
    !>
    !>              CHBEV computes all eigenvalues and, optionally,
    !>              eigenvectors of a complex Hermitian band matrix.
    !>
    !>      When CDRVST2STG is called, a number of matrix  () and a
    !>      number of matrix  are specified.  For each size ()
    !>      and each type of matrix, one matrix will be generated and used
    !>      to test the appropriate drivers.  For each matrix and each
    !>      driver routine called, the following tests will be performed:
    !>
    !>      (1)     | A - Z D Z' | / ( |A| n ulp )
    !>
    !>      (2)     | I - Z Z' | / ( n ulp )
    !>
    !>      (3)     | D1 - D2 | / ( |D1| ulp )
    !>
    !>      where Z is the matrix of eigenvectors returned when the
    !>      eigenvector option is given and D1 and D2 are the eigenvalues
    !>      returned with and without the eigenvector option.
    !>
    !>      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 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  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) A band matrix with half bandwidth randomly chosen between
    !>           0 and N-1, with evenly spaced eigenvalues 1, ..., ULP
    !>           with random signs.
    !>      (17) Same as (16), but multiplied by SQRT( overflow threshold )
    !>      (18) Same as (16), but multiplied by SQRT( underflow threshold )
    !>

    !>  NSIZES  INTEGER
    !>          The number of sizes of matrices to use.  If it is zero,
    !>          CDRVST2STG 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, CDRVST2STG
    !>          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 CDRVST2STG 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. 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 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.
    !>
    !>  D1      REAL             array, dimension (max(NN))
    !>          The eigenvalues of A, as computed by CSTEQR simultaneously
    !>          with Z.  On exit, the eigenvalues in D1 correspond with the
    !>          matrix in A.
    !>          Modified.
    !>
    !>  D2      REAL             array, dimension (max(NN))
    !>          The eigenvalues of A, as computed by CSTEQR if Z is not
    !>          computed.  On exit, the eigenvalues in D2 correspond with
    !>          the matrix in A.
    !>          Modified.
    !>
    !>  D3      REAL             array, dimension (max(NN))
    !>          The eigenvalues of A, as computed by SSTERF.  On exit, the
    !>          eigenvalues in D3 correspond with the matrix in A.
    !>          Modified.
    !>
    !>  WA1     REAL array, dimension
    !>
    !>  WA2     REAL array, dimension
    !>
    !>  WA3     REAL array, dimension
    !>
    !>  U       COMPLEX array, dimension (LDU, max(NN))
    !>          The unitary matrix computed by CHETRD + CUNGC3.
    !>          Modified.
    !>
    !>  LDU     INTEGER
    !>          The leading dimension of U, Z, and V.  It must be at
    !>          least 1 and at least max( NN ).
    !>          Not modified.
    !>
    !>  V       COMPLEX array, dimension (LDU, max(NN))
    !>          The Housholder vectors computed by CHETRD in reducing A to
    !>          tridiagonal form.
    !>          Modified.
    !>
    !>  TAU     COMPLEX array, dimension (max(NN))
    !>          The Householder factors computed by CHETRD in reducing A
    !>          to tridiagonal form.
    !>          Modified.
    !>
    !>  Z       COMPLEX array, dimension (LDU, max(NN))
    !>          The unitary matrix of eigenvectors computed by CHEEVD,
    !>          CHEEVX, CHPEVD, CHPEVX, CHBEVD, and CHBEVX.
    !>          Modified.
    !>
    !>  WORK  - COMPLEX array of dimension ( LWORK )
    !>           Workspace.
    !>           Modified.
    !>
    !>  LWORK - INTEGER
    !>           The number of entries in WORK.  This must be at least
    !>           2*max( NN(j), 2 )**2.
    !>           Not modified.
    !>
    !>  RWORK   REAL array, dimension (3*max(NN))
    !>           Workspace.
    !>           Modified.
    !>
    !>  LRWORK - INTEGER
    !>           The number of entries in RWORK.
    !>
    !>  IWORK   INTEGER array, dimension (6*max(NN))
    !>          Workspace.
    !>          Modified.
    !>
    !>  LIWORK - INTEGER
    !>           The number of entries in IWORK.
    !>
    !>  RESULT  REAL array, dimension (??)
    !>          The values computed by the tests described above.
    !>          The values are currently limited to 1/ulp, to avoid
    !>          overflow.
    !>          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: LDU < 1 or LDU < NMAX.
    !>          -21: LWORK too small.
    !>          If  SLATMR, SLATMS, CHETRD, SORGC3, CSTEQR, SSTERF,
    !>              or SORMC2 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 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 (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 334 of file cdrvst2stg.f.

Author

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