TESTING/MATGEN/zlatme.f(3)

NAME
TESTING/MATGEN/zlatme.f

SYNOPSIS

  Functions/Subroutines
subroutine zlatme (n, dist, iseed, d, mode, cond, dmax, rsign, upper, sim, ds, modes, conds, kl, ku, anorm, a, lda, work, info)
ZLATME

Function/Subroutine Documentation

  subroutine zlatme (integer n, character dist, integer, dimension( 4 ) iseed, complex*16, dimension( * ) d, integer mode, double precision cond, complex*16 dmax, character rsign, character upper, character sim, double precision, dimension( * ) ds, integer modes, double precision conds, integer kl, integer ku, double precision anorm, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) work, integer info)

ZLATME

Purpose:

        ZLATME generates random non-symmetric square matrices with
        specified eigenvalues for testing LAPACK programs.
        ZLATME operates by applying the following sequence of
        operations:
        1. Set the diagonal to D, where D may be input or
             computed according to MODE, COND, DMAX, and RSIGN
             as described below.
        2. If UPPER='T', the upper triangle of A is set to random values
             out of distribution DIST.
        3. If SIM='T', A is multiplied on the left by a random matrix
             X, whose singular values are specified by DS, MODES, and
             CONDS, and on the right by X inverse.
        4. If KL < N-1, the lower bandwidth is reduced to KL using
             Householder transformations.  If KU < N-1, the upper
             bandwidth is reduced to KU.
        5. If ANORM is not negative, the matrix is scaled to have
             maximum-element-norm ANORM.
        (Note: since the matrix cannot be reduced beyond Hessenberg form,
         no packing options are available.)

Parameters
    N

              N is INTEGER
               The number of columns (or rows) of A. Not modified.

    DIST

              DIST is CHARACTER*1
               On entry, DIST specifies the type of distribution to be used
               to generate the random eigen-/singular values, and on the
               upper triangle (see UPPER).
               'U' => UNIFORM( 0, 1 )  ( 'U' for uniform )
               'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric )
               'N' => NORMAL( 0, 1 )   ( 'N' for normal )
               'D' => uniform on the complex disc |z| < 1.
               Not modified.

    ISEED

              ISEED is INTEGER array, dimension ( 4 )
               On entry ISEED specifies the seed of the random number
               generator. They should lie between 0 and 4095 inclusive,
               and ISEED(4) should 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 ZLATME
               to continue the same random number sequence.
               Changed on exit.

    D

              D is COMPLEX*16 array, dimension ( N )
               This array is used to specify the eigenvalues of A.  If
               MODE=0, then D is assumed to contain the eigenvalues
               otherwise they will be computed according to MODE, COND,
               DMAX, and RSIGN and placed in D.
               Modified if MODE is nonzero.

    MODE

              MODE is INTEGER
               On entry this describes how the eigenvalues are to
               be specified:
               MODE = 0 means use D as input
               MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND
               MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND
               MODE = 3 sets D(I)=COND**(-(I-1)/(N-1))
               MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND)
               MODE = 5 sets D to random numbers in the range
                        ( 1/COND , 1 ) such that their logarithms
                        are uniformly distributed.
               MODE = 6 set D to random numbers from same distribution
                        as the rest of the matrix.
               MODE < 0 has the same meaning as ABS(MODE), except that
                  the order of the elements of D is reversed.
               Thus if MODE is between 1 and 4, D has entries ranging
                  from 1 to 1/COND, if between -1 and -4, D has entries
                  ranging from 1/COND to 1,
               Not modified.

    COND

              COND is DOUBLE PRECISION
               On entry, this is used as described under MODE above.
               If used, it must be >= 1. Not modified.

    DMAX

              DMAX is COMPLEX*16
               If MODE is neither -6, 0 nor 6, the contents of D, as
               computed according to MODE and COND, will be scaled by
               DMAX / max(abs(D(i))).  Note that DMAX need not be
               positive or real: if DMAX is negative or complex (or zero),
               D will be scaled by a negative or complex number (or zero).
               If RSIGN='F' then the largest (absolute) eigenvalue will be
               equal to DMAX.
               Not modified.

    RSIGN

              RSIGN is CHARACTER*1
               If MODE is not 0, 6, or -6, and RSIGN='T', then the
               elements of D, as computed according to MODE and COND, will
               be multiplied by a random complex number from the unit
               circle |z| = 1.  If RSIGN='F', they will not be.  RSIGN may
               only have the values 'T' or 'F'.
               Not modified.

    UPPER

              UPPER is CHARACTER*1
               If UPPER='T', then the elements of A above the diagonal
               will be set to random numbers out of DIST.  If UPPER='F',
               they will not.  UPPER may only have the values 'T' or 'F'.
               Not modified.

    SIM

              SIM is CHARACTER*1
               If SIM='T', then A will be operated on by a 'similarity
               transform', i.e., multiplied on the left by a matrix X and
               on the right by X inverse.  X = U S V, where U and V are
               random unitary matrices and S is a (diagonal) matrix of
               singular values specified by DS, MODES, and CONDS.  If
               SIM='F', then A will not be transformed.
               Not modified.

    DS

              DS is DOUBLE PRECISION array, dimension ( N )
               This array is used to specify the singular values of X,
               in the same way that D specifies the eigenvalues of A.
               If MODE=0, the DS contains the singular values, which
               may not be zero.
               Modified if MODE is nonzero.

    MODES

              MODES is INTEGER

    CONDS

              CONDS is DOUBLE PRECISION
               Similar to MODE and COND, but for specifying the diagonal
               of S.  MODES=-6 and +6 are not allowed (since they would
               result in randomly ill-conditioned eigenvalues.)

    KL

              KL is INTEGER
               This specifies the lower bandwidth of the  matrix.  KL=1
               specifies upper Hessenberg form.  If KL is at least N-1,
               then A will have full lower bandwidth.
               Not modified.

    KU

              KU is INTEGER
               This specifies the upper bandwidth of the  matrix.  KU=1
               specifies lower Hessenberg form.  If KU is at least N-1,
               then A will have full upper bandwidth; if KU and KL
               are both at least N-1, then A will be dense.  Only one of
               KU and KL may be less than N-1.
               Not modified.

    ANORM

              ANORM is DOUBLE PRECISION
               If ANORM is not negative, then A will be scaled by a non-
               negative real number to make the maximum-element-norm of A
               to be ANORM.
               Not modified.

    A

              A is COMPLEX*16 array, dimension ( LDA, N )
               On exit A is the desired test matrix.
               Modified.

    LDA

              LDA is INTEGER
               LDA specifies the first dimension of A as declared in the
               calling program.  LDA must be at least M.
               Not modified.

    WORK

              WORK is COMPLEX*16 array, dimension ( 3*N )
               Workspace.
               Modified.

    INFO

              INFO is INTEGER
               Error code.  On exit, INFO will be set to one of the
               following values:
                 0 => normal return
                -1 => N negative
                -2 => DIST illegal string
                -5 => MODE not in range -6 to 6
                -6 => COND less than 1.0, and MODE neither -6, 0 nor 6
                -9 => RSIGN is not 'T' or 'F'
               -10 => UPPER is not 'T' or 'F'
               -11 => SIM   is not 'T' or 'F'
               -12 => MODES=0 and DS has a zero singular value.
               -13 => MODES is not in the range -5 to 5.
               -14 => MODES is nonzero and CONDS is less than 1.
               -15 => KL is less than 1.
               -16 => KU is less than 1, or KL and KU are both less than
                      N-1.
               -19 => LDA is less than M.
                1  => Error return from ZLATM1 (computing D)
                2  => Cannot scale to DMAX (max. eigenvalue is 0)
                3  => Error return from DLATM1 (computing DS)
                4  => Error return from ZLARGE
                5  => Zero singular value from DLATM1.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 296 of file zlatme.f.

Author

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