TESTING/MATGEN/slatme.f(3)

NAME
TESTING/MATGEN/slatme.f

SYNOPSIS

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

Function/Subroutine Documentation

  subroutine slatme (integer n, character dist, integer, dimension( 4 ) iseed, real, dimension( * ) d, integer mode, real cond, real dmax, character, dimension( * ) ei, character rsign, character upper, character sim, real, dimension( * ) ds, integer modes, real conds, integer kl, integer ku, real anorm, real, dimension( lda, * ) a, integer lda, real, dimension( * ) work, integer info)

SLATME

Purpose:

    !>
    !>    SLATME generates random non-symmetric square matrices with
    !>    specified eigenvalues for testing LAPACK programs.
    !>
    !>    SLATME 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 complex conjugate pairs are desired (MODE=0 and EI(1)='R',
    !>         or MODE=5), certain pairs of adjacent elements of D are
    !>         interpreted as the real and complex parts of a complex
    !>         conjugate pair; A thus becomes block diagonal, with 1x1
    !>         and 2x2 blocks.
    !>
    !>    3. If UPPER='T', the upper triangle of A is set to random values
    !>         out of distribution DIST.
    !>
    !>    4. 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.
    !>
    !>    5. 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.
    !>
    !>    6. 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 for 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 )
    !>           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 SLATME
    !>           to continue the same random number sequence.
    !>           Changed on exit.
    !>

    D

    !>          D is REAL array, dimension ( N )
    !>           This array is used to specify the eigenvalues of A.  If
    !>           MODE=0, then D is assumed to contain the eigenvalues (but
    !>           see the description of EI), 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 (with EI) 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.  Each odd-even pair
    !>                    of elements will be either used as two real
    !>                    eigenvalues or as the real and imaginary part
    !>                    of a complex conjugate pair of eigenvalues;
    !>                    the choice of which is done is random, with
    !>                    50-50 probability, for each pair.
    !>           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 REAL
    !>           On entry, this is used as described under MODE above.
    !>           If used, it must be >= 1. Not modified.
    !>

    DMAX

    !>          DMAX is REAL
    !>           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: if DMAX is negative (or zero), D will be
    !>           scaled by a negative number (or zero).
    !>           Not modified.
    !>

    EI

    !>          EI is CHARACTER*1 array, dimension ( N )
    !>           If MODE is 0, and EI(1) is not ' ' (space character),
    !>           this array specifies which elements of D (on input) are
    !>           real eigenvalues and which are the real and imaginary parts
    !>           of a complex conjugate pair of eigenvalues.  The elements
    !>           of EI may then only have the values 'R' and 'I'.  If
    !>           EI(j)='R' and EI(j+1)='I', then the j-th eigenvalue is
    !>           CMPLX( D(j) , D(j+1) ), and the (j+1)-th is the complex
    !>           conjugate thereof.  If EI(j)=EI(j+1)='R', then the j-th
    !>           eigenvalue is D(j) (i.e., real).  EI(1) may not be 'I',
    !>           nor may two adjacent elements of EI both have the value 'I'.
    !>           If MODE is not 0, then EI is ignored.  If MODE is 0 and
    !>           EI(1)=' ', then the eigenvalues will all be real.
    !>           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 sign (+1 or -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
    !>           (and above the 2x2 diagonal blocks, if A has complex
    !>           eigenvalues) 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 , 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 REAL 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 REAL
    !>           Same as 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.  KL must be at
    !>           least 1.
    !>           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.  KU must be at least 1.
    !>           Not modified.
    !>

    ANORM

    !>          ANORM is REAL
    !>           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 REAL 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 N.
    !>           Not modified.
    !>

    WORK

    !>          WORK is REAL 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
    !>            -8 => EI(1) is not ' ' or 'R', EI(j) is not 'R' or 'I', or
    !>                  two adjacent elements of EI are 'I'.
    !>            -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 N.
    !>            1  => Error return from SLATM1 (computing D)
    !>            2  => Cannot scale to DMAX (max. eigenvalue is 0)
    !>            3  => Error return from SLATM1 (computing DS)
    !>            4  => Error return from SLARGE
    !>            5  => Zero singular value from SLATM1.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 327 of file slatme.f.

Author

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