dlatme.f3

!>
!>    DLATME generates random non-symmetric square matrices with
!>    specified eigenvalues for testing LAPACK programs.
!>
!>    DLATME 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.)
!> 

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 DLATME
!>           to continue the same random number sequence.
!>           Changed on exit.
!> 

D

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

DMAX

!>          DMAX is DOUBLE PRECISION
!>           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 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
!>           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 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DLATM1 (computing D)
!>            2  => Cannot scale to DMAX (max. eigenvalue is 0)
!>            3  => Error return from DLATM1 (computing DS)
!>            4  => Error return from DLARGE
!>            5  => Zero singular value from DLATM1.
!> 

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