.TH "TESTING/MATGEN/zlatme.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
TESTING/MATGEN/zlatme.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBzlatme\fP (n, dist, iseed, d, mode, cond, dmax, rsign, upper, sim, ds, modes, conds, kl, ku, anorm, a, lda, work, info)"
.br
.RI "\fBZLATME\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "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)"

.PP
\fBZLATME\fP 
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!>    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\&.)
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>           The number of columns (or rows) of A\&. Not modified\&.
!> 
.fi
.PP
.br
\fIDIST\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIISEED\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fID\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIMODE\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fICOND\fP 
.PP
.nf
!>          COND is DOUBLE PRECISION
!>           On entry, this is used as described under MODE above\&.
!>           If used, it must be >= 1\&. Not modified\&.
!> 
.fi
.PP
.br
\fIDMAX\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIRSIGN\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIUPPER\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fISIM\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIDS\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIMODES\fP 
.PP
.nf
!>          MODES is INTEGER
!> 
.fi
.PP
.br
\fICONDS\fP 
.PP
.nf
!>          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\&.)
!> 
.fi
.PP
.br
\fIKL\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIKU\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIANORM\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIA\fP 
.PP
.nf
!>          A is COMPLEX*16 array, dimension ( LDA, N )
!>           On exit A is the desired test matrix\&.
!>           Modified\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>           LDA specifies the first dimension of A as declared in the
!>           calling program\&.  LDA must be at least M\&.
!>           Not modified\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is COMPLEX*16 array, dimension ( 3*N )
!>           Workspace\&.
!>           Modified\&.
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP

.PP
Definition at line \fB296\fP of file \fBzlatme\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.