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

.in +1c
.ti -1c
.RI "subroutine \fBzdrvev\fP (nsizes, nn, ntypes, dotype, iseed, thresh, nounit, a, lda, h, w, w1, vl, ldvl, vr, ldvr, lre, ldlre, result, work, nwork, rwork, iwork, info)"
.br
.RI "\fBZDRVEV\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine zdrvev (integer nsizes, integer, dimension( * ) nn, integer ntypes, logical, dimension( * ) dotype, integer, dimension( 4 ) iseed, double precision thresh, integer nounit, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( lda, * ) h, complex*16, dimension( * ) w, complex*16, dimension( * ) w1, complex*16, dimension( ldvl, * ) vl, integer ldvl, complex*16, dimension( ldvr, * ) vr, integer ldvr, complex*16, dimension( ldlre, * ) lre, integer ldlre, double precision, dimension( 7 ) result, complex*16, dimension( * ) work, integer nwork, double precision, dimension( * ) rwork, integer, dimension( * ) iwork, integer info)"

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

.PP
.nf
!>
!>    ZDRVEV  checks the nonsymmetric eigenvalue problem driver ZGEEV\&.
!>
!>    When ZDRVEV 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 nonsymmetric eigenroutines\&.  For each matrix, 7
!>    tests will be performed:
!>
!>    (1)     | A * VR - VR * W | / ( n |A| ulp )
!>
!>      Here VR is the matrix of unit right eigenvectors\&.
!>      W is a diagonal matrix with diagonal entries W(j)\&.
!>
!>    (2)     | A**H * VL - VL * W**H | / ( n |A| ulp )
!>
!>      Here VL is the matrix of unit left eigenvectors, A**H is the
!>      conjugate-transpose of A, and W is as above\&.
!>
!>    (3)     | |VR(i)| - 1 | / ulp and whether largest component real
!>
!>      VR(i) denotes the i-th column of VR\&.
!>
!>    (4)     | |VL(i)| - 1 | / ulp and whether largest component real
!>
!>      VL(i) denotes the i-th column of VL\&.
!>
!>    (5)     W(full) = W(partial)
!>
!>      W(full) denotes the eigenvalues computed when both VR and VL
!>      are also computed, and W(partial) denotes the eigenvalues
!>      computed when only W, only W and VR, or only W and VL are
!>      computed\&.
!>
!>    (6)     VR(full) = VR(partial)
!>
!>      VR(full) denotes the right eigenvectors computed when both VR
!>      and VL are computed, and VR(partial) denotes the result
!>      when only VR is computed\&.
!>
!>     (7)     VL(full) = VL(partial)
!>
!>      VL(full) denotes the left eigenvectors computed when both VR
!>      and VL are also computed, and VL(partial) denotes the result
!>      when only VL is computed\&.
!>
!>    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 (transposed) Jordan block, with 1's on the diagonal\&.
!>
!>    (4)  A diagonal matrix with evenly spaced entries
!>         1, \&.\&.\&., ULP  and random complex angles\&.
!>         (ULP = (first number larger than 1) - 1 )
!>    (5)  A diagonal matrix with geometrically spaced entries
!>         1, \&.\&.\&., ULP  and random complex angles\&.
!>    (6)  A diagonal matrix with  entries 1, ULP, \&.\&.\&., ULP
!>         and random complex angles\&.
!>
!>    (7)  Same as (4), but multiplied by a constant near
!>         the overflow threshold
!>    (8)  Same as (4), but multiplied by a constant near
!>         the underflow threshold
!>
!>    (9)  A matrix of the form  U' T U, where U is unitary and
!>         T has evenly spaced entries 1, \&.\&.\&., ULP with random complex
!>         angles on the diagonal and random O(1) entries in the upper
!>         triangle\&.
!>
!>    (10) A matrix of the form  U' T U, where U is unitary and
!>         T has geometrically spaced entries 1, \&.\&.\&., ULP with random
!>         complex angles on the diagonal and random O(1) entries in
!>         the upper triangle\&.
!>
!>    (11) A matrix of the form  U' T U, where U is unitary and
!>         T has  entries 1, ULP,\&.\&.\&., ULP with random
!>         complex angles on the diagonal and random O(1) entries in
!>         the upper triangle\&.
!>
!>    (12) A matrix of the form  U' T U, where U is unitary and
!>         T has complex eigenvalues randomly chosen from
!>         ULP < |z| < 1   and random O(1) entries in the upper
!>         triangle\&.
!>
!>    (13) A matrix of the form  X' T X, where X has condition
!>         SQRT( ULP ) and T has evenly spaced entries 1, \&.\&.\&., ULP
!>         with random complex angles on the diagonal and random O(1)
!>         entries in the upper triangle\&.
!>
!>    (14) A matrix of the form  X' T X, where X has condition
!>         SQRT( ULP ) and T has geometrically spaced entries
!>         1, \&.\&.\&., ULP with random complex angles on the diagonal
!>         and random O(1) entries in the upper triangle\&.
!>
!>    (15) A matrix of the form  X' T X, where X has condition
!>         SQRT( ULP ) and T has  entries 1, ULP,\&.\&.\&., ULP
!>         with random complex angles on the diagonal and random O(1)
!>         entries in the upper triangle\&.
!>
!>    (16) A matrix of the form  X' T X, where X has condition
!>         SQRT( ULP ) and T has complex eigenvalues randomly chosen
!>         from ULP < |z| < 1 and random O(1) entries in the upper
!>         triangle\&.
!>
!>    (17) Same as (16), but multiplied by a constant
!>         near the overflow threshold
!>    (18) Same as (16), but multiplied by a constant
!>         near the underflow threshold
!>
!>    (19) Nonsymmetric matrix with random entries chosen from |z| < 1
!>         If N is at least 4, all entries in first two rows and last
!>         row, and first column and last two columns are zero\&.
!>    (20) Same as (19), but multiplied by a constant
!>         near the overflow threshold
!>    (21) Same as (19), but multiplied by a constant
!>         near the underflow threshold
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fINSIZES\fP 
.PP
.nf
!>          NSIZES is INTEGER
!>          The number of sizes of matrices to use\&.  If it is zero,
!>          ZDRVEV does nothing\&.  It must be at least zero\&.
!> 
.fi
.PP
.br
\fINN\fP 
.PP
.nf
!>          NN is 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\&.
!> 
.fi
.PP
.br
\fINTYPES\fP 
.PP
.nf
!>          NTYPES is INTEGER
!>          The number of elements in DOTYPE\&.   If it is zero, ZDRVEV
!>          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\&. \&.
!> 
.fi
.PP
.br
\fIDOTYPE\fP 
.PP
.nf
!>          DOTYPE is 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\&.
!> 
.fi
.PP
.br
\fIISEED\fP 
.PP
.nf
!>          ISEED is 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 ZDRVEV to continue the same random number
!>          sequence\&.
!> 
.fi
.PP
.br
\fITHRESH\fP 
.PP
.nf
!>          THRESH is DOUBLE PRECISION
!>          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\&.
!> 
.fi
.PP
.br
\fINOUNIT\fP 
.PP
.nf
!>          NOUNIT is INTEGER
!>          The FORTRAN unit number for printing out error messages
!>          (e\&.g\&., if a routine returns INFO not equal to 0\&.)
!> 
.fi
.PP
.br
\fIA\fP 
.PP
.nf
!>          A is COMPLEX*16 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\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The leading dimension of A, and H\&. LDA must be at
!>          least 1 and at least max(NN)\&.
!> 
.fi
.PP
.br
\fIH\fP 
.PP
.nf
!>          H is COMPLEX*16 array, dimension (LDA, max(NN))
!>          Another copy of the test matrix A, modified by ZGEEV\&.
!> 
.fi
.PP
.br
\fIW\fP 
.PP
.nf
!>          W is COMPLEX*16 array, dimension (max(NN))
!>          The eigenvalues of A\&. On exit, W are the eigenvalues of
!>          the matrix in A\&.
!> 
.fi
.PP
.br
\fIW1\fP 
.PP
.nf
!>          W1 is COMPLEX*16 array, dimension (max(NN))
!>          Like W, this array contains the eigenvalues of A,
!>          but those computed when ZGEEV only computes a partial
!>          eigendecomposition, i\&.e\&. not the eigenvalues and left
!>          and right eigenvectors\&.
!> 
.fi
.PP
.br
\fIVL\fP 
.PP
.nf
!>          VL is COMPLEX*16 array, dimension (LDVL, max(NN))
!>          VL holds the computed left eigenvectors\&.
!> 
.fi
.PP
.br
\fILDVL\fP 
.PP
.nf
!>          LDVL is INTEGER
!>          Leading dimension of VL\&. Must be at least max(1,max(NN))\&.
!> 
.fi
.PP
.br
\fIVR\fP 
.PP
.nf
!>          VR is COMPLEX*16 array, dimension (LDVR, max(NN))
!>          VR holds the computed right eigenvectors\&.
!> 
.fi
.PP
.br
\fILDVR\fP 
.PP
.nf
!>          LDVR is INTEGER
!>          Leading dimension of VR\&. Must be at least max(1,max(NN))\&.
!> 
.fi
.PP
.br
\fILRE\fP 
.PP
.nf
!>          LRE is COMPLEX*16 array, dimension (LDLRE, max(NN))
!>          LRE holds the computed right or left eigenvectors\&.
!> 
.fi
.PP
.br
\fILDLRE\fP 
.PP
.nf
!>          LDLRE is INTEGER
!>          Leading dimension of LRE\&. Must be at least max(1,max(NN))\&.
!> 
.fi
.PP
.br
\fIRESULT\fP 
.PP
.nf
!>          RESULT is DOUBLE PRECISION array, dimension (7)
!>          The values computed by the seven tests described above\&.
!>          The values are currently limited to 1/ulp, to avoid
!>          overflow\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is COMPLEX*16 array, dimension (NWORK)
!> 
.fi
.PP
.br
\fINWORK\fP 
.PP
.nf
!>          NWORK is INTEGER
!>          The number of entries in WORK\&.  This must be at least
!>          5*NN(j)+2*NN(j)**2 for all j\&.
!> 
.fi
.PP
.br
\fIRWORK\fP 
.PP
.nf
!>          RWORK is DOUBLE PRECISION array, dimension (2*max(NN))
!> 
.fi
.PP
.br
\fIIWORK\fP 
.PP
.nf
!>          IWORK is INTEGER array, dimension (max(NN))
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          INFO is INTEGER
!>          If 0, then everything ran OK\&.
!>           -1: NSIZES < 0
!>           -2: Some NN(j) < 0
!>           -3: NTYPES < 0
!>           -6: THRESH < 0
!>           -9: LDA < 1 or LDA < NMAX, where NMAX is max( NN(j) )\&.
!>          -14: LDVL < 1 or LDVL < NMAX, where NMAX is max( NN(j) )\&.
!>          -16: LDVR < 1 or LDVR < NMAX, where NMAX is max( NN(j) )\&.
!>          -18: LDLRE < 1 or LDLRE < NMAX, where NMAX is max( NN(j) )\&.
!>          -21: NWORK too small\&.
!>          If  ZLATMR, CLATMS, CLATME or ZGEEV returns an error code,
!>              the absolute value of it is returned\&.
!>
!>-----------------------------------------------------------------------
!>
!>     Some Local Variables and Parameters:
!>     ---- ----- --------- --- ----------
!>
!>     ZERO, ONE       Real 0 and 1\&.
!>     MAXTYP          The number of types defined\&.
!>     NMAX            Largest value in NN\&.
!>     NERRS           The number of tests which have exceeded THRESH
!>     COND, CONDS,
!>     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\&.
!>     RTULP, RTULPI   Square roots of the previous 4 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) )
!>     KCONDS(j)       Selectw whether CONDS is to be 1 or
!>                     1/sqrt(ulp)\&.  (0 means irrelevant\&.)
!> 
.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 \fB387\fP of file \fBzdrvev\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.