ZDRVEV  checks the nonsymmetric eigenvalue problem driver ZGEEV.


    When ZDRVEV is called, a number of matrix 'sizes' ('n's') and a


    number of matrix 'types' are specified.  For each size ('n')


    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 'sizes' are specified by an array NN(1:NSIZES); the value of


    each element NN(j) specifies one size.


    The 'types' are specified by a logical array DOTYPE( 1:NTYPES );


    if DOTYPE(j) is .TRUE., then matrix type 'j' 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 'clustered' 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 'clustered' 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 'clustered' 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

NSIZES

          NSIZES is INTEGER


          The number of sizes of matrices to use.  If it is zero,


          ZDRVEV does nothing.  It must be at least zero.

NN

          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.

NTYPES

          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. .

DOTYPE

          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.

ISEED

          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.

THRESH

          THRESH is DOUBLE PRECISION


          A test will count as 'failed' if the 'error', 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.

NOUNIT

          NOUNIT is INTEGER


          The FORTRAN unit number for printing out error messages


          (e.g., if a routine returns INFO not equal to 0.)

A

          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.

LDA

          LDA is INTEGER


          The leading dimension of A, and H. LDA must be at


          least 1 and at least max(NN).

H

          H is COMPLEX*16 array, dimension (LDA, max(NN))


          Another copy of the test matrix A, modified by ZGEEV.

W

          W is COMPLEX*16 array, dimension (max(NN))


          The eigenvalues of A. On exit, W are the eigenvalues of


          the matrix in A.

W1

          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.

VL

          VL is COMPLEX*16 array, dimension (LDVL, max(NN))


          VL holds the computed left eigenvectors.

LDVL

          LDVL is INTEGER


          Leading dimension of VL. Must be at least max(1,max(NN)).

VR

          VR is COMPLEX*16 array, dimension (LDVR, max(NN))


          VR holds the computed right eigenvectors.

LDVR

          LDVR is INTEGER


          Leading dimension of VR. Must be at least max(1,max(NN)).

LRE

          LRE is COMPLEX*16 array, dimension (LDLRE, max(NN))


          LRE holds the computed right or left eigenvectors.

LDLRE

          LDLRE is INTEGER


          Leading dimension of LRE. Must be at least max(1,max(NN)).

RESULT

          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.

WORK

          WORK is COMPLEX*16 array, dimension (NWORK)

NWORK

          NWORK is INTEGER


          The number of entries in WORK.  This must be at least


          5*NN(j)+2*NN(j)**2 for all j.

RWORK

          RWORK is DOUBLE PRECISION array, dimension (2*max(NN))

IWORK

          IWORK is INTEGER array, dimension (max(NN))

INFO

          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 'j'.


     KMODE(j)        The MODE value to be passed to the matrix


                     generator for type 'j'.


     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.)

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