LAPACK: TESTING/EIG/zdrgev.f Source File

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00001       SUBROUTINE ZDRGEV( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
00002      $                   NOUNIT, A, LDA, B, S, T, Q, LDQ, Z, QE, LDQE,
00003      $                   ALPHA, BETA, ALPHA1, BETA1, WORK, LWORK, RWORK,
00004      $                   RESULT, INFO )
00005 *
00006 *  -- LAPACK test routine (version 3.1.1) --
00007 *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
00008 *     February 2007
00009 *
00010 *     .. Scalar Arguments ..
00011       INTEGER            INFO, LDA, LDQ, LDQE, LWORK, NOUNIT, NSIZES,
00012      $                   NTYPES
00013       DOUBLE PRECISION   THRESH
00014 *     ..
00015 *     .. Array Arguments ..
00016       LOGICAL            DOTYPE( * )
00017       INTEGER            ISEED( 4 ), NN( * )
00018       DOUBLE PRECISION   RESULT( * ), RWORK( * )
00019       COMPLEX*16         A( LDA, * ), ALPHA( * ), ALPHA1( * ),
00020      $                   B( LDA, * ), BETA( * ), BETA1( * ),
00021      $                   Q( LDQ, * ), QE( LDQE, * ), S( LDA, * ),
00022      $                   T( LDA, * ), WORK( * ), Z( LDQ, * )
00023 *     ..
00024 *
00025 *  Purpose
00026 *  =======
00027 *
00028 *  ZDRGEV checks the nonsymmetric generalized eigenvalue problem driver
00029 *  routine ZGGEV.
00030 *
00031 *  ZGGEV computes for a pair of n-by-n nonsymmetric matrices (A,B) the
00032 *  generalized eigenvalues and, optionally, the left and right
00033 *  eigenvectors.
00034 *
00035 *  A generalized eigenvalue for a pair of matrices (A,B) is a scalar w
00036 *  or a ratio  alpha/beta = w, such that A - w*B is singular.  It is
00037 *  usually represented as the pair (alpha,beta), as there is reasonalbe
00038 *  interpretation for beta=0, and even for both being zero.
00039 *
00040 *  A right generalized eigenvector corresponding to a generalized
00041 *  eigenvalue  w  for a pair of matrices (A,B) is a vector r  such that
00042 *  (A - wB) * r = 0.  A left generalized eigenvector is a vector l such
00043 *  that l**H * (A - wB) = 0, where l**H is the conjugate-transpose of l.
00044 *
00045 *  When ZDRGEV is called, a number of matrix "sizes" ("n's") and a
00046 *  number of matrix "types" are specified.  For each size ("n")
00047 *  and each type of matrix, a pair of matrices (A, B) will be generated
00048 *  and used for testing.  For each matrix pair, the following tests
00049 *  will be performed and compared with the threshhold THRESH.
00050 *
00051 *  Results from ZGGEV:
00052 *
00053 *  (1)  max over all left eigenvalue/-vector pairs (alpha/beta,l) of
00054 *
00055 *       | VL**H * (beta A - alpha B) |/( ulp max(|beta A|, |alpha B|) )
00056 *
00057 *       where VL**H is the conjugate-transpose of VL.
00058 *
00059 *  (2)  | |VL(i)| - 1 | / ulp and whether largest component real
00060 *
00061 *       VL(i) denotes the i-th column of VL.
00062 *
00063 *  (3)  max over all left eigenvalue/-vector pairs (alpha/beta,r) of
00064 *
00065 *       | (beta A - alpha B) * VR | / ( ulp max(|beta A|, |alpha B|) )
00066 *
00067 *  (4)  | |VR(i)| - 1 | / ulp and whether largest component real
00068 *
00069 *       VR(i) denotes the i-th column of VR.
00070 *
00071 *  (5)  W(full) = W(partial)
00072 *       W(full) denotes the eigenvalues computed when both l and r
00073 *       are also computed, and W(partial) denotes the eigenvalues
00074 *       computed when only W, only W and r, or only W and l are
00075 *       computed.
00076 *
00077 *  (6)  VL(full) = VL(partial)
00078 *       VL(full) denotes the left eigenvectors computed when both l
00079 *       and r are computed, and VL(partial) denotes the result
00080 *       when only l is computed.
00081 *
00082 *  (7)  VR(full) = VR(partial)
00083 *       VR(full) denotes the right eigenvectors computed when both l
00084 *       and r are also computed, and VR(partial) denotes the result
00085 *       when only l is computed.
00086 *
00087 *
00088 *  Test Matrices
00089 *  ---- --------
00090 *
00091 *  The sizes of the test matrices are specified by an array
00092 *  NN(1:NSIZES); the value of each element NN(j) specifies one size.
00093 *  The "types" are specified by a logical array DOTYPE( 1:NTYPES ); if
00094 *  DOTYPE(j) is .TRUE., then matrix type "j" will be generated.
00095 *  Currently, the list of possible types is:
00096 *
00097 *  (1)  ( 0, 0 )         (a pair of zero matrices)
00098 *
00099 *  (2)  ( I, 0 )         (an identity and a zero matrix)
00100 *
00101 *  (3)  ( 0, I )         (an identity and a zero matrix)
00102 *
00103 *  (4)  ( I, I )         (a pair of identity matrices)
00104 *
00105 *          t   t
00106 *  (5)  ( J , J  )       (a pair of transposed Jordan blocks)
00107 *
00108 *                                      t                ( I   0  )
00109 *  (6)  ( X, Y )         where  X = ( J   0  )  and Y = (      t )
00110 *                                   ( 0   I  )          ( 0   J  )
00111 *                        and I is a k x k identity and J a (k+1)x(k+1)
00112 *                        Jordan block; k=(N-1)/2
00113 *
00114 *  (7)  ( D, I )         where D is diag( 0, 1,..., N-1 ) (a diagonal
00115 *                        matrix with those diagonal entries.)
00116 *  (8)  ( I, D )
00117 *
00118 *  (9)  ( big*D, small*I ) where "big" is near overflow and small=1/big
00119 *
00120 *  (10) ( small*D, big*I )
00121 *
00122 *  (11) ( big*I, small*D )
00123 *
00124 *  (12) ( small*I, big*D )
00125 *
00126 *  (13) ( big*D, big*I )
00127 *
00128 *  (14) ( small*D, small*I )
00129 *
00130 *  (15) ( D1, D2 )        where D1 is diag( 0, 0, 1, ..., N-3, 0 ) and
00131 *                         D2 is diag( 0, N-3, N-4,..., 1, 0, 0 )
00132 *            t   t
00133 *  (16) Q ( J , J ) Z     where Q and Z are random orthogonal matrices.
00134 *
00135 *  (17) Q ( T1, T2 ) Z    where T1 and T2 are upper triangular matrices
00136 *                         with random O(1) entries above the diagonal
00137 *                         and diagonal entries diag(T1) =
00138 *                         ( 0, 0, 1, ..., N-3, 0 ) and diag(T2) =
00139 *                         ( 0, N-3, N-4,..., 1, 0, 0 )
00140 *
00141 *  (18) Q ( T1, T2 ) Z    diag(T1) = ( 0, 0, 1, 1, s, ..., s, 0 )
00142 *                         diag(T2) = ( 0, 1, 0, 1,..., 1, 0 )
00143 *                         s = machine precision.
00144 *
00145 *  (19) Q ( T1, T2 ) Z    diag(T1)=( 0,0,1,1, 1-d, ..., 1-(N-5)*d=s, 0 )
00146 *                         diag(T2) = ( 0, 1, 0, 1, ..., 1, 0 )
00147 *
00148 *                                                         N-5
00149 *  (20) Q ( T1, T2 ) Z    diag(T1)=( 0, 0, 1, 1, a, ..., a   =s, 0 )
00150 *                         diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 )
00151 *
00152 *  (21) Q ( T1, T2 ) Z    diag(T1)=( 0, 0, 1, r1, r2, ..., r(N-4), 0 )
00153 *                         diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 )
00154 *                         where r1,..., r(N-4) are random.
00155 *
00156 *  (22) Q ( big*T1, small*T2 ) Z    diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
00157 *                                   diag(T2) = ( 0, 1, ..., 1, 0, 0 )
00158 *
00159 *  (23) Q ( small*T1, big*T2 ) Z    diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
00160 *                                   diag(T2) = ( 0, 1, ..., 1, 0, 0 )
00161 *
00162 *  (24) Q ( small*T1, small*T2 ) Z  diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
00163 *                                   diag(T2) = ( 0, 1, ..., 1, 0, 0 )
00164 *
00165 *  (25) Q ( big*T1, big*T2 ) Z      diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
00166 *                                   diag(T2) = ( 0, 1, ..., 1, 0, 0 )
00167 *
00168 *  (26) Q ( T1, T2 ) Z     where T1 and T2 are random upper-triangular
00169 *                          matrices.
00170 *
00171 *
00172 *  Arguments
00173 *  =========
00174 *
00175 *  NSIZES  (input) INTEGER
00176 *          The number of sizes of matrices to use.  If it is zero,
00177 *          ZDRGES does nothing.  NSIZES >= 0.
00178 *
00179 *  NN      (input) INTEGER array, dimension (NSIZES)
00180 *          An array containing the sizes to be used for the matrices.
00181 *          Zero values will be skipped.  NN >= 0.
00182 *
00183 *  NTYPES  (input) INTEGER
00184 *          The number of elements in DOTYPE.   If it is zero, ZDRGEV
00185 *          does nothing.  It must be at least zero.  If it is MAXTYP+1
00186 *          and NSIZES is 1, then an additional type, MAXTYP+1 is
00187 *          defined, which is to use whatever matrix is in A.  This
00188 *          is only useful if DOTYPE(1:MAXTYP) is .FALSE. and
00189 *          DOTYPE(MAXTYP+1) is .TRUE. .
00190 *
00191 *  DOTYPE  (input) LOGICAL array, dimension (NTYPES)
00192 *          If DOTYPE(j) is .TRUE., then for each size in NN a
00193 *          matrix of that size and of type j will be generated.
00194 *          If NTYPES is smaller than the maximum number of types
00195 *          defined (PARAMETER MAXTYP), then types NTYPES+1 through
00196 *          MAXTYP will not be generated. If NTYPES is larger
00197 *          than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES)
00198 *          will be ignored.
00199 *
00200 *  ISEED   (input/output) INTEGER array, dimension (4)
00201 *          On entry ISEED specifies the seed of the random number
00202 *          generator. The array elements should be between 0 and 4095;
00203 *          if not they will be reduced mod 4096. Also, ISEED(4) must
00204 *          be odd.  The random number generator uses a linear
00205 *          congruential sequence limited to small integers, and so
00206 *          should produce machine independent random numbers. The
00207 *          values of ISEED are changed on exit, and can be used in the
00208 *          next call to ZDRGES to continue the same random number
00209 *          sequence.
00210 *
00211 *  THRESH  (input) DOUBLE PRECISION
00212 *          A test will count as "failed" if the "error", computed as
00213 *          described above, exceeds THRESH.  Note that the error is
00214 *          scaled to be O(1), so THRESH should be a reasonably small
00215 *          multiple of 1, e.g., 10 or 100.  In particular, it should
00216 *          not depend on the precision (single vs. double) or the size
00217 *          of the matrix.  It must be at least zero.
00218 *
00219 *  NOUNIT  (input) INTEGER
00220 *          The FORTRAN unit number for printing out error messages
00221 *          (e.g., if a routine returns IERR not equal to 0.)
00222 *
00223 *  A       (input/workspace) COMPLEX*16 array, dimension(LDA, max(NN))
00224 *          Used to hold the original A matrix.  Used as input only
00225 *          if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and
00226 *          DOTYPE(MAXTYP+1)=.TRUE.
00227 *
00228 *  LDA     (input) INTEGER
00229 *          The leading dimension of A, B, S, and T.
00230 *          It must be at least 1 and at least max( NN ).
00231 *
00232 *  B       (input/workspace) COMPLEX*16 array, dimension(LDA, max(NN))
00233 *          Used to hold the original B matrix.  Used as input only
00234 *          if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and
00235 *          DOTYPE(MAXTYP+1)=.TRUE.
00236 *
00237 *  S       (workspace) COMPLEX*16 array, dimension (LDA, max(NN))
00238 *          The Schur form matrix computed from A by ZGGEV.  On exit, S
00239 *          contains the Schur form matrix corresponding to the matrix
00240 *          in A.
00241 *
00242 *  T       (workspace) COMPLEX*16 array, dimension (LDA, max(NN))
00243 *          The upper triangular matrix computed from B by ZGGEV.
00244 *
00245 *  Q      (workspace) COMPLEX*16 array, dimension (LDQ, max(NN))
00246 *          The (left) eigenvectors matrix computed by ZGGEV.
00247 *
00248 *  LDQ     (input) INTEGER
00249 *          The leading dimension of Q and Z. It must
00250 *          be at least 1 and at least max( NN ).
00251 *
00252 *  Z       (workspace) COMPLEX*16 array, dimension( LDQ, max(NN) )
00253 *          The (right) orthogonal matrix computed by ZGGEV.
00254 *
00255 *  QE      (workspace) COMPLEX*16 array, dimension( LDQ, max(NN) )
00256 *          QE holds the computed right or left eigenvectors.
00257 *
00258 *  LDQE    (input) INTEGER
00259 *          The leading dimension of QE. LDQE >= max(1,max(NN)).
00260 *
00261 *  ALPHA   (workspace) COMPLEX*16 array, dimension (max(NN))
00262 *  BETA    (workspace) COMPLEX*16 array, dimension (max(NN))
00263 *          The generalized eigenvalues of (A,B) computed by ZGGEV.
00264 *          ( ALPHAR(k)+ALPHAI(k)*i ) / BETA(k) is the k-th
00265 *          generalized eigenvalue of A and B.
00266 *
00267 *  ALPHA1  (workspace) COMPLEX*16 array, dimension (max(NN))
00268 *  BETA1   (workspace) COMPLEX*16 array, dimension (max(NN))
00269 *          Like ALPHAR, ALPHAI, BETA, these arrays contain the
00270 *          eigenvalues of A and B, but those computed when ZGGEV only
00271 *          computes a partial eigendecomposition, i.e. not the
00272 *          eigenvalues and left and right eigenvectors.
00273 *
00274 *  WORK    (workspace) COMPLEX*16 array, dimension (LWORK)
00275 *
00276 *  LWORK   (input) INTEGER
00277 *          The number of entries in WORK.  LWORK >= N*(N+1)
00278 *
00279 *  RWORK   (workspace) DOUBLE PRECISION array, dimension (8*N)
00280 *          Real workspace.
00281 *
00282 *  RESULT  (output) DOUBLE PRECISION array, dimension (2)
00283 *          The values computed by the tests described above.
00284 *          The values are currently limited to 1/ulp, to avoid overflow.
00285 *
00286 *  INFO    (output) INTEGER
00287 *          = 0:  successful exit
00288 *          < 0:  if INFO = -i, the i-th argument had an illegal value.
00289 *          > 0:  A routine returned an error code.  INFO is the
00290 *                absolute value of the INFO value returned.
00291 *
00292 *  =====================================================================
00293 *
00294 *     .. Parameters ..
00295       DOUBLE PRECISION   ZERO, ONE
00296       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
00297       COMPLEX*16         CZERO, CONE
00298       PARAMETER          ( CZERO = ( 0.0D+0, 0.0D+0 ),
00299      $                   CONE = ( 1.0D+0, 0.0D+0 ) )
00300       INTEGER            MAXTYP
00301       PARAMETER          ( MAXTYP = 26 )
00302 *     ..
00303 *     .. Local Scalars ..
00304       LOGICAL            BADNN
00305       INTEGER            I, IADD, IERR, IN, J, JC, JR, JSIZE, JTYPE,
00306      $                   MAXWRK, MINWRK, MTYPES, N, N1, NB, NERRS,
00307      $                   NMATS, NMAX, NTESTT
00308       DOUBLE PRECISION   SAFMAX, SAFMIN, ULP, ULPINV
00309       COMPLEX*16         CTEMP
00310 *     ..
00311 *     .. Local Arrays ..
00312       LOGICAL            LASIGN( MAXTYP ), LBSIGN( MAXTYP )
00313       INTEGER            IOLDSD( 4 ), KADD( 6 ), KAMAGN( MAXTYP ),
00314      $                   KATYPE( MAXTYP ), KAZERO( MAXTYP ),
00315      $                   KBMAGN( MAXTYP ), KBTYPE( MAXTYP ),
00316      $                   KBZERO( MAXTYP ), KCLASS( MAXTYP ),
00317      $                   KTRIAN( MAXTYP ), KZ1( 6 ), KZ2( 6 )
00318       DOUBLE PRECISION   RMAGN( 0: 3 )
00319 *     ..
00320 *     .. External Functions ..
00321       INTEGER            ILAENV
00322       DOUBLE PRECISION   DLAMCH
00323       COMPLEX*16         ZLARND
00324       EXTERNAL           ILAENV, DLAMCH, ZLARND
00325 *     ..
00326 *     .. External Subroutines ..
00327       EXTERNAL           ALASVM, DLABAD, XERBLA, ZGET52, ZGGEV, ZLACPY,
00328      $                   ZLARFG, ZLASET, ZLATM4, ZUNM2R
00329 *     ..
00330 *     .. Intrinsic Functions ..
00331       INTRINSIC          ABS, DBLE, DCONJG, MAX, MIN, SIGN
00332 *     ..
00333 *     .. Data statements ..
00334       DATA               KCLASS / 15*1, 10*2, 1*3 /
00335       DATA               KZ1 / 0, 1, 2, 1, 3, 3 /
00336       DATA               KZ2 / 0, 0, 1, 2, 1, 1 /
00337       DATA               KADD / 0, 0, 0, 0, 3, 2 /
00338       DATA               KATYPE / 0, 1, 0, 1, 2, 3, 4, 1, 4, 4, 1, 1, 4,
00339      $                   4, 4, 2, 4, 5, 8, 7, 9, 4*4, 0 /
00340       DATA               KBTYPE / 0, 0, 1, 1, 2, -3, 1, 4, 1, 1, 4, 4,
00341      $                   1, 1, -4, 2, -4, 8*8, 0 /
00342       DATA               KAZERO / 6*1, 2, 1, 2*2, 2*1, 2*2, 3, 1, 3,
00343      $                   4*5, 4*3, 1 /
00344       DATA               KBZERO / 6*1, 1, 2, 2*1, 2*2, 2*1, 4, 1, 4,
00345      $                   4*6, 4*4, 1 /
00346       DATA               KAMAGN / 8*1, 2, 3, 2, 3, 2, 3, 7*1, 2, 3, 3,
00347      $                   2, 1 /
00348       DATA               KBMAGN / 8*1, 3, 2, 3, 2, 2, 3, 7*1, 3, 2, 3,
00349      $                   2, 1 /
00350       DATA               KTRIAN / 16*0, 10*1 /
00351       DATA               LASIGN / 6*.FALSE., .TRUE., .FALSE., 2*.TRUE.,
00352      $                   2*.FALSE., 3*.TRUE., .FALSE., .TRUE.,
00353      $                   3*.FALSE., 5*.TRUE., .FALSE. /
00354       DATA               LBSIGN / 7*.FALSE., .TRUE., 2*.FALSE.,
00355      $                   2*.TRUE., 2*.FALSE., .TRUE., .FALSE., .TRUE.,
00356      $                   9*.FALSE. /
00357 *     ..
00358 *     .. Executable Statements ..
00359 *
00360 *     Check for errors
00361 *
00362       INFO = 0
00363 *
00364       BADNN = .FALSE.
00365       NMAX = 1
00366       DO 10 J = 1, NSIZES
00367          NMAX = MAX( NMAX, NN( J ) )
00368          IF( NN( J ).LT.0 )
00369      $      BADNN = .TRUE.
00370    10 CONTINUE
00371 *
00372       IF( NSIZES.LT.0 ) THEN
00373          INFO = -1
00374       ELSE IF( BADNN ) THEN
00375          INFO = -2
00376       ELSE IF( NTYPES.LT.0 ) THEN
00377          INFO = -3
00378       ELSE IF( THRESH.LT.ZERO ) THEN
00379          INFO = -6
00380       ELSE IF( LDA.LE.1 .OR. LDA.LT.NMAX ) THEN
00381          INFO = -9
00382       ELSE IF( LDQ.LE.1 .OR. LDQ.LT.NMAX ) THEN
00383          INFO = -14
00384       ELSE IF( LDQE.LE.1 .OR. LDQE.LT.NMAX ) THEN
00385          INFO = -17
00386       END IF
00387 *
00388 *     Compute workspace
00389 *      (Note: Comments in the code beginning "Workspace:" describe the
00390 *       minimal amount of workspace needed at that point in the code,
00391 *       as well as the preferred amount for good performance.
00392 *       NB refers to the optimal block size for the immediately
00393 *       following subroutine, as returned by ILAENV.
00394 *
00395       MINWRK = 1
00396       IF( INFO.EQ.0 .AND. LWORK.GE.1 ) THEN
00397          MINWRK = NMAX*( NMAX+1 )
00398          NB = MAX( 1, ILAENV( 1, 'ZGEQRF', ' ', NMAX, NMAX, -1, -1 ),
00399      $        ILAENV( 1, 'ZUNMQR', 'LC', NMAX, NMAX, NMAX, -1 ),
00400      $        ILAENV( 1, 'ZUNGQR', ' ', NMAX, NMAX, NMAX, -1 ) )
00401          MAXWRK = MAX( 2*NMAX, NMAX*( NB+1 ), NMAX*( NMAX+1 ) )
00402          WORK( 1 ) = MAXWRK
00403       END IF
00404 *
00405       IF( LWORK.LT.MINWRK )
00406      $   INFO = -23
00407 *
00408       IF( INFO.NE.0 ) THEN
00409          CALL XERBLA( 'ZDRGEV', -INFO )
00410          RETURN
00411       END IF
00412 *
00413 *     Quick return if possible
00414 *
00415       IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 )
00416      $   RETURN
00417 *
00418       ULP = DLAMCH( 'Precision' )
00419       SAFMIN = DLAMCH( 'Safe minimum' )
00420       SAFMIN = SAFMIN / ULP
00421       SAFMAX = ONE / SAFMIN
00422       CALL DLABAD( SAFMIN, SAFMAX )
00423       ULPINV = ONE / ULP
00424 *
00425 *     The values RMAGN(2:3) depend on N, see below.
00426 *
00427       RMAGN( 0 ) = ZERO
00428       RMAGN( 1 ) = ONE
00429 *
00430 *     Loop over sizes, types
00431 *
00432       NTESTT = 0
00433       NERRS = 0
00434       NMATS = 0
00435 *
00436       DO 220 JSIZE = 1, NSIZES
00437          N = NN( JSIZE )
00438          N1 = MAX( 1, N )
00439          RMAGN( 2 ) = SAFMAX*ULP / DBLE( N1 )
00440          RMAGN( 3 ) = SAFMIN*ULPINV*N1
00441 *
00442          IF( NSIZES.NE.1 ) THEN
00443             MTYPES = MIN( MAXTYP, NTYPES )
00444          ELSE
00445             MTYPES = MIN( MAXTYP+1, NTYPES )
00446          END IF
00447 *
00448          DO 210 JTYPE = 1, MTYPES
00449             IF( .NOT.DOTYPE( JTYPE ) )
00450      $         GO TO 210
00451             NMATS = NMATS + 1
00452 *
00453 *           Save ISEED in case of an error.
00454 *
00455             DO 20 J = 1, 4
00456                IOLDSD( J ) = ISEED( J )
00457    20       CONTINUE
00458 *
00459 *           Generate test matrices A and B
00460 *
00461 *           Description of control parameters:
00462 *
00463 *           KZLASS: =1 means w/o rotation, =2 means w/ rotation,
00464 *                   =3 means random.
00465 *           KATYPE: the "type" to be passed to ZLATM4 for computing A.
00466 *           KAZERO: the pattern of zeros on the diagonal for A:
00467 *                   =1: ( xxx ), =2: (0, xxx ) =3: ( 0, 0, xxx, 0 ),
00468 *                   =4: ( 0, xxx, 0, 0 ), =5: ( 0, 0, 1, xxx, 0 ),
00469 *                   =6: ( 0, 1, 0, xxx, 0 ).  (xxx means a string of
00470 *                   non-zero entries.)
00471 *           KAMAGN: the magnitude of the matrix: =0: zero, =1: O(1),
00472 *                   =2: large, =3: small.
00473 *           LASIGN: .TRUE. if the diagonal elements of A are to be
00474 *                   multiplied by a random magnitude 1 number.
00475 *           KBTYPE, KBZERO, KBMAGN, LBSIGN: the same, but for B.
00476 *           KTRIAN: =0: don't fill in the upper triangle, =1: do.
00477 *           KZ1, KZ2, KADD: used to implement KAZERO and KBZERO.
00478 *           RMAGN: used to implement KAMAGN and KBMAGN.
00479 *
00480             IF( MTYPES.GT.MAXTYP )
00481      $         GO TO 100
00482             IERR = 0
00483             IF( KCLASS( JTYPE ).LT.3 ) THEN
00484 *
00485 *              Generate A (w/o rotation)
00486 *
00487                IF( ABS( KATYPE( JTYPE ) ).EQ.3 ) THEN
00488                   IN = 2*( ( N-1 ) / 2 ) + 1
00489                   IF( IN.NE.N )
00490      $               CALL ZLASET( 'Full', N, N, CZERO, CZERO, A, LDA )
00491                ELSE
00492                   IN = N
00493                END IF
00494                CALL ZLATM4( KATYPE( JTYPE ), IN, KZ1( KAZERO( JTYPE ) ),
00495      $                      KZ2( KAZERO( JTYPE ) ), LASIGN( JTYPE ),
00496      $                      RMAGN( KAMAGN( JTYPE ) ), ULP,
00497      $                      RMAGN( KTRIAN( JTYPE )*KAMAGN( JTYPE ) ), 2,
00498      $                      ISEED, A, LDA )
00499                IADD = KADD( KAZERO( JTYPE ) )
00500                IF( IADD.GT.0 .AND. IADD.LE.N )
00501      $            A( IADD, IADD ) = RMAGN( KAMAGN( JTYPE ) )
00502 *
00503 *              Generate B (w/o rotation)
00504 *
00505                IF( ABS( KBTYPE( JTYPE ) ).EQ.3 ) THEN
00506                   IN = 2*( ( N-1 ) / 2 ) + 1
00507                   IF( IN.NE.N )
00508      $               CALL ZLASET( 'Full', N, N, CZERO, CZERO, B, LDA )
00509                ELSE
00510                   IN = N
00511                END IF
00512                CALL ZLATM4( KBTYPE( JTYPE ), IN, KZ1( KBZERO( JTYPE ) ),
00513      $                      KZ2( KBZERO( JTYPE ) ), LBSIGN( JTYPE ),
00514      $                      RMAGN( KBMAGN( JTYPE ) ), ONE,
00515      $                      RMAGN( KTRIAN( JTYPE )*KBMAGN( JTYPE ) ), 2,
00516      $                      ISEED, B, LDA )
00517                IADD = KADD( KBZERO( JTYPE ) )
00518                IF( IADD.NE.0 .AND. IADD.LE.N )
00519      $            B( IADD, IADD ) = RMAGN( KBMAGN( JTYPE ) )
00520 *
00521                IF( KCLASS( JTYPE ).EQ.2 .AND. N.GT.0 ) THEN
00522 *
00523 *                 Include rotations
00524 *
00525 *                 Generate Q, Z as Householder transformations times
00526 *                 a diagonal matrix.
00527 *
00528                   DO 40 JC = 1, N - 1
00529                      DO 30 JR = JC, N
00530                         Q( JR, JC ) = ZLARND( 3, ISEED )
00531                         Z( JR, JC ) = ZLARND( 3, ISEED )
00532    30                CONTINUE
00533                      CALL ZLARFG( N+1-JC, Q( JC, JC ), Q( JC+1, JC ), 1,
00534      $                            WORK( JC ) )
00535                      WORK( 2*N+JC ) = SIGN( ONE, DBLE( Q( JC, JC ) ) )
00536                      Q( JC, JC ) = CONE
00537                      CALL ZLARFG( N+1-JC, Z( JC, JC ), Z( JC+1, JC ), 1,
00538      $                            WORK( N+JC ) )
00539                      WORK( 3*N+JC ) = SIGN( ONE, DBLE( Z( JC, JC ) ) )
00540                      Z( JC, JC ) = CONE
00541    40             CONTINUE
00542                   CTEMP = ZLARND( 3, ISEED )
00543                   Q( N, N ) = CONE
00544                   WORK( N ) = CZERO
00545                   WORK( 3*N ) = CTEMP / ABS( CTEMP )
00546                   CTEMP = ZLARND( 3, ISEED )
00547                   Z( N, N ) = CONE
00548                   WORK( 2*N ) = CZERO
00549                   WORK( 4*N ) = CTEMP / ABS( CTEMP )
00550 *
00551 *                 Apply the diagonal matrices
00552 *
00553                   DO 60 JC = 1, N
00554                      DO 50 JR = 1, N
00555                         A( JR, JC ) = WORK( 2*N+JR )*
00556      $                                DCONJG( WORK( 3*N+JC ) )*
00557      $                                A( JR, JC )
00558                         B( JR, JC ) = WORK( 2*N+JR )*
00559      $                                DCONJG( WORK( 3*N+JC ) )*
00560      $                                B( JR, JC )
00561    50                CONTINUE
00562    60             CONTINUE
00563                   CALL ZUNM2R( 'L', 'N', N, N, N-1, Q, LDQ, WORK, A,
00564      $                         LDA, WORK( 2*N+1 ), IERR )
00565                   IF( IERR.NE.0 )
00566      $               GO TO 90
00567                   CALL ZUNM2R( 'R', 'C', N, N, N-1, Z, LDQ, WORK( N+1 ),
00568      $                         A, LDA, WORK( 2*N+1 ), IERR )
00569                   IF( IERR.NE.0 )
00570      $               GO TO 90
00571                   CALL ZUNM2R( 'L', 'N', N, N, N-1, Q, LDQ, WORK, B,
00572      $                         LDA, WORK( 2*N+1 ), IERR )
00573                   IF( IERR.NE.0 )
00574      $               GO TO 90
00575                   CALL ZUNM2R( 'R', 'C', N, N, N-1, Z, LDQ, WORK( N+1 ),
00576      $                         B, LDA, WORK( 2*N+1 ), IERR )
00577                   IF( IERR.NE.0 )
00578      $               GO TO 90
00579                END IF
00580             ELSE
00581 *
00582 *              Random matrices
00583 *
00584                DO 80 JC = 1, N
00585                   DO 70 JR = 1, N
00586                      A( JR, JC ) = RMAGN( KAMAGN( JTYPE ) )*
00587      $                             ZLARND( 4, ISEED )
00588                      B( JR, JC ) = RMAGN( KBMAGN( JTYPE ) )*
00589      $                             ZLARND( 4, ISEED )
00590    70             CONTINUE
00591    80          CONTINUE
00592             END IF
00593 *
00594    90       CONTINUE
00595 *
00596             IF( IERR.NE.0 ) THEN
00597                WRITE( NOUNIT, FMT = 9999 )'Generator', IERR, N, JTYPE,
00598      $            IOLDSD
00599                INFO = ABS( IERR )
00600                RETURN
00601             END IF
00602 *
00603   100       CONTINUE
00604 *
00605             DO 110 I = 1, 7
00606                RESULT( I ) = -ONE
00607   110       CONTINUE
00608 *
00609 *           Call ZGGEV to compute eigenvalues and eigenvectors.
00610 *
00611             CALL ZLACPY( ' ', N, N, A, LDA, S, LDA )
00612             CALL ZLACPY( ' ', N, N, B, LDA, T, LDA )
00613             CALL ZGGEV( 'V', 'V', N, S, LDA, T, LDA, ALPHA, BETA, Q,
00614      $                  LDQ, Z, LDQ, WORK, LWORK, RWORK, IERR )
00615             IF( IERR.NE.0 .AND. IERR.NE.N+1 ) THEN
00616                RESULT( 1 ) = ULPINV
00617                WRITE( NOUNIT, FMT = 9999 )'ZGGEV1', IERR, N, JTYPE,
00618      $            IOLDSD
00619                INFO = ABS( IERR )
00620                GO TO 190
00621             END IF
00622 *
00623 *           Do the tests (1) and (2)
00624 *
00625             CALL ZGET52( .TRUE., N, A, LDA, B, LDA, Q, LDQ, ALPHA, BETA,
00626      $                   WORK, RWORK, RESULT( 1 ) )
00627             IF( RESULT( 2 ).GT.THRESH ) THEN
00628                WRITE( NOUNIT, FMT = 9998 )'Left', 'ZGGEV1',
00629      $            RESULT( 2 ), N, JTYPE, IOLDSD
00630             END IF
00631 *
00632 *           Do the tests (3) and (4)
00633 *
00634             CALL ZGET52( .FALSE., N, A, LDA, B, LDA, Z, LDQ, ALPHA,
00635      $                   BETA, WORK, RWORK, RESULT( 3 ) )
00636             IF( RESULT( 4 ).GT.THRESH ) THEN
00637                WRITE( NOUNIT, FMT = 9998 )'Right', 'ZGGEV1',
00638      $            RESULT( 4 ), N, JTYPE, IOLDSD
00639             END IF
00640 *
00641 *           Do test (5)
00642 *
00643             CALL ZLACPY( ' ', N, N, A, LDA, S, LDA )
00644             CALL ZLACPY( ' ', N, N, B, LDA, T, LDA )
00645             CALL ZGGEV( 'N', 'N', N, S, LDA, T, LDA, ALPHA1, BETA1, Q,
00646      $                  LDQ, Z, LDQ, WORK, LWORK, RWORK, IERR )
00647             IF( IERR.NE.0 .AND. IERR.NE.N+1 ) THEN
00648                RESULT( 1 ) = ULPINV
00649                WRITE( NOUNIT, FMT = 9999 )'ZGGEV2', IERR, N, JTYPE,
00650      $            IOLDSD
00651                INFO = ABS( IERR )
00652                GO TO 190
00653             END IF
00654 *
00655             DO 120 J = 1, N
00656                IF( ALPHA( J ).NE.ALPHA1( J ) .OR. BETA( J ).NE.
00657      $             BETA1( J ) )RESULT( 5 ) = ULPINV
00658   120       CONTINUE
00659 *
00660 *           Do test (6): Compute eigenvalues and left eigenvectors,
00661 *           and test them
00662 *
00663             CALL ZLACPY( ' ', N, N, A, LDA, S, LDA )
00664             CALL ZLACPY( ' ', N, N, B, LDA, T, LDA )
00665             CALL ZGGEV( 'V', 'N', N, S, LDA, T, LDA, ALPHA1, BETA1, QE,
00666      $                  LDQE, Z, LDQ, WORK, LWORK, RWORK, IERR )
00667             IF( IERR.NE.0 .AND. IERR.NE.N+1 ) THEN
00668                RESULT( 1 ) = ULPINV
00669                WRITE( NOUNIT, FMT = 9999 )'ZGGEV3', IERR, N, JTYPE,
00670      $            IOLDSD
00671                INFO = ABS( IERR )
00672                GO TO 190
00673             END IF
00674 *
00675             DO 130 J = 1, N
00676                IF( ALPHA( J ).NE.ALPHA1( J ) .OR. BETA( J ).NE.
00677      $             BETA1( J ) )RESULT( 6 ) = ULPINV
00678   130       CONTINUE
00679 *
00680             DO 150 J = 1, N
00681                DO 140 JC = 1, N
00682                   IF( Q( J, JC ).NE.QE( J, JC ) )
00683      $               RESULT( 6 ) = ULPINV
00684   140          CONTINUE
00685   150       CONTINUE
00686 *
00687 *           Do test (7): Compute eigenvalues and right eigenvectors,
00688 *           and test them
00689 *
00690             CALL ZLACPY( ' ', N, N, A, LDA, S, LDA )
00691             CALL ZLACPY( ' ', N, N, B, LDA, T, LDA )
00692             CALL ZGGEV( 'N', 'V', N, S, LDA, T, LDA, ALPHA1, BETA1, Q,
00693      $                  LDQ, QE, LDQE, WORK, LWORK, RWORK, IERR )
00694             IF( IERR.NE.0 .AND. IERR.NE.N+1 ) THEN
00695                RESULT( 1 ) = ULPINV
00696                WRITE( NOUNIT, FMT = 9999 )'ZGGEV4', IERR, N, JTYPE,
00697      $            IOLDSD
00698                INFO = ABS( IERR )
00699                GO TO 190
00700             END IF
00701 *
00702             DO 160 J = 1, N
00703                IF( ALPHA( J ).NE.ALPHA1( J ) .OR. BETA( J ).NE.
00704      $             BETA1( J ) )RESULT( 7 ) = ULPINV
00705   160       CONTINUE
00706 *
00707             DO 180 J = 1, N
00708                DO 170 JC = 1, N
00709                   IF( Z( J, JC ).NE.QE( J, JC ) )
00710      $               RESULT( 7 ) = ULPINV
00711   170          CONTINUE
00712   180       CONTINUE
00713 *
00714 *           End of Loop -- Check for RESULT(j) > THRESH
00715 *
00716   190       CONTINUE
00717 *
00718             NTESTT = NTESTT + 7
00719 *
00720 *           Print out tests which fail.
00721 *
00722             DO 200 JR = 1, 7
00723                IF( RESULT( JR ).GE.THRESH ) THEN
00724 *
00725 *                 If this is the first test to fail,
00726 *                 print a header to the data file.
00727 *
00728                   IF( NERRS.EQ.0 ) THEN
00729                      WRITE( NOUNIT, FMT = 9997 )'ZGV'
00730 *
00731 *                    Matrix types
00732 *
00733                      WRITE( NOUNIT, FMT = 9996 )
00734                      WRITE( NOUNIT, FMT = 9995 )
00735                      WRITE( NOUNIT, FMT = 9994 )'Orthogonal'
00736 *
00737 *                    Tests performed
00738 *
00739                      WRITE( NOUNIT, FMT = 9993 )
00740 *
00741                   END IF
00742                   NERRS = NERRS + 1
00743                   IF( RESULT( JR ).LT.10000.0D0 ) THEN
00744                      WRITE( NOUNIT, FMT = 9992 )N, JTYPE, IOLDSD, JR,
00745      $                  RESULT( JR )
00746                   ELSE
00747                      WRITE( NOUNIT, FMT = 9991 )N, JTYPE, IOLDSD, JR,
00748      $                  RESULT( JR )
00749                   END IF
00750                END IF
00751   200       CONTINUE
00752 *
00753   210    CONTINUE
00754   220 CONTINUE
00755 *
00756 *     Summary
00757 *
00758       CALL ALASVM( 'ZGV', NOUNIT, NERRS, NTESTT, 0 )
00759 *
00760       WORK( 1 ) = MAXWRK
00761 *
00762       RETURN
00763 *
00764  9999 FORMAT( ' ZDRGEV: ', A, ' returned INFO=', I6, '.', / 3X, 'N=',
00765      $      I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' )
00766 *
00767  9998 FORMAT( ' ZDRGEV: ', A, ' Eigenvectors from ', A, ' incorrectly ',
00768      $      'normalized.', / ' Bits of error=', 0P, G10.3, ',', 3X,
00769      $      'N=', I4, ', JTYPE=', I3, ', ISEED=(', 3( I4, ',' ), I5,
00770      $      ')' )
00771 *
00772  9997 FORMAT( / 1X, A3, ' -- Complex Generalized eigenvalue problem ',
00773      $      'driver' )
00774 *
00775  9996 FORMAT( ' Matrix types (see ZDRGEV for details): ' )
00776 *
00777  9995 FORMAT( ' Special Matrices:', 23X,
00778      $      '(J''=transposed Jordan block)',
00779      $      / '   1=(0,0)  2=(I,0)  3=(0,I)  4=(I,I)  5=(J'',J'')  ',
00780      $      '6=(diag(J'',I), diag(I,J''))', / ' Diagonal Matrices:  ( ',
00781      $      'D=diag(0,1,2,...) )', / '   7=(D,I)   9=(large*D, small*I',
00782      $      ')  11=(large*I, small*D)  13=(large*D, large*I)', /
00783      $      '   8=(I,D)  10=(small*D, large*I)  12=(small*I, large*D) ',
00784      $      ' 14=(small*D, small*I)', / '  15=(D, reversed D)' )
00785  9994 FORMAT( ' Matrices Rotated by Random ', A, ' Matrices U, V:',
00786      $      / '  16=Transposed Jordan Blocks             19=geometric ',
00787      $      'alpha, beta=0,1', / '  17=arithm. alpha&beta             ',
00788      $      '      20=arithmetic alpha, beta=0,1', / '  18=clustered ',
00789      $      'alpha, beta=0,1            21=random alpha, beta=0,1',
00790      $      / ' Large & Small Matrices:', / '  22=(large, small)   ',
00791      $      '23=(small,large)    24=(small,small)    25=(large,large)',
00792      $      / '  26=random O(1) matrices.' )
00793 *
00794  9993 FORMAT( / ' Tests performed:    ',
00795      $      / ' 1 = max | ( b A - a B )''*l | / const.,',
00796      $      / ' 2 = | |VR(i)| - 1 | / ulp,',
00797      $      / ' 3 = max | ( b A - a B )*r | / const.',
00798      $      / ' 4 = | |VL(i)| - 1 | / ulp,',
00799      $      / ' 5 = 0 if W same no matter if r or l computed,',
00800      $      / ' 6 = 0 if l same no matter if l computed,',
00801      $      / ' 7 = 0 if r same no matter if r computed,', / 1X )
00802  9992 FORMAT( ' Matrix order=', I5, ', type=', I2, ', seed=',
00803      $      4( I4, ',' ), ' result ', I2, ' is', 0P, F8.2 )
00804  9991 FORMAT( ' Matrix order=', I5, ', type=', I2, ', seed=',
00805      $      4( I4, ',' ), ' result ', I2, ' is', 1P, D10.3 )
00806 *
00807 *     End of ZDRGEV
00808 *
00809       END