LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
cdrvgg.f
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00001 *> \brief \b CDRVGG
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *  Definition:
00009 *  ===========
00010 *
00011 *       SUBROUTINE CDRVGG( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
00012 *                          THRSHN, NOUNIT, A, LDA, B, S, T, S2, T2, Q,
00013 *                          LDQ, Z, ALPHA1, BETA1, ALPHA2, BETA2, VL, VR,
00014 *                          WORK, LWORK, RWORK, RESULT, INFO )
00015 * 
00016 *       .. Scalar Arguments ..
00017 *       INTEGER            INFO, LDA, LDQ, LWORK, NOUNIT, NSIZES, NTYPES
00018 *       REAL               THRESH, THRSHN
00019 *       ..
00020 *       .. Array Arguments ..
00021 *  
00022 *
00023 *> \par Purpose:
00024 *  =============
00025 *>
00026 *> \verbatim
00027 *>
00028 *> CDRVGG  checks the nonsymmetric generalized eigenvalue driver
00029 *> routines.
00030 *>                               T          T        T
00031 *> CGEGS factors A and B as Q S Z  and Q T Z , where   means
00032 *> transpose, T is upper triangular, S is in generalized Schur form
00033 *> (upper triangular), and Q and Z are unitary.  It also
00034 *> computes the generalized eigenvalues (alpha(1),beta(1)), ...,
00035 *> (alpha(n),beta(n)), where alpha(j)=S(j,j) and beta(j)=T(j,j) --
00036 *> thus, w(j) = alpha(j)/beta(j) is a root of the generalized
00037 *> eigenvalue problem
00038 *>
00039 *>     det( A - w(j) B ) = 0
00040 *>
00041 *> and m(j) = beta(j)/alpha(j) is a root of the essentially equivalent
00042 *> problem
00043 *>
00044 *>     det( m(j) A - B ) = 0
00045 *>
00046 *> CGEGV computes the generalized eigenvalues (alpha(1),beta(1)), ...,
00047 *> (alpha(n),beta(n)), the matrix L whose columns contain the
00048 *> generalized left eigenvectors l, and the matrix R whose columns
00049 *> contain the generalized right eigenvectors r for the pair (A,B).
00050 *>
00051 *> When CDRVGG is called, a number of matrix "sizes" ("n's") and a
00052 *> number of matrix "types" are specified.  For each size ("n")
00053 *> and each type of matrix, one matrix will be generated and used
00054 *> to test the nonsymmetric eigenroutines.  For each matrix, 7
00055 *> tests will be performed and compared with the threshhold THRESH:
00056 *>
00057 *> Results from CGEGS:
00058 *>
00059 *>                  H
00060 *> (1)   | A - Q S Z  | / ( |A| n ulp )
00061 *>
00062 *>                  H
00063 *> (2)   | B - Q T Z  | / ( |B| n ulp )
00064 *>
00065 *>               H
00066 *> (3)   | I - QQ  | / ( n ulp )
00067 *>
00068 *>               H
00069 *> (4)   | I - ZZ  | / ( n ulp )
00070 *>
00071 *> (5)   maximum over j of D(j)  where:
00072 *>
00073 *>                     |alpha(j) - S(j,j)|        |beta(j) - T(j,j)|
00074 *>           D(j) = ------------------------ + -----------------------
00075 *>                  max(|alpha(j)|,|S(j,j)|)   max(|beta(j)|,|T(j,j)|)
00076 *>
00077 *> Results from CGEGV:
00078 *>
00079 *> (6)   max over all left eigenvalue/-vector pairs (beta/alpha,l) of
00080 *>
00081 *>    | l**H * (beta A - alpha B) | / ( ulp max( |beta A|, |alpha B| ) )
00082 *>
00083 *>       where l**H is the conjugate tranpose of l.
00084 *>
00085 *> (7)   max over all right eigenvalue/-vector pairs (beta/alpha,r) of
00086 *>
00087 *>       | (beta A - alpha B) r | / ( ulp max( |beta A|, |alpha B| ) )
00088 *>
00089 *> Test Matrices
00090 *> ---- --------
00091 *>
00092 *> The sizes of the test matrices are specified by an array
00093 *> NN(1:NSIZES); the value of each element NN(j) specifies one size.
00094 *> The "types" are specified by a logical array DOTYPE( 1:NTYPES ); if
00095 *> DOTYPE(j) is .TRUE., then matrix type "j" will be generated.
00096 *> Currently, the list of possible types is:
00097 *>
00098 *> (1)  ( 0, 0 )         (a pair of zero matrices)
00099 *>
00100 *> (2)  ( I, 0 )         (an identity and a zero matrix)
00101 *>
00102 *> (3)  ( 0, I )         (an identity and a zero matrix)
00103 *>
00104 *> (4)  ( I, I )         (a pair of identity matrices)
00105 *>
00106 *>         t   t
00107 *> (5)  ( J , J  )       (a pair of transposed Jordan blocks)
00108 *>
00109 *>                                     t                ( I   0  )
00110 *> (6)  ( X, Y )         where  X = ( J   0  )  and Y = (      t )
00111 *>                                  ( 0   I  )          ( 0   J  )
00112 *>                       and I is a k x k identity and J a (k+1)x(k+1)
00113 *>                       Jordan block; k=(N-1)/2
00114 *>
00115 *> (7)  ( D, I )         where D is diag( 0, 1,..., N-1 ) (a diagonal
00116 *>                       matrix with those diagonal entries.)
00117 *> (8)  ( I, D )
00118 *>
00119 *> (9)  ( big*D, small*I ) where "big" is near overflow and small=1/big
00120 *>
00121 *> (10) ( small*D, big*I )
00122 *>
00123 *> (11) ( big*I, small*D )
00124 *>
00125 *> (12) ( small*I, big*D )
00126 *>
00127 *> (13) ( big*D, big*I )
00128 *>
00129 *> (14) ( small*D, small*I )
00130 *>
00131 *> (15) ( D1, D2 )        where D1 is diag( 0, 0, 1, ..., N-3, 0 ) and
00132 *>                        D2 is diag( 0, N-3, N-4,..., 1, 0, 0 )
00133 *>           t   t
00134 *> (16) Q ( J , J ) Z     where Q and Z are random unitary matrices.
00135 *>
00136 *> (17) Q ( T1, T2 ) Z    where T1 and T2 are upper triangular matrices
00137 *>                        with random O(1) entries above the diagonal
00138 *>                        and diagonal entries diag(T1) =
00139 *>                        ( 0, 0, 1, ..., N-3, 0 ) and diag(T2) =
00140 *>                        ( 0, N-3, N-4,..., 1, 0, 0 )
00141 *>
00142 *> (18) Q ( T1, T2 ) Z    diag(T1) = ( 0, 0, 1, 1, s, ..., s, 0 )
00143 *>                        diag(T2) = ( 0, 1, 0, 1,..., 1, 0 )
00144 *>                        s = machine precision.
00145 *>
00146 *> (19) Q ( T1, T2 ) Z    diag(T1)=( 0,0,1,1, 1-d, ..., 1-(N-5)*d=s, 0 )
00147 *>                        diag(T2) = ( 0, 1, 0, 1, ..., 1, 0 )
00148 *>
00149 *>                                                        N-5
00150 *> (20) Q ( T1, T2 ) Z    diag(T1)=( 0, 0, 1, 1, a, ..., a   =s, 0 )
00151 *>                        diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 )
00152 *>
00153 *> (21) Q ( T1, T2 ) Z    diag(T1)=( 0, 0, 1, r1, r2, ..., r(N-4), 0 )
00154 *>                        diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 )
00155 *>                        where r1,..., r(N-4) are random.
00156 *>
00157 *> (22) Q ( big*T1, small*T2 ) Z    diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
00158 *>                                  diag(T2) = ( 0, 1, ..., 1, 0, 0 )
00159 *>
00160 *> (23) Q ( small*T1, big*T2 ) Z    diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
00161 *>                                  diag(T2) = ( 0, 1, ..., 1, 0, 0 )
00162 *>
00163 *> (24) Q ( small*T1, small*T2 ) Z  diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
00164 *>                                  diag(T2) = ( 0, 1, ..., 1, 0, 0 )
00165 *>
00166 *> (25) Q ( big*T1, big*T2 ) Z      diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
00167 *>                                  diag(T2) = ( 0, 1, ..., 1, 0, 0 )
00168 *>
00169 *> (26) Q ( T1, T2 ) Z     where T1 and T2 are random upper-triangular
00170 *>                         matrices.
00171 *> \endverbatim
00172 *
00173 *  Arguments:
00174 *  ==========
00175 *
00176 *> \param[in] NSIZES
00177 *> \verbatim
00178 *>          NSIZES is INTEGER
00179 *>          The number of sizes of matrices to use.  If it is zero,
00180 *>          CDRVGG does nothing.  It must be at least zero.
00181 *> \endverbatim
00182 *>
00183 *> \param[in] NN
00184 *> \verbatim
00185 *>          NN is INTEGER array, dimension (NSIZES)
00186 *>          An array containing the sizes to be used for the matrices.
00187 *>          Zero values will be skipped.  The values must be at least
00188 *>          zero.
00189 *> \endverbatim
00190 *>
00191 *> \param[in] NTYPES
00192 *> \verbatim
00193 *>          NTYPES is INTEGER
00194 *>          The number of elements in DOTYPE.   If it is zero, CDRVGG
00195 *>          does nothing.  It must be at least zero.  If it is MAXTYP+1
00196 *>          and NSIZES is 1, then an additional type, MAXTYP+1 is
00197 *>          defined, which is to use whatever matrix is in A.  This
00198 *>          is only useful if DOTYPE(1:MAXTYP) is .FALSE. and
00199 *>          DOTYPE(MAXTYP+1) is .TRUE. .
00200 *> \endverbatim
00201 *>
00202 *> \param[in] DOTYPE
00203 *> \verbatim
00204 *>          DOTYPE is LOGICAL array, dimension (NTYPES)
00205 *>          If DOTYPE(j) is .TRUE., then for each size in NN a
00206 *>          matrix of that size and of type j will be generated.
00207 *>          If NTYPES is smaller than the maximum number of types
00208 *>          defined (PARAMETER MAXTYP), then types NTYPES+1 through
00209 *>          MAXTYP will not be generated.  If NTYPES is larger
00210 *>          than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES)
00211 *>          will be ignored.
00212 *> \endverbatim
00213 *>
00214 *> \param[in,out] ISEED
00215 *> \verbatim
00216 *>          ISEED is INTEGER array, dimension (4)
00217 *>          On entry ISEED specifies the seed of the random number
00218 *>          generator. The array elements should be between 0 and 4095;
00219 *>          if not they will be reduced mod 4096.  Also, ISEED(4) must
00220 *>          be odd.  The random number generator uses a linear
00221 *>          congruential sequence limited to small integers, and so
00222 *>          should produce machine independent random numbers. The
00223 *>          values of ISEED are changed on exit, and can be used in the
00224 *>          next call to CDRVGG to continue the same random number
00225 *>          sequence.
00226 *> \endverbatim
00227 *>
00228 *> \param[in] THRESH
00229 *> \verbatim
00230 *>          THRESH is REAL
00231 *>          A test will count as "failed" if the "error", computed as
00232 *>          described above, exceeds THRESH.  Note that the error is
00233 *>          scaled to be O(1), so THRESH should be a reasonably small
00234 *>          multiple of 1, e.g., 10 or 100.  In particular, it should
00235 *>          not depend on the precision (single vs. double) or the size
00236 *>          of the matrix.  It must be at least zero.
00237 *> \endverbatim
00238 *>
00239 *> \param[in] THRSHN
00240 *> \verbatim
00241 *>          THRSHN is REAL
00242 *>          Threshhold for reporting eigenvector normalization error.
00243 *>          If the normalization of any eigenvector differs from 1 by
00244 *>          more than THRSHN*ulp, then a special error message will be
00245 *>          printed.  (This is handled separately from the other tests,
00246 *>          since only a compiler or programming error should cause an
00247 *>          error message, at least if THRSHN is at least 5--10.)
00248 *> \endverbatim
00249 *>
00250 *> \param[in] NOUNIT
00251 *> \verbatim
00252 *>          NOUNIT is INTEGER
00253 *>          The FORTRAN unit number for printing out error messages
00254 *>          (e.g., if a routine returns IINFO not equal to 0.)
00255 *> \endverbatim
00256 *>
00257 *> \param[in,out] A
00258 *> \verbatim
00259 *>          A is COMPLEX array, dimension (LDA, max(NN))
00260 *>          Used to hold the original A matrix.  Used as input only
00261 *>          if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and
00262 *>          DOTYPE(MAXTYP+1)=.TRUE.
00263 *> \endverbatim
00264 *>
00265 *> \param[in] LDA
00266 *> \verbatim
00267 *>          LDA is INTEGER
00268 *>          The leading dimension of A, B, S, T, S2, and T2.
00269 *>          It must be at least 1 and at least max( NN ).
00270 *> \endverbatim
00271 *>
00272 *> \param[in,out] B
00273 *> \verbatim
00274 *>          B is COMPLEX array, dimension (LDA, max(NN))
00275 *>          Used to hold the original B matrix.  Used as input only
00276 *>          if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and
00277 *>          DOTYPE(MAXTYP+1)=.TRUE.
00278 *> \endverbatim
00279 *>
00280 *> \param[out] S
00281 *> \verbatim
00282 *>          S is COMPLEX array, dimension (LDA, max(NN))
00283 *>          The upper triangular matrix computed from A by CGEGS.
00284 *> \endverbatim
00285 *>
00286 *> \param[out] T
00287 *> \verbatim
00288 *>          T is COMPLEX array, dimension (LDA, max(NN))
00289 *>          The upper triangular matrix computed from B by CGEGS.
00290 *> \endverbatim
00291 *>
00292 *> \param[out] S2
00293 *> \verbatim
00294 *>          S2 is COMPLEX array, dimension (LDA, max(NN))
00295 *>          The matrix computed from A by CGEGV.  This will be the
00296 *>          Schur (upper triangular) form of some matrix related to A,
00297 *>          but will not, in general, be the same as S.
00298 *> \endverbatim
00299 *>
00300 *> \param[out] T2
00301 *> \verbatim
00302 *>          T2 is COMPLEX array, dimension (LDA, max(NN))
00303 *>          The matrix computed from B by CGEGV.  This will be the
00304 *>          Schur form of some matrix related to B, but will not, in
00305 *>          general, be the same as T.
00306 *> \endverbatim
00307 *>
00308 *> \param[out] Q
00309 *> \verbatim
00310 *>          Q is COMPLEX array, dimension (LDQ, max(NN))
00311 *>          The (left) unitary matrix computed by CGEGS.
00312 *> \endverbatim
00313 *>
00314 *> \param[in] LDQ
00315 *> \verbatim
00316 *>          LDQ is INTEGER
00317 *>          The leading dimension of Q, Z, VL, and VR.  It must
00318 *>          be at least 1 and at least max( NN ).
00319 *> \endverbatim
00320 *>
00321 *> \param[out] Z
00322 *> \verbatim
00323 *>          Z is COMPLEX array, dimension (LDQ, max(NN))
00324 *>          The (right) unitary matrix computed by CGEGS.
00325 *> \endverbatim
00326 *>
00327 *> \param[out] ALPHA1
00328 *> \verbatim
00329 *>          ALPHA1 is COMPLEX array, dimension (max(NN))
00330 *> \endverbatim
00331 *>
00332 *> \param[out] BETA1
00333 *> \verbatim
00334 *>          BETA1 is COMPLEX array, dimension (max(NN))
00335 *>
00336 *>          The generalized eigenvalues of (A,B) computed by CGEGS.
00337 *>          ALPHA1(k) / BETA1(k)  is the k-th generalized eigenvalue of
00338 *>          the matrices in A and B.
00339 *> \endverbatim
00340 *>
00341 *> \param[out] ALPHA2
00342 *> \verbatim
00343 *>          ALPHA2 is COMPLEX array, dimension (max(NN))
00344 *> \endverbatim
00345 *>
00346 *> \param[out] BETA2
00347 *> \verbatim
00348 *>          BETA2 is COMPLEX array, dimension (max(NN))
00349 *>
00350 *>          The generalized eigenvalues of (A,B) computed by CGEGV.
00351 *>          ALPHA2(k) / BETA2(k)  is the k-th generalized eigenvalue of
00352 *>          the matrices in A and B.
00353 *> \endverbatim
00354 *>
00355 *> \param[out] VL
00356 *> \verbatim
00357 *>          VL is COMPLEX array, dimension (LDQ, max(NN))
00358 *>          The (lower triangular) left eigenvector matrix for the
00359 *>          matrices in A and B.
00360 *> \endverbatim
00361 *>
00362 *> \param[out] VR
00363 *> \verbatim
00364 *>          VR is COMPLEX array, dimension (LDQ, max(NN))
00365 *>          The (upper triangular) right eigenvector matrix for the
00366 *>          matrices in A and B.
00367 *> \endverbatim
00368 *>
00369 *> \param[out] WORK
00370 *> \verbatim
00371 *>          WORK is COMPLEX array, dimension (LWORK)
00372 *> \endverbatim
00373 *>
00374 *> \param[in] LWORK
00375 *> \verbatim
00376 *>          LWORK is INTEGER
00377 *>          The number of entries in WORK.  This must be at least
00378 *>          MAX( 2*N, N*(NB+1), (k+1)*(2*k+N+1) ), where "k" is the
00379 *>          sum of the blocksize and number-of-shifts for CHGEQZ, and
00380 *>          NB is the greatest of the blocksizes for CGEQRF, CUNMQR,
00381 *>          and CUNGQR.  (The blocksizes and the number-of-shifts are
00382 *>          retrieved through calls to ILAENV.)
00383 *> \endverbatim
00384 *>
00385 *> \param[out] RWORK
00386 *> \verbatim
00387 *>          RWORK is REAL array, dimension (8*N)
00388 *> \endverbatim
00389 *>
00390 *> \param[out] RESULT
00391 *> \verbatim
00392 *>          RESULT is REAL array, dimension (7)
00393 *>          The values computed by the tests described above.
00394 *>          The values are currently limited to 1/ulp, to avoid
00395 *>          overflow.
00396 *> \endverbatim
00397 *>
00398 *> \param[out] INFO
00399 *> \verbatim
00400 *>          INFO is INTEGER
00401 *>          = 0:  successful exit
00402 *>          < 0:  if INFO = -i, the i-th argument had an illegal value.
00403 *>          > 0:  A routine returned an error code.  INFO is the
00404 *>                absolute value of the INFO value returned.
00405 *> \endverbatim
00406 *
00407 *  Authors:
00408 *  ========
00409 *
00410 *> \author Univ. of Tennessee 
00411 *> \author Univ. of California Berkeley 
00412 *> \author Univ. of Colorado Denver 
00413 *> \author NAG Ltd. 
00414 *
00415 *> \date November 2011
00416 *
00417 *> \ingroup complex_eig
00418 *
00419 *  =====================================================================
00420       SUBROUTINE CDRVGG( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
00421      $                   THRSHN, NOUNIT, A, LDA, B, S, T, S2, T2, Q,
00422      $                   LDQ, Z, ALPHA1, BETA1, ALPHA2, BETA2, VL, VR,
00423      $                   WORK, LWORK, RWORK, RESULT, INFO )
00424 *
00425 *  -- LAPACK test routine (version 3.4.0) --
00426 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00427 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00428 *     November 2011
00429 *
00430 *     .. Scalar Arguments ..
00431       INTEGER            INFO, LDA, LDQ, LWORK, NOUNIT, NSIZES, NTYPES
00432       REAL               THRESH, THRSHN
00433 *     ..
00434 *     .. Array Arguments ..
00435 *
00436 *  =====================================================================
00437 *
00438       LOGICAL            DOTYPE( * )
00439       INTEGER            ISEED( 4 ), NN( * )
00440       REAL               RESULT( * ), RWORK( * )
00441       COMPLEX            A( LDA, * ), ALPHA1( * ), ALPHA2( * ),
00442      $                   B( LDA, * ), BETA1( * ), BETA2( * ),
00443      $                   Q( LDQ, * ), S( LDA, * ), S2( LDA, * ),
00444      $                   T( LDA, * ), T2( LDA, * ), VL( LDQ, * ),
00445      $                   VR( LDQ, * ), WORK( * ), Z( LDQ, * )
00446 *     ..
00447 *     .. Parameters ..
00448       REAL               ZERO, ONE
00449       PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
00450       COMPLEX            CZERO, CONE
00451       PARAMETER          ( CZERO = ( 0.0E+0, 0.0E+0 ),
00452      $                   CONE = ( 1.0E+0, 0.0E+0 ) )
00453       INTEGER            MAXTYP
00454       PARAMETER          ( MAXTYP = 26 )
00455 *     ..
00456 *     .. Local Scalars ..
00457       LOGICAL            BADNN
00458       INTEGER            I1, IADD, IINFO, IN, J, JC, JR, JSIZE, JTYPE,
00459      $                   LWKOPT, MTYPES, N, N1, NB, NBZ, NERRS, NMATS,
00460      $                   NMAX, NS, NTEST, NTESTT
00461       REAL               SAFMAX, SAFMIN, TEMP1, TEMP2, ULP, ULPINV
00462       COMPLEX            CTEMP, X
00463 *     ..
00464 *     .. Local Arrays ..
00465       LOGICAL            LASIGN( MAXTYP ), LBSIGN( MAXTYP )
00466       INTEGER            IOLDSD( 4 ), KADD( 6 ), KAMAGN( MAXTYP ),
00467      $                   KATYPE( MAXTYP ), KAZERO( MAXTYP ),
00468      $                   KBMAGN( MAXTYP ), KBTYPE( MAXTYP ),
00469      $                   KBZERO( MAXTYP ), KCLASS( MAXTYP ),
00470      $                   KTRIAN( MAXTYP ), KZ1( 6 ), KZ2( 6 )
00471       REAL               DUMMA( 4 ), RMAGN( 0: 3 )
00472 *     ..
00473 *     .. External Functions ..
00474       INTEGER            ILAENV
00475       REAL               SLAMCH
00476       COMPLEX            CLARND
00477       EXTERNAL           ILAENV, SLAMCH, CLARND
00478 *     ..
00479 *     .. External Subroutines ..
00480       EXTERNAL           ALASVM, CGEGS, CGEGV, CGET51, CGET52, CLACPY,
00481      $                   CLARFG, CLASET, CLATM4, CUNM2R, SLABAD, XERBLA
00482 *     ..
00483 *     .. Intrinsic Functions ..
00484       INTRINSIC          ABS, AIMAG, CONJG, MAX, MIN, REAL, SIGN
00485 *     ..
00486 *     .. Statement Functions ..
00487       REAL               ABS1
00488 *     ..
00489 *     .. Statement Function definitions ..
00490       ABS1( X ) = ABS( REAL( X ) ) + ABS( AIMAG( X ) )
00491 *     ..
00492 *     .. Data statements ..
00493       DATA               KCLASS / 15*1, 10*2, 1*3 /
00494       DATA               KZ1 / 0, 1, 2, 1, 3, 3 /
00495       DATA               KZ2 / 0, 0, 1, 2, 1, 1 /
00496       DATA               KADD / 0, 0, 0, 0, 3, 2 /
00497       DATA               KATYPE / 0, 1, 0, 1, 2, 3, 4, 1, 4, 4, 1, 1, 4,
00498      $                   4, 4, 2, 4, 5, 8, 7, 9, 4*4, 0 /
00499       DATA               KBTYPE / 0, 0, 1, 1, 2, -3, 1, 4, 1, 1, 4, 4,
00500      $                   1, 1, -4, 2, -4, 8*8, 0 /
00501       DATA               KAZERO / 6*1, 2, 1, 2*2, 2*1, 2*2, 3, 1, 3,
00502      $                   4*5, 4*3, 1 /
00503       DATA               KBZERO / 6*1, 1, 2, 2*1, 2*2, 2*1, 4, 1, 4,
00504      $                   4*6, 4*4, 1 /
00505       DATA               KAMAGN / 8*1, 2, 3, 2, 3, 2, 3, 7*1, 2, 3, 3,
00506      $                   2, 1 /
00507       DATA               KBMAGN / 8*1, 3, 2, 3, 2, 2, 3, 7*1, 3, 2, 3,
00508      $                   2, 1 /
00509       DATA               KTRIAN / 16*0, 10*1 /
00510       DATA               LASIGN / 6*.FALSE., .TRUE., .FALSE., 2*.TRUE.,
00511      $                   2*.FALSE., 3*.TRUE., .FALSE., .TRUE.,
00512      $                   3*.FALSE., 5*.TRUE., .FALSE. /
00513       DATA               LBSIGN / 7*.FALSE., .TRUE., 2*.FALSE.,
00514      $                   2*.TRUE., 2*.FALSE., .TRUE., .FALSE., .TRUE.,
00515      $                   9*.FALSE. /
00516 *     ..
00517 *     .. Executable Statements ..
00518 *
00519 *     Check for errors
00520 *
00521       INFO = 0
00522 *
00523       BADNN = .FALSE.
00524       NMAX = 1
00525       DO 10 J = 1, NSIZES
00526          NMAX = MAX( NMAX, NN( J ) )
00527          IF( NN( J ).LT.0 )
00528      $      BADNN = .TRUE.
00529    10 CONTINUE
00530 *
00531 *     Maximum blocksize and shift -- we assume that blocksize and number
00532 *     of shifts are monotone increasing functions of N.
00533 *
00534       NB = MAX( 1, ILAENV( 1, 'CGEQRF', ' ', NMAX, NMAX, -1, -1 ),
00535      $     ILAENV( 1, 'CUNMQR', 'LC', NMAX, NMAX, NMAX, -1 ),
00536      $     ILAENV( 1, 'CUNGQR', ' ', NMAX, NMAX, NMAX, -1 ) )
00537       NBZ = ILAENV( 1, 'CHGEQZ', 'SII', NMAX, 1, NMAX, 0 )
00538       NS = ILAENV( 4, 'CHGEQZ', 'SII', NMAX, 1, NMAX, 0 )
00539       I1 = NBZ + NS
00540       LWKOPT = MAX( 2*NMAX, NMAX*( NB+1 ), ( 2*I1+NMAX+1 )*( I1+1 ) )
00541 *
00542 *     Check for errors
00543 *
00544       IF( NSIZES.LT.0 ) THEN
00545          INFO = -1
00546       ELSE IF( BADNN ) THEN
00547          INFO = -2
00548       ELSE IF( NTYPES.LT.0 ) THEN
00549          INFO = -3
00550       ELSE IF( THRESH.LT.ZERO ) THEN
00551          INFO = -6
00552       ELSE IF( LDA.LE.1 .OR. LDA.LT.NMAX ) THEN
00553          INFO = -10
00554       ELSE IF( LDQ.LE.1 .OR. LDQ.LT.NMAX ) THEN
00555          INFO = -19
00556       ELSE IF( LWKOPT.GT.LWORK ) THEN
00557          INFO = -30
00558       END IF
00559 *
00560       IF( INFO.NE.0 ) THEN
00561          CALL XERBLA( 'CDRVGG', -INFO )
00562          RETURN
00563       END IF
00564 *
00565 *     Quick return if possible
00566 *
00567       IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 )
00568      $   RETURN
00569 *
00570       ULP = SLAMCH( 'Precision' )
00571       SAFMIN = SLAMCH( 'Safe minimum' )
00572       SAFMIN = SAFMIN / ULP
00573       SAFMAX = ONE / SAFMIN
00574       CALL SLABAD( SAFMIN, SAFMAX )
00575       ULPINV = ONE / ULP
00576 *
00577 *     The values RMAGN(2:3) depend on N, see below.
00578 *
00579       RMAGN( 0 ) = ZERO
00580       RMAGN( 1 ) = ONE
00581 *
00582 *     Loop over sizes, types
00583 *
00584       NTESTT = 0
00585       NERRS = 0
00586       NMATS = 0
00587 *
00588       DO 160 JSIZE = 1, NSIZES
00589          N = NN( JSIZE )
00590          N1 = MAX( 1, N )
00591          RMAGN( 2 ) = SAFMAX*ULP / REAL( N1 )
00592          RMAGN( 3 ) = SAFMIN*ULPINV*N1
00593 *
00594          IF( NSIZES.NE.1 ) THEN
00595             MTYPES = MIN( MAXTYP, NTYPES )
00596          ELSE
00597             MTYPES = MIN( MAXTYP+1, NTYPES )
00598          END IF
00599 *
00600          DO 150 JTYPE = 1, MTYPES
00601             IF( .NOT.DOTYPE( JTYPE ) )
00602      $         GO TO 150
00603             NMATS = NMATS + 1
00604             NTEST = 0
00605 *
00606 *           Save ISEED in case of an error.
00607 *
00608             DO 20 J = 1, 4
00609                IOLDSD( J ) = ISEED( J )
00610    20       CONTINUE
00611 *
00612 *           Initialize RESULT
00613 *
00614             DO 30 J = 1, 7
00615                RESULT( J ) = ZERO
00616    30       CONTINUE
00617 *
00618 *           Compute A and B
00619 *
00620 *           Description of control parameters:
00621 *
00622 *           KCLASS: =1 means w/o rotation, =2 means w/ rotation,
00623 *                   =3 means random.
00624 *           KATYPE: the "type" to be passed to CLATM4 for computing A.
00625 *           KAZERO: the pattern of zeros on the diagonal for A:
00626 *                   =1: ( xxx ), =2: (0, xxx ) =3: ( 0, 0, xxx, 0 ),
00627 *                   =4: ( 0, xxx, 0, 0 ), =5: ( 0, 0, 1, xxx, 0 ),
00628 *                   =6: ( 0, 1, 0, xxx, 0 ).  (xxx means a string of
00629 *                   non-zero entries.)
00630 *           KAMAGN: the magnitude of the matrix: =0: zero, =1: O(1),
00631 *                   =2: large, =3: small.
00632 *           LASIGN: .TRUE. if the diagonal elements of A are to be
00633 *                   multiplied by a random magnitude 1 number.
00634 *           KBTYPE, KBZERO, KBMAGN, IBSIGN: the same, but for B.
00635 *           KTRIAN: =0: don't fill in the upper triangle, =1: do.
00636 *           KZ1, KZ2, KADD: used to implement KAZERO and KBZERO.
00637 *           RMAGN:  used to implement KAMAGN and KBMAGN.
00638 *
00639             IF( MTYPES.GT.MAXTYP )
00640      $         GO TO 110
00641             IINFO = 0
00642             IF( KCLASS( JTYPE ).LT.3 ) THEN
00643 *
00644 *              Generate A (w/o rotation)
00645 *
00646                IF( ABS( KATYPE( JTYPE ) ).EQ.3 ) THEN
00647                   IN = 2*( ( N-1 ) / 2 ) + 1
00648                   IF( IN.NE.N )
00649      $               CALL CLASET( 'Full', N, N, CZERO, CZERO, A, LDA )
00650                ELSE
00651                   IN = N
00652                END IF
00653                CALL CLATM4( KATYPE( JTYPE ), IN, KZ1( KAZERO( JTYPE ) ),
00654      $                      KZ2( KAZERO( JTYPE ) ), LASIGN( JTYPE ),
00655      $                      RMAGN( KAMAGN( JTYPE ) ), ULP,
00656      $                      RMAGN( KTRIAN( JTYPE )*KAMAGN( JTYPE ) ), 2,
00657      $                      ISEED, A, LDA )
00658                IADD = KADD( KAZERO( JTYPE ) )
00659                IF( IADD.GT.0 .AND. IADD.LE.N )
00660      $            A( IADD, IADD ) = RMAGN( KAMAGN( JTYPE ) )
00661 *
00662 *              Generate B (w/o rotation)
00663 *
00664                IF( ABS( KBTYPE( JTYPE ) ).EQ.3 ) THEN
00665                   IN = 2*( ( N-1 ) / 2 ) + 1
00666                   IF( IN.NE.N )
00667      $               CALL CLASET( 'Full', N, N, CZERO, CZERO, B, LDA )
00668                ELSE
00669                   IN = N
00670                END IF
00671                CALL CLATM4( KBTYPE( JTYPE ), IN, KZ1( KBZERO( JTYPE ) ),
00672      $                      KZ2( KBZERO( JTYPE ) ), LBSIGN( JTYPE ),
00673      $                      RMAGN( KBMAGN( JTYPE ) ), ONE,
00674      $                      RMAGN( KTRIAN( JTYPE )*KBMAGN( JTYPE ) ), 2,
00675      $                      ISEED, B, LDA )
00676                IADD = KADD( KBZERO( JTYPE ) )
00677                IF( IADD.NE.0 .AND. IADD.LE.N )
00678      $            B( IADD, IADD ) = RMAGN( KBMAGN( JTYPE ) )
00679 *
00680                IF( KCLASS( JTYPE ).EQ.2 .AND. N.GT.0 ) THEN
00681 *
00682 *                 Include rotations
00683 *
00684 *                 Generate Q, Z as Householder transformations times
00685 *                 a diagonal matrix.
00686 *
00687                   DO 50 JC = 1, N - 1
00688                      DO 40 JR = JC, N
00689                         Q( JR, JC ) = CLARND( 3, ISEED )
00690                         Z( JR, JC ) = CLARND( 3, ISEED )
00691    40                CONTINUE
00692                      CALL CLARFG( N+1-JC, Q( JC, JC ), Q( JC+1, JC ), 1,
00693      $                            WORK( JC ) )
00694                      WORK( 2*N+JC ) = SIGN( ONE, REAL( Q( JC, JC ) ) )
00695                      Q( JC, JC ) = CONE
00696                      CALL CLARFG( N+1-JC, Z( JC, JC ), Z( JC+1, JC ), 1,
00697      $                            WORK( N+JC ) )
00698                      WORK( 3*N+JC ) = SIGN( ONE, REAL( Z( JC, JC ) ) )
00699                      Z( JC, JC ) = CONE
00700    50             CONTINUE
00701                   CTEMP = CLARND( 3, ISEED )
00702                   Q( N, N ) = CONE
00703                   WORK( N ) = CZERO
00704                   WORK( 3*N ) = CTEMP / ABS( CTEMP )
00705                   CTEMP = CLARND( 3, ISEED )
00706                   Z( N, N ) = CONE
00707                   WORK( 2*N ) = CZERO
00708                   WORK( 4*N ) = CTEMP / ABS( CTEMP )
00709 *
00710 *                 Apply the diagonal matrices
00711 *
00712                   DO 70 JC = 1, N
00713                      DO 60 JR = 1, N
00714                         A( JR, JC ) = WORK( 2*N+JR )*
00715      $                                CONJG( WORK( 3*N+JC ) )*
00716      $                                A( JR, JC )
00717                         B( JR, JC ) = WORK( 2*N+JR )*
00718      $                                CONJG( WORK( 3*N+JC ) )*
00719      $                                B( JR, JC )
00720    60                CONTINUE
00721    70             CONTINUE
00722                   CALL CUNM2R( 'L', 'N', N, N, N-1, Q, LDQ, WORK, A,
00723      $                         LDA, WORK( 2*N+1 ), IINFO )
00724                   IF( IINFO.NE.0 )
00725      $               GO TO 100
00726                   CALL CUNM2R( 'R', 'C', N, N, N-1, Z, LDQ, WORK( N+1 ),
00727      $                         A, LDA, WORK( 2*N+1 ), IINFO )
00728                   IF( IINFO.NE.0 )
00729      $               GO TO 100
00730                   CALL CUNM2R( 'L', 'N', N, N, N-1, Q, LDQ, WORK, B,
00731      $                         LDA, WORK( 2*N+1 ), IINFO )
00732                   IF( IINFO.NE.0 )
00733      $               GO TO 100
00734                   CALL CUNM2R( 'R', 'C', N, N, N-1, Z, LDQ, WORK( N+1 ),
00735      $                         B, LDA, WORK( 2*N+1 ), IINFO )
00736                   IF( IINFO.NE.0 )
00737      $               GO TO 100
00738                END IF
00739             ELSE
00740 *
00741 *              Random matrices
00742 *
00743                DO 90 JC = 1, N
00744                   DO 80 JR = 1, N
00745                      A( JR, JC ) = RMAGN( KAMAGN( JTYPE ) )*
00746      $                             CLARND( 4, ISEED )
00747                      B( JR, JC ) = RMAGN( KBMAGN( JTYPE ) )*
00748      $                             CLARND( 4, ISEED )
00749    80             CONTINUE
00750    90          CONTINUE
00751             END IF
00752 *
00753   100       CONTINUE
00754 *
00755             IF( IINFO.NE.0 ) THEN
00756                WRITE( NOUNIT, FMT = 9999 )'Generator', IINFO, N, JTYPE,
00757      $            IOLDSD
00758                INFO = ABS( IINFO )
00759                RETURN
00760             END IF
00761 *
00762   110       CONTINUE
00763 *
00764 *           Call CGEGS to compute H, T, Q, Z, alpha, and beta.
00765 *
00766             CALL CLACPY( ' ', N, N, A, LDA, S, LDA )
00767             CALL CLACPY( ' ', N, N, B, LDA, T, LDA )
00768             NTEST = 1
00769             RESULT( 1 ) = ULPINV
00770 *
00771             CALL CGEGS( 'V', 'V', N, S, LDA, T, LDA, ALPHA1, BETA1, Q,
00772      $                  LDQ, Z, LDQ, WORK, LWORK, RWORK, IINFO )
00773             IF( IINFO.NE.0 ) THEN
00774                WRITE( NOUNIT, FMT = 9999 )'CGEGS', IINFO, N, JTYPE,
00775      $            IOLDSD
00776                INFO = ABS( IINFO )
00777                GO TO 130
00778             END IF
00779 *
00780             NTEST = 4
00781 *
00782 *           Do tests 1--4
00783 *
00784             CALL CGET51( 1, N, A, LDA, S, LDA, Q, LDQ, Z, LDQ, WORK,
00785      $                   RWORK, RESULT( 1 ) )
00786             CALL CGET51( 1, N, B, LDA, T, LDA, Q, LDQ, Z, LDQ, WORK,
00787      $                   RWORK, RESULT( 2 ) )
00788             CALL CGET51( 3, N, B, LDA, T, LDA, Q, LDQ, Q, LDQ, WORK,
00789      $                   RWORK, RESULT( 3 ) )
00790             CALL CGET51( 3, N, B, LDA, T, LDA, Z, LDQ, Z, LDQ, WORK,
00791      $                   RWORK, RESULT( 4 ) )
00792 *
00793 *           Do test 5: compare eigenvalues with diagonals.
00794 *
00795             TEMP1 = ZERO
00796 *
00797             DO 120 J = 1, N
00798                TEMP2 = ( ABS1( ALPHA1( J )-S( J, J ) ) /
00799      $                 MAX( SAFMIN, ABS1( ALPHA1( J ) ), ABS1( S( J,
00800      $                 J ) ) )+ABS1( BETA1( J )-T( J, J ) ) /
00801      $                 MAX( SAFMIN, ABS1( BETA1( J ) ), ABS1( T( J,
00802      $                 J ) ) ) ) / ULP
00803                TEMP1 = MAX( TEMP1, TEMP2 )
00804   120       CONTINUE
00805             RESULT( 5 ) = TEMP1
00806 *
00807 *           Call CGEGV to compute S2, T2, VL, and VR, do tests.
00808 *
00809 *           Eigenvalues and Eigenvectors
00810 *
00811             CALL CLACPY( ' ', N, N, A, LDA, S2, LDA )
00812             CALL CLACPY( ' ', N, N, B, LDA, T2, LDA )
00813             NTEST = 6
00814             RESULT( 6 ) = ULPINV
00815 *
00816             CALL CGEGV( 'V', 'V', N, S2, LDA, T2, LDA, ALPHA2, BETA2,
00817      $                  VL, LDQ, VR, LDQ, WORK, LWORK, RWORK, IINFO )
00818             IF( IINFO.NE.0 ) THEN
00819                WRITE( NOUNIT, FMT = 9999 )'CGEGV', IINFO, N, JTYPE,
00820      $            IOLDSD
00821                INFO = ABS( IINFO )
00822                GO TO 130
00823             END IF
00824 *
00825             NTEST = 7
00826 *
00827 *           Do Tests 6 and 7
00828 *
00829             CALL CGET52( .TRUE., N, A, LDA, B, LDA, VL, LDQ, ALPHA2,
00830      $                   BETA2, WORK, RWORK, DUMMA( 1 ) )
00831             RESULT( 6 ) = DUMMA( 1 )
00832             IF( DUMMA( 2 ).GT.THRSHN ) THEN
00833                WRITE( NOUNIT, FMT = 9998 )'Left', 'CGEGV', DUMMA( 2 ),
00834      $            N, JTYPE, IOLDSD
00835             END IF
00836 *
00837             CALL CGET52( .FALSE., N, A, LDA, B, LDA, VR, LDQ, ALPHA2,
00838      $                   BETA2, WORK, RWORK, DUMMA( 1 ) )
00839             RESULT( 7 ) = DUMMA( 1 )
00840             IF( DUMMA( 2 ).GT.THRESH ) THEN
00841                WRITE( NOUNIT, FMT = 9998 )'Right', 'CGEGV', DUMMA( 2 ),
00842      $            N, JTYPE, IOLDSD
00843             END IF
00844 *
00845 *           End of Loop -- Check for RESULT(j) > THRESH
00846 *
00847   130       CONTINUE
00848 *
00849             NTESTT = NTESTT + NTEST
00850 *
00851 *           Print out tests which fail.
00852 *
00853             DO 140 JR = 1, NTEST
00854                IF( RESULT( JR ).GE.THRESH ) THEN
00855 *
00856 *                 If this is the first test to fail,
00857 *                 print a header to the data file.
00858 *
00859                   IF( NERRS.EQ.0 ) THEN
00860                      WRITE( NOUNIT, FMT = 9997 )'CGG'
00861 *
00862 *                    Matrix types
00863 *
00864                      WRITE( NOUNIT, FMT = 9996 )
00865                      WRITE( NOUNIT, FMT = 9995 )
00866                      WRITE( NOUNIT, FMT = 9994 )'Unitary'
00867 *
00868 *                    Tests performed
00869 *
00870                      WRITE( NOUNIT, FMT = 9993 )'unitary', '*',
00871      $                  'conjugate transpose', ( '*', J = 1, 5 )
00872 *
00873                   END IF
00874                   NERRS = NERRS + 1
00875                   IF( RESULT( JR ).LT.10000.0 ) THEN
00876                      WRITE( NOUNIT, FMT = 9992 )N, JTYPE, IOLDSD, JR,
00877      $                  RESULT( JR )
00878                   ELSE
00879                      WRITE( NOUNIT, FMT = 9991 )N, JTYPE, IOLDSD, JR,
00880      $                  RESULT( JR )
00881                   END IF
00882                END IF
00883   140       CONTINUE
00884 *
00885   150    CONTINUE
00886   160 CONTINUE
00887 *
00888 *     Summary
00889 *
00890       CALL ALASVM( 'CGG', NOUNIT, NERRS, NTESTT, 0 )
00891       RETURN
00892 *
00893  9999 FORMAT( ' CDRVGG: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
00894      $      I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' )
00895 *
00896  9998 FORMAT( ' CDRVGG: ', A, ' Eigenvectors from ', A, ' incorrectly ',
00897      $      'normalized.', / ' Bits of error=', 0P, G10.3, ',', 9X,
00898      $      'N=', I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5,
00899      $      ')' )
00900 *
00901  9997 FORMAT( / 1X, A3,
00902      $      ' -- Complex Generalized eigenvalue problem driver' )
00903 *
00904  9996 FORMAT( ' Matrix types (see CDRVGG for details): ' )
00905 *
00906  9995 FORMAT( ' Special Matrices:', 23X,
00907      $      '(J''=transposed Jordan block)',
00908      $      / '   1=(0,0)  2=(I,0)  3=(0,I)  4=(I,I)  5=(J'',J'')  ',
00909      $      '6=(diag(J'',I), diag(I,J''))', / ' Diagonal Matrices:  ( ',
00910      $      'D=diag(0,1,2,...) )', / '   7=(D,I)   9=(large*D, small*I',
00911      $      ')  11=(large*I, small*D)  13=(large*D, large*I)', /
00912      $      '   8=(I,D)  10=(small*D, large*I)  12=(small*I, large*D) ',
00913      $      ' 14=(small*D, small*I)', / '  15=(D, reversed D)' )
00914  9994 FORMAT( ' Matrices Rotated by Random ', A, ' Matrices U, V:',
00915      $      / '  16=Transposed Jordan Blocks             19=geometric ',
00916      $      'alpha, beta=0,1', / '  17=arithm. alpha&beta             ',
00917      $      '      20=arithmetic alpha, beta=0,1', / '  18=clustered ',
00918      $      'alpha, beta=0,1            21=random alpha, beta=0,1',
00919      $      / ' Large & Small Matrices:', / '  22=(large, small)   ',
00920      $      '23=(small,large)    24=(small,small)    25=(large,large)',
00921      $      / '  26=random O(1) matrices.' )
00922 *
00923  9993 FORMAT( / ' Tests performed:  (S is Schur, T is triangular, ',
00924      $      'Q and Z are ', A, ',', / 20X,
00925      $      'l and r are the appropriate left and right', / 19X,
00926      $      'eigenvectors, resp., a is alpha, b is beta, and', / 19X, A,
00927      $      ' means ', A, '.)', / ' 1 = | A - Q S Z', A,
00928      $      ' | / ( |A| n ulp )      2 = | B - Q T Z', A,
00929      $      ' | / ( |B| n ulp )', / ' 3 = | I - QQ', A,
00930      $      ' | / ( n ulp )             4 = | I - ZZ', A,
00931      $      ' | / ( n ulp )', /
00932      $      ' 5 = difference between (alpha,beta) and diagonals of',
00933      $      ' (S,T)', / ' 6 = max | ( b A - a B )', A,
00934      $      ' l | / const.   7 = max | ( b A - a B ) r | / const.',
00935      $      / 1X )
00936  9992 FORMAT( ' Matrix order=', I5, ', type=', I2, ', seed=',
00937      $      4( I4, ',' ), ' result ', I3, ' is', 0P, F8.2 )
00938  9991 FORMAT( ' Matrix order=', I5, ', type=', I2, ', seed=',
00939      $      4( I4, ',' ), ' result ', I3, ' is', 1P, E10.3 )
00940 *
00941 *     End of CDRVGG
00942 *
00943       END
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