LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
cdrges.f
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00001 *> \brief \b CDRGES
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 CDRGES( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
00012 *                          NOUNIT, A, LDA, B, S, T, Q, LDQ, Z, ALPHA,
00013 *                          BETA, WORK, LWORK, RWORK, RESULT, BWORK, INFO )
00014 * 
00015 *       .. Scalar Arguments ..
00016 *       INTEGER            INFO, LDA, LDQ, LWORK, NOUNIT, NSIZES, NTYPES
00017 *       REAL               THRESH
00018 *       ..
00019 *       .. Array Arguments ..
00020 *       LOGICAL            BWORK( * ), DOTYPE( * )
00021 *       INTEGER            ISEED( 4 ), NN( * )
00022 *       REAL               RESULT( 13 ), RWORK( * )
00023 *       COMPLEX            A( LDA, * ), ALPHA( * ), B( LDA, * ),
00024 *      $                   BETA( * ), Q( LDQ, * ), S( LDA, * ),
00025 *      $                   T( LDA, * ), WORK( * ), Z( LDQ, * )
00026 *       ..
00027 *  
00028 *
00029 *> \par Purpose:
00030 *  =============
00031 *>
00032 *> \verbatim
00033 *>
00034 *> CDRGES checks the nonsymmetric generalized eigenvalue (Schur form)
00035 *> problem driver CGGES.
00036 *>
00037 *> CGGES factors A and B as Q*S*Z'  and Q*T*Z' , where ' means conjugate
00038 *> transpose, S and T are  upper triangular (i.e., in generalized Schur
00039 *> form), and Q and Z are unitary. It also computes the generalized
00040 *> eigenvalues (alpha(j),beta(j)), j=1,...,n.  Thus,
00041 *> w(j) = alpha(j)/beta(j) is a root of the characteristic equation
00042 *>
00043 *>                 det( A - w(j) B ) = 0
00044 *>
00045 *> Optionally it also reorder the eigenvalues so that a selected
00046 *> cluster of eigenvalues appears in the leading diagonal block of the
00047 *> Schur forms.
00048 *>
00049 *> When CDRGES is called, a number of matrix "sizes" ("N's") and a
00050 *> number of matrix "TYPES" are specified.  For each size ("N")
00051 *> and each TYPE of matrix, a pair of matrices (A, B) will be generated
00052 *> and used for testing. For each matrix pair, the following 13 tests
00053 *> will be performed and compared with the threshhold THRESH except
00054 *> the tests (5), (11) and (13).
00055 *>
00056 *>
00057 *> (1)   | A - Q S Z' | / ( |A| n ulp ) (no sorting of eigenvalues)
00058 *>
00059 *>
00060 *> (2)   | B - Q T Z' | / ( |B| n ulp ) (no sorting of eigenvalues)
00061 *>
00062 *>
00063 *> (3)   | I - QQ' | / ( n ulp ) (no sorting of eigenvalues)
00064 *>
00065 *>
00066 *> (4)   | I - ZZ' | / ( n ulp ) (no sorting of eigenvalues)
00067 *>
00068 *> (5)   if A is in Schur form (i.e. triangular form) (no sorting of
00069 *>       eigenvalues)
00070 *>
00071 *> (6)   if eigenvalues = diagonal elements of the Schur form (S, T),
00072 *>       i.e., test the maximum over j of D(j)  where:
00073 *>
00074 *>                     |alpha(j) - S(j,j)|        |beta(j) - T(j,j)|
00075 *>           D(j) = ------------------------ + -----------------------
00076 *>                  max(|alpha(j)|,|S(j,j)|)   max(|beta(j)|,|T(j,j)|)
00077 *>
00078 *>       (no sorting of eigenvalues)
00079 *>
00080 *> (7)   | (A,B) - Q (S,T) Z' | / ( |(A,B)| n ulp )
00081 *>       (with sorting of eigenvalues).
00082 *>
00083 *> (8)   | I - QQ' | / ( n ulp ) (with sorting of eigenvalues).
00084 *>
00085 *> (9)   | I - ZZ' | / ( n ulp ) (with sorting of eigenvalues).
00086 *>
00087 *> (10)  if A is in Schur form (i.e. quasi-triangular form)
00088 *>       (with sorting of eigenvalues).
00089 *>
00090 *> (11)  if eigenvalues = diagonal elements of the Schur form (S, T),
00091 *>       i.e. test the maximum over j of D(j)  where:
00092 *>
00093 *>                     |alpha(j) - S(j,j)|        |beta(j) - T(j,j)|
00094 *>           D(j) = ------------------------ + -----------------------
00095 *>                  max(|alpha(j)|,|S(j,j)|)   max(|beta(j)|,|T(j,j)|)
00096 *>
00097 *>       (with sorting of eigenvalues).
00098 *>
00099 *> (12)  if sorting worked and SDIM is the number of eigenvalues
00100 *>       which were CELECTed.
00101 *>
00102 *> Test Matrices
00103 *> =============
00104 *>
00105 *> The sizes of the test matrices are specified by an array
00106 *> NN(1:NSIZES); the value of each element NN(j) specifies one size.
00107 *> The "types" are specified by a logical array DOTYPE( 1:NTYPES ); if
00108 *> DOTYPE(j) is .TRUE., then matrix type "j" will be generated.
00109 *> Currently, the list of possible types is:
00110 *>
00111 *> (1)  ( 0, 0 )         (a pair of zero matrices)
00112 *>
00113 *> (2)  ( I, 0 )         (an identity and a zero matrix)
00114 *>
00115 *> (3)  ( 0, I )         (an identity and a zero matrix)
00116 *>
00117 *> (4)  ( I, I )         (a pair of identity matrices)
00118 *>
00119 *>         t   t
00120 *> (5)  ( J , J  )       (a pair of transposed Jordan blocks)
00121 *>
00122 *>                                     t                ( I   0  )
00123 *> (6)  ( X, Y )         where  X = ( J   0  )  and Y = (      t )
00124 *>                                  ( 0   I  )          ( 0   J  )
00125 *>                       and I is a k x k identity and J a (k+1)x(k+1)
00126 *>                       Jordan block; k=(N-1)/2
00127 *>
00128 *> (7)  ( D, I )         where D is diag( 0, 1,..., N-1 ) (a diagonal
00129 *>                       matrix with those diagonal entries.)
00130 *> (8)  ( I, D )
00131 *>
00132 *> (9)  ( big*D, small*I ) where "big" is near overflow and small=1/big
00133 *>
00134 *> (10) ( small*D, big*I )
00135 *>
00136 *> (11) ( big*I, small*D )
00137 *>
00138 *> (12) ( small*I, big*D )
00139 *>
00140 *> (13) ( big*D, big*I )
00141 *>
00142 *> (14) ( small*D, small*I )
00143 *>
00144 *> (15) ( D1, D2 )        where D1 is diag( 0, 0, 1, ..., N-3, 0 ) and
00145 *>                        D2 is diag( 0, N-3, N-4,..., 1, 0, 0 )
00146 *>           t   t
00147 *> (16) Q ( J , J ) Z     where Q and Z are random orthogonal matrices.
00148 *>
00149 *> (17) Q ( T1, T2 ) Z    where T1 and T2 are upper triangular matrices
00150 *>                        with random O(1) entries above the diagonal
00151 *>                        and diagonal entries diag(T1) =
00152 *>                        ( 0, 0, 1, ..., N-3, 0 ) and diag(T2) =
00153 *>                        ( 0, N-3, N-4,..., 1, 0, 0 )
00154 *>
00155 *> (18) Q ( T1, T2 ) Z    diag(T1) = ( 0, 0, 1, 1, s, ..., s, 0 )
00156 *>                        diag(T2) = ( 0, 1, 0, 1,..., 1, 0 )
00157 *>                        s = machine precision.
00158 *>
00159 *> (19) Q ( T1, T2 ) Z    diag(T1)=( 0,0,1,1, 1-d, ..., 1-(N-5)*d=s, 0 )
00160 *>                        diag(T2) = ( 0, 1, 0, 1, ..., 1, 0 )
00161 *>
00162 *>                                                        N-5
00163 *> (20) Q ( T1, T2 ) Z    diag(T1)=( 0, 0, 1, 1, a, ..., a   =s, 0 )
00164 *>                        diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 )
00165 *>
00166 *> (21) Q ( T1, T2 ) Z    diag(T1)=( 0, 0, 1, r1, r2, ..., r(N-4), 0 )
00167 *>                        diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 )
00168 *>                        where r1,..., r(N-4) are random.
00169 *>
00170 *> (22) Q ( big*T1, small*T2 ) Z    diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
00171 *>                                  diag(T2) = ( 0, 1, ..., 1, 0, 0 )
00172 *>
00173 *> (23) Q ( small*T1, big*T2 ) Z    diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
00174 *>                                  diag(T2) = ( 0, 1, ..., 1, 0, 0 )
00175 *>
00176 *> (24) Q ( small*T1, small*T2 ) Z  diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
00177 *>                                  diag(T2) = ( 0, 1, ..., 1, 0, 0 )
00178 *>
00179 *> (25) Q ( big*T1, big*T2 ) Z      diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
00180 *>                                  diag(T2) = ( 0, 1, ..., 1, 0, 0 )
00181 *>
00182 *> (26) Q ( T1, T2 ) Z     where T1 and T2 are random upper-triangular
00183 *>                         matrices.
00184 *>
00185 *> \endverbatim
00186 *
00187 *  Arguments:
00188 *  ==========
00189 *
00190 *> \param[in] NSIZES
00191 *> \verbatim
00192 *>          NSIZES is INTEGER
00193 *>          The number of sizes of matrices to use.  If it is zero,
00194 *>          SDRGES does nothing.  NSIZES >= 0.
00195 *> \endverbatim
00196 *>
00197 *> \param[in] NN
00198 *> \verbatim
00199 *>          NN is INTEGER array, dimension (NSIZES)
00200 *>          An array containing the sizes to be used for the matrices.
00201 *>          Zero values will be skipped.  NN >= 0.
00202 *> \endverbatim
00203 *>
00204 *> \param[in] NTYPES
00205 *> \verbatim
00206 *>          NTYPES is INTEGER
00207 *>          The number of elements in DOTYPE.   If it is zero, SDRGES
00208 *>          does nothing.  It must be at least zero.  If it is MAXTYP+1
00209 *>          and NSIZES is 1, then an additional type, MAXTYP+1 is
00210 *>          defined, which is to use whatever matrix is in A on input.
00211 *>          This is only useful if DOTYPE(1:MAXTYP) is .FALSE. and
00212 *>          DOTYPE(MAXTYP+1) is .TRUE. .
00213 *> \endverbatim
00214 *>
00215 *> \param[in] DOTYPE
00216 *> \verbatim
00217 *>          DOTYPE is LOGICAL array, dimension (NTYPES)
00218 *>          If DOTYPE(j) is .TRUE., then for each size in NN a
00219 *>          matrix of that size and of type j will be generated.
00220 *>          If NTYPES is smaller than the maximum number of types
00221 *>          defined (PARAMETER MAXTYP), then types NTYPES+1 through
00222 *>          MAXTYP will not be generated. If NTYPES is larger
00223 *>          than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES)
00224 *>          will be ignored.
00225 *> \endverbatim
00226 *>
00227 *> \param[in,out] ISEED
00228 *> \verbatim
00229 *>          ISEED is INTEGER array, dimension (4)
00230 *>          On entry ISEED specifies the seed of the random number
00231 *>          generator. The array elements should be between 0 and 4095;
00232 *>          if not they will be reduced mod 4096. Also, ISEED(4) must
00233 *>          be odd.  The random number generator uses a linear
00234 *>          congruential sequence limited to small integers, and so
00235 *>          should produce machine independent random numbers. The
00236 *>          values of ISEED are changed on exit, and can be used in the
00237 *>          next call to SDRGES to continue the same random number
00238 *>          sequence.
00239 *> \endverbatim
00240 *>
00241 *> \param[in] THRESH
00242 *> \verbatim
00243 *>          THRESH is REAL
00244 *>          A test will count as "failed" if the "error", computed as
00245 *>          described above, exceeds THRESH.  Note that the error is
00246 *>          scaled to be O(1), so THRESH should be a reasonably small
00247 *>          multiple of 1, e.g., 10 or 100.  In particular, it should
00248 *>          not depend on the precision (single vs. double) or the size
00249 *>          of the matrix.  THRESH >= 0.
00250 *> \endverbatim
00251 *>
00252 *> \param[in] NOUNIT
00253 *> \verbatim
00254 *>          NOUNIT is INTEGER
00255 *>          The FORTRAN unit number for printing out error messages
00256 *>          (e.g., if a routine returns IINFO not equal to 0.)
00257 *> \endverbatim
00258 *>
00259 *> \param[in,out] A
00260 *> \verbatim
00261 *>          A is COMPLEX array, dimension(LDA, max(NN))
00262 *>          Used to hold the original A matrix.  Used as input only
00263 *>          if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and
00264 *>          DOTYPE(MAXTYP+1)=.TRUE.
00265 *> \endverbatim
00266 *>
00267 *> \param[in] LDA
00268 *> \verbatim
00269 *>          LDA is INTEGER
00270 *>          The leading dimension of A, B, S, and T.
00271 *>          It must be at least 1 and at least max( NN ).
00272 *> \endverbatim
00273 *>
00274 *> \param[in,out] B
00275 *> \verbatim
00276 *>          B is COMPLEX array, dimension(LDA, max(NN))
00277 *>          Used to hold the original B matrix.  Used as input only
00278 *>          if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and
00279 *>          DOTYPE(MAXTYP+1)=.TRUE.
00280 *> \endverbatim
00281 *>
00282 *> \param[out] S
00283 *> \verbatim
00284 *>          S is COMPLEX array, dimension (LDA, max(NN))
00285 *>          The Schur form matrix computed from A by CGGES.  On exit, S
00286 *>          contains the Schur form matrix corresponding to the matrix
00287 *>          in A.
00288 *> \endverbatim
00289 *>
00290 *> \param[out] T
00291 *> \verbatim
00292 *>          T is COMPLEX array, dimension (LDA, max(NN))
00293 *>          The upper triangular matrix computed from B by CGGES.
00294 *> \endverbatim
00295 *>
00296 *> \param[out] Q
00297 *> \verbatim
00298 *>          Q is COMPLEX array, dimension (LDQ, max(NN))
00299 *>          The (left) orthogonal matrix computed by CGGES.
00300 *> \endverbatim
00301 *>
00302 *> \param[in] LDQ
00303 *> \verbatim
00304 *>          LDQ is INTEGER
00305 *>          The leading dimension of Q and Z. It must
00306 *>          be at least 1 and at least max( NN ).
00307 *> \endverbatim
00308 *>
00309 *> \param[out] Z
00310 *> \verbatim
00311 *>          Z is COMPLEX array, dimension( LDQ, max(NN) )
00312 *>          The (right) orthogonal matrix computed by CGGES.
00313 *> \endverbatim
00314 *>
00315 *> \param[out] ALPHA
00316 *> \verbatim
00317 *>          ALPHA is COMPLEX array, dimension (max(NN))
00318 *> \endverbatim
00319 *>
00320 *> \param[out] BETA
00321 *> \verbatim
00322 *>          BETA is COMPLEX array, dimension (max(NN))
00323 *>
00324 *>          The generalized eigenvalues of (A,B) computed by CGGES.
00325 *>          ALPHA(k) / BETA(k) is the k-th generalized eigenvalue of A
00326 *>          and B.
00327 *> \endverbatim
00328 *>
00329 *> \param[out] WORK
00330 *> \verbatim
00331 *>          WORK is COMPLEX array, dimension (LWORK)
00332 *> \endverbatim
00333 *>
00334 *> \param[in] LWORK
00335 *> \verbatim
00336 *>          LWORK is INTEGER
00337 *>          The dimension of the array WORK.  LWORK >= 3*N*N.
00338 *> \endverbatim
00339 *>
00340 *> \param[out] RWORK
00341 *> \verbatim
00342 *>          RWORK is REAL array, dimension ( 8*N )
00343 *>          Real workspace.
00344 *> \endverbatim
00345 *>
00346 *> \param[out] RESULT
00347 *> \verbatim
00348 *>          RESULT is REAL array, dimension (15)
00349 *>          The values computed by the tests described above.
00350 *>          The values are currently limited to 1/ulp, to avoid overflow.
00351 *> \endverbatim
00352 *>
00353 *> \param[out] BWORK
00354 *> \verbatim
00355 *>          BWORK is LOGICAL array, dimension (N)
00356 *> \endverbatim
00357 *>
00358 *> \param[out] INFO
00359 *> \verbatim
00360 *>          INFO is INTEGER
00361 *>          = 0:  successful exit
00362 *>          < 0:  if INFO = -i, the i-th argument had an illegal value.
00363 *>          > 0:  A routine returned an error code.  INFO is the
00364 *>                absolute value of the INFO value returned.
00365 *> \endverbatim
00366 *
00367 *  Authors:
00368 *  ========
00369 *
00370 *> \author Univ. of Tennessee 
00371 *> \author Univ. of California Berkeley 
00372 *> \author Univ. of Colorado Denver 
00373 *> \author NAG Ltd. 
00374 *
00375 *> \date November 2011
00376 *
00377 *> \ingroup complex_eig
00378 *
00379 *  =====================================================================
00380       SUBROUTINE CDRGES( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
00381      $                   NOUNIT, A, LDA, B, S, T, Q, LDQ, Z, ALPHA,
00382      $                   BETA, WORK, LWORK, RWORK, RESULT, BWORK, INFO )
00383 *
00384 *  -- LAPACK test routine (version 3.4.0) --
00385 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00386 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00387 *     November 2011
00388 *
00389 *     .. Scalar Arguments ..
00390       INTEGER            INFO, LDA, LDQ, LWORK, NOUNIT, NSIZES, NTYPES
00391       REAL               THRESH
00392 *     ..
00393 *     .. Array Arguments ..
00394       LOGICAL            BWORK( * ), DOTYPE( * )
00395       INTEGER            ISEED( 4 ), NN( * )
00396       REAL               RESULT( 13 ), RWORK( * )
00397       COMPLEX            A( LDA, * ), ALPHA( * ), B( LDA, * ),
00398      $                   BETA( * ), Q( LDQ, * ), S( LDA, * ),
00399      $                   T( LDA, * ), WORK( * ), Z( LDQ, * )
00400 *     ..
00401 *
00402 *  =====================================================================
00403 *
00404 *     .. Parameters ..
00405       REAL               ZERO, ONE
00406       PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
00407       COMPLEX            CZERO, CONE
00408       PARAMETER          ( CZERO = ( 0.0E+0, 0.0E+0 ),
00409      $                   CONE = ( 1.0E+0, 0.0E+0 ) )
00410       INTEGER            MAXTYP
00411       PARAMETER          ( MAXTYP = 26 )
00412 *     ..
00413 *     .. Local Scalars ..
00414       LOGICAL            BADNN, ILABAD
00415       CHARACTER          SORT
00416       INTEGER            I, IADD, IINFO, IN, ISORT, J, JC, JR, JSIZE,
00417      $                   JTYPE, KNTEIG, MAXWRK, MINWRK, MTYPES, N, N1,
00418      $                   NB, NERRS, NMATS, NMAX, NTEST, NTESTT, RSUB,
00419      $                   SDIM
00420       REAL               SAFMAX, SAFMIN, TEMP1, TEMP2, ULP, ULPINV
00421       COMPLEX            CTEMP, X
00422 *     ..
00423 *     .. Local Arrays ..
00424       LOGICAL            LASIGN( MAXTYP ), LBSIGN( MAXTYP )
00425       INTEGER            IOLDSD( 4 ), KADD( 6 ), KAMAGN( MAXTYP ),
00426      $                   KATYPE( MAXTYP ), KAZERO( MAXTYP ),
00427      $                   KBMAGN( MAXTYP ), KBTYPE( MAXTYP ),
00428      $                   KBZERO( MAXTYP ), KCLASS( MAXTYP ),
00429      $                   KTRIAN( MAXTYP ), KZ1( 6 ), KZ2( 6 )
00430       REAL               RMAGN( 0: 3 )
00431 *     ..
00432 *     .. External Functions ..
00433       LOGICAL            CLCTES
00434       INTEGER            ILAENV
00435       REAL               SLAMCH
00436       COMPLEX            CLARND
00437       EXTERNAL           CLCTES, ILAENV, SLAMCH, CLARND
00438 *     ..
00439 *     .. External Subroutines ..
00440       EXTERNAL           ALASVM, CGET51, CGET54, CGGES, CLACPY, CLARFG,
00441      $                   CLASET, CLATM4, CUNM2R, SLABAD, XERBLA
00442 *     ..
00443 *     .. Intrinsic Functions ..
00444       INTRINSIC          ABS, AIMAG, CONJG, MAX, MIN, REAL, SIGN
00445 *     ..
00446 *     .. Statement Functions ..
00447       REAL               ABS1
00448 *     ..
00449 *     .. Statement Function definitions ..
00450       ABS1( X ) = ABS( REAL( X ) ) + ABS( AIMAG( X ) )
00451 *     ..
00452 *     .. Data statements ..
00453       DATA               KCLASS / 15*1, 10*2, 1*3 /
00454       DATA               KZ1 / 0, 1, 2, 1, 3, 3 /
00455       DATA               KZ2 / 0, 0, 1, 2, 1, 1 /
00456       DATA               KADD / 0, 0, 0, 0, 3, 2 /
00457       DATA               KATYPE / 0, 1, 0, 1, 2, 3, 4, 1, 4, 4, 1, 1, 4,
00458      $                   4, 4, 2, 4, 5, 8, 7, 9, 4*4, 0 /
00459       DATA               KBTYPE / 0, 0, 1, 1, 2, -3, 1, 4, 1, 1, 4, 4,
00460      $                   1, 1, -4, 2, -4, 8*8, 0 /
00461       DATA               KAZERO / 6*1, 2, 1, 2*2, 2*1, 2*2, 3, 1, 3,
00462      $                   4*5, 4*3, 1 /
00463       DATA               KBZERO / 6*1, 1, 2, 2*1, 2*2, 2*1, 4, 1, 4,
00464      $                   4*6, 4*4, 1 /
00465       DATA               KAMAGN / 8*1, 2, 3, 2, 3, 2, 3, 7*1, 2, 3, 3,
00466      $                   2, 1 /
00467       DATA               KBMAGN / 8*1, 3, 2, 3, 2, 2, 3, 7*1, 3, 2, 3,
00468      $                   2, 1 /
00469       DATA               KTRIAN / 16*0, 10*1 /
00470       DATA               LASIGN / 6*.FALSE., .TRUE., .FALSE., 2*.TRUE.,
00471      $                   2*.FALSE., 3*.TRUE., .FALSE., .TRUE.,
00472      $                   3*.FALSE., 5*.TRUE., .FALSE. /
00473       DATA               LBSIGN / 7*.FALSE., .TRUE., 2*.FALSE.,
00474      $                   2*.TRUE., 2*.FALSE., .TRUE., .FALSE., .TRUE.,
00475      $                   9*.FALSE. /
00476 *     ..
00477 *     .. Executable Statements ..
00478 *
00479 *     Check for errors
00480 *
00481       INFO = 0
00482 *
00483       BADNN = .FALSE.
00484       NMAX = 1
00485       DO 10 J = 1, NSIZES
00486          NMAX = MAX( NMAX, NN( J ) )
00487          IF( NN( J ).LT.0 )
00488      $      BADNN = .TRUE.
00489    10 CONTINUE
00490 *
00491       IF( NSIZES.LT.0 ) THEN
00492          INFO = -1
00493       ELSE IF( BADNN ) THEN
00494          INFO = -2
00495       ELSE IF( NTYPES.LT.0 ) THEN
00496          INFO = -3
00497       ELSE IF( THRESH.LT.ZERO ) THEN
00498          INFO = -6
00499       ELSE IF( LDA.LE.1 .OR. LDA.LT.NMAX ) THEN
00500          INFO = -9
00501       ELSE IF( LDQ.LE.1 .OR. LDQ.LT.NMAX ) THEN
00502          INFO = -14
00503       END IF
00504 *
00505 *     Compute workspace
00506 *      (Note: Comments in the code beginning "Workspace:" describe the
00507 *       minimal amount of workspace needed at that point in the code,
00508 *       as well as the preferred amount for good performance.
00509 *       NB refers to the optimal block size for the immediately
00510 *       following subroutine, as returned by ILAENV.
00511 *
00512       MINWRK = 1
00513       IF( INFO.EQ.0 .AND. LWORK.GE.1 ) THEN
00514          MINWRK = 3*NMAX*NMAX
00515          NB = MAX( 1, ILAENV( 1, 'CGEQRF', ' ', NMAX, NMAX, -1, -1 ),
00516      $        ILAENV( 1, 'CUNMQR', 'LC', NMAX, NMAX, NMAX, -1 ),
00517      $        ILAENV( 1, 'CUNGQR', ' ', NMAX, NMAX, NMAX, -1 ) )
00518          MAXWRK = MAX( NMAX+NMAX*NB, 3*NMAX*NMAX )
00519          WORK( 1 ) = MAXWRK
00520       END IF
00521 *
00522       IF( LWORK.LT.MINWRK )
00523      $   INFO = -19
00524 *
00525       IF( INFO.NE.0 ) THEN
00526          CALL XERBLA( 'CDRGES', -INFO )
00527          RETURN
00528       END IF
00529 *
00530 *     Quick return if possible
00531 *
00532       IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 )
00533      $   RETURN
00534 *
00535       ULP = SLAMCH( 'Precision' )
00536       SAFMIN = SLAMCH( 'Safe minimum' )
00537       SAFMIN = SAFMIN / ULP
00538       SAFMAX = ONE / SAFMIN
00539       CALL SLABAD( SAFMIN, SAFMAX )
00540       ULPINV = ONE / ULP
00541 *
00542 *     The values RMAGN(2:3) depend on N, see below.
00543 *
00544       RMAGN( 0 ) = ZERO
00545       RMAGN( 1 ) = ONE
00546 *
00547 *     Loop over matrix sizes
00548 *
00549       NTESTT = 0
00550       NERRS = 0
00551       NMATS = 0
00552 *
00553       DO 190 JSIZE = 1, NSIZES
00554          N = NN( JSIZE )
00555          N1 = MAX( 1, N )
00556          RMAGN( 2 ) = SAFMAX*ULP / REAL( N1 )
00557          RMAGN( 3 ) = SAFMIN*ULPINV*REAL( N1 )
00558 *
00559          IF( NSIZES.NE.1 ) THEN
00560             MTYPES = MIN( MAXTYP, NTYPES )
00561          ELSE
00562             MTYPES = MIN( MAXTYP+1, NTYPES )
00563          END IF
00564 *
00565 *        Loop over matrix types
00566 *
00567          DO 180 JTYPE = 1, MTYPES
00568             IF( .NOT.DOTYPE( JTYPE ) )
00569      $         GO TO 180
00570             NMATS = NMATS + 1
00571             NTEST = 0
00572 *
00573 *           Save ISEED in case of an error.
00574 *
00575             DO 20 J = 1, 4
00576                IOLDSD( J ) = ISEED( J )
00577    20       CONTINUE
00578 *
00579 *           Initialize RESULT
00580 *
00581             DO 30 J = 1, 13
00582                RESULT( J ) = ZERO
00583    30       CONTINUE
00584 *
00585 *           Generate test matrices A and B
00586 *
00587 *           Description of control parameters:
00588 *
00589 *           KCLASS: =1 means w/o rotation, =2 means w/ rotation,
00590 *                   =3 means random.
00591 *           KATYPE: the "type" to be passed to CLATM4 for computing A.
00592 *           KAZERO: the pattern of zeros on the diagonal for A:
00593 *                   =1: ( xxx ), =2: (0, xxx ) =3: ( 0, 0, xxx, 0 ),
00594 *                   =4: ( 0, xxx, 0, 0 ), =5: ( 0, 0, 1, xxx, 0 ),
00595 *                   =6: ( 0, 1, 0, xxx, 0 ).  (xxx means a string of
00596 *                   non-zero entries.)
00597 *           KAMAGN: the magnitude of the matrix: =0: zero, =1: O(1),
00598 *                   =2: large, =3: small.
00599 *           LASIGN: .TRUE. if the diagonal elements of A are to be
00600 *                   multiplied by a random magnitude 1 number.
00601 *           KBTYPE, KBZERO, KBMAGN, LBSIGN: the same, but for B.
00602 *           KTRIAN: =0: don't fill in the upper triangle, =1: do.
00603 *           KZ1, KZ2, KADD: used to implement KAZERO and KBZERO.
00604 *           RMAGN: used to implement KAMAGN and KBMAGN.
00605 *
00606             IF( MTYPES.GT.MAXTYP )
00607      $         GO TO 110
00608             IINFO = 0
00609             IF( KCLASS( JTYPE ).LT.3 ) THEN
00610 *
00611 *              Generate A (w/o rotation)
00612 *
00613                IF( ABS( KATYPE( JTYPE ) ).EQ.3 ) THEN
00614                   IN = 2*( ( N-1 ) / 2 ) + 1
00615                   IF( IN.NE.N )
00616      $               CALL CLASET( 'Full', N, N, CZERO, CZERO, A, LDA )
00617                ELSE
00618                   IN = N
00619                END IF
00620                CALL CLATM4( KATYPE( JTYPE ), IN, KZ1( KAZERO( JTYPE ) ),
00621      $                      KZ2( KAZERO( JTYPE ) ), LASIGN( JTYPE ),
00622      $                      RMAGN( KAMAGN( JTYPE ) ), ULP,
00623      $                      RMAGN( KTRIAN( JTYPE )*KAMAGN( JTYPE ) ), 2,
00624      $                      ISEED, A, LDA )
00625                IADD = KADD( KAZERO( JTYPE ) )
00626                IF( IADD.GT.0 .AND. IADD.LE.N )
00627      $            A( IADD, IADD ) = RMAGN( KAMAGN( JTYPE ) )
00628 *
00629 *              Generate B (w/o rotation)
00630 *
00631                IF( ABS( KBTYPE( JTYPE ) ).EQ.3 ) THEN
00632                   IN = 2*( ( N-1 ) / 2 ) + 1
00633                   IF( IN.NE.N )
00634      $               CALL CLASET( 'Full', N, N, CZERO, CZERO, B, LDA )
00635                ELSE
00636                   IN = N
00637                END IF
00638                CALL CLATM4( KBTYPE( JTYPE ), IN, KZ1( KBZERO( JTYPE ) ),
00639      $                      KZ2( KBZERO( JTYPE ) ), LBSIGN( JTYPE ),
00640      $                      RMAGN( KBMAGN( JTYPE ) ), ONE,
00641      $                      RMAGN( KTRIAN( JTYPE )*KBMAGN( JTYPE ) ), 2,
00642      $                      ISEED, B, LDA )
00643                IADD = KADD( KBZERO( JTYPE ) )
00644                IF( IADD.NE.0 .AND. IADD.LE.N )
00645      $            B( IADD, IADD ) = RMAGN( KBMAGN( JTYPE ) )
00646 *
00647                IF( KCLASS( JTYPE ).EQ.2 .AND. N.GT.0 ) THEN
00648 *
00649 *                 Include rotations
00650 *
00651 *                 Generate Q, Z as Householder transformations times
00652 *                 a diagonal matrix.
00653 *
00654                   DO 50 JC = 1, N - 1
00655                      DO 40 JR = JC, N
00656                         Q( JR, JC ) = CLARND( 3, ISEED )
00657                         Z( JR, JC ) = CLARND( 3, ISEED )
00658    40                CONTINUE
00659                      CALL CLARFG( N+1-JC, Q( JC, JC ), Q( JC+1, JC ), 1,
00660      $                            WORK( JC ) )
00661                      WORK( 2*N+JC ) = SIGN( ONE, REAL( Q( JC, JC ) ) )
00662                      Q( JC, JC ) = CONE
00663                      CALL CLARFG( N+1-JC, Z( JC, JC ), Z( JC+1, JC ), 1,
00664      $                            WORK( N+JC ) )
00665                      WORK( 3*N+JC ) = SIGN( ONE, REAL( Z( JC, JC ) ) )
00666                      Z( JC, JC ) = CONE
00667    50             CONTINUE
00668                   CTEMP = CLARND( 3, ISEED )
00669                   Q( N, N ) = CONE
00670                   WORK( N ) = CZERO
00671                   WORK( 3*N ) = CTEMP / ABS( CTEMP )
00672                   CTEMP = CLARND( 3, ISEED )
00673                   Z( N, N ) = CONE
00674                   WORK( 2*N ) = CZERO
00675                   WORK( 4*N ) = CTEMP / ABS( CTEMP )
00676 *
00677 *                 Apply the diagonal matrices
00678 *
00679                   DO 70 JC = 1, N
00680                      DO 60 JR = 1, N
00681                         A( JR, JC ) = WORK( 2*N+JR )*
00682      $                                CONJG( WORK( 3*N+JC ) )*
00683      $                                A( JR, JC )
00684                         B( JR, JC ) = WORK( 2*N+JR )*
00685      $                                CONJG( WORK( 3*N+JC ) )*
00686      $                                B( JR, JC )
00687    60                CONTINUE
00688    70             CONTINUE
00689                   CALL CUNM2R( 'L', 'N', N, N, N-1, Q, LDQ, WORK, A,
00690      $                         LDA, WORK( 2*N+1 ), IINFO )
00691                   IF( IINFO.NE.0 )
00692      $               GO TO 100
00693                   CALL CUNM2R( 'R', 'C', N, N, N-1, Z, LDQ, WORK( N+1 ),
00694      $                         A, LDA, WORK( 2*N+1 ), IINFO )
00695                   IF( IINFO.NE.0 )
00696      $               GO TO 100
00697                   CALL CUNM2R( 'L', 'N', N, N, N-1, Q, LDQ, WORK, B,
00698      $                         LDA, WORK( 2*N+1 ), IINFO )
00699                   IF( IINFO.NE.0 )
00700      $               GO TO 100
00701                   CALL CUNM2R( 'R', 'C', N, N, N-1, Z, LDQ, WORK( N+1 ),
00702      $                         B, LDA, WORK( 2*N+1 ), IINFO )
00703                   IF( IINFO.NE.0 )
00704      $               GO TO 100
00705                END IF
00706             ELSE
00707 *
00708 *              Random matrices
00709 *
00710                DO 90 JC = 1, N
00711                   DO 80 JR = 1, N
00712                      A( JR, JC ) = RMAGN( KAMAGN( JTYPE ) )*
00713      $                             CLARND( 4, ISEED )
00714                      B( JR, JC ) = RMAGN( KBMAGN( JTYPE ) )*
00715      $                             CLARND( 4, ISEED )
00716    80             CONTINUE
00717    90          CONTINUE
00718             END IF
00719 *
00720   100       CONTINUE
00721 *
00722             IF( IINFO.NE.0 ) THEN
00723                WRITE( NOUNIT, FMT = 9999 )'Generator', IINFO, N, JTYPE,
00724      $            IOLDSD
00725                INFO = ABS( IINFO )
00726                RETURN
00727             END IF
00728 *
00729   110       CONTINUE
00730 *
00731             DO 120 I = 1, 13
00732                RESULT( I ) = -ONE
00733   120       CONTINUE
00734 *
00735 *           Test with and without sorting of eigenvalues
00736 *
00737             DO 150 ISORT = 0, 1
00738                IF( ISORT.EQ.0 ) THEN
00739                   SORT = 'N'
00740                   RSUB = 0
00741                ELSE
00742                   SORT = 'S'
00743                   RSUB = 5
00744                END IF
00745 *
00746 *              Call CGGES to compute H, T, Q, Z, alpha, and beta.
00747 *
00748                CALL CLACPY( 'Full', N, N, A, LDA, S, LDA )
00749                CALL CLACPY( 'Full', N, N, B, LDA, T, LDA )
00750                NTEST = 1 + RSUB + ISORT
00751                RESULT( 1+RSUB+ISORT ) = ULPINV
00752                CALL CGGES( 'V', 'V', SORT, CLCTES, N, S, LDA, T, LDA,
00753      $                     SDIM, ALPHA, BETA, Q, LDQ, Z, LDQ, WORK,
00754      $                     LWORK, RWORK, BWORK, IINFO )
00755                IF( IINFO.NE.0 .AND. IINFO.NE.N+2 ) THEN
00756                   RESULT( 1+RSUB+ISORT ) = ULPINV
00757                   WRITE( NOUNIT, FMT = 9999 )'CGGES', IINFO, N, JTYPE,
00758      $               IOLDSD
00759                   INFO = ABS( IINFO )
00760                   GO TO 160
00761                END IF
00762 *
00763                NTEST = 4 + RSUB
00764 *
00765 *              Do tests 1--4 (or tests 7--9 when reordering )
00766 *
00767                IF( ISORT.EQ.0 ) THEN
00768                   CALL CGET51( 1, N, A, LDA, S, LDA, Q, LDQ, Z, LDQ,
00769      $                         WORK, RWORK, RESULT( 1 ) )
00770                   CALL CGET51( 1, N, B, LDA, T, LDA, Q, LDQ, Z, LDQ,
00771      $                         WORK, RWORK, RESULT( 2 ) )
00772                ELSE
00773                   CALL CGET54( N, A, LDA, B, LDA, S, LDA, T, LDA, Q,
00774      $                         LDQ, Z, LDQ, WORK, RESULT( 2+RSUB ) )
00775                END IF
00776 *
00777                CALL CGET51( 3, N, B, LDA, T, LDA, Q, LDQ, Q, LDQ, WORK,
00778      $                      RWORK, RESULT( 3+RSUB ) )
00779                CALL CGET51( 3, N, B, LDA, T, LDA, Z, LDQ, Z, LDQ, WORK,
00780      $                      RWORK, RESULT( 4+RSUB ) )
00781 *
00782 *              Do test 5 and 6 (or Tests 10 and 11 when reordering):
00783 *              check Schur form of A and compare eigenvalues with
00784 *              diagonals.
00785 *
00786                NTEST = 6 + RSUB
00787                TEMP1 = ZERO
00788 *
00789                DO 130 J = 1, N
00790                   ILABAD = .FALSE.
00791                   TEMP2 = ( ABS1( ALPHA( J )-S( J, J ) ) /
00792      $                    MAX( SAFMIN, ABS1( ALPHA( J ) ), ABS1( S( J,
00793      $                    J ) ) )+ABS1( BETA( J )-T( J, J ) ) /
00794      $                    MAX( SAFMIN, ABS1( BETA( J ) ), ABS1( T( J,
00795      $                    J ) ) ) ) / ULP
00796 *
00797                   IF( J.LT.N ) THEN
00798                      IF( S( J+1, J ).NE.ZERO ) THEN
00799                         ILABAD = .TRUE.
00800                         RESULT( 5+RSUB ) = ULPINV
00801                      END IF
00802                   END IF
00803                   IF( J.GT.1 ) THEN
00804                      IF( S( J, J-1 ).NE.ZERO ) THEN
00805                         ILABAD = .TRUE.
00806                         RESULT( 5+RSUB ) = ULPINV
00807                      END IF
00808                   END IF
00809                   TEMP1 = MAX( TEMP1, TEMP2 )
00810                   IF( ILABAD ) THEN
00811                      WRITE( NOUNIT, FMT = 9998 )J, N, JTYPE, IOLDSD
00812                   END IF
00813   130          CONTINUE
00814                RESULT( 6+RSUB ) = TEMP1
00815 *
00816                IF( ISORT.GE.1 ) THEN
00817 *
00818 *                 Do test 12
00819 *
00820                   NTEST = 12
00821                   RESULT( 12 ) = ZERO
00822                   KNTEIG = 0
00823                   DO 140 I = 1, N
00824                      IF( CLCTES( ALPHA( I ), BETA( I ) ) )
00825      $                  KNTEIG = KNTEIG + 1
00826   140             CONTINUE
00827                   IF( SDIM.NE.KNTEIG )
00828      $               RESULT( 13 ) = ULPINV
00829                END IF
00830 *
00831   150       CONTINUE
00832 *
00833 *           End of Loop -- Check for RESULT(j) > THRESH
00834 *
00835   160       CONTINUE
00836 *
00837             NTESTT = NTESTT + NTEST
00838 *
00839 *           Print out tests which fail.
00840 *
00841             DO 170 JR = 1, NTEST
00842                IF( RESULT( JR ).GE.THRESH ) THEN
00843 *
00844 *                 If this is the first test to fail,
00845 *                 print a header to the data file.
00846 *
00847                   IF( NERRS.EQ.0 ) THEN
00848                      WRITE( NOUNIT, FMT = 9997 )'CGS'
00849 *
00850 *                    Matrix types
00851 *
00852                      WRITE( NOUNIT, FMT = 9996 )
00853                      WRITE( NOUNIT, FMT = 9995 )
00854                      WRITE( NOUNIT, FMT = 9994 )'Unitary'
00855 *
00856 *                    Tests performed
00857 *
00858                      WRITE( NOUNIT, FMT = 9993 )'unitary', '''',
00859      $                  'transpose', ( '''', J = 1, 8 )
00860 *
00861                   END IF
00862                   NERRS = NERRS + 1
00863                   IF( RESULT( JR ).LT.10000.0 ) THEN
00864                      WRITE( NOUNIT, FMT = 9992 )N, JTYPE, IOLDSD, JR,
00865      $                  RESULT( JR )
00866                   ELSE
00867                      WRITE( NOUNIT, FMT = 9991 )N, JTYPE, IOLDSD, JR,
00868      $                  RESULT( JR )
00869                   END IF
00870                END IF
00871   170       CONTINUE
00872 *
00873   180    CONTINUE
00874   190 CONTINUE
00875 *
00876 *     Summary
00877 *
00878       CALL ALASVM( 'CGS', NOUNIT, NERRS, NTESTT, 0 )
00879 *
00880       WORK( 1 ) = MAXWRK
00881 *
00882       RETURN
00883 *
00884  9999 FORMAT( ' CDRGES: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
00885      $      I6, ', JTYPE=', I6, ', ISEED=(', 4( I4, ',' ), I5, ')' )
00886 *
00887  9998 FORMAT( ' CDRGES: S not in Schur form at eigenvalue ', I6, '.',
00888      $      / 9X, 'N=', I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ),
00889      $      I5, ')' )
00890 *
00891  9997 FORMAT( / 1X, A3, ' -- Complex Generalized Schur from problem ',
00892      $      'driver' )
00893 *
00894  9996 FORMAT( ' Matrix types (see CDRGES for details): ' )
00895 *
00896  9995 FORMAT( ' Special Matrices:', 23X,
00897      $      '(J''=transposed Jordan block)',
00898      $      / '   1=(0,0)  2=(I,0)  3=(0,I)  4=(I,I)  5=(J'',J'')  ',
00899      $      '6=(diag(J'',I), diag(I,J''))', / ' Diagonal Matrices:  ( ',
00900      $      'D=diag(0,1,2,...) )', / '   7=(D,I)   9=(large*D, small*I',
00901      $      ')  11=(large*I, small*D)  13=(large*D, large*I)', /
00902      $      '   8=(I,D)  10=(small*D, large*I)  12=(small*I, large*D) ',
00903      $      ' 14=(small*D, small*I)', / '  15=(D, reversed D)' )
00904  9994 FORMAT( ' Matrices Rotated by Random ', A, ' Matrices U, V:',
00905      $      / '  16=Transposed Jordan Blocks             19=geometric ',
00906      $      'alpha, beta=0,1', / '  17=arithm. alpha&beta             ',
00907      $      '      20=arithmetic alpha, beta=0,1', / '  18=clustered ',
00908      $      'alpha, beta=0,1            21=random alpha, beta=0,1',
00909      $      / ' Large & Small Matrices:', / '  22=(large, small)   ',
00910      $      '23=(small,large)    24=(small,small)    25=(large,large)',
00911      $      / '  26=random O(1) matrices.' )
00912 *
00913  9993 FORMAT( / ' Tests performed:  (S is Schur, T is triangular, ',
00914      $      'Q and Z are ', A, ',', / 19X,
00915      $      'l and r are the appropriate left and right', / 19X,
00916      $      'eigenvectors, resp., a is alpha, b is beta, and', / 19X, A,
00917      $      ' means ', A, '.)', / ' Without ordering: ',
00918      $      / '  1 = | A - Q S Z', A,
00919      $      ' | / ( |A| n ulp )      2 = | B - Q T Z', A,
00920      $      ' | / ( |B| n ulp )', / '  3 = | I - QQ', A,
00921      $      ' | / ( n ulp )             4 = | I - ZZ', A,
00922      $      ' | / ( n ulp )', / '  5 = A is in Schur form S',
00923      $      / '  6 = difference between (alpha,beta)',
00924      $      ' and diagonals of (S,T)', / ' With ordering: ',
00925      $      / '  7 = | (A,B) - Q (S,T) Z', A, ' | / ( |(A,B)| n ulp )',
00926      $      / '  8 = | I - QQ', A,
00927      $      ' | / ( n ulp )             9 = | I - ZZ', A,
00928      $      ' | / ( n ulp )', / ' 10 = A is in Schur form S',
00929      $      / ' 11 = difference between (alpha,beta) and diagonals',
00930      $      ' of (S,T)', / ' 12 = SDIM is the correct number of ',
00931      $      'selected eigenvalues', / )
00932  9992 FORMAT( ' Matrix order=', I5, ', type=', I2, ', seed=',
00933      $      4( I4, ',' ), ' result ', I2, ' is', 0P, F8.2 )
00934  9991 FORMAT( ' Matrix order=', I5, ', type=', I2, ', seed=',
00935      $      4( I4, ',' ), ' result ', I2, ' is', 1P, E10.3 )
00936 *
00937 *     End of CDRGES
00938 *
00939       END
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