LAPACK: TESTING/EIG/cdrges.f Source File

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00001       SUBROUTINE CDRGES( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
00002      $                   NOUNIT, A, LDA, B, S, T, Q, LDQ, Z, ALPHA,
00003      $                   BETA, WORK, LWORK, RWORK, RESULT, BWORK, INFO )
00004 *
00005 *  -- LAPACK test routine (version 3.1.1) --
00006 *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
00007 *     February 2007
00008 *
00009 *     .. Scalar Arguments ..
00010       INTEGER            INFO, LDA, LDQ, LWORK, NOUNIT, NSIZES, NTYPES
00011       REAL               THRESH
00012 *     ..
00013 *     .. Array Arguments ..
00014       LOGICAL            BWORK( * ), DOTYPE( * )
00015       INTEGER            ISEED( 4 ), NN( * )
00016       REAL               RESULT( 13 ), RWORK( * )
00017       COMPLEX            A( LDA, * ), ALPHA( * ), B( LDA, * ),
00018      $                   BETA( * ), Q( LDQ, * ), S( LDA, * ),
00019      $                   T( LDA, * ), WORK( * ), Z( LDQ, * )
00020 *     ..
00021 *
00022 *  Purpose
00023 *  =======
00024 *
00025 *  CDRGES checks the nonsymmetric generalized eigenvalue (Schur form)
00026 *  problem driver CGGES.
00027 *
00028 *  CGGES factors A and B as Q*S*Z'  and Q*T*Z' , where ' means conjugate
00029 *  transpose, S and T are  upper triangular (i.e., in generalized Schur
00030 *  form), and Q and Z are unitary. It also computes the generalized
00031 *  eigenvalues (alpha(j),beta(j)), j=1,...,n.  Thus,
00032 *  w(j) = alpha(j)/beta(j) is a root of the characteristic equation
00033 *
00034 *                  det( A - w(j) B ) = 0
00035 *
00036 *  Optionally it also reorder the eigenvalues so that a selected
00037 *  cluster of eigenvalues appears in the leading diagonal block of the
00038 *  Schur forms.
00039 *
00040 *  When CDRGES is called, a number of matrix "sizes" ("N's") and a
00041 *  number of matrix "TYPES" are specified.  For each size ("N")
00042 *  and each TYPE of matrix, a pair of matrices (A, B) will be generated
00043 *  and used for testing. For each matrix pair, the following 13 tests
00044 *  will be performed and compared with the threshhold THRESH except
00045 *  the tests (5), (11) and (13).
00046 *
00047 *
00048 *  (1)   | A - Q S Z' | / ( |A| n ulp ) (no sorting of eigenvalues)
00049 *
00050 *
00051 *  (2)   | B - Q T Z' | / ( |B| n ulp ) (no sorting of eigenvalues)
00052 *
00053 *
00054 *  (3)   | I - QQ' | / ( n ulp ) (no sorting of eigenvalues)
00055 *
00056 *
00057 *  (4)   | I - ZZ' | / ( n ulp ) (no sorting of eigenvalues)
00058 *
00059 *  (5)   if A is in Schur form (i.e. triangular form) (no sorting of
00060 *        eigenvalues)
00061 *
00062 *  (6)   if eigenvalues = diagonal elements of the Schur form (S, T),
00063 *        i.e., test the maximum over j of D(j)  where:
00064 *
00065 *                      |alpha(j) - S(j,j)|        |beta(j) - T(j,j)|
00066 *            D(j) = ------------------------ + -----------------------
00067 *                   max(|alpha(j)|,|S(j,j)|)   max(|beta(j)|,|T(j,j)|)
00068 *
00069 *        (no sorting of eigenvalues)
00070 *
00071 *  (7)   | (A,B) - Q (S,T) Z' | / ( |(A,B)| n ulp )
00072 *        (with sorting of eigenvalues).
00073 *
00074 *  (8)   | I - QQ' | / ( n ulp ) (with sorting of eigenvalues).
00075 *
00076 *  (9)   | I - ZZ' | / ( n ulp ) (with sorting of eigenvalues).
00077 *
00078 *  (10)  if A is in Schur form (i.e. quasi-triangular form)
00079 *        (with sorting of eigenvalues).
00080 *
00081 *  (11)  if eigenvalues = diagonal elements of the Schur form (S, T),
00082 *        i.e. test the maximum over j of D(j)  where:
00083 *
00084 *                      |alpha(j) - S(j,j)|        |beta(j) - T(j,j)|
00085 *            D(j) = ------------------------ + -----------------------
00086 *                   max(|alpha(j)|,|S(j,j)|)   max(|beta(j)|,|T(j,j)|)
00087 *
00088 *        (with sorting of eigenvalues).
00089 *
00090 *  (12)  if sorting worked and SDIM is the number of eigenvalues
00091 *        which were CELECTed.
00092 *
00093 *  Test Matrices
00094 *  =============
00095 *
00096 *  The sizes of the test matrices are specified by an array
00097 *  NN(1:NSIZES); the value of each element NN(j) specifies one size.
00098 *  The "types" are specified by a logical array DOTYPE( 1:NTYPES ); if
00099 *  DOTYPE(j) is .TRUE., then matrix type "j" will be generated.
00100 *  Currently, the list of possible types is:
00101 *
00102 *  (1)  ( 0, 0 )         (a pair of zero matrices)
00103 *
00104 *  (2)  ( I, 0 )         (an identity and a zero matrix)
00105 *
00106 *  (3)  ( 0, I )         (an identity and a zero matrix)
00107 *
00108 *  (4)  ( I, I )         (a pair of identity matrices)
00109 *
00110 *          t   t
00111 *  (5)  ( J , J  )       (a pair of transposed Jordan blocks)
00112 *
00113 *                                      t                ( I   0  )
00114 *  (6)  ( X, Y )         where  X = ( J   0  )  and Y = (      t )
00115 *                                   ( 0   I  )          ( 0   J  )
00116 *                        and I is a k x k identity and J a (k+1)x(k+1)
00117 *                        Jordan block; k=(N-1)/2
00118 *
00119 *  (7)  ( D, I )         where D is diag( 0, 1,..., N-1 ) (a diagonal
00120 *                        matrix with those diagonal entries.)
00121 *  (8)  ( I, D )
00122 *
00123 *  (9)  ( big*D, small*I ) where "big" is near overflow and small=1/big
00124 *
00125 *  (10) ( small*D, big*I )
00126 *
00127 *  (11) ( big*I, small*D )
00128 *
00129 *  (12) ( small*I, big*D )
00130 *
00131 *  (13) ( big*D, big*I )
00132 *
00133 *  (14) ( small*D, small*I )
00134 *
00135 *  (15) ( D1, D2 )        where D1 is diag( 0, 0, 1, ..., N-3, 0 ) and
00136 *                         D2 is diag( 0, N-3, N-4,..., 1, 0, 0 )
00137 *            t   t
00138 *  (16) Q ( J , J ) Z     where Q and Z are random orthogonal matrices.
00139 *
00140 *  (17) Q ( T1, T2 ) Z    where T1 and T2 are upper triangular matrices
00141 *                         with random O(1) entries above the diagonal
00142 *                         and diagonal entries diag(T1) =
00143 *                         ( 0, 0, 1, ..., N-3, 0 ) and diag(T2) =
00144 *                         ( 0, N-3, N-4,..., 1, 0, 0 )
00145 *
00146 *  (18) Q ( T1, T2 ) Z    diag(T1) = ( 0, 0, 1, 1, s, ..., s, 0 )
00147 *                         diag(T2) = ( 0, 1, 0, 1,..., 1, 0 )
00148 *                         s = machine precision.
00149 *
00150 *  (19) Q ( T1, T2 ) Z    diag(T1)=( 0,0,1,1, 1-d, ..., 1-(N-5)*d=s, 0 )
00151 *                         diag(T2) = ( 0, 1, 0, 1, ..., 1, 0 )
00152 *
00153 *                                                         N-5
00154 *  (20) Q ( T1, T2 ) Z    diag(T1)=( 0, 0, 1, 1, a, ..., a   =s, 0 )
00155 *                         diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 )
00156 *
00157 *  (21) Q ( T1, T2 ) Z    diag(T1)=( 0, 0, 1, r1, r2, ..., r(N-4), 0 )
00158 *                         diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 )
00159 *                         where r1,..., r(N-4) are random.
00160 *
00161 *  (22) Q ( big*T1, small*T2 ) Z    diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
00162 *                                   diag(T2) = ( 0, 1, ..., 1, 0, 0 )
00163 *
00164 *  (23) Q ( small*T1, big*T2 ) Z    diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
00165 *                                   diag(T2) = ( 0, 1, ..., 1, 0, 0 )
00166 *
00167 *  (24) Q ( small*T1, small*T2 ) Z  diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
00168 *                                   diag(T2) = ( 0, 1, ..., 1, 0, 0 )
00169 *
00170 *  (25) Q ( big*T1, big*T2 ) Z      diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
00171 *                                   diag(T2) = ( 0, 1, ..., 1, 0, 0 )
00172 *
00173 *  (26) Q ( T1, T2 ) Z     where T1 and T2 are random upper-triangular
00174 *                          matrices.
00175 *
00176 *
00177 *  Arguments
00178 *  =========
00179 *
00180 *  NSIZES  (input) INTEGER
00181 *          The number of sizes of matrices to use.  If it is zero,
00182 *          SDRGES does nothing.  NSIZES >= 0.
00183 *
00184 *  NN      (input) INTEGER array, dimension (NSIZES)
00185 *          An array containing the sizes to be used for the matrices.
00186 *          Zero values will be skipped.  NN >= 0.
00187 *
00188 *  NTYPES  (input) INTEGER
00189 *          The number of elements in DOTYPE.   If it is zero, SDRGES
00190 *          does nothing.  It must be at least zero.  If it is MAXTYP+1
00191 *          and NSIZES is 1, then an additional type, MAXTYP+1 is
00192 *          defined, which is to use whatever matrix is in A on input.
00193 *          This is only useful if DOTYPE(1:MAXTYP) is .FALSE. and
00194 *          DOTYPE(MAXTYP+1) is .TRUE. .
00195 *
00196 *  DOTYPE  (input) LOGICAL array, dimension (NTYPES)
00197 *          If DOTYPE(j) is .TRUE., then for each size in NN a
00198 *          matrix of that size and of type j will be generated.
00199 *          If NTYPES is smaller than the maximum number of types
00200 *          defined (PARAMETER MAXTYP), then types NTYPES+1 through
00201 *          MAXTYP will not be generated. If NTYPES is larger
00202 *          than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES)
00203 *          will be ignored.
00204 *
00205 *  ISEED   (input/output) INTEGER array, dimension (4)
00206 *          On entry ISEED specifies the seed of the random number
00207 *          generator. The array elements should be between 0 and 4095;
00208 *          if not they will be reduced mod 4096. Also, ISEED(4) must
00209 *          be odd.  The random number generator uses a linear
00210 *          congruential sequence limited to small integers, and so
00211 *          should produce machine independent random numbers. The
00212 *          values of ISEED are changed on exit, and can be used in the
00213 *          next call to SDRGES to continue the same random number
00214 *          sequence.
00215 *
00216 *  THRESH  (input) REAL
00217 *          A test will count as "failed" if the "error", computed as
00218 *          described above, exceeds THRESH.  Note that the error is
00219 *          scaled to be O(1), so THRESH should be a reasonably small
00220 *          multiple of 1, e.g., 10 or 100.  In particular, it should
00221 *          not depend on the precision (single vs. double) or the size
00222 *          of the matrix.  THRESH >= 0.
00223 *
00224 *  NOUNIT  (input) INTEGER
00225 *          The FORTRAN unit number for printing out error messages
00226 *          (e.g., if a routine returns IINFO not equal to 0.)
00227 *
00228 *  A       (input/workspace) COMPLEX array, dimension(LDA, max(NN))
00229 *          Used to hold the original A matrix.  Used as input only
00230 *          if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and
00231 *          DOTYPE(MAXTYP+1)=.TRUE.
00232 *
00233 *  LDA     (input) INTEGER
00234 *          The leading dimension of A, B, S, and T.
00235 *          It must be at least 1 and at least max( NN ).
00236 *
00237 *  B       (input/workspace) COMPLEX array, dimension(LDA, max(NN))
00238 *          Used to hold the original B matrix.  Used as input only
00239 *          if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and
00240 *          DOTYPE(MAXTYP+1)=.TRUE.
00241 *
00242 *  S       (workspace) COMPLEX array, dimension (LDA, max(NN))
00243 *          The Schur form matrix computed from A by CGGES.  On exit, S
00244 *          contains the Schur form matrix corresponding to the matrix
00245 *          in A.
00246 *
00247 *  T       (workspace) COMPLEX array, dimension (LDA, max(NN))
00248 *          The upper triangular matrix computed from B by CGGES.
00249 *
00250 *  Q       (workspace) COMPLEX array, dimension (LDQ, max(NN))
00251 *          The (left) orthogonal matrix computed by CGGES.
00252 *
00253 *  LDQ     (input) INTEGER
00254 *          The leading dimension of Q and Z. It must
00255 *          be at least 1 and at least max( NN ).
00256 *
00257 *  Z       (workspace) COMPLEX array, dimension( LDQ, max(NN) )
00258 *          The (right) orthogonal matrix computed by CGGES.
00259 *
00260 *  ALPHA   (workspace) COMPLEX array, dimension (max(NN))
00261 *  BETA    (workspace) COMPLEX array, dimension (max(NN))
00262 *          The generalized eigenvalues of (A,B) computed by CGGES.
00263 *          ALPHA(k) / BETA(k) is the k-th generalized eigenvalue of A
00264 *          and B.
00265 *
00266 *  WORK    (workspace) COMPLEX array, dimension (LWORK)
00267 *
00268 *  LWORK   (input) INTEGER
00269 *          The dimension of the array WORK.  LWORK >= 3*N*N.
00270 *
00271 *  RWORK   (workspace) REAL array, dimension ( 8*N )
00272 *          Real workspace.
00273 *
00274 *  RESULT  (output) REAL array, dimension (15)
00275 *          The values computed by the tests described above.
00276 *          The values are currently limited to 1/ulp, to avoid overflow.
00277 *
00278 *  BWORK   (workspace) LOGICAL array, dimension (N)
00279 *
00280 *  INFO    (output) INTEGER
00281 *          = 0:  successful exit
00282 *          < 0:  if INFO = -i, the i-th argument had an illegal value.
00283 *          > 0:  A routine returned an error code.  INFO is the
00284 *                absolute value of the INFO value returned.
00285 *
00286 *  =====================================================================
00287 *
00288 *     .. Parameters ..
00289       REAL               ZERO, ONE
00290       PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
00291       COMPLEX            CZERO, CONE
00292       PARAMETER          ( CZERO = ( 0.0E+0, 0.0E+0 ),
00293      $                   CONE = ( 1.0E+0, 0.0E+0 ) )
00294       INTEGER            MAXTYP
00295       PARAMETER          ( MAXTYP = 26 )
00296 *     ..
00297 *     .. Local Scalars ..
00298       LOGICAL            BADNN, ILABAD
00299       CHARACTER          SORT
00300       INTEGER            I, IADD, IINFO, IN, ISORT, J, JC, JR, JSIZE,
00301      $                   JTYPE, KNTEIG, MAXWRK, MINWRK, MTYPES, N, N1,
00302      $                   NB, NERRS, NMATS, NMAX, NTEST, NTESTT, RSUB,
00303      $                   SDIM
00304       REAL               SAFMAX, SAFMIN, TEMP1, TEMP2, ULP, ULPINV
00305       COMPLEX            CTEMP, X
00306 *     ..
00307 *     .. Local Arrays ..
00308       LOGICAL            LASIGN( MAXTYP ), LBSIGN( MAXTYP )
00309       INTEGER            IOLDSD( 4 ), KADD( 6 ), KAMAGN( MAXTYP ),
00310      $                   KATYPE( MAXTYP ), KAZERO( MAXTYP ),
00311      $                   KBMAGN( MAXTYP ), KBTYPE( MAXTYP ),
00312      $                   KBZERO( MAXTYP ), KCLASS( MAXTYP ),
00313      $                   KTRIAN( MAXTYP ), KZ1( 6 ), KZ2( 6 )
00314       REAL               RMAGN( 0: 3 )
00315 *     ..
00316 *     .. External Functions ..
00317       LOGICAL            CLCTES
00318       INTEGER            ILAENV
00319       REAL               SLAMCH
00320       COMPLEX            CLARND
00321       EXTERNAL           CLCTES, ILAENV, SLAMCH, CLARND
00322 *     ..
00323 *     .. External Subroutines ..
00324       EXTERNAL           ALASVM, CGET51, CGET54, CGGES, CLACPY, CLARFG,
00325      $                   CLASET, CLATM4, CUNM2R, SLABAD, XERBLA
00326 *     ..
00327 *     .. Intrinsic Functions ..
00328       INTRINSIC          ABS, AIMAG, CONJG, MAX, MIN, REAL, SIGN
00329 *     ..
00330 *     .. Statement Functions ..
00331       REAL               ABS1
00332 *     ..
00333 *     .. Statement Function definitions ..
00334       ABS1( X ) = ABS( REAL( X ) ) + ABS( AIMAG( X ) )
00335 *     ..
00336 *     .. Data statements ..
00337       DATA               KCLASS / 15*1, 10*2, 1*3 /
00338       DATA               KZ1 / 0, 1, 2, 1, 3, 3 /
00339       DATA               KZ2 / 0, 0, 1, 2, 1, 1 /
00340       DATA               KADD / 0, 0, 0, 0, 3, 2 /
00341       DATA               KATYPE / 0, 1, 0, 1, 2, 3, 4, 1, 4, 4, 1, 1, 4,
00342      $                   4, 4, 2, 4, 5, 8, 7, 9, 4*4, 0 /
00343       DATA               KBTYPE / 0, 0, 1, 1, 2, -3, 1, 4, 1, 1, 4, 4,
00344      $                   1, 1, -4, 2, -4, 8*8, 0 /
00345       DATA               KAZERO / 6*1, 2, 1, 2*2, 2*1, 2*2, 3, 1, 3,
00346      $                   4*5, 4*3, 1 /
00347       DATA               KBZERO / 6*1, 1, 2, 2*1, 2*2, 2*1, 4, 1, 4,
00348      $                   4*6, 4*4, 1 /
00349       DATA               KAMAGN / 8*1, 2, 3, 2, 3, 2, 3, 7*1, 2, 3, 3,
00350      $                   2, 1 /
00351       DATA               KBMAGN / 8*1, 3, 2, 3, 2, 2, 3, 7*1, 3, 2, 3,
00352      $                   2, 1 /
00353       DATA               KTRIAN / 16*0, 10*1 /
00354       DATA               LASIGN / 6*.FALSE., .TRUE., .FALSE., 2*.TRUE.,
00355      $                   2*.FALSE., 3*.TRUE., .FALSE., .TRUE.,
00356      $                   3*.FALSE., 5*.TRUE., .FALSE. /
00357       DATA               LBSIGN / 7*.FALSE., .TRUE., 2*.FALSE.,
00358      $                   2*.TRUE., 2*.FALSE., .TRUE., .FALSE., .TRUE.,
00359      $                   9*.FALSE. /
00360 *     ..
00361 *     .. Executable Statements ..
00362 *
00363 *     Check for errors
00364 *
00365       INFO = 0
00366 *
00367       BADNN = .FALSE.
00368       NMAX = 1
00369       DO 10 J = 1, NSIZES
00370          NMAX = MAX( NMAX, NN( J ) )
00371          IF( NN( J ).LT.0 )
00372      $      BADNN = .TRUE.
00373    10 CONTINUE
00374 *
00375       IF( NSIZES.LT.0 ) THEN
00376          INFO = -1
00377       ELSE IF( BADNN ) THEN
00378          INFO = -2
00379       ELSE IF( NTYPES.LT.0 ) THEN
00380          INFO = -3
00381       ELSE IF( THRESH.LT.ZERO ) THEN
00382          INFO = -6
00383       ELSE IF( LDA.LE.1 .OR. LDA.LT.NMAX ) THEN
00384          INFO = -9
00385       ELSE IF( LDQ.LE.1 .OR. LDQ.LT.NMAX ) THEN
00386          INFO = -14
00387       END IF
00388 *
00389 *     Compute workspace
00390 *      (Note: Comments in the code beginning "Workspace:" describe the
00391 *       minimal amount of workspace needed at that point in the code,
00392 *       as well as the preferred amount for good performance.
00393 *       NB refers to the optimal block size for the immediately
00394 *       following subroutine, as returned by ILAENV.
00395 *
00396       MINWRK = 1
00397       IF( INFO.EQ.0 .AND. LWORK.GE.1 ) THEN
00398          MINWRK = 3*NMAX*NMAX
00399          NB = MAX( 1, ILAENV( 1, 'CGEQRF', ' ', NMAX, NMAX, -1, -1 ),
00400      $        ILAENV( 1, 'CUNMQR', 'LC', NMAX, NMAX, NMAX, -1 ),
00401      $        ILAENV( 1, 'CUNGQR', ' ', NMAX, NMAX, NMAX, -1 ) )
00402          MAXWRK = MAX( NMAX+NMAX*NB, 3*NMAX*NMAX )
00403          WORK( 1 ) = MAXWRK
00404       END IF
00405 *
00406       IF( LWORK.LT.MINWRK )
00407      $   INFO = -19
00408 *
00409       IF( INFO.NE.0 ) THEN
00410          CALL XERBLA( 'CDRGES', -INFO )
00411          RETURN
00412       END IF
00413 *
00414 *     Quick return if possible
00415 *
00416       IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 )
00417      $   RETURN
00418 *
00419       ULP = SLAMCH( 'Precision' )
00420       SAFMIN = SLAMCH( 'Safe minimum' )
00421       SAFMIN = SAFMIN / ULP
00422       SAFMAX = ONE / SAFMIN
00423       CALL SLABAD( SAFMIN, SAFMAX )
00424       ULPINV = ONE / ULP
00425 *
00426 *     The values RMAGN(2:3) depend on N, see below.
00427 *
00428       RMAGN( 0 ) = ZERO
00429       RMAGN( 1 ) = ONE
00430 *
00431 *     Loop over matrix sizes
00432 *
00433       NTESTT = 0
00434       NERRS = 0
00435       NMATS = 0
00436 *
00437       DO 190 JSIZE = 1, NSIZES
00438          N = NN( JSIZE )
00439          N1 = MAX( 1, N )
00440          RMAGN( 2 ) = SAFMAX*ULP / REAL( N1 )
00441          RMAGN( 3 ) = SAFMIN*ULPINV*REAL( N1 )
00442 *
00443          IF( NSIZES.NE.1 ) THEN
00444             MTYPES = MIN( MAXTYP, NTYPES )
00445          ELSE
00446             MTYPES = MIN( MAXTYP+1, NTYPES )
00447          END IF
00448 *
00449 *        Loop over matrix types
00450 *
00451          DO 180 JTYPE = 1, MTYPES
00452             IF( .NOT.DOTYPE( JTYPE ) )
00453      $         GO TO 180
00454             NMATS = NMATS + 1
00455             NTEST = 0
00456 *
00457 *           Save ISEED in case of an error.
00458 *
00459             DO 20 J = 1, 4
00460                IOLDSD( J ) = ISEED( J )
00461    20       CONTINUE
00462 *
00463 *           Initialize RESULT
00464 *
00465             DO 30 J = 1, 13
00466                RESULT( J ) = ZERO
00467    30       CONTINUE
00468 *
00469 *           Generate test matrices A and B
00470 *
00471 *           Description of control parameters:
00472 *
00473 *           KCLASS: =1 means w/o rotation, =2 means w/ rotation,
00474 *                   =3 means random.
00475 *           KATYPE: the "type" to be passed to CLATM4 for computing A.
00476 *           KAZERO: the pattern of zeros on the diagonal for A:
00477 *                   =1: ( xxx ), =2: (0, xxx ) =3: ( 0, 0, xxx, 0 ),
00478 *                   =4: ( 0, xxx, 0, 0 ), =5: ( 0, 0, 1, xxx, 0 ),
00479 *                   =6: ( 0, 1, 0, xxx, 0 ).  (xxx means a string of
00480 *                   non-zero entries.)
00481 *           KAMAGN: the magnitude of the matrix: =0: zero, =1: O(1),
00482 *                   =2: large, =3: small.
00483 *           LASIGN: .TRUE. if the diagonal elements of A are to be
00484 *                   multiplied by a random magnitude 1 number.
00485 *           KBTYPE, KBZERO, KBMAGN, LBSIGN: the same, but for B.
00486 *           KTRIAN: =0: don't fill in the upper triangle, =1: do.
00487 *           KZ1, KZ2, KADD: used to implement KAZERO and KBZERO.
00488 *           RMAGN: used to implement KAMAGN and KBMAGN.
00489 *
00490             IF( MTYPES.GT.MAXTYP )
00491      $         GO TO 110
00492             IINFO = 0
00493             IF( KCLASS( JTYPE ).LT.3 ) THEN
00494 *
00495 *              Generate A (w/o rotation)
00496 *
00497                IF( ABS( KATYPE( JTYPE ) ).EQ.3 ) THEN
00498                   IN = 2*( ( N-1 ) / 2 ) + 1
00499                   IF( IN.NE.N )
00500      $               CALL CLASET( 'Full', N, N, CZERO, CZERO, A, LDA )
00501                ELSE
00502                   IN = N
00503                END IF
00504                CALL CLATM4( KATYPE( JTYPE ), IN, KZ1( KAZERO( JTYPE ) ),
00505      $                      KZ2( KAZERO( JTYPE ) ), LASIGN( JTYPE ),
00506      $                      RMAGN( KAMAGN( JTYPE ) ), ULP,
00507      $                      RMAGN( KTRIAN( JTYPE )*KAMAGN( JTYPE ) ), 2,
00508      $                      ISEED, A, LDA )
00509                IADD = KADD( KAZERO( JTYPE ) )
00510                IF( IADD.GT.0 .AND. IADD.LE.N )
00511      $            A( IADD, IADD ) = RMAGN( KAMAGN( JTYPE ) )
00512 *
00513 *              Generate B (w/o rotation)
00514 *
00515                IF( ABS( KBTYPE( JTYPE ) ).EQ.3 ) THEN
00516                   IN = 2*( ( N-1 ) / 2 ) + 1
00517                   IF( IN.NE.N )
00518      $               CALL CLASET( 'Full', N, N, CZERO, CZERO, B, LDA )
00519                ELSE
00520                   IN = N
00521                END IF
00522                CALL CLATM4( KBTYPE( JTYPE ), IN, KZ1( KBZERO( JTYPE ) ),
00523      $                      KZ2( KBZERO( JTYPE ) ), LBSIGN( JTYPE ),
00524      $                      RMAGN( KBMAGN( JTYPE ) ), ONE,
00525      $                      RMAGN( KTRIAN( JTYPE )*KBMAGN( JTYPE ) ), 2,
00526      $                      ISEED, B, LDA )
00527                IADD = KADD( KBZERO( JTYPE ) )
00528                IF( IADD.NE.0 .AND. IADD.LE.N )
00529      $            B( IADD, IADD ) = RMAGN( KBMAGN( JTYPE ) )
00530 *
00531                IF( KCLASS( JTYPE ).EQ.2 .AND. N.GT.0 ) THEN
00532 *
00533 *                 Include rotations
00534 *
00535 *                 Generate Q, Z as Householder transformations times
00536 *                 a diagonal matrix.
00537 *
00538                   DO 50 JC = 1, N - 1
00539                      DO 40 JR = JC, N
00540                         Q( JR, JC ) = CLARND( 3, ISEED )
00541                         Z( JR, JC ) = CLARND( 3, ISEED )
00542    40                CONTINUE
00543                      CALL CLARFG( N+1-JC, Q( JC, JC ), Q( JC+1, JC ), 1,
00544      $                            WORK( JC ) )
00545                      WORK( 2*N+JC ) = SIGN( ONE, REAL( Q( JC, JC ) ) )
00546                      Q( JC, JC ) = CONE
00547                      CALL CLARFG( N+1-JC, Z( JC, JC ), Z( JC+1, JC ), 1,
00548      $                            WORK( N+JC ) )
00549                      WORK( 3*N+JC ) = SIGN( ONE, REAL( Z( JC, JC ) ) )
00550                      Z( JC, JC ) = CONE
00551    50             CONTINUE
00552                   CTEMP = CLARND( 3, ISEED )
00553                   Q( N, N ) = CONE
00554                   WORK( N ) = CZERO
00555                   WORK( 3*N ) = CTEMP / ABS( CTEMP )
00556                   CTEMP = CLARND( 3, ISEED )
00557                   Z( N, N ) = CONE
00558                   WORK( 2*N ) = CZERO
00559                   WORK( 4*N ) = CTEMP / ABS( CTEMP )
00560 *
00561 *                 Apply the diagonal matrices
00562 *
00563                   DO 70 JC = 1, N
00564                      DO 60 JR = 1, N
00565                         A( JR, JC ) = WORK( 2*N+JR )*
00566      $                                CONJG( WORK( 3*N+JC ) )*
00567      $                                A( JR, JC )
00568                         B( JR, JC ) = WORK( 2*N+JR )*
00569      $                                CONJG( WORK( 3*N+JC ) )*
00570      $                                B( JR, JC )
00571    60                CONTINUE
00572    70             CONTINUE
00573                   CALL CUNM2R( 'L', 'N', N, N, N-1, Q, LDQ, WORK, A,
00574      $                         LDA, WORK( 2*N+1 ), IINFO )
00575                   IF( IINFO.NE.0 )
00576      $               GO TO 100
00577                   CALL CUNM2R( 'R', 'C', N, N, N-1, Z, LDQ, WORK( N+1 ),
00578      $                         A, LDA, WORK( 2*N+1 ), IINFO )
00579                   IF( IINFO.NE.0 )
00580      $               GO TO 100
00581                   CALL CUNM2R( 'L', 'N', N, N, N-1, Q, LDQ, WORK, B,
00582      $                         LDA, WORK( 2*N+1 ), IINFO )
00583                   IF( IINFO.NE.0 )
00584      $               GO TO 100
00585                   CALL CUNM2R( 'R', 'C', N, N, N-1, Z, LDQ, WORK( N+1 ),
00586      $                         B, LDA, WORK( 2*N+1 ), IINFO )
00587                   IF( IINFO.NE.0 )
00588      $               GO TO 100
00589                END IF
00590             ELSE
00591 *
00592 *              Random matrices
00593 *
00594                DO 90 JC = 1, N
00595                   DO 80 JR = 1, N
00596                      A( JR, JC ) = RMAGN( KAMAGN( JTYPE ) )*
00597      $                             CLARND( 4, ISEED )
00598                      B( JR, JC ) = RMAGN( KBMAGN( JTYPE ) )*
00599      $                             CLARND( 4, ISEED )
00600    80             CONTINUE
00601    90          CONTINUE
00602             END IF
00603 *
00604   100       CONTINUE
00605 *
00606             IF( IINFO.NE.0 ) THEN
00607                WRITE( NOUNIT, FMT = 9999 )'Generator', IINFO, N, JTYPE,
00608      $            IOLDSD
00609                INFO = ABS( IINFO )
00610                RETURN
00611             END IF
00612 *
00613   110       CONTINUE
00614 *
00615             DO 120 I = 1, 13
00616                RESULT( I ) = -ONE
00617   120       CONTINUE
00618 *
00619 *           Test with and without sorting of eigenvalues
00620 *
00621             DO 150 ISORT = 0, 1
00622                IF( ISORT.EQ.0 ) THEN
00623                   SORT = 'N'
00624                   RSUB = 0
00625                ELSE
00626                   SORT = 'S'
00627                   RSUB = 5
00628                END IF
00629 *
00630 *              Call CGGES to compute H, T, Q, Z, alpha, and beta.
00631 *
00632                CALL CLACPY( 'Full', N, N, A, LDA, S, LDA )
00633                CALL CLACPY( 'Full', N, N, B, LDA, T, LDA )
00634                NTEST = 1 + RSUB + ISORT
00635                RESULT( 1+RSUB+ISORT ) = ULPINV
00636                CALL CGGES( 'V', 'V', SORT, CLCTES, N, S, LDA, T, LDA,
00637      $                     SDIM, ALPHA, BETA, Q, LDQ, Z, LDQ, WORK,
00638      $                     LWORK, RWORK, BWORK, IINFO )
00639                IF( IINFO.NE.0 .AND. IINFO.NE.N+2 ) THEN
00640                   RESULT( 1+RSUB+ISORT ) = ULPINV
00641                   WRITE( NOUNIT, FMT = 9999 )'CGGES', IINFO, N, JTYPE,
00642      $               IOLDSD
00643                   INFO = ABS( IINFO )
00644                   GO TO 160
00645                END IF
00646 *
00647                NTEST = 4 + RSUB
00648 *
00649 *              Do tests 1--4 (or tests 7--9 when reordering )
00650 *
00651                IF( ISORT.EQ.0 ) THEN
00652                   CALL CGET51( 1, N, A, LDA, S, LDA, Q, LDQ, Z, LDQ,
00653      $                         WORK, RWORK, RESULT( 1 ) )
00654                   CALL CGET51( 1, N, B, LDA, T, LDA, Q, LDQ, Z, LDQ,
00655      $                         WORK, RWORK, RESULT( 2 ) )
00656                ELSE
00657                   CALL CGET54( N, A, LDA, B, LDA, S, LDA, T, LDA, Q,
00658      $                         LDQ, Z, LDQ, WORK, RESULT( 2+RSUB ) )
00659                END IF
00660 *
00661                CALL CGET51( 3, N, B, LDA, T, LDA, Q, LDQ, Q, LDQ, WORK,
00662      $                      RWORK, RESULT( 3+RSUB ) )
00663                CALL CGET51( 3, N, B, LDA, T, LDA, Z, LDQ, Z, LDQ, WORK,
00664      $                      RWORK, RESULT( 4+RSUB ) )
00665 *
00666 *              Do test 5 and 6 (or Tests 10 and 11 when reordering):
00667 *              check Schur form of A and compare eigenvalues with
00668 *              diagonals.
00669 *
00670                NTEST = 6 + RSUB
00671                TEMP1 = ZERO
00672 *
00673                DO 130 J = 1, N
00674                   ILABAD = .FALSE.
00675                   TEMP2 = ( ABS1( ALPHA( J )-S( J, J ) ) /
00676      $                    MAX( SAFMIN, ABS1( ALPHA( J ) ), ABS1( S( J,
00677      $                    J ) ) )+ABS1( BETA( J )-T( J, J ) ) /
00678      $                    MAX( SAFMIN, ABS1( BETA( J ) ), ABS1( T( J,
00679      $                    J ) ) ) ) / ULP
00680 *
00681                   IF( J.LT.N ) THEN
00682                      IF( S( J+1, J ).NE.ZERO ) THEN
00683                         ILABAD = .TRUE.
00684                         RESULT( 5+RSUB ) = ULPINV
00685                      END IF
00686                   END IF
00687                   IF( J.GT.1 ) THEN
00688                      IF( S( J, J-1 ).NE.ZERO ) THEN
00689                         ILABAD = .TRUE.
00690                         RESULT( 5+RSUB ) = ULPINV
00691                      END IF
00692                   END IF
00693                   TEMP1 = MAX( TEMP1, TEMP2 )
00694                   IF( ILABAD ) THEN
00695                      WRITE( NOUNIT, FMT = 9998 )J, N, JTYPE, IOLDSD
00696                   END IF
00697   130          CONTINUE
00698                RESULT( 6+RSUB ) = TEMP1
00699 *
00700                IF( ISORT.GE.1 ) THEN
00701 *
00702 *                 Do test 12
00703 *
00704                   NTEST = 12
00705                   RESULT( 12 ) = ZERO
00706                   KNTEIG = 0
00707                   DO 140 I = 1, N
00708                      IF( CLCTES( ALPHA( I ), BETA( I ) ) )
00709      $                  KNTEIG = KNTEIG + 1
00710   140             CONTINUE
00711                   IF( SDIM.NE.KNTEIG )
00712      $               RESULT( 13 ) = ULPINV
00713                END IF
00714 *
00715   150       CONTINUE
00716 *
00717 *           End of Loop -- Check for RESULT(j) > THRESH
00718 *
00719   160       CONTINUE
00720 *
00721             NTESTT = NTESTT + NTEST
00722 *
00723 *           Print out tests which fail.
00724 *
00725             DO 170 JR = 1, NTEST
00726                IF( RESULT( JR ).GE.THRESH ) THEN
00727 *
00728 *                 If this is the first test to fail,
00729 *                 print a header to the data file.
00730 *
00731                   IF( NERRS.EQ.0 ) THEN
00732                      WRITE( NOUNIT, FMT = 9997 )'CGS'
00733 *
00734 *                    Matrix types
00735 *
00736                      WRITE( NOUNIT, FMT = 9996 )
00737                      WRITE( NOUNIT, FMT = 9995 )
00738                      WRITE( NOUNIT, FMT = 9994 )'Unitary'
00739 *
00740 *                    Tests performed
00741 *
00742                      WRITE( NOUNIT, FMT = 9993 )'unitary', '''',
00743      $                  'transpose', ( '''', J = 1, 8 )
00744 *
00745                   END IF
00746                   NERRS = NERRS + 1
00747                   IF( RESULT( JR ).LT.10000.0 ) THEN
00748                      WRITE( NOUNIT, FMT = 9992 )N, JTYPE, IOLDSD, JR,
00749      $                  RESULT( JR )
00750                   ELSE
00751                      WRITE( NOUNIT, FMT = 9991 )N, JTYPE, IOLDSD, JR,
00752      $                  RESULT( JR )
00753                   END IF
00754                END IF
00755   170       CONTINUE
00756 *
00757   180    CONTINUE
00758   190 CONTINUE
00759 *
00760 *     Summary
00761 *
00762       CALL ALASVM( 'CGS', NOUNIT, NERRS, NTESTT, 0 )
00763 *
00764       WORK( 1 ) = MAXWRK
00765 *
00766       RETURN
00767 *
00768  9999 FORMAT( ' CDRGES: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
00769      $      I6, ', JTYPE=', I6, ', ISEED=(', 4( I4, ',' ), I5, ')' )
00770 *
00771  9998 FORMAT( ' CDRGES: S not in Schur form at eigenvalue ', I6, '.',
00772      $      / 9X, 'N=', I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ),
00773      $      I5, ')' )
00774 *
00775  9997 FORMAT( / 1X, A3, ' -- Complex Generalized Schur from problem ',
00776      $      'driver' )
00777 *
00778  9996 FORMAT( ' Matrix types (see CDRGES for details): ' )
00779 *
00780  9995 FORMAT( ' Special Matrices:', 23X,
00781      $      '(J''=transposed Jordan block)',
00782      $      / '   1=(0,0)  2=(I,0)  3=(0,I)  4=(I,I)  5=(J'',J'')  ',
00783      $      '6=(diag(J'',I), diag(I,J''))', / ' Diagonal Matrices:  ( ',
00784      $      'D=diag(0,1,2,...) )', / '   7=(D,I)   9=(large*D, small*I',
00785      $      ')  11=(large*I, small*D)  13=(large*D, large*I)', /
00786      $      '   8=(I,D)  10=(small*D, large*I)  12=(small*I, large*D) ',
00787      $      ' 14=(small*D, small*I)', / '  15=(D, reversed D)' )
00788  9994 FORMAT( ' Matrices Rotated by Random ', A, ' Matrices U, V:',
00789      $      / '  16=Transposed Jordan Blocks             19=geometric ',
00790      $      'alpha, beta=0,1', / '  17=arithm. alpha&beta             ',
00791      $      '      20=arithmetic alpha, beta=0,1', / '  18=clustered ',
00792      $      'alpha, beta=0,1            21=random alpha, beta=0,1',
00793      $      / ' Large & Small Matrices:', / '  22=(large, small)   ',
00794      $      '23=(small,large)    24=(small,small)    25=(large,large)',
00795      $      / '  26=random O(1) matrices.' )
00796 *
00797  9993 FORMAT( / ' Tests performed:  (S is Schur, T is triangular, ',
00798      $      'Q and Z are ', A, ',', / 19X,
00799      $      'l and r are the appropriate left and right', / 19X,
00800      $      'eigenvectors, resp., a is alpha, b is beta, and', / 19X, A,
00801      $      ' means ', A, '.)', / ' Without ordering: ',
00802      $      / '  1 = | A - Q S Z', A,
00803      $      ' | / ( |A| n ulp )      2 = | B - Q T Z', A,
00804      $      ' | / ( |B| n ulp )', / '  3 = | I - QQ', A,
00805      $      ' | / ( n ulp )             4 = | I - ZZ', A,
00806      $      ' | / ( n ulp )', / '  5 = A is in Schur form S',
00807      $      / '  6 = difference between (alpha,beta)',
00808      $      ' and diagonals of (S,T)', / ' With ordering: ',
00809      $      / '  7 = | (A,B) - Q (S,T) Z', A, ' | / ( |(A,B)| n ulp )',
00810      $      / '  8 = | I - QQ', A,
00811      $      ' | / ( n ulp )             9 = | I - ZZ', A,
00812      $      ' | / ( n ulp )', / ' 10 = A is in Schur form S',
00813      $      / ' 11 = difference between (alpha,beta) and diagonals',
00814      $      ' of (S,T)', / ' 12 = SDIM is the correct number of ',
00815      $      'selected eigenvalues', / )
00816  9992 FORMAT( ' Matrix order=', I5, ', type=', I2, ', seed=',
00817      $      4( I4, ',' ), ' result ', I2, ' is', 0P, F8.2 )
00818  9991 FORMAT( ' Matrix order=', I5, ', type=', I2, ', seed=',
00819      $      4( I4, ',' ), ' result ', I2, ' is', 1P, E10.3 )
00820 *
00821 *     End of CDRGES
00822 *
00823       END