LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
sdrges.f
Go to the documentation of this file.
00001 *> \brief \b SDRGES
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 SDRGES( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
00012 *                          NOUNIT, A, LDA, B, S, T, Q, LDQ, Z, ALPHAR,
00013 *                          ALPHAI, BETA, WORK, LWORK, RESULT, BWORK,
00014 *                          INFO )
00015 * 
00016 *       .. Scalar Arguments ..
00017 *       INTEGER            INFO, LDA, LDQ, LWORK, NOUNIT, NSIZES, NTYPES
00018 *       REAL               THRESH
00019 *       ..
00020 *       .. Array Arguments ..
00021 *       LOGICAL            BWORK( * ), DOTYPE( * )
00022 *       INTEGER            ISEED( 4 ), NN( * )
00023 *       REAL               A( LDA, * ), ALPHAI( * ), ALPHAR( * ),
00024 *      $                   B( LDA, * ), BETA( * ), Q( LDQ, * ),
00025 *      $                   RESULT( 13 ), S( LDA, * ), T( LDA, * ),
00026 *      $                   WORK( * ), Z( LDQ, * )
00027 *       ..
00028 *  
00029 *
00030 *> \par Purpose:
00031 *  =============
00032 *>
00033 *> \verbatim
00034 *>
00035 *> SDRGES checks the nonsymmetric generalized eigenvalue (Schur form)
00036 *> problem driver SGGES.
00037 *>
00038 *> SGGES factors A and B as Q S Z'  and Q T Z' , where ' means
00039 *> transpose, T is upper triangular, S is in generalized Schur form
00040 *> (block upper triangular, with 1x1 and 2x2 blocks on the diagonal,
00041 *> the 2x2 blocks corresponding to complex conjugate pairs of
00042 *> generalized eigenvalues), and Q and Z are orthogonal. It also
00043 *> computes the generalized eigenvalues (alpha(j),beta(j)), j=1,...,n,
00044 *> Thus, w(j) = alpha(j)/beta(j) is a root of the characteristic
00045 *> equation
00046 *>                 det( A - w(j) B ) = 0
00047 *> Optionally it also reorder the eigenvalues so that a selected
00048 *> cluster of eigenvalues appears in the leading diagonal block of the
00049 *> Schur forms.
00050 *>
00051 *> When SDRGES 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, a pair of matrices (A, B) will be generated
00054 *> and used for testing. For each matrix pair, the following 13 tests
00055 *> will be performed and compared with the threshhold THRESH except
00056 *> the tests (5), (11) and (13).
00057 *>
00058 *>
00059 *> (1)   | A - Q S Z' | / ( |A| n ulp ) (no sorting of eigenvalues)
00060 *>
00061 *>
00062 *> (2)   | B - Q T Z' | / ( |B| n ulp ) (no sorting of eigenvalues)
00063 *>
00064 *>
00065 *> (3)   | I - QQ' | / ( n ulp ) (no sorting of eigenvalues)
00066 *>
00067 *>
00068 *> (4)   | I - ZZ' | / ( n ulp ) (no sorting of eigenvalues)
00069 *>
00070 *> (5)   if A is in Schur form (i.e. quasi-triangular form)
00071 *>       (no sorting of eigenvalues)
00072 *>
00073 *> (6)   if eigenvalues = diagonal blocks of the Schur form (S, T),
00074 *>       i.e., test the maximum over j of D(j)  where:
00075 *>
00076 *>       if alpha(j) is real:
00077 *>                     |alpha(j) - S(j,j)|        |beta(j) - T(j,j)|
00078 *>           D(j) = ------------------------ + -----------------------
00079 *>                  max(|alpha(j)|,|S(j,j)|)   max(|beta(j)|,|T(j,j)|)
00080 *>
00081 *>       if alpha(j) is complex:
00082 *>                                 | det( s S - w T ) |
00083 *>           D(j) = ---------------------------------------------------
00084 *>                  ulp max( s norm(S), |w| norm(T) )*norm( s S - w T )
00085 *>
00086 *>       and S and T are here the 2 x 2 diagonal blocks of S and T
00087 *>       corresponding to the j-th and j+1-th eigenvalues.
00088 *>       (no sorting of eigenvalues)
00089 *>
00090 *> (7)   | (A,B) - Q (S,T) Z' | / ( | (A,B) | n ulp )
00091 *>            (with sorting of eigenvalues).
00092 *>
00093 *> (8)   | I - QQ' | / ( n ulp ) (with sorting of eigenvalues).
00094 *>
00095 *> (9)   | I - ZZ' | / ( n ulp ) (with sorting of eigenvalues).
00096 *>
00097 *> (10)  if A is in Schur form (i.e. quasi-triangular form)
00098 *>       (with sorting of eigenvalues).
00099 *>
00100 *> (11)  if eigenvalues = diagonal blocks of the Schur form (S, T),
00101 *>       i.e. test the maximum over j of D(j)  where:
00102 *>
00103 *>       if alpha(j) is real:
00104 *>                     |alpha(j) - S(j,j)|        |beta(j) - T(j,j)|
00105 *>           D(j) = ------------------------ + -----------------------
00106 *>                  max(|alpha(j)|,|S(j,j)|)   max(|beta(j)|,|T(j,j)|)
00107 *>
00108 *>       if alpha(j) is complex:
00109 *>                                 | det( s S - w T ) |
00110 *>           D(j) = ---------------------------------------------------
00111 *>                  ulp max( s norm(S), |w| norm(T) )*norm( s S - w T )
00112 *>
00113 *>       and S and T are here the 2 x 2 diagonal blocks of S and T
00114 *>       corresponding to the j-th and j+1-th eigenvalues.
00115 *>       (with sorting of eigenvalues).
00116 *>
00117 *> (12)  if sorting worked and SDIM is the number of eigenvalues
00118 *>       which were SELECTed.
00119 *>
00120 *> Test Matrices
00121 *> =============
00122 *>
00123 *> The sizes of the test matrices are specified by an array
00124 *> NN(1:NSIZES); the value of each element NN(j) specifies one size.
00125 *> The "types" are specified by a logical array DOTYPE( 1:NTYPES ); if
00126 *> DOTYPE(j) is .TRUE., then matrix type "j" will be generated.
00127 *> Currently, the list of possible types is:
00128 *>
00129 *> (1)  ( 0, 0 )         (a pair of zero matrices)
00130 *>
00131 *> (2)  ( I, 0 )         (an identity and a zero matrix)
00132 *>
00133 *> (3)  ( 0, I )         (an identity and a zero matrix)
00134 *>
00135 *> (4)  ( I, I )         (a pair of identity matrices)
00136 *>
00137 *>         t   t
00138 *> (5)  ( J , J  )       (a pair of transposed Jordan blocks)
00139 *>
00140 *>                                     t                ( I   0  )
00141 *> (6)  ( X, Y )         where  X = ( J   0  )  and Y = (      t )
00142 *>                                  ( 0   I  )          ( 0   J  )
00143 *>                       and I is a k x k identity and J a (k+1)x(k+1)
00144 *>                       Jordan block; k=(N-1)/2
00145 *>
00146 *> (7)  ( D, I )         where D is diag( 0, 1,..., N-1 ) (a diagonal
00147 *>                       matrix with those diagonal entries.)
00148 *> (8)  ( I, D )
00149 *>
00150 *> (9)  ( big*D, small*I ) where "big" is near overflow and small=1/big
00151 *>
00152 *> (10) ( small*D, big*I )
00153 *>
00154 *> (11) ( big*I, small*D )
00155 *>
00156 *> (12) ( small*I, big*D )
00157 *>
00158 *> (13) ( big*D, big*I )
00159 *>
00160 *> (14) ( small*D, small*I )
00161 *>
00162 *> (15) ( D1, D2 )        where D1 is diag( 0, 0, 1, ..., N-3, 0 ) and
00163 *>                        D2 is diag( 0, N-3, N-4,..., 1, 0, 0 )
00164 *>           t   t
00165 *> (16) Q ( J , J ) Z     where Q and Z are random orthogonal matrices.
00166 *>
00167 *> (17) Q ( T1, T2 ) Z    where T1 and T2 are upper triangular matrices
00168 *>                        with random O(1) entries above the diagonal
00169 *>                        and diagonal entries diag(T1) =
00170 *>                        ( 0, 0, 1, ..., N-3, 0 ) and diag(T2) =
00171 *>                        ( 0, N-3, N-4,..., 1, 0, 0 )
00172 *>
00173 *> (18) Q ( T1, T2 ) Z    diag(T1) = ( 0, 0, 1, 1, s, ..., s, 0 )
00174 *>                        diag(T2) = ( 0, 1, 0, 1,..., 1, 0 )
00175 *>                        s = machine precision.
00176 *>
00177 *> (19) Q ( T1, T2 ) Z    diag(T1)=( 0,0,1,1, 1-d, ..., 1-(N-5)*d=s, 0 )
00178 *>                        diag(T2) = ( 0, 1, 0, 1, ..., 1, 0 )
00179 *>
00180 *>                                                        N-5
00181 *> (20) Q ( T1, T2 ) Z    diag(T1)=( 0, 0, 1, 1, a, ..., a   =s, 0 )
00182 *>                        diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 )
00183 *>
00184 *> (21) Q ( T1, T2 ) Z    diag(T1)=( 0, 0, 1, r1, r2, ..., r(N-4), 0 )
00185 *>                        diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 )
00186 *>                        where r1,..., r(N-4) are random.
00187 *>
00188 *> (22) Q ( big*T1, small*T2 ) Z    diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
00189 *>                                  diag(T2) = ( 0, 1, ..., 1, 0, 0 )
00190 *>
00191 *> (23) Q ( small*T1, big*T2 ) Z    diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
00192 *>                                  diag(T2) = ( 0, 1, ..., 1, 0, 0 )
00193 *>
00194 *> (24) Q ( small*T1, small*T2 ) Z  diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
00195 *>                                  diag(T2) = ( 0, 1, ..., 1, 0, 0 )
00196 *>
00197 *> (25) Q ( big*T1, big*T2 ) Z      diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
00198 *>                                  diag(T2) = ( 0, 1, ..., 1, 0, 0 )
00199 *>
00200 *> (26) Q ( T1, T2 ) Z     where T1 and T2 are random upper-triangular
00201 *>                         matrices.
00202 *>
00203 *> \endverbatim
00204 *
00205 *  Arguments:
00206 *  ==========
00207 *
00208 *> \param[in] NSIZES
00209 *> \verbatim
00210 *>          NSIZES is INTEGER
00211 *>          The number of sizes of matrices to use.  If it is zero,
00212 *>          SDRGES does nothing.  NSIZES >= 0.
00213 *> \endverbatim
00214 *>
00215 *> \param[in] NN
00216 *> \verbatim
00217 *>          NN is INTEGER array, dimension (NSIZES)
00218 *>          An array containing the sizes to be used for the matrices.
00219 *>          Zero values will be skipped.  NN >= 0.
00220 *> \endverbatim
00221 *>
00222 *> \param[in] NTYPES
00223 *> \verbatim
00224 *>          NTYPES is INTEGER
00225 *>          The number of elements in DOTYPE.   If it is zero, SDRGES
00226 *>          does nothing.  It must be at least zero.  If it is MAXTYP+1
00227 *>          and NSIZES is 1, then an additional type, MAXTYP+1 is
00228 *>          defined, which is to use whatever matrix is in A on input.
00229 *>          This is only useful if DOTYPE(1:MAXTYP) is .FALSE. and
00230 *>          DOTYPE(MAXTYP+1) is .TRUE. .
00231 *> \endverbatim
00232 *>
00233 *> \param[in] DOTYPE
00234 *> \verbatim
00235 *>          DOTYPE is LOGICAL array, dimension (NTYPES)
00236 *>          If DOTYPE(j) is .TRUE., then for each size in NN a
00237 *>          matrix of that size and of type j will be generated.
00238 *>          If NTYPES is smaller than the maximum number of types
00239 *>          defined (PARAMETER MAXTYP), then types NTYPES+1 through
00240 *>          MAXTYP will not be generated. If NTYPES is larger
00241 *>          than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES)
00242 *>          will be ignored.
00243 *> \endverbatim
00244 *>
00245 *> \param[in,out] ISEED
00246 *> \verbatim
00247 *>          ISEED is INTEGER array, dimension (4)
00248 *>          On entry ISEED specifies the seed of the random number
00249 *>          generator. The array elements should be between 0 and 4095;
00250 *>          if not they will be reduced mod 4096. Also, ISEED(4) must
00251 *>          be odd.  The random number generator uses a linear
00252 *>          congruential sequence limited to small integers, and so
00253 *>          should produce machine independent random numbers. The
00254 *>          values of ISEED are changed on exit, and can be used in the
00255 *>          next call to SDRGES to continue the same random number
00256 *>          sequence.
00257 *> \endverbatim
00258 *>
00259 *> \param[in] THRESH
00260 *> \verbatim
00261 *>          THRESH is REAL
00262 *>          A test will count as "failed" if the "error", computed as
00263 *>          described above, exceeds THRESH.  Note that the error is
00264 *>          scaled to be O(1), so THRESH should be a reasonably small
00265 *>          multiple of 1, e.g., 10 or 100.  In particular, it should
00266 *>          not depend on the precision (single vs. double) or the size
00267 *>          of the matrix.  THRESH >= 0.
00268 *> \endverbatim
00269 *>
00270 *> \param[in] NOUNIT
00271 *> \verbatim
00272 *>          NOUNIT is INTEGER
00273 *>          The FORTRAN unit number for printing out error messages
00274 *>          (e.g., if a routine returns IINFO not equal to 0.)
00275 *> \endverbatim
00276 *>
00277 *> \param[in,out] A
00278 *> \verbatim
00279 *>          A is REAL array,
00280 *>                                       dimension(LDA, max(NN))
00281 *>          Used to hold the original A matrix.  Used as input only
00282 *>          if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and
00283 *>          DOTYPE(MAXTYP+1)=.TRUE.
00284 *> \endverbatim
00285 *>
00286 *> \param[in] LDA
00287 *> \verbatim
00288 *>          LDA is INTEGER
00289 *>          The leading dimension of A, B, S, and T.
00290 *>          It must be at least 1 and at least max( NN ).
00291 *> \endverbatim
00292 *>
00293 *> \param[in,out] B
00294 *> \verbatim
00295 *>          B is REAL array,
00296 *>                                       dimension(LDA, max(NN))
00297 *>          Used to hold the original B matrix.  Used as input only
00298 *>          if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and
00299 *>          DOTYPE(MAXTYP+1)=.TRUE.
00300 *> \endverbatim
00301 *>
00302 *> \param[out] S
00303 *> \verbatim
00304 *>          S is REAL array, dimension (LDA, max(NN))
00305 *>          The Schur form matrix computed from A by SGGES.  On exit, S
00306 *>          contains the Schur form matrix corresponding to the matrix
00307 *>          in A.
00308 *> \endverbatim
00309 *>
00310 *> \param[out] T
00311 *> \verbatim
00312 *>          T is REAL array, dimension (LDA, max(NN))
00313 *>          The upper triangular matrix computed from B by SGGES.
00314 *> \endverbatim
00315 *>
00316 *> \param[out] Q
00317 *> \verbatim
00318 *>          Q is REAL array, dimension (LDQ, max(NN))
00319 *>          The (left) orthogonal matrix computed by SGGES.
00320 *> \endverbatim
00321 *>
00322 *> \param[in] LDQ
00323 *> \verbatim
00324 *>          LDQ is INTEGER
00325 *>          The leading dimension of Q and Z. It must
00326 *>          be at least 1 and at least max( NN ).
00327 *> \endverbatim
00328 *>
00329 *> \param[out] Z
00330 *> \verbatim
00331 *>          Z is REAL array, dimension( LDQ, max(NN) )
00332 *>          The (right) orthogonal matrix computed by SGGES.
00333 *> \endverbatim
00334 *>
00335 *> \param[out] ALPHAR
00336 *> \verbatim
00337 *>          ALPHAR is REAL array, dimension (max(NN))
00338 *> \endverbatim
00339 *>
00340 *> \param[out] ALPHAI
00341 *> \verbatim
00342 *>          ALPHAI is REAL array, dimension (max(NN))
00343 *> \endverbatim
00344 *>
00345 *> \param[out] BETA
00346 *> \verbatim
00347 *>          BETA is REAL array, dimension (max(NN))
00348 *>
00349 *>          The generalized eigenvalues of (A,B) computed by SGGES.
00350 *>          ( ALPHAR(k)+ALPHAI(k)*i ) / BETA(k) is the k-th
00351 *>          generalized eigenvalue of A and B.
00352 *> \endverbatim
00353 *>
00354 *> \param[out] WORK
00355 *> \verbatim
00356 *>          WORK is REAL array, dimension (LWORK)
00357 *> \endverbatim
00358 *>
00359 *> \param[in] LWORK
00360 *> \verbatim
00361 *>          LWORK is INTEGER
00362 *>          The dimension of the array WORK.
00363 *>          LWORK >= MAX( 10*(N+1), 3*N*N ), where N is the largest
00364 *>          matrix dimension.
00365 *> \endverbatim
00366 *>
00367 *> \param[out] RESULT
00368 *> \verbatim
00369 *>          RESULT is REAL array, dimension (15)
00370 *>          The values computed by the tests described above.
00371 *>          The values are currently limited to 1/ulp, to avoid overflow.
00372 *> \endverbatim
00373 *>
00374 *> \param[out] BWORK
00375 *> \verbatim
00376 *>          BWORK is LOGICAL array, dimension (N)
00377 *> \endverbatim
00378 *>
00379 *> \param[out] INFO
00380 *> \verbatim
00381 *>          INFO is INTEGER
00382 *>          = 0:  successful exit
00383 *>          < 0:  if INFO = -i, the i-th argument had an illegal value.
00384 *>          > 0:  A routine returned an error code.  INFO is the
00385 *>                absolute value of the INFO value returned.
00386 *> \endverbatim
00387 *
00388 *  Authors:
00389 *  ========
00390 *
00391 *> \author Univ. of Tennessee 
00392 *> \author Univ. of California Berkeley 
00393 *> \author Univ. of Colorado Denver 
00394 *> \author NAG Ltd. 
00395 *
00396 *> \date November 2011
00397 *
00398 *> \ingroup single_eig
00399 *
00400 *  =====================================================================
00401       SUBROUTINE SDRGES( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
00402      $                   NOUNIT, A, LDA, B, S, T, Q, LDQ, Z, ALPHAR,
00403      $                   ALPHAI, BETA, WORK, LWORK, RESULT, BWORK,
00404      $                   INFO )
00405 *
00406 *  -- LAPACK test routine (version 3.4.0) --
00407 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00408 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00409 *     November 2011
00410 *
00411 *     .. Scalar Arguments ..
00412       INTEGER            INFO, LDA, LDQ, LWORK, NOUNIT, NSIZES, NTYPES
00413       REAL               THRESH
00414 *     ..
00415 *     .. Array Arguments ..
00416       LOGICAL            BWORK( * ), DOTYPE( * )
00417       INTEGER            ISEED( 4 ), NN( * )
00418       REAL               A( LDA, * ), ALPHAI( * ), ALPHAR( * ),
00419      $                   B( LDA, * ), BETA( * ), Q( LDQ, * ),
00420      $                   RESULT( 13 ), S( LDA, * ), T( LDA, * ),
00421      $                   WORK( * ), Z( LDQ, * )
00422 *     ..
00423 *
00424 *  =====================================================================
00425 *
00426 *     .. Parameters ..
00427       REAL               ZERO, ONE
00428       PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
00429       INTEGER            MAXTYP
00430       PARAMETER          ( MAXTYP = 26 )
00431 *     ..
00432 *     .. Local Scalars ..
00433       LOGICAL            BADNN, ILABAD
00434       CHARACTER          SORT
00435       INTEGER            I, I1, IADD, IERR, IINFO, IN, ISORT, J, JC, JR,
00436      $                   JSIZE, JTYPE, KNTEIG, MAXWRK, MINWRK, MTYPES,
00437      $                   N, N1, NB, NERRS, NMATS, NMAX, NTEST, NTESTT,
00438      $                   RSUB, SDIM
00439       REAL               SAFMAX, SAFMIN, TEMP1, TEMP2, ULP, ULPINV
00440 *     ..
00441 *     .. Local Arrays ..
00442       INTEGER            IASIGN( MAXTYP ), IBSIGN( MAXTYP ),
00443      $                   IOLDSD( 4 ), KADD( 6 ), KAMAGN( MAXTYP ),
00444      $                   KATYPE( MAXTYP ), KAZERO( MAXTYP ),
00445      $                   KBMAGN( MAXTYP ), KBTYPE( MAXTYP ),
00446      $                   KBZERO( MAXTYP ), KCLASS( MAXTYP ),
00447      $                   KTRIAN( MAXTYP ), KZ1( 6 ), KZ2( 6 )
00448       REAL               RMAGN( 0: 3 )
00449 *     ..
00450 *     .. External Functions ..
00451       LOGICAL            SLCTES
00452       INTEGER            ILAENV
00453       REAL               SLAMCH, SLARND
00454       EXTERNAL           SLCTES, ILAENV, SLAMCH, SLARND
00455 *     ..
00456 *     .. External Subroutines ..
00457       EXTERNAL           ALASVM, SGET51, SGET53, SGET54, SGGES, SLABAD,
00458      $                   SLACPY, SLARFG, SLASET, SLATM4, SORM2R, XERBLA
00459 *     ..
00460 *     .. Intrinsic Functions ..
00461       INTRINSIC          ABS, MAX, MIN, REAL, SIGN
00462 *     ..
00463 *     .. Data statements ..
00464       DATA               KCLASS / 15*1, 10*2, 1*3 /
00465       DATA               KZ1 / 0, 1, 2, 1, 3, 3 /
00466       DATA               KZ2 / 0, 0, 1, 2, 1, 1 /
00467       DATA               KADD / 0, 0, 0, 0, 3, 2 /
00468       DATA               KATYPE / 0, 1, 0, 1, 2, 3, 4, 1, 4, 4, 1, 1, 4,
00469      $                   4, 4, 2, 4, 5, 8, 7, 9, 4*4, 0 /
00470       DATA               KBTYPE / 0, 0, 1, 1, 2, -3, 1, 4, 1, 1, 4, 4,
00471      $                   1, 1, -4, 2, -4, 8*8, 0 /
00472       DATA               KAZERO / 6*1, 2, 1, 2*2, 2*1, 2*2, 3, 1, 3,
00473      $                   4*5, 4*3, 1 /
00474       DATA               KBZERO / 6*1, 1, 2, 2*1, 2*2, 2*1, 4, 1, 4,
00475      $                   4*6, 4*4, 1 /
00476       DATA               KAMAGN / 8*1, 2, 3, 2, 3, 2, 3, 7*1, 2, 3, 3,
00477      $                   2, 1 /
00478       DATA               KBMAGN / 8*1, 3, 2, 3, 2, 2, 3, 7*1, 3, 2, 3,
00479      $                   2, 1 /
00480       DATA               KTRIAN / 16*0, 10*1 /
00481       DATA               IASIGN / 6*0, 2, 0, 2*2, 2*0, 3*2, 0, 2, 3*0,
00482      $                   5*2, 0 /
00483       DATA               IBSIGN / 7*0, 2, 2*0, 2*2, 2*0, 2, 0, 2, 9*0 /
00484 *     ..
00485 *     .. Executable Statements ..
00486 *
00487 *     Check for errors
00488 *
00489       INFO = 0
00490 *
00491       BADNN = .FALSE.
00492       NMAX = 1
00493       DO 10 J = 1, NSIZES
00494          NMAX = MAX( NMAX, NN( J ) )
00495          IF( NN( J ).LT.0 )
00496      $      BADNN = .TRUE.
00497    10 CONTINUE
00498 *
00499       IF( NSIZES.LT.0 ) THEN
00500          INFO = -1
00501       ELSE IF( BADNN ) THEN
00502          INFO = -2
00503       ELSE IF( NTYPES.LT.0 ) THEN
00504          INFO = -3
00505       ELSE IF( THRESH.LT.ZERO ) THEN
00506          INFO = -6
00507       ELSE IF( LDA.LE.1 .OR. LDA.LT.NMAX ) THEN
00508          INFO = -9
00509       ELSE IF( LDQ.LE.1 .OR. LDQ.LT.NMAX ) THEN
00510          INFO = -14
00511       END IF
00512 *
00513 *     Compute workspace
00514 *      (Note: Comments in the code beginning "Workspace:" describe the
00515 *       minimal amount of workspace needed at that point in the code,
00516 *       as well as the preferred amount for good performance.
00517 *       NB refers to the optimal block size for the immediately
00518 *       following subroutine, as returned by ILAENV.
00519 *
00520       MINWRK = 1
00521       IF( INFO.EQ.0 .AND. LWORK.GE.1 ) THEN
00522          MINWRK = MAX( 10*( NMAX+1 ), 3*NMAX*NMAX )
00523          NB = MAX( 1, ILAENV( 1, 'SGEQRF', ' ', NMAX, NMAX, -1, -1 ),
00524      $        ILAENV( 1, 'SORMQR', 'LT', NMAX, NMAX, NMAX, -1 ),
00525      $        ILAENV( 1, 'SORGQR', ' ', NMAX, NMAX, NMAX, -1 ) )
00526          MAXWRK = MAX( 10*( NMAX+1 ), 2*NMAX+NMAX*NB, 3*NMAX*NMAX )
00527          WORK( 1 ) = MAXWRK
00528       END IF
00529 *
00530       IF( LWORK.LT.MINWRK )
00531      $   INFO = -20
00532 *
00533       IF( INFO.NE.0 ) THEN
00534          CALL XERBLA( 'SDRGES', -INFO )
00535          RETURN
00536       END IF
00537 *
00538 *     Quick return if possible
00539 *
00540       IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 )
00541      $   RETURN
00542 *
00543       SAFMIN = SLAMCH( 'Safe minimum' )
00544       ULP = SLAMCH( 'Epsilon' )*SLAMCH( 'Base' )
00545       SAFMIN = SAFMIN / ULP
00546       SAFMAX = ONE / SAFMIN
00547       CALL SLABAD( SAFMIN, SAFMAX )
00548       ULPINV = ONE / ULP
00549 *
00550 *     The values RMAGN(2:3) depend on N, see below.
00551 *
00552       RMAGN( 0 ) = ZERO
00553       RMAGN( 1 ) = ONE
00554 *
00555 *     Loop over matrix sizes
00556 *
00557       NTESTT = 0
00558       NERRS = 0
00559       NMATS = 0
00560 *
00561       DO 190 JSIZE = 1, NSIZES
00562          N = NN( JSIZE )
00563          N1 = MAX( 1, N )
00564          RMAGN( 2 ) = SAFMAX*ULP / REAL( N1 )
00565          RMAGN( 3 ) = SAFMIN*ULPINV*REAL( N1 )
00566 *
00567          IF( NSIZES.NE.1 ) THEN
00568             MTYPES = MIN( MAXTYP, NTYPES )
00569          ELSE
00570             MTYPES = MIN( MAXTYP+1, NTYPES )
00571          END IF
00572 *
00573 *        Loop over matrix types
00574 *
00575          DO 180 JTYPE = 1, MTYPES
00576             IF( .NOT.DOTYPE( JTYPE ) )
00577      $         GO TO 180
00578             NMATS = NMATS + 1
00579             NTEST = 0
00580 *
00581 *           Save ISEED in case of an error.
00582 *
00583             DO 20 J = 1, 4
00584                IOLDSD( J ) = ISEED( J )
00585    20       CONTINUE
00586 *
00587 *           Initialize RESULT
00588 *
00589             DO 30 J = 1, 13
00590                RESULT( J ) = ZERO
00591    30       CONTINUE
00592 *
00593 *           Generate test matrices A and B
00594 *
00595 *           Description of control parameters:
00596 *
00597 *           KCLASS: =1 means w/o rotation, =2 means w/ rotation,
00598 *                   =3 means random.
00599 *           KATYPE: the "type" to be passed to SLATM4 for computing A.
00600 *           KAZERO: the pattern of zeros on the diagonal for A:
00601 *                   =1: ( xxx ), =2: (0, xxx ) =3: ( 0, 0, xxx, 0 ),
00602 *                   =4: ( 0, xxx, 0, 0 ), =5: ( 0, 0, 1, xxx, 0 ),
00603 *                   =6: ( 0, 1, 0, xxx, 0 ).  (xxx means a string of
00604 *                   non-zero entries.)
00605 *           KAMAGN: the magnitude of the matrix: =0: zero, =1: O(1),
00606 *                   =2: large, =3: small.
00607 *           IASIGN: 1 if the diagonal elements of A are to be
00608 *                   multiplied by a random magnitude 1 number, =2 if
00609 *                   randomly chosen diagonal blocks are to be rotated
00610 *                   to form 2x2 blocks.
00611 *           KBTYPE, KBZERO, KBMAGN, IBSIGN: the same, but for B.
00612 *           KTRIAN: =0: don't fill in the upper triangle, =1: do.
00613 *           KZ1, KZ2, KADD: used to implement KAZERO and KBZERO.
00614 *           RMAGN: used to implement KAMAGN and KBMAGN.
00615 *
00616             IF( MTYPES.GT.MAXTYP )
00617      $         GO TO 110
00618             IINFO = 0
00619             IF( KCLASS( JTYPE ).LT.3 ) THEN
00620 *
00621 *              Generate A (w/o rotation)
00622 *
00623                IF( ABS( KATYPE( JTYPE ) ).EQ.3 ) THEN
00624                   IN = 2*( ( N-1 ) / 2 ) + 1
00625                   IF( IN.NE.N )
00626      $               CALL SLASET( 'Full', N, N, ZERO, ZERO, A, LDA )
00627                ELSE
00628                   IN = N
00629                END IF
00630                CALL SLATM4( KATYPE( JTYPE ), IN, KZ1( KAZERO( JTYPE ) ),
00631      $                      KZ2( KAZERO( JTYPE ) ), IASIGN( JTYPE ),
00632      $                      RMAGN( KAMAGN( JTYPE ) ), ULP,
00633      $                      RMAGN( KTRIAN( JTYPE )*KAMAGN( JTYPE ) ), 2,
00634      $                      ISEED, A, LDA )
00635                IADD = KADD( KAZERO( JTYPE ) )
00636                IF( IADD.GT.0 .AND. IADD.LE.N )
00637      $            A( IADD, IADD ) = ONE
00638 *
00639 *              Generate B (w/o rotation)
00640 *
00641                IF( ABS( KBTYPE( JTYPE ) ).EQ.3 ) THEN
00642                   IN = 2*( ( N-1 ) / 2 ) + 1
00643                   IF( IN.NE.N )
00644      $               CALL SLASET( 'Full', N, N, ZERO, ZERO, B, LDA )
00645                ELSE
00646                   IN = N
00647                END IF
00648                CALL SLATM4( KBTYPE( JTYPE ), IN, KZ1( KBZERO( JTYPE ) ),
00649      $                      KZ2( KBZERO( JTYPE ) ), IBSIGN( JTYPE ),
00650      $                      RMAGN( KBMAGN( JTYPE ) ), ONE,
00651      $                      RMAGN( KTRIAN( JTYPE )*KBMAGN( JTYPE ) ), 2,
00652      $                      ISEED, B, LDA )
00653                IADD = KADD( KBZERO( JTYPE ) )
00654                IF( IADD.NE.0 .AND. IADD.LE.N )
00655      $            B( IADD, IADD ) = ONE
00656 *
00657                IF( KCLASS( JTYPE ).EQ.2 .AND. N.GT.0 ) THEN
00658 *
00659 *                 Include rotations
00660 *
00661 *                 Generate Q, Z as Householder transformations times
00662 *                 a diagonal matrix.
00663 *
00664                   DO 50 JC = 1, N - 1
00665                      DO 40 JR = JC, N
00666                         Q( JR, JC ) = SLARND( 3, ISEED )
00667                         Z( JR, JC ) = SLARND( 3, ISEED )
00668    40                CONTINUE
00669                      CALL SLARFG( N+1-JC, Q( JC, JC ), Q( JC+1, JC ), 1,
00670      $                            WORK( JC ) )
00671                      WORK( 2*N+JC ) = SIGN( ONE, Q( JC, JC ) )
00672                      Q( JC, JC ) = ONE
00673                      CALL SLARFG( N+1-JC, Z( JC, JC ), Z( JC+1, JC ), 1,
00674      $                            WORK( N+JC ) )
00675                      WORK( 3*N+JC ) = SIGN( ONE, Z( JC, JC ) )
00676                      Z( JC, JC ) = ONE
00677    50             CONTINUE
00678                   Q( N, N ) = ONE
00679                   WORK( N ) = ZERO
00680                   WORK( 3*N ) = SIGN( ONE, SLARND( 2, ISEED ) )
00681                   Z( N, N ) = ONE
00682                   WORK( 2*N ) = ZERO
00683                   WORK( 4*N ) = SIGN( ONE, SLARND( 2, ISEED ) )
00684 *
00685 *                 Apply the diagonal matrices
00686 *
00687                   DO 70 JC = 1, N
00688                      DO 60 JR = 1, N
00689                         A( JR, JC ) = WORK( 2*N+JR )*WORK( 3*N+JC )*
00690      $                                A( JR, JC )
00691                         B( JR, JC ) = WORK( 2*N+JR )*WORK( 3*N+JC )*
00692      $                                B( JR, JC )
00693    60                CONTINUE
00694    70             CONTINUE
00695                   CALL SORM2R( 'L', 'N', N, N, N-1, Q, LDQ, WORK, A,
00696      $                         LDA, WORK( 2*N+1 ), IINFO )
00697                   IF( IINFO.NE.0 )
00698      $               GO TO 100
00699                   CALL SORM2R( 'R', 'T', N, N, N-1, Z, LDQ, WORK( N+1 ),
00700      $                         A, LDA, WORK( 2*N+1 ), IINFO )
00701                   IF( IINFO.NE.0 )
00702      $               GO TO 100
00703                   CALL SORM2R( 'L', 'N', N, N, N-1, Q, LDQ, WORK, B,
00704      $                         LDA, WORK( 2*N+1 ), IINFO )
00705                   IF( IINFO.NE.0 )
00706      $               GO TO 100
00707                   CALL SORM2R( 'R', 'T', N, N, N-1, Z, LDQ, WORK( N+1 ),
00708      $                         B, LDA, WORK( 2*N+1 ), IINFO )
00709                   IF( IINFO.NE.0 )
00710      $               GO TO 100
00711                END IF
00712             ELSE
00713 *
00714 *              Random matrices
00715 *
00716                DO 90 JC = 1, N
00717                   DO 80 JR = 1, N
00718                      A( JR, JC ) = RMAGN( KAMAGN( JTYPE ) )*
00719      $                             SLARND( 2, ISEED )
00720                      B( JR, JC ) = RMAGN( KBMAGN( JTYPE ) )*
00721      $                             SLARND( 2, ISEED )
00722    80             CONTINUE
00723    90          CONTINUE
00724             END IF
00725 *
00726   100       CONTINUE
00727 *
00728             IF( IINFO.NE.0 ) THEN
00729                WRITE( NOUNIT, FMT = 9999 )'Generator', IINFO, N, JTYPE,
00730      $            IOLDSD
00731                INFO = ABS( IINFO )
00732                RETURN
00733             END IF
00734 *
00735   110       CONTINUE
00736 *
00737             DO 120 I = 1, 13
00738                RESULT( I ) = -ONE
00739   120       CONTINUE
00740 *
00741 *           Test with and without sorting of eigenvalues
00742 *
00743             DO 150 ISORT = 0, 1
00744                IF( ISORT.EQ.0 ) THEN
00745                   SORT = 'N'
00746                   RSUB = 0
00747                ELSE
00748                   SORT = 'S'
00749                   RSUB = 5
00750                END IF
00751 *
00752 *              Call SGGES to compute H, T, Q, Z, alpha, and beta.
00753 *
00754                CALL SLACPY( 'Full', N, N, A, LDA, S, LDA )
00755                CALL SLACPY( 'Full', N, N, B, LDA, T, LDA )
00756                NTEST = 1 + RSUB + ISORT
00757                RESULT( 1+RSUB+ISORT ) = ULPINV
00758                CALL SGGES( 'V', 'V', SORT, SLCTES, N, S, LDA, T, LDA,
00759      $                     SDIM, ALPHAR, ALPHAI, BETA, Q, LDQ, Z, LDQ,
00760      $                     WORK, LWORK, BWORK, IINFO )
00761                IF( IINFO.NE.0 .AND. IINFO.NE.N+2 ) THEN
00762                   RESULT( 1+RSUB+ISORT ) = ULPINV
00763                   WRITE( NOUNIT, FMT = 9999 )'SGGES', IINFO, N, JTYPE,
00764      $               IOLDSD
00765                   INFO = ABS( IINFO )
00766                   GO TO 160
00767                END IF
00768 *
00769                NTEST = 4 + RSUB
00770 *
00771 *              Do tests 1--4 (or tests 7--9 when reordering )
00772 *
00773                IF( ISORT.EQ.0 ) THEN
00774                   CALL SGET51( 1, N, A, LDA, S, LDA, Q, LDQ, Z, LDQ,
00775      $                         WORK, RESULT( 1 ) )
00776                   CALL SGET51( 1, N, B, LDA, T, LDA, Q, LDQ, Z, LDQ,
00777      $                         WORK, RESULT( 2 ) )
00778                ELSE
00779                   CALL SGET54( N, A, LDA, B, LDA, S, LDA, T, LDA, Q,
00780      $                         LDQ, Z, LDQ, WORK, RESULT( 7 ) )
00781                END IF
00782                CALL SGET51( 3, N, A, LDA, T, LDA, Q, LDQ, Q, LDQ, WORK,
00783      $                      RESULT( 3+RSUB ) )
00784                CALL SGET51( 3, N, B, LDA, T, LDA, Z, LDQ, Z, LDQ, WORK,
00785      $                      RESULT( 4+RSUB ) )
00786 *
00787 *              Do test 5 and 6 (or Tests 10 and 11 when reordering):
00788 *              check Schur form of A and compare eigenvalues with
00789 *              diagonals.
00790 *
00791                NTEST = 6 + RSUB
00792                TEMP1 = ZERO
00793 *
00794                DO 130 J = 1, N
00795                   ILABAD = .FALSE.
00796                   IF( ALPHAI( J ).EQ.ZERO ) THEN
00797                      TEMP2 = ( ABS( ALPHAR( J )-S( J, J ) ) /
00798      $                       MAX( SAFMIN, ABS( ALPHAR( J ) ), ABS( S( J,
00799      $                       J ) ) )+ABS( BETA( J )-T( J, J ) ) /
00800      $                       MAX( SAFMIN, ABS( BETA( J ) ), ABS( T( J,
00801      $                       J ) ) ) ) / ULP
00802 *
00803                      IF( J.LT.N ) THEN
00804                         IF( S( J+1, J ).NE.ZERO ) THEN
00805                            ILABAD = .TRUE.
00806                            RESULT( 5+RSUB ) = ULPINV
00807                         END IF
00808                      END IF
00809                      IF( J.GT.1 ) THEN
00810                         IF( S( J, J-1 ).NE.ZERO ) THEN
00811                            ILABAD = .TRUE.
00812                            RESULT( 5+RSUB ) = ULPINV
00813                         END IF
00814                      END IF
00815 *
00816                   ELSE
00817                      IF( ALPHAI( J ).GT.ZERO ) THEN
00818                         I1 = J
00819                      ELSE
00820                         I1 = J - 1
00821                      END IF
00822                      IF( I1.LE.0 .OR. I1.GE.N ) THEN
00823                         ILABAD = .TRUE.
00824                      ELSE IF( I1.LT.N-1 ) THEN
00825                         IF( S( I1+2, I1+1 ).NE.ZERO ) THEN
00826                            ILABAD = .TRUE.
00827                            RESULT( 5+RSUB ) = ULPINV
00828                         END IF
00829                      ELSE IF( I1.GT.1 ) THEN
00830                         IF( S( I1, I1-1 ).NE.ZERO ) THEN
00831                            ILABAD = .TRUE.
00832                            RESULT( 5+RSUB ) = ULPINV
00833                         END IF
00834                      END IF
00835                      IF( .NOT.ILABAD ) THEN
00836                         CALL SGET53( S( I1, I1 ), LDA, T( I1, I1 ), LDA,
00837      $                               BETA( J ), ALPHAR( J ),
00838      $                               ALPHAI( J ), TEMP2, IERR )
00839                         IF( IERR.GE.3 ) THEN
00840                            WRITE( NOUNIT, FMT = 9998 )IERR, J, N,
00841      $                        JTYPE, IOLDSD
00842                            INFO = ABS( IERR )
00843                         END IF
00844                      ELSE
00845                         TEMP2 = ULPINV
00846                      END IF
00847 *
00848                   END IF
00849                   TEMP1 = MAX( TEMP1, TEMP2 )
00850                   IF( ILABAD ) THEN
00851                      WRITE( NOUNIT, FMT = 9997 )J, N, JTYPE, IOLDSD
00852                   END IF
00853   130          CONTINUE
00854                RESULT( 6+RSUB ) = TEMP1
00855 *
00856                IF( ISORT.GE.1 ) THEN
00857 *
00858 *                 Do test 12
00859 *
00860                   NTEST = 12
00861                   RESULT( 12 ) = ZERO
00862                   KNTEIG = 0
00863                   DO 140 I = 1, N
00864                      IF( SLCTES( ALPHAR( I ), ALPHAI( I ),
00865      $                   BETA( I ) ) .OR. SLCTES( ALPHAR( I ),
00866      $                   -ALPHAI( I ), BETA( I ) ) ) THEN
00867                         KNTEIG = KNTEIG + 1
00868                      END IF
00869                      IF( I.LT.N ) THEN
00870                         IF( ( SLCTES( ALPHAR( I+1 ), ALPHAI( I+1 ),
00871      $                      BETA( I+1 ) ) .OR. SLCTES( ALPHAR( I+1 ),
00872      $                      -ALPHAI( I+1 ), BETA( I+1 ) ) ) .AND.
00873      $                      ( .NOT.( SLCTES( ALPHAR( I ), ALPHAI( I ),
00874      $                      BETA( I ) ) .OR. SLCTES( ALPHAR( I ),
00875      $                      -ALPHAI( I ), BETA( I ) ) ) ) .AND.
00876      $                      IINFO.NE.N+2 ) THEN
00877                            RESULT( 12 ) = ULPINV
00878                         END IF
00879                      END IF
00880   140             CONTINUE
00881                   IF( SDIM.NE.KNTEIG ) THEN
00882                      RESULT( 12 ) = ULPINV
00883                   END IF
00884                END IF
00885 *
00886   150       CONTINUE
00887 *
00888 *           End of Loop -- Check for RESULT(j) > THRESH
00889 *
00890   160       CONTINUE
00891 *
00892             NTESTT = NTESTT + NTEST
00893 *
00894 *           Print out tests which fail.
00895 *
00896             DO 170 JR = 1, NTEST
00897                IF( RESULT( JR ).GE.THRESH ) THEN
00898 *
00899 *                 If this is the first test to fail,
00900 *                 print a header to the data file.
00901 *
00902                   IF( NERRS.EQ.0 ) THEN
00903                      WRITE( NOUNIT, FMT = 9996 )'SGS'
00904 *
00905 *                    Matrix types
00906 *
00907                      WRITE( NOUNIT, FMT = 9995 )
00908                      WRITE( NOUNIT, FMT = 9994 )
00909                      WRITE( NOUNIT, FMT = 9993 )'Orthogonal'
00910 *
00911 *                    Tests performed
00912 *
00913                      WRITE( NOUNIT, FMT = 9992 )'orthogonal', '''',
00914      $                  'transpose', ( '''', J = 1, 8 )
00915 *
00916                   END IF
00917                   NERRS = NERRS + 1
00918                   IF( RESULT( JR ).LT.10000.0 ) THEN
00919                      WRITE( NOUNIT, FMT = 9991 )N, JTYPE, IOLDSD, JR,
00920      $                  RESULT( JR )
00921                   ELSE
00922                      WRITE( NOUNIT, FMT = 9990 )N, JTYPE, IOLDSD, JR,
00923      $                  RESULT( JR )
00924                   END IF
00925                END IF
00926   170       CONTINUE
00927 *
00928   180    CONTINUE
00929   190 CONTINUE
00930 *
00931 *     Summary
00932 *
00933       CALL ALASVM( 'SGS', NOUNIT, NERRS, NTESTT, 0 )
00934 *
00935       WORK( 1 ) = MAXWRK
00936 *
00937       RETURN
00938 *
00939  9999 FORMAT( ' SDRGES: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
00940      $      I6, ', JTYPE=', I6, ', ISEED=(', 4( I4, ',' ), I5, ')' )
00941 *
00942  9998 FORMAT( ' SDRGES: SGET53 returned INFO=', I1, ' for eigenvalue ',
00943      $      I6, '.', / 9X, 'N=', I6, ', JTYPE=', I6, ', ISEED=(',
00944      $      4( I4, ',' ), I5, ')' )
00945 *
00946  9997 FORMAT( ' SDRGES: S not in Schur form at eigenvalue ', I6, '.',
00947      $      / 9X, 'N=', I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ),
00948      $      I5, ')' )
00949 *
00950  9996 FORMAT( / 1X, A3, ' -- Real Generalized Schur form driver' )
00951 *
00952  9995 FORMAT( ' Matrix types (see SDRGES for details): ' )
00953 *
00954  9994 FORMAT( ' Special Matrices:', 23X,
00955      $      '(J''=transposed Jordan block)',
00956      $      / '   1=(0,0)  2=(I,0)  3=(0,I)  4=(I,I)  5=(J'',J'')  ',
00957      $      '6=(diag(J'',I), diag(I,J''))', / ' Diagonal Matrices:  ( ',
00958      $      'D=diag(0,1,2,...) )', / '   7=(D,I)   9=(large*D, small*I',
00959      $      ')  11=(large*I, small*D)  13=(large*D, large*I)', /
00960      $      '   8=(I,D)  10=(small*D, large*I)  12=(small*I, large*D) ',
00961      $      ' 14=(small*D, small*I)', / '  15=(D, reversed D)' )
00962  9993 FORMAT( ' Matrices Rotated by Random ', A, ' Matrices U, V:',
00963      $      / '  16=Transposed Jordan Blocks             19=geometric ',
00964      $      'alpha, beta=0,1', / '  17=arithm. alpha&beta             ',
00965      $      '      20=arithmetic alpha, beta=0,1', / '  18=clustered ',
00966      $      'alpha, beta=0,1            21=random alpha, beta=0,1',
00967      $      / ' Large & Small Matrices:', / '  22=(large, small)   ',
00968      $      '23=(small,large)    24=(small,small)    25=(large,large)',
00969      $      / '  26=random O(1) matrices.' )
00970 *
00971  9992 FORMAT( / ' Tests performed:  (S is Schur, T is triangular, ',
00972      $      'Q and Z are ', A, ',', / 19X,
00973      $      'l and r are the appropriate left and right', / 19X,
00974      $      'eigenvectors, resp., a is alpha, b is beta, and', / 19X, A,
00975      $      ' means ', A, '.)', / ' Without ordering: ',
00976      $      / '  1 = | A - Q S Z', A,
00977      $      ' | / ( |A| n ulp )      2 = | B - Q T Z', A,
00978      $      ' | / ( |B| n ulp )', / '  3 = | I - QQ', A,
00979      $      ' | / ( n ulp )             4 = | I - ZZ', A,
00980      $      ' | / ( n ulp )', / '  5 = A is in Schur form S',
00981      $      / '  6 = difference between (alpha,beta)',
00982      $      ' and diagonals of (S,T)', / ' With ordering: ',
00983      $      / '  7 = | (A,B) - Q (S,T) Z', A,
00984      $      ' | / ( |(A,B)| n ulp )  ', / '  8 = | I - QQ', A,
00985      $      ' | / ( n ulp )            9 = | I - ZZ', A,
00986      $      ' | / ( n ulp )', / ' 10 = A is in Schur form S',
00987      $      / ' 11 = difference between (alpha,beta) and diagonals',
00988      $      ' of (S,T)', / ' 12 = SDIM is the correct number of ',
00989      $      'selected eigenvalues', / )
00990  9991 FORMAT( ' Matrix order=', I5, ', type=', I2, ', seed=',
00991      $      4( I4, ',' ), ' result ', I2, ' is', 0P, F8.2 )
00992  9990 FORMAT( ' Matrix order=', I5, ', type=', I2, ', seed=',
00993      $      4( I4, ',' ), ' result ', I2, ' is', 1P, E10.3 )
00994 *
00995 *     End of SDRGES
00996 *
00997       END
 All Files Functions