LAPACK: TESTING/EIG/dchkgg.f Source File

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00001       SUBROUTINE DCHKGG( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
00002      $                   TSTDIF, THRSHN, NOUNIT, A, LDA, B, H, T, S1,
00003      $                   S2, P1, P2, U, LDU, V, Q, Z, ALPHR1, ALPHI1,
00004      $                   BETA1, ALPHR3, ALPHI3, BETA3, EVECTL, EVECTR,
00005      $                   WORK, LWORK, LLWORK, RESULT, INFO )
00006 *
00007 *  -- LAPACK test routine (version 3.1) --
00008 *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
00009 *     November 2006
00010 *
00011 *     .. Scalar Arguments ..
00012       LOGICAL            TSTDIF
00013       INTEGER            INFO, LDA, LDU, LWORK, NOUNIT, NSIZES, NTYPES
00014       DOUBLE PRECISION   THRESH, THRSHN
00015 *     ..
00016 *     .. Array Arguments ..
00017       LOGICAL            DOTYPE( * ), LLWORK( * )
00018       INTEGER            ISEED( 4 ), NN( * )
00019       DOUBLE PRECISION   A( LDA, * ), ALPHI1( * ), ALPHI3( * ),
00020      $                   ALPHR1( * ), ALPHR3( * ), B( LDA, * ),
00021      $                   BETA1( * ), BETA3( * ), EVECTL( LDU, * ),
00022      $                   EVECTR( LDU, * ), H( LDA, * ), P1( LDA, * ),
00023      $                   P2( LDA, * ), Q( LDU, * ), RESULT( 15 ),
00024      $                   S1( LDA, * ), S2( LDA, * ), T( LDA, * ),
00025      $                   U( LDU, * ), V( LDU, * ), WORK( * ),
00026      $                   Z( LDU, * )
00027 *     ..
00028 *
00029 *  Purpose
00030 *  =======
00031 *
00032 *  DCHKGG  checks the nonsymmetric generalized eigenvalue problem
00033 *  routines.
00034 *                                 T          T        T
00035 *  DGGHRD factors A and B as U H V  and U T V , where   means
00036 *  transpose, H is hessenberg, T is triangular and U and V are
00037 *  orthogonal.
00038 *                                  T          T
00039 *  DHGEQZ factors H and T as  Q S Z  and Q P Z , where P is upper
00040 *  triangular, S is in generalized Schur form (block upper triangular,
00041 *  with 1x1 and 2x2 blocks on the diagonal, the 2x2 blocks
00042 *  corresponding to complex conjugate pairs of generalized
00043 *  eigenvalues), and Q and Z are orthogonal.  It also computes the
00044 *  generalized eigenvalues (alpha(1),beta(1)),...,(alpha(n),beta(n)),
00045 *  where alpha(j)=S(j,j) and beta(j)=P(j,j) -- thus,
00046 *  w(j) = alpha(j)/beta(j) is a root of the generalized eigenvalue
00047 *  problem
00048 *
00049 *      det( A - w(j) B ) = 0
00050 *
00051 *  and m(j) = beta(j)/alpha(j) is a root of the essentially equivalent
00052 *  problem
00053 *
00054 *      det( m(j) A - B ) = 0
00055 *
00056 *  DTGEVC computes the matrix L of left eigenvectors and the matrix R
00057 *  of right eigenvectors for the matrix pair ( S, P ).  In the
00058 *  description below,  l and r are left and right eigenvectors
00059 *  corresponding to the generalized eigenvalues (alpha,beta).
00060 *
00061 *  When DCHKGG is called, a number of matrix "sizes" ("n's") and a
00062 *  number of matrix "types" are specified.  For each size ("n")
00063 *  and each type of matrix, one matrix will be generated and used
00064 *  to test the nonsymmetric eigenroutines.  For each matrix, 15
00065 *  tests will be performed.  The first twelve "test ratios" should be
00066 *  small -- O(1).  They will be compared with the threshhold THRESH:
00067 *
00068 *                   T
00069 *  (1)   | A - U H V  | / ( |A| n ulp )
00070 *
00071 *                   T
00072 *  (2)   | B - U T V  | / ( |B| n ulp )
00073 *
00074 *                T
00075 *  (3)   | I - UU  | / ( n ulp )
00076 *
00077 *                T
00078 *  (4)   | I - VV  | / ( n ulp )
00079 *
00080 *                   T
00081 *  (5)   | H - Q S Z  | / ( |H| n ulp )
00082 *
00083 *                   T
00084 *  (6)   | T - Q P Z  | / ( |T| n ulp )
00085 *
00086 *                T
00087 *  (7)   | I - QQ  | / ( n ulp )
00088 *
00089 *                T
00090 *  (8)   | I - ZZ  | / ( n ulp )
00091 *
00092 *  (9)   max over all left eigenvalue/-vector pairs (beta/alpha,l) of
00093 *
00094 *     | l**H * (beta S - alpha P) | / ( ulp max( |beta S|, |alpha P| ) )
00095 *
00096 *  (10)  max over all left eigenvalue/-vector pairs (beta/alpha,l') of
00097 *                            T
00098 *    | l'**H * (beta H - alpha T) | / ( ulp max( |beta H|, |alpha T| ) )
00099 *
00100 *        where the eigenvectors l' are the result of passing Q to
00101 *        DTGEVC and back transforming (HOWMNY='B').
00102 *
00103 *  (11)  max over all right eigenvalue/-vector pairs (beta/alpha,r) of
00104 *
00105 *        | (beta S - alpha T) r | / ( ulp max( |beta S|, |alpha T| ) )
00106 *
00107 *  (12)  max over all right eigenvalue/-vector pairs (beta/alpha,r') of
00108 *
00109 *        | (beta H - alpha T) r' | / ( ulp max( |beta H|, |alpha T| ) )
00110 *
00111 *        where the eigenvectors r' are the result of passing Z to
00112 *        DTGEVC and back transforming (HOWMNY='B').
00113 *
00114 *  The last three test ratios will usually be small, but there is no
00115 *  mathematical requirement that they be so.  They are therefore
00116 *  compared with THRESH only if TSTDIF is .TRUE.
00117 *
00118 *  (13)  | S(Q,Z computed) - S(Q,Z not computed) | / ( |S| ulp )
00119 *
00120 *  (14)  | P(Q,Z computed) - P(Q,Z not computed) | / ( |P| ulp )
00121 *
00122 *  (15)  max( |alpha(Q,Z computed) - alpha(Q,Z not computed)|/|S| ,
00123 *             |beta(Q,Z computed) - beta(Q,Z not computed)|/|P| ) / ulp
00124 *
00125 *  In addition, the normalization of L and R are checked, and compared
00126 *  with the threshhold THRSHN.
00127 *
00128 *  Test Matrices
00129 *  ---- --------
00130 *
00131 *  The sizes of the test matrices are specified by an array
00132 *  NN(1:NSIZES); the value of each element NN(j) specifies one size.
00133 *  The "types" are specified by a logical array DOTYPE( 1:NTYPES ); if
00134 *  DOTYPE(j) is .TRUE., then matrix type "j" will be generated.
00135 *  Currently, the list of possible types is:
00136 *
00137 *  (1)  ( 0, 0 )         (a pair of zero matrices)
00138 *
00139 *  (2)  ( I, 0 )         (an identity and a zero matrix)
00140 *
00141 *  (3)  ( 0, I )         (an identity and a zero matrix)
00142 *
00143 *  (4)  ( I, I )         (a pair of identity matrices)
00144 *
00145 *          t   t
00146 *  (5)  ( J , J  )       (a pair of transposed Jordan blocks)
00147 *
00148 *                                      t                ( I   0  )
00149 *  (6)  ( X, Y )         where  X = ( J   0  )  and Y = (      t )
00150 *                                   ( 0   I  )          ( 0   J  )
00151 *                        and I is a k x k identity and J a (k+1)x(k+1)
00152 *                        Jordan block; k=(N-1)/2
00153 *
00154 *  (7)  ( D, I )         where D is diag( 0, 1,..., N-1 ) (a diagonal
00155 *                        matrix with those diagonal entries.)
00156 *  (8)  ( I, D )
00157 *
00158 *  (9)  ( big*D, small*I ) where "big" is near overflow and small=1/big
00159 *
00160 *  (10) ( small*D, big*I )
00161 *
00162 *  (11) ( big*I, small*D )
00163 *
00164 *  (12) ( small*I, big*D )
00165 *
00166 *  (13) ( big*D, big*I )
00167 *
00168 *  (14) ( small*D, small*I )
00169 *
00170 *  (15) ( D1, D2 )        where D1 is diag( 0, 0, 1, ..., N-3, 0 ) and
00171 *                         D2 is diag( 0, N-3, N-4,..., 1, 0, 0 )
00172 *            t   t
00173 *  (16) U ( J , J ) V     where U and V are random orthogonal matrices.
00174 *
00175 *  (17) U ( T1, T2 ) V    where T1 and T2 are upper triangular matrices
00176 *                         with random O(1) entries above the diagonal
00177 *                         and diagonal entries diag(T1) =
00178 *                         ( 0, 0, 1, ..., N-3, 0 ) and diag(T2) =
00179 *                         ( 0, N-3, N-4,..., 1, 0, 0 )
00180 *
00181 *  (18) U ( T1, T2 ) V    diag(T1) = ( 0, 0, 1, 1, s, ..., s, 0 )
00182 *                         diag(T2) = ( 0, 1, 0, 1,..., 1, 0 )
00183 *                         s = machine precision.
00184 *
00185 *  (19) U ( T1, T2 ) V    diag(T1)=( 0,0,1,1, 1-d, ..., 1-(N-5)*d=s, 0 )
00186 *                         diag(T2) = ( 0, 1, 0, 1, ..., 1, 0 )
00187 *
00188 *                                                         N-5
00189 *  (20) U ( T1, T2 ) V    diag(T1)=( 0, 0, 1, 1, a, ..., a   =s, 0 )
00190 *                         diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 )
00191 *
00192 *  (21) U ( T1, T2 ) V    diag(T1)=( 0, 0, 1, r1, r2, ..., r(N-4), 0 )
00193 *                         diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 )
00194 *                         where r1,..., r(N-4) are random.
00195 *
00196 *  (22) U ( big*T1, small*T2 ) V    diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
00197 *                                   diag(T2) = ( 0, 1, ..., 1, 0, 0 )
00198 *
00199 *  (23) U ( small*T1, big*T2 ) V    diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
00200 *                                   diag(T2) = ( 0, 1, ..., 1, 0, 0 )
00201 *
00202 *  (24) U ( small*T1, small*T2 ) V  diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
00203 *                                   diag(T2) = ( 0, 1, ..., 1, 0, 0 )
00204 *
00205 *  (25) U ( big*T1, big*T2 ) V      diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
00206 *                                   diag(T2) = ( 0, 1, ..., 1, 0, 0 )
00207 *
00208 *  (26) U ( T1, T2 ) V     where T1 and T2 are random upper-triangular
00209 *                          matrices.
00210 *
00211 *  Arguments
00212 *  =========
00213 *
00214 *  NSIZES  (input) INTEGER
00215 *          The number of sizes of matrices to use.  If it is zero,
00216 *          DCHKGG does nothing.  It must be at least zero.
00217 *
00218 *  NN      (input) INTEGER array, dimension (NSIZES)
00219 *          An array containing the sizes to be used for the matrices.
00220 *          Zero values will be skipped.  The values must be at least
00221 *          zero.
00222 *
00223 *  NTYPES  (input) INTEGER
00224 *          The number of elements in DOTYPE.   If it is zero, DCHKGG
00225 *          does nothing.  It must be at least zero.  If it is MAXTYP+1
00226 *          and NSIZES is 1, then an additional type, MAXTYP+1 is
00227 *          defined, which is to use whatever matrix is in A.  This
00228 *          is only useful if DOTYPE(1:MAXTYP) is .FALSE. and
00229 *          DOTYPE(MAXTYP+1) is .TRUE. .
00230 *
00231 *  DOTYPE  (input) LOGICAL array, dimension (NTYPES)
00232 *          If DOTYPE(j) is .TRUE., then for each size in NN a
00233 *          matrix of that size and of type j will be generated.
00234 *          If NTYPES is smaller than the maximum number of types
00235 *          defined (PARAMETER MAXTYP), then types NTYPES+1 through
00236 *          MAXTYP will not be generated.  If NTYPES is larger
00237 *          than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES)
00238 *          will be ignored.
00239 *
00240 *  ISEED   (input/output) INTEGER array, dimension (4)
00241 *          On entry ISEED specifies the seed of the random number
00242 *          generator. The array elements should be between 0 and 4095;
00243 *          if not they will be reduced mod 4096.  Also, ISEED(4) must
00244 *          be odd.  The random number generator uses a linear
00245 *          congruential sequence limited to small integers, and so
00246 *          should produce machine independent random numbers. The
00247 *          values of ISEED are changed on exit, and can be used in the
00248 *          next call to DCHKGG to continue the same random number
00249 *          sequence.
00250 *
00251 *  THRESH  (input) DOUBLE PRECISION
00252 *          A test will count as "failed" if the "error", computed as
00253 *          described above, exceeds THRESH.  Note that the error is
00254 *          scaled to be O(1), so THRESH should be a reasonably small
00255 *          multiple of 1, e.g., 10 or 100.  In particular, it should
00256 *          not depend on the precision (single vs. double) or the size
00257 *          of the matrix.  It must be at least zero.
00258 *
00259 *  TSTDIF  (input) LOGICAL
00260 *          Specifies whether test ratios 13-15 will be computed and
00261 *          compared with THRESH.
00262 *          = .FALSE.: Only test ratios 1-12 will be computed and tested.
00263 *                     Ratios 13-15 will be set to zero.
00264 *          = .TRUE.:  All the test ratios 1-15 will be computed and
00265 *                     tested.
00266 *
00267 *  THRSHN  (input) DOUBLE PRECISION
00268 *          Threshhold for reporting eigenvector normalization error.
00269 *          If the normalization of any eigenvector differs from 1 by
00270 *          more than THRSHN*ulp, then a special error message will be
00271 *          printed.  (This is handled separately from the other tests,
00272 *          since only a compiler or programming error should cause an
00273 *          error message, at least if THRSHN is at least 5--10.)
00274 *
00275 *  NOUNIT  (input) INTEGER
00276 *          The FORTRAN unit number for printing out error messages
00277 *          (e.g., if a routine returns IINFO not equal to 0.)
00278 *
00279 *  A       (input/workspace) DOUBLE PRECISION array, dimension
00280 *                            (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 *
00285 *  LDA     (input) INTEGER
00286 *          The leading dimension of A, B, H, T, S1, P1, S2, and P2.
00287 *          It must be at least 1 and at least max( NN ).
00288 *
00289 *  B       (input/workspace) DOUBLE PRECISION array, dimension
00290 *                            (LDA, max(NN))
00291 *          Used to hold the original B matrix.  Used as input only
00292 *          if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and
00293 *          DOTYPE(MAXTYP+1)=.TRUE.
00294 *
00295 *  H       (workspace) DOUBLE PRECISION array, dimension (LDA, max(NN))
00296 *          The upper Hessenberg matrix computed from A by DGGHRD.
00297 *
00298 *  T       (workspace) DOUBLE PRECISION array, dimension (LDA, max(NN))
00299 *          The upper triangular matrix computed from B by DGGHRD.
00300 *
00301 *  S1      (workspace) DOUBLE PRECISION array, dimension (LDA, max(NN))
00302 *          The Schur (block upper triangular) matrix computed from H by
00303 *          DHGEQZ when Q and Z are also computed.
00304 *
00305 *  S2      (workspace) DOUBLE PRECISION array, dimension (LDA, max(NN))
00306 *          The Schur (block upper triangular) matrix computed from H by
00307 *          DHGEQZ when Q and Z are not computed.
00308 *
00309 *  P1      (workspace) DOUBLE PRECISION array, dimension (LDA, max(NN))
00310 *          The upper triangular matrix computed from T by DHGEQZ
00311 *          when Q and Z are also computed.
00312 *
00313 *  P2      (workspace) DOUBLE PRECISION array, dimension (LDA, max(NN))
00314 *          The upper triangular matrix computed from T by DHGEQZ
00315 *          when Q and Z are not computed.
00316 *
00317 *  U       (workspace) DOUBLE PRECISION array, dimension (LDU, max(NN))
00318 *          The (left) orthogonal matrix computed by DGGHRD.
00319 *
00320 *  LDU     (input) INTEGER
00321 *          The leading dimension of U, V, Q, Z, EVECTL, and EVEZTR.  It
00322 *          must be at least 1 and at least max( NN ).
00323 *
00324 *  V       (workspace) DOUBLE PRECISION array, dimension (LDU, max(NN))
00325 *          The (right) orthogonal matrix computed by DGGHRD.
00326 *
00327 *  Q       (workspace) DOUBLE PRECISION array, dimension (LDU, max(NN))
00328 *          The (left) orthogonal matrix computed by DHGEQZ.
00329 *
00330 *  Z       (workspace) DOUBLE PRECISION array, dimension (LDU, max(NN))
00331 *          The (left) orthogonal matrix computed by DHGEQZ.
00332 *
00333 *  ALPHR1  (workspace) DOUBLE PRECISION array, dimension (max(NN))
00334 *  ALPHI1  (workspace) DOUBLE PRECISION array, dimension (max(NN))
00335 *  BETA1   (workspace) DOUBLE PRECISION array, dimension (max(NN))
00336 *
00337 *          The generalized eigenvalues of (A,B) computed by DHGEQZ
00338 *          when Q, Z, and the full Schur matrices are computed.
00339 *          On exit, ( ALPHR1(k)+ALPHI1(k)*i ) / BETA1(k) is the k-th
00340 *          generalized eigenvalue of the matrices in A and B.
00341 *
00342 *  ALPHR3  (workspace) DOUBLE PRECISION array, dimension (max(NN))
00343 *  ALPHI3  (workspace) DOUBLE PRECISION array, dimension (max(NN))
00344 *  BETA3   (workspace) DOUBLE PRECISION array, dimension (max(NN))
00345 *
00346 *  EVECTL  (workspace) DOUBLE PRECISION array, dimension (LDU, max(NN))
00347 *          The (block lower triangular) left eigenvector matrix for
00348 *          the matrices in S1 and P1.  (See DTGEVC for the format.)
00349 *
00350 *  EVEZTR  (workspace) DOUBLE PRECISION array, dimension (LDU, max(NN))
00351 *          The (block upper triangular) right eigenvector matrix for
00352 *          the matrices in S1 and P1.  (See DTGEVC for the format.)
00353 *
00354 *  WORK    (workspace) DOUBLE PRECISION array, dimension (LWORK)
00355 *
00356 *  LWORK   (input) INTEGER
00357 *          The number of entries in WORK.  This must be at least
00358 *          max( 2 * N**2, 6*N, 1 ), for all N=NN(j).
00359 *
00360 *  LLWORK  (workspace) LOGICAL array, dimension (max(NN))
00361 *
00362 *  RESULT  (output) DOUBLE PRECISION array, dimension (15)
00363 *          The values computed by the tests described above.
00364 *          The values are currently limited to 1/ulp, to avoid
00365 *          overflow.
00366 *
00367 *  INFO    (output) INTEGER
00368 *          = 0:  successful exit
00369 *          < 0:  if INFO = -i, the i-th argument had an illegal value
00370 *          > 0:  A routine returned an error code.  INFO is the
00371 *                absolute value of the INFO value returned.
00372 *
00373 *  =====================================================================
00374 *
00375 *     .. Parameters ..
00376       DOUBLE PRECISION   ZERO, ONE
00377       PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
00378       INTEGER            MAXTYP
00379       PARAMETER          ( MAXTYP = 26 )
00380 *     ..
00381 *     .. Local Scalars ..
00382       LOGICAL            BADNN
00383       INTEGER            I1, IADD, IINFO, IN, J, JC, JR, JSIZE, JTYPE,
00384      $                   LWKOPT, MTYPES, N, N1, NERRS, NMATS, NMAX,
00385      $                   NTEST, NTESTT
00386       DOUBLE PRECISION   ANORM, BNORM, SAFMAX, SAFMIN, TEMP1, TEMP2,
00387      $                   ULP, ULPINV
00388 *     ..
00389 *     .. Local Arrays ..
00390       INTEGER            IASIGN( MAXTYP ), IBSIGN( MAXTYP ),
00391      $                   IOLDSD( 4 ), KADD( 6 ), KAMAGN( MAXTYP ),
00392      $                   KATYPE( MAXTYP ), KAZERO( MAXTYP ),
00393      $                   KBMAGN( MAXTYP ), KBTYPE( MAXTYP ),
00394      $                   KBZERO( MAXTYP ), KCLASS( MAXTYP ),
00395      $                   KTRIAN( MAXTYP ), KZ1( 6 ), KZ2( 6 )
00396       DOUBLE PRECISION   DUMMA( 4 ), RMAGN( 0: 3 )
00397 *     ..
00398 *     .. External Functions ..
00399       DOUBLE PRECISION   DLAMCH, DLANGE, DLARND
00400       EXTERNAL           DLAMCH, DLANGE, DLARND
00401 *     ..
00402 *     .. External Subroutines ..
00403       EXTERNAL           DGEQR2, DGET51, DGET52, DGGHRD, DHGEQZ, DLABAD,
00404      $                   DLACPY, DLARFG, DLASET, DLASUM, DLATM4, DORM2R,
00405      $                   DTGEVC, XERBLA
00406 *     ..
00407 *     .. Intrinsic Functions ..
00408       INTRINSIC          ABS, DBLE, MAX, MIN, SIGN
00409 *     ..
00410 *     .. Data statements ..
00411       DATA               KCLASS / 15*1, 10*2, 1*3 /
00412       DATA               KZ1 / 0, 1, 2, 1, 3, 3 /
00413       DATA               KZ2 / 0, 0, 1, 2, 1, 1 /
00414       DATA               KADD / 0, 0, 0, 0, 3, 2 /
00415       DATA               KATYPE / 0, 1, 0, 1, 2, 3, 4, 1, 4, 4, 1, 1, 4,
00416      $                   4, 4, 2, 4, 5, 8, 7, 9, 4*4, 0 /
00417       DATA               KBTYPE / 0, 0, 1, 1, 2, -3, 1, 4, 1, 1, 4, 4,
00418      $                   1, 1, -4, 2, -4, 8*8, 0 /
00419       DATA               KAZERO / 6*1, 2, 1, 2*2, 2*1, 2*2, 3, 1, 3,
00420      $                   4*5, 4*3, 1 /
00421       DATA               KBZERO / 6*1, 1, 2, 2*1, 2*2, 2*1, 4, 1, 4,
00422      $                   4*6, 4*4, 1 /
00423       DATA               KAMAGN / 8*1, 2, 3, 2, 3, 2, 3, 7*1, 2, 3, 3,
00424      $                   2, 1 /
00425       DATA               KBMAGN / 8*1, 3, 2, 3, 2, 2, 3, 7*1, 3, 2, 3,
00426      $                   2, 1 /
00427       DATA               KTRIAN / 16*0, 10*1 /
00428       DATA               IASIGN / 6*0, 2, 0, 2*2, 2*0, 3*2, 0, 2, 3*0,
00429      $                   5*2, 0 /
00430       DATA               IBSIGN / 7*0, 2, 2*0, 2*2, 2*0, 2, 0, 2, 9*0 /
00431 *     ..
00432 *     .. Executable Statements ..
00433 *
00434 *     Check for errors
00435 *
00436       INFO = 0
00437 *
00438       BADNN = .FALSE.
00439       NMAX = 1
00440       DO 10 J = 1, NSIZES
00441          NMAX = MAX( NMAX, NN( J ) )
00442          IF( NN( J ).LT.0 )
00443      $      BADNN = .TRUE.
00444    10 CONTINUE
00445 *
00446 *     Maximum blocksize and shift -- we assume that blocksize and number
00447 *     of shifts are monotone increasing functions of N.
00448 *
00449       LWKOPT = MAX( 6*NMAX, 2*NMAX*NMAX, 1 )
00450 *
00451 *     Check for errors
00452 *
00453       IF( NSIZES.LT.0 ) THEN
00454          INFO = -1
00455       ELSE IF( BADNN ) THEN
00456          INFO = -2
00457       ELSE IF( NTYPES.LT.0 ) THEN
00458          INFO = -3
00459       ELSE IF( THRESH.LT.ZERO ) THEN
00460          INFO = -6
00461       ELSE IF( LDA.LE.1 .OR. LDA.LT.NMAX ) THEN
00462          INFO = -10
00463       ELSE IF( LDU.LE.1 .OR. LDU.LT.NMAX ) THEN
00464          INFO = -19
00465       ELSE IF( LWKOPT.GT.LWORK ) THEN
00466          INFO = -30
00467       END IF
00468 *
00469       IF( INFO.NE.0 ) THEN
00470          CALL XERBLA( 'DCHKGG', -INFO )
00471          RETURN
00472       END IF
00473 *
00474 *     Quick return if possible
00475 *
00476       IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 )
00477      $   RETURN
00478 *
00479       SAFMIN = DLAMCH( 'Safe minimum' )
00480       ULP = DLAMCH( 'Epsilon' )*DLAMCH( 'Base' )
00481       SAFMIN = SAFMIN / ULP
00482       SAFMAX = ONE / SAFMIN
00483       CALL DLABAD( SAFMIN, SAFMAX )
00484       ULPINV = ONE / ULP
00485 *
00486 *     The values RMAGN(2:3) depend on N, see below.
00487 *
00488       RMAGN( 0 ) = ZERO
00489       RMAGN( 1 ) = ONE
00490 *
00491 *     Loop over sizes, types
00492 *
00493       NTESTT = 0
00494       NERRS = 0
00495       NMATS = 0
00496 *
00497       DO 240 JSIZE = 1, NSIZES
00498          N = NN( JSIZE )
00499          N1 = MAX( 1, N )
00500          RMAGN( 2 ) = SAFMAX*ULP / DBLE( N1 )
00501          RMAGN( 3 ) = SAFMIN*ULPINV*N1
00502 *
00503          IF( NSIZES.NE.1 ) THEN
00504             MTYPES = MIN( MAXTYP, NTYPES )
00505          ELSE
00506             MTYPES = MIN( MAXTYP+1, NTYPES )
00507          END IF
00508 *
00509          DO 230 JTYPE = 1, MTYPES
00510             IF( .NOT.DOTYPE( JTYPE ) )
00511      $         GO TO 230
00512             NMATS = NMATS + 1
00513             NTEST = 0
00514 *
00515 *           Save ISEED in case of an error.
00516 *
00517             DO 20 J = 1, 4
00518                IOLDSD( J ) = ISEED( J )
00519    20       CONTINUE
00520 *
00521 *           Initialize RESULT
00522 *
00523             DO 30 J = 1, 15
00524                RESULT( J ) = ZERO
00525    30       CONTINUE
00526 *
00527 *           Compute A and B
00528 *
00529 *           Description of control parameters:
00530 *
00531 *           KZLASS: =1 means w/o rotation, =2 means w/ rotation,
00532 *                   =3 means random.
00533 *           KATYPE: the "type" to be passed to DLATM4 for computing A.
00534 *           KAZERO: the pattern of zeros on the diagonal for A:
00535 *                   =1: ( xxx ), =2: (0, xxx ) =3: ( 0, 0, xxx, 0 ),
00536 *                   =4: ( 0, xxx, 0, 0 ), =5: ( 0, 0, 1, xxx, 0 ),
00537 *                   =6: ( 0, 1, 0, xxx, 0 ).  (xxx means a string of
00538 *                   non-zero entries.)
00539 *           KAMAGN: the magnitude of the matrix: =0: zero, =1: O(1),
00540 *                   =2: large, =3: small.
00541 *           IASIGN: 1 if the diagonal elements of A are to be
00542 *                   multiplied by a random magnitude 1 number, =2 if
00543 *                   randomly chosen diagonal blocks are to be rotated
00544 *                   to form 2x2 blocks.
00545 *           KBTYPE, KBZERO, KBMAGN, IBSIGN: the same, but for B.
00546 *           KTRIAN: =0: don't fill in the upper triangle, =1: do.
00547 *           KZ1, KZ2, KADD: used to implement KAZERO and KBZERO.
00548 *           RMAGN: used to implement KAMAGN and KBMAGN.
00549 *
00550             IF( MTYPES.GT.MAXTYP )
00551      $         GO TO 110
00552             IINFO = 0
00553             IF( KCLASS( JTYPE ).LT.3 ) THEN
00554 *
00555 *              Generate A (w/o rotation)
00556 *
00557                IF( ABS( KATYPE( JTYPE ) ).EQ.3 ) THEN
00558                   IN = 2*( ( N-1 ) / 2 ) + 1
00559                   IF( IN.NE.N )
00560      $               CALL DLASET( 'Full', N, N, ZERO, ZERO, A, LDA )
00561                ELSE
00562                   IN = N
00563                END IF
00564                CALL DLATM4( KATYPE( JTYPE ), IN, KZ1( KAZERO( JTYPE ) ),
00565      $                      KZ2( KAZERO( JTYPE ) ), IASIGN( JTYPE ),
00566      $                      RMAGN( KAMAGN( JTYPE ) ), ULP,
00567      $                      RMAGN( KTRIAN( JTYPE )*KAMAGN( JTYPE ) ), 2,
00568      $                      ISEED, A, LDA )
00569                IADD = KADD( KAZERO( JTYPE ) )
00570                IF( IADD.GT.0 .AND. IADD.LE.N )
00571      $            A( IADD, IADD ) = RMAGN( KAMAGN( JTYPE ) )
00572 *
00573 *              Generate B (w/o rotation)
00574 *
00575                IF( ABS( KBTYPE( JTYPE ) ).EQ.3 ) THEN
00576                   IN = 2*( ( N-1 ) / 2 ) + 1
00577                   IF( IN.NE.N )
00578      $               CALL DLASET( 'Full', N, N, ZERO, ZERO, B, LDA )
00579                ELSE
00580                   IN = N
00581                END IF
00582                CALL DLATM4( KBTYPE( JTYPE ), IN, KZ1( KBZERO( JTYPE ) ),
00583      $                      KZ2( KBZERO( JTYPE ) ), IBSIGN( JTYPE ),
00584      $                      RMAGN( KBMAGN( JTYPE ) ), ONE,
00585      $                      RMAGN( KTRIAN( JTYPE )*KBMAGN( JTYPE ) ), 2,
00586      $                      ISEED, B, LDA )
00587                IADD = KADD( KBZERO( JTYPE ) )
00588                IF( IADD.NE.0 .AND. IADD.LE.N )
00589      $            B( IADD, IADD ) = RMAGN( KBMAGN( JTYPE ) )
00590 *
00591                IF( KCLASS( JTYPE ).EQ.2 .AND. N.GT.0 ) THEN
00592 *
00593 *                 Include rotations
00594 *
00595 *                 Generate U, V as Householder transformations times
00596 *                 a diagonal matrix.
00597 *
00598                   DO 50 JC = 1, N - 1
00599                      DO 40 JR = JC, N
00600                         U( JR, JC ) = DLARND( 3, ISEED )
00601                         V( JR, JC ) = DLARND( 3, ISEED )
00602    40                CONTINUE
00603                      CALL DLARFG( N+1-JC, U( JC, JC ), U( JC+1, JC ), 1,
00604      $                            WORK( JC ) )
00605                      WORK( 2*N+JC ) = SIGN( ONE, U( JC, JC ) )
00606                      U( JC, JC ) = ONE
00607                      CALL DLARFG( N+1-JC, V( JC, JC ), V( JC+1, JC ), 1,
00608      $                            WORK( N+JC ) )
00609                      WORK( 3*N+JC ) = SIGN( ONE, V( JC, JC ) )
00610                      V( JC, JC ) = ONE
00611    50             CONTINUE
00612                   U( N, N ) = ONE
00613                   WORK( N ) = ZERO
00614                   WORK( 3*N ) = SIGN( ONE, DLARND( 2, ISEED ) )
00615                   V( N, N ) = ONE
00616                   WORK( 2*N ) = ZERO
00617                   WORK( 4*N ) = SIGN( ONE, DLARND( 2, ISEED ) )
00618 *
00619 *                 Apply the diagonal matrices
00620 *
00621                   DO 70 JC = 1, N
00622                      DO 60 JR = 1, N
00623                         A( JR, JC ) = WORK( 2*N+JR )*WORK( 3*N+JC )*
00624      $                                A( JR, JC )
00625                         B( JR, JC ) = WORK( 2*N+JR )*WORK( 3*N+JC )*
00626      $                                B( JR, JC )
00627    60                CONTINUE
00628    70             CONTINUE
00629                   CALL DORM2R( 'L', 'N', N, N, N-1, U, LDU, WORK, A,
00630      $                         LDA, WORK( 2*N+1 ), IINFO )
00631                   IF( IINFO.NE.0 )
00632      $               GO TO 100
00633                   CALL DORM2R( 'R', 'T', N, N, N-1, V, LDU, WORK( N+1 ),
00634      $                         A, LDA, WORK( 2*N+1 ), IINFO )
00635                   IF( IINFO.NE.0 )
00636      $               GO TO 100
00637                   CALL DORM2R( 'L', 'N', N, N, N-1, U, LDU, WORK, B,
00638      $                         LDA, WORK( 2*N+1 ), IINFO )
00639                   IF( IINFO.NE.0 )
00640      $               GO TO 100
00641                   CALL DORM2R( 'R', 'T', N, N, N-1, V, LDU, WORK( N+1 ),
00642      $                         B, LDA, WORK( 2*N+1 ), IINFO )
00643                   IF( IINFO.NE.0 )
00644      $               GO TO 100
00645                END IF
00646             ELSE
00647 *
00648 *              Random matrices
00649 *
00650                DO 90 JC = 1, N
00651                   DO 80 JR = 1, N
00652                      A( JR, JC ) = RMAGN( KAMAGN( JTYPE ) )*
00653      $                             DLARND( 2, ISEED )
00654                      B( JR, JC ) = RMAGN( KBMAGN( JTYPE ) )*
00655      $                             DLARND( 2, ISEED )
00656    80             CONTINUE
00657    90          CONTINUE
00658             END IF
00659 *
00660             ANORM = DLANGE( '1', N, N, A, LDA, WORK )
00661             BNORM = DLANGE( '1', N, N, B, LDA, WORK )
00662 *
00663   100       CONTINUE
00664 *
00665             IF( IINFO.NE.0 ) THEN
00666                WRITE( NOUNIT, FMT = 9999 )'Generator', IINFO, N, JTYPE,
00667      $            IOLDSD
00668                INFO = ABS( IINFO )
00669                RETURN
00670             END IF
00671 *
00672   110       CONTINUE
00673 *
00674 *           Call DGEQR2, DORM2R, and DGGHRD to compute H, T, U, and V
00675 *
00676             CALL DLACPY( ' ', N, N, A, LDA, H, LDA )
00677             CALL DLACPY( ' ', N, N, B, LDA, T, LDA )
00678             NTEST = 1
00679             RESULT( 1 ) = ULPINV
00680 *
00681             CALL DGEQR2( N, N, T, LDA, WORK, WORK( N+1 ), IINFO )
00682             IF( IINFO.NE.0 ) THEN
00683                WRITE( NOUNIT, FMT = 9999 )'DGEQR2', IINFO, N, JTYPE,
00684      $            IOLDSD
00685                INFO = ABS( IINFO )
00686                GO TO 210
00687             END IF
00688 *
00689             CALL DORM2R( 'L', 'T', N, N, N, T, LDA, WORK, H, LDA,
00690      $                   WORK( N+1 ), IINFO )
00691             IF( IINFO.NE.0 ) THEN
00692                WRITE( NOUNIT, FMT = 9999 )'DORM2R', IINFO, N, JTYPE,
00693      $            IOLDSD
00694                INFO = ABS( IINFO )
00695                GO TO 210
00696             END IF
00697 *
00698             CALL DLASET( 'Full', N, N, ZERO, ONE, U, LDU )
00699             CALL DORM2R( 'R', 'N', N, N, N, T, LDA, WORK, U, LDU,
00700      $                   WORK( N+1 ), IINFO )
00701             IF( IINFO.NE.0 ) THEN
00702                WRITE( NOUNIT, FMT = 9999 )'DORM2R', IINFO, N, JTYPE,
00703      $            IOLDSD
00704                INFO = ABS( IINFO )
00705                GO TO 210
00706             END IF
00707 *
00708             CALL DGGHRD( 'V', 'I', N, 1, N, H, LDA, T, LDA, U, LDU, V,
00709      $                   LDU, IINFO )
00710             IF( IINFO.NE.0 ) THEN
00711                WRITE( NOUNIT, FMT = 9999 )'DGGHRD', IINFO, N, JTYPE,
00712      $            IOLDSD
00713                INFO = ABS( IINFO )
00714                GO TO 210
00715             END IF
00716             NTEST = 4
00717 *
00718 *           Do tests 1--4
00719 *
00720             CALL DGET51( 1, N, A, LDA, H, LDA, U, LDU, V, LDU, WORK,
00721      $                   RESULT( 1 ) )
00722             CALL DGET51( 1, N, B, LDA, T, LDA, U, LDU, V, LDU, WORK,
00723      $                   RESULT( 2 ) )
00724             CALL DGET51( 3, N, B, LDA, T, LDA, U, LDU, U, LDU, WORK,
00725      $                   RESULT( 3 ) )
00726             CALL DGET51( 3, N, B, LDA, T, LDA, V, LDU, V, LDU, WORK,
00727      $                   RESULT( 4 ) )
00728 *
00729 *           Call DHGEQZ to compute S1, P1, S2, P2, Q, and Z, do tests.
00730 *
00731 *           Compute T1 and UZ
00732 *
00733 *           Eigenvalues only
00734 *
00735             CALL DLACPY( ' ', N, N, H, LDA, S2, LDA )
00736             CALL DLACPY( ' ', N, N, T, LDA, P2, LDA )
00737             NTEST = 5
00738             RESULT( 5 ) = ULPINV
00739 *
00740             CALL DHGEQZ( 'E', 'N', 'N', N, 1, N, S2, LDA, P2, LDA,
00741      $                   ALPHR3, ALPHI3, BETA3, Q, LDU, Z, LDU, WORK,
00742      $                   LWORK, IINFO )
00743             IF( IINFO.NE.0 ) THEN
00744                WRITE( NOUNIT, FMT = 9999 )'DHGEQZ(E)', IINFO, N, JTYPE,
00745      $            IOLDSD
00746                INFO = ABS( IINFO )
00747                GO TO 210
00748             END IF
00749 *
00750 *           Eigenvalues and Full Schur Form
00751 *
00752             CALL DLACPY( ' ', N, N, H, LDA, S2, LDA )
00753             CALL DLACPY( ' ', N, N, T, LDA, P2, LDA )
00754 *
00755             CALL DHGEQZ( 'S', 'N', 'N', N, 1, N, S2, LDA, P2, LDA,
00756      $                   ALPHR1, ALPHI1, BETA1, Q, LDU, Z, LDU, WORK,
00757      $                   LWORK, IINFO )
00758             IF( IINFO.NE.0 ) THEN
00759                WRITE( NOUNIT, FMT = 9999 )'DHGEQZ(S)', IINFO, N, JTYPE,
00760      $            IOLDSD
00761                INFO = ABS( IINFO )
00762                GO TO 210
00763             END IF
00764 *
00765 *           Eigenvalues, Schur Form, and Schur Vectors
00766 *
00767             CALL DLACPY( ' ', N, N, H, LDA, S1, LDA )
00768             CALL DLACPY( ' ', N, N, T, LDA, P1, LDA )
00769 *
00770             CALL DHGEQZ( 'S', 'I', 'I', N, 1, N, S1, LDA, P1, LDA,
00771      $                   ALPHR1, ALPHI1, BETA1, Q, LDU, Z, LDU, WORK,
00772      $                   LWORK, IINFO )
00773             IF( IINFO.NE.0 ) THEN
00774                WRITE( NOUNIT, FMT = 9999 )'DHGEQZ(V)', IINFO, N, JTYPE,
00775      $            IOLDSD
00776                INFO = ABS( IINFO )
00777                GO TO 210
00778             END IF
00779 *
00780             NTEST = 8
00781 *
00782 *           Do Tests 5--8
00783 *
00784             CALL DGET51( 1, N, H, LDA, S1, LDA, Q, LDU, Z, LDU, WORK,
00785      $                   RESULT( 5 ) )
00786             CALL DGET51( 1, N, T, LDA, P1, LDA, Q, LDU, Z, LDU, WORK,
00787      $                   RESULT( 6 ) )
00788             CALL DGET51( 3, N, T, LDA, P1, LDA, Q, LDU, Q, LDU, WORK,
00789      $                   RESULT( 7 ) )
00790             CALL DGET51( 3, N, T, LDA, P1, LDA, Z, LDU, Z, LDU, WORK,
00791      $                   RESULT( 8 ) )
00792 *
00793 *           Compute the Left and Right Eigenvectors of (S1,P1)
00794 *
00795 *           9: Compute the left eigenvector Matrix without
00796 *              back transforming:
00797 *
00798             NTEST = 9
00799             RESULT( 9 ) = ULPINV
00800 *
00801 *           To test "SELECT" option, compute half of the eigenvectors
00802 *           in one call, and half in another
00803 *
00804             I1 = N / 2
00805             DO 120 J = 1, I1
00806                LLWORK( J ) = .TRUE.
00807   120       CONTINUE
00808             DO 130 J = I1 + 1, N
00809                LLWORK( J ) = .FALSE.
00810   130       CONTINUE
00811 *
00812             CALL DTGEVC( 'L', 'S', LLWORK, N, S1, LDA, P1, LDA, EVECTL,
00813      $                   LDU, DUMMA, LDU, N, IN, WORK, IINFO )
00814             IF( IINFO.NE.0 ) THEN
00815                WRITE( NOUNIT, FMT = 9999 )'DTGEVC(L,S1)', IINFO, N,
00816      $            JTYPE, IOLDSD
00817                INFO = ABS( IINFO )
00818                GO TO 210
00819             END IF
00820 *
00821             I1 = IN
00822             DO 140 J = 1, I1
00823                LLWORK( J ) = .FALSE.
00824   140       CONTINUE
00825             DO 150 J = I1 + 1, N
00826                LLWORK( J ) = .TRUE.
00827   150       CONTINUE
00828 *
00829             CALL DTGEVC( 'L', 'S', LLWORK, N, S1, LDA, P1, LDA,
00830      $                   EVECTL( 1, I1+1 ), LDU, DUMMA, LDU, N, IN,
00831      $                   WORK, IINFO )
00832             IF( IINFO.NE.0 ) THEN
00833                WRITE( NOUNIT, FMT = 9999 )'DTGEVC(L,S2)', IINFO, N,
00834      $            JTYPE, IOLDSD
00835                INFO = ABS( IINFO )
00836                GO TO 210
00837             END IF
00838 *
00839             CALL DGET52( .TRUE., N, S1, LDA, P1, LDA, EVECTL, LDU,
00840      $                   ALPHR1, ALPHI1, BETA1, WORK, DUMMA( 1 ) )
00841             RESULT( 9 ) = DUMMA( 1 )
00842             IF( DUMMA( 2 ).GT.THRSHN ) THEN
00843                WRITE( NOUNIT, FMT = 9998 )'Left', 'DTGEVC(HOWMNY=S)',
00844      $            DUMMA( 2 ), N, JTYPE, IOLDSD
00845             END IF
00846 *
00847 *           10: Compute the left eigenvector Matrix with
00848 *               back transforming:
00849 *
00850             NTEST = 10
00851             RESULT( 10 ) = ULPINV
00852             CALL DLACPY( 'F', N, N, Q, LDU, EVECTL, LDU )
00853             CALL DTGEVC( 'L', 'B', LLWORK, N, S1, LDA, P1, LDA, EVECTL,
00854      $                   LDU, DUMMA, LDU, N, IN, WORK, IINFO )
00855             IF( IINFO.NE.0 ) THEN
00856                WRITE( NOUNIT, FMT = 9999 )'DTGEVC(L,B)', IINFO, N,
00857      $            JTYPE, IOLDSD
00858                INFO = ABS( IINFO )
00859                GO TO 210
00860             END IF
00861 *
00862             CALL DGET52( .TRUE., N, H, LDA, T, LDA, EVECTL, LDU, ALPHR1,
00863      $                   ALPHI1, BETA1, WORK, DUMMA( 1 ) )
00864             RESULT( 10 ) = DUMMA( 1 )
00865             IF( DUMMA( 2 ).GT.THRSHN ) THEN
00866                WRITE( NOUNIT, FMT = 9998 )'Left', 'DTGEVC(HOWMNY=B)',
00867      $            DUMMA( 2 ), N, JTYPE, IOLDSD
00868             END IF
00869 *
00870 *           11: Compute the right eigenvector Matrix without
00871 *               back transforming:
00872 *
00873             NTEST = 11
00874             RESULT( 11 ) = ULPINV
00875 *
00876 *           To test "SELECT" option, compute half of the eigenvectors
00877 *           in one call, and half in another
00878 *
00879             I1 = N / 2
00880             DO 160 J = 1, I1
00881                LLWORK( J ) = .TRUE.
00882   160       CONTINUE
00883             DO 170 J = I1 + 1, N
00884                LLWORK( J ) = .FALSE.
00885   170       CONTINUE
00886 *
00887             CALL DTGEVC( 'R', 'S', LLWORK, N, S1, LDA, P1, LDA, DUMMA,
00888      $                   LDU, EVECTR, LDU, N, IN, WORK, IINFO )
00889             IF( IINFO.NE.0 ) THEN
00890                WRITE( NOUNIT, FMT = 9999 )'DTGEVC(R,S1)', IINFO, N,
00891      $            JTYPE, IOLDSD
00892                INFO = ABS( IINFO )
00893                GO TO 210
00894             END IF
00895 *
00896             I1 = IN
00897             DO 180 J = 1, I1
00898                LLWORK( J ) = .FALSE.
00899   180       CONTINUE
00900             DO 190 J = I1 + 1, N
00901                LLWORK( J ) = .TRUE.
00902   190       CONTINUE
00903 *
00904             CALL DTGEVC( 'R', 'S', LLWORK, N, S1, LDA, P1, LDA, DUMMA,
00905      $                   LDU, EVECTR( 1, I1+1 ), LDU, N, IN, WORK,
00906      $                   IINFO )
00907             IF( IINFO.NE.0 ) THEN
00908                WRITE( NOUNIT, FMT = 9999 )'DTGEVC(R,S2)', IINFO, N,
00909      $            JTYPE, IOLDSD
00910                INFO = ABS( IINFO )
00911                GO TO 210
00912             END IF
00913 *
00914             CALL DGET52( .FALSE., N, S1, LDA, P1, LDA, EVECTR, LDU,
00915      $                   ALPHR1, ALPHI1, BETA1, WORK, DUMMA( 1 ) )
00916             RESULT( 11 ) = DUMMA( 1 )
00917             IF( DUMMA( 2 ).GT.THRESH ) THEN
00918                WRITE( NOUNIT, FMT = 9998 )'Right', 'DTGEVC(HOWMNY=S)',
00919      $            DUMMA( 2 ), N, JTYPE, IOLDSD
00920             END IF
00921 *
00922 *           12: Compute the right eigenvector Matrix with
00923 *               back transforming:
00924 *
00925             NTEST = 12
00926             RESULT( 12 ) = ULPINV
00927             CALL DLACPY( 'F', N, N, Z, LDU, EVECTR, LDU )
00928             CALL DTGEVC( 'R', 'B', LLWORK, N, S1, LDA, P1, LDA, DUMMA,
00929      $                   LDU, EVECTR, LDU, N, IN, WORK, IINFO )
00930             IF( IINFO.NE.0 ) THEN
00931                WRITE( NOUNIT, FMT = 9999 )'DTGEVC(R,B)', IINFO, N,
00932      $            JTYPE, IOLDSD
00933                INFO = ABS( IINFO )
00934                GO TO 210
00935             END IF
00936 *
00937             CALL DGET52( .FALSE., N, H, LDA, T, LDA, EVECTR, LDU,
00938      $                   ALPHR1, ALPHI1, BETA1, WORK, DUMMA( 1 ) )
00939             RESULT( 12 ) = DUMMA( 1 )
00940             IF( DUMMA( 2 ).GT.THRESH ) THEN
00941                WRITE( NOUNIT, FMT = 9998 )'Right', 'DTGEVC(HOWMNY=B)',
00942      $            DUMMA( 2 ), N, JTYPE, IOLDSD
00943             END IF
00944 *
00945 *           Tests 13--15 are done only on request
00946 *
00947             IF( TSTDIF ) THEN
00948 *
00949 *              Do Tests 13--14
00950 *
00951                CALL DGET51( 2, N, S1, LDA, S2, LDA, Q, LDU, Z, LDU,
00952      $                      WORK, RESULT( 13 ) )
00953                CALL DGET51( 2, N, P1, LDA, P2, LDA, Q, LDU, Z, LDU,
00954      $                      WORK, RESULT( 14 ) )
00955 *
00956 *              Do Test 15
00957 *
00958                TEMP1 = ZERO
00959                TEMP2 = ZERO
00960                DO 200 J = 1, N
00961                   TEMP1 = MAX( TEMP1, ABS( ALPHR1( J )-ALPHR3( J ) )+
00962      $                    ABS( ALPHI1( J )-ALPHI3( J ) ) )
00963                   TEMP2 = MAX( TEMP2, ABS( BETA1( J )-BETA3( J ) ) )
00964   200          CONTINUE
00965 *
00966                TEMP1 = TEMP1 / MAX( SAFMIN, ULP*MAX( TEMP1, ANORM ) )
00967                TEMP2 = TEMP2 / MAX( SAFMIN, ULP*MAX( TEMP2, BNORM ) )
00968                RESULT( 15 ) = MAX( TEMP1, TEMP2 )
00969                NTEST = 15
00970             ELSE
00971                RESULT( 13 ) = ZERO
00972                RESULT( 14 ) = ZERO
00973                RESULT( 15 ) = ZERO
00974                NTEST = 12
00975             END IF
00976 *
00977 *           End of Loop -- Check for RESULT(j) > THRESH
00978 *
00979   210       CONTINUE
00980 *
00981             NTESTT = NTESTT + NTEST
00982 *
00983 *           Print out tests which fail.
00984 *
00985             DO 220 JR = 1, NTEST
00986                IF( RESULT( JR ).GE.THRESH ) THEN
00987 *
00988 *                 If this is the first test to fail,
00989 *                 print a header to the data file.
00990 *
00991                   IF( NERRS.EQ.0 ) THEN
00992                      WRITE( NOUNIT, FMT = 9997 )'DGG'
00993 *
00994 *                    Matrix types
00995 *
00996                      WRITE( NOUNIT, FMT = 9996 )
00997                      WRITE( NOUNIT, FMT = 9995 )
00998                      WRITE( NOUNIT, FMT = 9994 )'Orthogonal'
00999 *
01000 *                    Tests performed
01001 *
01002                      WRITE( NOUNIT, FMT = 9993 )'orthogonal', '''',
01003      $                  'transpose', ( '''', J = 1, 10 )
01004 *
01005                   END IF
01006                   NERRS = NERRS + 1
01007                   IF( RESULT( JR ).LT.10000.0D0 ) THEN
01008                      WRITE( NOUNIT, FMT = 9992 )N, JTYPE, IOLDSD, JR,
01009      $                  RESULT( JR )
01010                   ELSE
01011                      WRITE( NOUNIT, FMT = 9991 )N, JTYPE, IOLDSD, JR,
01012      $                  RESULT( JR )
01013                   END IF
01014                END IF
01015   220       CONTINUE
01016 *
01017   230    CONTINUE
01018   240 CONTINUE
01019 *
01020 *     Summary
01021 *
01022       CALL DLASUM( 'DGG', NOUNIT, NERRS, NTESTT )
01023       RETURN
01024 *
01025  9999 FORMAT( ' DCHKGG: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
01026      $      I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' )
01027 *
01028  9998 FORMAT( ' DCHKGG: ', A, ' Eigenvectors from ', A, ' incorrectly ',
01029      $      'normalized.', / ' Bits of error=', 0P, G10.3, ',', 9X,
01030      $      'N=', I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5,
01031      $      ')' )
01032 *
01033  9997 FORMAT( / 1X, A3, ' -- Real Generalized eigenvalue problem' )
01034 *
01035  9996 FORMAT( ' Matrix types (see DCHKGG for details): ' )
01036 *
01037  9995 FORMAT( ' Special Matrices:', 23X,
01038      $      '(J''=transposed Jordan block)',
01039      $      / '   1=(0,0)  2=(I,0)  3=(0,I)  4=(I,I)  5=(J'',J'')  ',
01040      $      '6=(diag(J'',I), diag(I,J''))', / ' Diagonal Matrices:  ( ',
01041      $      'D=diag(0,1,2,...) )', / '   7=(D,I)   9=(large*D, small*I',
01042      $      ')  11=(large*I, small*D)  13=(large*D, large*I)', /
01043      $      '   8=(I,D)  10=(small*D, large*I)  12=(small*I, large*D) ',
01044      $      ' 14=(small*D, small*I)', / '  15=(D, reversed D)' )
01045  9994 FORMAT( ' Matrices Rotated by Random ', A, ' Matrices U, V:',
01046      $      / '  16=Transposed Jordan Blocks             19=geometric ',
01047      $      'alpha, beta=0,1', / '  17=arithm. alpha&beta             ',
01048      $      '      20=arithmetic alpha, beta=0,1', / '  18=clustered ',
01049      $      'alpha, beta=0,1            21=random alpha, beta=0,1',
01050      $      / ' Large & Small Matrices:', / '  22=(large, small)   ',
01051      $      '23=(small,large)    24=(small,small)    25=(large,large)',
01052      $      / '  26=random O(1) matrices.' )
01053 *
01054  9993 FORMAT( / ' Tests performed:   (H is Hessenberg, S is Schur, B, ',
01055      $      'T, P are triangular,', / 20X, 'U, V, Q, and Z are ', A,
01056      $      ', l and r are the', / 20X,
01057      $      'appropriate left and right eigenvectors, resp., a is',
01058      $      / 20X, 'alpha, b is beta, and ', A, ' means ', A, '.)',
01059      $      / ' 1 = | A - U H V', A,
01060      $      ' | / ( |A| n ulp )      2 = | B - U T V', A,
01061      $      ' | / ( |B| n ulp )', / ' 3 = | I - UU', A,
01062      $      ' | / ( n ulp )             4 = | I - VV', A,
01063      $      ' | / ( n ulp )', / ' 5 = | H - Q S Z', A,
01064      $      ' | / ( |H| n ulp )', 6X, '6 = | T - Q P Z', A,
01065      $      ' | / ( |T| n ulp )', / ' 7 = | I - QQ', A,
01066      $      ' | / ( n ulp )             8 = | I - ZZ', A,
01067      $      ' | / ( n ulp )', / ' 9 = max | ( b S - a P )', A,
01068      $      ' l | / const.  10 = max | ( b H - a T )', A,
01069      $      ' l | / const.', /
01070      $      ' 11= max | ( b S - a P ) r | / const.   12 = max | ( b H',
01071      $      ' - a T ) r | / const.', / 1X )
01072 *
01073  9992 FORMAT( ' Matrix order=', I5, ', type=', I2, ', seed=',
01074      $      4( I4, ',' ), ' result ', I2, ' is', 0P, F8.2 )
01075  9991 FORMAT( ' Matrix order=', I5, ', type=', I2, ', seed=',
01076      $      4( I4, ',' ), ' result ', I2, ' is', 1P, D10.3 )
01077 *
01078 *     End of DCHKGG
01079 *
01080       END