LAPACK 3.3.1 Linear Algebra PACKage

# ddrves.f

Go to the documentation of this file.
```00001       SUBROUTINE DDRVES( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
00002      \$                   NOUNIT, A, LDA, H, HT, WR, WI, WRT, WIT, VS,
00003      \$                   LDVS, RESULT, WORK, NWORK, IWORK, BWORK, INFO )
00004 *
00005 *  -- LAPACK test routine (version 3.1) --
00006 *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
00007 *     November 2006
00008 *
00009 *     .. Scalar Arguments ..
00010       INTEGER            INFO, LDA, LDVS, NOUNIT, NSIZES, NTYPES, NWORK
00011       DOUBLE PRECISION   THRESH
00012 *     ..
00013 *     .. Array Arguments ..
00014       LOGICAL            BWORK( * ), DOTYPE( * )
00015       INTEGER            ISEED( 4 ), IWORK( * ), NN( * )
00016       DOUBLE PRECISION   A( LDA, * ), H( LDA, * ), HT( LDA, * ),
00017      \$                   RESULT( 13 ), VS( LDVS, * ), WI( * ), WIT( * ),
00018      \$                   WORK( * ), WR( * ), WRT( * )
00019 *     ..
00020 *
00021 *  Purpose
00022 *  =======
00023 *
00024 *     DDRVES checks the nonsymmetric eigenvalue (Schur form) problem
00025 *     driver DGEES.
00026 *
00027 *     When DDRVES is called, a number of matrix "sizes" ("n's") and a
00028 *     number of matrix "types" are specified.  For each size ("n")
00029 *     and each type of matrix, one matrix will be generated and used
00030 *     to test the nonsymmetric eigenroutines.  For each matrix, 13
00031 *     tests will be performed:
00032 *
00033 *     (1)     0 if T is in Schur form, 1/ulp otherwise
00034 *            (no sorting of eigenvalues)
00035 *
00036 *     (2)     | A - VS T VS' | / ( n |A| ulp )
00037 *
00038 *       Here VS is the matrix of Schur eigenvectors, and T is in Schur
00039 *       form  (no sorting of eigenvalues).
00040 *
00041 *     (3)     | I - VS VS' | / ( n ulp ) (no sorting of eigenvalues).
00042 *
00043 *     (4)     0     if WR+sqrt(-1)*WI are eigenvalues of T
00044 *             1/ulp otherwise
00045 *             (no sorting of eigenvalues)
00046 *
00047 *     (5)     0     if T(with VS) = T(without VS),
00048 *             1/ulp otherwise
00049 *             (no sorting of eigenvalues)
00050 *
00051 *     (6)     0     if eigenvalues(with VS) = eigenvalues(without VS),
00052 *             1/ulp otherwise
00053 *             (no sorting of eigenvalues)
00054 *
00055 *     (7)     0 if T is in Schur form, 1/ulp otherwise
00056 *             (with sorting of eigenvalues)
00057 *
00058 *     (8)     | A - VS T VS' | / ( n |A| ulp )
00059 *
00060 *       Here VS is the matrix of Schur eigenvectors, and T is in Schur
00061 *       form  (with sorting of eigenvalues).
00062 *
00063 *     (9)     | I - VS VS' | / ( n ulp ) (with sorting of eigenvalues).
00064 *
00065 *     (10)    0     if WR+sqrt(-1)*WI are eigenvalues of T
00066 *             1/ulp otherwise
00067 *             (with sorting of eigenvalues)
00068 *
00069 *     (11)    0     if T(with VS) = T(without VS),
00070 *             1/ulp otherwise
00071 *             (with sorting of eigenvalues)
00072 *
00073 *     (12)    0     if eigenvalues(with VS) = eigenvalues(without VS),
00074 *             1/ulp otherwise
00075 *             (with sorting of eigenvalues)
00076 *
00077 *     (13)    if sorting worked and SDIM is the number of
00078 *             eigenvalues which were SELECTed
00079 *
00080 *     The "sizes" are specified by an array NN(1:NSIZES); the value of
00081 *     each element NN(j) specifies one size.
00082 *     The "types" are specified by a logical array DOTYPE( 1:NTYPES );
00083 *     if DOTYPE(j) is .TRUE., then matrix type "j" will be generated.
00084 *     Currently, the list of possible types is:
00085 *
00086 *     (1)  The zero matrix.
00087 *     (2)  The identity matrix.
00088 *     (3)  A (transposed) Jordan block, with 1's on the diagonal.
00089 *
00090 *     (4)  A diagonal matrix with evenly spaced entries
00091 *          1, ..., ULP  and random signs.
00092 *          (ULP = (first number larger than 1) - 1 )
00093 *     (5)  A diagonal matrix with geometrically spaced entries
00094 *          1, ..., ULP  and random signs.
00095 *     (6)  A diagonal matrix with "clustered" entries 1, ULP, ..., ULP
00096 *          and random signs.
00097 *
00098 *     (7)  Same as (4), but multiplied by a constant near
00099 *          the overflow threshold
00100 *     (8)  Same as (4), but multiplied by a constant near
00101 *          the underflow threshold
00102 *
00103 *     (9)  A matrix of the form  U' T U, where U is orthogonal and
00104 *          T has evenly spaced entries 1, ..., ULP with random signs
00105 *          on the diagonal and random O(1) entries in the upper
00106 *          triangle.
00107 *
00108 *     (10) A matrix of the form  U' T U, where U is orthogonal and
00109 *          T has geometrically spaced entries 1, ..., ULP with random
00110 *          signs on the diagonal and random O(1) entries in the upper
00111 *          triangle.
00112 *
00113 *     (11) A matrix of the form  U' T U, where U is orthogonal and
00114 *          T has "clustered" entries 1, ULP,..., ULP with random
00115 *          signs on the diagonal and random O(1) entries in the upper
00116 *          triangle.
00117 *
00118 *     (12) A matrix of the form  U' T U, where U is orthogonal and
00119 *          T has real or complex conjugate paired eigenvalues randomly
00120 *          chosen from ( ULP, 1 ) and random O(1) entries in the upper
00121 *          triangle.
00122 *
00123 *     (13) A matrix of the form  X' T X, where X has condition
00124 *          SQRT( ULP ) and T has evenly spaced entries 1, ..., ULP
00125 *          with random signs on the diagonal and random O(1) entries
00126 *          in the upper triangle.
00127 *
00128 *     (14) A matrix of the form  X' T X, where X has condition
00129 *          SQRT( ULP ) and T has geometrically spaced entries
00130 *          1, ..., ULP with random signs on the diagonal and random
00131 *          O(1) entries in the upper triangle.
00132 *
00133 *     (15) A matrix of the form  X' T X, where X has condition
00134 *          SQRT( ULP ) and T has "clustered" entries 1, ULP,..., ULP
00135 *          with random signs on the diagonal and random O(1) entries
00136 *          in the upper triangle.
00137 *
00138 *     (16) A matrix of the form  X' T X, where X has condition
00139 *          SQRT( ULP ) and T has real or complex conjugate paired
00140 *          eigenvalues randomly chosen from ( ULP, 1 ) and random
00141 *          O(1) entries in the upper triangle.
00142 *
00143 *     (17) Same as (16), but multiplied by a constant
00144 *          near the overflow threshold
00145 *     (18) Same as (16), but multiplied by a constant
00146 *          near the underflow threshold
00147 *
00148 *     (19) Nonsymmetric matrix with random entries chosen from (-1,1).
00149 *          If N is at least 4, all entries in first two rows and last
00150 *          row, and first column and last two columns are zero.
00151 *     (20) Same as (19), but multiplied by a constant
00152 *          near the overflow threshold
00153 *     (21) Same as (19), but multiplied by a constant
00154 *          near the underflow threshold
00155 *
00156 *  Arguments
00157 *  =========
00158 *
00159 *  NSIZES  (input) INTEGER
00160 *          The number of sizes of matrices to use.  If it is zero,
00161 *          DDRVES does nothing.  It must be at least zero.
00162 *
00163 *  NN      (input) INTEGER array, dimension (NSIZES)
00164 *          An array containing the sizes to be used for the matrices.
00165 *          Zero values will be skipped.  The values must be at least
00166 *          zero.
00167 *
00168 *  NTYPES  (input) INTEGER
00169 *          The number of elements in DOTYPE.   If it is zero, DDRVES
00170 *          does nothing.  It must be at least zero.  If it is MAXTYP+1
00171 *          and NSIZES is 1, then an additional type, MAXTYP+1 is
00172 *          defined, which is to use whatever matrix is in A.  This
00173 *          is only useful if DOTYPE(1:MAXTYP) is .FALSE. and
00174 *          DOTYPE(MAXTYP+1) is .TRUE. .
00175 *
00176 *  DOTYPE  (input) LOGICAL array, dimension (NTYPES)
00177 *          If DOTYPE(j) is .TRUE., then for each size in NN a
00178 *          matrix of that size and of type j will be generated.
00179 *          If NTYPES is smaller than the maximum number of types
00180 *          defined (PARAMETER MAXTYP), then types NTYPES+1 through
00181 *          MAXTYP will not be generated.  If NTYPES is larger
00182 *          than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES)
00183 *          will be ignored.
00184 *
00185 *  ISEED   (input/output) INTEGER array, dimension (4)
00186 *          On entry ISEED specifies the seed of the random number
00187 *          generator. The array elements should be between 0 and 4095;
00188 *          if not they will be reduced mod 4096.  Also, ISEED(4) must
00189 *          be odd.  The random number generator uses a linear
00190 *          congruential sequence limited to small integers, and so
00191 *          should produce machine independent random numbers. The
00192 *          values of ISEED are changed on exit, and can be used in the
00193 *          next call to DDRVES to continue the same random number
00194 *          sequence.
00195 *
00196 *  THRESH  (input) DOUBLE PRECISION
00197 *          A test will count as "failed" if the "error", computed as
00198 *          described above, exceeds THRESH.  Note that the error
00199 *          is scaled to be O(1), so THRESH should be a reasonably
00200 *          small multiple of 1, e.g., 10 or 100.  In particular,
00201 *          it should not depend on the precision (single vs. double)
00202 *          or the size of the matrix.  It must be at least zero.
00203 *
00204 *  NOUNIT  (input) INTEGER
00205 *          The FORTRAN unit number for printing out error messages
00206 *          (e.g., if a routine returns INFO not equal to 0.)
00207 *
00208 *  A       (workspace) DOUBLE PRECISION array, dimension (LDA, max(NN))
00209 *          Used to hold the matrix whose eigenvalues are to be
00210 *          computed.  On exit, A contains the last matrix actually used.
00211 *
00212 *  LDA     (input) INTEGER
00213 *          The leading dimension of A, and H. LDA must be at
00214 *          least 1 and at least max(NN).
00215 *
00216 *  H       (workspace) DOUBLE PRECISION array, dimension (LDA, max(NN))
00217 *          Another copy of the test matrix A, modified by DGEES.
00218 *
00219 *  HT      (workspace) DOUBLE PRECISION array, dimension (LDA, max(NN))
00220 *          Yet another copy of the test matrix A, modified by DGEES.
00221 *
00222 *  WR      (workspace) DOUBLE PRECISION array, dimension (max(NN))
00223 *  WI      (workspace) DOUBLE PRECISION array, dimension (max(NN))
00224 *          The real and imaginary parts of the eigenvalues of A.
00225 *          On exit, WR + WI*i are the eigenvalues of the matrix in A.
00226 *
00227 *  WRT     (workspace) DOUBLE PRECISION array, dimension (max(NN))
00228 *  WIT     (workspace) DOUBLE PRECISION array, dimension (max(NN))
00229 *          Like WR, WI, these arrays contain the eigenvalues of A,
00230 *          but those computed when DGEES only computes a partial
00231 *          eigendecomposition, i.e. not Schur vectors
00232 *
00233 *  VS      (workspace) DOUBLE PRECISION array, dimension (LDVS, max(NN))
00234 *          VS holds the computed Schur vectors.
00235 *
00236 *  LDVS    (input) INTEGER
00237 *          Leading dimension of VS. Must be at least max(1,max(NN)).
00238 *
00239 *  RESULT  (output) DOUBLE PRECISION array, dimension (13)
00240 *          The values computed by the 13 tests described above.
00241 *          The values are currently limited to 1/ulp, to avoid overflow.
00242 *
00243 *  WORK    (workspace) DOUBLE PRECISION array, dimension (NWORK)
00244 *
00245 *  NWORK   (input) INTEGER
00246 *          The number of entries in WORK.  This must be at least
00247 *          5*NN(j)+2*NN(j)**2 for all j.
00248 *
00249 *  IWORK   (workspace) INTEGER array, dimension (max(NN))
00250 *
00251 *  INFO    (output) INTEGER
00252 *          If 0, then everything ran OK.
00253 *           -1: NSIZES < 0
00254 *           -2: Some NN(j) < 0
00255 *           -3: NTYPES < 0
00256 *           -6: THRESH < 0
00257 *           -9: LDA < 1 or LDA < NMAX, where NMAX is max( NN(j) ).
00258 *          -17: LDVS < 1 or LDVS < NMAX, where NMAX is max( NN(j) ).
00259 *          -20: NWORK too small.
00260 *          If  DLATMR, SLATMS, SLATME or DGEES returns an error code,
00261 *              the absolute value of it is returned.
00262 *
00263 *-----------------------------------------------------------------------
00264 *
00265 *     Some Local Variables and Parameters:
00266 *     ---- ----- --------- --- ----------
00267 *
00268 *     ZERO, ONE       Real 0 and 1.
00269 *     MAXTYP          The number of types defined.
00270 *     NMAX            Largest value in NN.
00271 *     NERRS           The number of tests which have exceeded THRESH
00272 *     COND, CONDS,
00273 *     IMODE           Values to be passed to the matrix generators.
00274 *     ANORM           Norm of A; passed to matrix generators.
00275 *
00276 *     OVFL, UNFL      Overflow and underflow thresholds.
00277 *     ULP, ULPINV     Finest relative precision and its inverse.
00278 *     RTULP, RTULPI   Square roots of the previous 4 values.
00279 *
00280 *             The following four arrays decode JTYPE:
00281 *     KTYPE(j)        The general type (1-10) for type "j".
00282 *     KMODE(j)        The MODE value to be passed to the matrix
00283 *                     generator for type "j".
00284 *     KMAGN(j)        The order of magnitude ( O(1),
00285 *                     O(overflow^(1/2) ), O(underflow^(1/2) )
00286 *     KCONDS(j)       Selectw whether CONDS is to be 1 or
00287 *                     1/sqrt(ulp).  (0 means irrelevant.)
00288 *
00289 *  =====================================================================
00290 *
00291 *     .. Parameters ..
00292       DOUBLE PRECISION   ZERO, ONE
00293       PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
00294       INTEGER            MAXTYP
00295       PARAMETER          ( MAXTYP = 21 )
00296 *     ..
00297 *     .. Local Scalars ..
00299       CHARACTER          SORT
00300       CHARACTER*3        PATH
00301       INTEGER            I, IINFO, IMODE, ISORT, ITYPE, IWK, J, JCOL,
00302      \$                   JSIZE, JTYPE, KNTEIG, LWORK, MTYPES, N, NERRS,
00303      \$                   NFAIL, NMAX, NNWORK, NTEST, NTESTF, NTESTT,
00304      \$                   RSUB, SDIM
00305       DOUBLE PRECISION   ANORM, COND, CONDS, OVFL, RTULP, RTULPI, TMP,
00306      \$                   ULP, ULPINV, UNFL
00307 *     ..
00308 *     .. Local Arrays ..
00310       INTEGER            IDUMMA( 1 ), IOLDSD( 4 ), KCONDS( MAXTYP ),
00311      \$                   KMAGN( MAXTYP ), KMODE( MAXTYP ),
00312      \$                   KTYPE( MAXTYP )
00313       DOUBLE PRECISION   RES( 2 )
00314 *     ..
00315 *     .. Arrays in Common ..
00316       LOGICAL            SELVAL( 20 )
00317       DOUBLE PRECISION   SELWI( 20 ), SELWR( 20 )
00318 *     ..
00319 *     .. Scalars in Common ..
00320       INTEGER            SELDIM, SELOPT
00321 *     ..
00322 *     .. Common blocks ..
00323       COMMON             / SSLCT / SELOPT, SELDIM, SELVAL, SELWR, SELWI
00324 *     ..
00325 *     .. External Functions ..
00326       LOGICAL            DSLECT
00327       DOUBLE PRECISION   DLAMCH
00328       EXTERNAL           DSLECT, DLAMCH
00329 *     ..
00330 *     .. External Subroutines ..
00331       EXTERNAL           DGEES, DHST01, DLABAD, DLACPY, DLASET, DLASUM,
00332      \$                   DLATME, DLATMR, DLATMS, XERBLA
00333 *     ..
00334 *     .. Intrinsic Functions ..
00335       INTRINSIC          ABS, MAX, SIGN, SQRT
00336 *     ..
00337 *     .. Data statements ..
00338       DATA               KTYPE / 1, 2, 3, 5*4, 4*6, 6*6, 3*9 /
00339       DATA               KMAGN / 3*1, 1, 1, 1, 2, 3, 4*1, 1, 1, 1, 1, 2,
00340      \$                   3, 1, 2, 3 /
00341       DATA               KMODE / 3*0, 4, 3, 1, 4, 4, 4, 3, 1, 5, 4, 3,
00342      \$                   1, 5, 5, 5, 4, 3, 1 /
00343       DATA               KCONDS / 3*0, 5*0, 4*1, 6*2, 3*0 /
00344 *     ..
00345 *     .. Executable Statements ..
00346 *
00347       PATH( 1: 1 ) = 'Double precision'
00348       PATH( 2: 3 ) = 'ES'
00349 *
00350 *     Check for errors
00351 *
00352       NTESTT = 0
00353       NTESTF = 0
00354       INFO = 0
00355       SELOPT = 0
00356 *
00357 *     Important constants
00358 *
00360       NMAX = 0
00361       DO 10 J = 1, NSIZES
00362          NMAX = MAX( NMAX, NN( J ) )
00363          IF( NN( J ).LT.0 )
00365    10 CONTINUE
00366 *
00367 *     Check for errors
00368 *
00369       IF( NSIZES.LT.0 ) THEN
00370          INFO = -1
00371       ELSE IF( BADNN ) THEN
00372          INFO = -2
00373       ELSE IF( NTYPES.LT.0 ) THEN
00374          INFO = -3
00375       ELSE IF( THRESH.LT.ZERO ) THEN
00376          INFO = -6
00377       ELSE IF( NOUNIT.LE.0 ) THEN
00378          INFO = -7
00379       ELSE IF( LDA.LT.1 .OR. LDA.LT.NMAX ) THEN
00380          INFO = -9
00381       ELSE IF( LDVS.LT.1 .OR. LDVS.LT.NMAX ) THEN
00382          INFO = -17
00383       ELSE IF( 5*NMAX+2*NMAX**2.GT.NWORK ) THEN
00384          INFO = -20
00385       END IF
00386 *
00387       IF( INFO.NE.0 ) THEN
00388          CALL XERBLA( 'DDRVES', -INFO )
00389          RETURN
00390       END IF
00391 *
00392 *     Quick return if nothing to do
00393 *
00394       IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 )
00395      \$   RETURN
00396 *
00397 *     More Important constants
00398 *
00399       UNFL = DLAMCH( 'Safe minimum' )
00400       OVFL = ONE / UNFL
00401       CALL DLABAD( UNFL, OVFL )
00402       ULP = DLAMCH( 'Precision' )
00403       ULPINV = ONE / ULP
00404       RTULP = SQRT( ULP )
00405       RTULPI = ONE / RTULP
00406 *
00407 *     Loop over sizes, types
00408 *
00409       NERRS = 0
00410 *
00411       DO 270 JSIZE = 1, NSIZES
00412          N = NN( JSIZE )
00413          MTYPES = MAXTYP
00414          IF( NSIZES.EQ.1 .AND. NTYPES.EQ.MAXTYP+1 )
00415      \$      MTYPES = MTYPES + 1
00416 *
00417          DO 260 JTYPE = 1, MTYPES
00418             IF( .NOT.DOTYPE( JTYPE ) )
00419      \$         GO TO 260
00420 *
00421 *           Save ISEED in case of an error.
00422 *
00423             DO 20 J = 1, 4
00424                IOLDSD( J ) = ISEED( J )
00425    20       CONTINUE
00426 *
00427 *           Compute "A"
00428 *
00429 *           Control parameters:
00430 *
00431 *           KMAGN  KCONDS  KMODE        KTYPE
00432 *       =1  O(1)   1       clustered 1  zero
00433 *       =2  large  large   clustered 2  identity
00434 *       =3  small          exponential  Jordan
00435 *       =4                 arithmetic   diagonal, (w/ eigenvalues)
00436 *       =5                 random log   symmetric, w/ eigenvalues
00437 *       =6                 random       general, w/ eigenvalues
00438 *       =7                              random diagonal
00439 *       =8                              random symmetric
00440 *       =9                              random general
00441 *       =10                             random triangular
00442 *
00443             IF( MTYPES.GT.MAXTYP )
00444      \$         GO TO 90
00445 *
00446             ITYPE = KTYPE( JTYPE )
00447             IMODE = KMODE( JTYPE )
00448 *
00449 *           Compute norm
00450 *
00451             GO TO ( 30, 40, 50 )KMAGN( JTYPE )
00452 *
00453    30       CONTINUE
00454             ANORM = ONE
00455             GO TO 60
00456 *
00457    40       CONTINUE
00458             ANORM = OVFL*ULP
00459             GO TO 60
00460 *
00461    50       CONTINUE
00462             ANORM = UNFL*ULPINV
00463             GO TO 60
00464 *
00465    60       CONTINUE
00466 *
00467             CALL DLASET( 'Full', LDA, N, ZERO, ZERO, A, LDA )
00468             IINFO = 0
00469             COND = ULPINV
00470 *
00471 *           Special Matrices -- Identity & Jordan block
00472 *
00473 *              Zero
00474 *
00475             IF( ITYPE.EQ.1 ) THEN
00476                IINFO = 0
00477 *
00478             ELSE IF( ITYPE.EQ.2 ) THEN
00479 *
00480 *              Identity
00481 *
00482                DO 70 JCOL = 1, N
00483                   A( JCOL, JCOL ) = ANORM
00484    70          CONTINUE
00485 *
00486             ELSE IF( ITYPE.EQ.3 ) THEN
00487 *
00488 *              Jordan Block
00489 *
00490                DO 80 JCOL = 1, N
00491                   A( JCOL, JCOL ) = ANORM
00492                   IF( JCOL.GT.1 )
00493      \$               A( JCOL, JCOL-1 ) = ONE
00494    80          CONTINUE
00495 *
00496             ELSE IF( ITYPE.EQ.4 ) THEN
00497 *
00498 *              Diagonal Matrix, [Eigen]values Specified
00499 *
00500                CALL DLATMS( N, N, 'S', ISEED, 'S', WORK, IMODE, COND,
00501      \$                      ANORM, 0, 0, 'N', A, LDA, WORK( N+1 ),
00502      \$                      IINFO )
00503 *
00504             ELSE IF( ITYPE.EQ.5 ) THEN
00505 *
00506 *              Symmetric, eigenvalues specified
00507 *
00508                CALL DLATMS( N, N, 'S', ISEED, 'S', WORK, IMODE, COND,
00509      \$                      ANORM, N, N, 'N', A, LDA, WORK( N+1 ),
00510      \$                      IINFO )
00511 *
00512             ELSE IF( ITYPE.EQ.6 ) THEN
00513 *
00514 *              General, eigenvalues specified
00515 *
00516                IF( KCONDS( JTYPE ).EQ.1 ) THEN
00517                   CONDS = ONE
00518                ELSE IF( KCONDS( JTYPE ).EQ.2 ) THEN
00519                   CONDS = RTULPI
00520                ELSE
00521                   CONDS = ZERO
00522                END IF
00523 *
00524                ADUMMA( 1 ) = ' '
00525                CALL DLATME( N, 'S', ISEED, WORK, IMODE, COND, ONE,
00526      \$                      ADUMMA, 'T', 'T', 'T', WORK( N+1 ), 4,
00527      \$                      CONDS, N, N, ANORM, A, LDA, WORK( 2*N+1 ),
00528      \$                      IINFO )
00529 *
00530             ELSE IF( ITYPE.EQ.7 ) THEN
00531 *
00532 *              Diagonal, random eigenvalues
00533 *
00534                CALL DLATMR( N, N, 'S', ISEED, 'S', WORK, 6, ONE, ONE,
00535      \$                      'T', 'N', WORK( N+1 ), 1, ONE,
00536      \$                      WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, 0, 0,
00537      \$                      ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
00538 *
00539             ELSE IF( ITYPE.EQ.8 ) THEN
00540 *
00541 *              Symmetric, random eigenvalues
00542 *
00543                CALL DLATMR( N, N, 'S', ISEED, 'S', WORK, 6, ONE, ONE,
00544      \$                      'T', 'N', WORK( N+1 ), 1, ONE,
00545      \$                      WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, N, N,
00546      \$                      ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
00547 *
00548             ELSE IF( ITYPE.EQ.9 ) THEN
00549 *
00550 *              General, random eigenvalues
00551 *
00552                CALL DLATMR( N, N, 'S', ISEED, 'N', WORK, 6, ONE, ONE,
00553      \$                      'T', 'N', WORK( N+1 ), 1, ONE,
00554      \$                      WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, N, N,
00555      \$                      ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
00556                IF( N.GE.4 ) THEN
00557                   CALL DLASET( 'Full', 2, N, ZERO, ZERO, A, LDA )
00558                   CALL DLASET( 'Full', N-3, 1, ZERO, ZERO, A( 3, 1 ),
00559      \$                         LDA )
00560                   CALL DLASET( 'Full', N-3, 2, ZERO, ZERO, A( 3, N-1 ),
00561      \$                         LDA )
00562                   CALL DLASET( 'Full', 1, N, ZERO, ZERO, A( N, 1 ),
00563      \$                         LDA )
00564                END IF
00565 *
00566             ELSE IF( ITYPE.EQ.10 ) THEN
00567 *
00568 *              Triangular, random eigenvalues
00569 *
00570                CALL DLATMR( N, N, 'S', ISEED, 'N', WORK, 6, ONE, ONE,
00571      \$                      'T', 'N', WORK( N+1 ), 1, ONE,
00572      \$                      WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, N, 0,
00573      \$                      ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
00574 *
00575             ELSE
00576 *
00577                IINFO = 1
00578             END IF
00579 *
00580             IF( IINFO.NE.0 ) THEN
00581                WRITE( NOUNIT, FMT = 9992 )'Generator', IINFO, N, JTYPE,
00582      \$            IOLDSD
00583                INFO = ABS( IINFO )
00584                RETURN
00585             END IF
00586 *
00587    90       CONTINUE
00588 *
00589 *           Test for minimal and generous workspace
00590 *
00591             DO 250 IWK = 1, 2
00592                IF( IWK.EQ.1 ) THEN
00593                   NNWORK = 3*N
00594                ELSE
00595                   NNWORK = 5*N + 2*N**2
00596                END IF
00597                NNWORK = MAX( NNWORK, 1 )
00598 *
00599 *              Initialize RESULT
00600 *
00601                DO 100 J = 1, 13
00602                   RESULT( J ) = -ONE
00603   100          CONTINUE
00604 *
00605 *              Test with and without sorting of eigenvalues
00606 *
00607                DO 210 ISORT = 0, 1
00608                   IF( ISORT.EQ.0 ) THEN
00609                      SORT = 'N'
00610                      RSUB = 0
00611                   ELSE
00612                      SORT = 'S'
00613                      RSUB = 6
00614                   END IF
00615 *
00616 *                 Compute Schur form and Schur vectors, and test them
00617 *
00618                   CALL DLACPY( 'F', N, N, A, LDA, H, LDA )
00619                   CALL DGEES( 'V', SORT, DSLECT, N, H, LDA, SDIM, WR,
00620      \$                        WI, VS, LDVS, WORK, NNWORK, BWORK, IINFO )
00621                   IF( IINFO.NE.0 .AND. IINFO.NE.N+2 ) THEN
00622                      RESULT( 1+RSUB ) = ULPINV
00623                      WRITE( NOUNIT, FMT = 9992 )'DGEES1', IINFO, N,
00624      \$                  JTYPE, IOLDSD
00625                      INFO = ABS( IINFO )
00626                      GO TO 220
00627                   END IF
00628 *
00629 *                 Do Test (1) or Test (7)
00630 *
00631                   RESULT( 1+RSUB ) = ZERO
00632                   DO 120 J = 1, N - 2
00633                      DO 110 I = J + 2, N
00634                         IF( H( I, J ).NE.ZERO )
00635      \$                     RESULT( 1+RSUB ) = ULPINV
00636   110                CONTINUE
00637   120             CONTINUE
00638                   DO 130 I = 1, N - 2
00639                      IF( H( I+1, I ).NE.ZERO .AND. H( I+2, I+1 ).NE.
00640      \$                   ZERO )RESULT( 1+RSUB ) = ULPINV
00641   130             CONTINUE
00642                   DO 140 I = 1, N - 1
00643                      IF( H( I+1, I ).NE.ZERO ) THEN
00644                         IF( H( I, I ).NE.H( I+1, I+1 ) .OR.
00645      \$                      H( I, I+1 ).EQ.ZERO .OR.
00646      \$                      SIGN( ONE, H( I+1, I ) ).EQ.
00647      \$                      SIGN( ONE, H( I, I+1 ) ) )RESULT( 1+RSUB )
00648      \$                      = ULPINV
00649                      END IF
00650   140             CONTINUE
00651 *
00652 *                 Do Tests (2) and (3) or Tests (8) and (9)
00653 *
00654                   LWORK = MAX( 1, 2*N*N )
00655                   CALL DHST01( N, 1, N, A, LDA, H, LDA, VS, LDVS, WORK,
00656      \$                         LWORK, RES )
00657                   RESULT( 2+RSUB ) = RES( 1 )
00658                   RESULT( 3+RSUB ) = RES( 2 )
00659 *
00660 *                 Do Test (4) or Test (10)
00661 *
00662                   RESULT( 4+RSUB ) = ZERO
00663                   DO 150 I = 1, N
00664                      IF( H( I, I ).NE.WR( I ) )
00665      \$                  RESULT( 4+RSUB ) = ULPINV
00666   150             CONTINUE
00667                   IF( N.GT.1 ) THEN
00668                      IF( H( 2, 1 ).EQ.ZERO .AND. WI( 1 ).NE.ZERO )
00669      \$                  RESULT( 4+RSUB ) = ULPINV
00670                      IF( H( N, N-1 ).EQ.ZERO .AND. WI( N ).NE.ZERO )
00671      \$                  RESULT( 4+RSUB ) = ULPINV
00672                   END IF
00673                   DO 160 I = 1, N - 1
00674                      IF( H( I+1, I ).NE.ZERO ) THEN
00675                         TMP = SQRT( ABS( H( I+1, I ) ) )*
00676      \$                        SQRT( ABS( H( I, I+1 ) ) )
00677                         RESULT( 4+RSUB ) = MAX( RESULT( 4+RSUB ),
00678      \$                                     ABS( WI( I )-TMP ) /
00679      \$                                     MAX( ULP*TMP, UNFL ) )
00680                         RESULT( 4+RSUB ) = MAX( RESULT( 4+RSUB ),
00681      \$                                     ABS( WI( I+1 )+TMP ) /
00682      \$                                     MAX( ULP*TMP, UNFL ) )
00683                      ELSE IF( I.GT.1 ) THEN
00684                         IF( H( I+1, I ).EQ.ZERO .AND. H( I, I-1 ).EQ.
00685      \$                      ZERO .AND. WI( I ).NE.ZERO )RESULT( 4+RSUB )
00686      \$                       = ULPINV
00687                      END IF
00688   160             CONTINUE
00689 *
00690 *                 Do Test (5) or Test (11)
00691 *
00692                   CALL DLACPY( 'F', N, N, A, LDA, HT, LDA )
00693                   CALL DGEES( 'N', SORT, DSLECT, N, HT, LDA, SDIM, WRT,
00694      \$                        WIT, VS, LDVS, WORK, NNWORK, BWORK,
00695      \$                        IINFO )
00696                   IF( IINFO.NE.0 .AND. IINFO.NE.N+2 ) THEN
00697                      RESULT( 5+RSUB ) = ULPINV
00698                      WRITE( NOUNIT, FMT = 9992 )'DGEES2', IINFO, N,
00699      \$                  JTYPE, IOLDSD
00700                      INFO = ABS( IINFO )
00701                      GO TO 220
00702                   END IF
00703 *
00704                   RESULT( 5+RSUB ) = ZERO
00705                   DO 180 J = 1, N
00706                      DO 170 I = 1, N
00707                         IF( H( I, J ).NE.HT( I, J ) )
00708      \$                     RESULT( 5+RSUB ) = ULPINV
00709   170                CONTINUE
00710   180             CONTINUE
00711 *
00712 *                 Do Test (6) or Test (12)
00713 *
00714                   RESULT( 6+RSUB ) = ZERO
00715                   DO 190 I = 1, N
00716                      IF( WR( I ).NE.WRT( I ) .OR. WI( I ).NE.WIT( I ) )
00717      \$                  RESULT( 6+RSUB ) = ULPINV
00718   190             CONTINUE
00719 *
00720 *                 Do Test (13)
00721 *
00722                   IF( ISORT.EQ.1 ) THEN
00723                      RESULT( 13 ) = ZERO
00724                      KNTEIG = 0
00725                      DO 200 I = 1, N
00726                         IF( DSLECT( WR( I ), WI( I ) ) .OR.
00727      \$                      DSLECT( WR( I ), -WI( I ) ) )
00728      \$                      KNTEIG = KNTEIG + 1
00729                         IF( I.LT.N ) THEN
00730                            IF( ( DSLECT( WR( I+1 ),
00731      \$                         WI( I+1 ) ) .OR. DSLECT( WR( I+1 ),
00732      \$                         -WI( I+1 ) ) ) .AND.
00733      \$                         ( .NOT.( DSLECT( WR( I ),
00734      \$                         WI( I ) ) .OR. DSLECT( WR( I ),
00735      \$                         -WI( I ) ) ) ) .AND. IINFO.NE.N+2 )
00736      \$                         RESULT( 13 ) = ULPINV
00737                         END IF
00738   200                CONTINUE
00739                      IF( SDIM.NE.KNTEIG ) THEN
00740                         RESULT( 13 ) = ULPINV
00741                      END IF
00742                   END IF
00743 *
00744   210          CONTINUE
00745 *
00746 *              End of Loop -- Check for RESULT(j) > THRESH
00747 *
00748   220          CONTINUE
00749 *
00750                NTEST = 0
00751                NFAIL = 0
00752                DO 230 J = 1, 13
00753                   IF( RESULT( J ).GE.ZERO )
00754      \$               NTEST = NTEST + 1
00755                   IF( RESULT( J ).GE.THRESH )
00756      \$               NFAIL = NFAIL + 1
00757   230          CONTINUE
00758 *
00759                IF( NFAIL.GT.0 )
00760      \$            NTESTF = NTESTF + 1
00761                IF( NTESTF.EQ.1 ) THEN
00762                   WRITE( NOUNIT, FMT = 9999 )PATH
00763                   WRITE( NOUNIT, FMT = 9998 )
00764                   WRITE( NOUNIT, FMT = 9997 )
00765                   WRITE( NOUNIT, FMT = 9996 )
00766                   WRITE( NOUNIT, FMT = 9995 )THRESH
00767                   WRITE( NOUNIT, FMT = 9994 )
00768                   NTESTF = 2
00769                END IF
00770 *
00771                DO 240 J = 1, 13
00772                   IF( RESULT( J ).GE.THRESH ) THEN
00773                      WRITE( NOUNIT, FMT = 9993 )N, IWK, IOLDSD, JTYPE,
00774      \$                  J, RESULT( J )
00775                   END IF
00776   240          CONTINUE
00777 *
00778                NERRS = NERRS + NFAIL
00779                NTESTT = NTESTT + NTEST
00780 *
00781   250       CONTINUE
00782   260    CONTINUE
00783   270 CONTINUE
00784 *
00785 *     Summary
00786 *
00787       CALL DLASUM( PATH, NOUNIT, NERRS, NTESTT )
00788 *
00789  9999 FORMAT( / 1X, A3, ' -- Real Schur Form Decomposition Driver',
00790      \$      / ' Matrix types (see DDRVES for details): ' )
00791 *
00792  9998 FORMAT( / ' Special Matrices:', / '  1=Zero matrix.             ',
00793      \$      '           ', '  5=Diagonal: geometr. spaced entries.',
00794      \$      / '  2=Identity matrix.                    ', '  6=Diagona',
00795      \$      'l: clustered entries.', / '  3=Transposed Jordan block.  ',
00796      \$      '          ', '  7=Diagonal: large, evenly spaced.', / '  ',
00797      \$      '4=Diagonal: evenly spaced entries.    ', '  8=Diagonal: s',
00798      \$      'mall, evenly spaced.' )
00799  9997 FORMAT( ' Dense, Non-Symmetric Matrices:', / '  9=Well-cond., ev',
00800      \$      'enly spaced eigenvals.', ' 14=Ill-cond., geomet. spaced e',
00801      \$      'igenals.', / ' 10=Well-cond., geom. spaced eigenvals. ',
00802      \$      ' 15=Ill-conditioned, clustered e.vals.', / ' 11=Well-cond',
00803      \$      'itioned, clustered e.vals. ', ' 16=Ill-cond., random comp',
00804      \$      'lex ', / ' 12=Well-cond., random complex ', 6X, '   ',
00805      \$      ' 17=Ill-cond., large rand. complx ', / ' 13=Ill-condi',
00806      \$      'tioned, evenly spaced.     ', ' 18=Ill-cond., small rand.',
00807      \$      ' complx ' )
00808  9996 FORMAT( ' 19=Matrix with random O(1) entries.    ', ' 21=Matrix ',
00809      \$      'with small random entries.', / ' 20=Matrix with large ran',
00810      \$      'dom entries.   ', / )
00811  9995 FORMAT( ' Tests performed with test threshold =', F8.2,
00812      \$      / ' ( A denotes A on input and T denotes A on output)',
00813      \$      / / ' 1 = 0 if T in Schur form (no sort), ',
00814      \$      '  1/ulp otherwise', /
00815      \$      ' 2 = | A - VS T transpose(VS) | / ( n |A| ulp ) (no sort)',
00816      \$      / ' 3 = | I - VS transpose(VS) | / ( n ulp ) (no sort) ', /
00817      \$      ' 4 = 0 if WR+sqrt(-1)*WI are eigenvalues of T (no sort),',
00818      \$      '  1/ulp otherwise', /
00819      \$      ' 5 = 0 if T same no matter if VS computed (no sort),',
00820      \$      '  1/ulp otherwise', /
00821      \$      ' 6 = 0 if WR, WI same no matter if VS computed (no sort)',
00822      \$      ',  1/ulp otherwise' )
00823  9994 FORMAT( ' 7 = 0 if T in Schur form (sort), ', '  1/ulp otherwise',
00824      \$      / ' 8 = | A - VS T transpose(VS) | / ( n |A| ulp ) (sort)',
00825      \$      / ' 9 = | I - VS transpose(VS) | / ( n ulp ) (sort) ',
00826      \$      / ' 10 = 0 if WR+sqrt(-1)*WI are eigenvalues of T (sort),',
00827      \$      '  1/ulp otherwise', /
00828      \$      ' 11 = 0 if T same no matter if VS computed (sort),',
00829      \$      '  1/ulp otherwise', /
00830      \$      ' 12 = 0 if WR, WI same no matter if VS computed (sort),',
00831      \$      '  1/ulp otherwise', /
00832      \$      ' 13 = 0 if sorting succesful, 1/ulp otherwise', / )
00833  9993 FORMAT( ' N=', I5, ', IWK=', I2, ', seed=', 4( I4, ',' ),
00834      \$      ' type ', I2, ', test(', I2, ')=', G10.3 )
00835  9992 FORMAT( ' DDRVES: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
00836      \$      I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' )
00837 *
00838       RETURN
00839 *
00840 *     End of DDRVES
00841 *
00842       END
```