LAPACK: TESTING/EIG/ddrvsx.f Source File

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00001       SUBROUTINE DDRVSX( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
00002      $                   NIUNIT, NOUNIT, A, LDA, H, HT, WR, WI, WRT,
00003      $                   WIT, WRTMP, WITMP, VS, LDVS, VS1, RESULT, WORK,
00004      $                   LWORK, IWORK, BWORK, INFO )
00005 *
00006 *  -- LAPACK test routine (version 3.1) --
00007 *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
00008 *     November 2006
00009 *
00010 *     .. Scalar Arguments ..
00011       INTEGER            INFO, LDA, LDVS, LWORK, NIUNIT, NOUNIT, NSIZES,
00012      $                   NTYPES
00013       DOUBLE PRECISION   THRESH
00014 *     ..
00015 *     .. Array Arguments ..
00016       LOGICAL            BWORK( * ), DOTYPE( * )
00017       INTEGER            ISEED( 4 ), IWORK( * ), NN( * )
00018       DOUBLE PRECISION   A( LDA, * ), H( LDA, * ), HT( LDA, * ),
00019      $                   RESULT( 17 ), VS( LDVS, * ), VS1( LDVS, * ),
00020      $                   WI( * ), WIT( * ), WITMP( * ), WORK( * ),
00021      $                   WR( * ), WRT( * ), WRTMP( * )
00022 *     ..
00023 *
00024 *  Purpose
00025 *  =======
00026 *
00027 *     DDRVSX checks the nonsymmetric eigenvalue (Schur form) problem
00028 *     expert driver DGEESX.
00029 *
00030 *     DDRVSX uses both test matrices generated randomly depending on
00031 *     data supplied in the calling sequence, as well as on data
00032 *     read from an input file and including precomputed condition
00033 *     numbers to which it compares the ones it computes.
00034 *
00035 *     When DDRVSX is called, a number of matrix "sizes" ("n's") and a
00036 *     number of matrix "types" are specified.  For each size ("n")
00037 *     and each type of matrix, one matrix will be generated and used
00038 *     to test the nonsymmetric eigenroutines.  For each matrix, 15
00039 *     tests will be performed:
00040 *
00041 *     (1)     0 if T is in Schur form, 1/ulp otherwise
00042 *            (no sorting of eigenvalues)
00043 *
00044 *     (2)     | A - VS T VS' | / ( n |A| ulp )
00045 *
00046 *       Here VS is the matrix of Schur eigenvectors, and T is in Schur
00047 *       form  (no sorting of eigenvalues).
00048 *
00049 *     (3)     | I - VS VS' | / ( n ulp ) (no sorting of eigenvalues).
00050 *
00051 *     (4)     0     if WR+sqrt(-1)*WI are eigenvalues of T
00052 *             1/ulp otherwise
00053 *             (no sorting of eigenvalues)
00054 *
00055 *     (5)     0     if T(with VS) = T(without VS),
00056 *             1/ulp otherwise
00057 *             (no sorting of eigenvalues)
00058 *
00059 *     (6)     0     if eigenvalues(with VS) = eigenvalues(without VS),
00060 *             1/ulp otherwise
00061 *             (no sorting of eigenvalues)
00062 *
00063 *     (7)     0 if T is in Schur form, 1/ulp otherwise
00064 *             (with sorting of eigenvalues)
00065 *
00066 *     (8)     | A - VS T VS' | / ( n |A| ulp )
00067 *
00068 *       Here VS is the matrix of Schur eigenvectors, and T is in Schur
00069 *       form  (with sorting of eigenvalues).
00070 *
00071 *     (9)     | I - VS VS' | / ( n ulp ) (with sorting of eigenvalues).
00072 *
00073 *     (10)    0     if WR+sqrt(-1)*WI are eigenvalues of T
00074 *             1/ulp otherwise
00075 *             If workspace sufficient, also compare WR, WI with and
00076 *             without reciprocal condition numbers
00077 *             (with sorting of eigenvalues)
00078 *
00079 *     (11)    0     if T(with VS) = T(without VS),
00080 *             1/ulp otherwise
00081 *             If workspace sufficient, also compare T with and without
00082 *             reciprocal condition numbers
00083 *             (with sorting of eigenvalues)
00084 *
00085 *     (12)    0     if eigenvalues(with VS) = eigenvalues(without VS),
00086 *             1/ulp otherwise
00087 *             If workspace sufficient, also compare VS with and without
00088 *             reciprocal condition numbers
00089 *             (with sorting of eigenvalues)
00090 *
00091 *     (13)    if sorting worked and SDIM is the number of
00092 *             eigenvalues which were SELECTed
00093 *             If workspace sufficient, also compare SDIM with and
00094 *             without reciprocal condition numbers
00095 *
00096 *     (14)    if RCONDE the same no matter if VS and/or RCONDV computed
00097 *
00098 *     (15)    if RCONDV the same no matter if VS and/or RCONDE computed
00099 *
00100 *     The "sizes" are specified by an array NN(1:NSIZES); the value of
00101 *     each element NN(j) specifies one size.
00102 *     The "types" are specified by a logical array DOTYPE( 1:NTYPES );
00103 *     if DOTYPE(j) is .TRUE., then matrix type "j" will be generated.
00104 *     Currently, the list of possible types is:
00105 *
00106 *     (1)  The zero matrix.
00107 *     (2)  The identity matrix.
00108 *     (3)  A (transposed) Jordan block, with 1's on the diagonal.
00109 *
00110 *     (4)  A diagonal matrix with evenly spaced entries
00111 *          1, ..., ULP  and random signs.
00112 *          (ULP = (first number larger than 1) - 1 )
00113 *     (5)  A diagonal matrix with geometrically spaced entries
00114 *          1, ..., ULP  and random signs.
00115 *     (6)  A diagonal matrix with "clustered" entries 1, ULP, ..., ULP
00116 *          and random signs.
00117 *
00118 *     (7)  Same as (4), but multiplied by a constant near
00119 *          the overflow threshold
00120 *     (8)  Same as (4), but multiplied by a constant near
00121 *          the underflow threshold
00122 *
00123 *     (9)  A matrix of the form  U' T U, where U is orthogonal and
00124 *          T has evenly spaced entries 1, ..., ULP with random signs
00125 *          on the diagonal and random O(1) entries in the upper
00126 *          triangle.
00127 *
00128 *     (10) A matrix of the form  U' T U, where U is orthogonal and
00129 *          T has geometrically spaced entries 1, ..., ULP with random
00130 *          signs on the diagonal and random O(1) entries in the upper
00131 *          triangle.
00132 *
00133 *     (11) A matrix of the form  U' T U, where U is orthogonal and
00134 *          T has "clustered" entries 1, ULP,..., ULP with random
00135 *          signs on the diagonal and random O(1) entries in the upper
00136 *          triangle.
00137 *
00138 *     (12) A matrix of the form  U' T U, where U is orthogonal and
00139 *          T has real or complex conjugate paired eigenvalues randomly
00140 *          chosen from ( ULP, 1 ) and random O(1) entries in the upper
00141 *          triangle.
00142 *
00143 *     (13) A matrix of the form  X' T X, where X has condition
00144 *          SQRT( ULP ) and T has evenly spaced entries 1, ..., ULP
00145 *          with random signs on the diagonal and random O(1) entries
00146 *          in the upper triangle.
00147 *
00148 *     (14) A matrix of the form  X' T X, where X has condition
00149 *          SQRT( ULP ) and T has geometrically spaced entries
00150 *          1, ..., ULP with random signs on the diagonal and random
00151 *          O(1) entries in the upper triangle.
00152 *
00153 *     (15) A matrix of the form  X' T X, where X has condition
00154 *          SQRT( ULP ) and T has "clustered" entries 1, ULP,..., ULP
00155 *          with random signs on the diagonal and random O(1) entries
00156 *          in the upper triangle.
00157 *
00158 *     (16) A matrix of the form  X' T X, where X has condition
00159 *          SQRT( ULP ) and T has real or complex conjugate paired
00160 *          eigenvalues randomly chosen from ( ULP, 1 ) and random
00161 *          O(1) entries in the upper triangle.
00162 *
00163 *     (17) Same as (16), but multiplied by a constant
00164 *          near the overflow threshold
00165 *     (18) Same as (16), but multiplied by a constant
00166 *          near the underflow threshold
00167 *
00168 *     (19) Nonsymmetric matrix with random entries chosen from (-1,1).
00169 *          If N is at least 4, all entries in first two rows and last
00170 *          row, and first column and last two columns are zero.
00171 *     (20) Same as (19), but multiplied by a constant
00172 *          near the overflow threshold
00173 *     (21) Same as (19), but multiplied by a constant
00174 *          near the underflow threshold
00175 *
00176 *     In addition, an input file will be read from logical unit number
00177 *     NIUNIT. The file contains matrices along with precomputed
00178 *     eigenvalues and reciprocal condition numbers for the eigenvalue
00179 *     average and right invariant subspace. For these matrices, in
00180 *     addition to tests (1) to (15) we will compute the following two
00181 *     tests:
00182 *
00183 *    (16)  |RCONDE - RCDEIN| / cond(RCONDE)
00184 *
00185 *       RCONDE is the reciprocal average eigenvalue condition number
00186 *       computed by DGEESX and RCDEIN (the precomputed true value)
00187 *       is supplied as input.  cond(RCONDE) is the condition number
00188 *       of RCONDE, and takes errors in computing RCONDE into account,
00189 *       so that the resulting quantity should be O(ULP). cond(RCONDE)
00190 *       is essentially given by norm(A)/RCONDV.
00191 *
00192 *    (17)  |RCONDV - RCDVIN| / cond(RCONDV)
00193 *
00194 *       RCONDV is the reciprocal right invariant subspace condition
00195 *       number computed by DGEESX and RCDVIN (the precomputed true
00196 *       value) is supplied as input. cond(RCONDV) is the condition
00197 *       number of RCONDV, and takes errors in computing RCONDV into
00198 *       account, so that the resulting quantity should be O(ULP).
00199 *       cond(RCONDV) is essentially given by norm(A)/RCONDE.
00200 *
00201 *  Arguments
00202 *  =========
00203 *
00204 *  NSIZES  (input) INTEGER
00205 *          The number of sizes of matrices to use.  NSIZES must be at
00206 *          least zero. If it is zero, no randomly generated matrices
00207 *          are tested, but any test matrices read from NIUNIT will be
00208 *          tested.
00209 *
00210 *  NN      (input) INTEGER array, dimension (NSIZES)
00211 *          An array containing the sizes to be used for the matrices.
00212 *          Zero values will be skipped.  The values must be at least
00213 *          zero.
00214 *
00215 *  NTYPES  (input) INTEGER
00216 *          The number of elements in DOTYPE. NTYPES must be at least
00217 *          zero. If it is zero, no randomly generated test matrices
00218 *          are tested, but and test matrices read from NIUNIT will be
00219 *          tested. If it is MAXTYP+1 and NSIZES is 1, then an
00220 *          additional type, MAXTYP+1 is defined, which is to use
00221 *          whatever matrix is in A.  This is only useful if
00222 *          DOTYPE(1:MAXTYP) is .FALSE. and DOTYPE(MAXTYP+1) is .TRUE. .
00223 *
00224 *  DOTYPE  (input) LOGICAL array, dimension (NTYPES)
00225 *          If DOTYPE(j) is .TRUE., then for each size in NN a
00226 *          matrix of that size and of type j will be generated.
00227 *          If NTYPES is smaller than the maximum number of types
00228 *          defined (PARAMETER MAXTYP), then types NTYPES+1 through
00229 *          MAXTYP will not be generated.  If NTYPES is larger
00230 *          than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES)
00231 *          will be ignored.
00232 *
00233 *  ISEED   (input/output) INTEGER array, dimension (4)
00234 *          On entry ISEED specifies the seed of the random number
00235 *          generator. The array elements should be between 0 and 4095;
00236 *          if not they will be reduced mod 4096.  Also, ISEED(4) must
00237 *          be odd.  The random number generator uses a linear
00238 *          congruential sequence limited to small integers, and so
00239 *          should produce machine independent random numbers. The
00240 *          values of ISEED are changed on exit, and can be used in the
00241 *          next call to DDRVSX to continue the same random number
00242 *          sequence.
00243 *
00244 *  THRESH  (input) DOUBLE PRECISION
00245 *          A test will count as "failed" if the "error", computed as
00246 *          described above, exceeds THRESH.  Note that the error
00247 *          is scaled to be O(1), so THRESH should be a reasonably
00248 *          small multiple of 1, e.g., 10 or 100.  In particular,
00249 *          it should not depend on the precision (single vs. double)
00250 *          or the size of the matrix.  It must be at least zero.
00251 *
00252 *  NIUNIT  (input) INTEGER
00253 *          The FORTRAN unit number for reading in the data file of
00254 *          problems to solve.
00255 *
00256 *  NOUNIT  (input) INTEGER
00257 *          The FORTRAN unit number for printing out error messages
00258 *          (e.g., if a routine returns INFO not equal to 0.)
00259 *
00260 *  A       (workspace) DOUBLE PRECISION array, dimension (LDA, max(NN))
00261 *          Used to hold the matrix whose eigenvalues are to be
00262 *          computed.  On exit, A contains the last matrix actually used.
00263 *
00264 *  LDA     (input) INTEGER
00265 *          The leading dimension of A, and H. LDA must be at
00266 *          least 1 and at least max( NN ).
00267 *
00268 *  H       (workspace) DOUBLE PRECISION array, dimension (LDA, max(NN))
00269 *          Another copy of the test matrix A, modified by DGEESX.
00270 *
00271 *  HT      (workspace) DOUBLE PRECISION array, dimension (LDA, max(NN))
00272 *          Yet another copy of the test matrix A, modified by DGEESX.
00273 *
00274 *  WR      (workspace) DOUBLE PRECISION array, dimension (max(NN))
00275 *  WI      (workspace) DOUBLE PRECISION array, dimension (max(NN))
00276 *          The real and imaginary parts of the eigenvalues of A.
00277 *          On exit, WR + WI*i are the eigenvalues of the matrix in A.
00278 *
00279 *  WRT     (workspace) DOUBLE PRECISION array, dimension (max(NN))
00280 *  WIT     (workspace) DOUBLE PRECISION array, dimension (max(NN))
00281 *          Like WR, WI, these arrays contain the eigenvalues of A,
00282 *          but those computed when DGEESX only computes a partial
00283 *          eigendecomposition, i.e. not Schur vectors
00284 *
00285 *  WRTMP   (workspace) DOUBLE PRECISION array, dimension (max(NN))
00286 *  WITMP   (workspace) DOUBLE PRECISION array, dimension (max(NN))
00287 *          More temporary storage for eigenvalues.
00288 *
00289 *  VS      (workspace) DOUBLE PRECISION array, dimension (LDVS, max(NN))
00290 *          VS holds the computed Schur vectors.
00291 *
00292 *  LDVS    (input) INTEGER
00293 *          Leading dimension of VS. Must be at least max(1,max(NN)).
00294 *
00295 *  VS1     (workspace) DOUBLE PRECISION array, dimension (LDVS, max(NN))
00296 *          VS1 holds another copy of the computed Schur vectors.
00297 *
00298 *  RESULT  (output) DOUBLE PRECISION array, dimension (17)
00299 *          The values computed by the 17 tests described above.
00300 *          The values are currently limited to 1/ulp, to avoid overflow.
00301 *
00302 *  WORK    (workspace) DOUBLE PRECISION array, dimension (LWORK)
00303 *
00304 *  LWORK   (input) INTEGER
00305 *          The number of entries in WORK.  This must be at least
00306 *          max(3*NN(j),2*NN(j)**2) for all j.
00307 *
00308 *  IWORK   (workspace) INTEGER array, dimension (max(NN)*max(NN))
00309 *
00310 *  INFO    (output) INTEGER
00311 *          If 0,  successful exit.
00312 *            <0,  input parameter -INFO is incorrect
00313 *            >0,  DLATMR, SLATMS, SLATME or DGET24 returned an error
00314 *                 code and INFO is its absolute value
00315 *
00316 *-----------------------------------------------------------------------
00317 *
00318 *     Some Local Variables and Parameters:
00319 *     ---- ----- --------- --- ----------
00320 *     ZERO, ONE       Real 0 and 1.
00321 *     MAXTYP          The number of types defined.
00322 *     NMAX            Largest value in NN.
00323 *     NERRS           The number of tests which have exceeded THRESH
00324 *     COND, CONDS,
00325 *     IMODE           Values to be passed to the matrix generators.
00326 *     ANORM           Norm of A; passed to matrix generators.
00327 *
00328 *     OVFL, UNFL      Overflow and underflow thresholds.
00329 *     ULP, ULPINV     Finest relative precision and its inverse.
00330 *     RTULP, RTULPI   Square roots of the previous 4 values.
00331 *             The following four arrays decode JTYPE:
00332 *     KTYPE(j)        The general type (1-10) for type "j".
00333 *     KMODE(j)        The MODE value to be passed to the matrix
00334 *                     generator for type "j".
00335 *     KMAGN(j)        The order of magnitude ( O(1),
00336 *                     O(overflow^(1/2) ), O(underflow^(1/2) )
00337 *     KCONDS(j)       Selectw whether CONDS is to be 1 or
00338 *                     1/sqrt(ulp).  (0 means irrelevant.)
00339 *
00340 *  =====================================================================
00341 *
00342 *     .. Parameters ..
00343       DOUBLE PRECISION   ZERO, ONE
00344       PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
00345       INTEGER            MAXTYP
00346       PARAMETER          ( MAXTYP = 21 )
00347 *     ..
00348 *     .. Local Scalars ..
00349       LOGICAL            BADNN
00350       CHARACTER*3        PATH
00351       INTEGER            I, IINFO, IMODE, ITYPE, IWK, J, JCOL, JSIZE,
00352      $                   JTYPE, MTYPES, N, NERRS, NFAIL, NMAX, NNWORK,
00353      $                   NSLCT, NTEST, NTESTF, NTESTT
00354       DOUBLE PRECISION   ANORM, COND, CONDS, OVFL, RCDEIN, RCDVIN,
00355      $                   RTULP, RTULPI, ULP, ULPINV, UNFL
00356 *     ..
00357 *     .. Local Arrays ..
00358       CHARACTER          ADUMMA( 1 )
00359       INTEGER            IDUMMA( 1 ), IOLDSD( 4 ), ISLCT( 20 ),
00360      $                   KCONDS( MAXTYP ), KMAGN( MAXTYP ),
00361      $                   KMODE( MAXTYP ), KTYPE( MAXTYP )
00362 *     ..
00363 *     .. Arrays in Common ..
00364       LOGICAL            SELVAL( 20 )
00365       DOUBLE PRECISION   SELWI( 20 ), SELWR( 20 )
00366 *     ..
00367 *     .. Scalars in Common ..
00368       INTEGER            SELDIM, SELOPT
00369 *     ..
00370 *     .. Common blocks ..
00371       COMMON             / SSLCT / SELOPT, SELDIM, SELVAL, SELWR, SELWI
00372 *     ..
00373 *     .. External Functions ..
00374       DOUBLE PRECISION   DLAMCH
00375       EXTERNAL           DLAMCH
00376 *     ..
00377 *     .. External Subroutines ..
00378       EXTERNAL           DGET24, DLABAD, DLASET, DLASUM, DLATME, DLATMR,
00379      $                   DLATMS, XERBLA
00380 *     ..
00381 *     .. Intrinsic Functions ..
00382       INTRINSIC          ABS, MAX, MIN, SQRT
00383 *     ..
00384 *     .. Data statements ..
00385       DATA               KTYPE / 1, 2, 3, 5*4, 4*6, 6*6, 3*9 /
00386       DATA               KMAGN / 3*1, 1, 1, 1, 2, 3, 4*1, 1, 1, 1, 1, 2,
00387      $                   3, 1, 2, 3 /
00388       DATA               KMODE / 3*0, 4, 3, 1, 4, 4, 4, 3, 1, 5, 4, 3,
00389      $                   1, 5, 5, 5, 4, 3, 1 /
00390       DATA               KCONDS / 3*0, 5*0, 4*1, 6*2, 3*0 /
00391 *     ..
00392 *     .. Executable Statements ..
00393 *
00394       PATH( 1: 1 ) = 'Double precision'
00395       PATH( 2: 3 ) = 'SX'
00396 *
00397 *     Check for errors
00398 *
00399       NTESTT = 0
00400       NTESTF = 0
00401       INFO = 0
00402 *
00403 *     Important constants
00404 *
00405       BADNN = .FALSE.
00406 *
00407 *     12 is the largest dimension in the input file of precomputed
00408 *     problems
00409 *
00410       NMAX = 12
00411       DO 10 J = 1, NSIZES
00412          NMAX = MAX( NMAX, NN( J ) )
00413          IF( NN( J ).LT.0 )
00414      $      BADNN = .TRUE.
00415    10 CONTINUE
00416 *
00417 *     Check for errors
00418 *
00419       IF( NSIZES.LT.0 ) THEN
00420          INFO = -1
00421       ELSE IF( BADNN ) THEN
00422          INFO = -2
00423       ELSE IF( NTYPES.LT.0 ) THEN
00424          INFO = -3
00425       ELSE IF( THRESH.LT.ZERO ) THEN
00426          INFO = -6
00427       ELSE IF( NIUNIT.LE.0 ) THEN
00428          INFO = -7
00429       ELSE IF( NOUNIT.LE.0 ) THEN
00430          INFO = -8
00431       ELSE IF( LDA.LT.1 .OR. LDA.LT.NMAX ) THEN
00432          INFO = -10
00433       ELSE IF( LDVS.LT.1 .OR. LDVS.LT.NMAX ) THEN
00434          INFO = -20
00435       ELSE IF( MAX( 3*NMAX, 2*NMAX**2 ).GT.LWORK ) THEN
00436          INFO = -24
00437       END IF
00438 *
00439       IF( INFO.NE.0 ) THEN
00440          CALL XERBLA( 'DDRVSX', -INFO )
00441          RETURN
00442       END IF
00443 *
00444 *     If nothing to do check on NIUNIT
00445 *
00446       IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 )
00447      $   GO TO 150
00448 *
00449 *     More Important constants
00450 *
00451       UNFL = DLAMCH( 'Safe minimum' )
00452       OVFL = ONE / UNFL
00453       CALL DLABAD( UNFL, OVFL )
00454       ULP = DLAMCH( 'Precision' )
00455       ULPINV = ONE / ULP
00456       RTULP = SQRT( ULP )
00457       RTULPI = ONE / RTULP
00458 *
00459 *     Loop over sizes, types
00460 *
00461       NERRS = 0
00462 *
00463       DO 140 JSIZE = 1, NSIZES
00464          N = NN( JSIZE )
00465          IF( NSIZES.NE.1 ) THEN
00466             MTYPES = MIN( MAXTYP, NTYPES )
00467          ELSE
00468             MTYPES = MIN( MAXTYP+1, NTYPES )
00469          END IF
00470 *
00471          DO 130 JTYPE = 1, MTYPES
00472             IF( .NOT.DOTYPE( JTYPE ) )
00473      $         GO TO 130
00474 *
00475 *           Save ISEED in case of an error.
00476 *
00477             DO 20 J = 1, 4
00478                IOLDSD( J ) = ISEED( J )
00479    20       CONTINUE
00480 *
00481 *           Compute "A"
00482 *
00483 *           Control parameters:
00484 *
00485 *           KMAGN  KCONDS  KMODE        KTYPE
00486 *       =1  O(1)   1       clustered 1  zero
00487 *       =2  large  large   clustered 2  identity
00488 *       =3  small          exponential  Jordan
00489 *       =4                 arithmetic   diagonal, (w/ eigenvalues)
00490 *       =5                 random log   symmetric, w/ eigenvalues
00491 *       =6                 random       general, w/ eigenvalues
00492 *       =7                              random diagonal
00493 *       =8                              random symmetric
00494 *       =9                              random general
00495 *       =10                             random triangular
00496 *
00497             IF( MTYPES.GT.MAXTYP )
00498      $         GO TO 90
00499 *
00500             ITYPE = KTYPE( JTYPE )
00501             IMODE = KMODE( JTYPE )
00502 *
00503 *           Compute norm
00504 *
00505             GO TO ( 30, 40, 50 )KMAGN( JTYPE )
00506 *
00507    30       CONTINUE
00508             ANORM = ONE
00509             GO TO 60
00510 *
00511    40       CONTINUE
00512             ANORM = OVFL*ULP
00513             GO TO 60
00514 *
00515    50       CONTINUE
00516             ANORM = UNFL*ULPINV
00517             GO TO 60
00518 *
00519    60       CONTINUE
00520 *
00521             CALL DLASET( 'Full', LDA, N, ZERO, ZERO, A, LDA )
00522             IINFO = 0
00523             COND = ULPINV
00524 *
00525 *           Special Matrices -- Identity & Jordan block
00526 *
00527 *              Zero
00528 *
00529             IF( ITYPE.EQ.1 ) THEN
00530                IINFO = 0
00531 *
00532             ELSE IF( ITYPE.EQ.2 ) THEN
00533 *
00534 *              Identity
00535 *
00536                DO 70 JCOL = 1, N
00537                   A( JCOL, JCOL ) = ANORM
00538    70          CONTINUE
00539 *
00540             ELSE IF( ITYPE.EQ.3 ) THEN
00541 *
00542 *              Jordan Block
00543 *
00544                DO 80 JCOL = 1, N
00545                   A( JCOL, JCOL ) = ANORM
00546                   IF( JCOL.GT.1 )
00547      $               A( JCOL, JCOL-1 ) = ONE
00548    80          CONTINUE
00549 *
00550             ELSE IF( ITYPE.EQ.4 ) THEN
00551 *
00552 *              Diagonal Matrix, [Eigen]values Specified
00553 *
00554                CALL DLATMS( N, N, 'S', ISEED, 'S', WORK, IMODE, COND,
00555      $                      ANORM, 0, 0, 'N', A, LDA, WORK( N+1 ),
00556      $                      IINFO )
00557 *
00558             ELSE IF( ITYPE.EQ.5 ) THEN
00559 *
00560 *              Symmetric, eigenvalues specified
00561 *
00562                CALL DLATMS( N, N, 'S', ISEED, 'S', WORK, IMODE, COND,
00563      $                      ANORM, N, N, 'N', A, LDA, WORK( N+1 ),
00564      $                      IINFO )
00565 *
00566             ELSE IF( ITYPE.EQ.6 ) THEN
00567 *
00568 *              General, eigenvalues specified
00569 *
00570                IF( KCONDS( JTYPE ).EQ.1 ) THEN
00571                   CONDS = ONE
00572                ELSE IF( KCONDS( JTYPE ).EQ.2 ) THEN
00573                   CONDS = RTULPI
00574                ELSE
00575                   CONDS = ZERO
00576                END IF
00577 *
00578                ADUMMA( 1 ) = ' '
00579                CALL DLATME( N, 'S', ISEED, WORK, IMODE, COND, ONE,
00580      $                      ADUMMA, 'T', 'T', 'T', WORK( N+1 ), 4,
00581      $                      CONDS, N, N, ANORM, A, LDA, WORK( 2*N+1 ),
00582      $                      IINFO )
00583 *
00584             ELSE IF( ITYPE.EQ.7 ) THEN
00585 *
00586 *              Diagonal, random eigenvalues
00587 *
00588                CALL DLATMR( N, N, 'S', ISEED, 'S', WORK, 6, ONE, ONE,
00589      $                      'T', 'N', WORK( N+1 ), 1, ONE,
00590      $                      WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, 0, 0,
00591      $                      ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
00592 *
00593             ELSE IF( ITYPE.EQ.8 ) THEN
00594 *
00595 *              Symmetric, random eigenvalues
00596 *
00597                CALL DLATMR( N, N, 'S', ISEED, 'S', WORK, 6, ONE, ONE,
00598      $                      'T', 'N', WORK( N+1 ), 1, ONE,
00599      $                      WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, N, N,
00600      $                      ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
00601 *
00602             ELSE IF( ITYPE.EQ.9 ) THEN
00603 *
00604 *              General, random eigenvalues
00605 *
00606                CALL DLATMR( N, N, 'S', ISEED, 'N', WORK, 6, ONE, ONE,
00607      $                      'T', 'N', WORK( N+1 ), 1, ONE,
00608      $                      WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, N, N,
00609      $                      ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
00610                IF( N.GE.4 ) THEN
00611                   CALL DLASET( 'Full', 2, N, ZERO, ZERO, A, LDA )
00612                   CALL DLASET( 'Full', N-3, 1, ZERO, ZERO, A( 3, 1 ),
00613      $                         LDA )
00614                   CALL DLASET( 'Full', N-3, 2, ZERO, ZERO, A( 3, N-1 ),
00615      $                         LDA )
00616                   CALL DLASET( 'Full', 1, N, ZERO, ZERO, A( N, 1 ),
00617      $                         LDA )
00618                END IF
00619 *
00620             ELSE IF( ITYPE.EQ.10 ) THEN
00621 *
00622 *              Triangular, random eigenvalues
00623 *
00624                CALL DLATMR( N, N, 'S', ISEED, 'N', WORK, 6, ONE, ONE,
00625      $                      'T', 'N', WORK( N+1 ), 1, ONE,
00626      $                      WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, N, 0,
00627      $                      ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
00628 *
00629             ELSE
00630 *
00631                IINFO = 1
00632             END IF
00633 *
00634             IF( IINFO.NE.0 ) THEN
00635                WRITE( NOUNIT, FMT = 9991 )'Generator', IINFO, N, JTYPE,
00636      $            IOLDSD
00637                INFO = ABS( IINFO )
00638                RETURN
00639             END IF
00640 *
00641    90       CONTINUE
00642 *
00643 *           Test for minimal and generous workspace
00644 *
00645             DO 120 IWK = 1, 2
00646                IF( IWK.EQ.1 ) THEN
00647                   NNWORK = 3*N
00648                ELSE
00649                   NNWORK = MAX( 3*N, 2*N*N )
00650                END IF
00651                NNWORK = MAX( NNWORK, 1 )
00652 *
00653                CALL DGET24( .FALSE., JTYPE, THRESH, IOLDSD, NOUNIT, N,
00654      $                      A, LDA, H, HT, WR, WI, WRT, WIT, WRTMP,
00655      $                      WITMP, VS, LDVS, VS1, RCDEIN, RCDVIN, NSLCT,
00656      $                      ISLCT, RESULT, WORK, NNWORK, IWORK, BWORK,
00657      $                      INFO )
00658 *
00659 *              Check for RESULT(j) > THRESH
00660 *
00661                NTEST = 0
00662                NFAIL = 0
00663                DO 100 J = 1, 15
00664                   IF( RESULT( J ).GE.ZERO )
00665      $               NTEST = NTEST + 1
00666                   IF( RESULT( J ).GE.THRESH )
00667      $               NFAIL = NFAIL + 1
00668   100          CONTINUE
00669 *
00670                IF( NFAIL.GT.0 )
00671      $            NTESTF = NTESTF + 1
00672                IF( NTESTF.EQ.1 ) THEN
00673                   WRITE( NOUNIT, FMT = 9999 )PATH
00674                   WRITE( NOUNIT, FMT = 9998 )
00675                   WRITE( NOUNIT, FMT = 9997 )
00676                   WRITE( NOUNIT, FMT = 9996 )
00677                   WRITE( NOUNIT, FMT = 9995 )THRESH
00678                   WRITE( NOUNIT, FMT = 9994 )
00679                   NTESTF = 2
00680                END IF
00681 *
00682                DO 110 J = 1, 15
00683                   IF( RESULT( J ).GE.THRESH ) THEN
00684                      WRITE( NOUNIT, FMT = 9993 )N, IWK, IOLDSD, JTYPE,
00685      $                  J, RESULT( J )
00686                   END IF
00687   110          CONTINUE
00688 *
00689                NERRS = NERRS + NFAIL
00690                NTESTT = NTESTT + NTEST
00691 *
00692   120       CONTINUE
00693   130    CONTINUE
00694   140 CONTINUE
00695 *
00696   150 CONTINUE
00697 *
00698 *     Read in data from file to check accuracy of condition estimation
00699 *     Read input data until N=0
00700 *
00701       JTYPE = 0
00702   160 CONTINUE
00703       READ( NIUNIT, FMT = *, END = 200 )N, NSLCT
00704       IF( N.EQ.0 )
00705      $   GO TO 200
00706       JTYPE = JTYPE + 1
00707       ISEED( 1 ) = JTYPE
00708       IF( NSLCT.GT.0 )
00709      $   READ( NIUNIT, FMT = * )( ISLCT( I ), I = 1, NSLCT )
00710       DO 170 I = 1, N
00711          READ( NIUNIT, FMT = * )( A( I, J ), J = 1, N )
00712   170 CONTINUE
00713       READ( NIUNIT, FMT = * )RCDEIN, RCDVIN
00714 *
00715       CALL DGET24( .TRUE., 22, THRESH, ISEED, NOUNIT, N, A, LDA, H, HT,
00716      $             WR, WI, WRT, WIT, WRTMP, WITMP, VS, LDVS, VS1,
00717      $             RCDEIN, RCDVIN, NSLCT, ISLCT, RESULT, WORK, LWORK,
00718      $             IWORK, BWORK, INFO )
00719 *
00720 *     Check for RESULT(j) > THRESH
00721 *
00722       NTEST = 0
00723       NFAIL = 0
00724       DO 180 J = 1, 17
00725          IF( RESULT( J ).GE.ZERO )
00726      $      NTEST = NTEST + 1
00727          IF( RESULT( J ).GE.THRESH )
00728      $      NFAIL = NFAIL + 1
00729   180 CONTINUE
00730 *
00731       IF( NFAIL.GT.0 )
00732      $   NTESTF = NTESTF + 1
00733       IF( NTESTF.EQ.1 ) THEN
00734          WRITE( NOUNIT, FMT = 9999 )PATH
00735          WRITE( NOUNIT, FMT = 9998 )
00736          WRITE( NOUNIT, FMT = 9997 )
00737          WRITE( NOUNIT, FMT = 9996 )
00738          WRITE( NOUNIT, FMT = 9995 )THRESH
00739          WRITE( NOUNIT, FMT = 9994 )
00740          NTESTF = 2
00741       END IF
00742       DO 190 J = 1, 17
00743          IF( RESULT( J ).GE.THRESH ) THEN
00744             WRITE( NOUNIT, FMT = 9992 )N, JTYPE, J, RESULT( J )
00745          END IF
00746   190 CONTINUE
00747 *
00748       NERRS = NERRS + NFAIL
00749       NTESTT = NTESTT + NTEST
00750       GO TO 160
00751   200 CONTINUE
00752 *
00753 *     Summary
00754 *
00755       CALL DLASUM( PATH, NOUNIT, NERRS, NTESTT )
00756 *
00757  9999 FORMAT( / 1X, A3, ' -- Real Schur Form Decomposition Expert ',
00758      $      'Driver', / ' Matrix types (see DDRVSX for details):' )
00759 *
00760  9998 FORMAT( / ' Special Matrices:', / '  1=Zero matrix.             ',
00761      $      '           ', '  5=Diagonal: geometr. spaced entries.',
00762      $      / '  2=Identity matrix.                    ', '  6=Diagona',
00763      $      'l: clustered entries.', / '  3=Transposed Jordan block.  ',
00764      $      '          ', '  7=Diagonal: large, evenly spaced.', / '  ',
00765      $      '4=Diagonal: evenly spaced entries.    ', '  8=Diagonal: s',
00766      $      'mall, evenly spaced.' )
00767  9997 FORMAT( ' Dense, Non-Symmetric Matrices:', / '  9=Well-cond., ev',
00768      $      'enly spaced eigenvals.', ' 14=Ill-cond., geomet. spaced e',
00769      $      'igenals.', / ' 10=Well-cond., geom. spaced eigenvals. ',
00770      $      ' 15=Ill-conditioned, clustered e.vals.', / ' 11=Well-cond',
00771      $      'itioned, clustered e.vals. ', ' 16=Ill-cond., random comp',
00772      $      'lex ', / ' 12=Well-cond., random complex ', '         ',
00773      $      ' 17=Ill-cond., large rand. complx ', / ' 13=Ill-condi',
00774      $      'tioned, evenly spaced.     ', ' 18=Ill-cond., small rand.',
00775      $      ' complx ' )
00776  9996 FORMAT( ' 19=Matrix with random O(1) entries.    ', ' 21=Matrix ',
00777      $      'with small random entries.', / ' 20=Matrix with large ran',
00778      $      'dom entries.   ', / )
00779  9995 FORMAT( ' Tests performed with test threshold =', F8.2,
00780      $      / ' ( A denotes A on input and T denotes A on output)',
00781      $      / / ' 1 = 0 if T in Schur form (no sort), ',
00782      $      '  1/ulp otherwise', /
00783      $      ' 2 = | A - VS T transpose(VS) | / ( n |A| ulp ) (no sort)',
00784      $      / ' 3 = | I - VS transpose(VS) | / ( n ulp ) (no sort) ', /
00785      $      ' 4 = 0 if WR+sqrt(-1)*WI are eigenvalues of T (no sort),',
00786      $      '  1/ulp otherwise', /
00787      $      ' 5 = 0 if T same no matter if VS computed (no sort),',
00788      $      '  1/ulp otherwise', /
00789      $      ' 6 = 0 if WR, WI same no matter if VS computed (no sort)',
00790      $      ',  1/ulp otherwise' )
00791  9994 FORMAT( ' 7 = 0 if T in Schur form (sort), ', '  1/ulp otherwise',
00792      $      / ' 8 = | A - VS T transpose(VS) | / ( n |A| ulp ) (sort)',
00793      $      / ' 9 = | I - VS transpose(VS) | / ( n ulp ) (sort) ',
00794      $      / ' 10 = 0 if WR+sqrt(-1)*WI are eigenvalues of T (sort),',
00795      $      '  1/ulp otherwise', /
00796      $      ' 11 = 0 if T same no matter what else computed (sort),',
00797      $      '  1/ulp otherwise', /
00798      $      ' 12 = 0 if WR, WI same no matter what else computed ',
00799      $      '(sort), 1/ulp otherwise', /
00800      $      ' 13 = 0 if sorting succesful, 1/ulp otherwise',
00801      $      / ' 14 = 0 if RCONDE same no matter what else computed,',
00802      $      ' 1/ulp otherwise', /
00803      $      ' 15 = 0 if RCONDv same no matter what else computed,',
00804      $      ' 1/ulp otherwise', /
00805      $      ' 16 = | RCONDE - RCONDE(precomputed) | / cond(RCONDE),',
00806      $      / ' 17 = | RCONDV - RCONDV(precomputed) | / cond(RCONDV),' )
00807  9993 FORMAT( ' N=', I5, ', IWK=', I2, ', seed=', 4( I4, ',' ),
00808      $      ' type ', I2, ', test(', I2, ')=', G10.3 )
00809  9992 FORMAT( ' N=', I5, ', input example =', I3, ',  test(', I2, ')=',
00810      $      G10.3 )
00811  9991 FORMAT( ' DDRVSX: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
00812      $      I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' )
00813 *
00814       RETURN
00815 *
00816 *     End of DDRVSX
00817 *
00818       END