LAPACK: TESTING/EIG/ddrvev.f Source File

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00001       SUBROUTINE DDRVEV( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
00002      $                   NOUNIT, A, LDA, H, WR, WI, WR1, WI1, VL, LDVL,
00003      $                   VR, LDVR, LRE, LDLRE, RESULT, WORK, NWORK,
00004      $                   IWORK, 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, LDLRE, LDVL, LDVR, NOUNIT, NSIZES,
00012      $                   NTYPES, NWORK
00013       DOUBLE PRECISION   THRESH
00014 *     ..
00015 *     .. Array Arguments ..
00016       LOGICAL            DOTYPE( * )
00017       INTEGER            ISEED( 4 ), IWORK( * ), NN( * )
00018       DOUBLE PRECISION   A( LDA, * ), H( LDA, * ), LRE( LDLRE, * ),
00019      $                   RESULT( 7 ), VL( LDVL, * ), VR( LDVR, * ),
00020      $                   WI( * ), WI1( * ), WORK( * ), WR( * ), WR1( * )
00021 *     ..
00022 *
00023 *  Purpose
00024 *  =======
00025 *
00026 *     DDRVEV  checks the nonsymmetric eigenvalue problem driver DGEEV.
00027 *
00028 *     When DDRVEV is called, a number of matrix "sizes" ("n's") and a
00029 *     number of matrix "types" are specified.  For each size ("n")
00030 *     and each type of matrix, one matrix will be generated and used
00031 *     to test the nonsymmetric eigenroutines.  For each matrix, 7
00032 *     tests will be performed:
00033 *
00034 *     (1)     | A * VR - VR * W | / ( n |A| ulp )
00035 *
00036 *       Here VR is the matrix of unit right eigenvectors.
00037 *       W is a block diagonal matrix, with a 1x1 block for each
00038 *       real eigenvalue and a 2x2 block for each complex conjugate
00039 *       pair.  If eigenvalues j and j+1 are a complex conjugate pair,
00040 *       so WR(j) = WR(j+1) = wr and WI(j) = - WI(j+1) = wi, then the
00041 *       2 x 2 block corresponding to the pair will be:
00042 *
00043 *               (  wr  wi  )
00044 *               ( -wi  wr  )
00045 *
00046 *       Such a block multiplying an n x 2 matrix  ( ur ui ) on the
00047 *       right will be the same as multiplying  ur + i*ui  by  wr + i*wi.
00048 *
00049 *     (2)     | A**H * VL - VL * W**H | / ( n |A| ulp )
00050 *
00051 *       Here VL is the matrix of unit left eigenvectors, A**H is the
00052 *       conjugate transpose of A, and W is as above.
00053 *
00054 *     (3)     | |VR(i)| - 1 | / ulp and whether largest component real
00055 *
00056 *       VR(i) denotes the i-th column of VR.
00057 *
00058 *     (4)     | |VL(i)| - 1 | / ulp and whether largest component real
00059 *
00060 *       VL(i) denotes the i-th column of VL.
00061 *
00062 *     (5)     W(full) = W(partial)
00063 *
00064 *       W(full) denotes the eigenvalues computed when both VR and VL
00065 *       are also computed, and W(partial) denotes the eigenvalues
00066 *       computed when only W, only W and VR, or only W and VL are
00067 *       computed.
00068 *
00069 *     (6)     VR(full) = VR(partial)
00070 *
00071 *       VR(full) denotes the right eigenvectors computed when both VR
00072 *       and VL are computed, and VR(partial) denotes the result
00073 *       when only VR is computed.
00074 *
00075 *      (7)     VL(full) = VL(partial)
00076 *
00077 *       VL(full) denotes the left eigenvectors computed when both VR
00078 *       and VL are also computed, and VL(partial) denotes the result
00079 *       when only VL is computed.
00080 *
00081 *     The "sizes" are specified by an array NN(1:NSIZES); the value of
00082 *     each element NN(j) specifies one size.
00083 *     The "types" are specified by a logical array DOTYPE( 1:NTYPES );
00084 *     if DOTYPE(j) is .TRUE., then matrix type "j" will be generated.
00085 *     Currently, the list of possible types is:
00086 *
00087 *     (1)  The zero matrix.
00088 *     (2)  The identity matrix.
00089 *     (3)  A (transposed) Jordan block, with 1's on the diagonal.
00090 *
00091 *     (4)  A diagonal matrix with evenly spaced entries
00092 *          1, ..., ULP  and random signs.
00093 *          (ULP = (first number larger than 1) - 1 )
00094 *     (5)  A diagonal matrix with geometrically spaced entries
00095 *          1, ..., ULP  and random signs.
00096 *     (6)  A diagonal matrix with "clustered" entries 1, ULP, ..., ULP
00097 *          and random signs.
00098 *
00099 *     (7)  Same as (4), but multiplied by a constant near
00100 *          the overflow threshold
00101 *     (8)  Same as (4), but multiplied by a constant near
00102 *          the underflow threshold
00103 *
00104 *     (9)  A matrix of the form  U' T U, where U is orthogonal and
00105 *          T has evenly spaced entries 1, ..., ULP with random signs
00106 *          on the diagonal and random O(1) entries in the upper
00107 *          triangle.
00108 *
00109 *     (10) A matrix of the form  U' T U, where U is orthogonal and
00110 *          T has geometrically spaced entries 1, ..., ULP with random
00111 *          signs on the diagonal and random O(1) entries in the upper
00112 *          triangle.
00113 *
00114 *     (11) A matrix of the form  U' T U, where U is orthogonal and
00115 *          T has "clustered" entries 1, ULP,..., ULP with random
00116 *          signs on the diagonal and random O(1) entries in the upper
00117 *          triangle.
00118 *
00119 *     (12) A matrix of the form  U' T U, where U is orthogonal and
00120 *          T has real or complex conjugate paired eigenvalues randomly
00121 *          chosen from ( ULP, 1 ) and random O(1) entries in the upper
00122 *          triangle.
00123 *
00124 *     (13) A matrix of the form  X' T X, where X has condition
00125 *          SQRT( ULP ) and T has evenly spaced entries 1, ..., ULP
00126 *          with random signs on the diagonal and random O(1) entries
00127 *          in the upper triangle.
00128 *
00129 *     (14) A matrix of the form  X' T X, where X has condition
00130 *          SQRT( ULP ) and T has geometrically spaced entries
00131 *          1, ..., ULP with random signs on the diagonal and random
00132 *          O(1) entries in the upper triangle.
00133 *
00134 *     (15) A matrix of the form  X' T X, where X has condition
00135 *          SQRT( ULP ) and T has "clustered" entries 1, ULP,..., ULP
00136 *          with random signs on the diagonal and random O(1) entries
00137 *          in the upper triangle.
00138 *
00139 *     (16) A matrix of the form  X' T X, where X has condition
00140 *          SQRT( ULP ) and T has real or complex conjugate paired
00141 *          eigenvalues randomly chosen from ( ULP, 1 ) and random
00142 *          O(1) entries in the upper triangle.
00143 *
00144 *     (17) Same as (16), but multiplied by a constant
00145 *          near the overflow threshold
00146 *     (18) Same as (16), but multiplied by a constant
00147 *          near the underflow threshold
00148 *
00149 *     (19) Nonsymmetric matrix with random entries chosen from (-1,1).
00150 *          If N is at least 4, all entries in first two rows and last
00151 *          row, and first column and last two columns are zero.
00152 *     (20) Same as (19), but multiplied by a constant
00153 *          near the overflow threshold
00154 *     (21) Same as (19), but multiplied by a constant
00155 *          near the underflow threshold
00156 *
00157 *  Arguments
00158 *  ==========
00159 *
00160 *  NSIZES  (input) INTEGER
00161 *          The number of sizes of matrices to use.  If it is zero,
00162 *          DDRVEV does nothing.  It must be at least zero.
00163 *
00164 *  NN      (input) INTEGER array, dimension (NSIZES)
00165 *          An array containing the sizes to be used for the matrices.
00166 *          Zero values will be skipped.  The values must be at least
00167 *          zero.
00168 *
00169 *  NTYPES  (input) INTEGER
00170 *          The number of elements in DOTYPE.   If it is zero, DDRVEV
00171 *          does nothing.  It must be at least zero.  If it is MAXTYP+1
00172 *          and NSIZES is 1, then an additional type, MAXTYP+1 is
00173 *          defined, which is to use whatever matrix is in A.  This
00174 *          is only useful if DOTYPE(1:MAXTYP) is .FALSE. and
00175 *          DOTYPE(MAXTYP+1) is .TRUE. .
00176 *
00177 *  DOTYPE  (input) LOGICAL array, dimension (NTYPES)
00178 *          If DOTYPE(j) is .TRUE., then for each size in NN a
00179 *          matrix of that size and of type j will be generated.
00180 *          If NTYPES is smaller than the maximum number of types
00181 *          defined (PARAMETER MAXTYP), then types NTYPES+1 through
00182 *          MAXTYP will not be generated.  If NTYPES is larger
00183 *          than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES)
00184 *          will be ignored.
00185 *
00186 *  ISEED   (input/output) INTEGER array, dimension (4)
00187 *          On entry ISEED specifies the seed of the random number
00188 *          generator. The array elements should be between 0 and 4095;
00189 *          if not they will be reduced mod 4096.  Also, ISEED(4) must
00190 *          be odd.  The random number generator uses a linear
00191 *          congruential sequence limited to small integers, and so
00192 *          should produce machine independent random numbers. The
00193 *          values of ISEED are changed on exit, and can be used in the
00194 *          next call to DDRVEV to continue the same random number
00195 *          sequence.
00196 *
00197 *  THRESH  (input) DOUBLE PRECISION
00198 *          A test will count as "failed" if the "error", computed as
00199 *          described above, exceeds THRESH.  Note that the error
00200 *          is scaled to be O(1), so THRESH should be a reasonably
00201 *          small multiple of 1, e.g., 10 or 100.  In particular,
00202 *          it should not depend on the precision (single vs. double)
00203 *          or the size of the matrix.  It must be at least zero.
00204 *
00205 *  NOUNIT  (input) INTEGER
00206 *          The FORTRAN unit number for printing out error messages
00207 *          (e.g., if a routine returns INFO not equal to 0.)
00208 *
00209 *  A       (workspace) DOUBLE PRECISION array, dimension (LDA, max(NN))
00210 *          Used to hold the matrix whose eigenvalues are to be
00211 *          computed.  On exit, A contains the last matrix actually used.
00212 *
00213 *  LDA     (input) INTEGER
00214 *          The leading dimension of A, and H. LDA must be at
00215 *          least 1 and at least max(NN).
00216 *
00217 *  H       (workspace) DOUBLE PRECISION array, dimension (LDA, max(NN))
00218 *          Another copy of the test matrix A, modified by DGEEV.
00219 *
00220 *  WR      (workspace) DOUBLE PRECISION array, dimension (max(NN))
00221 *  WI      (workspace) DOUBLE PRECISION array, dimension (max(NN))
00222 *          The real and imaginary parts of the eigenvalues of A.
00223 *          On exit, WR + WI*i are the eigenvalues of the matrix in A.
00224 *
00225 *  WR1     (workspace) DOUBLE PRECISION array, dimension (max(NN))
00226 *  WI1     (workspace) DOUBLE PRECISION array, dimension (max(NN))
00227 *          Like WR, WI, these arrays contain the eigenvalues of A,
00228 *          but those computed when DGEEV only computes a partial
00229 *          eigendecomposition, i.e. not the eigenvalues and left
00230 *          and right eigenvectors.
00231 *
00232 *  VL      (workspace) DOUBLE PRECISION array, dimension (LDVL, max(NN))
00233 *          VL holds the computed left eigenvectors.
00234 *
00235 *  LDVL    (input) INTEGER
00236 *          Leading dimension of VL. Must be at least max(1,max(NN)).
00237 *
00238 *  VR      (workspace) DOUBLE PRECISION array, dimension (LDVR, max(NN))
00239 *          VR holds the computed right eigenvectors.
00240 *
00241 *  LDVR    (input) INTEGER
00242 *          Leading dimension of VR. Must be at least max(1,max(NN)).
00243 *
00244 *  LRE     (workspace) DOUBLE PRECISION array, dimension (LDLRE,max(NN))
00245 *          LRE holds the computed right or left eigenvectors.
00246 *
00247 *  LDLRE   (input) INTEGER
00248 *          Leading dimension of LRE. Must be at least max(1,max(NN)).
00249 *
00250 *  RESULT  (output) DOUBLE PRECISION array, dimension (7)
00251 *          The values computed by the seven tests described above.
00252 *          The values are currently limited to 1/ulp, to avoid overflow.
00253 *
00254 *  WORK    (workspace) DOUBLE PRECISION array, dimension (NWORK)
00255 *
00256 *  NWORK   (input) INTEGER
00257 *          The number of entries in WORK.  This must be at least
00258 *          5*NN(j)+2*NN(j)**2 for all j.
00259 *
00260 *  IWORK   (workspace) INTEGER array, dimension (max(NN))
00261 *
00262 *  INFO    (output) INTEGER
00263 *          If 0, then everything ran OK.
00264 *           -1: NSIZES < 0
00265 *           -2: Some NN(j) < 0
00266 *           -3: NTYPES < 0
00267 *           -6: THRESH < 0
00268 *           -9: LDA < 1 or LDA < NMAX, where NMAX is max( NN(j) ).
00269 *          -16: LDVL < 1 or LDVL < NMAX, where NMAX is max( NN(j) ).
00270 *          -18: LDVR < 1 or LDVR < NMAX, where NMAX is max( NN(j) ).
00271 *          -20: LDLRE < 1 or LDLRE < NMAX, where NMAX is max( NN(j) ).
00272 *          -23: NWORK too small.
00273 *          If  DLATMR, SLATMS, SLATME or DGEEV returns an error code,
00274 *              the absolute value of it is returned.
00275 *
00276 *-----------------------------------------------------------------------
00277 *
00278 *     Some Local Variables and Parameters:
00279 *     ---- ----- --------- --- ----------
00280 *
00281 *     ZERO, ONE       Real 0 and 1.
00282 *     MAXTYP          The number of types defined.
00283 *     NMAX            Largest value in NN.
00284 *     NERRS           The number of tests which have exceeded THRESH
00285 *     COND, CONDS,
00286 *     IMODE           Values to be passed to the matrix generators.
00287 *     ANORM           Norm of A; passed to matrix generators.
00288 *
00289 *     OVFL, UNFL      Overflow and underflow thresholds.
00290 *     ULP, ULPINV     Finest relative precision and its inverse.
00291 *     RTULP, RTULPI   Square roots of the previous 4 values.
00292 *
00293 *             The following four arrays decode JTYPE:
00294 *     KTYPE(j)        The general type (1-10) for type "j".
00295 *     KMODE(j)        The MODE value to be passed to the matrix
00296 *                     generator for type "j".
00297 *     KMAGN(j)        The order of magnitude ( O(1),
00298 *                     O(overflow^(1/2) ), O(underflow^(1/2) )
00299 *     KCONDS(j)       Selectw whether CONDS is to be 1 or
00300 *                     1/sqrt(ulp).  (0 means irrelevant.)
00301 *
00302 *  =====================================================================
00303 *
00304 *     .. Parameters ..
00305       DOUBLE PRECISION   ZERO, ONE
00306       PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
00307       DOUBLE PRECISION   TWO
00308       PARAMETER          ( TWO = 2.0D0 )
00309       INTEGER            MAXTYP
00310       PARAMETER          ( MAXTYP = 21 )
00311 *     ..
00312 *     .. Local Scalars ..
00313       LOGICAL            BADNN
00314       CHARACTER*3        PATH
00315       INTEGER            IINFO, IMODE, ITYPE, IWK, J, JCOL, JJ, JSIZE,
00316      $                   JTYPE, MTYPES, N, NERRS, NFAIL, NMAX, NNWORK,
00317      $                   NTEST, NTESTF, NTESTT
00318       DOUBLE PRECISION   ANORM, COND, CONDS, OVFL, RTULP, RTULPI, TNRM,
00319      $                   ULP, ULPINV, UNFL, VMX, VRMX, VTST
00320 *     ..
00321 *     .. Local Arrays ..
00322       CHARACTER          ADUMMA( 1 )
00323       INTEGER            IDUMMA( 1 ), IOLDSD( 4 ), KCONDS( MAXTYP ),
00324      $                   KMAGN( MAXTYP ), KMODE( MAXTYP ),
00325      $                   KTYPE( MAXTYP )
00326       DOUBLE PRECISION   DUM( 1 ), RES( 2 )
00327 *     ..
00328 *     .. External Functions ..
00329       DOUBLE PRECISION   DLAMCH, DLAPY2, DNRM2
00330       EXTERNAL           DLAMCH, DLAPY2, DNRM2
00331 *     ..
00332 *     .. External Subroutines ..
00333       EXTERNAL           DGEEV, DGET22, DLABAD, DLACPY, DLASET, DLASUM,
00334      $                   DLATME, DLATMR, DLATMS, XERBLA
00335 *     ..
00336 *     .. Intrinsic Functions ..
00337       INTRINSIC          ABS, MAX, MIN, SQRT
00338 *     ..
00339 *     .. Data statements ..
00340       DATA               KTYPE / 1, 2, 3, 5*4, 4*6, 6*6, 3*9 /
00341       DATA               KMAGN / 3*1, 1, 1, 1, 2, 3, 4*1, 1, 1, 1, 1, 2,
00342      $                   3, 1, 2, 3 /
00343       DATA               KMODE / 3*0, 4, 3, 1, 4, 4, 4, 3, 1, 5, 4, 3,
00344      $                   1, 5, 5, 5, 4, 3, 1 /
00345       DATA               KCONDS / 3*0, 5*0, 4*1, 6*2, 3*0 /
00346 *     ..
00347 *     .. Executable Statements ..
00348 *
00349       PATH( 1: 1 ) = 'Double precision'
00350       PATH( 2: 3 ) = 'EV'
00351 *
00352 *     Check for errors
00353 *
00354       NTESTT = 0
00355       NTESTF = 0
00356       INFO = 0
00357 *
00358 *     Important constants
00359 *
00360       BADNN = .FALSE.
00361       NMAX = 0
00362       DO 10 J = 1, NSIZES
00363          NMAX = MAX( NMAX, NN( J ) )
00364          IF( NN( J ).LT.0 )
00365      $      BADNN = .TRUE.
00366    10 CONTINUE
00367 *
00368 *     Check for errors
00369 *
00370       IF( NSIZES.LT.0 ) THEN
00371          INFO = -1
00372       ELSE IF( BADNN ) THEN
00373          INFO = -2
00374       ELSE IF( NTYPES.LT.0 ) THEN
00375          INFO = -3
00376       ELSE IF( THRESH.LT.ZERO ) THEN
00377          INFO = -6
00378       ELSE IF( NOUNIT.LE.0 ) THEN
00379          INFO = -7
00380       ELSE IF( LDA.LT.1 .OR. LDA.LT.NMAX ) THEN
00381          INFO = -9
00382       ELSE IF( LDVL.LT.1 .OR. LDVL.LT.NMAX ) THEN
00383          INFO = -16
00384       ELSE IF( LDVR.LT.1 .OR. LDVR.LT.NMAX ) THEN
00385          INFO = -18
00386       ELSE IF( LDLRE.LT.1 .OR. LDLRE.LT.NMAX ) THEN
00387          INFO = -20
00388       ELSE IF( 5*NMAX+2*NMAX**2.GT.NWORK ) THEN
00389          INFO = -23
00390       END IF
00391 *
00392       IF( INFO.NE.0 ) THEN
00393          CALL XERBLA( 'DDRVEV', -INFO )
00394          RETURN
00395       END IF
00396 *
00397 *     Quick return if nothing to do
00398 *
00399       IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 )
00400      $   RETURN
00401 *
00402 *     More Important constants
00403 *
00404       UNFL = DLAMCH( 'Safe minimum' )
00405       OVFL = ONE / UNFL
00406       CALL DLABAD( UNFL, OVFL )
00407       ULP = DLAMCH( 'Precision' )
00408       ULPINV = ONE / ULP
00409       RTULP = SQRT( ULP )
00410       RTULPI = ONE / RTULP
00411 *
00412 *     Loop over sizes, types
00413 *
00414       NERRS = 0
00415 *
00416       DO 270 JSIZE = 1, NSIZES
00417          N = NN( JSIZE )
00418          IF( NSIZES.NE.1 ) THEN
00419             MTYPES = MIN( MAXTYP, NTYPES )
00420          ELSE
00421             MTYPES = MIN( MAXTYP+1, NTYPES )
00422          END IF
00423 *
00424          DO 260 JTYPE = 1, MTYPES
00425             IF( .NOT.DOTYPE( JTYPE ) )
00426      $         GO TO 260
00427 *
00428 *           Save ISEED in case of an error.
00429 *
00430             DO 20 J = 1, 4
00431                IOLDSD( J ) = ISEED( J )
00432    20       CONTINUE
00433 *
00434 *           Compute "A"
00435 *
00436 *           Control parameters:
00437 *
00438 *           KMAGN  KCONDS  KMODE        KTYPE
00439 *       =1  O(1)   1       clustered 1  zero
00440 *       =2  large  large   clustered 2  identity
00441 *       =3  small          exponential  Jordan
00442 *       =4                 arithmetic   diagonal, (w/ eigenvalues)
00443 *       =5                 random log   symmetric, w/ eigenvalues
00444 *       =6                 random       general, w/ eigenvalues
00445 *       =7                              random diagonal
00446 *       =8                              random symmetric
00447 *       =9                              random general
00448 *       =10                             random triangular
00449 *
00450             IF( MTYPES.GT.MAXTYP )
00451      $         GO TO 90
00452 *
00453             ITYPE = KTYPE( JTYPE )
00454             IMODE = KMODE( JTYPE )
00455 *
00456 *           Compute norm
00457 *
00458             GO TO ( 30, 40, 50 )KMAGN( JTYPE )
00459 *
00460    30       CONTINUE
00461             ANORM = ONE
00462             GO TO 60
00463 *
00464    40       CONTINUE
00465             ANORM = OVFL*ULP
00466             GO TO 60
00467 *
00468    50       CONTINUE
00469             ANORM = UNFL*ULPINV
00470             GO TO 60
00471 *
00472    60       CONTINUE
00473 *
00474             CALL DLASET( 'Full', LDA, N, ZERO, ZERO, A, LDA )
00475             IINFO = 0
00476             COND = ULPINV
00477 *
00478 *           Special Matrices -- Identity & Jordan block
00479 *
00480 *              Zero
00481 *
00482             IF( ITYPE.EQ.1 ) THEN
00483                IINFO = 0
00484 *
00485             ELSE IF( ITYPE.EQ.2 ) THEN
00486 *
00487 *              Identity
00488 *
00489                DO 70 JCOL = 1, N
00490                   A( JCOL, JCOL ) = ANORM
00491    70          CONTINUE
00492 *
00493             ELSE IF( ITYPE.EQ.3 ) THEN
00494 *
00495 *              Jordan Block
00496 *
00497                DO 80 JCOL = 1, N
00498                   A( JCOL, JCOL ) = ANORM
00499                   IF( JCOL.GT.1 )
00500      $               A( JCOL, JCOL-1 ) = ONE
00501    80          CONTINUE
00502 *
00503             ELSE IF( ITYPE.EQ.4 ) THEN
00504 *
00505 *              Diagonal Matrix, [Eigen]values Specified
00506 *
00507                CALL DLATMS( N, N, 'S', ISEED, 'S', WORK, IMODE, COND,
00508      $                      ANORM, 0, 0, 'N', A, LDA, WORK( N+1 ),
00509      $                      IINFO )
00510 *
00511             ELSE IF( ITYPE.EQ.5 ) THEN
00512 *
00513 *              Symmetric, eigenvalues specified
00514 *
00515                CALL DLATMS( N, N, 'S', ISEED, 'S', WORK, IMODE, COND,
00516      $                      ANORM, N, N, 'N', A, LDA, WORK( N+1 ),
00517      $                      IINFO )
00518 *
00519             ELSE IF( ITYPE.EQ.6 ) THEN
00520 *
00521 *              General, eigenvalues specified
00522 *
00523                IF( KCONDS( JTYPE ).EQ.1 ) THEN
00524                   CONDS = ONE
00525                ELSE IF( KCONDS( JTYPE ).EQ.2 ) THEN
00526                   CONDS = RTULPI
00527                ELSE
00528                   CONDS = ZERO
00529                END IF
00530 *
00531                ADUMMA( 1 ) = ' '
00532                CALL DLATME( N, 'S', ISEED, WORK, IMODE, COND, ONE,
00533      $                      ADUMMA, 'T', 'T', 'T', WORK( N+1 ), 4,
00534      $                      CONDS, N, N, ANORM, A, LDA, WORK( 2*N+1 ),
00535      $                      IINFO )
00536 *
00537             ELSE IF( ITYPE.EQ.7 ) THEN
00538 *
00539 *              Diagonal, random eigenvalues
00540 *
00541                CALL DLATMR( N, N, 'S', ISEED, 'S', WORK, 6, ONE, ONE,
00542      $                      'T', 'N', WORK( N+1 ), 1, ONE,
00543      $                      WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, 0, 0,
00544      $                      ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
00545 *
00546             ELSE IF( ITYPE.EQ.8 ) THEN
00547 *
00548 *              Symmetric, random eigenvalues
00549 *
00550                CALL DLATMR( N, N, 'S', ISEED, 'S', WORK, 6, ONE, ONE,
00551      $                      'T', 'N', WORK( N+1 ), 1, ONE,
00552      $                      WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, N, N,
00553      $                      ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
00554 *
00555             ELSE IF( ITYPE.EQ.9 ) THEN
00556 *
00557 *              General, random eigenvalues
00558 *
00559                CALL DLATMR( N, N, 'S', ISEED, 'N', WORK, 6, ONE, ONE,
00560      $                      'T', 'N', WORK( N+1 ), 1, ONE,
00561      $                      WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, N, N,
00562      $                      ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
00563                IF( N.GE.4 ) THEN
00564                   CALL DLASET( 'Full', 2, N, ZERO, ZERO, A, LDA )
00565                   CALL DLASET( 'Full', N-3, 1, ZERO, ZERO, A( 3, 1 ),
00566      $                         LDA )
00567                   CALL DLASET( 'Full', N-3, 2, ZERO, ZERO, A( 3, N-1 ),
00568      $                         LDA )
00569                   CALL DLASET( 'Full', 1, N, ZERO, ZERO, A( N, 1 ),
00570      $                         LDA )
00571                END IF
00572 *
00573             ELSE IF( ITYPE.EQ.10 ) THEN
00574 *
00575 *              Triangular, random eigenvalues
00576 *
00577                CALL DLATMR( N, N, 'S', ISEED, 'N', WORK, 6, ONE, ONE,
00578      $                      'T', 'N', WORK( N+1 ), 1, ONE,
00579      $                      WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, N, 0,
00580      $                      ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
00581 *
00582             ELSE
00583 *
00584                IINFO = 1
00585             END IF
00586 *
00587             IF( IINFO.NE.0 ) THEN
00588                WRITE( NOUNIT, FMT = 9993 )'Generator', IINFO, N, JTYPE,
00589      $            IOLDSD
00590                INFO = ABS( IINFO )
00591                RETURN
00592             END IF
00593 *
00594    90       CONTINUE
00595 *
00596 *           Test for minimal and generous workspace
00597 *
00598             DO 250 IWK = 1, 2
00599                IF( IWK.EQ.1 ) THEN
00600                   NNWORK = 4*N
00601                ELSE
00602                   NNWORK = 5*N + 2*N**2
00603                END IF
00604                NNWORK = MAX( NNWORK, 1 )
00605 *
00606 *              Initialize RESULT
00607 *
00608                DO 100 J = 1, 7
00609                   RESULT( J ) = -ONE
00610   100          CONTINUE
00611 *
00612 *              Compute eigenvalues and eigenvectors, and test them
00613 *
00614                CALL DLACPY( 'F', N, N, A, LDA, H, LDA )
00615                CALL DGEEV( 'V', 'V', N, H, LDA, WR, WI, VL, LDVL, VR,
00616      $                     LDVR, WORK, NNWORK, IINFO )
00617                IF( IINFO.NE.0 ) THEN
00618                   RESULT( 1 ) = ULPINV
00619                   WRITE( NOUNIT, FMT = 9993 )'DGEEV1', IINFO, N, JTYPE,
00620      $               IOLDSD
00621                   INFO = ABS( IINFO )
00622                   GO TO 220
00623                END IF
00624 *
00625 *              Do Test (1)
00626 *
00627                CALL DGET22( 'N', 'N', 'N', N, A, LDA, VR, LDVR, WR, WI,
00628      $                      WORK, RES )
00629                RESULT( 1 ) = RES( 1 )
00630 *
00631 *              Do Test (2)
00632 *
00633                CALL DGET22( 'T', 'N', 'T', N, A, LDA, VL, LDVL, WR, WI,
00634      $                      WORK, RES )
00635                RESULT( 2 ) = RES( 1 )
00636 *
00637 *              Do Test (3)
00638 *
00639                DO 120 J = 1, N
00640                   TNRM = ONE
00641                   IF( WI( J ).EQ.ZERO ) THEN
00642                      TNRM = DNRM2( N, VR( 1, J ), 1 )
00643                   ELSE IF( WI( J ).GT.ZERO ) THEN
00644                      TNRM = DLAPY2( DNRM2( N, VR( 1, J ), 1 ),
00645      $                      DNRM2( N, VR( 1, J+1 ), 1 ) )
00646                   END IF
00647                   RESULT( 3 ) = MAX( RESULT( 3 ),
00648      $                          MIN( ULPINV, ABS( TNRM-ONE ) / ULP ) )
00649                   IF( WI( J ).GT.ZERO ) THEN
00650                      VMX = ZERO
00651                      VRMX = ZERO
00652                      DO 110 JJ = 1, N
00653                         VTST = DLAPY2( VR( JJ, J ), VR( JJ, J+1 ) )
00654                         IF( VTST.GT.VMX )
00655      $                     VMX = VTST
00656                         IF( VR( JJ, J+1 ).EQ.ZERO .AND.
00657      $                      ABS( VR( JJ, J ) ).GT.VRMX )
00658      $                      VRMX = ABS( VR( JJ, J ) )
00659   110                CONTINUE
00660                      IF( VRMX / VMX.LT.ONE-TWO*ULP )
00661      $                  RESULT( 3 ) = ULPINV
00662                   END IF
00663   120          CONTINUE
00664 *
00665 *              Do Test (4)
00666 *
00667                DO 140 J = 1, N
00668                   TNRM = ONE
00669                   IF( WI( J ).EQ.ZERO ) THEN
00670                      TNRM = DNRM2( N, VL( 1, J ), 1 )
00671                   ELSE IF( WI( J ).GT.ZERO ) THEN
00672                      TNRM = DLAPY2( DNRM2( N, VL( 1, J ), 1 ),
00673      $                      DNRM2( N, VL( 1, J+1 ), 1 ) )
00674                   END IF
00675                   RESULT( 4 ) = MAX( RESULT( 4 ),
00676      $                          MIN( ULPINV, ABS( TNRM-ONE ) / ULP ) )
00677                   IF( WI( J ).GT.ZERO ) THEN
00678                      VMX = ZERO
00679                      VRMX = ZERO
00680                      DO 130 JJ = 1, N
00681                         VTST = DLAPY2( VL( JJ, J ), VL( JJ, J+1 ) )
00682                         IF( VTST.GT.VMX )
00683      $                     VMX = VTST
00684                         IF( VL( JJ, J+1 ).EQ.ZERO .AND.
00685      $                      ABS( VL( JJ, J ) ).GT.VRMX )
00686      $                      VRMX = ABS( VL( JJ, J ) )
00687   130                CONTINUE
00688                      IF( VRMX / VMX.LT.ONE-TWO*ULP )
00689      $                  RESULT( 4 ) = ULPINV
00690                   END IF
00691   140          CONTINUE
00692 *
00693 *              Compute eigenvalues only, and test them
00694 *
00695                CALL DLACPY( 'F', N, N, A, LDA, H, LDA )
00696                CALL DGEEV( 'N', 'N', N, H, LDA, WR1, WI1, DUM, 1, DUM,
00697      $                     1, WORK, NNWORK, IINFO )
00698                IF( IINFO.NE.0 ) THEN
00699                   RESULT( 1 ) = ULPINV
00700                   WRITE( NOUNIT, FMT = 9993 )'DGEEV2', IINFO, N, JTYPE,
00701      $               IOLDSD
00702                   INFO = ABS( IINFO )
00703                   GO TO 220
00704                END IF
00705 *
00706 *              Do Test (5)
00707 *
00708                DO 150 J = 1, N
00709                   IF( WR( J ).NE.WR1( J ) .OR. WI( J ).NE.WI1( J ) )
00710      $               RESULT( 5 ) = ULPINV
00711   150          CONTINUE
00712 *
00713 *              Compute eigenvalues and right eigenvectors, and test them
00714 *
00715                CALL DLACPY( 'F', N, N, A, LDA, H, LDA )
00716                CALL DGEEV( 'N', 'V', N, H, LDA, WR1, WI1, DUM, 1, LRE,
00717      $                     LDLRE, WORK, NNWORK, IINFO )
00718                IF( IINFO.NE.0 ) THEN
00719                   RESULT( 1 ) = ULPINV
00720                   WRITE( NOUNIT, FMT = 9993 )'DGEEV3', IINFO, N, JTYPE,
00721      $               IOLDSD
00722                   INFO = ABS( IINFO )
00723                   GO TO 220
00724                END IF
00725 *
00726 *              Do Test (5) again
00727 *
00728                DO 160 J = 1, N
00729                   IF( WR( J ).NE.WR1( J ) .OR. WI( J ).NE.WI1( J ) )
00730      $               RESULT( 5 ) = ULPINV
00731   160          CONTINUE
00732 *
00733 *              Do Test (6)
00734 *
00735                DO 180 J = 1, N
00736                   DO 170 JJ = 1, N
00737                      IF( VR( J, JJ ).NE.LRE( J, JJ ) )
00738      $                  RESULT( 6 ) = ULPINV
00739   170             CONTINUE
00740   180          CONTINUE
00741 *
00742 *              Compute eigenvalues and left eigenvectors, and test them
00743 *
00744                CALL DLACPY( 'F', N, N, A, LDA, H, LDA )
00745                CALL DGEEV( 'V', 'N', N, H, LDA, WR1, WI1, LRE, LDLRE,
00746      $                     DUM, 1, WORK, NNWORK, IINFO )
00747                IF( IINFO.NE.0 ) THEN
00748                   RESULT( 1 ) = ULPINV
00749                   WRITE( NOUNIT, FMT = 9993 )'DGEEV4', IINFO, N, JTYPE,
00750      $               IOLDSD
00751                   INFO = ABS( IINFO )
00752                   GO TO 220
00753                END IF
00754 *
00755 *              Do Test (5) again
00756 *
00757                DO 190 J = 1, N
00758                   IF( WR( J ).NE.WR1( J ) .OR. WI( J ).NE.WI1( J ) )
00759      $               RESULT( 5 ) = ULPINV
00760   190          CONTINUE
00761 *
00762 *              Do Test (7)
00763 *
00764                DO 210 J = 1, N
00765                   DO 200 JJ = 1, N
00766                      IF( VL( J, JJ ).NE.LRE( J, JJ ) )
00767      $                  RESULT( 7 ) = ULPINV
00768   200             CONTINUE
00769   210          CONTINUE
00770 *
00771 *              End of Loop -- Check for RESULT(j) > THRESH
00772 *
00773   220          CONTINUE
00774 *
00775                NTEST = 0
00776                NFAIL = 0
00777                DO 230 J = 1, 7
00778                   IF( RESULT( J ).GE.ZERO )
00779      $               NTEST = NTEST + 1
00780                   IF( RESULT( J ).GE.THRESH )
00781      $               NFAIL = NFAIL + 1
00782   230          CONTINUE
00783 *
00784                IF( NFAIL.GT.0 )
00785      $            NTESTF = NTESTF + 1
00786                IF( NTESTF.EQ.1 ) THEN
00787                   WRITE( NOUNIT, FMT = 9999 )PATH
00788                   WRITE( NOUNIT, FMT = 9998 )
00789                   WRITE( NOUNIT, FMT = 9997 )
00790                   WRITE( NOUNIT, FMT = 9996 )
00791                   WRITE( NOUNIT, FMT = 9995 )THRESH
00792                   NTESTF = 2
00793                END IF
00794 *
00795                DO 240 J = 1, 7
00796                   IF( RESULT( J ).GE.THRESH ) THEN
00797                      WRITE( NOUNIT, FMT = 9994 )N, IWK, IOLDSD, JTYPE,
00798      $                  J, RESULT( J )
00799                   END IF
00800   240          CONTINUE
00801 *
00802                NERRS = NERRS + NFAIL
00803                NTESTT = NTESTT + NTEST
00804 *
00805   250       CONTINUE
00806   260    CONTINUE
00807   270 CONTINUE
00808 *
00809 *     Summary
00810 *
00811       CALL DLASUM( PATH, NOUNIT, NERRS, NTESTT )
00812 *
00813  9999 FORMAT( / 1X, A3, ' -- Real Eigenvalue-Eigenvector Decomposition',
00814      $      ' Driver', / ' Matrix types (see DDRVEV for details): ' )
00815 *
00816  9998 FORMAT( / ' Special Matrices:', / '  1=Zero matrix.             ',
00817      $      '           ', '  5=Diagonal: geometr. spaced entries.',
00818      $      / '  2=Identity matrix.                    ', '  6=Diagona',
00819      $      'l: clustered entries.', / '  3=Transposed Jordan block.  ',
00820      $      '          ', '  7=Diagonal: large, evenly spaced.', / '  ',
00821      $      '4=Diagonal: evenly spaced entries.    ', '  8=Diagonal: s',
00822      $      'mall, evenly spaced.' )
00823  9997 FORMAT( ' Dense, Non-Symmetric Matrices:', / '  9=Well-cond., ev',
00824      $      'enly spaced eigenvals.', ' 14=Ill-cond., geomet. spaced e',
00825      $      'igenals.', / ' 10=Well-cond., geom. spaced eigenvals. ',
00826      $      ' 15=Ill-conditioned, clustered e.vals.', / ' 11=Well-cond',
00827      $      'itioned, clustered e.vals. ', ' 16=Ill-cond., random comp',
00828      $      'lex ', / ' 12=Well-cond., random complex ', 6X, '   ',
00829      $      ' 17=Ill-cond., large rand. complx ', / ' 13=Ill-condi',
00830      $      'tioned, evenly spaced.     ', ' 18=Ill-cond., small rand.',
00831      $      ' complx ' )
00832  9996 FORMAT( ' 19=Matrix with random O(1) entries.    ', ' 21=Matrix ',
00833      $      'with small random entries.', / ' 20=Matrix with large ran',
00834      $      'dom entries.   ', / )
00835  9995 FORMAT( ' Tests performed with test threshold =', F8.2,
00836      $      / / ' 1 = | A VR - VR W | / ( n |A| ulp ) ',
00837      $      / ' 2 = | transpose(A) VL - VL W | / ( n |A| ulp ) ',
00838      $      / ' 3 = | |VR(i)| - 1 | / ulp ',
00839      $      / ' 4 = | |VL(i)| - 1 | / ulp ',
00840      $      / ' 5 = 0 if W same no matter if VR or VL computed,',
00841      $      ' 1/ulp otherwise', /
00842      $      ' 6 = 0 if VR same no matter if VL computed,',
00843      $      '  1/ulp otherwise', /
00844      $      ' 7 = 0 if VL same no matter if VR computed,',
00845      $      '  1/ulp otherwise', / )
00846  9994 FORMAT( ' N=', I5, ', IWK=', I2, ', seed=', 4( I4, ',' ),
00847      $      ' type ', I2, ', test(', I2, ')=', G10.3 )
00848  9993 FORMAT( ' DDRVEV: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
00849      $      I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' )
00850 *
00851       RETURN
00852 *
00853 *     End of DDRVEV
00854 *
00855       END