LAPACK: TESTING/EIG/cdrvgg.f Source File

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00001       SUBROUTINE CDRVGG( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
00002      $                   THRSHN, NOUNIT, A, LDA, B, S, T, S2, T2, Q,
00003      $                   LDQ, Z, ALPHA1, BETA1, ALPHA2, BETA2, VL, VR,
00004      $                   WORK, LWORK, RWORK, RESULT, 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, LDQ, LWORK, NOUNIT, NSIZES, NTYPES
00012       REAL               THRESH, THRSHN
00013 *     ..
00014 *     .. Array Arguments ..
00015 *
00016 *  Purpose
00017 *  =======
00018 *
00019 *  CDRVGG  checks the nonsymmetric generalized eigenvalue driver
00020 *  routines.
00021 *                                T          T        T
00022 *  CGEGS factors A and B as Q S Z  and Q T Z , where   means
00023 *  transpose, T is upper triangular, S is in generalized Schur form
00024 *  (upper triangular), and Q and Z are unitary.  It also
00025 *  computes the generalized eigenvalues (alpha(1),beta(1)), ...,
00026 *  (alpha(n),beta(n)), where alpha(j)=S(j,j) and beta(j)=T(j,j) --
00027 *  thus, w(j) = alpha(j)/beta(j) is a root of the generalized
00028 *  eigenvalue problem
00029 *
00030 *      det( A - w(j) B ) = 0
00031 *
00032 *  and m(j) = beta(j)/alpha(j) is a root of the essentially equivalent
00033 *  problem
00034 *
00035 *      det( m(j) A - B ) = 0
00036 *
00037 *  CGEGV computes the generalized eigenvalues (alpha(1),beta(1)), ...,
00038 *  (alpha(n),beta(n)), the matrix L whose columns contain the
00039 *  generalized left eigenvectors l, and the matrix R whose columns
00040 *  contain the generalized right eigenvectors r for the pair (A,B).
00041 *
00042 *  When CDRVGG is called, a number of matrix "sizes" ("n's") and a
00043 *  number of matrix "types" are specified.  For each size ("n")
00044 *  and each type of matrix, one matrix will be generated and used
00045 *  to test the nonsymmetric eigenroutines.  For each matrix, 7
00046 *  tests will be performed and compared with the threshhold THRESH:
00047 *
00048 *  Results from CGEGS:
00049 *
00050 *                   H
00051 *  (1)   | A - Q S Z  | / ( |A| n ulp )
00052 *
00053 *                   H
00054 *  (2)   | B - Q T Z  | / ( |B| n ulp )
00055 *
00056 *                H
00057 *  (3)   | I - QQ  | / ( n ulp )
00058 *
00059 *                H
00060 *  (4)   | I - ZZ  | / ( n ulp )
00061 *
00062 *  (5)   maximum over j of D(j)  where:
00063 *
00064 *                      |alpha(j) - S(j,j)|        |beta(j) - T(j,j)|
00065 *            D(j) = ------------------------ + -----------------------
00066 *                   max(|alpha(j)|,|S(j,j)|)   max(|beta(j)|,|T(j,j)|)
00067 *
00068 *  Results from CGEGV:
00069 *
00070 *  (6)   max over all left eigenvalue/-vector pairs (beta/alpha,l) of
00071 *
00072 *     | l**H * (beta A - alpha B) | / ( ulp max( |beta A|, |alpha B| ) )
00073 *
00074 *        where l**H is the conjugate tranpose of l.
00075 *
00076 *  (7)   max over all right eigenvalue/-vector pairs (beta/alpha,r) of
00077 *
00078 *        | (beta A - alpha B) r | / ( ulp max( |beta A|, |alpha B| ) )
00079 *
00080 *  Test Matrices
00081 *  ---- --------
00082 *
00083 *  The sizes of the test matrices are specified by an array
00084 *  NN(1:NSIZES); the value of each element NN(j) specifies one size.
00085 *  The "types" are specified by a logical array DOTYPE( 1:NTYPES ); if
00086 *  DOTYPE(j) is .TRUE., then matrix type "j" will be generated.
00087 *  Currently, the list of possible types is:
00088 *
00089 *  (1)  ( 0, 0 )         (a pair of zero matrices)
00090 *
00091 *  (2)  ( I, 0 )         (an identity and a zero matrix)
00092 *
00093 *  (3)  ( 0, I )         (an identity and a zero matrix)
00094 *
00095 *  (4)  ( I, I )         (a pair of identity matrices)
00096 *
00097 *          t   t
00098 *  (5)  ( J , J  )       (a pair of transposed Jordan blocks)
00099 *
00100 *                                      t                ( I   0  )
00101 *  (6)  ( X, Y )         where  X = ( J   0  )  and Y = (      t )
00102 *                                   ( 0   I  )          ( 0   J  )
00103 *                        and I is a k x k identity and J a (k+1)x(k+1)
00104 *                        Jordan block; k=(N-1)/2
00105 *
00106 *  (7)  ( D, I )         where D is diag( 0, 1,..., N-1 ) (a diagonal
00107 *                        matrix with those diagonal entries.)
00108 *  (8)  ( I, D )
00109 *
00110 *  (9)  ( big*D, small*I ) where "big" is near overflow and small=1/big
00111 *
00112 *  (10) ( small*D, big*I )
00113 *
00114 *  (11) ( big*I, small*D )
00115 *
00116 *  (12) ( small*I, big*D )
00117 *
00118 *  (13) ( big*D, big*I )
00119 *
00120 *  (14) ( small*D, small*I )
00121 *
00122 *  (15) ( D1, D2 )        where D1 is diag( 0, 0, 1, ..., N-3, 0 ) and
00123 *                         D2 is diag( 0, N-3, N-4,..., 1, 0, 0 )
00124 *            t   t
00125 *  (16) Q ( J , J ) Z     where Q and Z are random unitary matrices.
00126 *
00127 *  (17) Q ( T1, T2 ) Z    where T1 and T2 are upper triangular matrices
00128 *                         with random O(1) entries above the diagonal
00129 *                         and diagonal entries diag(T1) =
00130 *                         ( 0, 0, 1, ..., N-3, 0 ) and diag(T2) =
00131 *                         ( 0, N-3, N-4,..., 1, 0, 0 )
00132 *
00133 *  (18) Q ( T1, T2 ) Z    diag(T1) = ( 0, 0, 1, 1, s, ..., s, 0 )
00134 *                         diag(T2) = ( 0, 1, 0, 1,..., 1, 0 )
00135 *                         s = machine precision.
00136 *
00137 *  (19) Q ( T1, T2 ) Z    diag(T1)=( 0,0,1,1, 1-d, ..., 1-(N-5)*d=s, 0 )
00138 *                         diag(T2) = ( 0, 1, 0, 1, ..., 1, 0 )
00139 *
00140 *                                                         N-5
00141 *  (20) Q ( T1, T2 ) Z    diag(T1)=( 0, 0, 1, 1, a, ..., a   =s, 0 )
00142 *                         diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 )
00143 *
00144 *  (21) Q ( T1, T2 ) Z    diag(T1)=( 0, 0, 1, r1, r2, ..., r(N-4), 0 )
00145 *                         diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 )
00146 *                         where r1,..., r(N-4) are random.
00147 *
00148 *  (22) Q ( big*T1, small*T2 ) Z    diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
00149 *                                   diag(T2) = ( 0, 1, ..., 1, 0, 0 )
00150 *
00151 *  (23) Q ( small*T1, big*T2 ) Z    diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
00152 *                                   diag(T2) = ( 0, 1, ..., 1, 0, 0 )
00153 *
00154 *  (24) Q ( small*T1, small*T2 ) Z  diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
00155 *                                   diag(T2) = ( 0, 1, ..., 1, 0, 0 )
00156 *
00157 *  (25) Q ( big*T1, big*T2 ) Z      diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
00158 *                                   diag(T2) = ( 0, 1, ..., 1, 0, 0 )
00159 *
00160 *  (26) Q ( T1, T2 ) Z     where T1 and T2 are random upper-triangular
00161 *                          matrices.
00162 *
00163 *  Arguments
00164 *  =========
00165 *
00166 *  NSIZES  (input) INTEGER
00167 *          The number of sizes of matrices to use.  If it is zero,
00168 *          CDRVGG does nothing.  It must be at least zero.
00169 *
00170 *  NN      (input) INTEGER array, dimension (NSIZES)
00171 *          An array containing the sizes to be used for the matrices.
00172 *          Zero values will be skipped.  The values must be at least
00173 *          zero.
00174 *
00175 *  NTYPES  (input) INTEGER
00176 *          The number of elements in DOTYPE.   If it is zero, CDRVGG
00177 *          does nothing.  It must be at least zero.  If it is MAXTYP+1
00178 *          and NSIZES is 1, then an additional type, MAXTYP+1 is
00179 *          defined, which is to use whatever matrix is in A.  This
00180 *          is only useful if DOTYPE(1:MAXTYP) is .FALSE. and
00181 *          DOTYPE(MAXTYP+1) is .TRUE. .
00182 *
00183 *  DOTYPE  (input) LOGICAL array, dimension (NTYPES)
00184 *          If DOTYPE(j) is .TRUE., then for each size in NN a
00185 *          matrix of that size and of type j will be generated.
00186 *          If NTYPES is smaller than the maximum number of types
00187 *          defined (PARAMETER MAXTYP), then types NTYPES+1 through
00188 *          MAXTYP will not be generated.  If NTYPES is larger
00189 *          than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES)
00190 *          will be ignored.
00191 *
00192 *  ISEED   (input/output) INTEGER array, dimension (4)
00193 *          On entry ISEED specifies the seed of the random number
00194 *          generator. The array elements should be between 0 and 4095;
00195 *          if not they will be reduced mod 4096.  Also, ISEED(4) must
00196 *          be odd.  The random number generator uses a linear
00197 *          congruential sequence limited to small integers, and so
00198 *          should produce machine independent random numbers. The
00199 *          values of ISEED are changed on exit, and can be used in the
00200 *          next call to CDRVGG to continue the same random number
00201 *          sequence.
00202 *
00203 *  THRESH  (input) REAL
00204 *          A test will count as "failed" if the "error", computed as
00205 *          described above, exceeds THRESH.  Note that the error is
00206 *          scaled to be O(1), so THRESH should be a reasonably small
00207 *          multiple of 1, e.g., 10 or 100.  In particular, it should
00208 *          not depend on the precision (single vs. double) or the size
00209 *          of the matrix.  It must be at least zero.
00210 *
00211 *  THRSHN  (input) REAL
00212 *          Threshhold for reporting eigenvector normalization error.
00213 *          If the normalization of any eigenvector differs from 1 by
00214 *          more than THRSHN*ulp, then a special error message will be
00215 *          printed.  (This is handled separately from the other tests,
00216 *          since only a compiler or programming error should cause an
00217 *          error message, at least if THRSHN is at least 5--10.)
00218 *
00219 *  NOUNIT  (input) INTEGER
00220 *          The FORTRAN unit number for printing out error messages
00221 *          (e.g., if a routine returns IINFO not equal to 0.)
00222 *
00223 *  A       (input/workspace) COMPLEX array, dimension (LDA, max(NN))
00224 *          Used to hold the original A matrix.  Used as input only
00225 *          if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and
00226 *          DOTYPE(MAXTYP+1)=.TRUE.
00227 *
00228 *  LDA     (input) INTEGER
00229 *          The leading dimension of A, B, S, T, S2, and T2.
00230 *          It must be at least 1 and at least max( NN ).
00231 *
00232 *  B       (input/workspace) COMPLEX array, dimension (LDA, max(NN))
00233 *          Used to hold the original B matrix.  Used as input only
00234 *          if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and
00235 *          DOTYPE(MAXTYP+1)=.TRUE.
00236 *
00237 *  S       (workspace) COMPLEX array, dimension (LDA, max(NN))
00238 *          The upper triangular matrix computed from A by CGEGS.
00239 *
00240 *  T       (workspace) COMPLEX array, dimension (LDA, max(NN))
00241 *          The upper triangular matrix computed from B by CGEGS.
00242 *
00243 *  S2      (workspace) COMPLEX array, dimension (LDA, max(NN))
00244 *          The matrix computed from A by CGEGV.  This will be the
00245 *          Schur (upper triangular) form of some matrix related to A,
00246 *          but will not, in general, be the same as S.
00247 *
00248 *  T2      (workspace) COMPLEX array, dimension (LDA, max(NN))
00249 *          The matrix computed from B by CGEGV.  This will be the
00250 *          Schur form of some matrix related to B, but will not, in
00251 *          general, be the same as T.
00252 *
00253 *  Q       (workspace) COMPLEX array, dimension (LDQ, max(NN))
00254 *          The (left) unitary matrix computed by CGEGS.
00255 *
00256 *  LDQ     (input) INTEGER
00257 *          The leading dimension of Q, Z, VL, and VR.  It must
00258 *          be at least 1 and at least max( NN ).
00259 *
00260 *  Z       (workspace) COMPLEX array, dimension (LDQ, max(NN))
00261 *          The (right) unitary matrix computed by CGEGS.
00262 *
00263 *  ALPHA1  (workspace) COMPLEX array, dimension (max(NN))
00264 *  BETA1   (workspace) COMPLEX array, dimension (max(NN))
00265 *          The generalized eigenvalues of (A,B) computed by CGEGS.
00266 *          ALPHA1(k) / BETA1(k)  is the k-th generalized eigenvalue of
00267 *          the matrices in A and B.
00268 *
00269 *  ALPHA2  (workspace) COMPLEX array, dimension (max(NN))
00270 *  BETA2   (workspace) COMPLEX array, dimension (max(NN))
00271 *          The generalized eigenvalues of (A,B) computed by CGEGV.
00272 *          ALPHA2(k) / BETA2(k)  is the k-th generalized eigenvalue of
00273 *          the matrices in A and B.
00274 *
00275 *  VL      (workspace) COMPLEX array, dimension (LDQ, max(NN))
00276 *          The (lower triangular) left eigenvector matrix for the
00277 *          matrices in A and B.
00278 *
00279 *  VR      (workspace) COMPLEX array, dimension (LDQ, max(NN))
00280 *          The (upper triangular) right eigenvector matrix for the
00281 *          matrices in A and B.
00282 *
00283 *  WORK    (workspace) COMPLEX array, dimension (LWORK)
00284 *
00285 *  LWORK   (input) INTEGER
00286 *          The number of entries in WORK.  This must be at least
00287 *          MAX( 2*N, N*(NB+1), (k+1)*(2*k+N+1) ), where "k" is the
00288 *          sum of the blocksize and number-of-shifts for CHGEQZ, and
00289 *          NB is the greatest of the blocksizes for CGEQRF, CUNMQR,
00290 *          and CUNGQR.  (The blocksizes and the number-of-shifts are
00291 *          retrieved through calls to ILAENV.)
00292 *
00293 *  RWORK   (workspace) REAL array, dimension (8*N)
00294 *
00295 *  RESULT  (output) REAL array, dimension (7)
00296 *          The values computed by the tests described above.
00297 *          The values are currently limited to 1/ulp, to avoid
00298 *          overflow.
00299 *
00300 *  INFO    (output) INTEGER
00301 *          = 0:  successful exit
00302 *          < 0:  if INFO = -i, the i-th argument had an illegal value.
00303 *          > 0:  A routine returned an error code.  INFO is the
00304 *                absolute value of the INFO value returned.
00305 *
00306 *  =====================================================================
00307 *
00308       LOGICAL            DOTYPE( * )
00309       INTEGER            ISEED( 4 ), NN( * )
00310       REAL               RESULT( * ), RWORK( * )
00311       COMPLEX            A( LDA, * ), ALPHA1( * ), ALPHA2( * ),
00312      $                   B( LDA, * ), BETA1( * ), BETA2( * ),
00313      $                   Q( LDQ, * ), S( LDA, * ), S2( LDA, * ),
00314      $                   T( LDA, * ), T2( LDA, * ), VL( LDQ, * ),
00315      $                   VR( LDQ, * ), WORK( * ), Z( LDQ, * )
00316 *     ..
00317 *     .. Parameters ..
00318       REAL               ZERO, ONE
00319       PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
00320       COMPLEX            CZERO, CONE
00321       PARAMETER          ( CZERO = ( 0.0E+0, 0.0E+0 ),
00322      $                   CONE = ( 1.0E+0, 0.0E+0 ) )
00323       INTEGER            MAXTYP
00324       PARAMETER          ( MAXTYP = 26 )
00325 *     ..
00326 *     .. Local Scalars ..
00327       LOGICAL            BADNN
00328       INTEGER            I1, IADD, IINFO, IN, J, JC, JR, JSIZE, JTYPE,
00329      $                   LWKOPT, MTYPES, N, N1, NB, NBZ, NERRS, NMATS,
00330      $                   NMAX, NS, NTEST, NTESTT
00331       REAL               SAFMAX, SAFMIN, TEMP1, TEMP2, ULP, ULPINV
00332       COMPLEX            CTEMP, X
00333 *     ..
00334 *     .. Local Arrays ..
00335       LOGICAL            LASIGN( MAXTYP ), LBSIGN( MAXTYP )
00336       INTEGER            IOLDSD( 4 ), KADD( 6 ), KAMAGN( MAXTYP ),
00337      $                   KATYPE( MAXTYP ), KAZERO( MAXTYP ),
00338      $                   KBMAGN( MAXTYP ), KBTYPE( MAXTYP ),
00339      $                   KBZERO( MAXTYP ), KCLASS( MAXTYP ),
00340      $                   KTRIAN( MAXTYP ), KZ1( 6 ), KZ2( 6 )
00341       REAL               DUMMA( 4 ), RMAGN( 0: 3 )
00342 *     ..
00343 *     .. External Functions ..
00344       INTEGER            ILAENV
00345       REAL               SLAMCH
00346       COMPLEX            CLARND
00347       EXTERNAL           ILAENV, SLAMCH, CLARND
00348 *     ..
00349 *     .. External Subroutines ..
00350       EXTERNAL           ALASVM, CGEGS, CGEGV, CGET51, CGET52, CLACPY,
00351      $                   CLARFG, CLASET, CLATM4, CUNM2R, SLABAD, XERBLA
00352 *     ..
00353 *     .. Intrinsic Functions ..
00354       INTRINSIC          ABS, AIMAG, CONJG, MAX, MIN, REAL, SIGN
00355 *     ..
00356 *     .. Statement Functions ..
00357       REAL               ABS1
00358 *     ..
00359 *     .. Statement Function definitions ..
00360       ABS1( X ) = ABS( REAL( X ) ) + ABS( AIMAG( X ) )
00361 *     ..
00362 *     .. Data statements ..
00363       DATA               KCLASS / 15*1, 10*2, 1*3 /
00364       DATA               KZ1 / 0, 1, 2, 1, 3, 3 /
00365       DATA               KZ2 / 0, 0, 1, 2, 1, 1 /
00366       DATA               KADD / 0, 0, 0, 0, 3, 2 /
00367       DATA               KATYPE / 0, 1, 0, 1, 2, 3, 4, 1, 4, 4, 1, 1, 4,
00368      $                   4, 4, 2, 4, 5, 8, 7, 9, 4*4, 0 /
00369       DATA               KBTYPE / 0, 0, 1, 1, 2, -3, 1, 4, 1, 1, 4, 4,
00370      $                   1, 1, -4, 2, -4, 8*8, 0 /
00371       DATA               KAZERO / 6*1, 2, 1, 2*2, 2*1, 2*2, 3, 1, 3,
00372      $                   4*5, 4*3, 1 /
00373       DATA               KBZERO / 6*1, 1, 2, 2*1, 2*2, 2*1, 4, 1, 4,
00374      $                   4*6, 4*4, 1 /
00375       DATA               KAMAGN / 8*1, 2, 3, 2, 3, 2, 3, 7*1, 2, 3, 3,
00376      $                   2, 1 /
00377       DATA               KBMAGN / 8*1, 3, 2, 3, 2, 2, 3, 7*1, 3, 2, 3,
00378      $                   2, 1 /
00379       DATA               KTRIAN / 16*0, 10*1 /
00380       DATA               LASIGN / 6*.FALSE., .TRUE., .FALSE., 2*.TRUE.,
00381      $                   2*.FALSE., 3*.TRUE., .FALSE., .TRUE.,
00382      $                   3*.FALSE., 5*.TRUE., .FALSE. /
00383       DATA               LBSIGN / 7*.FALSE., .TRUE., 2*.FALSE.,
00384      $                   2*.TRUE., 2*.FALSE., .TRUE., .FALSE., .TRUE.,
00385      $                   9*.FALSE. /
00386 *     ..
00387 *     .. Executable Statements ..
00388 *
00389 *     Check for errors
00390 *
00391       INFO = 0
00392 *
00393       BADNN = .FALSE.
00394       NMAX = 1
00395       DO 10 J = 1, NSIZES
00396          NMAX = MAX( NMAX, NN( J ) )
00397          IF( NN( J ).LT.0 )
00398      $      BADNN = .TRUE.
00399    10 CONTINUE
00400 *
00401 *     Maximum blocksize and shift -- we assume that blocksize and number
00402 *     of shifts are monotone increasing functions of N.
00403 *
00404       NB = MAX( 1, ILAENV( 1, 'CGEQRF', ' ', NMAX, NMAX, -1, -1 ),
00405      $     ILAENV( 1, 'CUNMQR', 'LC', NMAX, NMAX, NMAX, -1 ),
00406      $     ILAENV( 1, 'CUNGQR', ' ', NMAX, NMAX, NMAX, -1 ) )
00407       NBZ = ILAENV( 1, 'CHGEQZ', 'SII', NMAX, 1, NMAX, 0 )
00408       NS = ILAENV( 4, 'CHGEQZ', 'SII', NMAX, 1, NMAX, 0 )
00409       I1 = NBZ + NS
00410       LWKOPT = MAX( 2*NMAX, NMAX*( NB+1 ), ( 2*I1+NMAX+1 )*( I1+1 ) )
00411 *
00412 *     Check for errors
00413 *
00414       IF( NSIZES.LT.0 ) THEN
00415          INFO = -1
00416       ELSE IF( BADNN ) THEN
00417          INFO = -2
00418       ELSE IF( NTYPES.LT.0 ) THEN
00419          INFO = -3
00420       ELSE IF( THRESH.LT.ZERO ) THEN
00421          INFO = -6
00422       ELSE IF( LDA.LE.1 .OR. LDA.LT.NMAX ) THEN
00423          INFO = -10
00424       ELSE IF( LDQ.LE.1 .OR. LDQ.LT.NMAX ) THEN
00425          INFO = -19
00426       ELSE IF( LWKOPT.GT.LWORK ) THEN
00427          INFO = -30
00428       END IF
00429 *
00430       IF( INFO.NE.0 ) THEN
00431          CALL XERBLA( 'CDRVGG', -INFO )
00432          RETURN
00433       END IF
00434 *
00435 *     Quick return if possible
00436 *
00437       IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 )
00438      $   RETURN
00439 *
00440       ULP = SLAMCH( 'Precision' )
00441       SAFMIN = SLAMCH( 'Safe minimum' )
00442       SAFMIN = SAFMIN / ULP
00443       SAFMAX = ONE / SAFMIN
00444       CALL SLABAD( SAFMIN, SAFMAX )
00445       ULPINV = ONE / ULP
00446 *
00447 *     The values RMAGN(2:3) depend on N, see below.
00448 *
00449       RMAGN( 0 ) = ZERO
00450       RMAGN( 1 ) = ONE
00451 *
00452 *     Loop over sizes, types
00453 *
00454       NTESTT = 0
00455       NERRS = 0
00456       NMATS = 0
00457 *
00458       DO 160 JSIZE = 1, NSIZES
00459          N = NN( JSIZE )
00460          N1 = MAX( 1, N )
00461          RMAGN( 2 ) = SAFMAX*ULP / REAL( N1 )
00462          RMAGN( 3 ) = SAFMIN*ULPINV*N1
00463 *
00464          IF( NSIZES.NE.1 ) THEN
00465             MTYPES = MIN( MAXTYP, NTYPES )
00466          ELSE
00467             MTYPES = MIN( MAXTYP+1, NTYPES )
00468          END IF
00469 *
00470          DO 150 JTYPE = 1, MTYPES
00471             IF( .NOT.DOTYPE( JTYPE ) )
00472      $         GO TO 150
00473             NMATS = NMATS + 1
00474             NTEST = 0
00475 *
00476 *           Save ISEED in case of an error.
00477 *
00478             DO 20 J = 1, 4
00479                IOLDSD( J ) = ISEED( J )
00480    20       CONTINUE
00481 *
00482 *           Initialize RESULT
00483 *
00484             DO 30 J = 1, 7
00485                RESULT( J ) = ZERO
00486    30       CONTINUE
00487 *
00488 *           Compute A and B
00489 *
00490 *           Description of control parameters:
00491 *
00492 *           KCLASS: =1 means w/o rotation, =2 means w/ rotation,
00493 *                   =3 means random.
00494 *           KATYPE: the "type" to be passed to CLATM4 for computing A.
00495 *           KAZERO: the pattern of zeros on the diagonal for A:
00496 *                   =1: ( xxx ), =2: (0, xxx ) =3: ( 0, 0, xxx, 0 ),
00497 *                   =4: ( 0, xxx, 0, 0 ), =5: ( 0, 0, 1, xxx, 0 ),
00498 *                   =6: ( 0, 1, 0, xxx, 0 ).  (xxx means a string of
00499 *                   non-zero entries.)
00500 *           KAMAGN: the magnitude of the matrix: =0: zero, =1: O(1),
00501 *                   =2: large, =3: small.
00502 *           LASIGN: .TRUE. if the diagonal elements of A are to be
00503 *                   multiplied by a random magnitude 1 number.
00504 *           KBTYPE, KBZERO, KBMAGN, IBSIGN: the same, but for B.
00505 *           KTRIAN: =0: don't fill in the upper triangle, =1: do.
00506 *           KZ1, KZ2, KADD: used to implement KAZERO and KBZERO.
00507 *           RMAGN:  used to implement KAMAGN and KBMAGN.
00508 *
00509             IF( MTYPES.GT.MAXTYP )
00510      $         GO TO 110
00511             IINFO = 0
00512             IF( KCLASS( JTYPE ).LT.3 ) THEN
00513 *
00514 *              Generate A (w/o rotation)
00515 *
00516                IF( ABS( KATYPE( JTYPE ) ).EQ.3 ) THEN
00517                   IN = 2*( ( N-1 ) / 2 ) + 1
00518                   IF( IN.NE.N )
00519      $               CALL CLASET( 'Full', N, N, CZERO, CZERO, A, LDA )
00520                ELSE
00521                   IN = N
00522                END IF
00523                CALL CLATM4( KATYPE( JTYPE ), IN, KZ1( KAZERO( JTYPE ) ),
00524      $                      KZ2( KAZERO( JTYPE ) ), LASIGN( JTYPE ),
00525      $                      RMAGN( KAMAGN( JTYPE ) ), ULP,
00526      $                      RMAGN( KTRIAN( JTYPE )*KAMAGN( JTYPE ) ), 2,
00527      $                      ISEED, A, LDA )
00528                IADD = KADD( KAZERO( JTYPE ) )
00529                IF( IADD.GT.0 .AND. IADD.LE.N )
00530      $            A( IADD, IADD ) = RMAGN( KAMAGN( JTYPE ) )
00531 *
00532 *              Generate B (w/o rotation)
00533 *
00534                IF( ABS( KBTYPE( JTYPE ) ).EQ.3 ) THEN
00535                   IN = 2*( ( N-1 ) / 2 ) + 1
00536                   IF( IN.NE.N )
00537      $               CALL CLASET( 'Full', N, N, CZERO, CZERO, B, LDA )
00538                ELSE
00539                   IN = N
00540                END IF
00541                CALL CLATM4( KBTYPE( JTYPE ), IN, KZ1( KBZERO( JTYPE ) ),
00542      $                      KZ2( KBZERO( JTYPE ) ), LBSIGN( JTYPE ),
00543      $                      RMAGN( KBMAGN( JTYPE ) ), ONE,
00544      $                      RMAGN( KTRIAN( JTYPE )*KBMAGN( JTYPE ) ), 2,
00545      $                      ISEED, B, LDA )
00546                IADD = KADD( KBZERO( JTYPE ) )
00547                IF( IADD.NE.0 .AND. IADD.LE.N )
00548      $            B( IADD, IADD ) = RMAGN( KBMAGN( JTYPE ) )
00549 *
00550                IF( KCLASS( JTYPE ).EQ.2 .AND. N.GT.0 ) THEN
00551 *
00552 *                 Include rotations
00553 *
00554 *                 Generate Q, Z as Householder transformations times
00555 *                 a diagonal matrix.
00556 *
00557                   DO 50 JC = 1, N - 1
00558                      DO 40 JR = JC, N
00559                         Q( JR, JC ) = CLARND( 3, ISEED )
00560                         Z( JR, JC ) = CLARND( 3, ISEED )
00561    40                CONTINUE
00562                      CALL CLARFG( N+1-JC, Q( JC, JC ), Q( JC+1, JC ), 1,
00563      $                            WORK( JC ) )
00564                      WORK( 2*N+JC ) = SIGN( ONE, REAL( Q( JC, JC ) ) )
00565                      Q( JC, JC ) = CONE
00566                      CALL CLARFG( N+1-JC, Z( JC, JC ), Z( JC+1, JC ), 1,
00567      $                            WORK( N+JC ) )
00568                      WORK( 3*N+JC ) = SIGN( ONE, REAL( Z( JC, JC ) ) )
00569                      Z( JC, JC ) = CONE
00570    50             CONTINUE
00571                   CTEMP = CLARND( 3, ISEED )
00572                   Q( N, N ) = CONE
00573                   WORK( N ) = CZERO
00574                   WORK( 3*N ) = CTEMP / ABS( CTEMP )
00575                   CTEMP = CLARND( 3, ISEED )
00576                   Z( N, N ) = CONE
00577                   WORK( 2*N ) = CZERO
00578                   WORK( 4*N ) = CTEMP / ABS( CTEMP )
00579 *
00580 *                 Apply the diagonal matrices
00581 *
00582                   DO 70 JC = 1, N
00583                      DO 60 JR = 1, N
00584                         A( JR, JC ) = WORK( 2*N+JR )*
00585      $                                CONJG( WORK( 3*N+JC ) )*
00586      $                                A( JR, JC )
00587                         B( JR, JC ) = WORK( 2*N+JR )*
00588      $                                CONJG( WORK( 3*N+JC ) )*
00589      $                                B( JR, JC )
00590    60                CONTINUE
00591    70             CONTINUE
00592                   CALL CUNM2R( 'L', 'N', N, N, N-1, Q, LDQ, WORK, A,
00593      $                         LDA, WORK( 2*N+1 ), IINFO )
00594                   IF( IINFO.NE.0 )
00595      $               GO TO 100
00596                   CALL CUNM2R( 'R', 'C', N, N, N-1, Z, LDQ, WORK( N+1 ),
00597      $                         A, LDA, WORK( 2*N+1 ), IINFO )
00598                   IF( IINFO.NE.0 )
00599      $               GO TO 100
00600                   CALL CUNM2R( 'L', 'N', N, N, N-1, Q, LDQ, WORK, B,
00601      $                         LDA, WORK( 2*N+1 ), IINFO )
00602                   IF( IINFO.NE.0 )
00603      $               GO TO 100
00604                   CALL CUNM2R( 'R', 'C', N, N, N-1, Z, LDQ, WORK( N+1 ),
00605      $                         B, LDA, WORK( 2*N+1 ), IINFO )
00606                   IF( IINFO.NE.0 )
00607      $               GO TO 100
00608                END IF
00609             ELSE
00610 *
00611 *              Random matrices
00612 *
00613                DO 90 JC = 1, N
00614                   DO 80 JR = 1, N
00615                      A( JR, JC ) = RMAGN( KAMAGN( JTYPE ) )*
00616      $                             CLARND( 4, ISEED )
00617                      B( JR, JC ) = RMAGN( KBMAGN( JTYPE ) )*
00618      $                             CLARND( 4, ISEED )
00619    80             CONTINUE
00620    90          CONTINUE
00621             END IF
00622 *
00623   100       CONTINUE
00624 *
00625             IF( IINFO.NE.0 ) THEN
00626                WRITE( NOUNIT, FMT = 9999 )'Generator', IINFO, N, JTYPE,
00627      $            IOLDSD
00628                INFO = ABS( IINFO )
00629                RETURN
00630             END IF
00631 *
00632   110       CONTINUE
00633 *
00634 *           Call CGEGS to compute H, T, Q, Z, alpha, and beta.
00635 *
00636             CALL CLACPY( ' ', N, N, A, LDA, S, LDA )
00637             CALL CLACPY( ' ', N, N, B, LDA, T, LDA )
00638             NTEST = 1
00639             RESULT( 1 ) = ULPINV
00640 *
00641             CALL CGEGS( 'V', 'V', N, S, LDA, T, LDA, ALPHA1, BETA1, Q,
00642      $                  LDQ, Z, LDQ, WORK, LWORK, RWORK, IINFO )
00643             IF( IINFO.NE.0 ) THEN
00644                WRITE( NOUNIT, FMT = 9999 )'CGEGS', IINFO, N, JTYPE,
00645      $            IOLDSD
00646                INFO = ABS( IINFO )
00647                GO TO 130
00648             END IF
00649 *
00650             NTEST = 4
00651 *
00652 *           Do tests 1--4
00653 *
00654             CALL CGET51( 1, N, A, LDA, S, LDA, Q, LDQ, Z, LDQ, WORK,
00655      $                   RWORK, RESULT( 1 ) )
00656             CALL CGET51( 1, N, B, LDA, T, LDA, Q, LDQ, Z, LDQ, WORK,
00657      $                   RWORK, RESULT( 2 ) )
00658             CALL CGET51( 3, N, B, LDA, T, LDA, Q, LDQ, Q, LDQ, WORK,
00659      $                   RWORK, RESULT( 3 ) )
00660             CALL CGET51( 3, N, B, LDA, T, LDA, Z, LDQ, Z, LDQ, WORK,
00661      $                   RWORK, RESULT( 4 ) )
00662 *
00663 *           Do test 5: compare eigenvalues with diagonals.
00664 *
00665             TEMP1 = ZERO
00666 *
00667             DO 120 J = 1, N
00668                TEMP2 = ( ABS1( ALPHA1( J )-S( J, J ) ) /
00669      $                 MAX( SAFMIN, ABS1( ALPHA1( J ) ), ABS1( S( J,
00670      $                 J ) ) )+ABS1( BETA1( J )-T( J, J ) ) /
00671      $                 MAX( SAFMIN, ABS1( BETA1( J ) ), ABS1( T( J,
00672      $                 J ) ) ) ) / ULP
00673                TEMP1 = MAX( TEMP1, TEMP2 )
00674   120       CONTINUE
00675             RESULT( 5 ) = TEMP1
00676 *
00677 *           Call CGEGV to compute S2, T2, VL, and VR, do tests.
00678 *
00679 *           Eigenvalues and Eigenvectors
00680 *
00681             CALL CLACPY( ' ', N, N, A, LDA, S2, LDA )
00682             CALL CLACPY( ' ', N, N, B, LDA, T2, LDA )
00683             NTEST = 6
00684             RESULT( 6 ) = ULPINV
00685 *
00686             CALL CGEGV( 'V', 'V', N, S2, LDA, T2, LDA, ALPHA2, BETA2,
00687      $                  VL, LDQ, VR, LDQ, WORK, LWORK, RWORK, IINFO )
00688             IF( IINFO.NE.0 ) THEN
00689                WRITE( NOUNIT, FMT = 9999 )'CGEGV', IINFO, N, JTYPE,
00690      $            IOLDSD
00691                INFO = ABS( IINFO )
00692                GO TO 130
00693             END IF
00694 *
00695             NTEST = 7
00696 *
00697 *           Do Tests 6 and 7
00698 *
00699             CALL CGET52( .TRUE., N, A, LDA, B, LDA, VL, LDQ, ALPHA2,
00700      $                   BETA2, WORK, RWORK, DUMMA( 1 ) )
00701             RESULT( 6 ) = DUMMA( 1 )
00702             IF( DUMMA( 2 ).GT.THRSHN ) THEN
00703                WRITE( NOUNIT, FMT = 9998 )'Left', 'CGEGV', DUMMA( 2 ),
00704      $            N, JTYPE, IOLDSD
00705             END IF
00706 *
00707             CALL CGET52( .FALSE., N, A, LDA, B, LDA, VR, LDQ, ALPHA2,
00708      $                   BETA2, WORK, RWORK, DUMMA( 1 ) )
00709             RESULT( 7 ) = DUMMA( 1 )
00710             IF( DUMMA( 2 ).GT.THRESH ) THEN
00711                WRITE( NOUNIT, FMT = 9998 )'Right', 'CGEGV', DUMMA( 2 ),
00712      $            N, JTYPE, IOLDSD
00713             END IF
00714 *
00715 *           End of Loop -- Check for RESULT(j) > THRESH
00716 *
00717   130       CONTINUE
00718 *
00719             NTESTT = NTESTT + NTEST
00720 *
00721 *           Print out tests which fail.
00722 *
00723             DO 140 JR = 1, NTEST
00724                IF( RESULT( JR ).GE.THRESH ) THEN
00725 *
00726 *                 If this is the first test to fail,
00727 *                 print a header to the data file.
00728 *
00729                   IF( NERRS.EQ.0 ) THEN
00730                      WRITE( NOUNIT, FMT = 9997 )'CGG'
00731 *
00732 *                    Matrix types
00733 *
00734                      WRITE( NOUNIT, FMT = 9996 )
00735                      WRITE( NOUNIT, FMT = 9995 )
00736                      WRITE( NOUNIT, FMT = 9994 )'Unitary'
00737 *
00738 *                    Tests performed
00739 *
00740                      WRITE( NOUNIT, FMT = 9993 )'unitary', '*',
00741      $                  'conjugate transpose', ( '*', J = 1, 5 )
00742 *
00743                   END IF
00744                   NERRS = NERRS + 1
00745                   IF( RESULT( JR ).LT.10000.0 ) THEN
00746                      WRITE( NOUNIT, FMT = 9992 )N, JTYPE, IOLDSD, JR,
00747      $                  RESULT( JR )
00748                   ELSE
00749                      WRITE( NOUNIT, FMT = 9991 )N, JTYPE, IOLDSD, JR,
00750      $                  RESULT( JR )
00751                   END IF
00752                END IF
00753   140       CONTINUE
00754 *
00755   150    CONTINUE
00756   160 CONTINUE
00757 *
00758 *     Summary
00759 *
00760       CALL ALASVM( 'CGG', NOUNIT, NERRS, NTESTT, 0 )
00761       RETURN
00762 *
00763  9999 FORMAT( ' CDRVGG: ', A, ' returned INFO=', I6, '.', / 9X, 'N=',
00764      $      I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' )
00765 *
00766  9998 FORMAT( ' CDRVGG: ', A, ' Eigenvectors from ', A, ' incorrectly ',
00767      $      'normalized.', / ' Bits of error=', 0P, G10.3, ',', 9X,
00768      $      'N=', I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5,
00769      $      ')' )
00770 *
00771  9997 FORMAT( / 1X, A3,
00772      $      ' -- Complex Generalized eigenvalue problem driver' )
00773 *
00774  9996 FORMAT( ' Matrix types (see CDRVGG for details): ' )
00775 *
00776  9995 FORMAT( ' Special Matrices:', 23X,
00777      $      '(J''=transposed Jordan block)',
00778      $      / '   1=(0,0)  2=(I,0)  3=(0,I)  4=(I,I)  5=(J'',J'')  ',
00779      $      '6=(diag(J'',I), diag(I,J''))', / ' Diagonal Matrices:  ( ',
00780      $      'D=diag(0,1,2,...) )', / '   7=(D,I)   9=(large*D, small*I',
00781      $      ')  11=(large*I, small*D)  13=(large*D, large*I)', /
00782      $      '   8=(I,D)  10=(small*D, large*I)  12=(small*I, large*D) ',
00783      $      ' 14=(small*D, small*I)', / '  15=(D, reversed D)' )
00784  9994 FORMAT( ' Matrices Rotated by Random ', A, ' Matrices U, V:',
00785      $      / '  16=Transposed Jordan Blocks             19=geometric ',
00786      $      'alpha, beta=0,1', / '  17=arithm. alpha&beta             ',
00787      $      '      20=arithmetic alpha, beta=0,1', / '  18=clustered ',
00788      $      'alpha, beta=0,1            21=random alpha, beta=0,1',
00789      $      / ' Large & Small Matrices:', / '  22=(large, small)   ',
00790      $      '23=(small,large)    24=(small,small)    25=(large,large)',
00791      $      / '  26=random O(1) matrices.' )
00792 *
00793  9993 FORMAT( / ' Tests performed:  (S is Schur, T is triangular, ',
00794      $      'Q and Z are ', A, ',', / 20X,
00795      $      'l and r are the appropriate left and right', / 19X,
00796      $      'eigenvectors, resp., a is alpha, b is beta, and', / 19X, A,
00797      $      ' means ', A, '.)', / ' 1 = | A - Q S Z', A,
00798      $      ' | / ( |A| n ulp )      2 = | B - Q T Z', A,
00799      $      ' | / ( |B| n ulp )', / ' 3 = | I - QQ', A,
00800      $      ' | / ( n ulp )             4 = | I - ZZ', A,
00801      $      ' | / ( n ulp )', /
00802      $      ' 5 = difference between (alpha,beta) and diagonals of',
00803      $      ' (S,T)', / ' 6 = max | ( b A - a B )', A,
00804      $      ' l | / const.   7 = max | ( b A - a B ) r | / const.',
00805      $      / 1X )
00806  9992 FORMAT( ' Matrix order=', I5, ', type=', I2, ', seed=',
00807      $      4( I4, ',' ), ' result ', I3, ' is', 0P, F8.2 )
00808  9991 FORMAT( ' Matrix order=', I5, ', type=', I2, ', seed=',
00809      $      4( I4, ',' ), ' result ', I3, ' is', 1P, E10.3 )
00810 *
00811 *     End of CDRVGG
00812 *
00813       END