1
       2
       3
       4
       5
       6
       7
       8
       9
      10
      11
      12
      13
      14
      15
      16
      17
      18
      19
      20
      21
      22
      23
      24
      25
      26
      27
      28
      29
      30
      31
      32
      33
      34
      35
      36
      37
      38
      39
      40
      41
      42
      43
      44
      45
      46
      47
      48
      49
      50
      51
      52
      53
      54
      55
      56
      57
      58
      59
      60
      61
      62
      63
      64
      65
      66
      67
      68
      69
      70
      71
      72
      73
      74
      75
      76
      77
      78
      79
      80
      81
      82
      83
      84
      85
      86
      87
      88
      89
      90
      91
      92
      93
      94
      95
      96
      97
      98
      99
     100
     101
     102
     103
     104
     105
     106
     107
     108
     109
     110
     111
     112
     113
     114
     115
     116
     117
     118
     119
     120
     121
     122
     123
     124
     125
     126
     127
     128
     129
     130
     131
     132
     133
     134
     135
     136
     137
     138
     139
     140
     141
     142
     143
     144
     145
     146
     147
     148
     149
     150
     151
     152
     153
     154
     155
     156
     157
     158
     159
     160
     161
     162
     163
     164
     165
     166
     167
     168
     169
     170
     171
     172
     173
     174
     175
     176
     177
     178
     179
     180
     181
     182
     183
     184
     185
     186
     187
     188
     189
     190
     191
     192
     193
     194
     195
     196
     197
     198
     199
     200
     201
     202
     203
     204
     205
     206
     207
     208
     209
     210
     211
     212
     213
     214
     215
     216
     217
     218
     219
     220
     221
     222
     223
     224
     225
     226
     227
     228
     229
     230
     231
     232
     233
     234
     235
     236
     237
     238
     239
     240
     241
     242
     243
     244
     245
     246
     247
     248
     249
     250
     251
     252
     253
     254
     255
     256
     257
     258
     259
     260
     261
     262
     263
     264
     265
     266
     267
     268
     269
     270
     271
     272
     273
     274
     275
     276
     277
     278
     279
     280
     281
     282
     283
     284
     285
     286
     287
     288
     289
     290
     291
     292
     293
     294
     295
     296
     297
     298
     299
     300
     301
     302
     303
     304
     305
     306
     307
     308
     309
     310
     311
     312
     313
     314
     315
     316
     317
     318
     319
     320
     321
     322
     323
     324
     325
     326
     327
     328
     329
     330
     331
     332
     333
     334
     335
     336
     337
     338
     339
     340
     341
     342
     343
     344
     345
     346
     347
     348
     349
     350
     351
     352
     353
     354
     355
     356
     357
     358
     359
     360
     361
     362
     363
     364
     365
     366
     367
     368
     369
     370
     371
     372
     373
     374
     375
     376
     377
     378
     379
     380
     381
     382
     383
     384
     385
     386
     387
     388
     389
     390
     391
     392
     393
     394
     395
     396
     397
     398
     399
     400
     401
     402
     403
     404
     405
     406
     407
     408
     409
     410
     411
     412
     413
     414
     415
     416
     417
     418
     419
     420
     421
     422
     423
     424
     425
     426
     427
     428
     429
     430
     431
     432
     433
     434
     435
     436
     437
     438
     439
     440
     441
      SUBROUTINE STGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
     $                   LDZ, IFST, ILST, WORK, LWORK, INFO )
*
*  -- LAPACK routine (version 3.3.1) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*  -- April 2011                                                      --
*
*     .. Scalar Arguments ..
      LOGICAL            WANTQ, WANTZ
      INTEGER            IFST, ILST, INFO, LDA, LDB, LDQ, LDZ, LWORK, N
*     ..
*     .. Array Arguments ..
      REAL               A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
     $                   WORK( * ), Z( LDZ, * )
*     ..
*
*  Purpose
*  =======
*
*  STGEXC reorders the generalized real Schur decomposition of a real
*  matrix pair (A,B) using an orthogonal equivalence transformation
*
*                 (A, B) = Q * (A, B) * Z**T,
*
*  so that the diagonal block of (A, B) with row index IFST is moved
*  to row ILST.
*
*  (A, B) must be in generalized real Schur canonical form (as returned
*  by SGGES), i.e. A is block upper triangular with 1-by-1 and 2-by-2
*  diagonal blocks. B is upper triangular.
*
*  Optionally, the matrices Q and Z of generalized Schur vectors are
*  updated.
*
*         Q(in) * A(in) * Z(in)**T = Q(out) * A(out) * Z(out)**T
*         Q(in) * B(in) * Z(in)**T = Q(out) * B(out) * Z(out)**T
*
*
*  Arguments
*  =========
*
*  WANTQ   (input) LOGICAL
*          .TRUE. : update the left transformation matrix Q;
*          .FALSE.: do not update Q.
*
*  WANTZ   (input) LOGICAL
*          .TRUE. : update the right transformation matrix Z;
*          .FALSE.: do not update Z.
*
*  N       (input) INTEGER
*          The order of the matrices A and B. N >= 0.
*
*  A       (input/output) REAL array, dimension (LDA,N)
*          On entry, the matrix A in generalized real Schur canonical
*          form.
*          On exit, the updated matrix A, again in generalized
*          real Schur canonical form.
*
*  LDA     (input)  INTEGER
*          The leading dimension of the array A. LDA >= max(1,N).
*
*  B       (input/output) REAL array, dimension (LDB,N)
*          On entry, the matrix B in generalized real Schur canonical
*          form (A,B).
*          On exit, the updated matrix B, again in generalized
*          real Schur canonical form (A,B).
*
*  LDB     (input)  INTEGER
*          The leading dimension of the array B. LDB >= max(1,N).
*
*  Q       (input/output) REAL array, dimension (LDZ,N)
*          On entry, if WANTQ = .TRUE., the orthogonal matrix Q.
*          On exit, the updated matrix Q.
*          If WANTQ = .FALSE., Q is not referenced.
*
*  LDQ     (input) INTEGER
*          The leading dimension of the array Q. LDQ >= 1.
*          If WANTQ = .TRUE., LDQ >= N.
*
*  Z       (input/output) REAL array, dimension (LDZ,N)
*          On entry, if WANTZ = .TRUE., the orthogonal matrix Z.
*          On exit, the updated matrix Z.
*          If WANTZ = .FALSE., Z is not referenced.
*
*  LDZ     (input) INTEGER
*          The leading dimension of the array Z. LDZ >= 1.
*          If WANTZ = .TRUE., LDZ >= N.
*
*  IFST    (input/output) INTEGER
*  ILST    (input/output) INTEGER
*          Specify the reordering of the diagonal blocks of (A, B).
*          The block with row index IFST is moved to row ILST, by a
*          sequence of swapping between adjacent blocks.
*          On exit, if IFST pointed on entry to the second row of
*          a 2-by-2 block, it is changed to point to the first row;
*          ILST always points to the first row of the block in its
*          final position (which may differ from its input value by
*          +1 or -1). 1 <= IFST, ILST <= N.
*
*  WORK    (workspace/output) REAL array, dimension (MAX(1,LWORK))
*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
*  LWORK   (input) INTEGER
*          The dimension of the array WORK.
*          LWORK >= 1 when N <= 1, otherwise LWORK >= 4*N + 16.
*
*          If LWORK = -1, then a workspace query is assumed; the routine
*          only calculates the optimal size of the WORK array, returns
*          this value as the first entry of the WORK array, and no error
*          message related to LWORK is issued by XERBLA.
*
*  INFO    (output) INTEGER
*           =0:  successful exit.
*           <0:  if INFO = -i, the i-th argument had an illegal value.
*           =1:  The transformed matrix pair (A, B) would be too far
*                from generalized Schur form; the problem is ill-
*                conditioned. (A, B) may have been partially reordered,
*                and ILST points to the first row of the current
*                position of the block being moved.
*
*  Further Details
*  ===============
*
*  Based on contributions by
*     Bo Kagstrom and Peter Poromaa, Department of Computing Science,
*     Umea University, S-901 87 Umea, Sweden.
*
*  [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the
*      Generalized Real Schur Form of a Regular Matrix Pair (A, B), in
*      M.S. Moonen et al (eds), Linear Algebra for Large Scale and
*      Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218.
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ZERO
      PARAMETER          ( ZERO = 0.0E+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            LQUERY
      INTEGER            HERE, LWMIN, NBF, NBL, NBNEXT
*     ..
*     .. External Subroutines ..
      EXTERNAL           STGEX2, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX
*     ..
*     .. Executable Statements ..
*
*     Decode and test input arguments.
*
      INFO = 0
      LQUERY = ( LWORK.EQ.-1 )
      IF( N.LT.0 ) THEN
         INFO = -3
      ELSE IF( LDA.LT.MAX1, N ) ) THEN
         INFO = -5
      ELSE IF( LDB.LT.MAX1, N ) ) THEN
         INFO = -7
      ELSE IF( LDQ.LT.1 .OR. WANTQ .AND. ( LDQ.LT.MAX1, N ) ) ) THEN
         INFO = -9
      ELSE IF( LDZ.LT.1 .OR. WANTZ .AND. ( LDZ.LT.MAX1, N ) ) ) THEN
         INFO = -11
      ELSE IF( IFST.LT.1 .OR. IFST.GT.N ) THEN
         INFO = -12
      ELSE IF( ILST.LT.1 .OR. ILST.GT.N ) THEN
         INFO = -13
      END IF
*
      IF( INFO.EQ.0 ) THEN
         IF( N.LE.1 ) THEN
            LWMIN = 1
         ELSE
            LWMIN = 4*+ 16
         END IF
         WORK(1= LWMIN
*
         IF (LWORK.LT.LWMIN .AND. .NOT.LQUERY) THEN
            INFO = -15
         END IF
      END IF
*
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'STGEXC'-INFO )
         RETURN
      ELSE IF( LQUERY ) THEN
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( N.LE.1 )
     $   RETURN
*
*     Determine the first row of the specified block and find out
*     if it is 1-by-1 or 2-by-2.
*
      IF( IFST.GT.1 ) THEN
         IF( A( IFST, IFST-1 ).NE.ZERO )
     $      IFST = IFST - 1
      END IF
      NBF = 1
      IF( IFST.LT.N ) THEN
         IF( A( IFST+1, IFST ).NE.ZERO )
     $      NBF = 2
      END IF
*
*     Determine the first row of the final block
*     and find out if it is 1-by-1 or 2-by-2.
*
      IF( ILST.GT.1 ) THEN
         IF( A( ILST, ILST-1 ).NE.ZERO )
     $      ILST = ILST - 1
      END IF
      NBL = 1
      IF( ILST.LT.N ) THEN
         IF( A( ILST+1, ILST ).NE.ZERO )
     $      NBL = 2
      END IF
      IF( IFST.EQ.ILST )
     $   RETURN
*
      IF( IFST.LT.ILST ) THEN
*
*        Update ILST.
*
         IF( NBF.EQ.2 .AND. NBL.EQ.1 )
     $      ILST = ILST - 1
         IF( NBF.EQ.1 .AND. NBL.EQ.2 )
     $      ILST = ILST + 1
*
         HERE = IFST
*
   10    CONTINUE
*
*        Swap with next one below.
*
         IF( NBF.EQ.1 .OR. NBF.EQ.2 ) THEN
*
*           Current block either 1-by-1 or 2-by-2.
*
            NBNEXT = 1
            IF( HERE+NBF+1.LE.N ) THEN
               IF( A( HERE+NBF+1, HERE+NBF ).NE.ZERO )
     $            NBNEXT = 2
            END IF
            CALL STGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
     $                   LDZ, HERE, NBF, NBNEXT, WORK, LWORK, INFO )
            IF( INFO.NE.0 ) THEN
               ILST = HERE
               RETURN
            END IF
            HERE = HERE + NBNEXT
*
*           Test if 2-by-2 block breaks into two 1-by-1 blocks.
*
            IF( NBF.EQ.2 ) THEN
               IF( A( HERE+1, HERE ).EQ.ZERO )
     $            NBF = 3
            END IF
*
         ELSE
*
*           Current block consists of two 1-by-1 blocks, each of which
*           must be swapped individually.
*
            NBNEXT = 1
            IF( HERE+3.LE.N ) THEN
               IF( A( HERE+3, HERE+2 ).NE.ZERO )
     $            NBNEXT = 2
            END IF
            CALL STGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
     $                   LDZ, HERE+11, NBNEXT, WORK, LWORK, INFO )
            IF( INFO.NE.0 ) THEN
               ILST = HERE
               RETURN
            END IF
            IF( NBNEXT.EQ.1 ) THEN
*
*              Swap two 1-by-1 blocks.
*
               CALL STGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
     $                      LDZ, HERE, 11, WORK, LWORK, INFO )
               IF( INFO.NE.0 ) THEN
                  ILST = HERE
                  RETURN
               END IF
               HERE = HERE + 1
*
            ELSE
*
*              Recompute NBNEXT in case of 2-by-2 split.
*
               IF( A( HERE+2, HERE+1 ).EQ.ZERO )
     $            NBNEXT = 1
               IF( NBNEXT.EQ.2 ) THEN
*
*                 2-by-2 block did not split.
*
                  CALL STGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ,
     $                         Z, LDZ, HERE, 1, NBNEXT, WORK, LWORK,
     $                         INFO )
                  IF( INFO.NE.0 ) THEN
                     ILST = HERE
                     RETURN
                  END IF
                  HERE = HERE + 2
               ELSE
*
*                 2-by-2 block did split.
*
                  CALL STGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ,
     $                         Z, LDZ, HERE, 11, WORK, LWORK, INFO )
                  IF( INFO.NE.0 ) THEN
                     ILST = HERE
                     RETURN
                  END IF
                  HERE = HERE + 1
                  CALL STGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ,
     $                         Z, LDZ, HERE, 11, WORK, LWORK, INFO )
                  IF( INFO.NE.0 ) THEN
                     ILST = HERE
                     RETURN
                  END IF
                  HERE = HERE + 1
               END IF
*
            END IF
         END IF
         IF( HERE.LT.ILST )
     $      GO TO 10
      ELSE
         HERE = IFST
*
   20    CONTINUE
*
*        Swap with next one below.
*
         IF( NBF.EQ.1 .OR. NBF.EQ.2 ) THEN
*
*           Current block either 1-by-1 or 2-by-2.
*
            NBNEXT = 1
            IF( HERE.GE.3 ) THEN
               IF( A( HERE-1, HERE-2 ).NE.ZERO )
     $            NBNEXT = 2
            END IF
            CALL STGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
     $                   LDZ, HERE-NBNEXT, NBNEXT, NBF, WORK, LWORK,
     $                   INFO )
            IF( INFO.NE.0 ) THEN
               ILST = HERE
               RETURN
            END IF
            HERE = HERE - NBNEXT
*
*           Test if 2-by-2 block breaks into two 1-by-1 blocks.
*
            IF( NBF.EQ.2 ) THEN
               IF( A( HERE+1, HERE ).EQ.ZERO )
     $            NBF = 3
            END IF
*
         ELSE
*
*           Current block consists of two 1-by-1 blocks, each of which
*           must be swapped individually.
*
            NBNEXT = 1
            IF( HERE.GE.3 ) THEN
               IF( A( HERE-1, HERE-2 ).NE.ZERO )
     $            NBNEXT = 2
            END IF
            CALL STGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
     $                   LDZ, HERE-NBNEXT, NBNEXT, 1, WORK, LWORK,
     $                   INFO )
            IF( INFO.NE.0 ) THEN
               ILST = HERE
               RETURN
            END IF
            IF( NBNEXT.EQ.1 ) THEN
*
*              Swap two 1-by-1 blocks.
*
               CALL STGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
     $                      LDZ, HERE, NBNEXT, 1, WORK, LWORK, INFO )
               IF( INFO.NE.0 ) THEN
                  ILST = HERE
                  RETURN
               END IF
               HERE = HERE - 1
            ELSE
*
*             Recompute NBNEXT in case of 2-by-2 split.
*
               IF( A( HERE, HERE-1 ).EQ.ZERO )
     $            NBNEXT = 1
               IF( NBNEXT.EQ.2 ) THEN
*
*                 2-by-2 block did not split.
*
                  CALL STGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ,
     $                         Z, LDZ, HERE-121, WORK, LWORK, INFO )
                  IF( INFO.NE.0 ) THEN
                     ILST = HERE
                     RETURN
                  END IF
                  HERE = HERE - 2
               ELSE
*
*                 2-by-2 block did split.
*
                  CALL STGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ,
     $                         Z, LDZ, HERE, 11, WORK, LWORK, INFO )
                  IF( INFO.NE.0 ) THEN
                     ILST = HERE
                     RETURN
                  END IF
                  HERE = HERE - 1
                  CALL STGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ,
     $                         Z, LDZ, HERE, 11, WORK, LWORK, INFO )
                  IF( INFO.NE.0 ) THEN
                     ILST = HERE
                     RETURN
                  END IF
                  HERE = HERE - 1
               END IF
            END IF
         END IF
         IF( HERE.GT.ILST )
     $      GO TO 20
      END IF
      ILST = HERE
      WORK( 1 ) = LWMIN
      RETURN
*
*     End of STGEXC
*
      END