LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
ctgsyl.f
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00001 *> \brief \b CTGSYL
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download CTGSYL + dependencies 
00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ctgsyl.f"> 
00011 *> [TGZ]</a> 
00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ctgsyl.f"> 
00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ctgsyl.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE CTGSYL( TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D,
00022 *                          LDD, E, LDE, F, LDF, SCALE, DIF, WORK, LWORK,
00023 *                          IWORK, INFO )
00024 * 
00025 *       .. Scalar Arguments ..
00026 *       CHARACTER          TRANS
00027 *       INTEGER            IJOB, INFO, LDA, LDB, LDC, LDD, LDE, LDF,
00028 *      $                   LWORK, M, N
00029 *       REAL               DIF, SCALE
00030 *       ..
00031 *       .. Array Arguments ..
00032 *       INTEGER            IWORK( * )
00033 *       COMPLEX            A( LDA, * ), B( LDB, * ), C( LDC, * ),
00034 *      $                   D( LDD, * ), E( LDE, * ), F( LDF, * ),
00035 *      $                   WORK( * )
00036 *       ..
00037 *  
00038 *
00039 *> \par Purpose:
00040 *  =============
00041 *>
00042 *> \verbatim
00043 *>
00044 *> CTGSYL solves the generalized Sylvester equation:
00045 *>
00046 *>             A * R - L * B = scale * C            (1)
00047 *>             D * R - L * E = scale * F
00048 *>
00049 *> where R and L are unknown m-by-n matrices, (A, D), (B, E) and
00050 *> (C, F) are given matrix pairs of size m-by-m, n-by-n and m-by-n,
00051 *> respectively, with complex entries. A, B, D and E are upper
00052 *> triangular (i.e., (A,D) and (B,E) in generalized Schur form).
00053 *>
00054 *> The solution (R, L) overwrites (C, F). 0 <= SCALE <= 1
00055 *> is an output scaling factor chosen to avoid overflow.
00056 *>
00057 *> In matrix notation (1) is equivalent to solve Zx = scale*b, where Z
00058 *> is defined as
00059 *>
00060 *>        Z = [ kron(In, A)  -kron(B**H, Im) ]        (2)
00061 *>            [ kron(In, D)  -kron(E**H, Im) ],
00062 *>
00063 *> Here Ix is the identity matrix of size x and X**H is the conjugate
00064 *> transpose of X. Kron(X, Y) is the Kronecker product between the
00065 *> matrices X and Y.
00066 *>
00067 *> If TRANS = 'C', y in the conjugate transposed system Z**H *y = scale*b
00068 *> is solved for, which is equivalent to solve for R and L in
00069 *>
00070 *>             A**H * R + D**H * L = scale * C           (3)
00071 *>             R * B**H + L * E**H = scale * -F
00072 *>
00073 *> This case (TRANS = 'C') is used to compute an one-norm-based estimate
00074 *> of Dif[(A,D), (B,E)], the separation between the matrix pairs (A,D)
00075 *> and (B,E), using CLACON.
00076 *>
00077 *> If IJOB >= 1, CTGSYL computes a Frobenius norm-based estimate of
00078 *> Dif[(A,D),(B,E)]. That is, the reciprocal of a lower bound on the
00079 *> reciprocal of the smallest singular value of Z.
00080 *>
00081 *> This is a level-3 BLAS algorithm.
00082 *> \endverbatim
00083 *
00084 *  Arguments:
00085 *  ==========
00086 *
00087 *> \param[in] TRANS
00088 *> \verbatim
00089 *>          TRANS is CHARACTER*1
00090 *>          = 'N': solve the generalized sylvester equation (1).
00091 *>          = 'C': solve the "conjugate transposed" system (3).
00092 *> \endverbatim
00093 *>
00094 *> \param[in] IJOB
00095 *> \verbatim
00096 *>          IJOB is INTEGER
00097 *>          Specifies what kind of functionality to be performed.
00098 *>          =0: solve (1) only.
00099 *>          =1: The functionality of 0 and 3.
00100 *>          =2: The functionality of 0 and 4.
00101 *>          =3: Only an estimate of Dif[(A,D), (B,E)] is computed.
00102 *>              (look ahead strategy is used).
00103 *>          =4: Only an estimate of Dif[(A,D), (B,E)] is computed.
00104 *>              (CGECON on sub-systems is used).
00105 *>          Not referenced if TRANS = 'C'.
00106 *> \endverbatim
00107 *>
00108 *> \param[in] M
00109 *> \verbatim
00110 *>          M is INTEGER
00111 *>          The order of the matrices A and D, and the row dimension of
00112 *>          the matrices C, F, R and L.
00113 *> \endverbatim
00114 *>
00115 *> \param[in] N
00116 *> \verbatim
00117 *>          N is INTEGER
00118 *>          The order of the matrices B and E, and the column dimension
00119 *>          of the matrices C, F, R and L.
00120 *> \endverbatim
00121 *>
00122 *> \param[in] A
00123 *> \verbatim
00124 *>          A is COMPLEX array, dimension (LDA, M)
00125 *>          The upper triangular matrix A.
00126 *> \endverbatim
00127 *>
00128 *> \param[in] LDA
00129 *> \verbatim
00130 *>          LDA is INTEGER
00131 *>          The leading dimension of the array A. LDA >= max(1, M).
00132 *> \endverbatim
00133 *>
00134 *> \param[in] B
00135 *> \verbatim
00136 *>          B is COMPLEX array, dimension (LDB, N)
00137 *>          The upper triangular matrix B.
00138 *> \endverbatim
00139 *>
00140 *> \param[in] LDB
00141 *> \verbatim
00142 *>          LDB is INTEGER
00143 *>          The leading dimension of the array B. LDB >= max(1, N).
00144 *> \endverbatim
00145 *>
00146 *> \param[in,out] C
00147 *> \verbatim
00148 *>          C is COMPLEX array, dimension (LDC, N)
00149 *>          On entry, C contains the right-hand-side of the first matrix
00150 *>          equation in (1) or (3).
00151 *>          On exit, if IJOB = 0, 1 or 2, C has been overwritten by
00152 *>          the solution R. If IJOB = 3 or 4 and TRANS = 'N', C holds R,
00153 *>          the solution achieved during the computation of the
00154 *>          Dif-estimate.
00155 *> \endverbatim
00156 *>
00157 *> \param[in] LDC
00158 *> \verbatim
00159 *>          LDC is INTEGER
00160 *>          The leading dimension of the array C. LDC >= max(1, M).
00161 *> \endverbatim
00162 *>
00163 *> \param[in] D
00164 *> \verbatim
00165 *>          D is COMPLEX array, dimension (LDD, M)
00166 *>          The upper triangular matrix D.
00167 *> \endverbatim
00168 *>
00169 *> \param[in] LDD
00170 *> \verbatim
00171 *>          LDD is INTEGER
00172 *>          The leading dimension of the array D. LDD >= max(1, M).
00173 *> \endverbatim
00174 *>
00175 *> \param[in] E
00176 *> \verbatim
00177 *>          E is COMPLEX array, dimension (LDE, N)
00178 *>          The upper triangular matrix E.
00179 *> \endverbatim
00180 *>
00181 *> \param[in] LDE
00182 *> \verbatim
00183 *>          LDE is INTEGER
00184 *>          The leading dimension of the array E. LDE >= max(1, N).
00185 *> \endverbatim
00186 *>
00187 *> \param[in,out] F
00188 *> \verbatim
00189 *>          F is COMPLEX array, dimension (LDF, N)
00190 *>          On entry, F contains the right-hand-side of the second matrix
00191 *>          equation in (1) or (3).
00192 *>          On exit, if IJOB = 0, 1 or 2, F has been overwritten by
00193 *>          the solution L. If IJOB = 3 or 4 and TRANS = 'N', F holds L,
00194 *>          the solution achieved during the computation of the
00195 *>          Dif-estimate.
00196 *> \endverbatim
00197 *>
00198 *> \param[in] LDF
00199 *> \verbatim
00200 *>          LDF is INTEGER
00201 *>          The leading dimension of the array F. LDF >= max(1, M).
00202 *> \endverbatim
00203 *>
00204 *> \param[out] DIF
00205 *> \verbatim
00206 *>          DIF is REAL
00207 *>          On exit DIF is the reciprocal of a lower bound of the
00208 *>          reciprocal of the Dif-function, i.e. DIF is an upper bound of
00209 *>          Dif[(A,D), (B,E)] = sigma-min(Z), where Z as in (2).
00210 *>          IF IJOB = 0 or TRANS = 'C', DIF is not referenced.
00211 *> \endverbatim
00212 *>
00213 *> \param[out] SCALE
00214 *> \verbatim
00215 *>          SCALE is REAL
00216 *>          On exit SCALE is the scaling factor in (1) or (3).
00217 *>          If 0 < SCALE < 1, C and F hold the solutions R and L, resp.,
00218 *>          to a slightly perturbed system but the input matrices A, B,
00219 *>          D and E have not been changed. If SCALE = 0, R and L will
00220 *>          hold the solutions to the homogenious system with C = F = 0.
00221 *> \endverbatim
00222 *>
00223 *> \param[out] WORK
00224 *> \verbatim
00225 *>          WORK is COMPLEX array, dimension (MAX(1,LWORK))
00226 *>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
00227 *> \endverbatim
00228 *>
00229 *> \param[in] LWORK
00230 *> \verbatim
00231 *>          LWORK is INTEGER
00232 *>          The dimension of the array WORK. LWORK > = 1.
00233 *>          If IJOB = 1 or 2 and TRANS = 'N', LWORK >= max(1,2*M*N).
00234 *>
00235 *>          If LWORK = -1, then a workspace query is assumed; the routine
00236 *>          only calculates the optimal size of the WORK array, returns
00237 *>          this value as the first entry of the WORK array, and no error
00238 *>          message related to LWORK is issued by XERBLA.
00239 *> \endverbatim
00240 *>
00241 *> \param[out] IWORK
00242 *> \verbatim
00243 *>          IWORK is INTEGER array, dimension (M+N+2)
00244 *> \endverbatim
00245 *>
00246 *> \param[out] INFO
00247 *> \verbatim
00248 *>          INFO is INTEGER
00249 *>            =0: successful exit
00250 *>            <0: If INFO = -i, the i-th argument had an illegal value.
00251 *>            >0: (A, D) and (B, E) have common or very close
00252 *>                eigenvalues.
00253 *> \endverbatim
00254 *
00255 *  Authors:
00256 *  ========
00257 *
00258 *> \author Univ. of Tennessee 
00259 *> \author Univ. of California Berkeley 
00260 *> \author Univ. of Colorado Denver 
00261 *> \author NAG Ltd. 
00262 *
00263 *> \date November 2011
00264 *
00265 *> \ingroup complexSYcomputational
00266 *
00267 *> \par Contributors:
00268 *  ==================
00269 *>
00270 *>     Bo Kagstrom and Peter Poromaa, Department of Computing Science,
00271 *>     Umea University, S-901 87 Umea, Sweden.
00272 *
00273 *> \par References:
00274 *  ================
00275 *>
00276 *>  [1] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software
00277 *>      for Solving the Generalized Sylvester Equation and Estimating the
00278 *>      Separation between Regular Matrix Pairs, Report UMINF - 93.23,
00279 *>      Department of Computing Science, Umea University, S-901 87 Umea,
00280 *>      Sweden, December 1993, Revised April 1994, Also as LAPACK Working
00281 *>      Note 75.  To appear in ACM Trans. on Math. Software, Vol 22,
00282 *>      No 1, 1996.
00283 *> \n
00284 *>  [2] B. Kagstrom, A Perturbation Analysis of the Generalized Sylvester
00285 *>      Equation (AR - LB, DR - LE ) = (C, F), SIAM J. Matrix Anal.
00286 *>      Appl., 15(4):1045-1060, 1994.
00287 *> \n
00288 *>  [3] B. Kagstrom and L. Westin, Generalized Schur Methods with
00289 *>      Condition Estimators for Solving the Generalized Sylvester
00290 *>      Equation, IEEE Transactions on Automatic Control, Vol. 34, No. 7,
00291 *>      July 1989, pp 745-751.
00292 *>
00293 *  =====================================================================
00294       SUBROUTINE CTGSYL( TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D,
00295      $                   LDD, E, LDE, F, LDF, SCALE, DIF, WORK, LWORK,
00296      $                   IWORK, INFO )
00297 *
00298 *  -- LAPACK computational routine (version 3.4.0) --
00299 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00300 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00301 *     November 2011
00302 *
00303 *     .. Scalar Arguments ..
00304       CHARACTER          TRANS
00305       INTEGER            IJOB, INFO, LDA, LDB, LDC, LDD, LDE, LDF,
00306      $                   LWORK, M, N
00307       REAL               DIF, SCALE
00308 *     ..
00309 *     .. Array Arguments ..
00310       INTEGER            IWORK( * )
00311       COMPLEX            A( LDA, * ), B( LDB, * ), C( LDC, * ),
00312      $                   D( LDD, * ), E( LDE, * ), F( LDF, * ),
00313      $                   WORK( * )
00314 *     ..
00315 *
00316 *  =====================================================================
00317 *  Replaced various illegal calls to CCOPY by calls to CLASET.
00318 *  Sven Hammarling, 1/5/02.
00319 *
00320 *     .. Parameters ..
00321       REAL               ZERO, ONE
00322       PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
00323       COMPLEX            CZERO
00324       PARAMETER          ( CZERO = (0.0E+0, 0.0E+0) )
00325 *     ..
00326 *     .. Local Scalars ..
00327       LOGICAL            LQUERY, NOTRAN
00328       INTEGER            I, IE, IFUNC, IROUND, IS, ISOLVE, J, JE, JS, K,
00329      $                   LINFO, LWMIN, MB, NB, P, PQ, Q
00330       REAL               DSCALE, DSUM, SCALE2, SCALOC
00331 *     ..
00332 *     .. External Functions ..
00333       LOGICAL            LSAME
00334       INTEGER            ILAENV
00335       EXTERNAL           LSAME, ILAENV
00336 *     ..
00337 *     .. External Subroutines ..
00338       EXTERNAL           CGEMM, CLACPY, CLASET, CSCAL, CTGSY2, XERBLA
00339 *     ..
00340 *     .. Intrinsic Functions ..
00341       INTRINSIC          CMPLX, MAX, REAL, SQRT
00342 *     ..
00343 *     .. Executable Statements ..
00344 *
00345 *     Decode and test input parameters
00346 *
00347       INFO = 0
00348       NOTRAN = LSAME( TRANS, 'N' )
00349       LQUERY = ( LWORK.EQ.-1 )
00350 *
00351       IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN
00352          INFO = -1
00353       ELSE IF( NOTRAN ) THEN
00354          IF( ( IJOB.LT.0 ) .OR. ( IJOB.GT.4 ) ) THEN
00355             INFO = -2
00356          END IF
00357       END IF
00358       IF( INFO.EQ.0 ) THEN
00359          IF( M.LE.0 ) THEN
00360             INFO = -3
00361          ELSE IF( N.LE.0 ) THEN
00362             INFO = -4
00363          ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
00364             INFO = -6
00365          ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
00366             INFO = -8
00367          ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
00368             INFO = -10
00369          ELSE IF( LDD.LT.MAX( 1, M ) ) THEN
00370             INFO = -12
00371          ELSE IF( LDE.LT.MAX( 1, N ) ) THEN
00372             INFO = -14
00373          ELSE IF( LDF.LT.MAX( 1, M ) ) THEN
00374             INFO = -16
00375          END IF
00376       END IF
00377 *
00378       IF( INFO.EQ.0 ) THEN
00379          IF( NOTRAN ) THEN
00380             IF( IJOB.EQ.1 .OR. IJOB.EQ.2 ) THEN
00381                LWMIN = MAX( 1, 2*M*N )
00382             ELSE
00383                LWMIN = 1
00384             END IF
00385          ELSE
00386             LWMIN = 1
00387          END IF
00388          WORK( 1 ) = LWMIN
00389 *
00390          IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
00391             INFO = -20
00392          END IF
00393       END IF
00394 *
00395       IF( INFO.NE.0 ) THEN
00396          CALL XERBLA( 'CTGSYL', -INFO )
00397          RETURN
00398       ELSE IF( LQUERY ) THEN
00399          RETURN
00400       END IF
00401 *
00402 *     Quick return if possible
00403 *
00404       IF( M.EQ.0 .OR. N.EQ.0 ) THEN
00405          SCALE = 1
00406          IF( NOTRAN ) THEN
00407             IF( IJOB.NE.0 ) THEN
00408                DIF = 0
00409             END IF
00410          END IF
00411          RETURN
00412       END IF
00413 *
00414 *     Determine  optimal block sizes MB and NB
00415 *
00416       MB = ILAENV( 2, 'CTGSYL', TRANS, M, N, -1, -1 )
00417       NB = ILAENV( 5, 'CTGSYL', TRANS, M, N, -1, -1 )
00418 *
00419       ISOLVE = 1
00420       IFUNC = 0
00421       IF( NOTRAN ) THEN
00422          IF( IJOB.GE.3 ) THEN
00423             IFUNC = IJOB - 2
00424             CALL CLASET( 'F', M, N, CZERO, CZERO, C, LDC )
00425             CALL CLASET( 'F', M, N, CZERO, CZERO, F, LDF )
00426          ELSE IF( IJOB.GE.1 .AND. NOTRAN ) THEN
00427             ISOLVE = 2
00428          END IF
00429       END IF
00430 *
00431       IF( ( MB.LE.1 .AND. NB.LE.1 ) .OR. ( MB.GE.M .AND. NB.GE.N ) )
00432      $     THEN
00433 *
00434 *        Use unblocked Level 2 solver
00435 *
00436          DO 30 IROUND = 1, ISOLVE
00437 *
00438             SCALE = ONE
00439             DSCALE = ZERO
00440             DSUM = ONE
00441             PQ = M*N
00442             CALL CTGSY2( TRANS, IFUNC, M, N, A, LDA, B, LDB, C, LDC, D,
00443      $                   LDD, E, LDE, F, LDF, SCALE, DSUM, DSCALE,
00444      $                   INFO )
00445             IF( DSCALE.NE.ZERO ) THEN
00446                IF( IJOB.EQ.1 .OR. IJOB.EQ.3 ) THEN
00447                   DIF = SQRT( REAL( 2*M*N ) ) / ( DSCALE*SQRT( DSUM ) )
00448                ELSE
00449                   DIF = SQRT( REAL( PQ ) ) / ( DSCALE*SQRT( DSUM ) )
00450                END IF
00451             END IF
00452             IF( ISOLVE.EQ.2 .AND. IROUND.EQ.1 ) THEN
00453                IF( NOTRAN ) THEN
00454                   IFUNC = IJOB
00455                END IF
00456                SCALE2 = SCALE
00457                CALL CLACPY( 'F', M, N, C, LDC, WORK, M )
00458                CALL CLACPY( 'F', M, N, F, LDF, WORK( M*N+1 ), M )
00459                CALL CLASET( 'F', M, N, CZERO, CZERO, C, LDC )
00460                CALL CLASET( 'F', M, N, CZERO, CZERO, F, LDF )
00461             ELSE IF( ISOLVE.EQ.2 .AND. IROUND.EQ.2 ) THEN
00462                CALL CLACPY( 'F', M, N, WORK, M, C, LDC )
00463                CALL CLACPY( 'F', M, N, WORK( M*N+1 ), M, F, LDF )
00464                SCALE = SCALE2
00465             END IF
00466    30    CONTINUE
00467 *
00468          RETURN
00469 *
00470       END IF
00471 *
00472 *     Determine block structure of A
00473 *
00474       P = 0
00475       I = 1
00476    40 CONTINUE
00477       IF( I.GT.M )
00478      $   GO TO 50
00479       P = P + 1
00480       IWORK( P ) = I
00481       I = I + MB
00482       IF( I.GE.M )
00483      $   GO TO 50
00484       GO TO 40
00485    50 CONTINUE
00486       IWORK( P+1 ) = M + 1
00487       IF( IWORK( P ).EQ.IWORK( P+1 ) )
00488      $   P = P - 1
00489 *
00490 *     Determine block structure of B
00491 *
00492       Q = P + 1
00493       J = 1
00494    60 CONTINUE
00495       IF( J.GT.N )
00496      $   GO TO 70
00497 *
00498       Q = Q + 1
00499       IWORK( Q ) = J
00500       J = J + NB
00501       IF( J.GE.N )
00502      $   GO TO 70
00503       GO TO 60
00504 *
00505    70 CONTINUE
00506       IWORK( Q+1 ) = N + 1
00507       IF( IWORK( Q ).EQ.IWORK( Q+1 ) )
00508      $   Q = Q - 1
00509 *
00510       IF( NOTRAN ) THEN
00511          DO 150 IROUND = 1, ISOLVE
00512 *
00513 *           Solve (I, J) - subsystem
00514 *               A(I, I) * R(I, J) - L(I, J) * B(J, J) = C(I, J)
00515 *               D(I, I) * R(I, J) - L(I, J) * E(J, J) = F(I, J)
00516 *           for I = P, P - 1, ..., 1; J = 1, 2, ..., Q
00517 *
00518             PQ = 0
00519             SCALE = ONE
00520             DSCALE = ZERO
00521             DSUM = ONE
00522             DO 130 J = P + 2, Q
00523                JS = IWORK( J )
00524                JE = IWORK( J+1 ) - 1
00525                NB = JE - JS + 1
00526                DO 120 I = P, 1, -1
00527                   IS = IWORK( I )
00528                   IE = IWORK( I+1 ) - 1
00529                   MB = IE - IS + 1
00530                   CALL CTGSY2( TRANS, IFUNC, MB, NB, A( IS, IS ), LDA,
00531      $                         B( JS, JS ), LDB, C( IS, JS ), LDC,
00532      $                         D( IS, IS ), LDD, E( JS, JS ), LDE,
00533      $                         F( IS, JS ), LDF, SCALOC, DSUM, DSCALE,
00534      $                         LINFO )
00535                   IF( LINFO.GT.0 )
00536      $               INFO = LINFO
00537                   PQ = PQ + MB*NB
00538                   IF( SCALOC.NE.ONE ) THEN
00539                      DO 80 K = 1, JS - 1
00540                         CALL CSCAL( M, CMPLX( SCALOC, ZERO ), C( 1, K ),
00541      $                              1 )
00542                         CALL CSCAL( M, CMPLX( SCALOC, ZERO ), F( 1, K ),
00543      $                              1 )
00544    80                CONTINUE
00545                      DO 90 K = JS, JE
00546                         CALL CSCAL( IS-1, CMPLX( SCALOC, ZERO ),
00547      $                              C( 1, K ), 1 )
00548                         CALL CSCAL( IS-1, CMPLX( SCALOC, ZERO ),
00549      $                              F( 1, K ), 1 )
00550    90                CONTINUE
00551                      DO 100 K = JS, JE
00552                         CALL CSCAL( M-IE, CMPLX( SCALOC, ZERO ),
00553      $                              C( IE+1, K ), 1 )
00554                         CALL CSCAL( M-IE, CMPLX( SCALOC, ZERO ),
00555      $                              F( IE+1, K ), 1 )
00556   100                CONTINUE
00557                      DO 110 K = JE + 1, N
00558                         CALL CSCAL( M, CMPLX( SCALOC, ZERO ), C( 1, K ),
00559      $                              1 )
00560                         CALL CSCAL( M, CMPLX( SCALOC, ZERO ), F( 1, K ),
00561      $                              1 )
00562   110                CONTINUE
00563                      SCALE = SCALE*SCALOC
00564                   END IF
00565 *
00566 *                 Substitute R(I,J) and L(I,J) into remaining equation.
00567 *
00568                   IF( I.GT.1 ) THEN
00569                      CALL CGEMM( 'N', 'N', IS-1, NB, MB,
00570      $                           CMPLX( -ONE, ZERO ), A( 1, IS ), LDA,
00571      $                           C( IS, JS ), LDC, CMPLX( ONE, ZERO ),
00572      $                           C( 1, JS ), LDC )
00573                      CALL CGEMM( 'N', 'N', IS-1, NB, MB,
00574      $                           CMPLX( -ONE, ZERO ), D( 1, IS ), LDD,
00575      $                           C( IS, JS ), LDC, CMPLX( ONE, ZERO ),
00576      $                           F( 1, JS ), LDF )
00577                   END IF
00578                   IF( J.LT.Q ) THEN
00579                      CALL CGEMM( 'N', 'N', MB, N-JE, NB,
00580      $                           CMPLX( ONE, ZERO ), F( IS, JS ), LDF,
00581      $                           B( JS, JE+1 ), LDB, CMPLX( ONE, ZERO ),
00582      $                           C( IS, JE+1 ), LDC )
00583                      CALL CGEMM( 'N', 'N', MB, N-JE, NB,
00584      $                           CMPLX( ONE, ZERO ), F( IS, JS ), LDF,
00585      $                           E( JS, JE+1 ), LDE, CMPLX( ONE, ZERO ),
00586      $                           F( IS, JE+1 ), LDF )
00587                   END IF
00588   120          CONTINUE
00589   130       CONTINUE
00590             IF( DSCALE.NE.ZERO ) THEN
00591                IF( IJOB.EQ.1 .OR. IJOB.EQ.3 ) THEN
00592                   DIF = SQRT( REAL( 2*M*N ) ) / ( DSCALE*SQRT( DSUM ) )
00593                ELSE
00594                   DIF = SQRT( REAL( PQ ) ) / ( DSCALE*SQRT( DSUM ) )
00595                END IF
00596             END IF
00597             IF( ISOLVE.EQ.2 .AND. IROUND.EQ.1 ) THEN
00598                IF( NOTRAN ) THEN
00599                   IFUNC = IJOB
00600                END IF
00601                SCALE2 = SCALE
00602                CALL CLACPY( 'F', M, N, C, LDC, WORK, M )
00603                CALL CLACPY( 'F', M, N, F, LDF, WORK( M*N+1 ), M )
00604                CALL CLASET( 'F', M, N, CZERO, CZERO, C, LDC )
00605                CALL CLASET( 'F', M, N, CZERO, CZERO, F, LDF )
00606             ELSE IF( ISOLVE.EQ.2 .AND. IROUND.EQ.2 ) THEN
00607                CALL CLACPY( 'F', M, N, WORK, M, C, LDC )
00608                CALL CLACPY( 'F', M, N, WORK( M*N+1 ), M, F, LDF )
00609                SCALE = SCALE2
00610             END IF
00611   150    CONTINUE
00612       ELSE
00613 *
00614 *        Solve transposed (I, J)-subsystem
00615 *            A(I, I)**H * R(I, J) + D(I, I)**H * L(I, J) = C(I, J)
00616 *            R(I, J) * B(J, J)  + L(I, J) * E(J, J) = -F(I, J)
00617 *        for I = 1,2,..., P; J = Q, Q-1,..., 1
00618 *
00619          SCALE = ONE
00620          DO 210 I = 1, P
00621             IS = IWORK( I )
00622             IE = IWORK( I+1 ) - 1
00623             MB = IE - IS + 1
00624             DO 200 J = Q, P + 2, -1
00625                JS = IWORK( J )
00626                JE = IWORK( J+1 ) - 1
00627                NB = JE - JS + 1
00628                CALL CTGSY2( TRANS, IFUNC, MB, NB, A( IS, IS ), LDA,
00629      $                      B( JS, JS ), LDB, C( IS, JS ), LDC,
00630      $                      D( IS, IS ), LDD, E( JS, JS ), LDE,
00631      $                      F( IS, JS ), LDF, SCALOC, DSUM, DSCALE,
00632      $                      LINFO )
00633                IF( LINFO.GT.0 )
00634      $            INFO = LINFO
00635                IF( SCALOC.NE.ONE ) THEN
00636                   DO 160 K = 1, JS - 1
00637                      CALL CSCAL( M, CMPLX( SCALOC, ZERO ), C( 1, K ),
00638      $                           1 )
00639                      CALL CSCAL( M, CMPLX( SCALOC, ZERO ), F( 1, K ),
00640      $                           1 )
00641   160             CONTINUE
00642                   DO 170 K = JS, JE
00643                      CALL CSCAL( IS-1, CMPLX( SCALOC, ZERO ), C( 1, K ),
00644      $                           1 )
00645                      CALL CSCAL( IS-1, CMPLX( SCALOC, ZERO ), F( 1, K ),
00646      $                           1 )
00647   170             CONTINUE
00648                   DO 180 K = JS, JE
00649                      CALL CSCAL( M-IE, CMPLX( SCALOC, ZERO ),
00650      $                           C( IE+1, K ), 1 )
00651                      CALL CSCAL( M-IE, CMPLX( SCALOC, ZERO ),
00652      $                           F( IE+1, K ), 1 )
00653   180             CONTINUE
00654                   DO 190 K = JE + 1, N
00655                      CALL CSCAL( M, CMPLX( SCALOC, ZERO ), C( 1, K ),
00656      $                           1 )
00657                      CALL CSCAL( M, CMPLX( SCALOC, ZERO ), F( 1, K ),
00658      $                           1 )
00659   190             CONTINUE
00660                   SCALE = SCALE*SCALOC
00661                END IF
00662 *
00663 *              Substitute R(I,J) and L(I,J) into remaining equation.
00664 *
00665                IF( J.GT.P+2 ) THEN
00666                   CALL CGEMM( 'N', 'C', MB, JS-1, NB,
00667      $                        CMPLX( ONE, ZERO ), C( IS, JS ), LDC,
00668      $                        B( 1, JS ), LDB, CMPLX( ONE, ZERO ),
00669      $                        F( IS, 1 ), LDF )
00670                   CALL CGEMM( 'N', 'C', MB, JS-1, NB,
00671      $                        CMPLX( ONE, ZERO ), F( IS, JS ), LDF,
00672      $                        E( 1, JS ), LDE, CMPLX( ONE, ZERO ),
00673      $                        F( IS, 1 ), LDF )
00674                END IF
00675                IF( I.LT.P ) THEN
00676                   CALL CGEMM( 'C', 'N', M-IE, NB, MB,
00677      $                        CMPLX( -ONE, ZERO ), A( IS, IE+1 ), LDA,
00678      $                        C( IS, JS ), LDC, CMPLX( ONE, ZERO ),
00679      $                        C( IE+1, JS ), LDC )
00680                   CALL CGEMM( 'C', 'N', M-IE, NB, MB,
00681      $                        CMPLX( -ONE, ZERO ), D( IS, IE+1 ), LDD,
00682      $                        F( IS, JS ), LDF, CMPLX( ONE, ZERO ),
00683      $                        C( IE+1, JS ), LDC )
00684                END IF
00685   200       CONTINUE
00686   210    CONTINUE
00687       END IF
00688 *
00689       WORK( 1 ) = LWMIN
00690 *
00691       RETURN
00692 *
00693 *     End of CTGSYL
00694 *
00695       END
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