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authorjofret2009-04-28 07:17:00 +0000
committerjofret2009-04-28 07:17:00 +0000
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Moving lapack to right place
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- SUBROUTINE ZTGSYL( TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D,
- $ LDD, E, LDE, F, LDF, SCALE, DIF, WORK, LWORK,
- $ IWORK, INFO )
-*
-* -- LAPACK routine (version 3.1) --
-* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
-* November 2006
-*
-* .. Scalar Arguments ..
- CHARACTER TRANS
- INTEGER IJOB, INFO, LDA, LDB, LDC, LDD, LDE, LDF,
- $ LWORK, M, N
- DOUBLE PRECISION DIF, SCALE
-* ..
-* .. Array Arguments ..
- INTEGER IWORK( * )
- COMPLEX*16 A( LDA, * ), B( LDB, * ), C( LDC, * ),
- $ D( LDD, * ), E( LDE, * ), F( LDF, * ),
- $ WORK( * )
-* ..
-*
-* Purpose
-* =======
-*
-* ZTGSYL solves the generalized Sylvester equation:
-*
-* A * R - L * B = scale * C (1)
-* D * R - L * E = scale * F
-*
-* where R and L are unknown m-by-n matrices, (A, D), (B, E) and
-* (C, F) are given matrix pairs of size m-by-m, n-by-n and m-by-n,
-* respectively, with complex entries. A, B, D and E are upper
-* triangular (i.e., (A,D) and (B,E) in generalized Schur form).
-*
-* The solution (R, L) overwrites (C, F). 0 <= SCALE <= 1
-* is an output scaling factor chosen to avoid overflow.
-*
-* In matrix notation (1) is equivalent to solve Zx = scale*b, where Z
-* is defined as
-*
-* Z = [ kron(In, A) -kron(B', Im) ] (2)
-* [ kron(In, D) -kron(E', Im) ],
-*
-* Here Ix is the identity matrix of size x and X' is the conjugate
-* transpose of X. Kron(X, Y) is the Kronecker product between the
-* matrices X and Y.
-*
-* If TRANS = 'C', y in the conjugate transposed system Z'*y = scale*b
-* is solved for, which is equivalent to solve for R and L in
-*
-* A' * R + D' * L = scale * C (3)
-* R * B' + L * E' = scale * -F
-*
-* This case (TRANS = 'C') is used to compute an one-norm-based estimate
-* of Dif[(A,D), (B,E)], the separation between the matrix pairs (A,D)
-* and (B,E), using ZLACON.
-*
-* If IJOB >= 1, ZTGSYL computes a Frobenius norm-based estimate of
-* Dif[(A,D),(B,E)]. That is, the reciprocal of a lower bound on the
-* reciprocal of the smallest singular value of Z.
-*
-* This is a level-3 BLAS algorithm.
-*
-* Arguments
-* =========
-*
-* TRANS (input) CHARACTER*1
-* = 'N': solve the generalized sylvester equation (1).
-* = 'C': solve the "conjugate transposed" system (3).
-*
-* IJOB (input) INTEGER
-* Specifies what kind of functionality to be performed.
-* =0: solve (1) only.
-* =1: The functionality of 0 and 3.
-* =2: The functionality of 0 and 4.
-* =3: Only an estimate of Dif[(A,D), (B,E)] is computed.
-* (look ahead strategy is used).
-* =4: Only an estimate of Dif[(A,D), (B,E)] is computed.
-* (ZGECON on sub-systems is used).
-* Not referenced if TRANS = 'C'.
-*
-* M (input) INTEGER
-* The order of the matrices A and D, and the row dimension of
-* the matrices C, F, R and L.
-*
-* N (input) INTEGER
-* The order of the matrices B and E, and the column dimension
-* of the matrices C, F, R and L.
-*
-* A (input) COMPLEX*16 array, dimension (LDA, M)
-* The upper triangular matrix A.
-*
-* LDA (input) INTEGER
-* The leading dimension of the array A. LDA >= max(1, M).
-*
-* B (input) COMPLEX*16 array, dimension (LDB, N)
-* The upper triangular matrix B.
-*
-* LDB (input) INTEGER
-* The leading dimension of the array B. LDB >= max(1, N).
-*
-* C (input/output) COMPLEX*16 array, dimension (LDC, N)
-* On entry, C contains the right-hand-side of the first matrix
-* equation in (1) or (3).
-* On exit, if IJOB = 0, 1 or 2, C has been overwritten by
-* the solution R. If IJOB = 3 or 4 and TRANS = 'N', C holds R,
-* the solution achieved during the computation of the
-* Dif-estimate.
-*
-* LDC (input) INTEGER
-* The leading dimension of the array C. LDC >= max(1, M).
-*
-* D (input) COMPLEX*16 array, dimension (LDD, M)
-* The upper triangular matrix D.
-*
-* LDD (input) INTEGER
-* The leading dimension of the array D. LDD >= max(1, M).
-*
-* E (input) COMPLEX*16 array, dimension (LDE, N)
-* The upper triangular matrix E.
-*
-* LDE (input) INTEGER
-* The leading dimension of the array E. LDE >= max(1, N).
-*
-* F (input/output) COMPLEX*16 array, dimension (LDF, N)
-* On entry, F contains the right-hand-side of the second matrix
-* equation in (1) or (3).
-* On exit, if IJOB = 0, 1 or 2, F has been overwritten by
-* the solution L. If IJOB = 3 or 4 and TRANS = 'N', F holds L,
-* the solution achieved during the computation of the
-* Dif-estimate.
-*
-* LDF (input) INTEGER
-* The leading dimension of the array F. LDF >= max(1, M).
-*
-* DIF (output) DOUBLE PRECISION
-* On exit DIF is the reciprocal of a lower bound of the
-* reciprocal of the Dif-function, i.e. DIF is an upper bound of
-* Dif[(A,D), (B,E)] = sigma-min(Z), where Z as in (2).
-* IF IJOB = 0 or TRANS = 'C', DIF is not referenced.
-*
-* SCALE (output) DOUBLE PRECISION
-* On exit SCALE is the scaling factor in (1) or (3).
-* If 0 < SCALE < 1, C and F hold the solutions R and L, resp.,
-* to a slightly perturbed system but the input matrices A, B,
-* D and E have not been changed. If SCALE = 0, R and L will
-* hold the solutions to the homogenious system with C = F = 0.
-*
-* WORK (workspace/output) COMPLEX*16 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.
-* If IJOB = 1 or 2 and TRANS = 'N', LWORK >= max(1,2*M*N).
-*
-* 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.
-*
-* IWORK (workspace) INTEGER array, dimension (M+N+2)
-* If IJOB = 0, IWORK is not referenced.
-*
-* INFO (output) INTEGER
-* =0: successful exit
-* <0: If INFO = -i, the i-th argument had an illegal value.
-* >0: (A, D) and (B, E) have common or very close
-* eigenvalues.
-*
-* 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 and P. Poromaa, LAPACK-Style Algorithms and Software
-* for Solving the Generalized Sylvester Equation and Estimating the
-* Separation between Regular Matrix Pairs, Report UMINF - 93.23,
-* Department of Computing Science, Umea University, S-901 87 Umea,
-* Sweden, December 1993, Revised April 1994, Also as LAPACK Working
-* Note 75. To appear in ACM Trans. on Math. Software, Vol 22,
-* No 1, 1996.
-*
-* [2] B. Kagstrom, A Perturbation Analysis of the Generalized Sylvester
-* Equation (AR - LB, DR - LE ) = (C, F), SIAM J. Matrix Anal.
-* Appl., 15(4):1045-1060, 1994.
-*
-* [3] B. Kagstrom and L. Westin, Generalized Schur Methods with
-* Condition Estimators for Solving the Generalized Sylvester
-* Equation, IEEE Transactions on Automatic Control, Vol. 34, No. 7,
-* July 1989, pp 745-751.
-*
-* =====================================================================
-* Replaced various illegal calls to CCOPY by calls to CLASET.
-* Sven Hammarling, 1/5/02.
-*
-* .. Parameters ..
- DOUBLE PRECISION ZERO, ONE
- PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
- COMPLEX*16 CZERO
- PARAMETER ( CZERO = (0.0D+0, 0.0D+0) )
-* ..
-* .. Local Scalars ..
- LOGICAL LQUERY, NOTRAN
- INTEGER I, IE, IFUNC, IROUND, IS, ISOLVE, J, JE, JS, K,
- $ LINFO, LWMIN, MB, NB, P, PQ, Q
- DOUBLE PRECISION DSCALE, DSUM, SCALE2, SCALOC
-* ..
-* .. External Functions ..
- LOGICAL LSAME
- INTEGER ILAENV
- EXTERNAL LSAME, ILAENV
-* ..
-* .. External Subroutines ..
- EXTERNAL XERBLA, ZGEMM, ZLACPY, ZLASET, ZSCAL, ZTGSY2
-* ..
-* .. Intrinsic Functions ..
- INTRINSIC DBLE, DCMPLX, MAX, SQRT
-* ..
-* .. Executable Statements ..
-*
-* Decode and test input parameters
-*
- INFO = 0
- NOTRAN = LSAME( TRANS, 'N' )
- LQUERY = ( LWORK.EQ.-1 )
-*
- IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN
- INFO = -1
- ELSE IF( NOTRAN ) THEN
- IF( ( IJOB.LT.0 ) .OR. ( IJOB.GT.4 ) ) THEN
- INFO = -2
- END IF
- END IF
- IF( INFO.EQ.0 ) THEN
- IF( M.LE.0 ) THEN
- INFO = -3
- ELSE IF( N.LE.0 ) THEN
- INFO = -4
- ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
- INFO = -6
- ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
- INFO = -8
- ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
- INFO = -10
- ELSE IF( LDD.LT.MAX( 1, M ) ) THEN
- INFO = -12
- ELSE IF( LDE.LT.MAX( 1, N ) ) THEN
- INFO = -14
- ELSE IF( LDF.LT.MAX( 1, M ) ) THEN
- INFO = -16
- END IF
- END IF
-*
- IF( INFO.EQ.0 ) THEN
- IF( NOTRAN ) THEN
- IF( IJOB.EQ.1 .OR. IJOB.EQ.2 ) THEN
- LWMIN = MAX( 1, 2*M*N )
- ELSE
- LWMIN = 1
- END IF
- ELSE
- LWMIN = 1
- END IF
- WORK( 1 ) = LWMIN
-*
- IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
- INFO = -20
- END IF
- END IF
-*
- IF( INFO.NE.0 ) THEN
- CALL XERBLA( 'ZTGSYL', -INFO )
- RETURN
- ELSE IF( LQUERY ) THEN
- RETURN
- END IF
-*
-* Quick return if possible
-*
- IF( M.EQ.0 .OR. N.EQ.0 ) THEN
- SCALE = 1
- IF( NOTRAN ) THEN
- IF( IJOB.NE.0 ) THEN
- DIF = 0
- END IF
- END IF
- RETURN
- END IF
-*
-* Determine optimal block sizes MB and NB
-*
- MB = ILAENV( 2, 'ZTGSYL', TRANS, M, N, -1, -1 )
- NB = ILAENV( 5, 'ZTGSYL', TRANS, M, N, -1, -1 )
-*
- ISOLVE = 1
- IFUNC = 0
- IF( NOTRAN ) THEN
- IF( IJOB.GE.3 ) THEN
- IFUNC = IJOB - 2
- CALL ZLASET( 'F', M, N, CZERO, CZERO, C, LDC )
- CALL ZLASET( 'F', M, N, CZERO, CZERO, F, LDF )
- ELSE IF( IJOB.GE.1 .AND. NOTRAN ) THEN
- ISOLVE = 2
- END IF
- END IF
-*
- IF( ( MB.LE.1 .AND. NB.LE.1 ) .OR. ( MB.GE.M .AND. NB.GE.N ) )
- $ THEN
-*
-* Use unblocked Level 2 solver
-*
- DO 30 IROUND = 1, ISOLVE
-*
- SCALE = ONE
- DSCALE = ZERO
- DSUM = ONE
- PQ = M*N
- CALL ZTGSY2( TRANS, IFUNC, M, N, A, LDA, B, LDB, C, LDC, D,
- $ LDD, E, LDE, F, LDF, SCALE, DSUM, DSCALE,
- $ INFO )
- IF( DSCALE.NE.ZERO ) THEN
- IF( IJOB.EQ.1 .OR. IJOB.EQ.3 ) THEN
- DIF = SQRT( DBLE( 2*M*N ) ) / ( DSCALE*SQRT( DSUM ) )
- ELSE
- DIF = SQRT( DBLE( PQ ) ) / ( DSCALE*SQRT( DSUM ) )
- END IF
- END IF
- IF( ISOLVE.EQ.2 .AND. IROUND.EQ.1 ) THEN
- IF( NOTRAN ) THEN
- IFUNC = IJOB
- END IF
- SCALE2 = SCALE
- CALL ZLACPY( 'F', M, N, C, LDC, WORK, M )
- CALL ZLACPY( 'F', M, N, F, LDF, WORK( M*N+1 ), M )
- CALL ZLASET( 'F', M, N, CZERO, CZERO, C, LDC )
- CALL ZLASET( 'F', M, N, CZERO, CZERO, F, LDF )
- ELSE IF( ISOLVE.EQ.2 .AND. IROUND.EQ.2 ) THEN
- CALL ZLACPY( 'F', M, N, WORK, M, C, LDC )
- CALL ZLACPY( 'F', M, N, WORK( M*N+1 ), M, F, LDF )
- SCALE = SCALE2
- END IF
- 30 CONTINUE
-*
- RETURN
-*
- END IF
-*
-* Determine block structure of A
-*
- P = 0
- I = 1
- 40 CONTINUE
- IF( I.GT.M )
- $ GO TO 50
- P = P + 1
- IWORK( P ) = I
- I = I + MB
- IF( I.GE.M )
- $ GO TO 50
- GO TO 40
- 50 CONTINUE
- IWORK( P+1 ) = M + 1
- IF( IWORK( P ).EQ.IWORK( P+1 ) )
- $ P = P - 1
-*
-* Determine block structure of B
-*
- Q = P + 1
- J = 1
- 60 CONTINUE
- IF( J.GT.N )
- $ GO TO 70
-*
- Q = Q + 1
- IWORK( Q ) = J
- J = J + NB
- IF( J.GE.N )
- $ GO TO 70
- GO TO 60
-*
- 70 CONTINUE
- IWORK( Q+1 ) = N + 1
- IF( IWORK( Q ).EQ.IWORK( Q+1 ) )
- $ Q = Q - 1
-*
- IF( NOTRAN ) THEN
- DO 150 IROUND = 1, ISOLVE
-*
-* Solve (I, J) - subsystem
-* A(I, I) * R(I, J) - L(I, J) * B(J, J) = C(I, J)
-* D(I, I) * R(I, J) - L(I, J) * E(J, J) = F(I, J)
-* for I = P, P - 1, ..., 1; J = 1, 2, ..., Q
-*
- PQ = 0
- SCALE = ONE
- DSCALE = ZERO
- DSUM = ONE
- DO 130 J = P + 2, Q
- JS = IWORK( J )
- JE = IWORK( J+1 ) - 1
- NB = JE - JS + 1
- DO 120 I = P, 1, -1
- IS = IWORK( I )
- IE = IWORK( I+1 ) - 1
- MB = IE - IS + 1
- CALL ZTGSY2( TRANS, IFUNC, MB, NB, A( IS, IS ), LDA,
- $ B( JS, JS ), LDB, C( IS, JS ), LDC,
- $ D( IS, IS ), LDD, E( JS, JS ), LDE,
- $ F( IS, JS ), LDF, SCALOC, DSUM, DSCALE,
- $ LINFO )
- IF( LINFO.GT.0 )
- $ INFO = LINFO
- PQ = PQ + MB*NB
- IF( SCALOC.NE.ONE ) THEN
- DO 80 K = 1, JS - 1
- CALL ZSCAL( M, DCMPLX( SCALOC, ZERO ),
- $ C( 1, K ), 1 )
- CALL ZSCAL( M, DCMPLX( SCALOC, ZERO ),
- $ F( 1, K ), 1 )
- 80 CONTINUE
- DO 90 K = JS, JE
- CALL ZSCAL( IS-1, DCMPLX( SCALOC, ZERO ),
- $ C( 1, K ), 1 )
- CALL ZSCAL( IS-1, DCMPLX( SCALOC, ZERO ),
- $ F( 1, K ), 1 )
- 90 CONTINUE
- DO 100 K = JS, JE
- CALL ZSCAL( M-IE, DCMPLX( SCALOC, ZERO ),
- $ C( IE+1, K ), 1 )
- CALL ZSCAL( M-IE, DCMPLX( SCALOC, ZERO ),
- $ F( IE+1, K ), 1 )
- 100 CONTINUE
- DO 110 K = JE + 1, N
- CALL ZSCAL( M, DCMPLX( SCALOC, ZERO ),
- $ C( 1, K ), 1 )
- CALL ZSCAL( M, DCMPLX( SCALOC, ZERO ),
- $ F( 1, K ), 1 )
- 110 CONTINUE
- SCALE = SCALE*SCALOC
- END IF
-*
-* Substitute R(I,J) and L(I,J) into remaining equation.
-*
- IF( I.GT.1 ) THEN
- CALL ZGEMM( 'N', 'N', IS-1, NB, MB,
- $ DCMPLX( -ONE, ZERO ), A( 1, IS ), LDA,
- $ C( IS, JS ), LDC, DCMPLX( ONE, ZERO ),
- $ C( 1, JS ), LDC )
- CALL ZGEMM( 'N', 'N', IS-1, NB, MB,
- $ DCMPLX( -ONE, ZERO ), D( 1, IS ), LDD,
- $ C( IS, JS ), LDC, DCMPLX( ONE, ZERO ),
- $ F( 1, JS ), LDF )
- END IF
- IF( J.LT.Q ) THEN
- CALL ZGEMM( 'N', 'N', MB, N-JE, NB,
- $ DCMPLX( ONE, ZERO ), F( IS, JS ), LDF,
- $ B( JS, JE+1 ), LDB,
- $ DCMPLX( ONE, ZERO ), C( IS, JE+1 ),
- $ LDC )
- CALL ZGEMM( 'N', 'N', MB, N-JE, NB,
- $ DCMPLX( ONE, ZERO ), F( IS, JS ), LDF,
- $ E( JS, JE+1 ), LDE,
- $ DCMPLX( ONE, ZERO ), F( IS, JE+1 ),
- $ LDF )
- END IF
- 120 CONTINUE
- 130 CONTINUE
- IF( DSCALE.NE.ZERO ) THEN
- IF( IJOB.EQ.1 .OR. IJOB.EQ.3 ) THEN
- DIF = SQRT( DBLE( 2*M*N ) ) / ( DSCALE*SQRT( DSUM ) )
- ELSE
- DIF = SQRT( DBLE( PQ ) ) / ( DSCALE*SQRT( DSUM ) )
- END IF
- END IF
- IF( ISOLVE.EQ.2 .AND. IROUND.EQ.1 ) THEN
- IF( NOTRAN ) THEN
- IFUNC = IJOB
- END IF
- SCALE2 = SCALE
- CALL ZLACPY( 'F', M, N, C, LDC, WORK, M )
- CALL ZLACPY( 'F', M, N, F, LDF, WORK( M*N+1 ), M )
- CALL ZLASET( 'F', M, N, CZERO, CZERO, C, LDC )
- CALL ZLASET( 'F', M, N, CZERO, CZERO, F, LDF )
- ELSE IF( ISOLVE.EQ.2 .AND. IROUND.EQ.2 ) THEN
- CALL ZLACPY( 'F', M, N, WORK, M, C, LDC )
- CALL ZLACPY( 'F', M, N, WORK( M*N+1 ), M, F, LDF )
- SCALE = SCALE2
- END IF
- 150 CONTINUE
- ELSE
-*
-* Solve transposed (I, J)-subsystem
-* A(I, I)' * R(I, J) + D(I, I)' * L(I, J) = C(I, J)
-* R(I, J) * B(J, J) + L(I, J) * E(J, J) = -F(I, J)
-* for I = 1,2,..., P; J = Q, Q-1,..., 1
-*
- SCALE = ONE
- DO 210 I = 1, P
- IS = IWORK( I )
- IE = IWORK( I+1 ) - 1
- MB = IE - IS + 1
- DO 200 J = Q, P + 2, -1
- JS = IWORK( J )
- JE = IWORK( J+1 ) - 1
- NB = JE - JS + 1
- CALL ZTGSY2( TRANS, IFUNC, MB, NB, A( IS, IS ), LDA,
- $ B( JS, JS ), LDB, C( IS, JS ), LDC,
- $ D( IS, IS ), LDD, E( JS, JS ), LDE,
- $ F( IS, JS ), LDF, SCALOC, DSUM, DSCALE,
- $ LINFO )
- IF( LINFO.GT.0 )
- $ INFO = LINFO
- IF( SCALOC.NE.ONE ) THEN
- DO 160 K = 1, JS - 1
- CALL ZSCAL( M, DCMPLX( SCALOC, ZERO ), C( 1, K ),
- $ 1 )
- CALL ZSCAL( M, DCMPLX( SCALOC, ZERO ), F( 1, K ),
- $ 1 )
- 160 CONTINUE
- DO 170 K = JS, JE
- CALL ZSCAL( IS-1, DCMPLX( SCALOC, ZERO ),
- $ C( 1, K ), 1 )
- CALL ZSCAL( IS-1, DCMPLX( SCALOC, ZERO ),
- $ F( 1, K ), 1 )
- 170 CONTINUE
- DO 180 K = JS, JE
- CALL ZSCAL( M-IE, DCMPLX( SCALOC, ZERO ),
- $ C( IE+1, K ), 1 )
- CALL ZSCAL( M-IE, DCMPLX( SCALOC, ZERO ),
- $ F( IE+1, K ), 1 )
- 180 CONTINUE
- DO 190 K = JE + 1, N
- CALL ZSCAL( M, DCMPLX( SCALOC, ZERO ), C( 1, K ),
- $ 1 )
- CALL ZSCAL( M, DCMPLX( SCALOC, ZERO ), F( 1, K ),
- $ 1 )
- 190 CONTINUE
- SCALE = SCALE*SCALOC
- END IF
-*
-* Substitute R(I,J) and L(I,J) into remaining equation.
-*
- IF( J.GT.P+2 ) THEN
- CALL ZGEMM( 'N', 'C', MB, JS-1, NB,
- $ DCMPLX( ONE, ZERO ), C( IS, JS ), LDC,
- $ B( 1, JS ), LDB, DCMPLX( ONE, ZERO ),
- $ F( IS, 1 ), LDF )
- CALL ZGEMM( 'N', 'C', MB, JS-1, NB,
- $ DCMPLX( ONE, ZERO ), F( IS, JS ), LDF,
- $ E( 1, JS ), LDE, DCMPLX( ONE, ZERO ),
- $ F( IS, 1 ), LDF )
- END IF
- IF( I.LT.P ) THEN
- CALL ZGEMM( 'C', 'N', M-IE, NB, MB,
- $ DCMPLX( -ONE, ZERO ), A( IS, IE+1 ), LDA,
- $ C( IS, JS ), LDC, DCMPLX( ONE, ZERO ),
- $ C( IE+1, JS ), LDC )
- CALL ZGEMM( 'C', 'N', M-IE, NB, MB,
- $ DCMPLX( -ONE, ZERO ), D( IS, IE+1 ), LDD,
- $ F( IS, JS ), LDF, DCMPLX( ONE, ZERO ),
- $ C( IE+1, JS ), LDC )
- END IF
- 200 CONTINUE
- 210 CONTINUE
- END IF
-*
- WORK( 1 ) = LWMIN
-*
- RETURN
-*
-* End of ZTGSYL
-*
- END