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author | jofret | 2009-04-28 07:17:00 +0000 |
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committer | jofret | 2009-04-28 07:17:00 +0000 |
commit | 8c8d2f518968ce7057eec6aa5cd5aec8faab861a (patch) | |
tree | 3dd1788b71d6a3ce2b73d2d475a3133580e17530 /src/lib/lapack/ztgsyl.f | |
parent | 9f652ffc16a310ac6641a9766c5b9e2671e0e9cb (diff) | |
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Moving lapack to right place
Diffstat (limited to 'src/lib/lapack/ztgsyl.f')
-rw-r--r-- | src/lib/lapack/ztgsyl.f | 575 |
1 files changed, 0 insertions, 575 deletions
diff --git a/src/lib/lapack/ztgsyl.f b/src/lib/lapack/ztgsyl.f deleted file mode 100644 index af808a31..00000000 --- a/src/lib/lapack/ztgsyl.f +++ /dev/null @@ -1,575 +0,0 @@ - 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 |