1: SUBROUTINE ZTGSYL( TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D,
2: $ LDD, E, LDE, F, LDF, SCALE, DIF, WORK, LWORK,
3: $ IWORK, INFO )
4: *
5: * -- LAPACK routine (version 3.2) --
6: * -- LAPACK is a software package provided by Univ. of Tennessee, --
7: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
8: * January 2007
9: *
10: * .. Scalar Arguments ..
11: CHARACTER TRANS
12: INTEGER IJOB, INFO, LDA, LDB, LDC, LDD, LDE, LDF,
13: $ LWORK, M, N
14: DOUBLE PRECISION DIF, SCALE
15: * ..
16: * .. Array Arguments ..
17: INTEGER IWORK( * )
18: COMPLEX*16 A( LDA, * ), B( LDB, * ), C( LDC, * ),
19: $ D( LDD, * ), E( LDE, * ), F( LDF, * ),
20: $ WORK( * )
21: * ..
22: *
23: * Purpose
24: * =======
25: *
26: * ZTGSYL solves the generalized Sylvester equation:
27: *
28: * A * R - L * B = scale * C (1)
29: * D * R - L * E = scale * F
30: *
31: * where R and L are unknown m-by-n matrices, (A, D), (B, E) and
32: * (C, F) are given matrix pairs of size m-by-m, n-by-n and m-by-n,
33: * respectively, with complex entries. A, B, D and E are upper
34: * triangular (i.e., (A,D) and (B,E) in generalized Schur form).
35: *
36: * The solution (R, L) overwrites (C, F). 0 <= SCALE <= 1
37: * is an output scaling factor chosen to avoid overflow.
38: *
39: * In matrix notation (1) is equivalent to solve Zx = scale*b, where Z
40: * is defined as
41: *
42: * Z = [ kron(In, A) -kron(B', Im) ] (2)
43: * [ kron(In, D) -kron(E', Im) ],
44: *
45: * Here Ix is the identity matrix of size x and X' is the conjugate
46: * transpose of X. Kron(X, Y) is the Kronecker product between the
47: * matrices X and Y.
48: *
49: * If TRANS = 'C', y in the conjugate transposed system Z'*y = scale*b
50: * is solved for, which is equivalent to solve for R and L in
51: *
52: * A' * R + D' * L = scale * C (3)
53: * R * B' + L * E' = scale * -F
54: *
55: * This case (TRANS = 'C') is used to compute an one-norm-based estimate
56: * of Dif[(A,D), (B,E)], the separation between the matrix pairs (A,D)
57: * and (B,E), using ZLACON.
58: *
59: * If IJOB >= 1, ZTGSYL computes a Frobenius norm-based estimate of
60: * Dif[(A,D),(B,E)]. That is, the reciprocal of a lower bound on the
61: * reciprocal of the smallest singular value of Z.
62: *
63: * This is a level-3 BLAS algorithm.
64: *
65: * Arguments
66: * =========
67: *
68: * TRANS (input) CHARACTER*1
69: * = 'N': solve the generalized sylvester equation (1).
70: * = 'C': solve the "conjugate transposed" system (3).
71: *
72: * IJOB (input) INTEGER
73: * Specifies what kind of functionality to be performed.
74: * =0: solve (1) only.
75: * =1: The functionality of 0 and 3.
76: * =2: The functionality of 0 and 4.
77: * =3: Only an estimate of Dif[(A,D), (B,E)] is computed.
78: * (look ahead strategy is used).
79: * =4: Only an estimate of Dif[(A,D), (B,E)] is computed.
80: * (ZGECON on sub-systems is used).
81: * Not referenced if TRANS = 'C'.
82: *
83: * M (input) INTEGER
84: * The order of the matrices A and D, and the row dimension of
85: * the matrices C, F, R and L.
86: *
87: * N (input) INTEGER
88: * The order of the matrices B and E, and the column dimension
89: * of the matrices C, F, R and L.
90: *
91: * A (input) COMPLEX*16 array, dimension (LDA, M)
92: * The upper triangular matrix A.
93: *
94: * LDA (input) INTEGER
95: * The leading dimension of the array A. LDA >= max(1, M).
96: *
97: * B (input) COMPLEX*16 array, dimension (LDB, N)
98: * The upper triangular matrix B.
99: *
100: * LDB (input) INTEGER
101: * The leading dimension of the array B. LDB >= max(1, N).
102: *
103: * C (input/output) COMPLEX*16 array, dimension (LDC, N)
104: * On entry, C contains the right-hand-side of the first matrix
105: * equation in (1) or (3).
106: * On exit, if IJOB = 0, 1 or 2, C has been overwritten by
107: * the solution R. If IJOB = 3 or 4 and TRANS = 'N', C holds R,
108: * the solution achieved during the computation of the
109: * Dif-estimate.
110: *
111: * LDC (input) INTEGER
112: * The leading dimension of the array C. LDC >= max(1, M).
113: *
114: * D (input) COMPLEX*16 array, dimension (LDD, M)
115: * The upper triangular matrix D.
116: *
117: * LDD (input) INTEGER
118: * The leading dimension of the array D. LDD >= max(1, M).
119: *
120: * E (input) COMPLEX*16 array, dimension (LDE, N)
121: * The upper triangular matrix E.
122: *
123: * LDE (input) INTEGER
124: * The leading dimension of the array E. LDE >= max(1, N).
125: *
126: * F (input/output) COMPLEX*16 array, dimension (LDF, N)
127: * On entry, F contains the right-hand-side of the second matrix
128: * equation in (1) or (3).
129: * On exit, if IJOB = 0, 1 or 2, F has been overwritten by
130: * the solution L. If IJOB = 3 or 4 and TRANS = 'N', F holds L,
131: * the solution achieved during the computation of the
132: * Dif-estimate.
133: *
134: * LDF (input) INTEGER
135: * The leading dimension of the array F. LDF >= max(1, M).
136: *
137: * DIF (output) DOUBLE PRECISION
138: * On exit DIF is the reciprocal of a lower bound of the
139: * reciprocal of the Dif-function, i.e. DIF is an upper bound of
140: * Dif[(A,D), (B,E)] = sigma-min(Z), where Z as in (2).
141: * IF IJOB = 0 or TRANS = 'C', DIF is not referenced.
142: *
143: * SCALE (output) DOUBLE PRECISION
144: * On exit SCALE is the scaling factor in (1) or (3).
145: * If 0 < SCALE < 1, C and F hold the solutions R and L, resp.,
146: * to a slightly perturbed system but the input matrices A, B,
147: * D and E have not been changed. If SCALE = 0, R and L will
148: * hold the solutions to the homogenious system with C = F = 0.
149: *
150: * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
151: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
152: *
153: * LWORK (input) INTEGER
154: * The dimension of the array WORK. LWORK > = 1.
155: * If IJOB = 1 or 2 and TRANS = 'N', LWORK >= max(1,2*M*N).
156: *
157: * If LWORK = -1, then a workspace query is assumed; the routine
158: * only calculates the optimal size of the WORK array, returns
159: * this value as the first entry of the WORK array, and no error
160: * message related to LWORK is issued by XERBLA.
161: *
162: * IWORK (workspace) INTEGER array, dimension (M+N+2)
163: *
164: * INFO (output) INTEGER
165: * =0: successful exit
166: * <0: If INFO = -i, the i-th argument had an illegal value.
167: * >0: (A, D) and (B, E) have common or very close
168: * eigenvalues.
169: *
170: * Further Details
171: * ===============
172: *
173: * Based on contributions by
174: * Bo Kagstrom and Peter Poromaa, Department of Computing Science,
175: * Umea University, S-901 87 Umea, Sweden.
176: *
177: * [1] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software
178: * for Solving the Generalized Sylvester Equation and Estimating the
179: * Separation between Regular Matrix Pairs, Report UMINF - 93.23,
180: * Department of Computing Science, Umea University, S-901 87 Umea,
181: * Sweden, December 1993, Revised April 1994, Also as LAPACK Working
182: * Note 75. To appear in ACM Trans. on Math. Software, Vol 22,
183: * No 1, 1996.
184: *
185: * [2] B. Kagstrom, A Perturbation Analysis of the Generalized Sylvester
186: * Equation (AR - LB, DR - LE ) = (C, F), SIAM J. Matrix Anal.
187: * Appl., 15(4):1045-1060, 1994.
188: *
189: * [3] B. Kagstrom and L. Westin, Generalized Schur Methods with
190: * Condition Estimators for Solving the Generalized Sylvester
191: * Equation, IEEE Transactions on Automatic Control, Vol. 34, No. 7,
192: * July 1989, pp 745-751.
193: *
194: * =====================================================================
195: * Replaced various illegal calls to CCOPY by calls to CLASET.
196: * Sven Hammarling, 1/5/02.
197: *
198: * .. Parameters ..
199: DOUBLE PRECISION ZERO, ONE
200: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
201: COMPLEX*16 CZERO
202: PARAMETER ( CZERO = (0.0D+0, 0.0D+0) )
203: * ..
204: * .. Local Scalars ..
205: LOGICAL LQUERY, NOTRAN
206: INTEGER I, IE, IFUNC, IROUND, IS, ISOLVE, J, JE, JS, K,
207: $ LINFO, LWMIN, MB, NB, P, PQ, Q
208: DOUBLE PRECISION DSCALE, DSUM, SCALE2, SCALOC
209: * ..
210: * .. External Functions ..
211: LOGICAL LSAME
212: INTEGER ILAENV
213: EXTERNAL LSAME, ILAENV
214: * ..
215: * .. External Subroutines ..
216: EXTERNAL XERBLA, ZGEMM, ZLACPY, ZLASET, ZSCAL, ZTGSY2
217: * ..
218: * .. Intrinsic Functions ..
219: INTRINSIC DBLE, DCMPLX, MAX, SQRT
220: * ..
221: * .. Executable Statements ..
222: *
223: * Decode and test input parameters
224: *
225: INFO = 0
226: NOTRAN = LSAME( TRANS, 'N' )
227: LQUERY = ( LWORK.EQ.-1 )
228: *
229: IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN
230: INFO = -1
231: ELSE IF( NOTRAN ) THEN
232: IF( ( IJOB.LT.0 ) .OR. ( IJOB.GT.4 ) ) THEN
233: INFO = -2
234: END IF
235: END IF
236: IF( INFO.EQ.0 ) THEN
237: IF( M.LE.0 ) THEN
238: INFO = -3
239: ELSE IF( N.LE.0 ) THEN
240: INFO = -4
241: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
242: INFO = -6
243: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
244: INFO = -8
245: ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
246: INFO = -10
247: ELSE IF( LDD.LT.MAX( 1, M ) ) THEN
248: INFO = -12
249: ELSE IF( LDE.LT.MAX( 1, N ) ) THEN
250: INFO = -14
251: ELSE IF( LDF.LT.MAX( 1, M ) ) THEN
252: INFO = -16
253: END IF
254: END IF
255: *
256: IF( INFO.EQ.0 ) THEN
257: IF( NOTRAN ) THEN
258: IF( IJOB.EQ.1 .OR. IJOB.EQ.2 ) THEN
259: LWMIN = MAX( 1, 2*M*N )
260: ELSE
261: LWMIN = 1
262: END IF
263: ELSE
264: LWMIN = 1
265: END IF
266: WORK( 1 ) = LWMIN
267: *
268: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
269: INFO = -20
270: END IF
271: END IF
272: *
273: IF( INFO.NE.0 ) THEN
274: CALL XERBLA( 'ZTGSYL', -INFO )
275: RETURN
276: ELSE IF( LQUERY ) THEN
277: RETURN
278: END IF
279: *
280: * Quick return if possible
281: *
282: IF( M.EQ.0 .OR. N.EQ.0 ) THEN
283: SCALE = 1
284: IF( NOTRAN ) THEN
285: IF( IJOB.NE.0 ) THEN
286: DIF = 0
287: END IF
288: END IF
289: RETURN
290: END IF
291: *
292: * Determine optimal block sizes MB and NB
293: *
294: MB = ILAENV( 2, 'ZTGSYL', TRANS, M, N, -1, -1 )
295: NB = ILAENV( 5, 'ZTGSYL', TRANS, M, N, -1, -1 )
296: *
297: ISOLVE = 1
298: IFUNC = 0
299: IF( NOTRAN ) THEN
300: IF( IJOB.GE.3 ) THEN
301: IFUNC = IJOB - 2
302: CALL ZLASET( 'F', M, N, CZERO, CZERO, C, LDC )
303: CALL ZLASET( 'F', M, N, CZERO, CZERO, F, LDF )
304: ELSE IF( IJOB.GE.1 .AND. NOTRAN ) THEN
305: ISOLVE = 2
306: END IF
307: END IF
308: *
309: IF( ( MB.LE.1 .AND. NB.LE.1 ) .OR. ( MB.GE.M .AND. NB.GE.N ) )
310: $ THEN
311: *
312: * Use unblocked Level 2 solver
313: *
314: DO 30 IROUND = 1, ISOLVE
315: *
316: SCALE = ONE
317: DSCALE = ZERO
318: DSUM = ONE
319: PQ = M*N
320: CALL ZTGSY2( TRANS, IFUNC, M, N, A, LDA, B, LDB, C, LDC, D,
321: $ LDD, E, LDE, F, LDF, SCALE, DSUM, DSCALE,
322: $ INFO )
323: IF( DSCALE.NE.ZERO ) THEN
324: IF( IJOB.EQ.1 .OR. IJOB.EQ.3 ) THEN
325: DIF = SQRT( DBLE( 2*M*N ) ) / ( DSCALE*SQRT( DSUM ) )
326: ELSE
327: DIF = SQRT( DBLE( PQ ) ) / ( DSCALE*SQRT( DSUM ) )
328: END IF
329: END IF
330: IF( ISOLVE.EQ.2 .AND. IROUND.EQ.1 ) THEN
331: IF( NOTRAN ) THEN
332: IFUNC = IJOB
333: END IF
334: SCALE2 = SCALE
335: CALL ZLACPY( 'F', M, N, C, LDC, WORK, M )
336: CALL ZLACPY( 'F', M, N, F, LDF, WORK( M*N+1 ), M )
337: CALL ZLASET( 'F', M, N, CZERO, CZERO, C, LDC )
338: CALL ZLASET( 'F', M, N, CZERO, CZERO, F, LDF )
339: ELSE IF( ISOLVE.EQ.2 .AND. IROUND.EQ.2 ) THEN
340: CALL ZLACPY( 'F', M, N, WORK, M, C, LDC )
341: CALL ZLACPY( 'F', M, N, WORK( M*N+1 ), M, F, LDF )
342: SCALE = SCALE2
343: END IF
344: 30 CONTINUE
345: *
346: RETURN
347: *
348: END IF
349: *
350: * Determine block structure of A
351: *
352: P = 0
353: I = 1
354: 40 CONTINUE
355: IF( I.GT.M )
356: $ GO TO 50
357: P = P + 1
358: IWORK( P ) = I
359: I = I + MB
360: IF( I.GE.M )
361: $ GO TO 50
362: GO TO 40
363: 50 CONTINUE
364: IWORK( P+1 ) = M + 1
365: IF( IWORK( P ).EQ.IWORK( P+1 ) )
366: $ P = P - 1
367: *
368: * Determine block structure of B
369: *
370: Q = P + 1
371: J = 1
372: 60 CONTINUE
373: IF( J.GT.N )
374: $ GO TO 70
375: *
376: Q = Q + 1
377: IWORK( Q ) = J
378: J = J + NB
379: IF( J.GE.N )
380: $ GO TO 70
381: GO TO 60
382: *
383: 70 CONTINUE
384: IWORK( Q+1 ) = N + 1
385: IF( IWORK( Q ).EQ.IWORK( Q+1 ) )
386: $ Q = Q - 1
387: *
388: IF( NOTRAN ) THEN
389: DO 150 IROUND = 1, ISOLVE
390: *
391: * Solve (I, J) - subsystem
392: * A(I, I) * R(I, J) - L(I, J) * B(J, J) = C(I, J)
393: * D(I, I) * R(I, J) - L(I, J) * E(J, J) = F(I, J)
394: * for I = P, P - 1, ..., 1; J = 1, 2, ..., Q
395: *
396: PQ = 0
397: SCALE = ONE
398: DSCALE = ZERO
399: DSUM = ONE
400: DO 130 J = P + 2, Q
401: JS = IWORK( J )
402: JE = IWORK( J+1 ) - 1
403: NB = JE - JS + 1
404: DO 120 I = P, 1, -1
405: IS = IWORK( I )
406: IE = IWORK( I+1 ) - 1
407: MB = IE - IS + 1
408: CALL ZTGSY2( TRANS, IFUNC, MB, NB, A( IS, IS ), LDA,
409: $ B( JS, JS ), LDB, C( IS, JS ), LDC,
410: $ D( IS, IS ), LDD, E( JS, JS ), LDE,
411: $ F( IS, JS ), LDF, SCALOC, DSUM, DSCALE,
412: $ LINFO )
413: IF( LINFO.GT.0 )
414: $ INFO = LINFO
415: PQ = PQ + MB*NB
416: IF( SCALOC.NE.ONE ) THEN
417: DO 80 K = 1, JS - 1
418: CALL ZSCAL( M, DCMPLX( SCALOC, ZERO ),
419: $ C( 1, K ), 1 )
420: CALL ZSCAL( M, DCMPLX( SCALOC, ZERO ),
421: $ F( 1, K ), 1 )
422: 80 CONTINUE
423: DO 90 K = JS, JE
424: CALL ZSCAL( IS-1, DCMPLX( SCALOC, ZERO ),
425: $ C( 1, K ), 1 )
426: CALL ZSCAL( IS-1, DCMPLX( SCALOC, ZERO ),
427: $ F( 1, K ), 1 )
428: 90 CONTINUE
429: DO 100 K = JS, JE
430: CALL ZSCAL( M-IE, DCMPLX( SCALOC, ZERO ),
431: $ C( IE+1, K ), 1 )
432: CALL ZSCAL( M-IE, DCMPLX( SCALOC, ZERO ),
433: $ F( IE+1, K ), 1 )
434: 100 CONTINUE
435: DO 110 K = JE + 1, N
436: CALL ZSCAL( M, DCMPLX( SCALOC, ZERO ),
437: $ C( 1, K ), 1 )
438: CALL ZSCAL( M, DCMPLX( SCALOC, ZERO ),
439: $ F( 1, K ), 1 )
440: 110 CONTINUE
441: SCALE = SCALE*SCALOC
442: END IF
443: *
444: * Substitute R(I,J) and L(I,J) into remaining equation.
445: *
446: IF( I.GT.1 ) THEN
447: CALL ZGEMM( 'N', 'N', IS-1, NB, MB,
448: $ DCMPLX( -ONE, ZERO ), A( 1, IS ), LDA,
449: $ C( IS, JS ), LDC, DCMPLX( ONE, ZERO ),
450: $ C( 1, JS ), LDC )
451: CALL ZGEMM( 'N', 'N', IS-1, NB, MB,
452: $ DCMPLX( -ONE, ZERO ), D( 1, IS ), LDD,
453: $ C( IS, JS ), LDC, DCMPLX( ONE, ZERO ),
454: $ F( 1, JS ), LDF )
455: END IF
456: IF( J.LT.Q ) THEN
457: CALL ZGEMM( 'N', 'N', MB, N-JE, NB,
458: $ DCMPLX( ONE, ZERO ), F( IS, JS ), LDF,
459: $ B( JS, JE+1 ), LDB,
460: $ DCMPLX( ONE, ZERO ), C( IS, JE+1 ),
461: $ LDC )
462: CALL ZGEMM( 'N', 'N', MB, N-JE, NB,
463: $ DCMPLX( ONE, ZERO ), F( IS, JS ), LDF,
464: $ E( JS, JE+1 ), LDE,
465: $ DCMPLX( ONE, ZERO ), F( IS, JE+1 ),
466: $ LDF )
467: END IF
468: 120 CONTINUE
469: 130 CONTINUE
470: IF( DSCALE.NE.ZERO ) THEN
471: IF( IJOB.EQ.1 .OR. IJOB.EQ.3 ) THEN
472: DIF = SQRT( DBLE( 2*M*N ) ) / ( DSCALE*SQRT( DSUM ) )
473: ELSE
474: DIF = SQRT( DBLE( PQ ) ) / ( DSCALE*SQRT( DSUM ) )
475: END IF
476: END IF
477: IF( ISOLVE.EQ.2 .AND. IROUND.EQ.1 ) THEN
478: IF( NOTRAN ) THEN
479: IFUNC = IJOB
480: END IF
481: SCALE2 = SCALE
482: CALL ZLACPY( 'F', M, N, C, LDC, WORK, M )
483: CALL ZLACPY( 'F', M, N, F, LDF, WORK( M*N+1 ), M )
484: CALL ZLASET( 'F', M, N, CZERO, CZERO, C, LDC )
485: CALL ZLASET( 'F', M, N, CZERO, CZERO, F, LDF )
486: ELSE IF( ISOLVE.EQ.2 .AND. IROUND.EQ.2 ) THEN
487: CALL ZLACPY( 'F', M, N, WORK, M, C, LDC )
488: CALL ZLACPY( 'F', M, N, WORK( M*N+1 ), M, F, LDF )
489: SCALE = SCALE2
490: END IF
491: 150 CONTINUE
492: ELSE
493: *
494: * Solve transposed (I, J)-subsystem
495: * A(I, I)' * R(I, J) + D(I, I)' * L(I, J) = C(I, J)
496: * R(I, J) * B(J, J) + L(I, J) * E(J, J) = -F(I, J)
497: * for I = 1,2,..., P; J = Q, Q-1,..., 1
498: *
499: SCALE = ONE
500: DO 210 I = 1, P
501: IS = IWORK( I )
502: IE = IWORK( I+1 ) - 1
503: MB = IE - IS + 1
504: DO 200 J = Q, P + 2, -1
505: JS = IWORK( J )
506: JE = IWORK( J+1 ) - 1
507: NB = JE - JS + 1
508: CALL ZTGSY2( TRANS, IFUNC, MB, NB, A( IS, IS ), LDA,
509: $ B( JS, JS ), LDB, C( IS, JS ), LDC,
510: $ D( IS, IS ), LDD, E( JS, JS ), LDE,
511: $ F( IS, JS ), LDF, SCALOC, DSUM, DSCALE,
512: $ LINFO )
513: IF( LINFO.GT.0 )
514: $ INFO = LINFO
515: IF( SCALOC.NE.ONE ) THEN
516: DO 160 K = 1, JS - 1
517: CALL ZSCAL( M, DCMPLX( SCALOC, ZERO ), C( 1, K ),
518: $ 1 )
519: CALL ZSCAL( M, DCMPLX( SCALOC, ZERO ), F( 1, K ),
520: $ 1 )
521: 160 CONTINUE
522: DO 170 K = JS, JE
523: CALL ZSCAL( IS-1, DCMPLX( SCALOC, ZERO ),
524: $ C( 1, K ), 1 )
525: CALL ZSCAL( IS-1, DCMPLX( SCALOC, ZERO ),
526: $ F( 1, K ), 1 )
527: 170 CONTINUE
528: DO 180 K = JS, JE
529: CALL ZSCAL( M-IE, DCMPLX( SCALOC, ZERO ),
530: $ C( IE+1, K ), 1 )
531: CALL ZSCAL( M-IE, DCMPLX( SCALOC, ZERO ),
532: $ F( IE+1, K ), 1 )
533: 180 CONTINUE
534: DO 190 K = JE + 1, N
535: CALL ZSCAL( M, DCMPLX( SCALOC, ZERO ), C( 1, K ),
536: $ 1 )
537: CALL ZSCAL( M, DCMPLX( SCALOC, ZERO ), F( 1, K ),
538: $ 1 )
539: 190 CONTINUE
540: SCALE = SCALE*SCALOC
541: END IF
542: *
543: * Substitute R(I,J) and L(I,J) into remaining equation.
544: *
545: IF( J.GT.P+2 ) THEN
546: CALL ZGEMM( 'N', 'C', MB, JS-1, NB,
547: $ DCMPLX( ONE, ZERO ), C( IS, JS ), LDC,
548: $ B( 1, JS ), LDB, DCMPLX( ONE, ZERO ),
549: $ F( IS, 1 ), LDF )
550: CALL ZGEMM( 'N', 'C', MB, JS-1, NB,
551: $ DCMPLX( ONE, ZERO ), F( IS, JS ), LDF,
552: $ E( 1, JS ), LDE, DCMPLX( ONE, ZERO ),
553: $ F( IS, 1 ), LDF )
554: END IF
555: IF( I.LT.P ) THEN
556: CALL ZGEMM( 'C', 'N', M-IE, NB, MB,
557: $ DCMPLX( -ONE, ZERO ), A( IS, IE+1 ), LDA,
558: $ C( IS, JS ), LDC, DCMPLX( ONE, ZERO ),
559: $ C( IE+1, JS ), LDC )
560: CALL ZGEMM( 'C', 'N', M-IE, NB, MB,
561: $ DCMPLX( -ONE, ZERO ), D( IS, IE+1 ), LDD,
562: $ F( IS, JS ), LDF, DCMPLX( ONE, ZERO ),
563: $ C( IE+1, JS ), LDC )
564: END IF
565: 200 CONTINUE
566: 210 CONTINUE
567: END IF
568: *
569: WORK( 1 ) = LWMIN
570: *
571: RETURN
572: *
573: * End of ZTGSYL
574: *
575: END
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