1: *> \brief \b ZLASYF
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
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7: *
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17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZLASYF( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO )
22: *
23: * .. Scalar Arguments ..
24: * CHARACTER UPLO
25: * INTEGER INFO, KB, LDA, LDW, N, NB
26: * ..
27: * .. Array Arguments ..
28: * INTEGER IPIV( * )
29: * COMPLEX*16 A( LDA, * ), W( LDW, * )
30: * ..
31: *
32: *
33: *> \par Purpose:
34: * =============
35: *>
36: *> \verbatim
37: *>
38: *> ZLASYF computes a partial factorization of a complex symmetric matrix
39: *> A using the Bunch-Kaufman diagonal pivoting method. The partial
40: *> factorization has the form:
41: *>
42: *> A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = 'U', or:
43: *> ( 0 U22 ) ( 0 D ) ( U12**T U22**T )
44: *>
45: *> A = ( L11 0 ) ( D 0 ) ( L11**T L21**T ) if UPLO = 'L'
46: *> ( L21 I ) ( 0 A22 ) ( 0 I )
47: *>
48: *> where the order of D is at most NB. The actual order is returned in
49: *> the argument KB, and is either NB or NB-1, or N if N <= NB.
50: *> Note that U**T denotes the transpose of U.
51: *>
52: *> ZLASYF is an auxiliary routine called by ZSYTRF. It uses blocked code
53: *> (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or
54: *> A22 (if UPLO = 'L').
55: *> \endverbatim
56: *
57: * Arguments:
58: * ==========
59: *
60: *> \param[in] UPLO
61: *> \verbatim
62: *> UPLO is CHARACTER*1
63: *> Specifies whether the upper or lower triangular part of the
64: *> symmetric matrix A is stored:
65: *> = 'U': Upper triangular
66: *> = 'L': Lower triangular
67: *> \endverbatim
68: *>
69: *> \param[in] N
70: *> \verbatim
71: *> N is INTEGER
72: *> The order of the matrix A. N >= 0.
73: *> \endverbatim
74: *>
75: *> \param[in] NB
76: *> \verbatim
77: *> NB is INTEGER
78: *> The maximum number of columns of the matrix A that should be
79: *> factored. NB should be at least 2 to allow for 2-by-2 pivot
80: *> blocks.
81: *> \endverbatim
82: *>
83: *> \param[out] KB
84: *> \verbatim
85: *> KB is INTEGER
86: *> The number of columns of A that were actually factored.
87: *> KB is either NB-1 or NB, or N if N <= NB.
88: *> \endverbatim
89: *>
90: *> \param[in,out] A
91: *> \verbatim
92: *> A is COMPLEX*16 array, dimension (LDA,N)
93: *> On entry, the symmetric matrix A. If UPLO = 'U', the leading
94: *> n-by-n upper triangular part of A contains the upper
95: *> triangular part of the matrix A, and the strictly lower
96: *> triangular part of A is not referenced. If UPLO = 'L', the
97: *> leading n-by-n lower triangular part of A contains the lower
98: *> triangular part of the matrix A, and the strictly upper
99: *> triangular part of A is not referenced.
100: *> On exit, A contains details of the partial factorization.
101: *> \endverbatim
102: *>
103: *> \param[in] LDA
104: *> \verbatim
105: *> LDA is INTEGER
106: *> The leading dimension of the array A. LDA >= max(1,N).
107: *> \endverbatim
108: *>
109: *> \param[out] IPIV
110: *> \verbatim
111: *> IPIV is INTEGER array, dimension (N)
112: *> Details of the interchanges and the block structure of D.
113: *> If UPLO = 'U', only the last KB elements of IPIV are set;
114: *> if UPLO = 'L', only the first KB elements are set.
115: *>
116: *> If IPIV(k) > 0, then rows and columns k and IPIV(k) were
117: *> interchanged and D(k,k) is a 1-by-1 diagonal block.
118: *> If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and
119: *> columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
120: *> is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) =
121: *> IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were
122: *> interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
123: *> \endverbatim
124: *>
125: *> \param[out] W
126: *> \verbatim
127: *> W is COMPLEX*16 array, dimension (LDW,NB)
128: *> \endverbatim
129: *>
130: *> \param[in] LDW
131: *> \verbatim
132: *> LDW is INTEGER
133: *> The leading dimension of the array W. LDW >= max(1,N).
134: *> \endverbatim
135: *>
136: *> \param[out] INFO
137: *> \verbatim
138: *> INFO is INTEGER
139: *> = 0: successful exit
140: *> > 0: if INFO = k, D(k,k) is exactly zero. The factorization
141: *> has been completed, but the block diagonal matrix D is
142: *> exactly singular.
143: *> \endverbatim
144: *
145: * Authors:
146: * ========
147: *
148: *> \author Univ. of Tennessee
149: *> \author Univ. of California Berkeley
150: *> \author Univ. of Colorado Denver
151: *> \author NAG Ltd.
152: *
153: *> \date November 2011
154: *
155: *> \ingroup complex16SYcomputational
156: *
157: * =====================================================================
158: SUBROUTINE ZLASYF( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO )
159: *
160: * -- LAPACK computational routine (version 3.4.0) --
161: * -- LAPACK is a software package provided by Univ. of Tennessee, --
162: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
163: * November 2011
164: *
165: * .. Scalar Arguments ..
166: CHARACTER UPLO
167: INTEGER INFO, KB, LDA, LDW, N, NB
168: * ..
169: * .. Array Arguments ..
170: INTEGER IPIV( * )
171: COMPLEX*16 A( LDA, * ), W( LDW, * )
172: * ..
173: *
174: * =====================================================================
175: *
176: * .. Parameters ..
177: DOUBLE PRECISION ZERO, ONE
178: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
179: DOUBLE PRECISION EIGHT, SEVTEN
180: PARAMETER ( EIGHT = 8.0D+0, SEVTEN = 17.0D+0 )
181: COMPLEX*16 CONE
182: PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) )
183: * ..
184: * .. Local Scalars ..
185: INTEGER IMAX, J, JB, JJ, JMAX, JP, K, KK, KKW, KP,
186: $ KSTEP, KW
187: DOUBLE PRECISION ABSAKK, ALPHA, COLMAX, ROWMAX
188: COMPLEX*16 D11, D21, D22, R1, T, Z
189: * ..
190: * .. External Functions ..
191: LOGICAL LSAME
192: INTEGER IZAMAX
193: EXTERNAL LSAME, IZAMAX
194: * ..
195: * .. External Subroutines ..
196: EXTERNAL ZCOPY, ZGEMM, ZGEMV, ZSCAL, ZSWAP
197: * ..
198: * .. Intrinsic Functions ..
199: INTRINSIC ABS, DBLE, DIMAG, MAX, MIN, SQRT
200: * ..
201: * .. Statement Functions ..
202: DOUBLE PRECISION CABS1
203: * ..
204: * .. Statement Function definitions ..
205: CABS1( Z ) = ABS( DBLE( Z ) ) + ABS( DIMAG( Z ) )
206: * ..
207: * .. Executable Statements ..
208: *
209: INFO = 0
210: *
211: * Initialize ALPHA for use in choosing pivot block size.
212: *
213: ALPHA = ( ONE+SQRT( SEVTEN ) ) / EIGHT
214: *
215: IF( LSAME( UPLO, 'U' ) ) THEN
216: *
217: * Factorize the trailing columns of A using the upper triangle
218: * of A and working backwards, and compute the matrix W = U12*D
219: * for use in updating A11
220: *
221: * K is the main loop index, decreasing from N in steps of 1 or 2
222: *
223: * KW is the column of W which corresponds to column K of A
224: *
225: K = N
226: 10 CONTINUE
227: KW = NB + K - N
228: *
229: * Exit from loop
230: *
231: IF( ( K.LE.N-NB+1 .AND. NB.LT.N ) .OR. K.LT.1 )
232: $ GO TO 30
233: *
234: * Copy column K of A to column KW of W and update it
235: *
236: CALL ZCOPY( K, A( 1, K ), 1, W( 1, KW ), 1 )
237: IF( K.LT.N )
238: $ CALL ZGEMV( 'No transpose', K, N-K, -CONE, A( 1, K+1 ), LDA,
239: $ W( K, KW+1 ), LDW, CONE, W( 1, KW ), 1 )
240: *
241: KSTEP = 1
242: *
243: * Determine rows and columns to be interchanged and whether
244: * a 1-by-1 or 2-by-2 pivot block will be used
245: *
246: ABSAKK = CABS1( W( K, KW ) )
247: *
248: * IMAX is the row-index of the largest off-diagonal element in
249: * column K, and COLMAX is its absolute value
250: *
251: IF( K.GT.1 ) THEN
252: IMAX = IZAMAX( K-1, W( 1, KW ), 1 )
253: COLMAX = CABS1( W( IMAX, KW ) )
254: ELSE
255: COLMAX = ZERO
256: END IF
257: *
258: IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
259: *
260: * Column K is zero: set INFO and continue
261: *
262: IF( INFO.EQ.0 )
263: $ INFO = K
264: KP = K
265: ELSE
266: IF( ABSAKK.GE.ALPHA*COLMAX ) THEN
267: *
268: * no interchange, use 1-by-1 pivot block
269: *
270: KP = K
271: ELSE
272: *
273: * Copy column IMAX to column KW-1 of W and update it
274: *
275: CALL ZCOPY( IMAX, A( 1, IMAX ), 1, W( 1, KW-1 ), 1 )
276: CALL ZCOPY( K-IMAX, A( IMAX, IMAX+1 ), LDA,
277: $ W( IMAX+1, KW-1 ), 1 )
278: IF( K.LT.N )
279: $ CALL ZGEMV( 'No transpose', K, N-K, -CONE,
280: $ A( 1, K+1 ), LDA, W( IMAX, KW+1 ), LDW,
281: $ CONE, W( 1, KW-1 ), 1 )
282: *
283: * JMAX is the column-index of the largest off-diagonal
284: * element in row IMAX, and ROWMAX is its absolute value
285: *
286: JMAX = IMAX + IZAMAX( K-IMAX, W( IMAX+1, KW-1 ), 1 )
287: ROWMAX = CABS1( W( JMAX, KW-1 ) )
288: IF( IMAX.GT.1 ) THEN
289: JMAX = IZAMAX( IMAX-1, W( 1, KW-1 ), 1 )
290: ROWMAX = MAX( ROWMAX, CABS1( W( JMAX, KW-1 ) ) )
291: END IF
292: *
293: IF( ABSAKK.GE.ALPHA*COLMAX*( COLMAX / ROWMAX ) ) THEN
294: *
295: * no interchange, use 1-by-1 pivot block
296: *
297: KP = K
298: ELSE IF( CABS1( W( IMAX, KW-1 ) ).GE.ALPHA*ROWMAX ) THEN
299: *
300: * interchange rows and columns K and IMAX, use 1-by-1
301: * pivot block
302: *
303: KP = IMAX
304: *
305: * copy column KW-1 of W to column KW
306: *
307: CALL ZCOPY( K, W( 1, KW-1 ), 1, W( 1, KW ), 1 )
308: ELSE
309: *
310: * interchange rows and columns K-1 and IMAX, use 2-by-2
311: * pivot block
312: *
313: KP = IMAX
314: KSTEP = 2
315: END IF
316: END IF
317: *
318: KK = K - KSTEP + 1
319: KKW = NB + KK - N
320: *
321: * Updated column KP is already stored in column KKW of W
322: *
323: IF( KP.NE.KK ) THEN
324: *
325: * Copy non-updated column KK to column KP
326: *
327: A( KP, K ) = A( KK, K )
328: CALL ZCOPY( K-1-KP, A( KP+1, KK ), 1, A( KP, KP+1 ),
329: $ LDA )
330: CALL ZCOPY( KP, A( 1, KK ), 1, A( 1, KP ), 1 )
331: *
332: * Interchange rows KK and KP in last KK columns of A and W
333: *
334: CALL ZSWAP( N-KK+1, A( KK, KK ), LDA, A( KP, KK ), LDA )
335: CALL ZSWAP( N-KK+1, W( KK, KKW ), LDW, W( KP, KKW ),
336: $ LDW )
337: END IF
338: *
339: IF( KSTEP.EQ.1 ) THEN
340: *
341: * 1-by-1 pivot block D(k): column KW of W now holds
342: *
343: * W(k) = U(k)*D(k)
344: *
345: * where U(k) is the k-th column of U
346: *
347: * Store U(k) in column k of A
348: *
349: CALL ZCOPY( K, W( 1, KW ), 1, A( 1, K ), 1 )
350: R1 = CONE / A( K, K )
351: CALL ZSCAL( K-1, R1, A( 1, K ), 1 )
352: ELSE
353: *
354: * 2-by-2 pivot block D(k): columns KW and KW-1 of W now
355: * hold
356: *
357: * ( W(k-1) W(k) ) = ( U(k-1) U(k) )*D(k)
358: *
359: * where U(k) and U(k-1) are the k-th and (k-1)-th columns
360: * of U
361: *
362: IF( K.GT.2 ) THEN
363: *
364: * Store U(k) and U(k-1) in columns k and k-1 of A
365: *
366: D21 = W( K-1, KW )
367: D11 = W( K, KW ) / D21
368: D22 = W( K-1, KW-1 ) / D21
369: T = CONE / ( D11*D22-CONE )
370: D21 = T / D21
371: DO 20 J = 1, K - 2
372: A( J, K-1 ) = D21*( D11*W( J, KW-1 )-W( J, KW ) )
373: A( J, K ) = D21*( D22*W( J, KW )-W( J, KW-1 ) )
374: 20 CONTINUE
375: END IF
376: *
377: * Copy D(k) to A
378: *
379: A( K-1, K-1 ) = W( K-1, KW-1 )
380: A( K-1, K ) = W( K-1, KW )
381: A( K, K ) = W( K, KW )
382: END IF
383: END IF
384: *
385: * Store details of the interchanges in IPIV
386: *
387: IF( KSTEP.EQ.1 ) THEN
388: IPIV( K ) = KP
389: ELSE
390: IPIV( K ) = -KP
391: IPIV( K-1 ) = -KP
392: END IF
393: *
394: * Decrease K and return to the start of the main loop
395: *
396: K = K - KSTEP
397: GO TO 10
398: *
399: 30 CONTINUE
400: *
401: * Update the upper triangle of A11 (= A(1:k,1:k)) as
402: *
403: * A11 := A11 - U12*D*U12**T = A11 - U12*W**T
404: *
405: * computing blocks of NB columns at a time
406: *
407: DO 50 J = ( ( K-1 ) / NB )*NB + 1, 1, -NB
408: JB = MIN( NB, K-J+1 )
409: *
410: * Update the upper triangle of the diagonal block
411: *
412: DO 40 JJ = J, J + JB - 1
413: CALL ZGEMV( 'No transpose', JJ-J+1, N-K, -CONE,
414: $ A( J, K+1 ), LDA, W( JJ, KW+1 ), LDW, CONE,
415: $ A( J, JJ ), 1 )
416: 40 CONTINUE
417: *
418: * Update the rectangular superdiagonal block
419: *
420: CALL ZGEMM( 'No transpose', 'Transpose', J-1, JB, N-K,
421: $ -CONE, A( 1, K+1 ), LDA, W( J, KW+1 ), LDW,
422: $ CONE, A( 1, J ), LDA )
423: 50 CONTINUE
424: *
425: * Put U12 in standard form by partially undoing the interchanges
426: * in columns k+1:n
427: *
428: J = K + 1
429: 60 CONTINUE
430: JJ = J
431: JP = IPIV( J )
432: IF( JP.LT.0 ) THEN
433: JP = -JP
434: J = J + 1
435: END IF
436: J = J + 1
437: IF( JP.NE.JJ .AND. J.LE.N )
438: $ CALL ZSWAP( N-J+1, A( JP, J ), LDA, A( JJ, J ), LDA )
439: IF( J.LE.N )
440: $ GO TO 60
441: *
442: * Set KB to the number of columns factorized
443: *
444: KB = N - K
445: *
446: ELSE
447: *
448: * Factorize the leading columns of A using the lower triangle
449: * of A and working forwards, and compute the matrix W = L21*D
450: * for use in updating A22
451: *
452: * K is the main loop index, increasing from 1 in steps of 1 or 2
453: *
454: K = 1
455: 70 CONTINUE
456: *
457: * Exit from loop
458: *
459: IF( ( K.GE.NB .AND. NB.LT.N ) .OR. K.GT.N )
460: $ GO TO 90
461: *
462: * Copy column K of A to column K of W and update it
463: *
464: CALL ZCOPY( N-K+1, A( K, K ), 1, W( K, K ), 1 )
465: CALL ZGEMV( 'No transpose', N-K+1, K-1, -CONE, A( K, 1 ), LDA,
466: $ W( K, 1 ), LDW, CONE, W( K, K ), 1 )
467: *
468: KSTEP = 1
469: *
470: * Determine rows and columns to be interchanged and whether
471: * a 1-by-1 or 2-by-2 pivot block will be used
472: *
473: ABSAKK = CABS1( W( K, K ) )
474: *
475: * IMAX is the row-index of the largest off-diagonal element in
476: * column K, and COLMAX is its absolute value
477: *
478: IF( K.LT.N ) THEN
479: IMAX = K + IZAMAX( N-K, W( K+1, K ), 1 )
480: COLMAX = CABS1( W( IMAX, K ) )
481: ELSE
482: COLMAX = ZERO
483: END IF
484: *
485: IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
486: *
487: * Column K is zero: set INFO and continue
488: *
489: IF( INFO.EQ.0 )
490: $ INFO = K
491: KP = K
492: ELSE
493: IF( ABSAKK.GE.ALPHA*COLMAX ) THEN
494: *
495: * no interchange, use 1-by-1 pivot block
496: *
497: KP = K
498: ELSE
499: *
500: * Copy column IMAX to column K+1 of W and update it
501: *
502: CALL ZCOPY( IMAX-K, A( IMAX, K ), LDA, W( K, K+1 ), 1 )
503: CALL ZCOPY( N-IMAX+1, A( IMAX, IMAX ), 1, W( IMAX, K+1 ),
504: $ 1 )
505: CALL ZGEMV( 'No transpose', N-K+1, K-1, -CONE, A( K, 1 ),
506: $ LDA, W( IMAX, 1 ), LDW, CONE, W( K, K+1 ),
507: $ 1 )
508: *
509: * JMAX is the column-index of the largest off-diagonal
510: * element in row IMAX, and ROWMAX is its absolute value
511: *
512: JMAX = K - 1 + IZAMAX( IMAX-K, W( K, K+1 ), 1 )
513: ROWMAX = CABS1( W( JMAX, K+1 ) )
514: IF( IMAX.LT.N ) THEN
515: JMAX = IMAX + IZAMAX( N-IMAX, W( IMAX+1, K+1 ), 1 )
516: ROWMAX = MAX( ROWMAX, CABS1( W( JMAX, K+1 ) ) )
517: END IF
518: *
519: IF( ABSAKK.GE.ALPHA*COLMAX*( COLMAX / ROWMAX ) ) THEN
520: *
521: * no interchange, use 1-by-1 pivot block
522: *
523: KP = K
524: ELSE IF( CABS1( W( IMAX, K+1 ) ).GE.ALPHA*ROWMAX ) THEN
525: *
526: * interchange rows and columns K and IMAX, use 1-by-1
527: * pivot block
528: *
529: KP = IMAX
530: *
531: * copy column K+1 of W to column K
532: *
533: CALL ZCOPY( N-K+1, W( K, K+1 ), 1, W( K, K ), 1 )
534: ELSE
535: *
536: * interchange rows and columns K+1 and IMAX, use 2-by-2
537: * pivot block
538: *
539: KP = IMAX
540: KSTEP = 2
541: END IF
542: END IF
543: *
544: KK = K + KSTEP - 1
545: *
546: * Updated column KP is already stored in column KK of W
547: *
548: IF( KP.NE.KK ) THEN
549: *
550: * Copy non-updated column KK to column KP
551: *
552: A( KP, K ) = A( KK, K )
553: CALL ZCOPY( KP-K-1, A( K+1, KK ), 1, A( KP, K+1 ), LDA )
554: CALL ZCOPY( N-KP+1, A( KP, KK ), 1, A( KP, KP ), 1 )
555: *
556: * Interchange rows KK and KP in first KK columns of A and W
557: *
558: CALL ZSWAP( KK, A( KK, 1 ), LDA, A( KP, 1 ), LDA )
559: CALL ZSWAP( KK, W( KK, 1 ), LDW, W( KP, 1 ), LDW )
560: END IF
561: *
562: IF( KSTEP.EQ.1 ) THEN
563: *
564: * 1-by-1 pivot block D(k): column k of W now holds
565: *
566: * W(k) = L(k)*D(k)
567: *
568: * where L(k) is the k-th column of L
569: *
570: * Store L(k) in column k of A
571: *
572: CALL ZCOPY( N-K+1, W( K, K ), 1, A( K, K ), 1 )
573: IF( K.LT.N ) THEN
574: R1 = CONE / A( K, K )
575: CALL ZSCAL( N-K, R1, A( K+1, K ), 1 )
576: END IF
577: ELSE
578: *
579: * 2-by-2 pivot block D(k): columns k and k+1 of W now hold
580: *
581: * ( W(k) W(k+1) ) = ( L(k) L(k+1) )*D(k)
582: *
583: * where L(k) and L(k+1) are the k-th and (k+1)-th columns
584: * of L
585: *
586: IF( K.LT.N-1 ) THEN
587: *
588: * Store L(k) and L(k+1) in columns k and k+1 of A
589: *
590: D21 = W( K+1, K )
591: D11 = W( K+1, K+1 ) / D21
592: D22 = W( K, K ) / D21
593: T = CONE / ( D11*D22-CONE )
594: D21 = T / D21
595: DO 80 J = K + 2, N
596: A( J, K ) = D21*( D11*W( J, K )-W( J, K+1 ) )
597: A( J, K+1 ) = D21*( D22*W( J, K+1 )-W( J, K ) )
598: 80 CONTINUE
599: END IF
600: *
601: * Copy D(k) to A
602: *
603: A( K, K ) = W( K, K )
604: A( K+1, K ) = W( K+1, K )
605: A( K+1, K+1 ) = W( K+1, K+1 )
606: END IF
607: END IF
608: *
609: * Store details of the interchanges in IPIV
610: *
611: IF( KSTEP.EQ.1 ) THEN
612: IPIV( K ) = KP
613: ELSE
614: IPIV( K ) = -KP
615: IPIV( K+1 ) = -KP
616: END IF
617: *
618: * Increase K and return to the start of the main loop
619: *
620: K = K + KSTEP
621: GO TO 70
622: *
623: 90 CONTINUE
624: *
625: * Update the lower triangle of A22 (= A(k:n,k:n)) as
626: *
627: * A22 := A22 - L21*D*L21**T = A22 - L21*W**T
628: *
629: * computing blocks of NB columns at a time
630: *
631: DO 110 J = K, N, NB
632: JB = MIN( NB, N-J+1 )
633: *
634: * Update the lower triangle of the diagonal block
635: *
636: DO 100 JJ = J, J + JB - 1
637: CALL ZGEMV( 'No transpose', J+JB-JJ, K-1, -CONE,
638: $ A( JJ, 1 ), LDA, W( JJ, 1 ), LDW, CONE,
639: $ A( JJ, JJ ), 1 )
640: 100 CONTINUE
641: *
642: * Update the rectangular subdiagonal block
643: *
644: IF( J+JB.LE.N )
645: $ CALL ZGEMM( 'No transpose', 'Transpose', N-J-JB+1, JB,
646: $ K-1, -CONE, A( J+JB, 1 ), LDA, W( J, 1 ),
647: $ LDW, CONE, A( J+JB, J ), LDA )
648: 110 CONTINUE
649: *
650: * Put L21 in standard form by partially undoing the interchanges
651: * in columns 1:k-1
652: *
653: J = K - 1
654: 120 CONTINUE
655: JJ = J
656: JP = IPIV( J )
657: IF( JP.LT.0 ) THEN
658: JP = -JP
659: J = J - 1
660: END IF
661: J = J - 1
662: IF( JP.NE.JJ .AND. J.GE.1 )
663: $ CALL ZSWAP( J, A( JP, 1 ), LDA, A( JJ, 1 ), LDA )
664: IF( J.GE.1 )
665: $ GO TO 120
666: *
667: * Set KB to the number of columns factorized
668: *
669: KB = K - 1
670: *
671: END IF
672: RETURN
673: *
674: * End of ZLASYF
675: *
676: END
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