1: SUBROUTINE ZLAHEF( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO )
2: *
3: * -- LAPACK routine (version 3.3.1) --
4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6: * -- April 2011 --
7: *
8: * .. Scalar Arguments ..
9: CHARACTER UPLO
10: INTEGER INFO, KB, LDA, LDW, N, NB
11: * ..
12: * .. Array Arguments ..
13: INTEGER IPIV( * )
14: COMPLEX*16 A( LDA, * ), W( LDW, * )
15: * ..
16: *
17: * Purpose
18: * =======
19: *
20: * ZLAHEF computes a partial factorization of a complex Hermitian
21: * matrix A using the Bunch-Kaufman diagonal pivoting method. The
22: * partial factorization has the form:
23: *
24: * A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = 'U', or:
25: * ( 0 U22 ) ( 0 D ) ( U12**H U22**H )
26: *
27: * A = ( L11 0 ) ( D 0 ) ( L11**H L21**H ) if UPLO = 'L'
28: * ( L21 I ) ( 0 A22 ) ( 0 I )
29: *
30: * where the order of D is at most NB. The actual order is returned in
31: * the argument KB, and is either NB or NB-1, or N if N <= NB.
32: * Note that U**H denotes the conjugate transpose of U.
33: *
34: * ZLAHEF is an auxiliary routine called by ZHETRF. It uses blocked code
35: * (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or
36: * A22 (if UPLO = 'L').
37: *
38: * Arguments
39: * =========
40: *
41: * UPLO (input) CHARACTER*1
42: * Specifies whether the upper or lower triangular part of the
43: * Hermitian matrix A is stored:
44: * = 'U': Upper triangular
45: * = 'L': Lower triangular
46: *
47: * N (input) INTEGER
48: * The order of the matrix A. N >= 0.
49: *
50: * NB (input) INTEGER
51: * The maximum number of columns of the matrix A that should be
52: * factored. NB should be at least 2 to allow for 2-by-2 pivot
53: * blocks.
54: *
55: * KB (output) INTEGER
56: * The number of columns of A that were actually factored.
57: * KB is either NB-1 or NB, or N if N <= NB.
58: *
59: * A (input/output) COMPLEX*16 array, dimension (LDA,N)
60: * On entry, the Hermitian matrix A. If UPLO = 'U', the leading
61: * n-by-n upper triangular part of A contains the upper
62: * triangular part of the matrix A, and the strictly lower
63: * triangular part of A is not referenced. If UPLO = 'L', the
64: * leading n-by-n lower triangular part of A contains the lower
65: * triangular part of the matrix A, and the strictly upper
66: * triangular part of A is not referenced.
67: * On exit, A contains details of the partial factorization.
68: *
69: * LDA (input) INTEGER
70: * The leading dimension of the array A. LDA >= max(1,N).
71: *
72: * IPIV (output) INTEGER array, dimension (N)
73: * Details of the interchanges and the block structure of D.
74: * If UPLO = 'U', only the last KB elements of IPIV are set;
75: * if UPLO = 'L', only the first KB elements are set.
76: *
77: * If IPIV(k) > 0, then rows and columns k and IPIV(k) were
78: * interchanged and D(k,k) is a 1-by-1 diagonal block.
79: * If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and
80: * columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
81: * is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) =
82: * IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were
83: * interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
84: *
85: * W (workspace) COMPLEX*16 array, dimension (LDW,NB)
86: *
87: * LDW (input) INTEGER
88: * The leading dimension of the array W. LDW >= max(1,N).
89: *
90: * INFO (output) INTEGER
91: * = 0: successful exit
92: * > 0: if INFO = k, D(k,k) is exactly zero. The factorization
93: * has been completed, but the block diagonal matrix D is
94: * exactly singular.
95: *
96: * =====================================================================
97: *
98: * .. Parameters ..
99: DOUBLE PRECISION ZERO, ONE
100: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
101: COMPLEX*16 CONE
102: PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) )
103: DOUBLE PRECISION EIGHT, SEVTEN
104: PARAMETER ( EIGHT = 8.0D+0, SEVTEN = 17.0D+0 )
105: * ..
106: * .. Local Scalars ..
107: INTEGER IMAX, J, JB, JJ, JMAX, JP, K, KK, KKW, KP,
108: $ KSTEP, KW
109: DOUBLE PRECISION ABSAKK, ALPHA, COLMAX, R1, ROWMAX, T
110: COMPLEX*16 D11, D21, D22, Z
111: * ..
112: * .. External Functions ..
113: LOGICAL LSAME
114: INTEGER IZAMAX
115: EXTERNAL LSAME, IZAMAX
116: * ..
117: * .. External Subroutines ..
118: EXTERNAL ZCOPY, ZDSCAL, ZGEMM, ZGEMV, ZLACGV, ZSWAP
119: * ..
120: * .. Intrinsic Functions ..
121: INTRINSIC ABS, DBLE, DCONJG, DIMAG, MAX, MIN, SQRT
122: * ..
123: * .. Statement Functions ..
124: DOUBLE PRECISION CABS1
125: * ..
126: * .. Statement Function definitions ..
127: CABS1( Z ) = ABS( DBLE( Z ) ) + ABS( DIMAG( Z ) )
128: * ..
129: * .. Executable Statements ..
130: *
131: INFO = 0
132: *
133: * Initialize ALPHA for use in choosing pivot block size.
134: *
135: ALPHA = ( ONE+SQRT( SEVTEN ) ) / EIGHT
136: *
137: IF( LSAME( UPLO, 'U' ) ) THEN
138: *
139: * Factorize the trailing columns of A using the upper triangle
140: * of A and working backwards, and compute the matrix W = U12*D
141: * for use in updating A11 (note that conjg(W) is actually stored)
142: *
143: * K is the main loop index, decreasing from N in steps of 1 or 2
144: *
145: * KW is the column of W which corresponds to column K of A
146: *
147: K = N
148: 10 CONTINUE
149: KW = NB + K - N
150: *
151: * Exit from loop
152: *
153: IF( ( K.LE.N-NB+1 .AND. NB.LT.N ) .OR. K.LT.1 )
154: $ GO TO 30
155: *
156: * Copy column K of A to column KW of W and update it
157: *
158: CALL ZCOPY( K-1, A( 1, K ), 1, W( 1, KW ), 1 )
159: W( K, KW ) = DBLE( A( K, K ) )
160: IF( K.LT.N ) THEN
161: CALL ZGEMV( 'No transpose', K, N-K, -CONE, A( 1, K+1 ), LDA,
162: $ W( K, KW+1 ), LDW, CONE, W( 1, KW ), 1 )
163: W( K, KW ) = DBLE( W( K, KW ) )
164: END IF
165: *
166: KSTEP = 1
167: *
168: * Determine rows and columns to be interchanged and whether
169: * a 1-by-1 or 2-by-2 pivot block will be used
170: *
171: ABSAKK = ABS( DBLE( W( K, KW ) ) )
172: *
173: * IMAX is the row-index of the largest off-diagonal element in
174: * column K, and COLMAX is its absolute value
175: *
176: IF( K.GT.1 ) THEN
177: IMAX = IZAMAX( K-1, W( 1, KW ), 1 )
178: COLMAX = CABS1( W( IMAX, KW ) )
179: ELSE
180: COLMAX = ZERO
181: END IF
182: *
183: IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
184: *
185: * Column K is zero: set INFO and continue
186: *
187: IF( INFO.EQ.0 )
188: $ INFO = K
189: KP = K
190: A( K, K ) = DBLE( A( K, K ) )
191: ELSE
192: IF( ABSAKK.GE.ALPHA*COLMAX ) THEN
193: *
194: * no interchange, use 1-by-1 pivot block
195: *
196: KP = K
197: ELSE
198: *
199: * Copy column IMAX to column KW-1 of W and update it
200: *
201: CALL ZCOPY( IMAX-1, A( 1, IMAX ), 1, W( 1, KW-1 ), 1 )
202: W( IMAX, KW-1 ) = DBLE( A( IMAX, IMAX ) )
203: CALL ZCOPY( K-IMAX, A( IMAX, IMAX+1 ), LDA,
204: $ W( IMAX+1, KW-1 ), 1 )
205: CALL ZLACGV( K-IMAX, W( IMAX+1, KW-1 ), 1 )
206: IF( K.LT.N ) THEN
207: CALL ZGEMV( 'No transpose', K, N-K, -CONE,
208: $ A( 1, K+1 ), LDA, W( IMAX, KW+1 ), LDW,
209: $ CONE, W( 1, KW-1 ), 1 )
210: W( IMAX, KW-1 ) = DBLE( W( IMAX, KW-1 ) )
211: END IF
212: *
213: * JMAX is the column-index of the largest off-diagonal
214: * element in row IMAX, and ROWMAX is its absolute value
215: *
216: JMAX = IMAX + IZAMAX( K-IMAX, W( IMAX+1, KW-1 ), 1 )
217: ROWMAX = CABS1( W( JMAX, KW-1 ) )
218: IF( IMAX.GT.1 ) THEN
219: JMAX = IZAMAX( IMAX-1, W( 1, KW-1 ), 1 )
220: ROWMAX = MAX( ROWMAX, CABS1( W( JMAX, KW-1 ) ) )
221: END IF
222: *
223: IF( ABSAKK.GE.ALPHA*COLMAX*( COLMAX / ROWMAX ) ) THEN
224: *
225: * no interchange, use 1-by-1 pivot block
226: *
227: KP = K
228: ELSE IF( ABS( DBLE( W( IMAX, KW-1 ) ) ).GE.ALPHA*ROWMAX )
229: $ THEN
230: *
231: * interchange rows and columns K and IMAX, use 1-by-1
232: * pivot block
233: *
234: KP = IMAX
235: *
236: * copy column KW-1 of W to column KW
237: *
238: CALL ZCOPY( K, W( 1, KW-1 ), 1, W( 1, KW ), 1 )
239: ELSE
240: *
241: * interchange rows and columns K-1 and IMAX, use 2-by-2
242: * pivot block
243: *
244: KP = IMAX
245: KSTEP = 2
246: END IF
247: END IF
248: *
249: KK = K - KSTEP + 1
250: KKW = NB + KK - N
251: *
252: * Updated column KP is already stored in column KKW of W
253: *
254: IF( KP.NE.KK ) THEN
255: *
256: * Copy non-updated column KK to column KP
257: *
258: A( KP, KP ) = DBLE( A( KK, KK ) )
259: CALL ZCOPY( KK-1-KP, A( KP+1, KK ), 1, A( KP, KP+1 ),
260: $ LDA )
261: CALL ZLACGV( KK-1-KP, A( KP, KP+1 ), LDA )
262: CALL ZCOPY( KP-1, A( 1, KK ), 1, A( 1, KP ), 1 )
263: *
264: * Interchange rows KK and KP in last KK columns of A and W
265: *
266: IF( KK.LT.N )
267: $ CALL ZSWAP( N-KK, A( KK, KK+1 ), LDA, A( KP, KK+1 ),
268: $ LDA )
269: CALL ZSWAP( N-KK+1, W( KK, KKW ), LDW, W( KP, KKW ),
270: $ LDW )
271: END IF
272: *
273: IF( KSTEP.EQ.1 ) THEN
274: *
275: * 1-by-1 pivot block D(k): column KW of W now holds
276: *
277: * W(k) = U(k)*D(k)
278: *
279: * where U(k) is the k-th column of U
280: *
281: * Store U(k) in column k of A
282: *
283: CALL ZCOPY( K, W( 1, KW ), 1, A( 1, K ), 1 )
284: R1 = ONE / DBLE( A( K, K ) )
285: CALL ZDSCAL( K-1, R1, A( 1, K ), 1 )
286: *
287: * Conjugate W(k)
288: *
289: CALL ZLACGV( K-1, W( 1, KW ), 1 )
290: ELSE
291: *
292: * 2-by-2 pivot block D(k): columns KW and KW-1 of W now
293: * hold
294: *
295: * ( W(k-1) W(k) ) = ( U(k-1) U(k) )*D(k)
296: *
297: * where U(k) and U(k-1) are the k-th and (k-1)-th columns
298: * of U
299: *
300: IF( K.GT.2 ) THEN
301: *
302: * Store U(k) and U(k-1) in columns k and k-1 of A
303: *
304: D21 = W( K-1, KW )
305: D11 = W( K, KW ) / DCONJG( D21 )
306: D22 = W( K-1, KW-1 ) / D21
307: T = ONE / ( DBLE( D11*D22 )-ONE )
308: D21 = T / D21
309: DO 20 J = 1, K - 2
310: A( J, K-1 ) = D21*( D11*W( J, KW-1 )-W( J, KW ) )
311: A( J, K ) = DCONJG( D21 )*
312: $ ( D22*W( J, KW )-W( J, KW-1 ) )
313: 20 CONTINUE
314: END IF
315: *
316: * Copy D(k) to A
317: *
318: A( K-1, K-1 ) = W( K-1, KW-1 )
319: A( K-1, K ) = W( K-1, KW )
320: A( K, K ) = W( K, KW )
321: *
322: * Conjugate W(k) and W(k-1)
323: *
324: CALL ZLACGV( K-1, W( 1, KW ), 1 )
325: CALL ZLACGV( K-2, W( 1, KW-1 ), 1 )
326: END IF
327: END IF
328: *
329: * Store details of the interchanges in IPIV
330: *
331: IF( KSTEP.EQ.1 ) THEN
332: IPIV( K ) = KP
333: ELSE
334: IPIV( K ) = -KP
335: IPIV( K-1 ) = -KP
336: END IF
337: *
338: * Decrease K and return to the start of the main loop
339: *
340: K = K - KSTEP
341: GO TO 10
342: *
343: 30 CONTINUE
344: *
345: * Update the upper triangle of A11 (= A(1:k,1:k)) as
346: *
347: * A11 := A11 - U12*D*U12**H = A11 - U12*W**H
348: *
349: * computing blocks of NB columns at a time (note that conjg(W) is
350: * actually stored)
351: *
352: DO 50 J = ( ( K-1 ) / NB )*NB + 1, 1, -NB
353: JB = MIN( NB, K-J+1 )
354: *
355: * Update the upper triangle of the diagonal block
356: *
357: DO 40 JJ = J, J + JB - 1
358: A( JJ, JJ ) = DBLE( A( JJ, JJ ) )
359: CALL ZGEMV( 'No transpose', JJ-J+1, N-K, -CONE,
360: $ A( J, K+1 ), LDA, W( JJ, KW+1 ), LDW, CONE,
361: $ A( J, JJ ), 1 )
362: A( JJ, JJ ) = DBLE( A( JJ, JJ ) )
363: 40 CONTINUE
364: *
365: * Update the rectangular superdiagonal block
366: *
367: CALL ZGEMM( 'No transpose', 'Transpose', J-1, JB, N-K,
368: $ -CONE, A( 1, K+1 ), LDA, W( J, KW+1 ), LDW,
369: $ CONE, A( 1, J ), LDA )
370: 50 CONTINUE
371: *
372: * Put U12 in standard form by partially undoing the interchanges
373: * in columns k+1:n
374: *
375: J = K + 1
376: 60 CONTINUE
377: JJ = J
378: JP = IPIV( J )
379: IF( JP.LT.0 ) THEN
380: JP = -JP
381: J = J + 1
382: END IF
383: J = J + 1
384: IF( JP.NE.JJ .AND. J.LE.N )
385: $ CALL ZSWAP( N-J+1, A( JP, J ), LDA, A( JJ, J ), LDA )
386: IF( J.LE.N )
387: $ GO TO 60
388: *
389: * Set KB to the number of columns factorized
390: *
391: KB = N - K
392: *
393: ELSE
394: *
395: * Factorize the leading columns of A using the lower triangle
396: * of A and working forwards, and compute the matrix W = L21*D
397: * for use in updating A22 (note that conjg(W) is actually stored)
398: *
399: * K is the main loop index, increasing from 1 in steps of 1 or 2
400: *
401: K = 1
402: 70 CONTINUE
403: *
404: * Exit from loop
405: *
406: IF( ( K.GE.NB .AND. NB.LT.N ) .OR. K.GT.N )
407: $ GO TO 90
408: *
409: * Copy column K of A to column K of W and update it
410: *
411: W( K, K ) = DBLE( A( K, K ) )
412: IF( K.LT.N )
413: $ CALL ZCOPY( N-K, A( K+1, K ), 1, W( K+1, K ), 1 )
414: CALL ZGEMV( 'No transpose', N-K+1, K-1, -CONE, A( K, 1 ), LDA,
415: $ W( K, 1 ), LDW, CONE, W( K, K ), 1 )
416: W( K, K ) = DBLE( W( K, K ) )
417: *
418: KSTEP = 1
419: *
420: * Determine rows and columns to be interchanged and whether
421: * a 1-by-1 or 2-by-2 pivot block will be used
422: *
423: ABSAKK = ABS( DBLE( W( K, K ) ) )
424: *
425: * IMAX is the row-index of the largest off-diagonal element in
426: * column K, and COLMAX is its absolute value
427: *
428: IF( K.LT.N ) THEN
429: IMAX = K + IZAMAX( N-K, W( K+1, K ), 1 )
430: COLMAX = CABS1( W( IMAX, K ) )
431: ELSE
432: COLMAX = ZERO
433: END IF
434: *
435: IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
436: *
437: * Column K is zero: set INFO and continue
438: *
439: IF( INFO.EQ.0 )
440: $ INFO = K
441: KP = K
442: A( K, K ) = DBLE( A( K, K ) )
443: ELSE
444: IF( ABSAKK.GE.ALPHA*COLMAX ) THEN
445: *
446: * no interchange, use 1-by-1 pivot block
447: *
448: KP = K
449: ELSE
450: *
451: * Copy column IMAX to column K+1 of W and update it
452: *
453: CALL ZCOPY( IMAX-K, A( IMAX, K ), LDA, W( K, K+1 ), 1 )
454: CALL ZLACGV( IMAX-K, W( K, K+1 ), 1 )
455: W( IMAX, K+1 ) = DBLE( A( IMAX, IMAX ) )
456: IF( IMAX.LT.N )
457: $ CALL ZCOPY( N-IMAX, A( IMAX+1, IMAX ), 1,
458: $ W( IMAX+1, K+1 ), 1 )
459: CALL ZGEMV( 'No transpose', N-K+1, K-1, -CONE, A( K, 1 ),
460: $ LDA, W( IMAX, 1 ), LDW, CONE, W( K, K+1 ),
461: $ 1 )
462: W( IMAX, K+1 ) = DBLE( W( IMAX, K+1 ) )
463: *
464: * JMAX is the column-index of the largest off-diagonal
465: * element in row IMAX, and ROWMAX is its absolute value
466: *
467: JMAX = K - 1 + IZAMAX( IMAX-K, W( K, K+1 ), 1 )
468: ROWMAX = CABS1( W( JMAX, K+1 ) )
469: IF( IMAX.LT.N ) THEN
470: JMAX = IMAX + IZAMAX( N-IMAX, W( IMAX+1, K+1 ), 1 )
471: ROWMAX = MAX( ROWMAX, CABS1( W( JMAX, K+1 ) ) )
472: END IF
473: *
474: IF( ABSAKK.GE.ALPHA*COLMAX*( COLMAX / ROWMAX ) ) THEN
475: *
476: * no interchange, use 1-by-1 pivot block
477: *
478: KP = K
479: ELSE IF( ABS( DBLE( W( IMAX, K+1 ) ) ).GE.ALPHA*ROWMAX )
480: $ THEN
481: *
482: * interchange rows and columns K and IMAX, use 1-by-1
483: * pivot block
484: *
485: KP = IMAX
486: *
487: * copy column K+1 of W to column K
488: *
489: CALL ZCOPY( N-K+1, W( K, K+1 ), 1, W( K, K ), 1 )
490: ELSE
491: *
492: * interchange rows and columns K+1 and IMAX, use 2-by-2
493: * pivot block
494: *
495: KP = IMAX
496: KSTEP = 2
497: END IF
498: END IF
499: *
500: KK = K + KSTEP - 1
501: *
502: * Updated column KP is already stored in column KK of W
503: *
504: IF( KP.NE.KK ) THEN
505: *
506: * Copy non-updated column KK to column KP
507: *
508: A( KP, KP ) = DBLE( A( KK, KK ) )
509: CALL ZCOPY( KP-KK-1, A( KK+1, KK ), 1, A( KP, KK+1 ),
510: $ LDA )
511: CALL ZLACGV( KP-KK-1, A( KP, KK+1 ), LDA )
512: IF( KP.LT.N )
513: $ CALL ZCOPY( N-KP, A( KP+1, KK ), 1, A( KP+1, KP ), 1 )
514: *
515: * Interchange rows KK and KP in first KK columns of A and W
516: *
517: CALL ZSWAP( KK-1, A( KK, 1 ), LDA, A( KP, 1 ), LDA )
518: CALL ZSWAP( KK, W( KK, 1 ), LDW, W( KP, 1 ), LDW )
519: END IF
520: *
521: IF( KSTEP.EQ.1 ) THEN
522: *
523: * 1-by-1 pivot block D(k): column k of W now holds
524: *
525: * W(k) = L(k)*D(k)
526: *
527: * where L(k) is the k-th column of L
528: *
529: * Store L(k) in column k of A
530: *
531: CALL ZCOPY( N-K+1, W( K, K ), 1, A( K, K ), 1 )
532: IF( K.LT.N ) THEN
533: R1 = ONE / DBLE( A( K, K ) )
534: CALL ZDSCAL( N-K, R1, A( K+1, K ), 1 )
535: *
536: * Conjugate W(k)
537: *
538: CALL ZLACGV( N-K, W( K+1, K ), 1 )
539: END IF
540: ELSE
541: *
542: * 2-by-2 pivot block D(k): columns k and k+1 of W now hold
543: *
544: * ( W(k) W(k+1) ) = ( L(k) L(k+1) )*D(k)
545: *
546: * where L(k) and L(k+1) are the k-th and (k+1)-th columns
547: * of L
548: *
549: IF( K.LT.N-1 ) THEN
550: *
551: * Store L(k) and L(k+1) in columns k and k+1 of A
552: *
553: D21 = W( K+1, K )
554: D11 = W( K+1, K+1 ) / D21
555: D22 = W( K, K ) / DCONJG( D21 )
556: T = ONE / ( DBLE( D11*D22 )-ONE )
557: D21 = T / D21
558: DO 80 J = K + 2, N
559: A( J, K ) = DCONJG( D21 )*
560: $ ( D11*W( J, K )-W( J, K+1 ) )
561: A( J, K+1 ) = D21*( D22*W( J, K+1 )-W( J, K ) )
562: 80 CONTINUE
563: END IF
564: *
565: * Copy D(k) to A
566: *
567: A( K, K ) = W( K, K )
568: A( K+1, K ) = W( K+1, K )
569: A( K+1, K+1 ) = W( K+1, K+1 )
570: *
571: * Conjugate W(k) and W(k+1)
572: *
573: CALL ZLACGV( N-K, W( K+1, K ), 1 )
574: CALL ZLACGV( N-K-1, W( K+2, K+1 ), 1 )
575: END IF
576: END IF
577: *
578: * Store details of the interchanges in IPIV
579: *
580: IF( KSTEP.EQ.1 ) THEN
581: IPIV( K ) = KP
582: ELSE
583: IPIV( K ) = -KP
584: IPIV( K+1 ) = -KP
585: END IF
586: *
587: * Increase K and return to the start of the main loop
588: *
589: K = K + KSTEP
590: GO TO 70
591: *
592: 90 CONTINUE
593: *
594: * Update the lower triangle of A22 (= A(k:n,k:n)) as
595: *
596: * A22 := A22 - L21*D*L21**H = A22 - L21*W**H
597: *
598: * computing blocks of NB columns at a time (note that conjg(W) is
599: * actually stored)
600: *
601: DO 110 J = K, N, NB
602: JB = MIN( NB, N-J+1 )
603: *
604: * Update the lower triangle of the diagonal block
605: *
606: DO 100 JJ = J, J + JB - 1
607: A( JJ, JJ ) = DBLE( A( JJ, JJ ) )
608: CALL ZGEMV( 'No transpose', J+JB-JJ, K-1, -CONE,
609: $ A( JJ, 1 ), LDA, W( JJ, 1 ), LDW, CONE,
610: $ A( JJ, JJ ), 1 )
611: A( JJ, JJ ) = DBLE( A( JJ, JJ ) )
612: 100 CONTINUE
613: *
614: * Update the rectangular subdiagonal block
615: *
616: IF( J+JB.LE.N )
617: $ CALL ZGEMM( 'No transpose', 'Transpose', N-J-JB+1, JB,
618: $ K-1, -CONE, A( J+JB, 1 ), LDA, W( J, 1 ),
619: $ LDW, CONE, A( J+JB, J ), LDA )
620: 110 CONTINUE
621: *
622: * Put L21 in standard form by partially undoing the interchanges
623: * in columns 1:k-1
624: *
625: J = K - 1
626: 120 CONTINUE
627: JJ = J
628: JP = IPIV( J )
629: IF( JP.LT.0 ) THEN
630: JP = -JP
631: J = J - 1
632: END IF
633: J = J - 1
634: IF( JP.NE.JJ .AND. J.GE.1 )
635: $ CALL ZSWAP( J, A( JP, 1 ), LDA, A( JJ, 1 ), LDA )
636: IF( J.GE.1 )
637: $ GO TO 120
638: *
639: * Set KB to the number of columns factorized
640: *
641: KB = K - 1
642: *
643: END IF
644: RETURN
645: *
646: * End of ZLAHEF
647: *
648: END
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