1: *> \brief \b ZHETRD_HB2ST reduces a complex Hermitian band matrix A to real symmetric tridiagonal form T
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZHETRD_HB2ST + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhetrd_hb2st.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhetrd_hb2st.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhetrd_hb2st.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZHETRD_HB2ST( STAGE1, VECT, UPLO, N, KD, AB, LDAB,
22: * D, E, HOUS, LHOUS, WORK, LWORK, INFO )
23: *
24: * #if defined(_OPENMP)
25: * use omp_lib
26: * #endif
27: *
28: * IMPLICIT NONE
29: *
30: * .. Scalar Arguments ..
31: * CHARACTER STAGE1, UPLO, VECT
32: * INTEGER N, KD, IB, LDAB, LHOUS, LWORK, INFO
33: * ..
34: * .. Array Arguments ..
35: * DOUBLE PRECISION D( * ), E( * )
36: * COMPLEX*16 AB( LDAB, * ), HOUS( * ), WORK( * )
37: * ..
38: *
39: *
40: *> \par Purpose:
41: * =============
42: *>
43: *> \verbatim
44: *>
45: *> ZHETRD_HB2ST reduces a complex Hermitian band matrix A to real symmetric
46: *> tridiagonal form T by a unitary similarity transformation:
47: *> Q**H * A * Q = T.
48: *> \endverbatim
49: *
50: * Arguments:
51: * ==========
52: *
53: *> \param[in] STAGE1
54: *> \verbatim
55: *> STAGE1 is CHARACTER*1
56: *> = 'N': "No": to mention that the stage 1 of the reduction
57: *> from dense to band using the zhetrd_he2hb routine
58: *> was not called before this routine to reproduce AB.
59: *> In other term this routine is called as standalone.
60: *> = 'Y': "Yes": to mention that the stage 1 of the
61: *> reduction from dense to band using the zhetrd_he2hb
62: *> routine has been called to produce AB (e.g., AB is
63: *> the output of zhetrd_he2hb.
64: *> \endverbatim
65: *>
66: *> \param[in] VECT
67: *> \verbatim
68: *> VECT is CHARACTER*1
69: *> = 'N': No need for the Housholder representation,
70: *> and thus LHOUS is of size max(1, 4*N);
71: *> = 'V': the Householder representation is needed to
72: *> either generate or to apply Q later on,
73: *> then LHOUS is to be queried and computed.
74: *> (NOT AVAILABLE IN THIS RELEASE).
75: *> \endverbatim
76: *>
77: *> \param[in] UPLO
78: *> \verbatim
79: *> UPLO is CHARACTER*1
80: *> = 'U': Upper triangle of A is stored;
81: *> = 'L': Lower triangle of A is stored.
82: *> \endverbatim
83: *>
84: *> \param[in] N
85: *> \verbatim
86: *> N is INTEGER
87: *> The order of the matrix A. N >= 0.
88: *> \endverbatim
89: *>
90: *> \param[in] KD
91: *> \verbatim
92: *> KD is INTEGER
93: *> The number of superdiagonals of the matrix A if UPLO = 'U',
94: *> or the number of subdiagonals if UPLO = 'L'. KD >= 0.
95: *> \endverbatim
96: *>
97: *> \param[in,out] AB
98: *> \verbatim
99: *> AB is COMPLEX*16 array, dimension (LDAB,N)
100: *> On entry, the upper or lower triangle of the Hermitian band
101: *> matrix A, stored in the first KD+1 rows of the array. The
102: *> j-th column of A is stored in the j-th column of the array AB
103: *> as follows:
104: *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
105: *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
106: *> On exit, the diagonal elements of AB are overwritten by the
107: *> diagonal elements of the tridiagonal matrix T; if KD > 0, the
108: *> elements on the first superdiagonal (if UPLO = 'U') or the
109: *> first subdiagonal (if UPLO = 'L') are overwritten by the
110: *> off-diagonal elements of T; the rest of AB is overwritten by
111: *> values generated during the reduction.
112: *> \endverbatim
113: *>
114: *> \param[in] LDAB
115: *> \verbatim
116: *> LDAB is INTEGER
117: *> The leading dimension of the array AB. LDAB >= KD+1.
118: *> \endverbatim
119: *>
120: *> \param[out] D
121: *> \verbatim
122: *> D is DOUBLE PRECISION array, dimension (N)
123: *> The diagonal elements of the tridiagonal matrix T.
124: *> \endverbatim
125: *>
126: *> \param[out] E
127: *> \verbatim
128: *> E is DOUBLE PRECISION array, dimension (N-1)
129: *> The off-diagonal elements of the tridiagonal matrix T:
130: *> E(i) = T(i,i+1) if UPLO = 'U'; E(i) = T(i+1,i) if UPLO = 'L'.
131: *> \endverbatim
132: *>
133: *> \param[out] HOUS
134: *> \verbatim
135: *> HOUS is COMPLEX*16 array, dimension LHOUS, that
136: *> store the Householder representation.
137: *> \endverbatim
138: *>
139: *> \param[in] LHOUS
140: *> \verbatim
141: *> LHOUS is INTEGER
142: *> The dimension of the array HOUS. LHOUS = MAX(1, dimension)
143: *> If LWORK = -1, or LHOUS=-1,
144: *> then a query is assumed; the routine
145: *> only calculates the optimal size of the HOUS array, returns
146: *> this value as the first entry of the HOUS array, and no error
147: *> message related to LHOUS is issued by XERBLA.
148: *> LHOUS = MAX(1, dimension) where
149: *> dimension = 4*N if VECT='N'
150: *> not available now if VECT='H'
151: *> \endverbatim
152: *>
153: *> \param[out] WORK
154: *> \verbatim
155: *> WORK is COMPLEX*16 array, dimension LWORK.
156: *> \endverbatim
157: *>
158: *> \param[in] LWORK
159: *> \verbatim
160: *> LWORK is INTEGER
161: *> The dimension of the array WORK. LWORK = MAX(1, dimension)
162: *> If LWORK = -1, or LHOUS=-1,
163: *> then a workspace query is assumed; the routine
164: *> only calculates the optimal size of the WORK array, returns
165: *> this value as the first entry of the WORK array, and no error
166: *> message related to LWORK is issued by XERBLA.
167: *> LWORK = MAX(1, dimension) where
168: *> dimension = (2KD+1)*N + KD*NTHREADS
169: *> where KD is the blocking size of the reduction,
170: *> FACTOPTNB is the blocking used by the QR or LQ
171: *> algorithm, usually FACTOPTNB=128 is a good choice
172: *> NTHREADS is the number of threads used when
173: *> openMP compilation is enabled, otherwise =1.
174: *> \endverbatim
175: *>
176: *> \param[out] INFO
177: *> \verbatim
178: *> INFO is INTEGER
179: *> = 0: successful exit
180: *> < 0: if INFO = -i, the i-th argument had an illegal value
181: *> \endverbatim
182: *
183: * Authors:
184: * ========
185: *
186: *> \author Univ. of Tennessee
187: *> \author Univ. of California Berkeley
188: *> \author Univ. of Colorado Denver
189: *> \author NAG Ltd.
190: *
191: *> \ingroup complex16OTHERcomputational
192: *
193: *> \par Further Details:
194: * =====================
195: *>
196: *> \verbatim
197: *>
198: *> Implemented by Azzam Haidar.
199: *>
200: *> All details are available on technical report, SC11, SC13 papers.
201: *>
202: *> Azzam Haidar, Hatem Ltaief, and Jack Dongarra.
203: *> Parallel reduction to condensed forms for symmetric eigenvalue problems
204: *> using aggregated fine-grained and memory-aware kernels. In Proceedings
205: *> of 2011 International Conference for High Performance Computing,
206: *> Networking, Storage and Analysis (SC '11), New York, NY, USA,
207: *> Article 8 , 11 pages.
208: *> http://doi.acm.org/10.1145/2063384.2063394
209: *>
210: *> A. Haidar, J. Kurzak, P. Luszczek, 2013.
211: *> An improved parallel singular value algorithm and its implementation
212: *> for multicore hardware, In Proceedings of 2013 International Conference
213: *> for High Performance Computing, Networking, Storage and Analysis (SC '13).
214: *> Denver, Colorado, USA, 2013.
215: *> Article 90, 12 pages.
216: *> http://doi.acm.org/10.1145/2503210.2503292
217: *>
218: *> A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra.
219: *> A novel hybrid CPU-GPU generalized eigensolver for electronic structure
220: *> calculations based on fine-grained memory aware tasks.
221: *> International Journal of High Performance Computing Applications.
222: *> Volume 28 Issue 2, Pages 196-209, May 2014.
223: *> http://hpc.sagepub.com/content/28/2/196
224: *>
225: *> \endverbatim
226: *>
227: * =====================================================================
228: SUBROUTINE ZHETRD_HB2ST( STAGE1, VECT, UPLO, N, KD, AB, LDAB,
229: $ D, E, HOUS, LHOUS, WORK, LWORK, INFO )
230: *
231: *
232: #if defined(_OPENMP)
233: use omp_lib
234: #endif
235: *
236: IMPLICIT NONE
237: *
238: * -- LAPACK computational routine --
239: * -- LAPACK is a software package provided by Univ. of Tennessee, --
240: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
241: *
242: * .. Scalar Arguments ..
243: CHARACTER STAGE1, UPLO, VECT
244: INTEGER N, KD, LDAB, LHOUS, LWORK, INFO
245: * ..
246: * .. Array Arguments ..
247: DOUBLE PRECISION D( * ), E( * )
248: COMPLEX*16 AB( LDAB, * ), HOUS( * ), WORK( * )
249: * ..
250: *
251: * =====================================================================
252: *
253: * .. Parameters ..
254: DOUBLE PRECISION RZERO
255: COMPLEX*16 ZERO, ONE
256: PARAMETER ( RZERO = 0.0D+0,
257: $ ZERO = ( 0.0D+0, 0.0D+0 ),
258: $ ONE = ( 1.0D+0, 0.0D+0 ) )
259: * ..
260: * .. Local Scalars ..
261: LOGICAL LQUERY, WANTQ, UPPER, AFTERS1
262: INTEGER I, M, K, IB, SWEEPID, MYID, SHIFT, STT, ST,
263: $ ED, STIND, EDIND, BLKLASTIND, COLPT, THED,
264: $ STEPERCOL, GRSIZ, THGRSIZ, THGRNB, THGRID,
265: $ NBTILES, TTYPE, TID, NTHREADS, DEBUG,
266: $ ABDPOS, ABOFDPOS, DPOS, OFDPOS, AWPOS,
267: $ INDA, INDW, APOS, SIZEA, LDA, INDV, INDTAU,
268: $ SIZEV, SIZETAU, LDV, LHMIN, LWMIN
269: DOUBLE PRECISION ABSTMP
270: COMPLEX*16 TMP
271: * ..
272: * .. External Subroutines ..
273: EXTERNAL ZHB2ST_KERNELS, ZLACPY, ZLASET, XERBLA
274: * ..
275: * .. Intrinsic Functions ..
276: INTRINSIC MIN, MAX, CEILING, DBLE, REAL
277: * ..
278: * .. External Functions ..
279: LOGICAL LSAME
280: INTEGER ILAENV2STAGE
281: EXTERNAL LSAME, ILAENV2STAGE
282: * ..
283: * .. Executable Statements ..
284: *
285: * Determine the minimal workspace size required.
286: * Test the input parameters
287: *
288: DEBUG = 0
289: INFO = 0
290: AFTERS1 = LSAME( STAGE1, 'Y' )
291: WANTQ = LSAME( VECT, 'V' )
292: UPPER = LSAME( UPLO, 'U' )
293: LQUERY = ( LWORK.EQ.-1 ) .OR. ( LHOUS.EQ.-1 )
294: *
295: * Determine the block size, the workspace size and the hous size.
296: *
297: IB = ILAENV2STAGE( 2, 'ZHETRD_HB2ST', VECT, N, KD, -1, -1 )
298: LHMIN = ILAENV2STAGE( 3, 'ZHETRD_HB2ST', VECT, N, KD, IB, -1 )
299: LWMIN = ILAENV2STAGE( 4, 'ZHETRD_HB2ST', VECT, N, KD, IB, -1 )
300: *
301: IF( .NOT.AFTERS1 .AND. .NOT.LSAME( STAGE1, 'N' ) ) THEN
302: INFO = -1
303: ELSE IF( .NOT.LSAME( VECT, 'N' ) ) THEN
304: INFO = -2
305: ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
306: INFO = -3
307: ELSE IF( N.LT.0 ) THEN
308: INFO = -4
309: ELSE IF( KD.LT.0 ) THEN
310: INFO = -5
311: ELSE IF( LDAB.LT.(KD+1) ) THEN
312: INFO = -7
313: ELSE IF( LHOUS.LT.LHMIN .AND. .NOT.LQUERY ) THEN
314: INFO = -11
315: ELSE IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
316: INFO = -13
317: END IF
318: *
319: IF( INFO.EQ.0 ) THEN
320: HOUS( 1 ) = LHMIN
321: WORK( 1 ) = LWMIN
322: END IF
323: *
324: IF( INFO.NE.0 ) THEN
325: CALL XERBLA( 'ZHETRD_HB2ST', -INFO )
326: RETURN
327: ELSE IF( LQUERY ) THEN
328: RETURN
329: END IF
330: *
331: * Quick return if possible
332: *
333: IF( N.EQ.0 ) THEN
334: HOUS( 1 ) = 1
335: WORK( 1 ) = 1
336: RETURN
337: END IF
338: *
339: * Determine pointer position
340: *
341: LDV = KD + IB
342: SIZETAU = 2 * N
343: SIZEV = 2 * N
344: INDTAU = 1
345: INDV = INDTAU + SIZETAU
346: LDA = 2 * KD + 1
347: SIZEA = LDA * N
348: INDA = 1
349: INDW = INDA + SIZEA
350: NTHREADS = 1
351: TID = 0
352: *
353: IF( UPPER ) THEN
354: APOS = INDA + KD
355: AWPOS = INDA
356: DPOS = APOS + KD
357: OFDPOS = DPOS - 1
358: ABDPOS = KD + 1
359: ABOFDPOS = KD
360: ELSE
361: APOS = INDA
362: AWPOS = INDA + KD + 1
363: DPOS = APOS
364: OFDPOS = DPOS + 1
365: ABDPOS = 1
366: ABOFDPOS = 2
367:
368: ENDIF
369: *
370: * Case KD=0:
371: * The matrix is diagonal. We just copy it (convert to "real" for
372: * complex because D is double and the imaginary part should be 0)
373: * and store it in D. A sequential code here is better or
374: * in a parallel environment it might need two cores for D and E
375: *
376: IF( KD.EQ.0 ) THEN
377: DO 30 I = 1, N
378: D( I ) = DBLE( AB( ABDPOS, I ) )
379: 30 CONTINUE
380: DO 40 I = 1, N-1
381: E( I ) = RZERO
382: 40 CONTINUE
383: *
384: HOUS( 1 ) = 1
385: WORK( 1 ) = 1
386: RETURN
387: END IF
388: *
389: * Case KD=1:
390: * The matrix is already Tridiagonal. We have to make diagonal
391: * and offdiagonal elements real, and store them in D and E.
392: * For that, for real precision just copy the diag and offdiag
393: * to D and E while for the COMPLEX case the bulge chasing is
394: * performed to convert the hermetian tridiagonal to symmetric
395: * tridiagonal. A simpler conversion formula might be used, but then
396: * updating the Q matrix will be required and based if Q is generated
397: * or not this might complicate the story.
398: *
399: IF( KD.EQ.1 ) THEN
400: DO 50 I = 1, N
401: D( I ) = DBLE( AB( ABDPOS, I ) )
402: 50 CONTINUE
403: *
404: * make off-diagonal elements real and copy them to E
405: *
406: IF( UPPER ) THEN
407: DO 60 I = 1, N - 1
408: TMP = AB( ABOFDPOS, I+1 )
409: ABSTMP = ABS( TMP )
410: AB( ABOFDPOS, I+1 ) = ABSTMP
411: E( I ) = ABSTMP
412: IF( ABSTMP.NE.RZERO ) THEN
413: TMP = TMP / ABSTMP
414: ELSE
415: TMP = ONE
416: END IF
417: IF( I.LT.N-1 )
418: $ AB( ABOFDPOS, I+2 ) = AB( ABOFDPOS, I+2 )*TMP
419: C IF( WANTZ ) THEN
420: C CALL ZSCAL( N, DCONJG( TMP ), Q( 1, I+1 ), 1 )
421: C END IF
422: 60 CONTINUE
423: ELSE
424: DO 70 I = 1, N - 1
425: TMP = AB( ABOFDPOS, I )
426: ABSTMP = ABS( TMP )
427: AB( ABOFDPOS, I ) = ABSTMP
428: E( I ) = ABSTMP
429: IF( ABSTMP.NE.RZERO ) THEN
430: TMP = TMP / ABSTMP
431: ELSE
432: TMP = ONE
433: END IF
434: IF( I.LT.N-1 )
435: $ AB( ABOFDPOS, I+1 ) = AB( ABOFDPOS, I+1 )*TMP
436: C IF( WANTQ ) THEN
437: C CALL ZSCAL( N, TMP, Q( 1, I+1 ), 1 )
438: C END IF
439: 70 CONTINUE
440: ENDIF
441: *
442: HOUS( 1 ) = 1
443: WORK( 1 ) = 1
444: RETURN
445: END IF
446: *
447: * Main code start here.
448: * Reduce the hermitian band of A to a tridiagonal matrix.
449: *
450: THGRSIZ = N
451: GRSIZ = 1
452: SHIFT = 3
453: NBTILES = CEILING( REAL(N)/REAL(KD) )
454: STEPERCOL = CEILING( REAL(SHIFT)/REAL(GRSIZ) )
455: THGRNB = CEILING( REAL(N-1)/REAL(THGRSIZ) )
456: *
457: CALL ZLACPY( "A", KD+1, N, AB, LDAB, WORK( APOS ), LDA )
458: CALL ZLASET( "A", KD, N, ZERO, ZERO, WORK( AWPOS ), LDA )
459: *
460: *
461: * openMP parallelisation start here
462: *
463: #if defined(_OPENMP)
464: !$OMP PARALLEL PRIVATE( TID, THGRID, BLKLASTIND )
465: !$OMP$ PRIVATE( THED, I, M, K, ST, ED, STT, SWEEPID )
466: !$OMP$ PRIVATE( MYID, TTYPE, COLPT, STIND, EDIND )
467: !$OMP$ SHARED ( UPLO, WANTQ, INDV, INDTAU, HOUS, WORK)
468: !$OMP$ SHARED ( N, KD, IB, NBTILES, LDA, LDV, INDA )
469: !$OMP$ SHARED ( STEPERCOL, THGRNB, THGRSIZ, GRSIZ, SHIFT )
470: !$OMP MASTER
471: #endif
472: *
473: * main bulge chasing loop
474: *
475: DO 100 THGRID = 1, THGRNB
476: STT = (THGRID-1)*THGRSIZ+1
477: THED = MIN( (STT + THGRSIZ -1), (N-1))
478: DO 110 I = STT, N-1
479: ED = MIN( I, THED )
480: IF( STT.GT.ED ) EXIT
481: DO 120 M = 1, STEPERCOL
482: ST = STT
483: DO 130 SWEEPID = ST, ED
484: DO 140 K = 1, GRSIZ
485: MYID = (I-SWEEPID)*(STEPERCOL*GRSIZ)
486: $ + (M-1)*GRSIZ + K
487: IF ( MYID.EQ.1 ) THEN
488: TTYPE = 1
489: ELSE
490: TTYPE = MOD( MYID, 2 ) + 2
491: ENDIF
492:
493: IF( TTYPE.EQ.2 ) THEN
494: COLPT = (MYID/2)*KD + SWEEPID
495: STIND = COLPT-KD+1
496: EDIND = MIN(COLPT,N)
497: BLKLASTIND = COLPT
498: ELSE
499: COLPT = ((MYID+1)/2)*KD + SWEEPID
500: STIND = COLPT-KD+1
501: EDIND = MIN(COLPT,N)
502: IF( ( STIND.GE.EDIND-1 ).AND.
503: $ ( EDIND.EQ.N ) ) THEN
504: BLKLASTIND = N
505: ELSE
506: BLKLASTIND = 0
507: ENDIF
508: ENDIF
509: *
510: * Call the kernel
511: *
512: #if defined(_OPENMP) && _OPENMP >= 201307
513:
514: IF( TTYPE.NE.1 ) THEN
515: !$OMP TASK DEPEND(in:WORK(MYID+SHIFT-1))
516: !$OMP$ DEPEND(in:WORK(MYID-1))
517: !$OMP$ DEPEND(out:WORK(MYID))
518: TID = OMP_GET_THREAD_NUM()
519: CALL ZHB2ST_KERNELS( UPLO, WANTQ, TTYPE,
520: $ STIND, EDIND, SWEEPID, N, KD, IB,
521: $ WORK ( INDA ), LDA,
522: $ HOUS( INDV ), HOUS( INDTAU ), LDV,
523: $ WORK( INDW + TID*KD ) )
524: !$OMP END TASK
525: ELSE
526: !$OMP TASK DEPEND(in:WORK(MYID+SHIFT-1))
527: !$OMP$ DEPEND(out:WORK(MYID))
528: TID = OMP_GET_THREAD_NUM()
529: CALL ZHB2ST_KERNELS( UPLO, WANTQ, TTYPE,
530: $ STIND, EDIND, SWEEPID, N, KD, IB,
531: $ WORK ( INDA ), LDA,
532: $ HOUS( INDV ), HOUS( INDTAU ), LDV,
533: $ WORK( INDW + TID*KD ) )
534: !$OMP END TASK
535: ENDIF
536: #else
537: CALL ZHB2ST_KERNELS( UPLO, WANTQ, TTYPE,
538: $ STIND, EDIND, SWEEPID, N, KD, IB,
539: $ WORK ( INDA ), LDA,
540: $ HOUS( INDV ), HOUS( INDTAU ), LDV,
541: $ WORK( INDW + TID*KD ) )
542: #endif
543: IF ( BLKLASTIND.GE.(N-1) ) THEN
544: STT = STT + 1
545: EXIT
546: ENDIF
547: 140 CONTINUE
548: 130 CONTINUE
549: 120 CONTINUE
550: 110 CONTINUE
551: 100 CONTINUE
552: *
553: #if defined(_OPENMP)
554: !$OMP END MASTER
555: !$OMP END PARALLEL
556: #endif
557: *
558: * Copy the diagonal from A to D. Note that D is REAL thus only
559: * the Real part is needed, the imaginary part should be zero.
560: *
561: DO 150 I = 1, N
562: D( I ) = DBLE( WORK( DPOS+(I-1)*LDA ) )
563: 150 CONTINUE
564: *
565: * Copy the off diagonal from A to E. Note that E is REAL thus only
566: * the Real part is needed, the imaginary part should be zero.
567: *
568: IF( UPPER ) THEN
569: DO 160 I = 1, N-1
570: E( I ) = DBLE( WORK( OFDPOS+I*LDA ) )
571: 160 CONTINUE
572: ELSE
573: DO 170 I = 1, N-1
574: E( I ) = DBLE( WORK( OFDPOS+(I-1)*LDA ) )
575: 170 CONTINUE
576: ENDIF
577: *
578: HOUS( 1 ) = LHMIN
579: WORK( 1 ) = LWMIN
580: RETURN
581: *
582: * End of ZHETRD_HB2ST
583: *
584: END
585:
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