LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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zsyconvf.f
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1*> \brief \b ZSYCONVF
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
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11*> [TGZ]</a>
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13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zsyconvf.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE ZSYCONVF( UPLO, WAY, N, A, LDA, E, IPIV, INFO )
22*
23* .. Scalar Arguments ..
24* CHARACTER UPLO, WAY
25* INTEGER INFO, LDA, N
26* ..
27* .. Array Arguments ..
28* INTEGER IPIV( * )
29* COMPLEX*16 A( LDA, * ), E( * )
30* ..
31*
32*
33*> \par Purpose:
34* =============
35*>
36*> \verbatim
37*> If parameter WAY = 'C':
38*> ZSYCONVF converts the factorization output format used in
39*> ZSYTRF provided on entry in parameter A into the factorization
40*> output format used in ZSYTRF_RK (or ZSYTRF_BK) that is stored
41*> on exit in parameters A and E. It also converts in place details of
42*> the intechanges stored in IPIV from the format used in ZSYTRF into
43*> the format used in ZSYTRF_RK (or ZSYTRF_BK).
44*>
45*> If parameter WAY = 'R':
46*> ZSYCONVF performs the conversion in reverse direction, i.e.
47*> converts the factorization output format used in ZSYTRF_RK
48*> (or ZSYTRF_BK) provided on entry in parameters A and E into
49*> the factorization output format used in ZSYTRF that is stored
50*> on exit in parameter A. It also converts in place details of
51*> the intechanges stored in IPIV from the format used in ZSYTRF_RK
52*> (or ZSYTRF_BK) into the format used in ZSYTRF.
53*>
54*> ZSYCONVF can also convert in Hermitian matrix case, i.e. between
55*> formats used in ZHETRF and ZHETRF_RK (or ZHETRF_BK).
56*> \endverbatim
57*
58* Arguments:
59* ==========
60*
61*> \param[in] UPLO
62*> \verbatim
63*> UPLO is CHARACTER*1
64*> Specifies whether the details of the factorization are
65*> stored as an upper or lower triangular matrix A.
66*> = 'U': Upper triangular
67*> = 'L': Lower triangular
68*> \endverbatim
69*>
70*> \param[in] WAY
71*> \verbatim
72*> WAY is CHARACTER*1
73*> = 'C': Convert
74*> = 'R': Revert
75*> \endverbatim
76*>
77*> \param[in] N
78*> \verbatim
79*> N is INTEGER
80*> The order of the matrix A. N >= 0.
81*> \endverbatim
82*>
83*> \param[in,out] A
84*> \verbatim
85*> A is COMPLEX*16 array, dimension (LDA,N)
86*>
87*> 1) If WAY ='C':
88*>
89*> On entry, contains factorization details in format used in
90*> ZSYTRF:
91*> a) all elements of the symmetric block diagonal
92*> matrix D on the diagonal of A and on superdiagonal
93*> (or subdiagonal) of A, and
94*> b) If UPLO = 'U': multipliers used to obtain factor U
95*> in the superdiagonal part of A.
96*> If UPLO = 'L': multipliers used to obtain factor L
97*> in the superdiagonal part of A.
98*>
99*> On exit, contains factorization details in format used in
100*> ZSYTRF_RK or ZSYTRF_BK:
101*> a) ONLY diagonal elements of the symmetric block diagonal
102*> matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
103*> (superdiagonal (or subdiagonal) elements of D
104*> are stored on exit in array E), and
105*> b) If UPLO = 'U': factor U in the superdiagonal part of A.
106*> If UPLO = 'L': factor L in the subdiagonal part of A.
107*>
108*> 2) If WAY = 'R':
109*>
110*> On entry, contains factorization details in format used in
111*> ZSYTRF_RK or ZSYTRF_BK:
112*> a) ONLY diagonal elements of the symmetric block diagonal
113*> matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
114*> (superdiagonal (or subdiagonal) elements of D
115*> are stored on exit in array E), and
116*> b) If UPLO = 'U': factor U in the superdiagonal part of A.
117*> If UPLO = 'L': factor L in the subdiagonal part of A.
118*>
119*> On exit, contains factorization details in format used in
120*> ZSYTRF:
121*> a) all elements of the symmetric block diagonal
122*> matrix D on the diagonal of A and on superdiagonal
123*> (or subdiagonal) of A, and
124*> b) If UPLO = 'U': multipliers used to obtain factor U
125*> in the superdiagonal part of A.
126*> If UPLO = 'L': multipliers used to obtain factor L
127*> in the superdiagonal part of A.
128*> \endverbatim
129*>
130*> \param[in] LDA
131*> \verbatim
132*> LDA is INTEGER
133*> The leading dimension of the array A. LDA >= max(1,N).
134*> \endverbatim
135*>
136*> \param[in,out] E
137*> \verbatim
138*> E is COMPLEX*16 array, dimension (N)
139*>
140*> 1) If WAY ='C':
141*>
142*> On entry, just a workspace.
143*>
144*> On exit, contains the superdiagonal (or subdiagonal)
145*> elements of the symmetric block diagonal matrix D
146*> with 1-by-1 or 2-by-2 diagonal blocks, where
147*> If UPLO = 'U': E(i) = D(i-1,i), i=2:N, E(1) is set to 0;
148*> If UPLO = 'L': E(i) = D(i+1,i), i=1:N-1, E(N) is set to 0.
149*>
150*> 2) If WAY = 'R':
151*>
152*> On entry, contains the superdiagonal (or subdiagonal)
153*> elements of the symmetric block diagonal matrix D
154*> with 1-by-1 or 2-by-2 diagonal blocks, where
155*> If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced;
156*> If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.
157*>
158*> On exit, is not changed
159*> \endverbatim
160*.
161*> \param[in,out] IPIV
162*> \verbatim
163*> IPIV is INTEGER array, dimension (N)
164*>
165*> 1) If WAY ='C':
166*> On entry, details of the interchanges and the block
167*> structure of D in the format used in ZSYTRF.
168*> On exit, details of the interchanges and the block
169*> structure of D in the format used in ZSYTRF_RK
170*> ( or ZSYTRF_BK).
171*>
172*> 1) If WAY ='R':
173*> On entry, details of the interchanges and the block
174*> structure of D in the format used in ZSYTRF_RK
175*> ( or ZSYTRF_BK).
176*> On exit, details of the interchanges and the block
177*> structure of D in the format used in ZSYTRF.
178*> \endverbatim
179*>
180*> \param[out] INFO
181*> \verbatim
182*> INFO is INTEGER
183*> = 0: successful exit
184*> < 0: if INFO = -i, the i-th argument had an illegal value
185*> \endverbatim
186*
187* Authors:
188* ========
189*
190*> \author Univ. of Tennessee
191*> \author Univ. of California Berkeley
192*> \author Univ. of Colorado Denver
193*> \author NAG Ltd.
194*
195*> \ingroup complex16SYcomputational
196*
197*> \par Contributors:
198* ==================
199*>
200*> \verbatim
201*>
202*> November 2017, Igor Kozachenko,
203*> Computer Science Division,
204*> University of California, Berkeley
205*>
206*> \endverbatim
207* =====================================================================
208 SUBROUTINE zsyconvf( UPLO, WAY, N, A, LDA, E, IPIV, INFO )
209*
210* -- LAPACK computational routine --
211* -- LAPACK is a software package provided by Univ. of Tennessee, --
212* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
213*
214* .. Scalar Arguments ..
215 CHARACTER UPLO, WAY
216 INTEGER INFO, LDA, N
217* ..
218* .. Array Arguments ..
219 INTEGER IPIV( * )
220 COMPLEX*16 A( LDA, * ), E( * )
221* ..
222*
223* =====================================================================
224*
225* .. Parameters ..
226 COMPLEX*16 ZERO
227 parameter( zero = ( 0.0d+0, 0.0d+0 ) )
228* ..
229* .. External Functions ..
230 LOGICAL LSAME
231 EXTERNAL lsame
232*
233* .. External Subroutines ..
234 EXTERNAL zswap, xerbla
235* .. Local Scalars ..
236 LOGICAL UPPER, CONVERT
237 INTEGER I, IP
238* ..
239* .. Executable Statements ..
240*
241 info = 0
242 upper = lsame( uplo, 'U' )
243 convert = lsame( way, 'C' )
244 IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
245 info = -1
246 ELSE IF( .NOT.convert .AND. .NOT.lsame( way, 'R' ) ) THEN
247 info = -2
248 ELSE IF( n.LT.0 ) THEN
249 info = -3
250 ELSE IF( lda.LT.max( 1, n ) ) THEN
251 info = -5
252
253 END IF
254 IF( info.NE.0 ) THEN
255 CALL xerbla( 'ZSYCONVF', -info )
256 RETURN
257 END IF
258*
259* Quick return if possible
260*
261 IF( n.EQ.0 )
262 \$ RETURN
263*
264 IF( upper ) THEN
265*
266* Begin A is UPPER
267*
268 IF ( convert ) THEN
269*
270* Convert A (A is upper)
271*
272*
273* Convert VALUE
274*
275* Assign superdiagonal entries of D to array E and zero out
276* corresponding entries in input storage A
277*
278 i = n
279 e( 1 ) = zero
280 DO WHILE ( i.GT.1 )
281 IF( ipiv( i ).LT.0 ) THEN
282 e( i ) = a( i-1, i )
283 e( i-1 ) = zero
284 a( i-1, i ) = zero
285 i = i - 1
286 ELSE
287 e( i ) = zero
288 END IF
289 i = i - 1
290 END DO
291*
292* Convert PERMUTATIONS and IPIV
293*
294* Apply permutations to submatrices of upper part of A
295* in factorization order where i decreases from N to 1
296*
297 i = n
298 DO WHILE ( i.GE.1 )
299 IF( ipiv( i ).GT.0 ) THEN
300*
301* 1-by-1 pivot interchange
302*
303* Swap rows i and IPIV(i) in A(1:i,N-i:N)
304*
305 ip = ipiv( i )
306 IF( i.LT.n ) THEN
307 IF( ip.NE.i ) THEN
308 CALL zswap( n-i, a( i, i+1 ), lda,
309 \$ a( ip, i+1 ), lda )
310 END IF
311 END IF
312*
313 ELSE
314*
315* 2-by-2 pivot interchange
316*
317* Swap rows i-1 and IPIV(i) in A(1:i,N-i:N)
318*
319 ip = -ipiv( i )
320 IF( i.LT.n ) THEN
321 IF( ip.NE.(i-1) ) THEN
322 CALL zswap( n-i, a( i-1, i+1 ), lda,
323 \$ a( ip, i+1 ), lda )
324 END IF
325 END IF
326*
327* Convert IPIV
328* There is no interchnge of rows i and and IPIV(i),
329* so this should be reflected in IPIV format for
330* *SYTRF_RK ( or *SYTRF_BK)
331*
332 ipiv( i ) = i
333*
334 i = i - 1
335*
336 END IF
337 i = i - 1
338 END DO
339*
340 ELSE
341*
342* Revert A (A is upper)
343*
344*
345* Revert PERMUTATIONS and IPIV
346*
347* Apply permutations to submatrices of upper part of A
348* in reverse factorization order where i increases from 1 to N
349*
350 i = 1
351 DO WHILE ( i.LE.n )
352 IF( ipiv( i ).GT.0 ) THEN
353*
354* 1-by-1 pivot interchange
355*
356* Swap rows i and IPIV(i) in A(1:i,N-i:N)
357*
358 ip = ipiv( i )
359 IF( i.LT.n ) THEN
360 IF( ip.NE.i ) THEN
361 CALL zswap( n-i, a( ip, i+1 ), lda,
362 \$ a( i, i+1 ), lda )
363 END IF
364 END IF
365*
366 ELSE
367*
368* 2-by-2 pivot interchange
369*
370* Swap rows i-1 and IPIV(i) in A(1:i,N-i:N)
371*
372 i = i + 1
373 ip = -ipiv( i )
374 IF( i.LT.n ) THEN
375 IF( ip.NE.(i-1) ) THEN
376 CALL zswap( n-i, a( ip, i+1 ), lda,
377 \$ a( i-1, i+1 ), lda )
378 END IF
379 END IF
380*
381* Convert IPIV
382* There is one interchange of rows i-1 and IPIV(i-1),
383* so this should be recorded in two consecutive entries
384* in IPIV format for *SYTRF
385*
386 ipiv( i ) = ipiv( i-1 )
387*
388 END IF
389 i = i + 1
390 END DO
391*
392* Revert VALUE
393* Assign superdiagonal entries of D from array E to
394* superdiagonal entries of A.
395*
396 i = n
397 DO WHILE ( i.GT.1 )
398 IF( ipiv( i ).LT.0 ) THEN
399 a( i-1, i ) = e( i )
400 i = i - 1
401 END IF
402 i = i - 1
403 END DO
404*
405* End A is UPPER
406*
407 END IF
408*
409 ELSE
410*
411* Begin A is LOWER
412*
413 IF ( convert ) THEN
414*
415* Convert A (A is lower)
416*
417*
418* Convert VALUE
419* Assign subdiagonal entries of D to array E and zero out
420* corresponding entries in input storage A
421*
422 i = 1
423 e( n ) = zero
424 DO WHILE ( i.LE.n )
425 IF( i.LT.n .AND. ipiv(i).LT.0 ) THEN
426 e( i ) = a( i+1, i )
427 e( i+1 ) = zero
428 a( i+1, i ) = zero
429 i = i + 1
430 ELSE
431 e( i ) = zero
432 END IF
433 i = i + 1
434 END DO
435*
436* Convert PERMUTATIONS and IPIV
437*
438* Apply permutations to submatrices of lower part of A
439* in factorization order where k increases from 1 to N
440*
441 i = 1
442 DO WHILE ( i.LE.n )
443 IF( ipiv( i ).GT.0 ) THEN
444*
445* 1-by-1 pivot interchange
446*
447* Swap rows i and IPIV(i) in A(i:N,1:i-1)
448*
449 ip = ipiv( i )
450 IF ( i.GT.1 ) THEN
451 IF( ip.NE.i ) THEN
452 CALL zswap( i-1, a( i, 1 ), lda,
453 \$ a( ip, 1 ), lda )
454 END IF
455 END IF
456*
457 ELSE
458*
459* 2-by-2 pivot interchange
460*
461* Swap rows i+1 and IPIV(i) in A(i:N,1:i-1)
462*
463 ip = -ipiv( i )
464 IF ( i.GT.1 ) THEN
465 IF( ip.NE.(i+1) ) THEN
466 CALL zswap( i-1, a( i+1, 1 ), lda,
467 \$ a( ip, 1 ), lda )
468 END IF
469 END IF
470*
471* Convert IPIV
472* There is no interchnge of rows i and and IPIV(i),
473* so this should be reflected in IPIV format for
474* *SYTRF_RK ( or *SYTRF_BK)
475*
476 ipiv( i ) = i
477*
478 i = i + 1
479*
480 END IF
481 i = i + 1
482 END DO
483*
484 ELSE
485*
486* Revert A (A is lower)
487*
488*
489* Revert PERMUTATIONS and IPIV
490*
491* Apply permutations to submatrices of lower part of A
492* in reverse factorization order where i decreases from N to 1
493*
494 i = n
495 DO WHILE ( i.GE.1 )
496 IF( ipiv( i ).GT.0 ) THEN
497*
498* 1-by-1 pivot interchange
499*
500* Swap rows i and IPIV(i) in A(i:N,1:i-1)
501*
502 ip = ipiv( i )
503 IF ( i.GT.1 ) THEN
504 IF( ip.NE.i ) THEN
505 CALL zswap( i-1, a( ip, 1 ), lda,
506 \$ a( i, 1 ), lda )
507 END IF
508 END IF
509*
510 ELSE
511*
512* 2-by-2 pivot interchange
513*
514* Swap rows i+1 and IPIV(i) in A(i:N,1:i-1)
515*
516 i = i - 1
517 ip = -ipiv( i )
518 IF ( i.GT.1 ) THEN
519 IF( ip.NE.(i+1) ) THEN
520 CALL zswap( i-1, a( ip, 1 ), lda,
521 \$ a( i+1, 1 ), lda )
522 END IF
523 END IF
524*
525* Convert IPIV
526* There is one interchange of rows i+1 and IPIV(i+1),
527* so this should be recorded in consecutive entries
528* in IPIV format for *SYTRF
529*
530 ipiv( i ) = ipiv( i+1 )
531*
532 END IF
533 i = i - 1
534 END DO
535*
536* Revert VALUE
537* Assign subdiagonal entries of D from array E to
538* subgiagonal entries of A.
539*
540 i = 1
541 DO WHILE ( i.LE.n-1 )
542 IF( ipiv( i ).LT.0 ) THEN
543 a( i + 1, i ) = e( i )
544 i = i + 1
545 END IF
546 i = i + 1
547 END DO
548*
549 END IF
550*
551* End A is LOWER
552*
553 END IF
554
555 RETURN
556*
557* End of ZSYCONVF
558*
559 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine zswap(N, ZX, INCX, ZY, INCY)
ZSWAP
Definition: zswap.f:81
subroutine zsyconvf(UPLO, WAY, N, A, LDA, E, IPIV, INFO)
ZSYCONVF
Definition: zsyconvf.f:209