 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ zsyconvf()

 subroutine zsyconvf ( character UPLO, character WAY, integer N, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( * ) E, integer, dimension( * ) IPIV, integer INFO )

ZSYCONVF

Purpose:
``` If parameter WAY = 'C':
ZSYCONVF converts the factorization output format used in
ZSYTRF provided on entry in parameter A into the factorization
output format used in ZSYTRF_RK (or ZSYTRF_BK) that is stored
on exit in parameters A and E. It also converts in place details of
the intechanges stored in IPIV from the format used in ZSYTRF into
the format used in ZSYTRF_RK (or ZSYTRF_BK).

If parameter WAY = 'R':
ZSYCONVF performs the conversion in reverse direction, i.e.
converts the factorization output format used in ZSYTRF_RK
(or ZSYTRF_BK) provided on entry in parameters A and E into
the factorization output format used in ZSYTRF that is stored
on exit in parameter A. It also converts in place details of
the intechanges stored in IPIV from the format used in ZSYTRF_RK
(or ZSYTRF_BK) into the format used in ZSYTRF.

ZSYCONVF can also convert in Hermitian matrix case, i.e. between
formats used in ZHETRF and ZHETRF_RK (or ZHETRF_BK).```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 Specifies whether the details of the factorization are stored as an upper or lower triangular matrix A. = 'U': Upper triangular = 'L': Lower triangular``` [in] WAY ``` WAY is CHARACTER*1 = 'C': Convert = 'R': Revert``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in,out] A ``` A is COMPLEX*16 array, dimension (LDA,N) 1) If WAY ='C': On entry, contains factorization details in format used in ZSYTRF: a) all elements of the symmetric block diagonal matrix D on the diagonal of A and on superdiagonal (or subdiagonal) of A, and b) If UPLO = 'U': multipliers used to obtain factor U in the superdiagonal part of A. If UPLO = 'L': multipliers used to obtain factor L in the superdiagonal part of A. On exit, contains factorization details in format used in ZSYTRF_RK or ZSYTRF_BK: a) ONLY diagonal elements of the symmetric block diagonal matrix D on the diagonal of A, i.e. D(k,k) = A(k,k); (superdiagonal (or subdiagonal) elements of D are stored on exit in array E), and b) If UPLO = 'U': factor U in the superdiagonal part of A. If UPLO = 'L': factor L in the subdiagonal part of A. 2) If WAY = 'R': On entry, contains factorization details in format used in ZSYTRF_RK or ZSYTRF_BK: a) ONLY diagonal elements of the symmetric block diagonal matrix D on the diagonal of A, i.e. D(k,k) = A(k,k); (superdiagonal (or subdiagonal) elements of D are stored on exit in array E), and b) If UPLO = 'U': factor U in the superdiagonal part of A. If UPLO = 'L': factor L in the subdiagonal part of A. On exit, contains factorization details in format used in ZSYTRF: a) all elements of the symmetric block diagonal matrix D on the diagonal of A and on superdiagonal (or subdiagonal) of A, and b) If UPLO = 'U': multipliers used to obtain factor U in the superdiagonal part of A. If UPLO = 'L': multipliers used to obtain factor L in the superdiagonal part of A.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [in,out] E ``` E is COMPLEX*16 array, dimension (N) 1) If WAY ='C': On entry, just a workspace. On exit, contains the superdiagonal (or subdiagonal) elements of the symmetric block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks, where If UPLO = 'U': E(i) = D(i-1,i), i=2:N, E(1) is set to 0; If UPLO = 'L': E(i) = D(i+1,i), i=1:N-1, E(N) is set to 0. 2) If WAY = 'R': On entry, contains the superdiagonal (or subdiagonal) elements of the symmetric block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks, where If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced; If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced. On exit, is not changed``` [in,out] IPIV ``` IPIV is INTEGER array, dimension (N) 1) If WAY ='C': On entry, details of the interchanges and the block structure of D in the format used in ZSYTRF. On exit, details of the interchanges and the block structure of D in the format used in ZSYTRF_RK ( or ZSYTRF_BK). 1) If WAY ='R': On entry, details of the interchanges and the block structure of D in the format used in ZSYTRF_RK ( or ZSYTRF_BK). On exit, details of the interchanges and the block structure of D in the format used in ZSYTRF.``` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value```
Contributors:
```  November 2017,  Igor Kozachenko,
Computer Science Division,
University of California, Berkeley```

Definition at line 208 of file zsyconvf.f.

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*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine zswap(N, ZX, INCX, ZY, INCY)
ZSWAP
Definition: zswap.f:81
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