LAPACK  3.9.0
LAPACK: Linear Algebra PACKage
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 coverts 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 coverts 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 *> \date November 2017
196 *
197 *> \ingroup complex16SYcomputational
198 *
199 *> \par Contributors:
200 * ==================
201 *>
202 *> \verbatim
203 *>
204 *> November 2017, Igor Kozachenko,
205 *> Computer Science Division,
206 *> University of California, Berkeley
207 *>
208 *> \endverbatim
209 * =====================================================================
210  SUBROUTINE zsyconvf( UPLO, WAY, N, A, LDA, E, IPIV, INFO )
211 *
212 * -- LAPACK computational routine (version 3.8.0) --
213 * -- LAPACK is a software package provided by Univ. of Tennessee, --
214 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
215 * November 2017
216 *
217 * .. Scalar Arguments ..
218  CHARACTER UPLO, WAY
219  INTEGER INFO, LDA, N
220 * ..
221 * .. Array Arguments ..
222  INTEGER IPIV( * )
223  COMPLEX*16 A( LDA, * ), E( * )
224 * ..
225 *
226 * =====================================================================
227 *
228 * .. Parameters ..
229  COMPLEX*16 ZERO
230  parameter( zero = ( 0.0d+0, 0.0d+0 ) )
231 * ..
232 * .. External Functions ..
233  LOGICAL LSAME
234  EXTERNAL lsame
235 *
236 * .. External Subroutines ..
237  EXTERNAL zswap, xerbla
238 * .. Local Scalars ..
239  LOGICAL UPPER, CONVERT
240  INTEGER I, IP
241 * ..
242 * .. Executable Statements ..
243 *
244  info = 0
245  upper = lsame( uplo, 'U' )
246  convert = lsame( way, 'C' )
247  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
248  info = -1
249  ELSE IF( .NOT.convert .AND. .NOT.lsame( way, 'R' ) ) THEN
250  info = -2
251  ELSE IF( n.LT.0 ) THEN
252  info = -3
253  ELSE IF( lda.LT.max( 1, n ) ) THEN
254  info = -5
255 
256  END IF
257  IF( info.NE.0 ) THEN
258  CALL xerbla( 'ZSYCONVF', -info )
259  RETURN
260  END IF
261 *
262 * Quick return if possible
263 *
264  IF( n.EQ.0 )
265  $ RETURN
266 *
267  IF( upper ) THEN
268 *
269 * Begin A is UPPER
270 *
271  IF ( convert ) THEN
272 *
273 * Convert A (A is upper)
274 *
275 *
276 * Convert VALUE
277 *
278 * Assign superdiagonal entries of D to array E and zero out
279 * corresponding entries in input storage A
280 *
281  i = n
282  e( 1 ) = zero
283  DO WHILE ( i.GT.1 )
284  IF( ipiv( i ).LT.0 ) THEN
285  e( i ) = a( i-1, i )
286  e( i-1 ) = zero
287  a( i-1, i ) = zero
288  i = i - 1
289  ELSE
290  e( i ) = zero
291  END IF
292  i = i - 1
293  END DO
294 *
295 * Convert PERMUTATIONS and IPIV
296 *
297 * Apply permutations to submatrices of upper part of A
298 * in factorization order where i decreases from N to 1
299 *
300  i = n
301  DO WHILE ( i.GE.1 )
302  IF( ipiv( i ).GT.0 ) THEN
303 *
304 * 1-by-1 pivot interchange
305 *
306 * Swap rows i and IPIV(i) in A(1:i,N-i:N)
307 *
308  ip = ipiv( i )
309  IF( i.LT.n ) THEN
310  IF( ip.NE.i ) THEN
311  CALL zswap( n-i, a( i, i+1 ), lda,
312  $ a( ip, i+1 ), lda )
313  END IF
314  END IF
315 *
316  ELSE
317 *
318 * 2-by-2 pivot interchange
319 *
320 * Swap rows i-1 and IPIV(i) in A(1:i,N-i:N)
321 *
322  ip = -ipiv( i )
323  IF( i.LT.n ) THEN
324  IF( ip.NE.(i-1) ) THEN
325  CALL zswap( n-i, a( i-1, i+1 ), lda,
326  $ a( ip, i+1 ), lda )
327  END IF
328  END IF
329 *
330 * Convert IPIV
331 * There is no interchnge of rows i and and IPIV(i),
332 * so this should be reflected in IPIV format for
333 * *SYTRF_RK ( or *SYTRF_BK)
334 *
335  ipiv( i ) = i
336 *
337  i = i - 1
338 *
339  END IF
340  i = i - 1
341  END DO
342 *
343  ELSE
344 *
345 * Revert A (A is upper)
346 *
347 *
348 * Revert PERMUTATIONS and IPIV
349 *
350 * Apply permutations to submatrices of upper part of A
351 * in reverse factorization order where i increases from 1 to N
352 *
353  i = 1
354  DO WHILE ( i.LE.n )
355  IF( ipiv( i ).GT.0 ) THEN
356 *
357 * 1-by-1 pivot interchange
358 *
359 * Swap rows i and IPIV(i) in A(1:i,N-i:N)
360 *
361  ip = ipiv( i )
362  IF( i.LT.n ) THEN
363  IF( ip.NE.i ) THEN
364  CALL zswap( n-i, a( ip, i+1 ), lda,
365  $ a( i, i+1 ), lda )
366  END IF
367  END IF
368 *
369  ELSE
370 *
371 * 2-by-2 pivot interchange
372 *
373 * Swap rows i-1 and IPIV(i) in A(1:i,N-i:N)
374 *
375  i = i + 1
376  ip = -ipiv( i )
377  IF( i.LT.n ) THEN
378  IF( ip.NE.(i-1) ) THEN
379  CALL zswap( n-i, a( ip, i+1 ), lda,
380  $ a( i-1, i+1 ), lda )
381  END IF
382  END IF
383 *
384 * Convert IPIV
385 * There is one interchange of rows i-1 and IPIV(i-1),
386 * so this should be recorded in two consecutive entries
387 * in IPIV format for *SYTRF
388 *
389  ipiv( i ) = ipiv( i-1 )
390 *
391  END IF
392  i = i + 1
393  END DO
394 *
395 * Revert VALUE
396 * Assign superdiagonal entries of D from array E to
397 * superdiagonal entries of A.
398 *
399  i = n
400  DO WHILE ( i.GT.1 )
401  IF( ipiv( i ).LT.0 ) THEN
402  a( i-1, i ) = e( i )
403  i = i - 1
404  END IF
405  i = i - 1
406  END DO
407 *
408 * End A is UPPER
409 *
410  END IF
411 *
412  ELSE
413 *
414 * Begin A is LOWER
415 *
416  IF ( convert ) THEN
417 *
418 * Convert A (A is lower)
419 *
420 *
421 * Convert VALUE
422 * Assign subdiagonal entries of D to array E and zero out
423 * corresponding entries in input storage A
424 *
425  i = 1
426  e( n ) = zero
427  DO WHILE ( i.LE.n )
428  IF( i.LT.n .AND. ipiv(i).LT.0 ) THEN
429  e( i ) = a( i+1, i )
430  e( i+1 ) = zero
431  a( i+1, i ) = zero
432  i = i + 1
433  ELSE
434  e( i ) = zero
435  END IF
436  i = i + 1
437  END DO
438 *
439 * Convert PERMUTATIONS and IPIV
440 *
441 * Apply permutations to submatrices of lower part of A
442 * in factorization order where k increases from 1 to N
443 *
444  i = 1
445  DO WHILE ( i.LE.n )
446  IF( ipiv( i ).GT.0 ) THEN
447 *
448 * 1-by-1 pivot interchange
449 *
450 * Swap rows i and IPIV(i) in A(i:N,1:i-1)
451 *
452  ip = ipiv( i )
453  IF ( i.GT.1 ) THEN
454  IF( ip.NE.i ) THEN
455  CALL zswap( i-1, a( i, 1 ), lda,
456  $ a( ip, 1 ), lda )
457  END IF
458  END IF
459 *
460  ELSE
461 *
462 * 2-by-2 pivot interchange
463 *
464 * Swap rows i+1 and IPIV(i) in A(i:N,1:i-1)
465 *
466  ip = -ipiv( i )
467  IF ( i.GT.1 ) THEN
468  IF( ip.NE.(i+1) ) THEN
469  CALL zswap( i-1, a( i+1, 1 ), lda,
470  $ a( ip, 1 ), lda )
471  END IF
472  END IF
473 *
474 * Convert IPIV
475 * There is no interchnge of rows i and and IPIV(i),
476 * so this should be reflected in IPIV format for
477 * *SYTRF_RK ( or *SYTRF_BK)
478 *
479  ipiv( i ) = i
480 *
481  i = i + 1
482 *
483  END IF
484  i = i + 1
485  END DO
486 *
487  ELSE
488 *
489 * Revert A (A is lower)
490 *
491 *
492 * Revert PERMUTATIONS and IPIV
493 *
494 * Apply permutations to submatrices of lower part of A
495 * in reverse factorization order where i decreases from N to 1
496 *
497  i = n
498  DO WHILE ( i.GE.1 )
499  IF( ipiv( i ).GT.0 ) THEN
500 *
501 * 1-by-1 pivot interchange
502 *
503 * Swap rows i and IPIV(i) in A(i:N,1:i-1)
504 *
505  ip = ipiv( i )
506  IF ( i.GT.1 ) THEN
507  IF( ip.NE.i ) THEN
508  CALL zswap( i-1, a( ip, 1 ), lda,
509  $ a( i, 1 ), lda )
510  END IF
511  END IF
512 *
513  ELSE
514 *
515 * 2-by-2 pivot interchange
516 *
517 * Swap rows i+1 and IPIV(i) in A(i:N,1:i-1)
518 *
519  i = i - 1
520  ip = -ipiv( i )
521  IF ( i.GT.1 ) THEN
522  IF( ip.NE.(i+1) ) THEN
523  CALL zswap( i-1, a( ip, 1 ), lda,
524  $ a( i+1, 1 ), lda )
525  END IF
526  END IF
527 *
528 * Convert IPIV
529 * There is one interchange of rows i+1 and IPIV(i+1),
530 * so this should be recorded in consecutive entries
531 * in IPIV format for *SYTRF
532 *
533  ipiv( i ) = ipiv( i+1 )
534 *
535  END IF
536  i = i - 1
537  END DO
538 *
539 * Revert VALUE
540 * Assign subdiagonal entries of D from array E to
541 * subgiagonal entries of A.
542 *
543  i = 1
544  DO WHILE ( i.LE.n-1 )
545  IF( ipiv( i ).LT.0 ) THEN
546  a( i + 1, i ) = e( i )
547  i = i + 1
548  END IF
549  i = i + 1
550  END DO
551 *
552  END IF
553 *
554 * End A is LOWER
555 *
556  END IF
557 
558  RETURN
559 *
560 * End of ZSYCONVF
561 *
562  END
xerbla
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
zswap
subroutine zswap(N, ZX, INCX, ZY, INCY)
ZSWAP
Definition: zswap.f:83
zsyconvf
subroutine zsyconvf(UPLO, WAY, N, A, LDA, E, IPIV, INFO)
ZSYCONVF
Definition: zsyconvf.f:211