1: *> \brief \b ZSYCONVF
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
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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
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