1: *> \brief \b ZHETRS_ROOK computes the solution to a system of linear equations A * X = B for HE matrices using factorization obtained with one of the bounded diagonal pivoting methods (max 2 interchanges)
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZHETRS_ROOK + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhetrs_rook.f">
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/zhetrs_rook.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZHETRS_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
22: *
23: * .. Scalar Arguments ..
24: * CHARACTER UPLO
25: * INTEGER INFO, LDA, LDB, N, NRHS
26: * ..
27: * .. Array Arguments ..
28: * INTEGER IPIV( * )
29: * COMPLEX A( LDA, * ), B( LDB, * )
30: * ..
31: *
32: *
33: *> \par Purpose:
34: * =============
35: *>
36: *> \verbatim
37: *>
38: *> ZHETRS_ROOK solves a system of linear equations A*X = B with a complex
39: *> Hermitian matrix A using the factorization A = U*D*U**H or
40: *> A = L*D*L**H computed by ZHETRF_ROOK.
41: *> \endverbatim
42: *
43: * Arguments:
44: * ==========
45: *
46: *> \param[in] UPLO
47: *> \verbatim
48: *> UPLO is CHARACTER*1
49: *> Specifies whether the details of the factorization are stored
50: *> as an upper or lower triangular matrix.
51: *> = 'U': Upper triangular, form is A = U*D*U**H;
52: *> = 'L': Lower triangular, form is A = L*D*L**H.
53: *> \endverbatim
54: *>
55: *> \param[in] N
56: *> \verbatim
57: *> N is INTEGER
58: *> The order of the matrix A. N >= 0.
59: *> \endverbatim
60: *>
61: *> \param[in] NRHS
62: *> \verbatim
63: *> NRHS is INTEGER
64: *> The number of right hand sides, i.e., the number of columns
65: *> of the matrix B. NRHS >= 0.
66: *> \endverbatim
67: *>
68: *> \param[in] A
69: *> \verbatim
70: *> A is COMPLEX*16 array, dimension (LDA,N)
71: *> The block diagonal matrix D and the multipliers used to
72: *> obtain the factor U or L as computed by ZHETRF_ROOK.
73: *> \endverbatim
74: *>
75: *> \param[in] LDA
76: *> \verbatim
77: *> LDA is INTEGER
78: *> The leading dimension of the array A. LDA >= max(1,N).
79: *> \endverbatim
80: *>
81: *> \param[in] IPIV
82: *> \verbatim
83: *> IPIV is INTEGER array, dimension (N)
84: *> Details of the interchanges and the block structure of D
85: *> as determined by ZHETRF_ROOK.
86: *> \endverbatim
87: *>
88: *> \param[in,out] B
89: *> \verbatim
90: *> B is COMPLEX*16 array, dimension (LDB,NRHS)
91: *> On entry, the right hand side matrix B.
92: *> On exit, the solution matrix X.
93: *> \endverbatim
94: *>
95: *> \param[in] LDB
96: *> \verbatim
97: *> LDB is INTEGER
98: *> The leading dimension of the array B. LDB >= max(1,N).
99: *> \endverbatim
100: *>
101: *> \param[out] INFO
102: *> \verbatim
103: *> INFO is INTEGER
104: *> = 0: successful exit
105: *> < 0: if INFO = -i, the i-th argument had an illegal value
106: *> \endverbatim
107: *
108: * Authors:
109: * ========
110: *
111: *> \author Univ. of Tennessee
112: *> \author Univ. of California Berkeley
113: *> \author Univ. of Colorado Denver
114: *> \author NAG Ltd.
115: *
116: *> \ingroup complex16HEcomputational
117: *
118: *> \par Contributors:
119: * ==================
120: *>
121: *> \verbatim
122: *>
123: *> November 2013, Igor Kozachenko,
124: *> Computer Science Division,
125: *> University of California, Berkeley
126: *>
127: *> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
128: *> School of Mathematics,
129: *> University of Manchester
130: *>
131: *> \endverbatim
132: *
133: * =====================================================================
134: SUBROUTINE ZHETRS_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
135: $ INFO )
136: *
137: * -- LAPACK computational routine --
138: * -- LAPACK is a software package provided by Univ. of Tennessee, --
139: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
140: *
141: * .. Scalar Arguments ..
142: CHARACTER UPLO
143: INTEGER INFO, LDA, LDB, N, NRHS
144: * ..
145: * .. Array Arguments ..
146: INTEGER IPIV( * )
147: COMPLEX*16 A( LDA, * ), B( LDB, * )
148: * ..
149: *
150: * =====================================================================
151: *
152: * .. Parameters ..
153: COMPLEX*16 ONE
154: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
155: * ..
156: * .. Local Scalars ..
157: LOGICAL UPPER
158: INTEGER J, K, KP
159: DOUBLE PRECISION S
160: COMPLEX*16 AK, AKM1, AKM1K, BK, BKM1, DENOM
161: * ..
162: * .. External Functions ..
163: LOGICAL LSAME
164: EXTERNAL LSAME
165: * ..
166: * .. External Subroutines ..
167: EXTERNAL ZGEMV, ZGERU, ZLACGV, ZDSCAL, ZSWAP, XERBLA
168: * ..
169: * .. Intrinsic Functions ..
170: INTRINSIC DCONJG, MAX, DBLE
171: * ..
172: * .. Executable Statements ..
173: *
174: INFO = 0
175: UPPER = LSAME( UPLO, 'U' )
176: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
177: INFO = -1
178: ELSE IF( N.LT.0 ) THEN
179: INFO = -2
180: ELSE IF( NRHS.LT.0 ) THEN
181: INFO = -3
182: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
183: INFO = -5
184: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
185: INFO = -8
186: END IF
187: IF( INFO.NE.0 ) THEN
188: CALL XERBLA( 'ZHETRS_ROOK', -INFO )
189: RETURN
190: END IF
191: *
192: * Quick return if possible
193: *
194: IF( N.EQ.0 .OR. NRHS.EQ.0 )
195: $ RETURN
196: *
197: IF( UPPER ) THEN
198: *
199: * Solve A*X = B, where A = U*D*U**H.
200: *
201: * First solve U*D*X = B, overwriting B with X.
202: *
203: * K is the main loop index, decreasing from N to 1 in steps of
204: * 1 or 2, depending on the size of the diagonal blocks.
205: *
206: K = N
207: 10 CONTINUE
208: *
209: * If K < 1, exit from loop.
210: *
211: IF( K.LT.1 )
212: $ GO TO 30
213: *
214: IF( IPIV( K ).GT.0 ) THEN
215: *
216: * 1 x 1 diagonal block
217: *
218: * Interchange rows K and IPIV(K).
219: *
220: KP = IPIV( K )
221: IF( KP.NE.K )
222: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
223: *
224: * Multiply by inv(U(K)), where U(K) is the transformation
225: * stored in column K of A.
226: *
227: CALL ZGERU( K-1, NRHS, -ONE, A( 1, K ), 1, B( K, 1 ), LDB,
228: $ B( 1, 1 ), LDB )
229: *
230: * Multiply by the inverse of the diagonal block.
231: *
232: S = DBLE( ONE ) / DBLE( A( K, K ) )
233: CALL ZDSCAL( NRHS, S, B( K, 1 ), LDB )
234: K = K - 1
235: ELSE
236: *
237: * 2 x 2 diagonal block
238: *
239: * Interchange rows K and -IPIV(K), then K-1 and -IPIV(K-1)
240: *
241: KP = -IPIV( K )
242: IF( KP.NE.K )
243: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
244: *
245: KP = -IPIV( K-1)
246: IF( KP.NE.K-1 )
247: $ CALL ZSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), LDB )
248: *
249: * Multiply by inv(U(K)), where U(K) is the transformation
250: * stored in columns K-1 and K of A.
251: *
252: CALL ZGERU( K-2, NRHS, -ONE, A( 1, K ), 1, B( K, 1 ), LDB,
253: $ B( 1, 1 ), LDB )
254: CALL ZGERU( K-2, NRHS, -ONE, A( 1, K-1 ), 1, B( K-1, 1 ),
255: $ LDB, B( 1, 1 ), LDB )
256: *
257: * Multiply by the inverse of the diagonal block.
258: *
259: AKM1K = A( K-1, K )
260: AKM1 = A( K-1, K-1 ) / AKM1K
261: AK = A( K, K ) / DCONJG( AKM1K )
262: DENOM = AKM1*AK - ONE
263: DO 20 J = 1, NRHS
264: BKM1 = B( K-1, J ) / AKM1K
265: BK = B( K, J ) / DCONJG( AKM1K )
266: B( K-1, J ) = ( AK*BKM1-BK ) / DENOM
267: B( K, J ) = ( AKM1*BK-BKM1 ) / DENOM
268: 20 CONTINUE
269: K = K - 2
270: END IF
271: *
272: GO TO 10
273: 30 CONTINUE
274: *
275: * Next solve U**H *X = B, overwriting B with X.
276: *
277: * K is the main loop index, increasing from 1 to N in steps of
278: * 1 or 2, depending on the size of the diagonal blocks.
279: *
280: K = 1
281: 40 CONTINUE
282: *
283: * If K > N, exit from loop.
284: *
285: IF( K.GT.N )
286: $ GO TO 50
287: *
288: IF( IPIV( K ).GT.0 ) THEN
289: *
290: * 1 x 1 diagonal block
291: *
292: * Multiply by inv(U**H(K)), where U(K) is the transformation
293: * stored in column K of A.
294: *
295: IF( K.GT.1 ) THEN
296: CALL ZLACGV( NRHS, B( K, 1 ), LDB )
297: CALL ZGEMV( 'Conjugate transpose', K-1, NRHS, -ONE, B,
298: $ LDB, A( 1, K ), 1, ONE, B( K, 1 ), LDB )
299: CALL ZLACGV( NRHS, B( K, 1 ), LDB )
300: END IF
301: *
302: * Interchange rows K and IPIV(K).
303: *
304: KP = IPIV( K )
305: IF( KP.NE.K )
306: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
307: K = K + 1
308: ELSE
309: *
310: * 2 x 2 diagonal block
311: *
312: * Multiply by inv(U**H(K+1)), where U(K+1) is the transformation
313: * stored in columns K and K+1 of A.
314: *
315: IF( K.GT.1 ) THEN
316: CALL ZLACGV( NRHS, B( K, 1 ), LDB )
317: CALL ZGEMV( 'Conjugate transpose', K-1, NRHS, -ONE, B,
318: $ LDB, A( 1, K ), 1, ONE, B( K, 1 ), LDB )
319: CALL ZLACGV( NRHS, B( K, 1 ), LDB )
320: *
321: CALL ZLACGV( NRHS, B( K+1, 1 ), LDB )
322: CALL ZGEMV( 'Conjugate transpose', K-1, NRHS, -ONE, B,
323: $ LDB, A( 1, K+1 ), 1, ONE, B( K+1, 1 ), LDB )
324: CALL ZLACGV( NRHS, B( K+1, 1 ), LDB )
325: END IF
326: *
327: * Interchange rows K and -IPIV(K), then K+1 and -IPIV(K+1)
328: *
329: KP = -IPIV( K )
330: IF( KP.NE.K )
331: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
332: *
333: KP = -IPIV( K+1 )
334: IF( KP.NE.K+1 )
335: $ CALL ZSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), LDB )
336: *
337: K = K + 2
338: END IF
339: *
340: GO TO 40
341: 50 CONTINUE
342: *
343: ELSE
344: *
345: * Solve A*X = B, where A = L*D*L**H.
346: *
347: * First solve L*D*X = B, overwriting B with X.
348: *
349: * K is the main loop index, increasing from 1 to N in steps of
350: * 1 or 2, depending on the size of the diagonal blocks.
351: *
352: K = 1
353: 60 CONTINUE
354: *
355: * If K > N, exit from loop.
356: *
357: IF( K.GT.N )
358: $ GO TO 80
359: *
360: IF( IPIV( K ).GT.0 ) THEN
361: *
362: * 1 x 1 diagonal block
363: *
364: * Interchange rows K and IPIV(K).
365: *
366: KP = IPIV( K )
367: IF( KP.NE.K )
368: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
369: *
370: * Multiply by inv(L(K)), where L(K) is the transformation
371: * stored in column K of A.
372: *
373: IF( K.LT.N )
374: $ CALL ZGERU( N-K, NRHS, -ONE, A( K+1, K ), 1, B( K, 1 ),
375: $ LDB, B( K+1, 1 ), LDB )
376: *
377: * Multiply by the inverse of the diagonal block.
378: *
379: S = DBLE( ONE ) / DBLE( A( K, K ) )
380: CALL ZDSCAL( NRHS, S, B( K, 1 ), LDB )
381: K = K + 1
382: ELSE
383: *
384: * 2 x 2 diagonal block
385: *
386: * Interchange rows K and -IPIV(K), then K+1 and -IPIV(K+1)
387: *
388: KP = -IPIV( K )
389: IF( KP.NE.K )
390: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
391: *
392: KP = -IPIV( K+1 )
393: IF( KP.NE.K+1 )
394: $ CALL ZSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), LDB )
395: *
396: * Multiply by inv(L(K)), where L(K) is the transformation
397: * stored in columns K and K+1 of A.
398: *
399: IF( K.LT.N-1 ) THEN
400: CALL ZGERU( N-K-1, NRHS, -ONE, A( K+2, K ), 1, B( K, 1 ),
401: $ LDB, B( K+2, 1 ), LDB )
402: CALL ZGERU( N-K-1, NRHS, -ONE, A( K+2, K+1 ), 1,
403: $ B( K+1, 1 ), LDB, B( K+2, 1 ), LDB )
404: END IF
405: *
406: * Multiply by the inverse of the diagonal block.
407: *
408: AKM1K = A( K+1, K )
409: AKM1 = A( K, K ) / DCONJG( AKM1K )
410: AK = A( K+1, K+1 ) / AKM1K
411: DENOM = AKM1*AK - ONE
412: DO 70 J = 1, NRHS
413: BKM1 = B( K, J ) / DCONJG( AKM1K )
414: BK = B( K+1, J ) / AKM1K
415: B( K, J ) = ( AK*BKM1-BK ) / DENOM
416: B( K+1, J ) = ( AKM1*BK-BKM1 ) / DENOM
417: 70 CONTINUE
418: K = K + 2
419: END IF
420: *
421: GO TO 60
422: 80 CONTINUE
423: *
424: * Next solve L**H *X = B, overwriting B with X.
425: *
426: * K is the main loop index, decreasing from N to 1 in steps of
427: * 1 or 2, depending on the size of the diagonal blocks.
428: *
429: K = N
430: 90 CONTINUE
431: *
432: * If K < 1, exit from loop.
433: *
434: IF( K.LT.1 )
435: $ GO TO 100
436: *
437: IF( IPIV( K ).GT.0 ) THEN
438: *
439: * 1 x 1 diagonal block
440: *
441: * Multiply by inv(L**H(K)), where L(K) is the transformation
442: * stored in column K of A.
443: *
444: IF( K.LT.N ) THEN
445: CALL ZLACGV( NRHS, B( K, 1 ), LDB )
446: CALL ZGEMV( 'Conjugate transpose', N-K, NRHS, -ONE,
447: $ B( K+1, 1 ), LDB, A( K+1, K ), 1, ONE,
448: $ B( K, 1 ), LDB )
449: CALL ZLACGV( NRHS, B( K, 1 ), LDB )
450: END IF
451: *
452: * Interchange rows K and IPIV(K).
453: *
454: KP = IPIV( K )
455: IF( KP.NE.K )
456: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
457: K = K - 1
458: ELSE
459: *
460: * 2 x 2 diagonal block
461: *
462: * Multiply by inv(L**H(K-1)), where L(K-1) is the transformation
463: * stored in columns K-1 and K of A.
464: *
465: IF( K.LT.N ) THEN
466: CALL ZLACGV( NRHS, B( K, 1 ), LDB )
467: CALL ZGEMV( 'Conjugate transpose', N-K, NRHS, -ONE,
468: $ B( K+1, 1 ), LDB, A( K+1, K ), 1, ONE,
469: $ B( K, 1 ), LDB )
470: CALL ZLACGV( NRHS, B( K, 1 ), LDB )
471: *
472: CALL ZLACGV( NRHS, B( K-1, 1 ), LDB )
473: CALL ZGEMV( 'Conjugate transpose', N-K, NRHS, -ONE,
474: $ B( K+1, 1 ), LDB, A( K+1, K-1 ), 1, ONE,
475: $ B( K-1, 1 ), LDB )
476: CALL ZLACGV( NRHS, B( K-1, 1 ), LDB )
477: END IF
478: *
479: * Interchange rows K and -IPIV(K), then K-1 and -IPIV(K-1)
480: *
481: KP = -IPIV( K )
482: IF( KP.NE.K )
483: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
484: *
485: KP = -IPIV( K-1 )
486: IF( KP.NE.K-1 )
487: $ CALL ZSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), LDB )
488: *
489: K = K - 2
490: END IF
491: *
492: GO TO 90
493: 100 CONTINUE
494: END IF
495: *
496: RETURN
497: *
498: * End of ZHETRS_ROOK
499: *
500: END
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