1: *> \brief \b ZHPTRS
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
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15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZHPTRS( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )
22: *
23: * .. Scalar Arguments ..
24: * CHARACTER UPLO
25: * INTEGER INFO, LDB, N, NRHS
26: * ..
27: * .. Array Arguments ..
28: * INTEGER IPIV( * )
29: * COMPLEX*16 AP( * ), B( LDB, * )
30: * ..
31: *
32: *
33: *> \par Purpose:
34: * =============
35: *>
36: *> \verbatim
37: *>
38: *> ZHPTRS solves a system of linear equations A*X = B with a complex
39: *> Hermitian matrix A stored in packed format using the factorization
40: *> A = U*D*U**H or A = L*D*L**H computed by ZHPTRF.
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] AP
69: *> \verbatim
70: *> AP is COMPLEX*16 array, dimension (N*(N+1)/2)
71: *> The block diagonal matrix D and the multipliers used to
72: *> obtain the factor U or L as computed by ZHPTRF, stored as a
73: *> packed triangular matrix.
74: *> \endverbatim
75: *>
76: *> \param[in] IPIV
77: *> \verbatim
78: *> IPIV is INTEGER array, dimension (N)
79: *> Details of the interchanges and the block structure of D
80: *> as determined by ZHPTRF.
81: *> \endverbatim
82: *>
83: *> \param[in,out] B
84: *> \verbatim
85: *> B is COMPLEX*16 array, dimension (LDB,NRHS)
86: *> On entry, the right hand side matrix B.
87: *> On exit, the solution matrix X.
88: *> \endverbatim
89: *>
90: *> \param[in] LDB
91: *> \verbatim
92: *> LDB is INTEGER
93: *> The leading dimension of the array B. LDB >= max(1,N).
94: *> \endverbatim
95: *>
96: *> \param[out] INFO
97: *> \verbatim
98: *> INFO is INTEGER
99: *> = 0: successful exit
100: *> < 0: if INFO = -i, the i-th argument had an illegal value
101: *> \endverbatim
102: *
103: * Authors:
104: * ========
105: *
106: *> \author Univ. of Tennessee
107: *> \author Univ. of California Berkeley
108: *> \author Univ. of Colorado Denver
109: *> \author NAG Ltd.
110: *
111: *> \ingroup complex16OTHERcomputational
112: *
113: * =====================================================================
114: SUBROUTINE ZHPTRS( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )
115: *
116: * -- LAPACK computational routine --
117: * -- LAPACK is a software package provided by Univ. of Tennessee, --
118: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
119: *
120: * .. Scalar Arguments ..
121: CHARACTER UPLO
122: INTEGER INFO, LDB, N, NRHS
123: * ..
124: * .. Array Arguments ..
125: INTEGER IPIV( * )
126: COMPLEX*16 AP( * ), B( LDB, * )
127: * ..
128: *
129: * =====================================================================
130: *
131: * .. Parameters ..
132: COMPLEX*16 ONE
133: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
134: * ..
135: * .. Local Scalars ..
136: LOGICAL UPPER
137: INTEGER J, K, KC, KP
138: DOUBLE PRECISION S
139: COMPLEX*16 AK, AKM1, AKM1K, BK, BKM1, DENOM
140: * ..
141: * .. External Functions ..
142: LOGICAL LSAME
143: EXTERNAL LSAME
144: * ..
145: * .. External Subroutines ..
146: EXTERNAL XERBLA, ZDSCAL, ZGEMV, ZGERU, ZLACGV, ZSWAP
147: * ..
148: * .. Intrinsic Functions ..
149: INTRINSIC DBLE, DCONJG, MAX
150: * ..
151: * .. Executable Statements ..
152: *
153: INFO = 0
154: UPPER = LSAME( UPLO, 'U' )
155: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
156: INFO = -1
157: ELSE IF( N.LT.0 ) THEN
158: INFO = -2
159: ELSE IF( NRHS.LT.0 ) THEN
160: INFO = -3
161: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
162: INFO = -7
163: END IF
164: IF( INFO.NE.0 ) THEN
165: CALL XERBLA( 'ZHPTRS', -INFO )
166: RETURN
167: END IF
168: *
169: * Quick return if possible
170: *
171: IF( N.EQ.0 .OR. NRHS.EQ.0 )
172: $ RETURN
173: *
174: IF( UPPER ) THEN
175: *
176: * Solve A*X = B, where A = U*D*U**H.
177: *
178: * First solve U*D*X = B, overwriting B with X.
179: *
180: * K is the main loop index, decreasing from N to 1 in steps of
181: * 1 or 2, depending on the size of the diagonal blocks.
182: *
183: K = N
184: KC = N*( N+1 ) / 2 + 1
185: 10 CONTINUE
186: *
187: * If K < 1, exit from loop.
188: *
189: IF( K.LT.1 )
190: $ GO TO 30
191: *
192: KC = KC - K
193: IF( IPIV( K ).GT.0 ) THEN
194: *
195: * 1 x 1 diagonal block
196: *
197: * Interchange rows K and IPIV(K).
198: *
199: KP = IPIV( K )
200: IF( KP.NE.K )
201: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
202: *
203: * Multiply by inv(U(K)), where U(K) is the transformation
204: * stored in column K of A.
205: *
206: CALL ZGERU( K-1, NRHS, -ONE, AP( KC ), 1, B( K, 1 ), LDB,
207: $ B( 1, 1 ), LDB )
208: *
209: * Multiply by the inverse of the diagonal block.
210: *
211: S = DBLE( ONE ) / DBLE( AP( KC+K-1 ) )
212: CALL ZDSCAL( NRHS, S, B( K, 1 ), LDB )
213: K = K - 1
214: ELSE
215: *
216: * 2 x 2 diagonal block
217: *
218: * Interchange rows K-1 and -IPIV(K).
219: *
220: KP = -IPIV( K )
221: IF( KP.NE.K-1 )
222: $ CALL ZSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), LDB )
223: *
224: * Multiply by inv(U(K)), where U(K) is the transformation
225: * stored in columns K-1 and K of A.
226: *
227: CALL ZGERU( K-2, NRHS, -ONE, AP( KC ), 1, B( K, 1 ), LDB,
228: $ B( 1, 1 ), LDB )
229: CALL ZGERU( K-2, NRHS, -ONE, AP( KC-( K-1 ) ), 1,
230: $ B( K-1, 1 ), LDB, B( 1, 1 ), LDB )
231: *
232: * Multiply by the inverse of the diagonal block.
233: *
234: AKM1K = AP( KC+K-2 )
235: AKM1 = AP( KC-1 ) / AKM1K
236: AK = AP( KC+K-1 ) / DCONJG( AKM1K )
237: DENOM = AKM1*AK - ONE
238: DO 20 J = 1, NRHS
239: BKM1 = B( K-1, J ) / AKM1K
240: BK = B( K, J ) / DCONJG( AKM1K )
241: B( K-1, J ) = ( AK*BKM1-BK ) / DENOM
242: B( K, J ) = ( AKM1*BK-BKM1 ) / DENOM
243: 20 CONTINUE
244: KC = KC - K + 1
245: K = K - 2
246: END IF
247: *
248: GO TO 10
249: 30 CONTINUE
250: *
251: * Next solve U**H *X = B, overwriting B with X.
252: *
253: * K is the main loop index, increasing from 1 to N in steps of
254: * 1 or 2, depending on the size of the diagonal blocks.
255: *
256: K = 1
257: KC = 1
258: 40 CONTINUE
259: *
260: * If K > N, exit from loop.
261: *
262: IF( K.GT.N )
263: $ GO TO 50
264: *
265: IF( IPIV( K ).GT.0 ) THEN
266: *
267: * 1 x 1 diagonal block
268: *
269: * Multiply by inv(U**H(K)), where U(K) is the transformation
270: * stored in column K of A.
271: *
272: IF( K.GT.1 ) THEN
273: CALL ZLACGV( NRHS, B( K, 1 ), LDB )
274: CALL ZGEMV( 'Conjugate transpose', K-1, NRHS, -ONE, B,
275: $ LDB, AP( KC ), 1, ONE, B( K, 1 ), LDB )
276: CALL ZLACGV( NRHS, B( K, 1 ), LDB )
277: END IF
278: *
279: * Interchange rows K and IPIV(K).
280: *
281: KP = IPIV( K )
282: IF( KP.NE.K )
283: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
284: KC = KC + K
285: K = K + 1
286: ELSE
287: *
288: * 2 x 2 diagonal block
289: *
290: * Multiply by inv(U**H(K+1)), where U(K+1) is the transformation
291: * stored in columns K and K+1 of A.
292: *
293: IF( K.GT.1 ) THEN
294: CALL ZLACGV( NRHS, B( K, 1 ), LDB )
295: CALL ZGEMV( 'Conjugate transpose', K-1, NRHS, -ONE, B,
296: $ LDB, AP( KC ), 1, ONE, B( K, 1 ), LDB )
297: CALL ZLACGV( NRHS, B( K, 1 ), LDB )
298: *
299: CALL ZLACGV( NRHS, B( K+1, 1 ), LDB )
300: CALL ZGEMV( 'Conjugate transpose', K-1, NRHS, -ONE, B,
301: $ LDB, AP( KC+K ), 1, ONE, B( K+1, 1 ), LDB )
302: CALL ZLACGV( NRHS, B( K+1, 1 ), LDB )
303: END IF
304: *
305: * Interchange rows K and -IPIV(K).
306: *
307: KP = -IPIV( K )
308: IF( KP.NE.K )
309: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
310: KC = KC + 2*K + 1
311: K = K + 2
312: END IF
313: *
314: GO TO 40
315: 50 CONTINUE
316: *
317: ELSE
318: *
319: * Solve A*X = B, where A = L*D*L**H.
320: *
321: * First solve L*D*X = B, overwriting B with X.
322: *
323: * K is the main loop index, increasing from 1 to N in steps of
324: * 1 or 2, depending on the size of the diagonal blocks.
325: *
326: K = 1
327: KC = 1
328: 60 CONTINUE
329: *
330: * If K > N, exit from loop.
331: *
332: IF( K.GT.N )
333: $ GO TO 80
334: *
335: IF( IPIV( K ).GT.0 ) THEN
336: *
337: * 1 x 1 diagonal block
338: *
339: * Interchange rows K and IPIV(K).
340: *
341: KP = IPIV( K )
342: IF( KP.NE.K )
343: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
344: *
345: * Multiply by inv(L(K)), where L(K) is the transformation
346: * stored in column K of A.
347: *
348: IF( K.LT.N )
349: $ CALL ZGERU( N-K, NRHS, -ONE, AP( KC+1 ), 1, B( K, 1 ),
350: $ LDB, B( K+1, 1 ), LDB )
351: *
352: * Multiply by the inverse of the diagonal block.
353: *
354: S = DBLE( ONE ) / DBLE( AP( KC ) )
355: CALL ZDSCAL( NRHS, S, B( K, 1 ), LDB )
356: KC = KC + N - K + 1
357: K = K + 1
358: ELSE
359: *
360: * 2 x 2 diagonal block
361: *
362: * Interchange rows K+1 and -IPIV(K).
363: *
364: KP = -IPIV( K )
365: IF( KP.NE.K+1 )
366: $ CALL ZSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), LDB )
367: *
368: * Multiply by inv(L(K)), where L(K) is the transformation
369: * stored in columns K and K+1 of A.
370: *
371: IF( K.LT.N-1 ) THEN
372: CALL ZGERU( N-K-1, NRHS, -ONE, AP( KC+2 ), 1, B( K, 1 ),
373: $ LDB, B( K+2, 1 ), LDB )
374: CALL ZGERU( N-K-1, NRHS, -ONE, AP( KC+N-K+2 ), 1,
375: $ B( K+1, 1 ), LDB, B( K+2, 1 ), LDB )
376: END IF
377: *
378: * Multiply by the inverse of the diagonal block.
379: *
380: AKM1K = AP( KC+1 )
381: AKM1 = AP( KC ) / DCONJG( AKM1K )
382: AK = AP( KC+N-K+1 ) / AKM1K
383: DENOM = AKM1*AK - ONE
384: DO 70 J = 1, NRHS
385: BKM1 = B( K, J ) / DCONJG( AKM1K )
386: BK = B( K+1, J ) / AKM1K
387: B( K, J ) = ( AK*BKM1-BK ) / DENOM
388: B( K+1, J ) = ( AKM1*BK-BKM1 ) / DENOM
389: 70 CONTINUE
390: KC = KC + 2*( N-K ) + 1
391: K = K + 2
392: END IF
393: *
394: GO TO 60
395: 80 CONTINUE
396: *
397: * Next solve L**H *X = B, overwriting B with X.
398: *
399: * K is the main loop index, decreasing from N to 1 in steps of
400: * 1 or 2, depending on the size of the diagonal blocks.
401: *
402: K = N
403: KC = N*( N+1 ) / 2 + 1
404: 90 CONTINUE
405: *
406: * If K < 1, exit from loop.
407: *
408: IF( K.LT.1 )
409: $ GO TO 100
410: *
411: KC = KC - ( N-K+1 )
412: IF( IPIV( K ).GT.0 ) THEN
413: *
414: * 1 x 1 diagonal block
415: *
416: * Multiply by inv(L**H(K)), where L(K) is the transformation
417: * stored in column K of A.
418: *
419: IF( K.LT.N ) THEN
420: CALL ZLACGV( NRHS, B( K, 1 ), LDB )
421: CALL ZGEMV( 'Conjugate transpose', N-K, NRHS, -ONE,
422: $ B( K+1, 1 ), LDB, AP( KC+1 ), 1, ONE,
423: $ B( K, 1 ), LDB )
424: CALL ZLACGV( NRHS, B( K, 1 ), LDB )
425: END IF
426: *
427: * Interchange rows K and IPIV(K).
428: *
429: KP = IPIV( K )
430: IF( KP.NE.K )
431: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
432: K = K - 1
433: ELSE
434: *
435: * 2 x 2 diagonal block
436: *
437: * Multiply by inv(L**H(K-1)), where L(K-1) is the transformation
438: * stored in columns K-1 and K of A.
439: *
440: IF( K.LT.N ) THEN
441: CALL ZLACGV( NRHS, B( K, 1 ), LDB )
442: CALL ZGEMV( 'Conjugate transpose', N-K, NRHS, -ONE,
443: $ B( K+1, 1 ), LDB, AP( KC+1 ), 1, ONE,
444: $ B( K, 1 ), LDB )
445: CALL ZLACGV( NRHS, B( K, 1 ), LDB )
446: *
447: CALL ZLACGV( NRHS, B( K-1, 1 ), LDB )
448: CALL ZGEMV( 'Conjugate transpose', N-K, NRHS, -ONE,
449: $ B( K+1, 1 ), LDB, AP( KC-( N-K ) ), 1, ONE,
450: $ B( K-1, 1 ), LDB )
451: CALL ZLACGV( NRHS, B( K-1, 1 ), LDB )
452: END IF
453: *
454: * Interchange rows K and -IPIV(K).
455: *
456: KP = -IPIV( K )
457: IF( KP.NE.K )
458: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
459: KC = KC - ( N-K+2 )
460: K = K - 2
461: END IF
462: *
463: GO TO 90
464: 100 CONTINUE
465: END IF
466: *
467: RETURN
468: *
469: * End of ZHPTRS
470: *
471: END
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