1: *> \brief \b ZHETRS2
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZHETRS2 + dependencies
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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/zhetrs2.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZHETRS2( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
22: * WORK, INFO )
23: *
24: * .. Scalar Arguments ..
25: * CHARACTER UPLO
26: * INTEGER INFO, LDA, LDB, N, NRHS
27: * ..
28: * .. Array Arguments ..
29: * INTEGER IPIV( * )
30: * COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
31: * ..
32: *
33: *
34: *> \par Purpose:
35: * =============
36: *>
37: *> \verbatim
38: *>
39: *> ZHETRS2 solves a system of linear equations A*X = B with a complex
40: *> Hermitian matrix A using the factorization A = U*D*U**H or
41: *> A = L*D*L**H computed by ZHETRF and converted by ZSYCONV.
42: *> \endverbatim
43: *
44: * Arguments:
45: * ==========
46: *
47: *> \param[in] UPLO
48: *> \verbatim
49: *> UPLO is CHARACTER*1
50: *> Specifies whether the details of the factorization are stored
51: *> as an upper or lower triangular matrix.
52: *> = 'U': Upper triangular, form is A = U*D*U**H;
53: *> = 'L': Lower triangular, form is A = L*D*L**H.
54: *> \endverbatim
55: *>
56: *> \param[in] N
57: *> \verbatim
58: *> N is INTEGER
59: *> The order of the matrix A. N >= 0.
60: *> \endverbatim
61: *>
62: *> \param[in] NRHS
63: *> \verbatim
64: *> NRHS is INTEGER
65: *> The number of right hand sides, i.e., the number of columns
66: *> of the matrix B. NRHS >= 0.
67: *> \endverbatim
68: *>
69: *> \param[in] A
70: *> \verbatim
71: *> A is COMPLEX*16 array, dimension (LDA,N)
72: *> The block diagonal matrix D and the multipliers used to
73: *> obtain the factor U or L as computed by ZHETRF.
74: *> \endverbatim
75: *>
76: *> \param[in] LDA
77: *> \verbatim
78: *> LDA is INTEGER
79: *> The leading dimension of the array A. LDA >= max(1,N).
80: *> \endverbatim
81: *>
82: *> \param[in] IPIV
83: *> \verbatim
84: *> IPIV is INTEGER array, dimension (N)
85: *> Details of the interchanges and the block structure of D
86: *> as determined by ZHETRF.
87: *> \endverbatim
88: *>
89: *> \param[in,out] B
90: *> \verbatim
91: *> B is COMPLEX*16 array, dimension (LDB,NRHS)
92: *> On entry, the right hand side matrix B.
93: *> On exit, the solution matrix X.
94: *> \endverbatim
95: *>
96: *> \param[in] LDB
97: *> \verbatim
98: *> LDB is INTEGER
99: *> The leading dimension of the array B. LDB >= max(1,N).
100: *> \endverbatim
101: *>
102: *> \param[out] WORK
103: *> \verbatim
104: *> WORK is COMPLEX*16 array, dimension (N)
105: *> \endverbatim
106: *>
107: *> \param[out] INFO
108: *> \verbatim
109: *> INFO is INTEGER
110: *> = 0: successful exit
111: *> < 0: if INFO = -i, the i-th argument had an illegal value
112: *> \endverbatim
113: *
114: * Authors:
115: * ========
116: *
117: *> \author Univ. of Tennessee
118: *> \author Univ. of California Berkeley
119: *> \author Univ. of Colorado Denver
120: *> \author NAG Ltd.
121: *
122: *> \ingroup complex16HEcomputational
123: *
124: * =====================================================================
125: SUBROUTINE ZHETRS2( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
126: $ WORK, INFO )
127: *
128: * -- LAPACK computational routine --
129: * -- LAPACK is a software package provided by Univ. of Tennessee, --
130: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
131: *
132: * .. Scalar Arguments ..
133: CHARACTER UPLO
134: INTEGER INFO, LDA, LDB, N, NRHS
135: * ..
136: * .. Array Arguments ..
137: INTEGER IPIV( * )
138: COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
139: * ..
140: *
141: * =====================================================================
142: *
143: * .. Parameters ..
144: COMPLEX*16 ONE
145: PARAMETER ( ONE = (1.0D+0,0.0D+0) )
146: * ..
147: * .. Local Scalars ..
148: LOGICAL UPPER
149: INTEGER I, IINFO, J, K, KP
150: DOUBLE PRECISION S
151: COMPLEX*16 AK, AKM1, AKM1K, BK, BKM1, DENOM
152: * ..
153: * .. External Functions ..
154: LOGICAL LSAME
155: EXTERNAL LSAME
156: * ..
157: * .. External Subroutines ..
158: EXTERNAL ZDSCAL, ZSYCONV, ZSWAP, ZTRSM, XERBLA
159: * ..
160: * .. Intrinsic Functions ..
161: INTRINSIC DBLE, DCONJG, MAX
162: * ..
163: * .. Executable Statements ..
164: *
165: INFO = 0
166: UPPER = LSAME( UPLO, 'U' )
167: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
168: INFO = -1
169: ELSE IF( N.LT.0 ) THEN
170: INFO = -2
171: ELSE IF( NRHS.LT.0 ) THEN
172: INFO = -3
173: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
174: INFO = -5
175: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
176: INFO = -8
177: END IF
178: IF( INFO.NE.0 ) THEN
179: CALL XERBLA( 'ZHETRS2', -INFO )
180: RETURN
181: END IF
182: *
183: * Quick return if possible
184: *
185: IF( N.EQ.0 .OR. NRHS.EQ.0 )
186: $ RETURN
187: *
188: * Convert A
189: *
190: CALL ZSYCONV( UPLO, 'C', N, A, LDA, IPIV, WORK, IINFO )
191: *
192: IF( UPPER ) THEN
193: *
194: * Solve A*X = B, where A = U*D*U**H.
195: *
196: * P**T * B
197: K=N
198: DO WHILE ( K .GE. 1 )
199: IF( IPIV( K ).GT.0 ) THEN
200: * 1 x 1 diagonal block
201: * Interchange rows K and IPIV(K).
202: KP = IPIV( K )
203: IF( KP.NE.K )
204: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
205: K=K-1
206: ELSE
207: * 2 x 2 diagonal block
208: * Interchange rows K-1 and -IPIV(K).
209: KP = -IPIV( K )
210: IF( KP.EQ.-IPIV( K-1 ) )
211: $ CALL ZSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), LDB )
212: K=K-2
213: END IF
214: END DO
215: *
216: * Compute (U \P**T * B) -> B [ (U \P**T * B) ]
217: *
218: CALL ZTRSM('L','U','N','U',N,NRHS,ONE,A,LDA,B,LDB)
219: *
220: * Compute D \ B -> B [ D \ (U \P**T * B) ]
221: *
222: I=N
223: DO WHILE ( I .GE. 1 )
224: IF( IPIV(I) .GT. 0 ) THEN
225: S = DBLE( ONE ) / DBLE( A( I, I ) )
226: CALL ZDSCAL( NRHS, S, B( I, 1 ), LDB )
227: ELSEIF ( I .GT. 1) THEN
228: IF ( IPIV(I-1) .EQ. IPIV(I) ) THEN
229: AKM1K = WORK(I)
230: AKM1 = A( I-1, I-1 ) / AKM1K
231: AK = A( I, I ) / DCONJG( AKM1K )
232: DENOM = AKM1*AK - ONE
233: DO 15 J = 1, NRHS
234: BKM1 = B( I-1, J ) / AKM1K
235: BK = B( I, J ) / DCONJG( AKM1K )
236: B( I-1, J ) = ( AK*BKM1-BK ) / DENOM
237: B( I, J ) = ( AKM1*BK-BKM1 ) / DENOM
238: 15 CONTINUE
239: I = I - 1
240: ENDIF
241: ENDIF
242: I = I - 1
243: END DO
244: *
245: * Compute (U**H \ B) -> B [ U**H \ (D \ (U \P**T * B) ) ]
246: *
247: CALL ZTRSM('L','U','C','U',N,NRHS,ONE,A,LDA,B,LDB)
248: *
249: * P * B [ P * (U**H \ (D \ (U \P**T * B) )) ]
250: *
251: K=1
252: DO WHILE ( K .LE. N )
253: IF( IPIV( K ).GT.0 ) THEN
254: * 1 x 1 diagonal block
255: * Interchange rows K and IPIV(K).
256: KP = IPIV( K )
257: IF( KP.NE.K )
258: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
259: K=K+1
260: ELSE
261: * 2 x 2 diagonal block
262: * Interchange rows K-1 and -IPIV(K).
263: KP = -IPIV( K )
264: IF( K .LT. N .AND. KP.EQ.-IPIV( K+1 ) )
265: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
266: K=K+2
267: ENDIF
268: END DO
269: *
270: ELSE
271: *
272: * Solve A*X = B, where A = L*D*L**H.
273: *
274: * P**T * B
275: K=1
276: DO WHILE ( K .LE. N )
277: IF( IPIV( K ).GT.0 ) THEN
278: * 1 x 1 diagonal block
279: * Interchange rows K and IPIV(K).
280: KP = IPIV( K )
281: IF( KP.NE.K )
282: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
283: K=K+1
284: ELSE
285: * 2 x 2 diagonal block
286: * Interchange rows K and -IPIV(K+1).
287: KP = -IPIV( K+1 )
288: IF( KP.EQ.-IPIV( K ) )
289: $ CALL ZSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), LDB )
290: K=K+2
291: ENDIF
292: END DO
293: *
294: * Compute (L \P**T * B) -> B [ (L \P**T * B) ]
295: *
296: CALL ZTRSM('L','L','N','U',N,NRHS,ONE,A,LDA,B,LDB)
297: *
298: * Compute D \ B -> B [ D \ (L \P**T * B) ]
299: *
300: I=1
301: DO WHILE ( I .LE. N )
302: IF( IPIV(I) .GT. 0 ) THEN
303: S = DBLE( ONE ) / DBLE( A( I, I ) )
304: CALL ZDSCAL( NRHS, S, B( I, 1 ), LDB )
305: ELSE
306: AKM1K = WORK(I)
307: AKM1 = A( I, I ) / DCONJG( AKM1K )
308: AK = A( I+1, I+1 ) / AKM1K
309: DENOM = AKM1*AK - ONE
310: DO 25 J = 1, NRHS
311: BKM1 = B( I, J ) / DCONJG( AKM1K )
312: BK = B( I+1, J ) / AKM1K
313: B( I, J ) = ( AK*BKM1-BK ) / DENOM
314: B( I+1, J ) = ( AKM1*BK-BKM1 ) / DENOM
315: 25 CONTINUE
316: I = I + 1
317: ENDIF
318: I = I + 1
319: END DO
320: *
321: * Compute (L**H \ B) -> B [ L**H \ (D \ (L \P**T * B) ) ]
322: *
323: CALL ZTRSM('L','L','C','U',N,NRHS,ONE,A,LDA,B,LDB)
324: *
325: * P * B [ P * (L**H \ (D \ (L \P**T * B) )) ]
326: *
327: K=N
328: DO WHILE ( K .GE. 1 )
329: IF( IPIV( K ).GT.0 ) THEN
330: * 1 x 1 diagonal block
331: * Interchange rows K and IPIV(K).
332: KP = IPIV( K )
333: IF( KP.NE.K )
334: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
335: K=K-1
336: ELSE
337: * 2 x 2 diagonal block
338: * Interchange rows K-1 and -IPIV(K).
339: KP = -IPIV( K )
340: IF( K.GT.1 .AND. KP.EQ.-IPIV( K-1 ) )
341: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
342: K=K-2
343: ENDIF
344: END DO
345: *
346: END IF
347: *
348: * Revert A
349: *
350: CALL ZSYCONV( UPLO, 'R', N, A, LDA, IPIV, WORK, IINFO )
351: *
352: RETURN
353: *
354: * End of ZHETRS2
355: *
356: END
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