1: *> \brief \b ZHETRS_AA
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZHETRS_AA + dependencies
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15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZHETRS_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
22: * WORK, LWORK, INFO )
23: *
24: * .. Scalar Arguments ..
25: * CHARACTER UPLO
26: * INTEGER N, NRHS, LDA, LDB, LWORK, INFO
27: * ..
28: * .. Array Arguments ..
29: * INTEGER IPIV( * )
30: * COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
31: * ..
32: *
33: *
34: *
35: *> \par Purpose:
36: * =============
37: *>
38: *> \verbatim
39: *>
40: *> ZHETRS_AA solves a system of linear equations A*X = B with a complex
41: *> hermitian matrix A using the factorization A = U*T*U**H or
42: *> A = L*T*L**T computed by ZHETRF_AA.
43: *> \endverbatim
44: *
45: * Arguments:
46: * ==========
47: *
48: *> \param[in] UPLO
49: *> \verbatim
50: *> UPLO is CHARACTER*1
51: *> Specifies whether the details of the factorization are stored
52: *> as an upper or lower triangular matrix.
53: *> = 'U': Upper triangular, form is A = U*T*U**H;
54: *> = 'L': Lower triangular, form is A = L*T*L**H.
55: *> \endverbatim
56: *>
57: *> \param[in] N
58: *> \verbatim
59: *> N is INTEGER
60: *> The order of the matrix A. N >= 0.
61: *> \endverbatim
62: *>
63: *> \param[in] NRHS
64: *> \verbatim
65: *> NRHS is INTEGER
66: *> The number of right hand sides, i.e., the number of columns
67: *> of the matrix B. NRHS >= 0.
68: *> \endverbatim
69: *>
70: *> \param[in,out] A
71: *> \verbatim
72: *> A is COMPLEX*16 array, dimension (LDA,N)
73: *> Details of factors computed by ZHETRF_AA.
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 as computed by ZHETRF_AA.
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[in] WORK
102: *> \verbatim
103: *> WORK is DOUBLE array, dimension (MAX(1,LWORK))
104: *> \endverbatim
105: *>
106: *> \param[in] LWORK
107: *> \verbatim
108: *> LWORK is INTEGER, LWORK >= MAX(1,3*N-2).
109: *>
110: *> \param[out] INFO
111: *> \verbatim
112: *> INFO is INTEGER
113: *> = 0: successful exit
114: *> < 0: if INFO = -i, the i-th argument had an illegal value
115: *> \endverbatim
116: *
117: * Authors:
118: * ========
119: *
120: *> \author Univ. of Tennessee
121: *> \author Univ. of California Berkeley
122: *> \author Univ. of Colorado Denver
123: *> \author NAG Ltd.
124: *
125: *> \date December 2016
126: *
127: *> \ingroup complex16HEcomputational
128: *
129: * =====================================================================
130: SUBROUTINE ZHETRS_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
131: $ WORK, LWORK, INFO )
132: *
133: * -- LAPACK computational routine (version 3.7.0) --
134: * -- LAPACK is a software package provided by Univ. of Tennessee, --
135: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
136: * December 2016
137: *
138: IMPLICIT NONE
139: *
140: * .. Scalar Arguments ..
141: CHARACTER UPLO
142: INTEGER N, NRHS, LDA, LDB, LWORK, INFO
143: * ..
144: * .. Array Arguments ..
145: INTEGER IPIV( * )
146: COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
147: * ..
148: *
149: * =====================================================================
150: *
151: COMPLEX*16 ONE
152: PARAMETER ( ONE = 1.0D+0 )
153: * ..
154: * .. Local Scalars ..
155: LOGICAL LQUERY, UPPER
156: INTEGER K, KP, LWKOPT
157: * ..
158: * .. External Functions ..
159: LOGICAL LSAME
160: EXTERNAL LSAME
161: * ..
162: * .. External Subroutines ..
163: EXTERNAL ZGTSV, ZSWAP, ZTRSM, XERBLA
164: * ..
165: * .. Intrinsic Functions ..
166: INTRINSIC MAX
167: * ..
168: * .. Executable Statements ..
169: *
170: INFO = 0
171: UPPER = LSAME( UPLO, 'U' )
172: LQUERY = ( LWORK.EQ.-1 )
173: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
174: INFO = -1
175: ELSE IF( N.LT.0 ) THEN
176: INFO = -2
177: ELSE IF( NRHS.LT.0 ) THEN
178: INFO = -3
179: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
180: INFO = -5
181: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
182: INFO = -8
183: ELSE IF( LWORK.LT.MAX( 1, 3*N-2 ) .AND. .NOT.LQUERY ) THEN
184: INFO = -10
185: END IF
186: IF( INFO.NE.0 ) THEN
187: CALL XERBLA( 'ZHETRS_AA', -INFO )
188: RETURN
189: ELSE IF( LQUERY ) THEN
190: LWKOPT = (3*N-2)
191: WORK( 1 ) = LWKOPT
192: RETURN
193: END IF
194: *
195: * Quick return if possible
196: *
197: IF( N.EQ.0 .OR. NRHS.EQ.0 )
198: $ RETURN
199: *
200: IF( UPPER ) THEN
201: *
202: * Solve A*X = B, where A = U*T*U**T.
203: *
204: * Pivot, P**T * B
205: *
206: DO K = 1, N
207: KP = IPIV( K )
208: IF( KP.NE.K )
209: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
210: END DO
211: *
212: * Compute (U \P**T * B) -> B [ (U \P**T * B) ]
213: *
214: CALL ZTRSM('L', 'U', 'C', 'U', N-1, NRHS, ONE, A( 1, 2 ), LDA,
215: $ B( 2, 1 ), LDB)
216: *
217: * Compute T \ B -> B [ T \ (U \P**T * B) ]
218: *
219: CALL ZLACPY( 'F', 1, N, A(1, 1), LDA+1, WORK(N), 1)
220: IF( N.GT.1 ) THEN
221: CALL ZLACPY( 'F', 1, N-1, A( 1, 2 ), LDA+1, WORK( 2*N ), 1)
222: CALL ZLACPY( 'F', 1, N-1, A( 1, 2 ), LDA+1, WORK( 1 ), 1)
223: CALL ZLACGV( N-1, WORK( 1 ), 1 )
224: END IF
225: CALL ZGTSV(N, NRHS, WORK(1), WORK(N), WORK(2*N), B, LDB,
226: $ INFO)
227: *
228: * Compute (U**T \ B) -> B [ U**T \ (T \ (U \P**T * B) ) ]
229: *
230: CALL ZTRSM( 'L', 'U', 'N', 'U', N-1, NRHS, ONE, A( 1, 2 ), LDA,
231: $ B(2, 1), LDB)
232: *
233: * Pivot, P * B [ P * (U**T \ (T \ (U \P**T * B) )) ]
234: *
235: DO K = N, 1, -1
236: KP = IPIV( K )
237: IF( KP.NE.K )
238: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
239: END DO
240: *
241: ELSE
242: *
243: * Solve A*X = B, where A = L*T*L**T.
244: *
245: * Pivot, P**T * B
246: *
247: DO K = 1, N
248: KP = IPIV( K )
249: IF( KP.NE.K )
250: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
251: END DO
252: *
253: * Compute (L \P**T * B) -> B [ (L \P**T * B) ]
254: *
255: CALL ZTRSM( 'L', 'L', 'N', 'U', N-1, NRHS, ONE, A( 2, 1 ), LDA,
256: $ B(2, 1), LDB)
257: *
258: * Compute T \ B -> B [ T \ (L \P**T * B) ]
259: *
260: CALL ZLACPY( 'F', 1, N, A(1, 1), LDA+1, WORK(N), 1)
261: IF( N.GT.1 ) THEN
262: CALL ZLACPY( 'F', 1, N-1, A( 2, 1 ), LDA+1, WORK( 1 ), 1)
263: CALL ZLACPY( 'F', 1, N-1, A( 2, 1 ), LDA+1, WORK( 2*N ), 1)
264: CALL ZLACGV( N-1, WORK( 2*N ), 1 )
265: END IF
266: CALL ZGTSV(N, NRHS, WORK(1), WORK(N), WORK(2*N), B, LDB,
267: $ INFO)
268: *
269: * Compute (L**T \ B) -> B [ L**T \ (T \ (L \P**T * B) ) ]
270: *
271: CALL ZTRSM( 'L', 'L', 'C', 'U', N-1, NRHS, ONE, A( 2, 1 ), LDA,
272: $ B( 2, 1 ), LDB)
273: *
274: * Pivot, P * B [ P * (L**T \ (T \ (L \P**T * B) )) ]
275: *
276: DO K = N, 1, -1
277: KP = IPIV( K )
278: IF( KP.NE.K )
279: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
280: END DO
281: *
282: END IF
283: *
284: RETURN
285: *
286: * End of ZHETRS_AA
287: *
288: END
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