1: *> \brief \b ZHETRS_AA_2STAGE
2: *
3: * @generated from SRC/dsytrs_aa_2stage.f, fortran d -> c, Mon Oct 30 11:59:02 2017
4: *
5: * =========== DOCUMENTATION ===========
6: *
7: * Online html documentation available at
8: * http://www.netlib.org/lapack/explore-html/
9: *
10: *> \htmlonly
11: *> Download ZHETRS_AA_2STAGE + dependencies
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13: *> [TGZ]</a>
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15: *> [ZIP]</a>
16: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhetrs_aa_2stage.f">
17: *> [TXT]</a>
18: *> \endhtmlonly
19: *
20: * Definition:
21: * ===========
22: *
23: * SUBROUTINE ZHETRS_AA_2STAGE( UPLO, N, NRHS, A, LDA, TB, LTB, IPIV,
24: * IPIV2, B, LDB, INFO )
25: *
26: * .. Scalar Arguments ..
27: * CHARACTER UPLO
28: * INTEGER N, NRHS, LDA, LTB, LDB, INFO
29: * ..
30: * .. Array Arguments ..
31: * INTEGER IPIV( * ), IPIV2( * )
32: * COMPLEX*16 A( LDA, * ), TB( * ), B( LDB, * )
33: * ..
34: *
35: *> \par Purpose:
36: * =============
37: *>
38: *> \verbatim
39: *>
40: *> ZHETRS_AA_2STAGE solves a system of linear equations A*X = B with a
41: *> hermitian matrix A using the factorization A = U**H*T*U or
42: *> A = L*T*L**H computed by ZHETRF_AA_2STAGE.
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**H*T*U;
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] A
71: *> \verbatim
72: *> A is COMPLEX*16 array, dimension (LDA,N)
73: *> Details of factors computed by ZHETRF_AA_2STAGE.
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[out] TB
83: *> \verbatim
84: *> TB is COMPLEX*16 array, dimension (LTB)
85: *> Details of factors computed by ZHETRF_AA_2STAGE.
86: *> \endverbatim
87: *>
88: *> \param[in] LTB
89: *> \verbatim
90: *> LTB is INTEGER
91: *> The size of the array TB. LTB >= 4*N.
92: *> \endverbatim
93: *>
94: *> \param[in] IPIV
95: *> \verbatim
96: *> IPIV is INTEGER array, dimension (N)
97: *> Details of the interchanges as computed by
98: *> ZHETRF_AA_2STAGE.
99: *> \endverbatim
100: *>
101: *> \param[in] IPIV2
102: *> \verbatim
103: *> IPIV2 is INTEGER array, dimension (N)
104: *> Details of the interchanges as computed by
105: *> ZHETRF_AA_2STAGE.
106: *> \endverbatim
107: *>
108: *> \param[in,out] B
109: *> \verbatim
110: *> B is COMPLEX*16 array, dimension (LDB,NRHS)
111: *> On entry, the right hand side matrix B.
112: *> On exit, the solution matrix X.
113: *> \endverbatim
114: *>
115: *> \param[in] LDB
116: *> \verbatim
117: *> LDB is INTEGER
118: *> The leading dimension of the array B. LDB >= max(1,N).
119: *> \endverbatim
120: *>
121: *> \param[out] INFO
122: *> \verbatim
123: *> INFO is INTEGER
124: *> = 0: successful exit
125: *> < 0: if INFO = -i, the i-th argument had an illegal value
126: *> \endverbatim
127: *
128: * Authors:
129: * ========
130: *
131: *> \author Univ. of Tennessee
132: *> \author Univ. of California Berkeley
133: *> \author Univ. of Colorado Denver
134: *> \author NAG Ltd.
135: *
136: *> \date November 2017
137: *
138: *> \ingroup complex16SYcomputational
139: *
140: * =====================================================================
141: SUBROUTINE ZHETRS_AA_2STAGE( UPLO, N, NRHS, A, LDA, TB, LTB,
142: $ IPIV, IPIV2, B, LDB, INFO )
143: *
144: * -- LAPACK computational routine (version 3.8.0) --
145: * -- LAPACK is a software package provided by Univ. of Tennessee, --
146: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
147: * November 2017
148: *
149: IMPLICIT NONE
150: *
151: * .. Scalar Arguments ..
152: CHARACTER UPLO
153: INTEGER N, NRHS, LDA, LTB, LDB, INFO
154: * ..
155: * .. Array Arguments ..
156: INTEGER IPIV( * ), IPIV2( * )
157: COMPLEX*16 A( LDA, * ), TB( * ), B( LDB, * )
158: * ..
159: *
160: * =====================================================================
161: *
162: COMPLEX*16 ONE
163: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
164: * ..
165: * .. Local Scalars ..
166: INTEGER LDTB, NB
167: LOGICAL UPPER
168: * ..
169: * .. External Functions ..
170: LOGICAL LSAME
171: EXTERNAL LSAME
172: * ..
173: * .. External Subroutines ..
174: EXTERNAL ZGBTRS, ZLASWP, ZTRSM, XERBLA
175: * ..
176: * .. Intrinsic Functions ..
177: INTRINSIC MAX
178: * ..
179: * .. Executable Statements ..
180: *
181: INFO = 0
182: UPPER = LSAME( UPLO, 'U' )
183: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
184: INFO = -1
185: ELSE IF( N.LT.0 ) THEN
186: INFO = -2
187: ELSE IF( NRHS.LT.0 ) THEN
188: INFO = -3
189: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
190: INFO = -5
191: ELSE IF( LTB.LT.( 4*N ) ) THEN
192: INFO = -7
193: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
194: INFO = -11
195: END IF
196: IF( INFO.NE.0 ) THEN
197: CALL XERBLA( 'ZHETRS_AA_2STAGE', -INFO )
198: RETURN
199: END IF
200: *
201: * Quick return if possible
202: *
203: IF( N.EQ.0 .OR. NRHS.EQ.0 )
204: $ RETURN
205: *
206: * Read NB and compute LDTB
207: *
208: NB = INT( TB( 1 ) )
209: LDTB = LTB/N
210: *
211: IF( UPPER ) THEN
212: *
213: * Solve A*X = B, where A = U**H*T*U.
214: *
215: IF( N.GT.NB ) THEN
216: *
217: * Pivot, P**T * B -> B
218: *
219: CALL ZLASWP( NRHS, B, LDB, NB+1, N, IPIV, 1 )
220: *
221: * Compute (U**H \ B) -> B [ (U**H \P**T * B) ]
222: *
223: CALL ZTRSM( 'L', 'U', 'C', 'U', N-NB, NRHS, ONE, A(1, NB+1),
224: $ LDA, B(NB+1, 1), LDB)
225: *
226: END IF
227: *
228: * Compute T \ B -> B [ T \ (U**H \P**T * B) ]
229: *
230: CALL ZGBTRS( 'N', N, NB, NB, NRHS, TB, LDTB, IPIV2, B, LDB,
231: $ INFO)
232: IF( N.GT.NB ) THEN
233: *
234: * Compute (U \ B) -> B [ U \ (T \ (U**H \P**T * B) ) ]
235: *
236: CALL ZTRSM( 'L', 'U', 'N', 'U', N-NB, NRHS, ONE, A(1, NB+1),
237: $ LDA, B(NB+1, 1), LDB)
238: *
239: * Pivot, P * B -> B [ P * (U \ (T \ (U**H \P**T * B) )) ]
240: *
241: CALL ZLASWP( NRHS, B, LDB, NB+1, N, IPIV, -1 )
242: *
243: END IF
244: *
245: ELSE
246: *
247: * Solve A*X = B, where A = L*T*L**H.
248: *
249: IF( N.GT.NB ) THEN
250: *
251: * Pivot, P**T * B -> B
252: *
253: CALL ZLASWP( NRHS, B, LDB, NB+1, N, IPIV, 1 )
254: *
255: * Compute (L \ B) -> B [ (L \P**T * B) ]
256: *
257: CALL ZTRSM( 'L', 'L', 'N', 'U', N-NB, NRHS, ONE, A(NB+1, 1),
258: $ LDA, B(NB+1, 1), LDB)
259: *
260: END IF
261: *
262: * Compute T \ B -> B [ T \ (L \P**T * B) ]
263: *
264: CALL ZGBTRS( 'N', N, NB, NB, NRHS, TB, LDTB, IPIV2, B, LDB,
265: $ INFO)
266: IF( N.GT.NB ) THEN
267: *
268: * Compute (L**H \ B) -> B [ L**H \ (T \ (L \P**T * B) ) ]
269: *
270: CALL ZTRSM( 'L', 'L', 'C', 'U', N-NB, NRHS, ONE, A(NB+1, 1),
271: $ LDA, B(NB+1, 1), LDB)
272: *
273: * Pivot, P * B -> B [ P * (L**H \ (T \ (L \P**T * B) )) ]
274: *
275: CALL ZLASWP( NRHS, B, LDB, NB+1, N, IPIV, -1 )
276: *
277: END IF
278: END IF
279: *
280: RETURN
281: *
282: * End of ZHETRS_AA_2STAGE
283: *
284: END
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