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: *> \ingroup complex16SYcomputational
137: *
138: * =====================================================================
139: SUBROUTINE ZHETRS_AA_2STAGE( UPLO, N, NRHS, A, LDA, TB, LTB,
140: $ IPIV, IPIV2, B, LDB, INFO )
141: *
142: * -- LAPACK computational routine --
143: * -- LAPACK is a software package provided by Univ. of Tennessee, --
144: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
145: *
146: IMPLICIT NONE
147: *
148: * .. Scalar Arguments ..
149: CHARACTER UPLO
150: INTEGER N, NRHS, LDA, LTB, LDB, INFO
151: * ..
152: * .. Array Arguments ..
153: INTEGER IPIV( * ), IPIV2( * )
154: COMPLEX*16 A( LDA, * ), TB( * ), B( LDB, * )
155: * ..
156: *
157: * =====================================================================
158: *
159: COMPLEX*16 ONE
160: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
161: * ..
162: * .. Local Scalars ..
163: INTEGER LDTB, NB
164: LOGICAL UPPER
165: * ..
166: * .. External Functions ..
167: LOGICAL LSAME
168: EXTERNAL LSAME
169: * ..
170: * .. External Subroutines ..
171: EXTERNAL ZGBTRS, ZLASWP, ZTRSM, XERBLA
172: * ..
173: * .. Intrinsic Functions ..
174: INTRINSIC MAX
175: * ..
176: * .. Executable Statements ..
177: *
178: INFO = 0
179: UPPER = LSAME( UPLO, 'U' )
180: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
181: INFO = -1
182: ELSE IF( N.LT.0 ) THEN
183: INFO = -2
184: ELSE IF( NRHS.LT.0 ) THEN
185: INFO = -3
186: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
187: INFO = -5
188: ELSE IF( LTB.LT.( 4*N ) ) THEN
189: INFO = -7
190: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
191: INFO = -11
192: END IF
193: IF( INFO.NE.0 ) THEN
194: CALL XERBLA( 'ZHETRS_AA_2STAGE', -INFO )
195: RETURN
196: END IF
197: *
198: * Quick return if possible
199: *
200: IF( N.EQ.0 .OR. NRHS.EQ.0 )
201: $ RETURN
202: *
203: * Read NB and compute LDTB
204: *
205: NB = INT( TB( 1 ) )
206: LDTB = LTB/N
207: *
208: IF( UPPER ) THEN
209: *
210: * Solve A*X = B, where A = U**H*T*U.
211: *
212: IF( N.GT.NB ) THEN
213: *
214: * Pivot, P**T * B -> B
215: *
216: CALL ZLASWP( NRHS, B, LDB, NB+1, N, IPIV, 1 )
217: *
218: * Compute (U**H \ B) -> B [ (U**H \P**T * B) ]
219: *
220: CALL ZTRSM( 'L', 'U', 'C', 'U', N-NB, NRHS, ONE, A(1, NB+1),
221: $ LDA, B(NB+1, 1), LDB)
222: *
223: END IF
224: *
225: * Compute T \ B -> B [ T \ (U**H \P**T * B) ]
226: *
227: CALL ZGBTRS( 'N', N, NB, NB, NRHS, TB, LDTB, IPIV2, B, LDB,
228: $ INFO)
229: IF( N.GT.NB ) THEN
230: *
231: * Compute (U \ B) -> B [ U \ (T \ (U**H \P**T * B) ) ]
232: *
233: CALL ZTRSM( 'L', 'U', 'N', 'U', N-NB, NRHS, ONE, A(1, NB+1),
234: $ LDA, B(NB+1, 1), LDB)
235: *
236: * Pivot, P * B -> B [ P * (U \ (T \ (U**H \P**T * B) )) ]
237: *
238: CALL ZLASWP( NRHS, B, LDB, NB+1, N, IPIV, -1 )
239: *
240: END IF
241: *
242: ELSE
243: *
244: * Solve A*X = B, where A = L*T*L**H.
245: *
246: IF( N.GT.NB ) THEN
247: *
248: * Pivot, P**T * B -> B
249: *
250: CALL ZLASWP( NRHS, B, LDB, NB+1, N, IPIV, 1 )
251: *
252: * Compute (L \ B) -> B [ (L \P**T * B) ]
253: *
254: CALL ZTRSM( 'L', 'L', 'N', 'U', N-NB, NRHS, ONE, A(NB+1, 1),
255: $ LDA, B(NB+1, 1), LDB)
256: *
257: END IF
258: *
259: * Compute T \ B -> B [ T \ (L \P**T * B) ]
260: *
261: CALL ZGBTRS( 'N', N, NB, NB, NRHS, TB, LDTB, IPIV2, B, LDB,
262: $ INFO)
263: IF( N.GT.NB ) THEN
264: *
265: * Compute (L**H \ B) -> B [ L**H \ (T \ (L \P**T * B) ) ]
266: *
267: CALL ZTRSM( 'L', 'L', 'C', 'U', N-NB, NRHS, ONE, A(NB+1, 1),
268: $ LDA, B(NB+1, 1), LDB)
269: *
270: * Pivot, P * B -> B [ P * (L**H \ (T \ (L \P**T * B) )) ]
271: *
272: CALL ZLASWP( NRHS, B, LDB, NB+1, N, IPIV, -1 )
273: *
274: END IF
275: END IF
276: *
277: RETURN
278: *
279: * End of ZHETRS_AA_2STAGE
280: *
281: END
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