1: *> \brief \b ZSYTRS_AA_2STAGE
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZSYTRS_AA_2STAGE + 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/zsytrs_aa_2stage.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZSYTRS_AA_2STAGE( UPLO, N, NRHS, A, LDA, TB, LTB, IPIV,
22: * IPIV2, B, LDB, INFO )
23: *
24: * .. Scalar Arguments ..
25: * CHARACTER UPLO
26: * INTEGER N, NRHS, LDA, LTB, LDB, INFO
27: * ..
28: * .. Array Arguments ..
29: * INTEGER IPIV( * ), IPIV2( * )
30: * COMPLEX*16 A( LDA, * ), TB( * ), B( LDB, * )
31: * ..
32: *
33: *> \par Purpose:
34: * =============
35: *>
36: *> \verbatim
37: *>
38: *> ZSYTRS_AA_2STAGE solves a system of linear equations A*X = B with a complex
39: *> symmetric matrix A using the factorization A = U**T*T*U or
40: *> A = L*T*L**T computed by ZSYTRF_AA_2STAGE.
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**T*T*U;
52: *> = 'L': Lower triangular, form is A = L*T*L**T.
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] A
69: *> \verbatim
70: *> A is COMPLEX*16 array, dimension (LDA,N)
71: *> Details of factors computed by ZSYTRF_AA_2STAGE.
72: *> \endverbatim
73: *>
74: *> \param[in] LDA
75: *> \verbatim
76: *> LDA is INTEGER
77: *> The leading dimension of the array A. LDA >= max(1,N).
78: *> \endverbatim
79: *>
80: *> \param[out] TB
81: *> \verbatim
82: *> TB is COMPLEX*16 array, dimension (LTB)
83: *> Details of factors computed by ZSYTRF_AA_2STAGE.
84: *> \endverbatim
85: *>
86: *> \param[in] LTB
87: *> \verbatim
88: *> LTB is INTEGER
89: *> The size of the array TB. LTB >= 4*N.
90: *> \endverbatim
91: *>
92: *> \param[in] IPIV
93: *> \verbatim
94: *> IPIV is INTEGER array, dimension (N)
95: *> Details of the interchanges as computed by
96: *> ZSYTRF_AA_2STAGE.
97: *> \endverbatim
98: *>
99: *> \param[in] IPIV2
100: *> \verbatim
101: *> IPIV2 is INTEGER array, dimension (N)
102: *> Details of the interchanges as computed by
103: *> ZSYTRF_AA_2STAGE.
104: *> \endverbatim
105: *>
106: *> \param[in,out] B
107: *> \verbatim
108: *> B is COMPLEX*16 array, dimension (LDB,NRHS)
109: *> On entry, the right hand side matrix B.
110: *> On exit, the solution matrix X.
111: *> \endverbatim
112: *>
113: *> \param[in] LDB
114: *> \verbatim
115: *> LDB is INTEGER
116: *> The leading dimension of the array B. LDB >= max(1,N).
117: *> \endverbatim
118: *>
119: *> \param[out] INFO
120: *> \verbatim
121: *> INFO is INTEGER
122: *> = 0: successful exit
123: *> < 0: if INFO = -i, the i-th argument had an illegal value
124: *> \endverbatim
125: *
126: * Authors:
127: * ========
128: *
129: *> \author Univ. of Tennessee
130: *> \author Univ. of California Berkeley
131: *> \author Univ. of Colorado Denver
132: *> \author NAG Ltd.
133: *
134: *> \date November 2017
135: *
136: *> \ingroup complex16SYcomputational
137: *
138: * =====================================================================
139: SUBROUTINE ZSYTRS_AA_2STAGE( UPLO, N, NRHS, A, LDA, TB, LTB,
140: $ IPIV, IPIV2, B, LDB, INFO )
141: *
142: * -- LAPACK computational routine (version 3.8.0) --
143: * -- LAPACK is a software package provided by Univ. of Tennessee, --
144: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
145: * November 2017
146: *
147: IMPLICIT NONE
148: *
149: * .. Scalar Arguments ..
150: CHARACTER UPLO
151: INTEGER N, NRHS, LDA, LTB, LDB, INFO
152: * ..
153: * .. Array Arguments ..
154: INTEGER IPIV( * ), IPIV2( * )
155: COMPLEX*16 A( LDA, * ), TB( * ), B( LDB, * )
156: * ..
157: *
158: * =====================================================================
159: *
160: COMPLEX*16 ONE
161: PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ) )
162: * ..
163: * .. Local Scalars ..
164: INTEGER LDTB, NB
165: LOGICAL UPPER
166: * ..
167: * .. External Functions ..
168: LOGICAL LSAME
169: EXTERNAL LSAME
170: * ..
171: * .. External Subroutines ..
172: EXTERNAL ZGBTRS, ZLASWP, ZTRSM, XERBLA
173: * ..
174: * .. Intrinsic Functions ..
175: INTRINSIC MAX
176: * ..
177: * .. Executable Statements ..
178: *
179: INFO = 0
180: UPPER = LSAME( UPLO, 'U' )
181: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
182: INFO = -1
183: ELSE IF( N.LT.0 ) THEN
184: INFO = -2
185: ELSE IF( NRHS.LT.0 ) THEN
186: INFO = -3
187: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
188: INFO = -5
189: ELSE IF( LTB.LT.( 4*N ) ) THEN
190: INFO = -7
191: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
192: INFO = -11
193: END IF
194: IF( INFO.NE.0 ) THEN
195: CALL XERBLA( 'ZSYTRS_AA_2STAGE', -INFO )
196: RETURN
197: END IF
198: *
199: * Quick return if possible
200: *
201: IF( N.EQ.0 .OR. NRHS.EQ.0 )
202: $ RETURN
203: *
204: * Read NB and compute LDTB
205: *
206: NB = INT( TB( 1 ) )
207: LDTB = LTB/N
208: *
209: IF( UPPER ) THEN
210: *
211: * Solve A*X = B, where A = U**T*T*U.
212: *
213: IF( N.GT.NB ) THEN
214: *
215: * Pivot, P**T * B -> B
216: *
217: CALL ZLASWP( NRHS, B, LDB, NB+1, N, IPIV, 1 )
218: *
219: * Compute (U**T \ B) -> B [ (U**T \P**T * B) ]
220: *
221: CALL ZTRSM( 'L', 'U', 'T', 'U', N-NB, NRHS, ONE, A(1, NB+1),
222: $ LDA, B(NB+1, 1), LDB)
223: *
224: END IF
225: *
226: * Compute T \ B -> B [ T \ (U**T \P**T * B) ]
227: *
228: CALL ZGBTRS( 'N', N, NB, NB, NRHS, TB, LDTB, IPIV2, B, LDB,
229: $ INFO)
230: IF( N.GT.NB ) THEN
231: *
232: * Compute (U \ B) -> B [ U \ (T \ (U**T \P**T * B) ) ]
233: *
234: CALL ZTRSM( 'L', 'U', 'N', 'U', N-NB, NRHS, ONE, A(1, NB+1),
235: $ LDA, B(NB+1, 1), LDB)
236: *
237: * Pivot, P * B -> B [ P * (U \ (T \ (U**T \P**T * B) )) ]
238: *
239: CALL ZLASWP( NRHS, B, LDB, NB+1, N, IPIV, -1 )
240: *
241: END IF
242: *
243: ELSE
244: *
245: * Solve A*X = B, where A = L*T*L**T.
246: *
247: IF( N.GT.NB ) THEN
248: *
249: * Pivot, P**T * B -> B
250: *
251: CALL ZLASWP( NRHS, B, LDB, NB+1, N, IPIV, 1 )
252: *
253: * Compute (L \ B) -> B [ (L \P**T * B) ]
254: *
255: CALL ZTRSM( 'L', 'L', 'N', 'U', N-NB, NRHS, ONE, A(NB+1, 1),
256: $ LDA, B(NB+1, 1), LDB)
257: *
258: END IF
259: *
260: * Compute T \ B -> B [ T \ (L \P**T * B) ]
261: *
262: CALL ZGBTRS( 'N', N, NB, NB, NRHS, TB, LDTB, IPIV2, B, LDB,
263: $ INFO)
264: IF( N.GT.NB ) THEN
265: *
266: * Compute (L**T \ B) -> B [ L**T \ (T \ (L \P**T * B) ) ]
267: *
268: CALL ZTRSM( 'L', 'L', 'T', 'U', N-NB, NRHS, ONE, A(NB+1, 1),
269: $ LDA, B(NB+1, 1), LDB)
270: *
271: * Pivot, P * B -> B [ P * (L**T \ (T \ (L \P**T * B) )) ]
272: *
273: CALL ZLASWP( NRHS, B, LDB, NB+1, N, IPIV, -1 )
274: *
275: END IF
276: END IF
277: *
278: RETURN
279: *
280: * End of ZSYTRS_AA_2STAGE
281: *
282: END
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