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*U**T 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*U**T;
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: *> The size of the array TB. LTB >= 4*N.
89: *> \endverbatim
90: *>
91: *> \param[in] IPIV
92: *> \verbatim
93: *> IPIV is INTEGER array, dimension (N)
94: *> Details of the interchanges as computed by
95: *> ZSYTRF_AA_2STAGE.
96: *> \endverbatim
97: *>
98: *> \param[in] IPIV2
99: *> \verbatim
100: *> IPIV2 is INTEGER array, dimension (N)
101: *> Details of the interchanges as computed by
102: *> ZSYTRF_AA_2STAGE.
103: *> \endverbatim
104: *>
105: *> \param[in,out] B
106: *> \verbatim
107: *> B is COMPLEX*16 array, dimension (LDB,NRHS)
108: *> On entry, the right hand side matrix B.
109: *> On exit, the solution matrix X.
110: *> \endverbatim
111: *>
112: *> \param[in] LDB
113: *> \verbatim
114: *> LDB is INTEGER
115: *> The leading dimension of the array B. LDB >= max(1,N).
116: *> \endverbatim
117: *>
118: *> \param[out] INFO
119: *> \verbatim
120: *> INFO is INTEGER
121: *> = 0: successful exit
122: *> < 0: if INFO = -i, the i-th argument had an illegal value
123: *> \endverbatim
124: *
125: * Authors:
126: * ========
127: *
128: *> \author Univ. of Tennessee
129: *> \author Univ. of California Berkeley
130: *> \author Univ. of Colorado Denver
131: *> \author NAG Ltd.
132: *
133: *> \date November 2017
134: *
135: *> \ingroup complex16SYcomputational
136: *
137: * =====================================================================
138: SUBROUTINE ZSYTRS_AA_2STAGE( UPLO, N, NRHS, A, LDA, TB, LTB,
139: $ IPIV, IPIV2, B, LDB, INFO )
140: *
141: * -- LAPACK computational routine (version 3.8.0) --
142: * -- LAPACK is a software package provided by Univ. of Tennessee, --
143: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
144: * November 2017
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 = ( 1.0E+0, 0.0E+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( 'ZSYTRS_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*T*U**T.
211: *
212: IF( N.GT.NB ) THEN
213: *
214: * Pivot, P**T * B
215: *
216: CALL ZLASWP( NRHS, B, LDB, NB+1, N, IPIV, 1 )
217: *
218: * Compute (U**T \P**T * B) -> B [ (U**T \P**T * B) ]
219: *
220: CALL ZTRSM( 'L', 'U', 'T', '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**T \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**T \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 [ P * (U \ (T \ (U**T \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**T.
245: *
246: IF( N.GT.NB ) THEN
247: *
248: * Pivot, P**T * B
249: *
250: CALL ZLASWP( NRHS, B, LDB, NB+1, N, IPIV, 1 )
251: *
252: * Compute (L \P**T * 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**T \ B) -> B [ L**T \ (T \ (L \P**T * B) ) ]
266: *
267: CALL ZTRSM( 'L', 'L', 'T', 'U', N-NB, NRHS, ONE, A(NB+1, 1),
268: $ LDA, B(NB+1, 1), LDB)
269: *
270: * Pivot, P * B [ P * (L**T \ (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 ZSYTRS_AA_2STAGE
280: *
281: END
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