LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
zsytrs_aa_2stage.f
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1 *> \brief \b ZSYTRS_AA_2STAGE
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
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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 *> \ingroup complex16SYcomputational
135 *
136 * =====================================================================
137  SUBROUTINE zsytrs_aa_2stage( UPLO, N, NRHS, A, LDA, TB, LTB,
138  $ IPIV, IPIV2, B, LDB, INFO )
139 *
140 * -- LAPACK computational routine --
141 * -- LAPACK is a software package provided by Univ. of Tennessee, --
142 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
143 *
144  IMPLICIT NONE
145 *
146 * .. Scalar Arguments ..
147  CHARACTER UPLO
148  INTEGER N, NRHS, LDA, LTB, LDB, INFO
149 * ..
150 * .. Array Arguments ..
151  INTEGER IPIV( * ), IPIV2( * )
152  COMPLEX*16 A( LDA, * ), TB( * ), B( LDB, * )
153 * ..
154 *
155 * =====================================================================
156 *
157  COMPLEX*16 ONE
158  parameter( one = ( 1.0e+0, 0.0e+0 ) )
159 * ..
160 * .. Local Scalars ..
161  INTEGER LDTB, NB
162  LOGICAL UPPER
163 * ..
164 * .. External Functions ..
165  LOGICAL LSAME
166  EXTERNAL lsame
167 * ..
168 * .. External Subroutines ..
169  EXTERNAL zgbtrs, zlaswp, ztrsm, xerbla
170 * ..
171 * .. Intrinsic Functions ..
172  INTRINSIC max
173 * ..
174 * .. Executable Statements ..
175 *
176  info = 0
177  upper = lsame( uplo, 'U' )
178  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
179  info = -1
180  ELSE IF( n.LT.0 ) THEN
181  info = -2
182  ELSE IF( nrhs.LT.0 ) THEN
183  info = -3
184  ELSE IF( lda.LT.max( 1, n ) ) THEN
185  info = -5
186  ELSE IF( ltb.LT.( 4*n ) ) THEN
187  info = -7
188  ELSE IF( ldb.LT.max( 1, n ) ) THEN
189  info = -11
190  END IF
191  IF( info.NE.0 ) THEN
192  CALL xerbla( 'ZSYTRS_AA_2STAGE', -info )
193  RETURN
194  END IF
195 *
196 * Quick return if possible
197 *
198  IF( n.EQ.0 .OR. nrhs.EQ.0 )
199  $ RETURN
200 *
201 * Read NB and compute LDTB
202 *
203  nb = int( tb( 1 ) )
204  ldtb = ltb/n
205 *
206  IF( upper ) THEN
207 *
208 * Solve A*X = B, where A = U**T*T*U.
209 *
210  IF( n.GT.nb ) THEN
211 *
212 * Pivot, P**T * B -> B
213 *
214  CALL zlaswp( nrhs, b, ldb, nb+1, n, ipiv, 1 )
215 *
216 * Compute (U**T \ B) -> B [ (U**T \P**T * B) ]
217 *
218  CALL ztrsm( 'L', 'U', 'T', 'U', n-nb, nrhs, one, a(1, nb+1),
219  $ lda, b(nb+1, 1), ldb)
220 *
221  END IF
222 *
223 * Compute T \ B -> B [ T \ (U**T \P**T * B) ]
224 *
225  CALL zgbtrs( 'N', n, nb, nb, nrhs, tb, ldtb, ipiv2, b, ldb,
226  $ info)
227  IF( n.GT.nb ) THEN
228 *
229 * Compute (U \ B) -> B [ U \ (T \ (U**T \P**T * B) ) ]
230 *
231  CALL ztrsm( 'L', 'U', 'N', 'U', n-nb, nrhs, one, a(1, nb+1),
232  $ lda, b(nb+1, 1), ldb)
233 *
234 * Pivot, P * B -> B [ P * (U \ (T \ (U**T \P**T * B) )) ]
235 *
236  CALL zlaswp( nrhs, b, ldb, nb+1, n, ipiv, -1 )
237 *
238  END IF
239 *
240  ELSE
241 *
242 * Solve A*X = B, where A = L*T*L**T.
243 *
244  IF( n.GT.nb ) THEN
245 *
246 * Pivot, P**T * B -> B
247 *
248  CALL zlaswp( nrhs, b, ldb, nb+1, n, ipiv, 1 )
249 *
250 * Compute (L \ B) -> B [ (L \P**T * B) ]
251 *
252  CALL ztrsm( 'L', 'L', 'N', 'U', n-nb, nrhs, one, a(nb+1, 1),
253  $ lda, b(nb+1, 1), ldb)
254 *
255  END IF
256 *
257 * Compute T \ B -> B [ T \ (L \P**T * B) ]
258 *
259  CALL zgbtrs( 'N', n, nb, nb, nrhs, tb, ldtb, ipiv2, b, ldb,
260  $ info)
261  IF( n.GT.nb ) THEN
262 *
263 * Compute (L**T \ B) -> B [ L**T \ (T \ (L \P**T * B) ) ]
264 *
265  CALL ztrsm( 'L', 'L', 'T', 'U', n-nb, nrhs, one, a(nb+1, 1),
266  $ lda, b(nb+1, 1), ldb)
267 *
268 * Pivot, P * B -> B [ P * (L**T \ (T \ (L \P**T * B) )) ]
269 *
270  CALL zlaswp( nrhs, b, ldb, nb+1, n, ipiv, -1 )
271 *
272  END IF
273  END IF
274 *
275  RETURN
276 *
277 * End of ZSYTRS_AA_2STAGE
278 *
279  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine ztrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
ZTRSM
Definition: ztrsm.f:180
subroutine zgbtrs(TRANS, N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO)
ZGBTRS
Definition: zgbtrs.f:138
subroutine zlaswp(N, A, LDA, K1, K2, IPIV, INCX)
ZLASWP performs a series of row interchanges on a general rectangular matrix.
Definition: zlaswp.f:115
subroutine zsytrs_aa_2stage(UPLO, N, NRHS, A, LDA, TB, LTB, IPIV, IPIV2, B, LDB, INFO)
ZSYTRS_AA_2STAGE