1*> \brief \b CHETRS_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 CHETRS_AA_2STAGE + dependencies
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/chetrs_aa_2stage.f">
13*> [TGZ]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/chetrs_aa_2stage.f">
15*> [ZIP]</a>
16*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/chetrs_aa_2stage.f">
17*> [TXT]</a>
18*> \endhtmlonly
19*
20*  Definition:
21*  ===========
22*
23*      SUBROUTINE CHETRS_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            A( LDA, * ), TB( * ), B( LDB, * )
33*       ..
34*
35*> \par Purpose:
36*  =============
37*>
38*> \verbatim
39*>
40*> CHETRS_AA_2STAGE solves a system of linear equations A*X = B with a real
41*> hermitian matrix A using the factorization A = U**T*T*U or
42*> A = L*T*L**T computed by CHETRF_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**T*T*U;
54*>          = 'L':  Lower triangular, form is A = L*T*L**T.
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 array, dimension (LDA,N)
73*>          Details of factors computed by CHETRF_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 array, dimension (LTB)
85*>          Details of factors computed by CHETRF_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*>          CHETRF_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*>          CHETRF_AA_2STAGE.
106*> \endverbatim
107*>
108*> \param[in,out] B
109*> \verbatim
110*>          B is COMPLEX 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 complexSYcomputational
137*
138*  =====================================================================
139      SUBROUTINE CHETRS_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            A( LDA, * ), TB( * ), B( LDB, * )
155*     ..
156*
157*  =====================================================================
158*
159      COMPLEX            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           CGBTRS, CLASWP, CTRSM, 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( 'CHETRS_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*T*U.
211*
212         IF( N.GT.NB ) THEN
213*
214*           Pivot, P**T * B -> B
215*
216            CALL CLASWP( NRHS, B, LDB, NB+1, N, IPIV, 1 )
217*
218*           Compute (U**T \ B) -> B    [ (U**T \P**T * B) ]
219*
220            CALL CTRSM( '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**T \P**T * B) ]
226*
227         CALL CGBTRS( '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 CTRSM( '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 CLASWP( 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 CLASWP( NRHS, B, LDB, NB+1, N, IPIV, 1 )
251*
252*           Compute (L \P**T * B) -> B    [ (L \P**T * B) ]
253*
254            CALL CTRSM( '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 CGBTRS( '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 CTRSM( 'L', 'L', 'C', '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 CLASWP( NRHS, B, LDB, NB+1, N, IPIV, -1 )
273*
274         END IF
275      END IF
276*
277      RETURN
278*
279*     End of CHETRS_AA_2STAGE
280*
281      END
282