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
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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*> \date November 2017
137*
138*> \ingroup complex16SYcomputational
139*
140*  =====================================================================
141      SUBROUTINE ZHETRS_AA_2STAGE( UPLO, N, NRHS, A, LDA, TB, LTB,
142     $                             IPIV, IPIV2, B, LDB, INFO )
143*
144*  -- LAPACK computational routine (version 3.8.0) --
145*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
146*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
147*     November 2017
148*
149      IMPLICIT NONE
150*
151*     .. Scalar Arguments ..
152      CHARACTER          UPLO
153      INTEGER            N, NRHS, LDA, LTB, LDB, INFO
154*     ..
155*     .. Array Arguments ..
156      INTEGER            IPIV( * ), IPIV2( * )
157      COMPLEX*16         A( LDA, * ), TB( * ), B( LDB, * )
158*     ..
159*
160*  =====================================================================
161*
162      COMPLEX*16         ONE
163      PARAMETER          ( ONE = ( 1.0D+0, 0.0D+0 ) )
164*     ..
165*     .. Local Scalars ..
166      INTEGER            LDTB, NB
167      LOGICAL            UPPER
168*     ..
169*     .. External Functions ..
170      LOGICAL            LSAME
171      EXTERNAL           LSAME
172*     ..
173*     .. External Subroutines ..
174      EXTERNAL           ZGBTRS, ZLASWP, ZTRSM, XERBLA
175*     ..
176*     .. Intrinsic Functions ..
177      INTRINSIC          MAX
178*     ..
179*     .. Executable Statements ..
180*
181      INFO = 0
182      UPPER = LSAME( UPLO, 'U' )
183      IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
184         INFO = -1
185      ELSE IF( N.LT.0 ) THEN
186         INFO = -2
187      ELSE IF( NRHS.LT.0 ) THEN
188         INFO = -3
189      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
190         INFO = -5
191      ELSE IF( LTB.LT.( 4*N ) ) THEN
192         INFO = -7
193      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
194         INFO = -11
195      END IF
196      IF( INFO.NE.0 ) THEN
197         CALL XERBLA( 'ZHETRS_AA_2STAGE', -INFO )
198         RETURN
199      END IF
200*
201*     Quick return if possible
202*
203      IF( N.EQ.0 .OR. NRHS.EQ.0 )
204     $   RETURN
205*
206*     Read NB and compute LDTB
207*
208      NB = INT( TB( 1 ) )
209      LDTB = LTB/N
210*
211      IF( UPPER ) THEN
212*
213*        Solve A*X = B, where A = U**H*T*U.
214*
215         IF( N.GT.NB ) THEN
216*
217*           Pivot, P**T * B -> B
218*
219            CALL ZLASWP( NRHS, B, LDB, NB+1, N, IPIV, 1 )
220*
221*           Compute (U**H \ B) -> B    [ (U**H \P**T * B) ]
222*
223            CALL ZTRSM( 'L', 'U', 'C', 'U', N-NB, NRHS, ONE, A(1, NB+1),
224     $                 LDA, B(NB+1, 1), LDB)
225*
226         END IF
227*
228*        Compute T \ B -> B   [ T \ (U**H \P**T * B) ]
229*
230         CALL ZGBTRS( 'N', N, NB, NB, NRHS, TB, LDTB, IPIV2, B, LDB,
231     $               INFO)
232         IF( N.GT.NB ) THEN
233*
234*           Compute (U \ B) -> B   [ U \ (T \ (U**H \P**T * B) ) ]
235*
236            CALL ZTRSM( 'L', 'U', 'N', 'U', N-NB, NRHS, ONE, A(1, NB+1),
237     $                  LDA, B(NB+1, 1), LDB)
238*
239*           Pivot, P * B -> B  [ P * (U \ (T \ (U**H \P**T * B) )) ]
240*
241            CALL ZLASWP( NRHS, B, LDB, NB+1, N, IPIV, -1 )
242*
243         END IF
244*
245      ELSE
246*
247*        Solve A*X = B, where A = L*T*L**H.
248*
249         IF( N.GT.NB ) THEN
250*
251*           Pivot, P**T * B -> B
252*
253            CALL ZLASWP( NRHS, B, LDB, NB+1, N, IPIV, 1 )
254*
255*           Compute (L \ B) -> B    [ (L \P**T * B) ]
256*
257            CALL ZTRSM( 'L', 'L', 'N', 'U', N-NB, NRHS, ONE, A(NB+1, 1),
258     $                 LDA, B(NB+1, 1), LDB)
259*
260         END IF
261*
262*        Compute T \ B -> B   [ T \ (L \P**T * B) ]
263*
264         CALL ZGBTRS( 'N', N, NB, NB, NRHS, TB, LDTB, IPIV2, B, LDB,
265     $               INFO)
266         IF( N.GT.NB ) THEN
267*
268*           Compute (L**H \ B) -> B   [ L**H \ (T \ (L \P**T * B) ) ]
269*
270            CALL ZTRSM( 'L', 'L', 'C', 'U', N-NB, NRHS, ONE, A(NB+1, 1),
271     $                  LDA, B(NB+1, 1), LDB)
272*
273*           Pivot, P * B -> B  [ P * (L**H \ (T \ (L \P**T * B) )) ]
274*
275            CALL ZLASWP( NRHS, B, LDB, NB+1, N, IPIV, -1 )
276*
277         END IF
278      END IF
279*
280      RETURN
281*
282*     End of ZHETRS_AA_2STAGE
283*
284      END
285