1*> \brief \b ZSYT01
2*
3*  =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6*            http://www.netlib.org/lapack/explore-html/
7*
8*  Definition:
9*  ===========
10*
11*       SUBROUTINE ZSYT01_AA( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC,
12*                             RWORK, RESID )
13*
14*       .. Scalar Arguments ..
15*       CHARACTER          UPLO
16*       INTEGER            LDA, LDAFAC, LDC, N
17*       DOUBLE PRECISION   RESID
18*       ..
19*       .. Array Arguments ..
20*       INTEGER            IPIV( * )
21*       DOUBLE PRECISION   RWORK( * )
22*       COMPLEX*16         A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ),
23*       ..
24*
25*
26*> \par Purpose:
27*  =============
28*>
29*> \verbatim
30*>
31*> ZSYT01 reconstructs a hermitian indefinite matrix A from its
32*> block L*D*L' or U*D*U' factorization and computes the residual
33*>    norm( C - A ) / ( N * norm(A) * EPS ),
34*> where C is the reconstructed matrix and EPS is the machine epsilon.
35*> \endverbatim
36*
37*  Arguments:
38*  ==========
39*
40*> \param[in] UPLO
41*> \verbatim
42*>          UPLO is CHARACTER*1
43*>          Specifies whether the upper or lower triangular part of the
44*>          hermitian matrix A is stored:
45*>          = 'U':  Upper triangular
46*>          = 'L':  Lower triangular
47*> \endverbatim
48*>
49*> \param[in] N
50*> \verbatim
51*>          N is INTEGER
52*>          The number of rows and columns of the matrix A.  N >= 0.
53*> \endverbatim
54*>
55*> \param[in] A
56*> \verbatim
57*>          A is COMPLEX*16 array, dimension (LDA,N)
58*>          The original hermitian matrix A.
59*> \endverbatim
60*>
61*> \param[in] LDA
62*> \verbatim
63*>          LDA is INTEGER
64*>          The leading dimension of the array A.  LDA >= max(1,N)
65*> \endverbatim
66*>
67*> \param[in] AFAC
68*> \verbatim
69*>          AFAC is COMPLEX*16 array, dimension (LDAFAC,N)
70*>          The factored form of the matrix A.  AFAC contains the block
71*>          diagonal matrix D and the multipliers used to obtain the
72*>          factor L or U from the block L*D*L' or U*D*U' factorization
73*>          as computed by ZSYTRF.
74*> \endverbatim
75*>
76*> \param[in] LDAFAC
77*> \verbatim
78*>          LDAFAC is INTEGER
79*>          The leading dimension of the array AFAC.  LDAFAC >= max(1,N).
80*> \endverbatim
81*>
82*> \param[in] IPIV
83*> \verbatim
84*>          IPIV is INTEGER array, dimension (N)
85*>          The pivot indices from ZSYTRF.
86*> \endverbatim
87*>
88*> \param[out] C
89*> \verbatim
90*>          C is COMPLEX*16 array, dimension (LDC,N)
91*> \endverbatim
92*>
93*> \param[in] LDC
94*> \verbatim
95*>          LDC is INTEGER
96*>          The leading dimension of the array C.  LDC >= max(1,N).
97*> \endverbatim
98*>
99*> \param[out] RWORK
100*> \verbatim
101*>          RWORK is COMPLEX*16 array, dimension (N)
102*> \endverbatim
103*>
104*> \param[out] RESID
105*> \verbatim
106*>          RESID is COMPLEX*16
107*>          If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
108*>          If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )
109*> \endverbatim
110*
111*  Authors:
112*  ========
113*
114*> \author Univ. of Tennessee
115*> \author Univ. of California Berkeley
116*> \author Univ. of Colorado Denver
117*> \author NAG Ltd.
118*
119*> \date December 2016
120*
121*  @generated from LIN/dsyt01_aa.f, fortran d -> z, Thu Nov 17 13:01:50 2016
122*
123*> \ingroup complex16_lin
124*
125*  =====================================================================
126      SUBROUTINE ZSYT01_AA( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C,
127     $                      LDC, RWORK, RESID )
128*
129*  -- LAPACK test routine (version 3.7.0) --
130*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
131*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
132*     December 2016
133*
134*     .. Scalar Arguments ..
135      CHARACTER          UPLO
136      INTEGER            LDA, LDAFAC, LDC, N
137      DOUBLE PRECISION   RESID
138*     ..
139*     .. Array Arguments ..
140      INTEGER            IPIV( * )
141      COMPLEX*16         A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * )
142      DOUBLE PRECISION   RWORK( * )
143*     ..
144*
145*  =====================================================================
146*
147*     .. Parameters ..
148      DOUBLE PRECISION   ZERO, ONE
149      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
150      COMPLEX*16         CZERO, CONE
151      PARAMETER          ( CZERO = 0.0E+0, CONE = 1.0E+0 )
152*     ..
153*     .. Local Scalars ..
154      INTEGER            I, J
155      DOUBLE PRECISION   ANORM, EPS
156*     ..
157*     .. External Functions ..
158      LOGICAL            LSAME
159      DOUBLE PRECISION   DLAMCH, ZLANSY
160      EXTERNAL           LSAME, DLAMCH, ZLANSY
161*     ..
162*     .. External Subroutines ..
163      EXTERNAL           ZLASET, ZLAVSY
164*     ..
165*     .. Intrinsic Functions ..
166      INTRINSIC          DBLE
167*     ..
168*     .. Executable Statements ..
169*
170*     Quick exit if N = 0.
171*
172      IF( N.LE.0 ) THEN
173         RESID = ZERO
174         RETURN
175      END IF
176*
177*     Determine EPS and the norm of A.
178*
179      EPS = DLAMCH( 'Epsilon' )
180      ANORM = ZLANSY( '1', UPLO, N, A, LDA, RWORK )
181*
182*     Initialize C to the tridiagonal matrix T.
183*
184      CALL ZLASET( 'Full', N, N, CZERO, CZERO, C, LDC )
185      CALL ZLACPY( 'F', 1, N, AFAC( 1, 1 ), LDAFAC+1, C( 1, 1 ), LDC+1 )
186      IF( N.GT.1 ) THEN
187         IF( LSAME( UPLO, 'U' ) ) THEN
188            CALL ZLACPY( 'F', 1, N-1, AFAC( 1, 2 ), LDAFAC+1, C( 1, 2 ),
189     $                   LDC+1 )
190            CALL ZLACPY( 'F', 1, N-1, AFAC( 1, 2 ), LDAFAC+1, C( 2, 1 ),
191     $                   LDC+1 )
192         ELSE
193            CALL ZLACPY( 'F', 1, N-1, AFAC( 2, 1 ), LDAFAC+1, C( 1, 2 ),
194     $                   LDC+1 )
195            CALL ZLACPY( 'F', 1, N-1, AFAC( 2, 1 ), LDAFAC+1, C( 2, 1 ),
196     $                   LDC+1 )
197         ENDIF
198*
199*        Call ZTRMM to form the product U' * D (or L * D ).
200*
201         IF( LSAME( UPLO, 'U' ) ) THEN
202            CALL ZTRMM( 'Left', UPLO, 'Transpose', 'Unit', N-1, N,
203     $                  CONE, AFAC( 1, 2 ), LDAFAC, C( 2, 1 ), LDC )
204         ELSE
205            CALL ZTRMM( 'Left', UPLO, 'No transpose', 'Unit', N-1, N,
206     $                  CONE, AFAC( 2, 1 ), LDAFAC, C( 2, 1 ), LDC )
207         END IF
208*
209*        Call ZTRMM again to multiply by U (or L ).
210*
211         IF( LSAME( UPLO, 'U' ) ) THEN
212            CALL ZTRMM( 'Right', UPLO, 'No transpose', 'Unit', N, N-1,
213     $                  CONE, AFAC( 1, 2 ), LDAFAC, C( 1, 2 ), LDC )
214         ELSE
215            CALL ZTRMM( 'Right', UPLO, 'Transpose', 'Unit', N, N-1,
216     $                  CONE, AFAC( 2, 1 ), LDAFAC, C( 1, 2 ), LDC )
217         END IF
218      ENDIF
219*
220*     Apply symmetric pivots
221*
222      DO J = N, 1, -1
223         I = IPIV( J )
224         IF( I.NE.J )
225     $      CALL ZSWAP( N, C( J, 1 ), LDC, C( I, 1 ), LDC )
226      END DO
227      DO J = N, 1, -1
228         I = IPIV( J )
229         IF( I.NE.J )
230     $      CALL ZSWAP( N, C( 1, J ), 1, C( 1, I ), 1 )
231      END DO
232*
233*
234*     Compute the difference  C - A .
235*
236      IF( LSAME( UPLO, 'U' ) ) THEN
237         DO J = 1, N
238            DO I = 1, J
239               C( I, J ) = C( I, J ) - A( I, J )
240            END DO
241         END DO
242      ELSE
243         DO J = 1, N
244            DO I = J, N
245               C( I, J ) = C( I, J ) - A( I, J )
246            END DO
247         END DO
248      END IF
249*
250*     Compute norm( C - A ) / ( N * norm(A) * EPS )
251*
252      RESID = ZLANSY( '1', UPLO, N, C, LDC, RWORK )
253*
254      IF( ANORM.LE.ZERO ) THEN
255         IF( RESID.NE.ZERO )
256     $      RESID = ONE / EPS
257      ELSE
258         RESID = ( ( RESID / DBLE( N ) ) / ANORM ) / EPS
259      END IF
260*
261      RETURN
262*
263*     End of ZSYT01
264*
265      END
266