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*> \ingroup complex16_lin
120*
121*  =====================================================================
122      SUBROUTINE ZSYT01_AA( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C,
123     $                      LDC, RWORK, RESID )
124*
125*  -- LAPACK test routine --
126*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
127*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
128*
129*     .. Scalar Arguments ..
130      CHARACTER          UPLO
131      INTEGER            LDA, LDAFAC, LDC, N
132      DOUBLE PRECISION   RESID
133*     ..
134*     .. Array Arguments ..
135      INTEGER            IPIV( * )
136      COMPLEX*16         A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * )
137      DOUBLE PRECISION   RWORK( * )
138*     ..
139*
140*  =====================================================================
141*
142*     .. Parameters ..
143      DOUBLE PRECISION   ZERO, ONE
144      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
145      COMPLEX*16         CZERO, CONE
146      PARAMETER          ( CZERO = 0.0E+0, CONE = 1.0E+0 )
147*     ..
148*     .. Local Scalars ..
149      INTEGER            I, J
150      DOUBLE PRECISION   ANORM, EPS
151*     ..
152*     .. External Functions ..
153      LOGICAL            LSAME
154      DOUBLE PRECISION   DLAMCH, ZLANSY
155      EXTERNAL           LSAME, DLAMCH, ZLANSY
156*     ..
157*     .. External Subroutines ..
158      EXTERNAL           ZLASET, ZLAVSY
159*     ..
160*     .. Intrinsic Functions ..
161      INTRINSIC          DBLE
162*     ..
163*     .. Executable Statements ..
164*
165*     Quick exit if N = 0.
166*
167      IF( N.LE.0 ) THEN
168         RESID = ZERO
169         RETURN
170      END IF
171*
172*     Determine EPS and the norm of A.
173*
174      EPS = DLAMCH( 'Epsilon' )
175      ANORM = ZLANSY( '1', UPLO, N, A, LDA, RWORK )
176*
177*     Initialize C to the tridiagonal matrix T.
178*
179      CALL ZLASET( 'Full', N, N, CZERO, CZERO, C, LDC )
180      CALL ZLACPY( 'F', 1, N, AFAC( 1, 1 ), LDAFAC+1, C( 1, 1 ), LDC+1 )
181      IF( N.GT.1 ) THEN
182         IF( LSAME( UPLO, 'U' ) ) THEN
183            CALL ZLACPY( 'F', 1, N-1, AFAC( 1, 2 ), LDAFAC+1, C( 1, 2 ),
184     $                   LDC+1 )
185            CALL ZLACPY( 'F', 1, N-1, AFAC( 1, 2 ), LDAFAC+1, C( 2, 1 ),
186     $                   LDC+1 )
187         ELSE
188            CALL ZLACPY( 'F', 1, N-1, AFAC( 2, 1 ), LDAFAC+1, C( 1, 2 ),
189     $                   LDC+1 )
190            CALL ZLACPY( 'F', 1, N-1, AFAC( 2, 1 ), LDAFAC+1, C( 2, 1 ),
191     $                   LDC+1 )
192         ENDIF
193*
194*        Call ZTRMM to form the product U' * D (or L * D ).
195*
196         IF( LSAME( UPLO, 'U' ) ) THEN
197            CALL ZTRMM( 'Left', UPLO, 'Transpose', 'Unit', N-1, N,
198     $                  CONE, AFAC( 1, 2 ), LDAFAC, C( 2, 1 ), LDC )
199         ELSE
200            CALL ZTRMM( 'Left', UPLO, 'No transpose', 'Unit', N-1, N,
201     $                  CONE, AFAC( 2, 1 ), LDAFAC, C( 2, 1 ), LDC )
202         END IF
203*
204*        Call ZTRMM again to multiply by U (or L ).
205*
206         IF( LSAME( UPLO, 'U' ) ) THEN
207            CALL ZTRMM( 'Right', UPLO, 'No transpose', 'Unit', N, N-1,
208     $                  CONE, AFAC( 1, 2 ), LDAFAC, C( 1, 2 ), LDC )
209         ELSE
210            CALL ZTRMM( 'Right', UPLO, 'Transpose', 'Unit', N, N-1,
211     $                  CONE, AFAC( 2, 1 ), LDAFAC, C( 1, 2 ), LDC )
212         END IF
213      ENDIF
214*
215*     Apply symmetric pivots
216*
217      DO J = N, 1, -1
218         I = IPIV( J )
219         IF( I.NE.J )
220     $      CALL ZSWAP( N, C( J, 1 ), LDC, C( I, 1 ), LDC )
221      END DO
222      DO J = N, 1, -1
223         I = IPIV( J )
224         IF( I.NE.J )
225     $      CALL ZSWAP( N, C( 1, J ), 1, C( 1, I ), 1 )
226      END DO
227*
228*
229*     Compute the difference  C - A .
230*
231      IF( LSAME( UPLO, 'U' ) ) THEN
232         DO J = 1, N
233            DO I = 1, J
234               C( I, J ) = C( I, J ) - A( I, J )
235            END DO
236         END DO
237      ELSE
238         DO J = 1, N
239            DO I = J, N
240               C( I, J ) = C( I, J ) - A( I, J )
241            END DO
242         END DO
243      END IF
244*
245*     Compute norm( C - A ) / ( N * norm(A) * EPS )
246*
247      RESID = ZLANSY( '1', UPLO, N, C, LDC, RWORK )
248*
249      IF( ANORM.LE.ZERO ) THEN
250         IF( RESID.NE.ZERO )
251     $      RESID = ONE / EPS
252      ELSE
253         RESID = ( ( RESID / DBLE( N ) ) / ANORM ) / EPS
254      END IF
255*
256      RETURN
257*
258*     End of ZSYT01_AA
259*
260      END
261