1*> \brief \b SSYT01_AA
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 SSYT01_AA( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV,
12*                             C, LDC, RWORK, RESID )
13*
14*       .. Scalar Arguments ..
15*       CHARACTER          UPLO
16*       INTEGER            LDA, LDAFAC, LDC, N
17*       REAL               RESID
18*       ..
19*       .. Array Arguments ..
20*       INTEGER            IPIV( * )
21*       REAL               A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ),
22*      $                   RWORK( * )
23*       ..
24*
25*
26*> \par Purpose:
27*  =============
28*>
29*> \verbatim
30*>
31*> SSYT01_AA reconstructs a symmetric 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*>          symmetric 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 REAL array, dimension (LDA,N)
58*>          The original symmetric 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 REAL 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 SSYTRF.
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 SSYTRF.
86*> \endverbatim
87*>
88*> \param[out] C
89*> \verbatim
90*>          C is REAL 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 REAL array, dimension (N)
102*> \endverbatim
103*>
104*> \param[out] RESID
105*> \verbatim
106*>          RESID is REAL
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 real_lin
120*
121*  =====================================================================
122      SUBROUTINE SSYT01_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      REAL               RESID
133*     ..
134*     .. Array Arguments ..
135      INTEGER            IPIV( * )
136      REAL               A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ),
137     $                   RWORK( * )
138*     ..
139*
140*  =====================================================================
141*
142*     .. Parameters ..
143      REAL               ZERO, ONE
144      PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
145*     ..
146*     .. Local Scalars ..
147      INTEGER            I, J
148      REAL               ANORM, EPS
149*     ..
150*     .. External Functions ..
151      LOGICAL            LSAME
152      REAL               SLAMCH, SLANSY
153      EXTERNAL           LSAME, SLAMCH, SLANSY
154*     ..
155*     .. External Subroutines ..
156      EXTERNAL           SLASET, SLAVSY, SSWAP, STRMM, SLACPY
157*     ..
158*     .. Intrinsic Functions ..
159      INTRINSIC          DBLE
160*     ..
161*     .. Executable Statements ..
162*
163*     Quick exit if N = 0.
164*
165      IF( N.LE.0 ) THEN
166         RESID = ZERO
167         RETURN
168      END IF
169*
170*     Determine EPS and the norm of A.
171*
172      EPS = SLAMCH( 'Epsilon' )
173      ANORM = SLANSY( '1', UPLO, N, A, LDA, RWORK )
174*
175*     Initialize C to the tridiagonal matrix T.
176*
177      CALL SLASET( 'Full', N, N, ZERO, ZERO, C, LDC )
178      CALL SLACPY( 'F', 1, N, AFAC( 1, 1 ), LDAFAC+1, C( 1, 1 ), LDC+1 )
179      IF( N.GT.1 ) THEN
180         IF( LSAME( UPLO, 'U' ) ) THEN
181            CALL SLACPY( 'F', 1, N-1, AFAC( 1, 2 ), LDAFAC+1, C( 1, 2 ),
182     $                   LDC+1 )
183            CALL SLACPY( 'F', 1, N-1, AFAC( 1, 2 ), LDAFAC+1, C( 2, 1 ),
184     $                   LDC+1 )
185         ELSE
186            CALL SLACPY( 'F', 1, N-1, AFAC( 2, 1 ), LDAFAC+1, C( 1, 2 ),
187     $                   LDC+1 )
188            CALL SLACPY( 'F', 1, N-1, AFAC( 2, 1 ), LDAFAC+1, C( 2, 1 ),
189     $                   LDC+1 )
190         ENDIF
191*
192*        Call STRMM to form the product U' * D (or L * D ).
193*
194         IF( LSAME( UPLO, 'U' ) ) THEN
195            CALL STRMM( 'Left', UPLO, 'Transpose', 'Unit', N-1, N,
196     $                  ONE, AFAC( 1, 2 ), LDAFAC, C( 2, 1 ), LDC )
197         ELSE
198            CALL STRMM( 'Left', UPLO, 'No transpose', 'Unit', N-1, N,
199     $                  ONE, AFAC( 2, 1 ), LDAFAC, C( 2, 1 ), LDC )
200         END IF
201*
202*        Call STRMM again to multiply by U (or L ).
203*
204         IF( LSAME( UPLO, 'U' ) ) THEN
205            CALL STRMM( 'Right', UPLO, 'No transpose', 'Unit', N, N-1,
206     $                  ONE, AFAC( 1, 2 ), LDAFAC, C( 1, 2 ), LDC )
207         ELSE
208            CALL STRMM( 'Right', UPLO, 'Transpose', 'Unit', N, N-1,
209     $                  ONE, AFAC( 2, 1 ), LDAFAC, C( 1, 2 ), LDC )
210         END IF
211      ENDIF
212*
213*     Apply symmetric pivots
214*
215      DO J = N, 1, -1
216         I = IPIV( J )
217         IF( I.NE.J )
218     $      CALL SSWAP( N, C( J, 1 ), LDC, C( I, 1 ), LDC )
219      END DO
220      DO J = N, 1, -1
221         I = IPIV( J )
222         IF( I.NE.J )
223     $      CALL SSWAP( N, C( 1, J ), 1, C( 1, I ), 1 )
224      END DO
225*
226*
227*     Compute the difference  C - A .
228*
229      IF( LSAME( UPLO, 'U' ) ) THEN
230         DO J = 1, N
231            DO I = 1, J
232               C( I, J ) = C( I, J ) - A( I, J )
233            END DO
234         END DO
235      ELSE
236         DO J = 1, N
237            DO I = J, N
238               C( I, J ) = C( I, J ) - A( I, J )
239            END DO
240         END DO
241      END IF
242*
243*     Compute norm( C - A ) / ( N * norm(A) * EPS )
244*
245      RESID = SLANSY( '1', UPLO, N, C, LDC, RWORK )
246*
247      IF( ANORM.LE.ZERO ) THEN
248         IF( RESID.NE.ZERO )
249     $      RESID = ONE / EPS
250      ELSE
251         RESID = ( ( RESID / DBLE( N ) ) / ANORM ) / EPS
252      END IF
253*
254      RETURN
255*
256*     End of SSYT01_AA
257*
258      END
259