1*> \brief \b DSYT01
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 DSYT01( 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   A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ),
22*      $                   RWORK( * )
23*       ..
24*
25*
26*> \par Purpose:
27*  =============
28*>
29*> \verbatim
30*>
31*> DSYT01 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DSYTRF.
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 DSYTRF.
86*> \endverbatim
87*>
88*> \param[out] C
89*> \verbatim
90*>          C is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (N)
102*> \endverbatim
103*>
104*> \param[out] RESID
105*> \verbatim
106*>          RESID is DOUBLE PRECISION
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 double_lin
120*
121*  =====================================================================
122      SUBROUTINE DSYT01( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC,
123     $                   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      DOUBLE PRECISION   A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ),
137     $                   RWORK( * )
138*     ..
139*
140*  =====================================================================
141*
142*     .. Parameters ..
143      DOUBLE PRECISION   ZERO, ONE
144      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
145*     ..
146*     .. Local Scalars ..
147      INTEGER            I, INFO, J
148      DOUBLE PRECISION   ANORM, EPS
149*     ..
150*     .. External Functions ..
151      LOGICAL            LSAME
152      DOUBLE PRECISION   DLAMCH, DLANSY
153      EXTERNAL           LSAME, DLAMCH, DLANSY
154*     ..
155*     .. External Subroutines ..
156      EXTERNAL           DLASET, DLAVSY
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 = DLAMCH( 'Epsilon' )
173      ANORM = DLANSY( '1', UPLO, N, A, LDA, RWORK )
174*
175*     Initialize C to the identity matrix.
176*
177      CALL DLASET( 'Full', N, N, ZERO, ONE, C, LDC )
178*
179*     Call DLAVSY to form the product D * U' (or D * L' ).
180*
181      CALL DLAVSY( UPLO, 'Transpose', 'Non-unit', N, N, AFAC, LDAFAC,
182     $             IPIV, C, LDC, INFO )
183*
184*     Call DLAVSY again to multiply by U (or L ).
185*
186      CALL DLAVSY( UPLO, 'No transpose', 'Unit', N, N, AFAC, LDAFAC,
187     $             IPIV, C, LDC, INFO )
188*
189*     Compute the difference  C - A .
190*
191      IF( LSAME( UPLO, 'U' ) ) THEN
192         DO 20 J = 1, N
193            DO 10 I = 1, J
194               C( I, J ) = C( I, J ) - A( I, J )
195   10       CONTINUE
196   20    CONTINUE
197      ELSE
198         DO 40 J = 1, N
199            DO 30 I = J, N
200               C( I, J ) = C( I, J ) - A( I, J )
201   30       CONTINUE
202   40    CONTINUE
203      END IF
204*
205*     Compute norm( C - A ) / ( N * norm(A) * EPS )
206*
207      RESID = DLANSY( '1', UPLO, N, C, LDC, RWORK )
208*
209      IF( ANORM.LE.ZERO ) THEN
210         IF( RESID.NE.ZERO )
211     $      RESID = ONE / EPS
212      ELSE
213         RESID = ( ( RESID / DBLE( N ) ) / ANORM ) / EPS
214      END IF
215*
216      RETURN
217*
218*     End of DSYT01
219*
220      END
221