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*> \date November 2013
120*
121*> \ingroup double_lin
122*
123*  =====================================================================
124      SUBROUTINE DSYT01( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC,
125     $                   RWORK, RESID )
126*
127*  -- LAPACK test routine (version 3.5.0) --
128*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
129*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
130*     November 2013
131*
132*     .. Scalar Arguments ..
133      CHARACTER          UPLO
134      INTEGER            LDA, LDAFAC, LDC, N
135      DOUBLE PRECISION   RESID
136*     ..
137*     .. Array Arguments ..
138      INTEGER            IPIV( * )
139      DOUBLE PRECISION   A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ),
140     $                   RWORK( * )
141*     ..
142*
143*  =====================================================================
144*
145*     .. Parameters ..
146      DOUBLE PRECISION   ZERO, ONE
147      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
148*     ..
149*     .. Local Scalars ..
150      INTEGER            I, INFO, J
151      DOUBLE PRECISION   ANORM, EPS
152*     ..
153*     .. External Functions ..
154      LOGICAL            LSAME
155      DOUBLE PRECISION   DLAMCH, DLANSY
156      EXTERNAL           LSAME, DLAMCH, DLANSY
157*     ..
158*     .. External Subroutines ..
159      EXTERNAL           DLASET, DLAVSY
160*     ..
161*     .. Intrinsic Functions ..
162      INTRINSIC          DBLE
163*     ..
164*     .. Executable Statements ..
165*
166*     Quick exit if N = 0.
167*
168      IF( N.LE.0 ) THEN
169         RESID = ZERO
170         RETURN
171      END IF
172*
173*     Determine EPS and the norm of A.
174*
175      EPS = DLAMCH( 'Epsilon' )
176      ANORM = DLANSY( '1', UPLO, N, A, LDA, RWORK )
177*
178*     Initialize C to the identity matrix.
179*
180      CALL DLASET( 'Full', N, N, ZERO, ONE, C, LDC )
181*
182*     Call DLAVSY to form the product D * U' (or D * L' ).
183*
184      CALL DLAVSY( UPLO, 'Transpose', 'Non-unit', N, N, AFAC, LDAFAC,
185     $             IPIV, C, LDC, INFO )
186*
187*     Call DLAVSY again to multiply by U (or L ).
188*
189      CALL DLAVSY( UPLO, 'No transpose', 'Unit', N, N, AFAC, LDAFAC,
190     $             IPIV, C, LDC, INFO )
191*
192*     Compute the difference  C - A .
193*
194      IF( LSAME( UPLO, 'U' ) ) THEN
195         DO 20 J = 1, N
196            DO 10 I = 1, J
197               C( I, J ) = C( I, J ) - A( I, J )
198   10       CONTINUE
199   20    CONTINUE
200      ELSE
201         DO 40 J = 1, N
202            DO 30 I = J, N
203               C( I, J ) = C( I, J ) - A( I, J )
204   30       CONTINUE
205   40    CONTINUE
206      END IF
207*
208*     Compute norm( C - A ) / ( N * norm(A) * EPS )
209*
210      RESID = DLANSY( '1', UPLO, N, C, LDC, RWORK )
211*
212      IF( ANORM.LE.ZERO ) THEN
213         IF( RESID.NE.ZERO )
214     $      RESID = ONE / EPS
215      ELSE
216         RESID = ( ( RESID / DBLE( N ) ) / ANORM ) / EPS
217      END IF
218*
219      RETURN
220*
221*     End of DSYT01
222*
223      END
224