1*> \brief \b DSYT01_3
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_3( UPLO, N, A, LDA, AFAC, LDAFAC, E, IPIV, C,
12*                            LDC, 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*      $                   E( * ), RWORK( * )
23*       ..
24*
25*
26*> \par Purpose:
27*  =============
28*>
29*> \verbatim
30*>
31*> DSYT01_3 reconstructs a symmetric indefinite matrix A from its
32*> block L*D*L' or U*D*U' factorization computed by DSYTRF_RK
33*> (or DSYTRF_BK) and computes the residual
34*>    norm( C - A ) / ( N * norm(A) * EPS ),
35*> where C is the reconstructed matrix and EPS is the machine epsilon.
36*> \endverbatim
37*
38*  Arguments:
39*  ==========
40*
41*> \param[in] UPLO
42*> \verbatim
43*>          UPLO is CHARACTER*1
44*>          Specifies whether the upper or lower triangular part of the
45*>          symmetric matrix A is stored:
46*>          = 'U':  Upper triangular
47*>          = 'L':  Lower triangular
48*> \endverbatim
49*>
50*> \param[in] N
51*> \verbatim
52*>          N is INTEGER
53*>          The number of rows and columns of the matrix A.  N >= 0.
54*> \endverbatim
55*>
56*> \param[in] A
57*> \verbatim
58*>          A is DOUBLE PRECISION array, dimension (LDA,N)
59*>          The original symmetric matrix A.
60*> \endverbatim
61*>
62*> \param[in] LDA
63*> \verbatim
64*>          LDA is INTEGER
65*>          The leading dimension of the array A.  LDA >= max(1,N)
66*> \endverbatim
67*>
68*> \param[in] AFAC
69*> \verbatim
70*>          AFAC is DOUBLE PRECISION array, dimension (LDAFAC,N)
71*>          Diagonal of the block diagonal matrix D and factors U or L
72*>          as computed by DSYTRF_RK and DSYTRF_BK:
73*>            a) ONLY diagonal elements of the symmetric block diagonal
74*>               matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
75*>               (superdiagonal (or subdiagonal) elements of D
76*>                should be provided on entry in array E), and
77*>            b) If UPLO = 'U': factor U in the superdiagonal part of A.
78*>               If UPLO = 'L': factor L in the subdiagonal part of A.
79*> \endverbatim
80*>
81*> \param[in] LDAFAC
82*> \verbatim
83*>          LDAFAC is INTEGER
84*>          The leading dimension of the array AFAC.
85*>          LDAFAC >= max(1,N).
86*> \endverbatim
87*>
88*> \param[in] E
89*> \verbatim
90*>          E is DOUBLE PRECISION array, dimension (N)
91*>          On entry, contains the superdiagonal (or subdiagonal)
92*>          elements of the symmetric block diagonal matrix D
93*>          with 1-by-1 or 2-by-2 diagonal blocks, where
94*>          If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced;
95*>          If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.
96*> \endverbatim
97*>
98*> \param[in] IPIV
99*> \verbatim
100*>          IPIV is INTEGER array, dimension (N)
101*>          The pivot indices from DSYTRF_RK (or DSYTRF_BK).
102*> \endverbatim
103*>
104*> \param[out] C
105*> \verbatim
106*>          C is DOUBLE PRECISION array, dimension (LDC,N)
107*> \endverbatim
108*>
109*> \param[in] LDC
110*> \verbatim
111*>          LDC is INTEGER
112*>          The leading dimension of the array C.  LDC >= max(1,N).
113*> \endverbatim
114*>
115*> \param[out] RWORK
116*> \verbatim
117*>          RWORK is DOUBLE PRECISION array, dimension (N)
118*> \endverbatim
119*>
120*> \param[out] RESID
121*> \verbatim
122*>          RESID is DOUBLE PRECISION
123*>          If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
124*>          If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )
125*> \endverbatim
126*
127*  Authors:
128*  ========
129*
130*> \author Univ. of Tennessee
131*> \author Univ. of California Berkeley
132*> \author Univ. of Colorado Denver
133*> \author NAG Ltd.
134*
135*> \date June 2017
136*
137*> \ingroup double_lin
138*
139*  =====================================================================
140      SUBROUTINE DSYT01_3( UPLO, N, A, LDA, AFAC, LDAFAC, E, IPIV, C,
141     $                     LDC, RWORK, RESID )
142*
143*  -- LAPACK test routine (version 3.7.1) --
144*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
145*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
146*     June 2017
147*
148*     .. Scalar Arguments ..
149      CHARACTER          UPLO
150      INTEGER            LDA, LDAFAC, LDC, N
151      DOUBLE PRECISION   RESID
152*     ..
153*     .. Array Arguments ..
154      INTEGER            IPIV( * )
155      DOUBLE PRECISION   A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ),
156     $                   E( * ), RWORK( * )
157*     ..
158*
159*  =====================================================================
160*
161*     .. Parameters ..
162      DOUBLE PRECISION   ZERO, ONE
163      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
164*     ..
165*     .. Local Scalars ..
166      INTEGER            I, INFO, J
167      DOUBLE PRECISION   ANORM, EPS
168*     ..
169*     .. External Functions ..
170      LOGICAL            LSAME
171      DOUBLE PRECISION   DLAMCH, DLANSY
172      EXTERNAL           LSAME, DLAMCH, DLANSY
173*     ..
174*     .. External Subroutines ..
175      EXTERNAL           DLASET, DLAVSY_ROOK, DSYCONVF_ROOK
176*     ..
177*     .. Intrinsic Functions ..
178      INTRINSIC          DBLE
179*     ..
180*     .. Executable Statements ..
181*
182*     Quick exit if N = 0.
183*
184      IF( N.LE.0 ) THEN
185         RESID = ZERO
186         RETURN
187      END IF
188*
189*     a) Revert to multiplyers of L
190*
191      CALL DSYCONVF_ROOK( UPLO, 'R', N, AFAC, LDAFAC, E, IPIV, INFO )
192*
193*     1) Determine EPS and the norm of A.
194*
195      EPS = DLAMCH( 'Epsilon' )
196      ANORM = DLANSY( '1', UPLO, N, A, LDA, RWORK )
197*
198*     2) Initialize C to the identity matrix.
199*
200      CALL DLASET( 'Full', N, N, ZERO, ONE, C, LDC )
201*
202*     3) Call DLAVSY_ROOK to form the product D * U' (or D * L' ).
203*
204      CALL DLAVSY_ROOK( UPLO, 'Transpose', 'Non-unit', N, N, AFAC,
205     $                  LDAFAC, IPIV, C, LDC, INFO )
206*
207*     4) Call DLAVSY_ROOK again to multiply by U (or L ).
208*
209      CALL DLAVSY_ROOK( UPLO, 'No transpose', 'Unit', N, N, AFAC,
210     $                  LDAFAC, IPIV, C, LDC, INFO )
211*
212*     5) Compute the difference  C - A.
213*
214      IF( LSAME( UPLO, 'U' ) ) THEN
215         DO J = 1, N
216            DO I = 1, J
217               C( I, J ) = C( I, J ) - A( I, J )
218            END DO
219         END DO
220      ELSE
221         DO J = 1, N
222            DO I = J, N
223               C( I, J ) = C( I, J ) - A( I, J )
224            END DO
225         END DO
226      END IF
227*
228*     6) Compute norm( C - A ) / ( N * norm(A) * EPS )
229*
230      RESID = DLANSY( '1', UPLO, N, C, LDC, RWORK )
231*
232      IF( ANORM.LE.ZERO ) THEN
233         IF( RESID.NE.ZERO )
234     $      RESID = ONE / EPS
235      ELSE
236         RESID = ( ( RESID / DBLE( N ) ) / ANORM ) / EPS
237      END IF
238
239*
240*     b) Convert to factor of L (or U)
241*
242      CALL DSYCONVF_ROOK( UPLO, 'C', N, AFAC, LDAFAC, E, IPIV, INFO )
243*
244      RETURN
245*
246*     End of DSYT01_3
247*
248      END
249