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( 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 complex 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, EPS is the machine epsilon,
35*> L' is the transpose of L, and U' is the transpose of U.
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*>          complex 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 COMPLEX*16 array, dimension (LDA,N)
59*>          The original complex 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 COMPLEX*16 array, dimension (LDAFAC,N)
71*>          The factored form of the matrix A.  AFAC contains the block
72*>          diagonal matrix D and the multipliers used to obtain the
73*>          factor L or U from the block L*D*L' or U*D*U' factorization
74*>          as computed by ZSYTRF.
75*> \endverbatim
76*>
77*> \param[in] LDAFAC
78*> \verbatim
79*>          LDAFAC is INTEGER
80*>          The leading dimension of the array AFAC.  LDAFAC >= max(1,N).
81*> \endverbatim
82*>
83*> \param[in] IPIV
84*> \verbatim
85*>          IPIV is INTEGER array, dimension (N)
86*>          The pivot indices from ZSYTRF.
87*> \endverbatim
88*>
89*> \param[out] C
90*> \verbatim
91*>          C is COMPLEX*16 array, dimension (LDC,N)
92*> \endverbatim
93*>
94*> \param[in] LDC
95*> \verbatim
96*>          LDC is INTEGER
97*>          The leading dimension of the array C.  LDC >= max(1,N).
98*> \endverbatim
99*>
100*> \param[out] RWORK
101*> \verbatim
102*>          RWORK is DOUBLE PRECISION array, dimension (N)
103*> \endverbatim
104*>
105*> \param[out] RESID
106*> \verbatim
107*>          RESID is DOUBLE PRECISION
108*>          If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
109*>          If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )
110*> \endverbatim
111*
112*  Authors:
113*  ========
114*
115*> \author Univ. of Tennessee
116*> \author Univ. of California Berkeley
117*> \author Univ. of Colorado Denver
118*> \author NAG Ltd.
119*
120*> \date November 2013
121*
122*> \ingroup complex16_lin
123*
124*  =====================================================================
125      SUBROUTINE ZSYT01( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC,
126     $                   RWORK, RESID )
127*
128*  -- LAPACK test routine (version 3.5.0) --
129*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
130*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
131*     November 2013
132*
133*     .. Scalar Arguments ..
134      CHARACTER          UPLO
135      INTEGER            LDA, LDAFAC, LDC, N
136      DOUBLE PRECISION   RESID
137*     ..
138*     .. Array Arguments ..
139      INTEGER            IPIV( * )
140      DOUBLE PRECISION   RWORK( * )
141      COMPLEX*16         A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * )
142*     ..
143*
144*  =====================================================================
145*
146*     .. Parameters ..
147      DOUBLE PRECISION   ZERO, ONE
148      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
149      COMPLEX*16         CZERO, CONE
150      PARAMETER          ( CZERO = ( 0.0D+0, 0.0D+0 ),
151     $                   CONE = ( 1.0D+0, 0.0D+0 ) )
152*     ..
153*     .. Local Scalars ..
154      INTEGER            I, INFO, J
155      DOUBLE PRECISION   ANORM, EPS
156*     ..
157*     .. External Functions ..
158      LOGICAL            LSAME
159      DOUBLE PRECISION   DLAMCH, ZLANSY
160      EXTERNAL           LSAME, DLAMCH, ZLANSY
161*     ..
162*     .. External Subroutines ..
163      EXTERNAL           ZLASET, ZLAVSY
164*     ..
165*     .. Intrinsic Functions ..
166      INTRINSIC          DBLE
167*     ..
168*     .. Executable Statements ..
169*
170*     Quick exit if N = 0.
171*
172      IF( N.LE.0 ) THEN
173         RESID = ZERO
174         RETURN
175      END IF
176*
177*     Determine EPS and the norm of A.
178*
179      EPS = DLAMCH( 'Epsilon' )
180      ANORM = ZLANSY( '1', UPLO, N, A, LDA, RWORK )
181*
182*     Initialize C to the identity matrix.
183*
184      CALL ZLASET( 'Full', N, N, CZERO, CONE, C, LDC )
185*
186*     Call ZLAVSY to form the product D * U' (or D * L' ).
187*
188      CALL ZLAVSY( UPLO, 'Transpose', 'Non-unit', N, N, AFAC, LDAFAC,
189     $             IPIV, C, LDC, INFO )
190*
191*     Call ZLAVSY again to multiply by U (or L ).
192*
193      CALL ZLAVSY( UPLO, 'No transpose', 'Unit', N, N, AFAC, LDAFAC,
194     $             IPIV, C, LDC, INFO )
195*
196*     Compute the difference  C - A .
197*
198      IF( LSAME( UPLO, 'U' ) ) THEN
199         DO 20 J = 1, N
200            DO 10 I = 1, J
201               C( I, J ) = C( I, J ) - A( I, J )
202   10       CONTINUE
203   20    CONTINUE
204      ELSE
205         DO 40 J = 1, N
206            DO 30 I = J, N
207               C( I, J ) = C( I, J ) - A( I, J )
208   30       CONTINUE
209   40    CONTINUE
210      END IF
211*
212*     Compute norm( C - A ) / ( N * norm(A) * EPS )
213*
214      RESID = ZLANSY( '1', UPLO, N, C, LDC, RWORK )
215*
216      IF( ANORM.LE.ZERO ) THEN
217         IF( RESID.NE.ZERO )
218     $      RESID = ONE / EPS
219      ELSE
220         RESID = ( ( RESID / DBLE( N ) ) / ANORM ) / EPS
221      END IF
222*
223      RETURN
224*
225*     End of ZSYT01
226*
227      END
228