1*> \brief \b CSPT01
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 CSPT01( UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID )
12*
13*       .. Scalar Arguments ..
14*       CHARACTER          UPLO
15*       INTEGER            LDC, N
16*       REAL               RESID
17*       ..
18*       .. Array Arguments ..
19*       INTEGER            IPIV( * )
20*       REAL               RWORK( * )
21*       COMPLEX            A( * ), AFAC( * ), C( LDC, * )
22*       ..
23*
24*
25*> \par Purpose:
26*  =============
27*>
28*> \verbatim
29*>
30*> CSPT01 reconstructs a symmetric indefinite packed matrix A from its
31*> diagonal pivoting factorization A = U*D*U' or A = L*D*L' and computes
32*> 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*>          Hermitian 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 order of the matrix A.  N >= 0.
53*> \endverbatim
54*>
55*> \param[in] A
56*> \verbatim
57*>          A is COMPLEX array, dimension (N*(N+1)/2)
58*>          The original symmetric matrix A, stored as a packed
59*>          triangular matrix.
60*> \endverbatim
61*>
62*> \param[in] AFAC
63*> \verbatim
64*>          AFAC is COMPLEX array, dimension (N*(N+1)/2)
65*>          The factored form of the matrix A, stored as a packed
66*>          triangular matrix.  AFAC contains the block diagonal matrix D
67*>          and the multipliers used to obtain the factor L or U from the
68*>          L*D*L' or U*D*U' factorization as computed by CSPTRF.
69*> \endverbatim
70*>
71*> \param[in] IPIV
72*> \verbatim
73*>          IPIV is INTEGER array, dimension (N)
74*>          The pivot indices from CSPTRF.
75*> \endverbatim
76*>
77*> \param[out] C
78*> \verbatim
79*>          C is COMPLEX array, dimension (LDC,N)
80*> \endverbatim
81*>
82*> \param[in] LDC
83*> \verbatim
84*>          LDC is INTEGER
85*>          The leading dimension of the array C.  LDC >= max(1,N).
86*> \endverbatim
87*>
88*> \param[out] RWORK
89*> \verbatim
90*>          RWORK is REAL array, dimension (N)
91*> \endverbatim
92*>
93*> \param[out] RESID
94*> \verbatim
95*>          RESID is REAL
96*>          If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
97*>          If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )
98*> \endverbatim
99*
100*  Authors:
101*  ========
102*
103*> \author Univ. of Tennessee
104*> \author Univ. of California Berkeley
105*> \author Univ. of Colorado Denver
106*> \author NAG Ltd.
107*
108*> \ingroup complex_lin
109*
110*  =====================================================================
111      SUBROUTINE CSPT01( UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID )
112*
113*  -- LAPACK test routine --
114*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
115*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
116*
117*     .. Scalar Arguments ..
118      CHARACTER          UPLO
119      INTEGER            LDC, N
120      REAL               RESID
121*     ..
122*     .. Array Arguments ..
123      INTEGER            IPIV( * )
124      REAL               RWORK( * )
125      COMPLEX            A( * ), AFAC( * ), C( LDC, * )
126*     ..
127*
128*  =====================================================================
129*
130*     .. Parameters ..
131      REAL               ZERO, ONE
132      PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
133      COMPLEX            CZERO, CONE
134      PARAMETER          ( CZERO = ( 0.0E+0, 0.0E+0 ),
135     $                   CONE = ( 1.0E+0, 0.0E+0 ) )
136*     ..
137*     .. Local Scalars ..
138      INTEGER            I, INFO, J, JC
139      REAL               ANORM, EPS
140*     ..
141*     .. External Functions ..
142      LOGICAL            LSAME
143      REAL               CLANSP, CLANSY, SLAMCH
144      EXTERNAL           LSAME, CLANSP, CLANSY, SLAMCH
145*     ..
146*     .. External Subroutines ..
147      EXTERNAL           CLAVSP, CLASET
148*     ..
149*     .. Intrinsic Functions ..
150      INTRINSIC          REAL
151*     ..
152*     .. Executable Statements ..
153*
154*     Quick exit if N = 0.
155*
156      IF( N.LE.0 ) THEN
157         RESID = ZERO
158         RETURN
159      END IF
160*
161*     Determine EPS and the norm of A.
162*
163      EPS = SLAMCH( 'Epsilon' )
164      ANORM = CLANSP( '1', UPLO, N, A, RWORK )
165*
166*     Initialize C to the identity matrix.
167*
168      CALL CLASET( 'Full', N, N, CZERO, CONE, C, LDC )
169*
170*     Call CLAVSP to form the product D * U' (or D * L' ).
171*
172      CALL CLAVSP( UPLO, 'Transpose', 'Non-unit', N, N, AFAC, IPIV, C,
173     $             LDC, INFO )
174*
175*     Call CLAVSP again to multiply by U ( or L ).
176*
177      CALL CLAVSP( UPLO, 'No transpose', 'Unit', N, N, AFAC, IPIV, C,
178     $             LDC, INFO )
179*
180*     Compute the difference  C - A .
181*
182      IF( LSAME( UPLO, 'U' ) ) THEN
183         JC = 0
184         DO 20 J = 1, N
185            DO 10 I = 1, J
186               C( I, J ) = C( I, J ) - A( JC+I )
187   10       CONTINUE
188            JC = JC + J
189   20    CONTINUE
190      ELSE
191         JC = 1
192         DO 40 J = 1, N
193            DO 30 I = J, N
194               C( I, J ) = C( I, J ) - A( JC+I-J )
195   30       CONTINUE
196            JC = JC + N - J + 1
197   40    CONTINUE
198      END IF
199*
200*     Compute norm( C - A ) / ( N * norm(A) * EPS )
201*
202      RESID = CLANSY( '1', UPLO, N, C, LDC, RWORK )
203*
204      IF( ANORM.LE.ZERO ) THEN
205         IF( RESID.NE.ZERO )
206     $      RESID = ONE / EPS
207      ELSE
208         RESID = ( ( RESID/REAL( N ) )/ANORM ) / EPS
209      END IF
210*
211      RETURN
212*
213*     End of CSPT01
214*
215      END
216