1*> \brief \b CHET01_ROOK
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 CHET01_ROOK( 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*       REAL               RESID
18*       ..
19*       .. Array Arguments ..
20*       INTEGER            IPIV( * )
21*       REAL               RWORK( * )
22*       COMPLEX            A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * )
23*       ..
24*
25*
26*> \par Purpose:
27*  =============
28*>
29*> \verbatim
30*>
31*> CHET01_ROOK reconstructs a complex Hermitian 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 Hermitian 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 array, dimension (LDA,N)
59*>          The original complex Hermitian 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 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 CSYTRF_ROOK.
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 CSYTRF_ROOK.
87*> \endverbatim
88*>
89*> \param[out] C
90*> \verbatim
91*>          C is COMPLEX 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 REAL array, dimension (N)
103*> \endverbatim
104*>
105*> \param[out] RESID
106*> \verbatim
107*>          RESID is REAL
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 complex_lin
123*
124*  =====================================================================
125      SUBROUTINE CHET01_ROOK( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C,
126     $                        LDC, 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      REAL               RESID
137*     ..
138*     .. Array Arguments ..
139      INTEGER            IPIV( * )
140      REAL               RWORK( * )
141      COMPLEX            A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * )
142*     ..
143*
144*  =====================================================================
145*
146*     .. Parameters ..
147      REAL               ZERO, ONE
148      PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
149      COMPLEX            CZERO, CONE
150      PARAMETER          ( CZERO = ( 0.0E+0, 0.0E+0 ),
151     $                   CONE = ( 1.0E+0, 0.0E+0 ) )
152*     ..
153*     .. Local Scalars ..
154      INTEGER            I, INFO, J
155      REAL               ANORM, EPS
156*     ..
157*     .. External Functions ..
158      LOGICAL            LSAME
159      REAL               CLANHE, SLAMCH
160      EXTERNAL           LSAME, CLANHE, SLAMCH
161*     ..
162*     .. External Subroutines ..
163      EXTERNAL           CLASET, CLAVHE_ROOK
164*     ..
165*     .. Intrinsic Functions ..
166      INTRINSIC          AIMAG, REAL
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 = SLAMCH( 'Epsilon' )
180      ANORM = CLANHE( '1', UPLO, N, A, LDA, RWORK )
181*
182*     Check the imaginary parts of the diagonal elements and return with
183*     an error code if any are nonzero.
184*
185      DO 10 J = 1, N
186         IF( AIMAG( AFAC( J, J ) ).NE.ZERO ) THEN
187            RESID = ONE / EPS
188            RETURN
189         END IF
190   10 CONTINUE
191*
192*     Initialize C to the identity matrix.
193*
194      CALL CLASET( 'Full', N, N, CZERO, CONE, C, LDC )
195*
196*     Call CLAVHE_ROOK to form the product D * U' (or D * L' ).
197*
198      CALL CLAVHE_ROOK( UPLO, 'Conjugate', 'Non-unit', N, N, AFAC,
199     $                  LDAFAC, IPIV, C, LDC, INFO )
200*
201*     Call CLAVHE_ROOK again to multiply by U (or L ).
202*
203      CALL CLAVHE_ROOK( UPLO, 'No transpose', 'Unit', N, N, AFAC,
204     $                  LDAFAC, IPIV, C, LDC, INFO )
205*
206*     Compute the difference  C - A .
207*
208      IF( LSAME( UPLO, 'U' ) ) THEN
209         DO 30 J = 1, N
210            DO 20 I = 1, J - 1
211               C( I, J ) = C( I, J ) - A( I, J )
212   20       CONTINUE
213            C( J, J ) = C( J, J ) - REAL( A( J, J ) )
214   30    CONTINUE
215      ELSE
216         DO 50 J = 1, N
217            C( J, J ) = C( J, J ) - REAL( A( J, J ) )
218            DO 40 I = J + 1, N
219               C( I, J ) = C( I, J ) - A( I, J )
220   40       CONTINUE
221   50    CONTINUE
222      END IF
223*
224*     Compute norm( C - A ) / ( N * norm(A) * EPS )
225*
226      RESID = CLANHE( '1', UPLO, N, C, LDC, RWORK )
227*
228      IF( ANORM.LE.ZERO ) THEN
229         IF( RESID.NE.ZERO )
230     $      RESID = ONE / EPS
231      ELSE
232         RESID = ( ( RESID/REAL( N ) )/ANORM ) / EPS
233      END IF
234*
235      RETURN
236*
237*     End of CHET01_ROOK
238*
239      END
240