1*> \brief \b CPOT02
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 CPOT02( UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK,
12*                          RESID )
13*
14*       .. Scalar Arguments ..
15*       CHARACTER          UPLO
16*       INTEGER            LDA, LDB, LDX, N, NRHS
17*       REAL               RESID
18*       ..
19*       .. Array Arguments ..
20*       REAL               RWORK( * )
21*       COMPLEX            A( LDA, * ), B( LDB, * ), X( LDX, * )
22*       ..
23*
24*
25*> \par Purpose:
26*  =============
27*>
28*> \verbatim
29*>
30*> CPOT02 computes the residual for the solution of a Hermitian system
31*> of linear equations  A*x = b:
32*>
33*>    RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS ),
34*>
35*> where 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*>          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] NRHS
57*> \verbatim
58*>          NRHS is INTEGER
59*>          The number of columns of B, the matrix of right hand sides.
60*>          NRHS >= 0.
61*> \endverbatim
62*>
63*> \param[in] A
64*> \verbatim
65*>          A is COMPLEX array, dimension (LDA,N)
66*>          The original Hermitian matrix A.
67*> \endverbatim
68*>
69*> \param[in] LDA
70*> \verbatim
71*>          LDA is INTEGER
72*>          The leading dimension of the array A.  LDA >= max(1,N)
73*> \endverbatim
74*>
75*> \param[in] X
76*> \verbatim
77*>          X is COMPLEX array, dimension (LDX,NRHS)
78*>          The computed solution vectors for the system of linear
79*>          equations.
80*> \endverbatim
81*>
82*> \param[in] LDX
83*> \verbatim
84*>          LDX is INTEGER
85*>          The leading dimension of the array X.   LDX >= max(1,N).
86*> \endverbatim
87*>
88*> \param[in,out] B
89*> \verbatim
90*>          B is COMPLEX array, dimension (LDB,NRHS)
91*>          On entry, the right hand side vectors for the system of
92*>          linear equations.
93*>          On exit, B is overwritten with the difference B - A*X.
94*> \endverbatim
95*>
96*> \param[in] LDB
97*> \verbatim
98*>          LDB is INTEGER
99*>          The leading dimension of the array B.  LDB >= max(1,N).
100*> \endverbatim
101*>
102*> \param[out] RWORK
103*> \verbatim
104*>          RWORK is REAL array, dimension (N)
105*> \endverbatim
106*>
107*> \param[out] RESID
108*> \verbatim
109*>          RESID is REAL
110*>          The maximum over the number of right hand sides of
111*>          norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
112*> \endverbatim
113*
114*  Authors:
115*  ========
116*
117*> \author Univ. of Tennessee
118*> \author Univ. of California Berkeley
119*> \author Univ. of Colorado Denver
120*> \author NAG Ltd.
121*
122*> \date November 2011
123*
124*> \ingroup complex_lin
125*
126*  =====================================================================
127      SUBROUTINE CPOT02( UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK,
128     $                   RESID )
129*
130*  -- LAPACK test routine (version 3.4.0) --
131*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
132*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
133*     November 2011
134*
135*     .. Scalar Arguments ..
136      CHARACTER          UPLO
137      INTEGER            LDA, LDB, LDX, N, NRHS
138      REAL               RESID
139*     ..
140*     .. Array Arguments ..
141      REAL               RWORK( * )
142      COMPLEX            A( LDA, * ), B( LDB, * ), X( LDX, * )
143*     ..
144*
145*  =====================================================================
146*
147*     .. Parameters ..
148      REAL               ZERO, ONE
149      PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
150      COMPLEX            CONE
151      PARAMETER          ( CONE = ( 1.0E+0, 0.0E+0 ) )
152*     ..
153*     .. Local Scalars ..
154      INTEGER            J
155      REAL               ANORM, BNORM, EPS, XNORM
156*     ..
157*     .. External Functions ..
158      REAL               CLANHE, SCASUM, SLAMCH
159      EXTERNAL           CLANHE, SCASUM, SLAMCH
160*     ..
161*     .. External Subroutines ..
162      EXTERNAL           CHEMM
163*     ..
164*     .. Intrinsic Functions ..
165      INTRINSIC          MAX
166*     ..
167*     .. Executable Statements ..
168*
169*     Quick exit if N = 0 or NRHS = 0.
170*
171      IF( N.LE.0 .OR. NRHS.LE.0 ) THEN
172         RESID = ZERO
173         RETURN
174      END IF
175*
176*     Exit with RESID = 1/EPS if ANORM = 0.
177*
178      EPS = SLAMCH( 'Epsilon' )
179      ANORM = CLANHE( '1', UPLO, N, A, LDA, RWORK )
180      IF( ANORM.LE.ZERO ) THEN
181         RESID = ONE / EPS
182         RETURN
183      END IF
184*
185*     Compute  B - A*X
186*
187      CALL CHEMM( 'Left', UPLO, N, NRHS, -CONE, A, LDA, X, LDX, CONE, B,
188     $            LDB )
189*
190*     Compute the maximum over the number of right hand sides of
191*        norm( B - A*X ) / ( norm(A) * norm(X) * EPS ) .
192*
193      RESID = ZERO
194      DO 10 J = 1, NRHS
195         BNORM = SCASUM( N, B( 1, J ), 1 )
196         XNORM = SCASUM( N, X( 1, J ), 1 )
197         IF( XNORM.LE.ZERO ) THEN
198            RESID = ONE / EPS
199         ELSE
200            RESID = MAX( RESID, ( ( BNORM/ANORM )/XNORM )/EPS )
201         END IF
202   10 CONTINUE
203*
204      RETURN
205*
206*     End of CPOT02
207*
208      END
209