1*> \brief \b ZPOT06
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 ZPOT06( UPLO, N, NRHS, A, LDA, X, LDX, B, LDB,
12*                          RWORK, RESID )
13*
14*       .. Scalar Arguments ..
15*       CHARACTER          UPLO
16*       INTEGER            LDA, LDB, LDX, N, NRHS
17*       DOUBLE PRECISION   RESID
18*       ..
19*       .. Array Arguments ..
20*       DOUBLE PRECISION   RWORK( * )
21*       COMPLEX*16         A( LDA, * ), B( LDB, * ), X( LDX, * )
22*       ..
23*
24*
25*> \par Purpose:
26*  =============
27*>
28*> \verbatim
29*>
30*> ZPOT06 computes the residual for a solution of a system of linear
31*> equations  A*x = b :
32*>    RESID = norm(B - A*X,inf) / ( norm(A,inf) * norm(X,inf) * EPS ),
33*> where EPS is the machine epsilon.
34*> \endverbatim
35*
36*  Arguments:
37*  ==========
38*
39*> \param[in] UPLO
40*> \verbatim
41*>          UPLO is CHARACTER*1
42*>          Specifies whether the upper or lower triangular part of the
43*>          symmetric matrix A is stored:
44*>          = 'U':  Upper triangular
45*>          = 'L':  Lower triangular
46*> \endverbatim
47*>
48*> \param[in] N
49*> \verbatim
50*>          N is INTEGER
51*>          The number of rows and columns of the matrix A.  N >= 0.
52*> \endverbatim
53*>
54*> \param[in] NRHS
55*> \verbatim
56*>          NRHS is INTEGER
57*>          The number of columns of B, the matrix of right hand sides.
58*>          NRHS >= 0.
59*> \endverbatim
60*>
61*> \param[in] A
62*> \verbatim
63*>          A is COMPLEX*16 array, dimension (LDA,N)
64*>          The original M x N matrix A.
65*> \endverbatim
66*>
67*> \param[in] LDA
68*> \verbatim
69*>          LDA is INTEGER
70*>          The leading dimension of the array A.  LDA >= max(1,N).
71*> \endverbatim
72*>
73*> \param[in] X
74*> \verbatim
75*>          X is COMPLEX*16 array, dimension (LDX,NRHS)
76*>          The computed solution vectors for the system of linear
77*>          equations.
78*> \endverbatim
79*>
80*> \param[in] LDX
81*> \verbatim
82*>          LDX is INTEGER
83*>          The leading dimension of the array X.  If TRANS = 'N',
84*>          LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,N).
85*> \endverbatim
86*>
87*> \param[in,out] B
88*> \verbatim
89*>          B is COMPLEX*16 array, dimension (LDB,NRHS)
90*>          On entry, the right hand side vectors for the system of
91*>          linear equations.
92*>          On exit, B is overwritten with the difference B - A*X.
93*> \endverbatim
94*>
95*> \param[in] LDB
96*> \verbatim
97*>          LDB is INTEGER
98*>          The leading dimension of the array B.  IF TRANS = 'N',
99*>          LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N).
100*> \endverbatim
101*>
102*> \param[out] RWORK
103*> \verbatim
104*>          RWORK is DOUBLE PRECISION array, dimension (N)
105*> \endverbatim
106*>
107*> \param[out] RESID
108*> \verbatim
109*>          RESID is DOUBLE PRECISION
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*> \ingroup complex16_lin
123*
124*  =====================================================================
125      SUBROUTINE ZPOT06( UPLO, N, NRHS, A, LDA, X, LDX, B, LDB,
126     $                   RWORK, RESID )
127*
128*  -- LAPACK test routine --
129*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
130*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
131*
132*     .. Scalar Arguments ..
133      CHARACTER          UPLO
134      INTEGER            LDA, LDB, LDX, N, NRHS
135      DOUBLE PRECISION   RESID
136*     ..
137*     .. Array Arguments ..
138      DOUBLE PRECISION   RWORK( * )
139      COMPLEX*16         A( LDA, * ), B( LDB, * ), X( LDX, * )
140*     ..
141*
142*  =====================================================================
143*
144*     .. Parameters ..
145      DOUBLE PRECISION   ZERO, ONE
146      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
147      COMPLEX*16         CONE, NEGCONE
148      PARAMETER          ( CONE = ( 1.0D+0, 0.0D+0 ) )
149      PARAMETER          ( NEGCONE = ( -1.0D+0, 0.0D+0 ) )
150*     ..
151*     .. Local Scalars ..
152      INTEGER            IFAIL, J
153      DOUBLE PRECISION   ANORM, BNORM, EPS, XNORM
154      COMPLEX*16         ZDUM
155*     ..
156*     .. External Functions ..
157      LOGICAL            LSAME
158      INTEGER            IZAMAX
159      DOUBLE PRECISION   DLAMCH, ZLANSY
160      EXTERNAL           LSAME, IZAMAX, DLAMCH, ZLANSY
161*     ..
162*     .. External Subroutines ..
163      EXTERNAL           ZHEMM
164*     ..
165*     .. Intrinsic Functions ..
166      INTRINSIC          ABS, DBLE, DIMAG, MAX
167*     ..
168*     .. Statement Functions ..
169      DOUBLE PRECISION   CABS1
170*     ..
171*     .. Statement Function definitions ..
172      CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
173*     ..
174*     ..
175*     .. Executable Statements ..
176*
177*     Quick exit if N = 0 or NRHS = 0
178*
179      IF( N.LE.0 .OR. NRHS.EQ.0 ) THEN
180         RESID = ZERO
181         RETURN
182      END IF
183*
184*     Exit with RESID = 1/EPS if ANORM = 0.
185*
186      EPS = DLAMCH( 'Epsilon' )
187      ANORM = ZLANSY( 'I', UPLO, N, A, LDA, RWORK )
188      IF( ANORM.LE.ZERO ) THEN
189         RESID = ONE / EPS
190         RETURN
191      END IF
192*
193*     Compute  B - A*X  and store in B.
194      IFAIL=0
195*
196      CALL ZHEMM( 'Left', UPLO, N, NRHS, NEGCONE, A, LDA, X,
197     $            LDX, CONE, B, LDB )
198*
199*     Compute the maximum over the number of right hand sides of
200*        norm(B - A*X) / ( norm(A) * norm(X) * EPS ) .
201*
202      RESID = ZERO
203      DO 10 J = 1, NRHS
204         BNORM = CABS1(B(IZAMAX( N, B( 1, J ), 1 ),J))
205         XNORM = CABS1(X(IZAMAX( N, X( 1, J ), 1 ),J))
206         IF( XNORM.LE.ZERO ) THEN
207            RESID = ONE / EPS
208         ELSE
209            RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS )
210         END IF
211   10 CONTINUE
212*
213      RETURN
214*
215*     End of ZPOT06
216*
217      END
218