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*> \date November 2011
123*
124*> \ingroup complex16_lin
125*
126*  =====================================================================
127      SUBROUTINE ZPOT06( UPLO, N, NRHS, A, LDA, X, LDX, B, LDB,
128     $                   RWORK, 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      DOUBLE PRECISION   RESID
139*     ..
140*     .. Array Arguments ..
141      DOUBLE PRECISION   RWORK( * )
142      COMPLEX*16         A( LDA, * ), B( LDB, * ), X( LDX, * )
143*     ..
144*
145*  =====================================================================
146*
147*     .. Parameters ..
148      DOUBLE PRECISION   ZERO, ONE
149      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
150      COMPLEX*16         CONE, NEGCONE
151      PARAMETER          ( CONE = ( 1.0D+0, 0.0D+0 ) )
152      PARAMETER          ( NEGCONE = ( -1.0D+0, 0.0D+0 ) )
153*     ..
154*     .. Local Scalars ..
155      INTEGER            IFAIL, J
156      DOUBLE PRECISION   ANORM, BNORM, EPS, XNORM
157      COMPLEX*16         ZDUM
158*     ..
159*     .. External Functions ..
160      LOGICAL            LSAME
161      INTEGER            IZAMAX
162      DOUBLE PRECISION   DLAMCH, ZLANSY
163      EXTERNAL           LSAME, IZAMAX, DLAMCH, ZLANSY
164*     ..
165*     .. External Subroutines ..
166      EXTERNAL           ZHEMM
167*     ..
168*     .. Intrinsic Functions ..
169      INTRINSIC          ABS, DBLE, DIMAG, MAX
170*     ..
171*     .. Statement Functions ..
172      DOUBLE PRECISION   CABS1
173*     ..
174*     .. Statement Function definitions ..
175      CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
176*     ..
177*     ..
178*     .. Executable Statements ..
179*
180*     Quick exit if N = 0 or NRHS = 0
181*
182      IF( N.LE.0 .OR. NRHS.EQ.0 ) THEN
183         RESID = ZERO
184         RETURN
185      END IF
186*
187*     Exit with RESID = 1/EPS if ANORM = 0.
188*
189      EPS = DLAMCH( 'Epsilon' )
190      ANORM = ZLANSY( 'I', UPLO, N, A, LDA, RWORK )
191      IF( ANORM.LE.ZERO ) THEN
192         RESID = ONE / EPS
193         RETURN
194      END IF
195*
196*     Compute  B - A*X  and store in B.
197      IFAIL=0
198*
199      CALL ZHEMM( 'Left', UPLO, N, NRHS, NEGCONE, A, LDA, X,
200     $            LDX, CONE, B, LDB )
201*
202*     Compute the maximum over the number of right hand sides of
203*        norm(B - A*X) / ( norm(A) * norm(X) * EPS ) .
204*
205      RESID = ZERO
206      DO 10 J = 1, NRHS
207         BNORM = CABS1(B(IZAMAX( N, B( 1, J ), 1 ),J))
208         XNORM = CABS1(X(IZAMAX( N, X( 1, J ), 1 ),J))
209         IF( XNORM.LE.ZERO ) THEN
210            RESID = ONE / EPS
211         ELSE
212            RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS )
213         END IF
214   10 CONTINUE
215*
216      RETURN
217*
218*     End of ZPOT06
219*
220      END
221