1*> \brief \b ZGET08
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 ZGET08( TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB,
12*                          RWORK, RESID )
13*
14*       .. Scalar Arguments ..
15*       CHARACTER          TRANS
16*       INTEGER            LDA, LDB, LDX, M, 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*> ZGET08 computes the residual for a solution of a system of linear
31*> equations  A*x = b  or  A'*x = b:
32*>    RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS ),
33*> where EPS is the machine epsilon.
34*> \endverbatim
35*
36*  Arguments:
37*  ==========
38*
39*> \param[in] TRANS
40*> \verbatim
41*>          TRANS is CHARACTER*1
42*>          Specifies the form of the system of equations:
43*>          = 'N':  A *x = b
44*>          = 'T':  A^T*x = b, where A^T is the transpose of A
45*>          = 'C':  A^H*x = b, where A^H is the conjugate transpose of A
46*> \endverbatim
47*>
48*> \param[in] M
49*> \verbatim
50*>          M is INTEGER
51*>          The number of rows of the matrix A.  M >= 0.
52*> \endverbatim
53*>
54*> \param[in] N
55*> \verbatim
56*>          N is INTEGER
57*>          The number of columns of the matrix A.  N >= 0.
58*> \endverbatim
59*>
60*> \param[in] NRHS
61*> \verbatim
62*>          NRHS is INTEGER
63*>          The number of columns of B, the matrix of right hand sides.
64*>          NRHS >= 0.
65*> \endverbatim
66*>
67*> \param[in] A
68*> \verbatim
69*>          A is COMPLEX*16 array, dimension (LDA,N)
70*>          The original M x N matrix A.
71*> \endverbatim
72*>
73*> \param[in] LDA
74*> \verbatim
75*>          LDA is INTEGER
76*>          The leading dimension of the array A.  LDA >= max(1,M).
77*> \endverbatim
78*>
79*> \param[in] X
80*> \verbatim
81*>          X is COMPLEX*16 array, dimension (LDX,NRHS)
82*>          The computed solution vectors for the system of linear
83*>          equations.
84*> \endverbatim
85*>
86*> \param[in] LDX
87*> \verbatim
88*>          LDX is INTEGER
89*>          The leading dimension of the array X.  If TRANS = 'N',
90*>          LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,M).
91*> \endverbatim
92*>
93*> \param[in,out] B
94*> \verbatim
95*>          B is COMPLEX*16 array, dimension (LDB,NRHS)
96*>          On entry, the right hand side vectors for the system of
97*>          linear equations.
98*>          On exit, B is overwritten with the difference B - A*X.
99*> \endverbatim
100*>
101*> \param[in] LDB
102*> \verbatim
103*>          LDB is INTEGER
104*>          The leading dimension of the array B.  IF TRANS = 'N',
105*>          LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N).
106*> \endverbatim
107*>
108*> \param[out] RWORK
109*> \verbatim
110*>          RWORK is DOUBLE PRECISION array, dimension (M)
111*> \endverbatim
112*>
113*> \param[out] RESID
114*> \verbatim
115*>          RESID is DOUBLE PRECISION
116*>          The maximum over the number of right hand sides of
117*>          norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
118*> \endverbatim
119*
120*  Authors:
121*  ========
122*
123*> \author Univ. of Tennessee
124*> \author Univ. of California Berkeley
125*> \author Univ. of Colorado Denver
126*> \author NAG Ltd.
127*
128*> \date November 2011
129*
130*> \ingroup complex16_lin
131*
132*  =====================================================================
133      SUBROUTINE ZGET08( TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB,
134     $                   RWORK, RESID )
135*
136*  -- LAPACK test routine (version 3.4.0) --
137*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
138*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
139*     November 2011
140*
141*     .. Scalar Arguments ..
142      CHARACTER          TRANS
143      INTEGER            LDA, LDB, LDX, M, N, NRHS
144      DOUBLE PRECISION   RESID
145*     ..
146*     .. Array Arguments ..
147      DOUBLE PRECISION   RWORK( * )
148      COMPLEX*16         A( LDA, * ), B( LDB, * ), X( LDX, * )
149*     ..
150*
151*  =====================================================================
152*
153*     .. Parameters ..
154      DOUBLE PRECISION   ZERO, ONE
155      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
156      COMPLEX*16         CONE
157      PARAMETER          ( CONE = ( 1.0D+0, 0.0D+0 ) )
158*     ..
159*     .. Local Scalars ..
160      INTEGER            J, N1, N2
161      DOUBLE PRECISION   ANORM, BNORM, EPS, XNORM
162      COMPLEX*16         ZDUM
163*     ..
164*     .. External Functions ..
165      LOGICAL            LSAME
166      INTEGER            IZAMAX
167      DOUBLE PRECISION   DLAMCH, ZLANGE
168      EXTERNAL           LSAME, IZAMAX, DLAMCH, ZLANGE
169*     ..
170*     .. External Subroutines ..
171      EXTERNAL           ZGEMM
172*     ..
173*     .. Intrinsic Functions ..
174      INTRINSIC          ABS, DBLE, DIMAG, MAX
175*     ..
176*     .. Statement Functions ..
177      DOUBLE PRECISION   CABS1
178*     ..
179*     .. Statement Function definitions ..
180      CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
181*     ..
182*     .. Executable Statements ..
183*
184*     Quick exit if M = 0 or N = 0 or NRHS = 0
185*
186      IF( M.LE.0 .OR. N.LE.0 .OR. NRHS.EQ.0 ) THEN
187         RESID = ZERO
188         RETURN
189      END IF
190*
191      IF( LSAME( TRANS, 'T' ) .OR. LSAME( TRANS, 'C' ) ) THEN
192         N1 = N
193         N2 = M
194      ELSE
195         N1 = M
196         N2 = N
197      END IF
198*
199*     Exit with RESID = 1/EPS if ANORM = 0.
200*
201      EPS = DLAMCH( 'Epsilon' )
202      ANORM = ZLANGE( 'I', N1, N2, A, LDA, RWORK )
203      IF( ANORM.LE.ZERO ) THEN
204         RESID = ONE / EPS
205         RETURN
206      END IF
207*
208*     Compute  B - A*X  (or  B - A'*X ) and store in B.
209*
210      CALL ZGEMM( TRANS, 'No transpose', N1, NRHS, N2, -CONE, A, LDA, X,
211     $            LDX, CONE, B, LDB )
212*
213*     Compute the maximum over the number of right hand sides of
214*        norm(B - A*X) / ( norm(A) * norm(X) * EPS ) .
215*
216      RESID = ZERO
217      DO 10 J = 1, NRHS
218         BNORM = CABS1( B( IZAMAX( N1, B( 1, J ), 1 ), J ) )
219         XNORM = CABS1( X( IZAMAX( N2, X( 1, J ), 1 ), J ) )
220         IF( XNORM.LE.ZERO ) THEN
221            RESID = ONE / EPS
222         ELSE
223            RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS )
224         END IF
225   10 CONTINUE
226*
227      RETURN
228*
229*     End of ZGET02
230*
231      END
232