1*> \brief \b SGET02
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 SGET02( 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*       REAL               RESID
18*       ..
19*       .. Array Arguments ..
20*       REAL               A( LDA, * ), B( LDB, * ), RWORK( * ),
21*      $                   X( LDX, * )
22*       ..
23*
24*
25*> \par Purpose:
26*  =============
27*>
28*> \verbatim
29*>
30*> SGET02 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'*x = b, where A' is the transpose of A
45*>          = 'C':  A'*x = b, where A' is the 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 REAL 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 REAL 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 REAL 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 REAL array, dimension (M)
111*> \endverbatim
112*>
113*> \param[out] RESID
114*> \verbatim
115*>          RESID is REAL
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 single_lin
131*
132*  =====================================================================
133      SUBROUTINE SGET02( 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      REAL               RESID
145*     ..
146*     .. Array Arguments ..
147      REAL               A( LDA, * ), B( LDB, * ), RWORK( * ),
148     $                   X( LDX, * )
149*     ..
150*
151*  =====================================================================
152*
153*     .. Parameters ..
154      REAL               ZERO, ONE
155      PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
156*     ..
157*     .. Local Scalars ..
158      INTEGER            J, N1, N2
159      REAL               ANORM, BNORM, EPS, XNORM
160*     ..
161*     .. External Functions ..
162      LOGICAL            LSAME
163      REAL               SASUM, SLAMCH, SLANGE
164      EXTERNAL           LSAME, SASUM, SLAMCH, SLANGE
165*     ..
166*     .. External Subroutines ..
167      EXTERNAL           SGEMM
168*     ..
169*     .. Intrinsic Functions ..
170      INTRINSIC          MAX
171*     ..
172*     .. Executable Statements ..
173*
174*     Quick exit if M = 0 or N = 0 or NRHS = 0
175*
176      IF( M.LE.0 .OR. N.LE.0 .OR. NRHS.EQ.0 ) THEN
177         RESID = ZERO
178         RETURN
179      END IF
180*
181      IF( LSAME( TRANS, 'T' ) .OR. LSAME( TRANS, 'C' ) ) THEN
182         N1 = N
183         N2 = M
184      ELSE
185         N1 = M
186         N2 = N
187      END IF
188*
189*     Exit with RESID = 1/EPS if ANORM = 0.
190*
191      EPS = SLAMCH( 'Epsilon' )
192      ANORM = SLANGE( '1', N1, N2, A, LDA, RWORK )
193      IF( ANORM.LE.ZERO ) THEN
194         RESID = ONE / EPS
195         RETURN
196      END IF
197*
198*     Compute  B - A*X  (or  B - A'*X ) and store in B.
199*
200      CALL SGEMM( TRANS, 'No transpose', N1, NRHS, N2, -ONE, A, LDA, X,
201     $            LDX, ONE, B, LDB )
202*
203*     Compute the maximum over the number of right hand sides of
204*        norm(B - A*X) / ( norm(A) * norm(X) * EPS ) .
205*
206      RESID = ZERO
207      DO 10 J = 1, NRHS
208         BNORM = SASUM( N1, B( 1, J ), 1 )
209         XNORM = SASUM( N2, X( 1, J ), 1 )
210         IF( XNORM.LE.ZERO ) THEN
211            RESID = ONE / EPS
212         ELSE
213            RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS )
214         END IF
215   10 CONTINUE
216*
217      RETURN
218*
219*     End of SGET02
220*
221      END
222