1*> \brief \b SPOT02
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 SPOT02( 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               A( LDA, * ), B( LDB, * ), RWORK( * ),
21*      $                   X( LDX, * )
22*       ..
23*
24*
25*> \par Purpose:
26*  =============
27*>
28*> \verbatim
29*>
30*> SPOT02 computes the residual for the solution of a symmetric 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*>          symmetric 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 REAL array, dimension (LDA,N)
66*>          The original symmetric 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 REAL 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 REAL 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*> \ingroup single_lin
123*
124*  =====================================================================
125      SUBROUTINE SPOT02( UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK,
126     $                   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      REAL               RESID
136*     ..
137*     .. Array Arguments ..
138      REAL               A( LDA, * ), B( LDB, * ), RWORK( * ),
139     $                   X( LDX, * )
140*     ..
141*
142*  =====================================================================
143*
144*     .. Parameters ..
145      REAL               ZERO, ONE
146      PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
147*     ..
148*     .. Local Scalars ..
149      INTEGER            J
150      REAL               ANORM, BNORM, EPS, XNORM
151*     ..
152*     .. External Functions ..
153      REAL               SASUM, SLAMCH, SLANSY
154      EXTERNAL           SASUM, SLAMCH, SLANSY
155*     ..
156*     .. External Subroutines ..
157      EXTERNAL           SSYMM
158*     ..
159*     .. Intrinsic Functions ..
160      INTRINSIC          MAX
161*     ..
162*     .. Executable Statements ..
163*
164*     Quick exit if N = 0 or NRHS = 0.
165*
166      IF( N.LE.0 .OR. NRHS.LE.0 ) THEN
167         RESID = ZERO
168         RETURN
169      END IF
170*
171*     Exit with RESID = 1/EPS if ANORM = 0.
172*
173      EPS = SLAMCH( 'Epsilon' )
174      ANORM = SLANSY( '1', UPLO, N, A, LDA, RWORK )
175      IF( ANORM.LE.ZERO ) THEN
176         RESID = ONE / EPS
177         RETURN
178      END IF
179*
180*     Compute  B - A*X
181*
182      CALL SSYMM( 'Left', UPLO, N, NRHS, -ONE, A, LDA, X, LDX, ONE, B,
183     $            LDB )
184*
185*     Compute the maximum over the number of right hand sides of
186*        norm( B - A*X ) / ( norm(A) * norm(X) * EPS ) .
187*
188      RESID = ZERO
189      DO 10 J = 1, NRHS
190         BNORM = SASUM( N, B( 1, J ), 1 )
191         XNORM = SASUM( N, X( 1, J ), 1 )
192         IF( XNORM.LE.ZERO ) THEN
193            RESID = ONE / EPS
194         ELSE
195            RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS )
196         END IF
197   10 CONTINUE
198*
199      RETURN
200*
201*     End of SPOT02
202*
203      END
204