1*> \brief \b SPBT02
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 SPBT02( UPLO, N, KD, NRHS, A, LDA, X, LDX, B, LDB,
12*                          RWORK, RESID )
13*
14*       .. Scalar Arguments ..
15*       CHARACTER          UPLO
16*       INTEGER            KD, 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*> SPBT02 computes the residual for a solution of a symmetric banded
31*> system of equations  A*x = b:
32*>    RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS)
33*> where EPS is the machine precision.
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] KD
55*> \verbatim
56*>          KD is INTEGER
57*>          The number of super-diagonals of the matrix A if UPLO = 'U',
58*>          or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.
59*> \endverbatim
60*>
61*> \param[in] NRHS
62*> \verbatim
63*>          NRHS is INTEGER
64*>          The number of right hand sides. NRHS >= 0.
65*> \endverbatim
66*>
67*> \param[in] A
68*> \verbatim
69*>          A is REAL array, dimension (LDA,N)
70*>          The original symmetric band matrix A.  If UPLO = 'U', the
71*>          upper triangular part of A is stored as a band matrix; if
72*>          UPLO = 'L', the lower triangular part of A is stored.  The
73*>          columns of the appropriate triangle are stored in the columns
74*>          of A and the diagonals of the triangle are stored in the rows
75*>          of A.  See SPBTRF for further details.
76*> \endverbatim
77*>
78*> \param[in] LDA
79*> \verbatim
80*>          LDA is INTEGER.
81*>          The leading dimension of the array A.  LDA >= max(1,KD+1).
82*> \endverbatim
83*>
84*> \param[in] X
85*> \verbatim
86*>          X is REAL array, dimension (LDX,NRHS)
87*>          The computed solution vectors for the system of linear
88*>          equations.
89*> \endverbatim
90*>
91*> \param[in] LDX
92*> \verbatim
93*>          LDX is INTEGER
94*>          The leading dimension of the array X.   LDX >= max(1,N).
95*> \endverbatim
96*>
97*> \param[in,out] B
98*> \verbatim
99*>          B is REAL array, dimension (LDB,NRHS)
100*>          On entry, the right hand side vectors for the system of
101*>          linear equations.
102*>          On exit, B is overwritten with the difference B - A*X.
103*> \endverbatim
104*>
105*> \param[in] LDB
106*> \verbatim
107*>          LDB is INTEGER
108*>          The leading dimension of the array B.  LDB >= max(1,N).
109*> \endverbatim
110*>
111*> \param[out] RWORK
112*> \verbatim
113*>          RWORK is REAL array, dimension (N)
114*> \endverbatim
115*>
116*> \param[out] RESID
117*> \verbatim
118*>          RESID is REAL
119*>          The maximum over the number of right hand sides of
120*>          norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
121*> \endverbatim
122*
123*  Authors:
124*  ========
125*
126*> \author Univ. of Tennessee
127*> \author Univ. of California Berkeley
128*> \author Univ. of Colorado Denver
129*> \author NAG Ltd.
130*
131*> \ingroup single_lin
132*
133*  =====================================================================
134      SUBROUTINE SPBT02( UPLO, N, KD, NRHS, A, LDA, X, LDX, B, LDB,
135     $                   RWORK, RESID )
136*
137*  -- LAPACK test routine --
138*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
139*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
140*
141*     .. Scalar Arguments ..
142      CHARACTER          UPLO
143      INTEGER            KD, LDA, LDB, LDX, 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
159      REAL               ANORM, BNORM, EPS, XNORM
160*     ..
161*     .. External Functions ..
162      REAL               SASUM, SLAMCH, SLANSB
163      EXTERNAL           SASUM, SLAMCH, SLANSB
164*     ..
165*     .. External Subroutines ..
166      EXTERNAL           SSBMV
167*     ..
168*     .. Intrinsic Functions ..
169      INTRINSIC          MAX
170*     ..
171*     .. Executable Statements ..
172*
173*     Quick exit if N = 0 or NRHS = 0.
174*
175      IF( N.LE.0 .OR. NRHS.LE.0 ) THEN
176         RESID = ZERO
177         RETURN
178      END IF
179*
180*     Exit with RESID = 1/EPS if ANORM = 0.
181*
182      EPS = SLAMCH( 'Epsilon' )
183      ANORM = SLANSB( '1', UPLO, N, KD, A, LDA, RWORK )
184      IF( ANORM.LE.ZERO ) THEN
185         RESID = ONE / EPS
186         RETURN
187      END IF
188*
189*     Compute  B - A*X
190*
191      DO 10 J = 1, NRHS
192         CALL SSBMV( UPLO, N, KD, -ONE, A, LDA, X( 1, J ), 1, ONE,
193     $               B( 1, J ), 1 )
194   10 CONTINUE
195*
196*     Compute the maximum over the number of right hand sides of
197*          norm( B - A*X ) / ( norm(A) * norm(X) * EPS )
198*
199      RESID = ZERO
200      DO 20 J = 1, NRHS
201         BNORM = SASUM( N, B( 1, J ), 1 )
202         XNORM = SASUM( N, X( 1, J ), 1 )
203         IF( XNORM.LE.ZERO ) THEN
204            RESID = ONE / EPS
205         ELSE
206            RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS )
207         END IF
208   20 CONTINUE
209*
210      RETURN
211*
212*     End of SPBT02
213*
214      END
215