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*> \date December 2016
132*
133*> \ingroup single_lin
134*
135*  =====================================================================
136      SUBROUTINE SPBT02( UPLO, N, KD, NRHS, A, LDA, X, LDX, B, LDB,
137     $                   RWORK, RESID )
138*
139*  -- LAPACK test routine (version 3.7.0) --
140*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
141*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
142*     December 2016
143*
144*     .. Scalar Arguments ..
145      CHARACTER          UPLO
146      INTEGER            KD, LDA, LDB, LDX, N, NRHS
147      REAL               RESID
148*     ..
149*     .. Array Arguments ..
150      REAL               A( LDA, * ), B( LDB, * ), RWORK( * ),
151     $                   X( LDX, * )
152*     ..
153*
154*  =====================================================================
155*
156*     .. Parameters ..
157      REAL               ZERO, ONE
158      PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
159*     ..
160*     .. Local Scalars ..
161      INTEGER            J
162      REAL               ANORM, BNORM, EPS, XNORM
163*     ..
164*     .. External Functions ..
165      REAL               SASUM, SLAMCH, SLANSB
166      EXTERNAL           SASUM, SLAMCH, SLANSB
167*     ..
168*     .. External Subroutines ..
169      EXTERNAL           SSBMV
170*     ..
171*     .. Intrinsic Functions ..
172      INTRINSIC          MAX
173*     ..
174*     .. Executable Statements ..
175*
176*     Quick exit if N = 0 or NRHS = 0.
177*
178      IF( N.LE.0 .OR. NRHS.LE.0 ) THEN
179         RESID = ZERO
180         RETURN
181      END IF
182*
183*     Exit with RESID = 1/EPS if ANORM = 0.
184*
185      EPS = SLAMCH( 'Epsilon' )
186      ANORM = SLANSB( '1', UPLO, N, KD, A, LDA, RWORK )
187      IF( ANORM.LE.ZERO ) THEN
188         RESID = ONE / EPS
189         RETURN
190      END IF
191*
192*     Compute  B - A*X
193*
194      DO 10 J = 1, NRHS
195         CALL SSBMV( UPLO, N, KD, -ONE, A, LDA, X( 1, J ), 1, ONE,
196     $               B( 1, J ), 1 )
197   10 CONTINUE
198*
199*     Compute the maximum over the number of right hand sides of
200*          norm( B - A*X ) / ( norm(A) * norm(X) * EPS )
201*
202      RESID = ZERO
203      DO 20 J = 1, NRHS
204         BNORM = SASUM( N, B( 1, J ), 1 )
205         XNORM = SASUM( N, X( 1, J ), 1 )
206         IF( XNORM.LE.ZERO ) THEN
207            RESID = ONE / EPS
208         ELSE
209            RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS )
210         END IF
211   20 CONTINUE
212*
213      RETURN
214*
215*     End of SPBT02
216*
217      END
218