1*> \brief \b DGBT02
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 DGBT02( TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B,
12*                          LDB, RESID )
13*
14*       .. Scalar Arguments ..
15*       CHARACTER          TRANS
16*       INTEGER            KL, KU, LDA, LDB, LDX, M, N, NRHS
17*       DOUBLE PRECISION   RESID
18*       ..
19*       .. Array Arguments ..
20*       DOUBLE PRECISION   A( LDA, * ), B( LDB, * ), X( LDX, * )
21*       ..
22*
23*
24*> \par Purpose:
25*  =============
26*>
27*> \verbatim
28*>
29*> DGBT02 computes the residual for a solution of a banded system of
30*> equations  A*x = b  or  A'*x = b:
31*>    RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS).
32*> where EPS is the machine precision.
33*> \endverbatim
34*
35*  Arguments:
36*  ==========
37*
38*> \param[in] TRANS
39*> \verbatim
40*>          TRANS is CHARACTER*1
41*>          Specifies the form of the system of equations:
42*>          = 'N':  A *x = b
43*>          = 'T':  A'*x = b, where A' is the transpose of A
44*>          = 'C':  A'*x = b, where A' is the transpose of A
45*> \endverbatim
46*>
47*> \param[in] M
48*> \verbatim
49*>          M is INTEGER
50*>          The number of rows of the matrix A.  M >= 0.
51*> \endverbatim
52*>
53*> \param[in] N
54*> \verbatim
55*>          N is INTEGER
56*>          The number of columns of the matrix A.  N >= 0.
57*> \endverbatim
58*>
59*> \param[in] KL
60*> \verbatim
61*>          KL is INTEGER
62*>          The number of subdiagonals within the band of A.  KL >= 0.
63*> \endverbatim
64*>
65*> \param[in] KU
66*> \verbatim
67*>          KU is INTEGER
68*>          The number of superdiagonals within the band of A.  KU >= 0.
69*> \endverbatim
70*>
71*> \param[in] NRHS
72*> \verbatim
73*>          NRHS is INTEGER
74*>          The number of columns of B.  NRHS >= 0.
75*> \endverbatim
76*>
77*> \param[in] A
78*> \verbatim
79*>          A is DOUBLE PRECISION array, dimension (LDA,N)
80*>          The original matrix A in band storage, stored in rows 1 to
81*>          KL+KU+1.
82*> \endverbatim
83*>
84*> \param[in] LDA
85*> \verbatim
86*>          LDA is INTEGER
87*>          The leading dimension of the array A.  LDA >= max(1,KL+KU+1).
88*> \endverbatim
89*>
90*> \param[in] X
91*> \verbatim
92*>          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
93*>          The computed solution vectors for the system of linear
94*>          equations.
95*> \endverbatim
96*>
97*> \param[in] LDX
98*> \verbatim
99*>          LDX is INTEGER
100*>          The leading dimension of the array X.  If TRANS = 'N',
101*>          LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,M).
102*> \endverbatim
103*>
104*> \param[in,out] B
105*> \verbatim
106*>          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
107*>          On entry, the right hand side vectors for the system of
108*>          linear equations.
109*>          On exit, B is overwritten with the difference B - A*X.
110*> \endverbatim
111*>
112*> \param[in] LDB
113*> \verbatim
114*>          LDB is INTEGER
115*>          The leading dimension of the array B.  IF TRANS = 'N',
116*>          LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N).
117*> \endverbatim
118*>
119*> \param[out] RESID
120*> \verbatim
121*>          RESID is DOUBLE PRECISION
122*>          The maximum over the number of right hand sides of
123*>          norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
124*> \endverbatim
125*
126*  Authors:
127*  ========
128*
129*> \author Univ. of Tennessee
130*> \author Univ. of California Berkeley
131*> \author Univ. of Colorado Denver
132*> \author NAG Ltd.
133*
134*> \date December 2016
135*
136*> \ingroup double_lin
137*
138*  =====================================================================
139      SUBROUTINE DGBT02( TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B,
140     $                   LDB, RESID )
141*
142*  -- LAPACK test routine (version 3.7.0) --
143*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
144*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
145*     December 2016
146*
147*     .. Scalar Arguments ..
148      CHARACTER          TRANS
149      INTEGER            KL, KU, LDA, LDB, LDX, M, N, NRHS
150      DOUBLE PRECISION   RESID
151*     ..
152*     .. Array Arguments ..
153      DOUBLE PRECISION   A( LDA, * ), B( LDB, * ), X( LDX, * )
154*     ..
155*
156*  =====================================================================
157*
158*     .. Parameters ..
159      DOUBLE PRECISION   ZERO, ONE
160      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
161*     ..
162*     .. Local Scalars ..
163      INTEGER            I1, I2, J, KD, N1
164      DOUBLE PRECISION   ANORM, BNORM, EPS, XNORM
165*     ..
166*     .. External Functions ..
167      LOGICAL            LSAME
168      DOUBLE PRECISION   DASUM, DLAMCH
169      EXTERNAL           LSAME, DASUM, DLAMCH
170*     ..
171*     .. External Subroutines ..
172      EXTERNAL           DGBMV
173*     ..
174*     .. Intrinsic Functions ..
175      INTRINSIC          MAX, MIN
176*     ..
177*     .. Executable Statements ..
178*
179*     Quick return if N = 0 pr NRHS = 0
180*
181      IF( M.LE.0 .OR. N.LE.0 .OR. NRHS.LE.0 ) THEN
182         RESID = ZERO
183         RETURN
184      END IF
185*
186*     Exit with RESID = 1/EPS if ANORM = 0.
187*
188      EPS = DLAMCH( 'Epsilon' )
189      KD = KU + 1
190      ANORM = ZERO
191      DO 10 J = 1, N
192         I1 = MAX( KD+1-J, 1 )
193         I2 = MIN( KD+M-J, KL+KD )
194         ANORM = MAX( ANORM, DASUM( I2-I1+1, A( I1, J ), 1 ) )
195   10 CONTINUE
196      IF( ANORM.LE.ZERO ) THEN
197         RESID = ONE / EPS
198         RETURN
199      END IF
200*
201      IF( LSAME( TRANS, 'T' ) .OR. LSAME( TRANS, 'C' ) ) THEN
202         N1 = N
203      ELSE
204         N1 = M
205      END IF
206*
207*     Compute  B - A*X (or  B - A'*X )
208*
209      DO 20 J = 1, NRHS
210         CALL DGBMV( TRANS, M, N, KL, KU, -ONE, A, LDA, X( 1, J ), 1,
211     $               ONE, B( 1, J ), 1 )
212   20 CONTINUE
213*
214*     Compute the maximum over the number of right hand sides of
215*        norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
216*
217      RESID = ZERO
218      DO 30 J = 1, NRHS
219         BNORM = DASUM( N1, B( 1, J ), 1 )
220         XNORM = DASUM( N1, X( 1, J ), 1 )
221         IF( XNORM.LE.ZERO ) THEN
222            RESID = ONE / EPS
223         ELSE
224            RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS )
225         END IF
226   30 CONTINUE
227*
228      RETURN
229*
230*     End of DGBT02
231*
232      END
233