1*> \brief \b SGBT02
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 SGBT02( TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B,
12*                          LDB, RWORK, RESID )
13*
14*       .. Scalar Arguments ..
15*       CHARACTER          TRANS
16*       INTEGER            KL, KU, LDA, LDB, LDX, M, N, NRHS
17*       REAL               RESID
18*       ..
19*       .. Array Arguments ..
20*       REAL               A( LDA, * ), B( LDB, * ), X( LDX, * ),
21*                          RWORK( * )
22*       ..
23*
24*
25*> \par Purpose:
26*  =============
27*>
28*> \verbatim
29*>
30*> SGBT02 computes the residual for a solution of a banded system of
31*> equations op(A)*X = B:
32*>    RESID = norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ),
33*> where op(A) = A or A**T, depending on TRANS, and EPS is the
34*> machine epsilon.
35*> The norm used is the 1-norm.
36*> \endverbatim
37*
38*  Arguments:
39*  ==========
40*
41*> \param[in] TRANS
42*> \verbatim
43*>          TRANS is CHARACTER*1
44*>          Specifies the form of the system of equations:
45*>          = 'N':  A    * X = B  (No transpose)
46*>          = 'T':  A**T * X = B  (Transpose)
47*>          = 'C':  A**H * X = B  (Conjugate transpose = Transpose)
48*> \endverbatim
49*>
50*> \param[in] M
51*> \verbatim
52*>          M is INTEGER
53*>          The number of rows of the matrix A.  M >= 0.
54*> \endverbatim
55*>
56*> \param[in] N
57*> \verbatim
58*>          N is INTEGER
59*>          The number of columns of the matrix A.  N >= 0.
60*> \endverbatim
61*>
62*> \param[in] KL
63*> \verbatim
64*>          KL is INTEGER
65*>          The number of subdiagonals within the band of A.  KL >= 0.
66*> \endverbatim
67*>
68*> \param[in] KU
69*> \verbatim
70*>          KU is INTEGER
71*>          The number of superdiagonals within the band of A.  KU >= 0.
72*> \endverbatim
73*>
74*> \param[in] NRHS
75*> \verbatim
76*>          NRHS is INTEGER
77*>          The number of columns of B.  NRHS >= 0.
78*> \endverbatim
79*>
80*> \param[in] A
81*> \verbatim
82*>          A is REAL array, dimension (LDA,N)
83*>          The original matrix A in band storage, stored in rows 1 to
84*>          KL+KU+1.
85*> \endverbatim
86*>
87*> \param[in] LDA
88*> \verbatim
89*>          LDA is INTEGER
90*>          The leading dimension of the array A.  LDA >= max(1,KL+KU+1).
91*> \endverbatim
92*>
93*> \param[in] X
94*> \verbatim
95*>          X is REAL array, dimension (LDX,NRHS)
96*>          The computed solution vectors for the system of linear
97*>          equations.
98*> \endverbatim
99*>
100*> \param[in] LDX
101*> \verbatim
102*>          LDX is INTEGER
103*>          The leading dimension of the array X.  If TRANS = 'N',
104*>          LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,M).
105*> \endverbatim
106*>
107*> \param[in,out] B
108*> \verbatim
109*>          B is REAL array, dimension (LDB,NRHS)
110*>          On entry, the right hand side vectors for the system of
111*>          linear equations.
112*>          On exit, B is overwritten with the difference B - A*X.
113*> \endverbatim
114*>
115*> \param[in] LDB
116*> \verbatim
117*>          LDB is INTEGER
118*>          The leading dimension of the array B.  IF TRANS = 'N',
119*>          LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N).
120*> \endverbatim
121*>
122*> \param[out] RWORK
123*> \verbatim
124*>          RWORK is REAL array, dimension (MAX(1,LRWORK)),
125*>          where LRWORK >= M when TRANS = 'T' or 'C'; otherwise, RWORK
126*>          is not referenced.
127*> \endverbatim
128*
129*> \param[out] RESID
130*> \verbatim
131*>          RESID is REAL
132*>          The maximum over the number of right hand sides of
133*>          norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ).
134*> \endverbatim
135*
136*  Authors:
137*  ========
138*
139*> \author Univ. of Tennessee
140*> \author Univ. of California Berkeley
141*> \author Univ. of Colorado Denver
142*> \author NAG Ltd.
143*
144*> \ingroup single_lin
145*
146*  =====================================================================
147      SUBROUTINE SGBT02( TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B,
148     $                   LDB, RWORK, RESID )
149*
150*  -- LAPACK test routine --
151*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
152*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
153*
154*     .. Scalar Arguments ..
155      CHARACTER          TRANS
156      INTEGER            KL, KU, LDA, LDB, LDX, M, N, NRHS
157      REAL               RESID
158*     ..
159*     .. Array Arguments ..
160      REAL               A( LDA, * ), B( LDB, * ), X( LDX, * ),
161     $                   RWORK( * )
162*     ..
163*
164*  =====================================================================
165*
166*     .. Parameters ..
167      REAL               ZERO, ONE
168      PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
169*     ..
170*     .. Local Scalars ..
171      INTEGER            I1, I2, J, KD, N1
172      REAL               ANORM, BNORM, EPS, TEMP, XNORM
173*     ..
174*     .. External Functions ..
175      LOGICAL            LSAME, SISNAN
176      REAL               SASUM, SLAMCH
177      EXTERNAL           LSAME, SASUM, SISNAN, SLAMCH
178*     ..
179*     .. External Subroutines ..
180      EXTERNAL           SGBMV
181*     ..
182*     .. Intrinsic Functions ..
183      INTRINSIC          ABS, MAX, MIN
184*     ..
185*     .. Executable Statements ..
186*
187*     Quick return if N = 0 pr NRHS = 0
188*
189      IF( M.LE.0 .OR. N.LE.0 .OR. NRHS.LE.0 ) THEN
190         RESID = ZERO
191         RETURN
192      END IF
193*
194*     Exit with RESID = 1/EPS if ANORM = 0.
195*
196      EPS = SLAMCH( 'Epsilon' )
197      ANORM = ZERO
198      IF( LSAME( TRANS, 'N' ) ) THEN
199*
200*        Find norm1(A).
201*
202         KD = KU + 1
203         DO 10 J = 1, N
204            I1 = MAX( KD+1-J, 1 )
205            I2 = MIN( KD+M-J, KL+KD )
206            IF( I2.GE.I1 ) THEN
207               TEMP = SASUM( I2-I1+1, A( I1, J ), 1 )
208               IF( ANORM.LT.TEMP .OR. SISNAN( TEMP ) ) ANORM = TEMP
209            END IF
210   10    CONTINUE
211      ELSE
212*
213*        Find normI(A).
214*
215         DO 12 I1 = 1, M
216            RWORK( I1 ) = ZERO
217   12    CONTINUE
218         DO 16 J = 1, N
219            KD = KU + 1 - J
220            DO 14 I1 = MAX( 1, J-KU ), MIN( M, J+KL )
221               RWORK( I1 ) = RWORK( I1 ) + ABS( A( KD+I1, J ) )
222   14       CONTINUE
223   16    CONTINUE
224         DO 18 I1 = 1, M
225            TEMP = RWORK( I1 )
226            IF( ANORM.LT.TEMP .OR. SISNAN( TEMP ) ) ANORM = TEMP
227   18    CONTINUE
228      END IF
229      IF( ANORM.LE.ZERO ) THEN
230         RESID = ONE / EPS
231         RETURN
232      END IF
233*
234      IF( LSAME( TRANS, 'T' ) .OR. LSAME( TRANS, 'C' ) ) THEN
235         N1 = N
236      ELSE
237         N1 = M
238      END IF
239*
240*     Compute B - op(A)*X
241*
242      DO 20 J = 1, NRHS
243         CALL SGBMV( TRANS, M, N, KL, KU, -ONE, A, LDA, X( 1, J ), 1,
244     $               ONE, B( 1, J ), 1 )
245   20 CONTINUE
246*
247*     Compute the maximum over the number of right hand sides of
248*        norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ).
249*
250      RESID = ZERO
251      DO 30 J = 1, NRHS
252         BNORM = SASUM( N1, B( 1, J ), 1 )
253         XNORM = SASUM( N1, X( 1, J ), 1 )
254         IF( XNORM.LE.ZERO ) THEN
255            RESID = ONE / EPS
256         ELSE
257            RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS )
258         END IF
259   30 CONTINUE
260*
261      RETURN
262*
263*     End of SGBT02
264*
265      END
266