LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
sgbt02.f
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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
subroutine sgbmv(TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
SGBMV
Definition: sgbmv.f:185
subroutine sgbt02(TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
SGBT02
Definition: sgbt02.f:149