LAPACK  3.8.0
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, 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 * ..
22 *
23 *
24 *> \par Purpose:
25 * =============
26 *>
27 *> \verbatim
28 *>
29 *> SGBT02 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 REAL 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 REAL 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 REAL 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 REAL
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 single_lin
137 *
138 * =====================================================================
139  SUBROUTINE sgbt02( 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  REAL RESID
151 * ..
152 * .. Array Arguments ..
153  REAL A( lda, * ), B( ldb, * ), X( ldx, * )
154 * ..
155 *
156 * =====================================================================
157 *
158 * .. Parameters ..
159  REAL ZERO, ONE
160  parameter( zero = 0.0e+0, one = 1.0e+0 )
161 * ..
162 * .. Local Scalars ..
163  INTEGER I1, I2, J, KD, N1
164  REAL ANORM, BNORM, EPS, XNORM
165 * ..
166 * .. External Functions ..
167  LOGICAL LSAME
168  REAL SASUM, SLAMCH
169  EXTERNAL lsame, sasum, slamch
170 * ..
171 * .. External Subroutines ..
172  EXTERNAL sgbmv
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 = slamch( '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, sasum( 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 sgbmv( 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 = sasum( n1, b( 1, j ), 1 )
220  xnorm = sasum( 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 SGBT02
231 *
232  END
subroutine sgbt02(TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, LDB, RESID)
SGBT02
Definition: sgbt02.f:141
subroutine sgbmv(TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
SGBMV
Definition: sgbmv.f:187