LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
spbt02.f
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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 *> \ingroup single_lin
132 *
133 * =====================================================================
134  SUBROUTINE spbt02( UPLO, N, KD, NRHS, A, LDA, X, LDX, B, LDB,
135  $ RWORK, RESID )
136 *
137 * -- LAPACK test routine --
138 * -- LAPACK is a software package provided by Univ. of Tennessee, --
139 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
140 *
141 * .. Scalar Arguments ..
142  CHARACTER UPLO
143  INTEGER KD, LDA, LDB, LDX, N, NRHS
144  REAL RESID
145 * ..
146 * .. Array Arguments ..
147  REAL A( LDA, * ), B( LDB, * ), RWORK( * ),
148  $ x( ldx, * )
149 * ..
150 *
151 * =====================================================================
152 *
153 * .. Parameters ..
154  REAL ZERO, ONE
155  parameter( zero = 0.0e+0, one = 1.0e+0 )
156 * ..
157 * .. Local Scalars ..
158  INTEGER J
159  REAL ANORM, BNORM, EPS, XNORM
160 * ..
161 * .. External Functions ..
162  REAL SASUM, SLAMCH, SLANSB
163  EXTERNAL sasum, slamch, slansb
164 * ..
165 * .. External Subroutines ..
166  EXTERNAL ssbmv
167 * ..
168 * .. Intrinsic Functions ..
169  INTRINSIC max
170 * ..
171 * .. Executable Statements ..
172 *
173 * Quick exit if N = 0 or NRHS = 0.
174 *
175  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
176  resid = zero
177  RETURN
178  END IF
179 *
180 * Exit with RESID = 1/EPS if ANORM = 0.
181 *
182  eps = slamch( 'Epsilon' )
183  anorm = slansb( '1', uplo, n, kd, a, lda, rwork )
184  IF( anorm.LE.zero ) THEN
185  resid = one / eps
186  RETURN
187  END IF
188 *
189 * Compute B - A*X
190 *
191  DO 10 j = 1, nrhs
192  CALL ssbmv( uplo, n, kd, -one, a, lda, x( 1, j ), 1, one,
193  $ b( 1, j ), 1 )
194  10 CONTINUE
195 *
196 * Compute the maximum over the number of right hand sides of
197 * norm( B - A*X ) / ( norm(A) * norm(X) * EPS )
198 *
199  resid = zero
200  DO 20 j = 1, nrhs
201  bnorm = sasum( n, b( 1, j ), 1 )
202  xnorm = sasum( n, x( 1, j ), 1 )
203  IF( xnorm.LE.zero ) THEN
204  resid = one / eps
205  ELSE
206  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
207  END IF
208  20 CONTINUE
209 *
210  RETURN
211 *
212 * End of SPBT02
213 *
214  END
subroutine ssbmv(UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
SSBMV
Definition: ssbmv.f:184
subroutine spbt02(UPLO, N, KD, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
SPBT02
Definition: spbt02.f:136