LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
dpot06.f
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1 *> \brief \b DPOT06
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 DPOT06( UPLO, N, NRHS, A, LDA, X, LDX, B, LDB,
12 * RWORK, RESID )
13 *
14 * .. Scalar Arguments ..
15 * CHARACTER UPLO
16 * INTEGER LDA, LDB, LDX, N, NRHS
17 * DOUBLE PRECISION RESID
18 * ..
19 * .. Array Arguments ..
20 * DOUBLE PRECISION A( LDA, * ), B( LDB, * ), RWORK( * ),
21 * $ X( LDX, * )
22 * ..
23 *
24 *
25 *> \par Purpose:
26 * =============
27 *>
28 *> \verbatim
29 *>
30 *> DPOT06 computes the residual for a solution of a system of linear
31 *> equations A*x = b :
32 *> RESID = norm(B - A*X,inf) / ( norm(A,inf) * norm(X,inf) * EPS ),
33 *> where EPS is the machine epsilon.
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] NRHS
55 *> \verbatim
56 *> NRHS is INTEGER
57 *> The number of columns of B, the matrix of right hand sides.
58 *> NRHS >= 0.
59 *> \endverbatim
60 *>
61 *> \param[in] A
62 *> \verbatim
63 *> A is DOUBLE PRECISION array, dimension (LDA,N)
64 *> The original M x N matrix A.
65 *> \endverbatim
66 *>
67 *> \param[in] LDA
68 *> \verbatim
69 *> LDA is INTEGER
70 *> The leading dimension of the array A. LDA >= max(1,N).
71 *> \endverbatim
72 *>
73 *> \param[in] X
74 *> \verbatim
75 *> X is DOUBLE PRECISION array, dimension (LDX,NRHS)
76 *> The computed solution vectors for the system of linear
77 *> equations.
78 *> \endverbatim
79 *>
80 *> \param[in] LDX
81 *> \verbatim
82 *> LDX is INTEGER
83 *> The leading dimension of the array X. If TRANS = 'N',
84 *> LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,N).
85 *> \endverbatim
86 *>
87 *> \param[in,out] B
88 *> \verbatim
89 *> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
90 *> On entry, the right hand side vectors for the system of
91 *> linear equations.
92 *> On exit, B is overwritten with the difference B - A*X.
93 *> \endverbatim
94 *>
95 *> \param[in] LDB
96 *> \verbatim
97 *> LDB is INTEGER
98 *> The leading dimension of the array B. IF TRANS = 'N',
99 *> LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N).
100 *> \endverbatim
101 *>
102 *> \param[out] RWORK
103 *> \verbatim
104 *> RWORK is DOUBLE PRECISION array, dimension (N)
105 *> \endverbatim
106 *>
107 *> \param[out] RESID
108 *> \verbatim
109 *> RESID is DOUBLE PRECISION
110 *> The maximum over the number of right hand sides of
111 *> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
112 *> \endverbatim
113 *
114 * Authors:
115 * ========
116 *
117 *> \author Univ. of Tennessee
118 *> \author Univ. of California Berkeley
119 *> \author Univ. of Colorado Denver
120 *> \author NAG Ltd.
121 *
122 *> \date December 2016
123 *
124 *> \ingroup double_lin
125 *
126 * =====================================================================
127  SUBROUTINE dpot06( UPLO, N, NRHS, A, LDA, X, LDX, B, LDB,
128  $ RWORK, RESID )
129 *
130 * -- LAPACK test routine (version 3.7.0) --
131 * -- LAPACK is a software package provided by Univ. of Tennessee, --
132 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
133 * December 2016
134 *
135 * .. Scalar Arguments ..
136  CHARACTER UPLO
137  INTEGER LDA, LDB, LDX, N, NRHS
138  DOUBLE PRECISION RESID
139 * ..
140 * .. Array Arguments ..
141  DOUBLE PRECISION A( lda, * ), B( ldb, * ), RWORK( * ),
142  $ x( ldx, * )
143 * ..
144 *
145 * =====================================================================
146 *
147 * .. Parameters ..
148  DOUBLE PRECISION ZERO, ONE, NEGONE
149  parameter( zero = 0.0d+0, one = 1.0d+0 )
150  parameter( negone = -1.0d+0 )
151 * ..
152 * .. Local Scalars ..
153  INTEGER IFAIL, J
154  DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
155 * ..
156 * .. External Functions ..
157  INTEGER IDAMAX
158  DOUBLE PRECISION DLAMCH, DLANSY
159  EXTERNAL idamax, dlamch, dlansy
160 * ..
161 * .. External Subroutines ..
162  EXTERNAL dsymm
163 * ..
164 * .. Intrinsic Functions ..
165  INTRINSIC max, abs
166 * ..
167 * .. Executable Statements ..
168 *
169 * Quick exit if N = 0 or NRHS = 0
170 *
171  IF( n.LE.0 .OR. nrhs.EQ.0 ) THEN
172  resid = zero
173  RETURN
174  END IF
175 *
176 * Exit with RESID = 1/EPS if ANORM = 0.
177 *
178  eps = dlamch( 'Epsilon' )
179  anorm = dlansy( 'I', uplo, n, a, lda, rwork )
180  IF( anorm.LE.zero ) THEN
181  resid = one / eps
182  RETURN
183  END IF
184 *
185 * Compute B - A*X and store in B.
186  ifail=0
187 *
188  CALL dsymm( 'Left', uplo, n, nrhs, negone, a, lda, x,
189  $ ldx, one, b, ldb )
190 *
191 * Compute the maximum over the number of right hand sides of
192 * norm(B - A*X) / ( norm(A) * norm(X) * EPS ) .
193 *
194  resid = zero
195  DO 10 j = 1, nrhs
196  bnorm = abs(b(idamax( n, b( 1, j ), 1 ),j))
197  xnorm = abs(x(idamax( n, x( 1, j ), 1 ),j))
198  IF( xnorm.LE.zero ) THEN
199  resid = one / eps
200  ELSE
201  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
202  END IF
203  10 CONTINUE
204 *
205  RETURN
206 *
207 * End of DPOT06
208 *
209  END
subroutine dsymm(SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DSYMM
Definition: dsymm.f:191
subroutine dpot06(UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
DPOT06
Definition: dpot06.f:129