LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
dppt02.f
Go to the documentation of this file.
1 *> \brief \b DPPT02
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 DPPT02( UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK,
12 * RESID )
13 *
14 * .. Scalar Arguments ..
15 * CHARACTER UPLO
16 * INTEGER LDB, LDX, N, NRHS
17 * DOUBLE PRECISION RESID
18 * ..
19 * .. Array Arguments ..
20 * DOUBLE PRECISION A( * ), B( LDB, * ), RWORK( * ), X( LDX, * )
21 * ..
22 *
23 *
24 *> \par Purpose:
25 * =============
26 *>
27 *> \verbatim
28 *>
29 *> DPPT02 computes the residual in the solution of a symmetric system
30 *> of linear equations A*x = b when packed storage is used for the
31 *> coefficient matrix. The ratio computed is
32 *>
33 *> RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS),
34 *>
35 *> where EPS is the machine precision.
36 *> \endverbatim
37 *
38 * Arguments:
39 * ==========
40 *
41 *> \param[in] UPLO
42 *> \verbatim
43 *> UPLO is CHARACTER*1
44 *> Specifies whether the upper or lower triangular part of the
45 *> symmetric matrix A is stored:
46 *> = 'U': Upper triangular
47 *> = 'L': Lower triangular
48 *> \endverbatim
49 *>
50 *> \param[in] N
51 *> \verbatim
52 *> N is INTEGER
53 *> The number of rows and columns of the matrix A. N >= 0.
54 *> \endverbatim
55 *>
56 *> \param[in] NRHS
57 *> \verbatim
58 *> NRHS is INTEGER
59 *> The number of columns of B, the matrix of right hand sides.
60 *> NRHS >= 0.
61 *> \endverbatim
62 *>
63 *> \param[in] A
64 *> \verbatim
65 *> A is DOUBLE PRECISION array, dimension (N*(N+1)/2)
66 *> The original symmetric matrix A, stored as a packed
67 *> triangular matrix.
68 *> \endverbatim
69 *>
70 *> \param[in] X
71 *> \verbatim
72 *> X is DOUBLE PRECISION array, dimension (LDX,NRHS)
73 *> The computed solution vectors for the system of linear
74 *> equations.
75 *> \endverbatim
76 *>
77 *> \param[in] LDX
78 *> \verbatim
79 *> LDX is INTEGER
80 *> The leading dimension of the array X. LDX >= max(1,N).
81 *> \endverbatim
82 *>
83 *> \param[in,out] B
84 *> \verbatim
85 *> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
86 *> On entry, the right hand side vectors for the system of
87 *> linear equations.
88 *> On exit, B is overwritten with the difference B - A*X.
89 *> \endverbatim
90 *>
91 *> \param[in] LDB
92 *> \verbatim
93 *> LDB is INTEGER
94 *> The leading dimension of the array B. LDB >= max(1,N).
95 *> \endverbatim
96 *>
97 *> \param[out] RWORK
98 *> \verbatim
99 *> RWORK is DOUBLE PRECISION array, dimension (N)
100 *> \endverbatim
101 *>
102 *> \param[out] RESID
103 *> \verbatim
104 *> RESID is DOUBLE PRECISION
105 *> The maximum over the number of right hand sides of
106 *> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
107 *> \endverbatim
108 *
109 * Authors:
110 * ========
111 *
112 *> \author Univ. of Tennessee
113 *> \author Univ. of California Berkeley
114 *> \author Univ. of Colorado Denver
115 *> \author NAG Ltd.
116 *
117 *> \date December 2016
118 *
119 *> \ingroup double_lin
120 *
121 * =====================================================================
122  SUBROUTINE dppt02( UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK,
123  $ RESID )
124 *
125 * -- LAPACK test routine (version 3.7.0) --
126 * -- LAPACK is a software package provided by Univ. of Tennessee, --
127 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
128 * December 2016
129 *
130 * .. Scalar Arguments ..
131  CHARACTER UPLO
132  INTEGER LDB, LDX, N, NRHS
133  DOUBLE PRECISION RESID
134 * ..
135 * .. Array Arguments ..
136  DOUBLE PRECISION A( * ), B( ldb, * ), RWORK( * ), X( ldx, * )
137 * ..
138 *
139 * =====================================================================
140 *
141 * .. Parameters ..
142  DOUBLE PRECISION ZERO, ONE
143  parameter( zero = 0.0d+0, one = 1.0d+0 )
144 * ..
145 * .. Local Scalars ..
146  INTEGER J
147  DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
148 * ..
149 * .. External Functions ..
150  DOUBLE PRECISION DASUM, DLAMCH, DLANSP
151  EXTERNAL dasum, dlamch, dlansp
152 * ..
153 * .. External Subroutines ..
154  EXTERNAL dspmv
155 * ..
156 * .. Intrinsic Functions ..
157  INTRINSIC max
158 * ..
159 * .. Executable Statements ..
160 *
161 * Quick exit if N = 0 or NRHS = 0.
162 *
163  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
164  resid = zero
165  RETURN
166  END IF
167 *
168 * Exit with RESID = 1/EPS if ANORM = 0.
169 *
170  eps = dlamch( 'Epsilon' )
171  anorm = dlansp( '1', uplo, n, a, rwork )
172  IF( anorm.LE.zero ) THEN
173  resid = one / eps
174  RETURN
175  END IF
176 *
177 * Compute B - A*X for the matrix of right hand sides B.
178 *
179  DO 10 j = 1, nrhs
180  CALL dspmv( uplo, n, -one, a, x( 1, j ), 1, one, b( 1, j ), 1 )
181  10 CONTINUE
182 *
183 * Compute the maximum over the number of right hand sides of
184 * norm( B - A*X ) / ( norm(A) * norm(X) * EPS ) .
185 *
186  resid = zero
187  DO 20 j = 1, nrhs
188  bnorm = dasum( n, b( 1, j ), 1 )
189  xnorm = dasum( n, x( 1, j ), 1 )
190  IF( xnorm.LE.zero ) THEN
191  resid = one / eps
192  ELSE
193  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
194  END IF
195  20 CONTINUE
196 *
197  RETURN
198 *
199 * End of DPPT02
200 *
201  END
subroutine dppt02(UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK, RESID)
DPPT02
Definition: dppt02.f:124
subroutine dspmv(UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY)
DSPMV
Definition: dspmv.f:149