LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
dget03.f
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1 *> \brief \b DGET03
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 DGET03( N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK,
12 * RCOND, RESID )
13 *
14 * .. Scalar Arguments ..
15 * INTEGER LDA, LDAINV, LDWORK, N
16 * DOUBLE PRECISION RCOND, RESID
17 * ..
18 * .. Array Arguments ..
19 * DOUBLE PRECISION A( LDA, * ), AINV( LDAINV, * ), RWORK( * ),
20 * $ WORK( LDWORK, * )
21 * ..
22 *
23 *
24 *> \par Purpose:
25 * =============
26 *>
27 *> \verbatim
28 *>
29 *> DGET03 computes the residual for a general matrix times its inverse:
30 *> norm( I - AINV*A ) / ( N * norm(A) * norm(AINV) * EPS ),
31 *> where EPS is the machine epsilon.
32 *> \endverbatim
33 *
34 * Arguments:
35 * ==========
36 *
37 *> \param[in] N
38 *> \verbatim
39 *> N is INTEGER
40 *> The number of rows and columns of the matrix A. N >= 0.
41 *> \endverbatim
42 *>
43 *> \param[in] A
44 *> \verbatim
45 *> A is DOUBLE PRECISION array, dimension (LDA,N)
46 *> The original N x N matrix A.
47 *> \endverbatim
48 *>
49 *> \param[in] LDA
50 *> \verbatim
51 *> LDA is INTEGER
52 *> The leading dimension of the array A. LDA >= max(1,N).
53 *> \endverbatim
54 *>
55 *> \param[in] AINV
56 *> \verbatim
57 *> AINV is DOUBLE PRECISION array, dimension (LDAINV,N)
58 *> The inverse of the matrix A.
59 *> \endverbatim
60 *>
61 *> \param[in] LDAINV
62 *> \verbatim
63 *> LDAINV is INTEGER
64 *> The leading dimension of the array AINV. LDAINV >= max(1,N).
65 *> \endverbatim
66 *>
67 *> \param[out] WORK
68 *> \verbatim
69 *> WORK is DOUBLE PRECISION array, dimension (LDWORK,N)
70 *> \endverbatim
71 *>
72 *> \param[in] LDWORK
73 *> \verbatim
74 *> LDWORK is INTEGER
75 *> The leading dimension of the array WORK. LDWORK >= max(1,N).
76 *> \endverbatim
77 *>
78 *> \param[out] RWORK
79 *> \verbatim
80 *> RWORK is DOUBLE PRECISION array, dimension (N)
81 *> \endverbatim
82 *>
83 *> \param[out] RCOND
84 *> \verbatim
85 *> RCOND is DOUBLE PRECISION
86 *> The reciprocal of the condition number of A, computed as
87 *> ( 1/norm(A) ) / norm(AINV).
88 *> \endverbatim
89 *>
90 *> \param[out] RESID
91 *> \verbatim
92 *> RESID is DOUBLE PRECISION
93 *> norm(I - AINV*A) / ( N * norm(A) * norm(AINV) * EPS )
94 *> \endverbatim
95 *
96 * Authors:
97 * ========
98 *
99 *> \author Univ. of Tennessee
100 *> \author Univ. of California Berkeley
101 *> \author Univ. of Colorado Denver
102 *> \author NAG Ltd.
103 *
104 *> \ingroup double_lin
105 *
106 * =====================================================================
107  SUBROUTINE dget03( N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK,
108  $ RCOND, RESID )
109 *
110 * -- LAPACK test routine --
111 * -- LAPACK is a software package provided by Univ. of Tennessee, --
112 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
113 *
114 * .. Scalar Arguments ..
115  INTEGER LDA, LDAINV, LDWORK, N
116  DOUBLE PRECISION RCOND, RESID
117 * ..
118 * .. Array Arguments ..
119  DOUBLE PRECISION A( LDA, * ), AINV( LDAINV, * ), RWORK( * ),
120  $ work( ldwork, * )
121 * ..
122 *
123 * =====================================================================
124 *
125 * .. Parameters ..
126  DOUBLE PRECISION ZERO, ONE
127  parameter( zero = 0.0d+0, one = 1.0d+0 )
128 * ..
129 * .. Local Scalars ..
130  INTEGER I
131  DOUBLE PRECISION AINVNM, ANORM, EPS
132 * ..
133 * .. External Functions ..
134  DOUBLE PRECISION DLAMCH, DLANGE
135  EXTERNAL dlamch, dlange
136 * ..
137 * .. External Subroutines ..
138  EXTERNAL dgemm
139 * ..
140 * .. Intrinsic Functions ..
141  INTRINSIC dble
142 * ..
143 * .. Executable Statements ..
144 *
145 * Quick exit if N = 0.
146 *
147  IF( n.LE.0 ) THEN
148  rcond = one
149  resid = zero
150  RETURN
151  END IF
152 *
153 * Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
154 *
155  eps = dlamch( 'Epsilon' )
156  anorm = dlange( '1', n, n, a, lda, rwork )
157  ainvnm = dlange( '1', n, n, ainv, ldainv, rwork )
158  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
159  rcond = zero
160  resid = one / eps
161  RETURN
162  END IF
163  rcond = ( one / anorm ) / ainvnm
164 *
165 * Compute I - A * AINV
166 *
167  CALL dgemm( 'No transpose', 'No transpose', n, n, n, -one, ainv,
168  $ ldainv, a, lda, zero, work, ldwork )
169  DO 10 i = 1, n
170  work( i, i ) = one + work( i, i )
171  10 CONTINUE
172 *
173 * Compute norm(I - AINV*A) / (N * norm(A) * norm(AINV) * EPS)
174 *
175  resid = dlange( '1', n, n, work, ldwork, rwork )
176 *
177  resid = ( ( resid*rcond ) / eps ) / dble( n )
178 *
179  RETURN
180 *
181 * End of DGET03
182 *
183  END
subroutine dgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DGEMM
Definition: dgemm.f:187
subroutine dget03(N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK, RCOND, RESID)
DGET03
Definition: dget03.f:109