LAPACK  3.8.0 LAPACK: Linear Algebra PACKage
sget03.f
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1 *> \brief \b SGET03
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 SGET03( N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK,
12 * RCOND, RESID )
13 *
14 * .. Scalar Arguments ..
15 * INTEGER LDA, LDAINV, LDWORK, N
16 * REAL RCOND, RESID
17 * ..
18 * .. Array Arguments ..
19 * REAL A( LDA, * ), AINV( LDAINV, * ), RWORK( * ),
20 * \$ WORK( LDWORK, * )
21 * ..
22 *
23 *
24 *> \par Purpose:
25 * =============
26 *>
27 *> \verbatim
28 *>
29 *> SGET03 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 REAL 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 REAL 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 REAL 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 REAL array, dimension (N)
81 *> \endverbatim
82 *>
83 *> \param[out] RCOND
84 *> \verbatim
85 *> RCOND is REAL
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 REAL
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 *> \date December 2016
105 *
106 *> \ingroup single_lin
107 *
108 * =====================================================================
109  SUBROUTINE sget03( N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK,
110  \$ RCOND, RESID )
111 *
112 * -- LAPACK test routine (version 3.7.0) --
113 * -- LAPACK is a software package provided by Univ. of Tennessee, --
114 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
115 * December 2016
116 *
117 * .. Scalar Arguments ..
118  INTEGER LDA, LDAINV, LDWORK, N
119  REAL RCOND, RESID
120 * ..
121 * .. Array Arguments ..
122  REAL A( lda, * ), AINV( ldainv, * ), RWORK( * ),
123  \$ work( ldwork, * )
124 * ..
125 *
126 * =====================================================================
127 *
128 * .. Parameters ..
129  REAL ZERO, ONE
130  parameter( zero = 0.0e+0, one = 1.0e+0 )
131 * ..
132 * .. Local Scalars ..
133  INTEGER I
134  REAL AINVNM, ANORM, EPS
135 * ..
136 * .. External Functions ..
137  REAL SLAMCH, SLANGE
138  EXTERNAL slamch, slange
139 * ..
140 * .. External Subroutines ..
141  EXTERNAL sgemm
142 * ..
143 * .. Intrinsic Functions ..
144  INTRINSIC real
145 * ..
146 * .. Executable Statements ..
147 *
148 * Quick exit if N = 0.
149 *
150  IF( n.LE.0 ) THEN
151  rcond = one
152  resid = zero
153  RETURN
154  END IF
155 *
156 * Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
157 *
158  eps = slamch( 'Epsilon' )
159  anorm = slange( '1', n, n, a, lda, rwork )
160  ainvnm = slange( '1', n, n, ainv, ldainv, rwork )
161  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
162  rcond = zero
163  resid = one / eps
164  RETURN
165  END IF
166  rcond = ( one / anorm ) / ainvnm
167 *
168 * Compute I - A * AINV
169 *
170  CALL sgemm( 'No transpose', 'No transpose', n, n, n, -one,
171  \$ ainv, ldainv, a, lda, zero, work, ldwork )
172  DO 10 i = 1, n
173  work( i, i ) = one + work( i, i )
174  10 CONTINUE
175 *
176 * Compute norm(I - AINV*A) / (N * norm(A) * norm(AINV) * EPS)
177 *
178  resid = slange( '1', n, n, work, ldwork, rwork )
179 *
180  resid = ( ( resid*rcond ) / eps ) / REAL( n )
181 *
182  RETURN
183 *
184 * End of SGET03
185 *
186  END
subroutine sget03(N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK, RCOND, RESID)
SGET03
Definition: sget03.f:111
subroutine sgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SGEMM
Definition: sgemm.f:189