LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
strt01.f
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1 *> \brief \b STRT01
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 STRT01( UPLO, DIAG, N, A, LDA, AINV, LDAINV, RCOND,
12 * WORK, RESID )
13 *
14 * .. Scalar Arguments ..
15 * CHARACTER DIAG, UPLO
16 * INTEGER LDA, LDAINV, N
17 * REAL RCOND, RESID
18 * ..
19 * .. Array Arguments ..
20 * REAL A( LDA, * ), AINV( LDAINV, * ), WORK( * )
21 * ..
22 *
23 *
24 *> \par Purpose:
25 * =============
26 *>
27 *> \verbatim
28 *>
29 *> STRT01 computes the residual for a triangular matrix A times its
30 *> inverse:
31 *> RESID = norm( A*AINV - I ) / ( N * norm(A) * norm(AINV) * EPS ),
32 *> where EPS is the machine epsilon.
33 *> \endverbatim
34 *
35 * Arguments:
36 * ==========
37 *
38 *> \param[in] UPLO
39 *> \verbatim
40 *> UPLO is CHARACTER*1
41 *> Specifies whether the matrix A is upper or lower triangular.
42 *> = 'U': Upper triangular
43 *> = 'L': Lower triangular
44 *> \endverbatim
45 *>
46 *> \param[in] DIAG
47 *> \verbatim
48 *> DIAG is CHARACTER*1
49 *> Specifies whether or not the matrix A is unit triangular.
50 *> = 'N': Non-unit triangular
51 *> = 'U': Unit triangular
52 *> \endverbatim
53 *>
54 *> \param[in] N
55 *> \verbatim
56 *> N is INTEGER
57 *> The order of the matrix A. N >= 0.
58 *> \endverbatim
59 *>
60 *> \param[in] A
61 *> \verbatim
62 *> A is REAL array, dimension (LDA,N)
63 *> The triangular matrix A. If UPLO = 'U', the leading n by n
64 *> upper triangular part of the array A contains the upper
65 *> triangular matrix, and the strictly lower triangular part of
66 *> A is not referenced. If UPLO = 'L', the leading n by n lower
67 *> triangular part of the array A contains the lower triangular
68 *> matrix, and the strictly upper triangular part of A is not
69 *> referenced. If DIAG = 'U', the diagonal elements of A are
70 *> also not referenced and are assumed to be 1.
71 *> \endverbatim
72 *>
73 *> \param[in] LDA
74 *> \verbatim
75 *> LDA is INTEGER
76 *> The leading dimension of the array A. LDA >= max(1,N).
77 *> \endverbatim
78 *>
79 *> \param[in,out] AINV
80 *> \verbatim
81 *> AINV is REAL array, dimension (LDAINV,N)
82 *> On entry, the (triangular) inverse of the matrix A, in the
83 *> same storage format as A.
84 *> On exit, the contents of AINV are destroyed.
85 *> \endverbatim
86 *>
87 *> \param[in] LDAINV
88 *> \verbatim
89 *> LDAINV is INTEGER
90 *> The leading dimension of the array AINV. LDAINV >= max(1,N).
91 *> \endverbatim
92 *>
93 *> \param[out] RCOND
94 *> \verbatim
95 *> RCOND is REAL
96 *> The reciprocal condition number of A, computed as
97 *> 1/(norm(A) * norm(AINV)).
98 *> \endverbatim
99 *>
100 *> \param[out] WORK
101 *> \verbatim
102 *> WORK is REAL array, dimension (N)
103 *> \endverbatim
104 *>
105 *> \param[out] RESID
106 *> \verbatim
107 *> RESID is REAL
108 *> norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS )
109 *> \endverbatim
110 *
111 * Authors:
112 * ========
113 *
114 *> \author Univ. of Tennessee
115 *> \author Univ. of California Berkeley
116 *> \author Univ. of Colorado Denver
117 *> \author NAG Ltd.
118 *
119 *> \ingroup single_lin
120 *
121 * =====================================================================
122  SUBROUTINE strt01( UPLO, DIAG, N, A, LDA, AINV, LDAINV, RCOND,
123  $ WORK, RESID )
124 *
125 * -- LAPACK test routine --
126 * -- LAPACK is a software package provided by Univ. of Tennessee, --
127 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
128 *
129 * .. Scalar Arguments ..
130  CHARACTER DIAG, UPLO
131  INTEGER LDA, LDAINV, N
132  REAL RCOND, RESID
133 * ..
134 * .. Array Arguments ..
135  REAL A( LDA, * ), AINV( LDAINV, * ), WORK( * )
136 * ..
137 *
138 * =====================================================================
139 *
140 * .. Parameters ..
141  REAL ZERO, ONE
142  parameter( zero = 0.0e+0, one = 1.0e+0 )
143 * ..
144 * .. Local Scalars ..
145  INTEGER J
146  REAL AINVNM, ANORM, EPS
147 * ..
148 * .. External Functions ..
149  LOGICAL LSAME
150  REAL SLAMCH, SLANTR
151  EXTERNAL lsame, slamch, slantr
152 * ..
153 * .. External Subroutines ..
154  EXTERNAL strmv
155 * ..
156 * .. Intrinsic Functions ..
157  INTRINSIC real
158 * ..
159 * .. Executable Statements ..
160 *
161 * Quick exit if N = 0
162 *
163  IF( n.LE.0 ) THEN
164  rcond = one
165  resid = zero
166  RETURN
167  END IF
168 *
169 * Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
170 *
171  eps = slamch( 'Epsilon' )
172  anorm = slantr( '1', uplo, diag, n, n, a, lda, work )
173  ainvnm = slantr( '1', uplo, diag, n, n, ainv, ldainv, work )
174  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
175  rcond = zero
176  resid = one / eps
177  RETURN
178  END IF
179  rcond = ( one / anorm ) / ainvnm
180 *
181 * Set the diagonal of AINV to 1 if AINV has unit diagonal.
182 *
183  IF( lsame( diag, 'U' ) ) THEN
184  DO 10 j = 1, n
185  ainv( j, j ) = one
186  10 CONTINUE
187  END IF
188 *
189 * Compute A * AINV, overwriting AINV.
190 *
191  IF( lsame( uplo, 'U' ) ) THEN
192  DO 20 j = 1, n
193  CALL strmv( 'Upper', 'No transpose', diag, j, a, lda,
194  $ ainv( 1, j ), 1 )
195  20 CONTINUE
196  ELSE
197  DO 30 j = 1, n
198  CALL strmv( 'Lower', 'No transpose', diag, n-j+1, a( j, j ),
199  $ lda, ainv( j, j ), 1 )
200  30 CONTINUE
201  END IF
202 *
203 * Subtract 1 from each diagonal element to form A*AINV - I.
204 *
205  DO 40 j = 1, n
206  ainv( j, j ) = ainv( j, j ) - one
207  40 CONTINUE
208 *
209 * Compute norm(A*AINV - I) / (N * norm(A) * norm(AINV) * EPS)
210 *
211  resid = slantr( '1', uplo, 'Non-unit', n, n, ainv, ldainv, work )
212 *
213  resid = ( ( resid*rcond ) / real( n ) ) / eps
214 *
215  RETURN
216 *
217 * End of STRT01
218 *
219  END
subroutine strmv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
STRMV
Definition: strmv.f:147
subroutine strt01(UPLO, DIAG, N, A, LDA, AINV, LDAINV, RCOND, WORK, RESID)
STRT01
Definition: strt01.f:124