LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
dsyt01.f
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1 *> \brief \b DSYT01
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 DSYT01( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC,
12 * RWORK, RESID )
13 *
14 * .. Scalar Arguments ..
15 * CHARACTER UPLO
16 * INTEGER LDA, LDAFAC, LDC, N
17 * DOUBLE PRECISION RESID
18 * ..
19 * .. Array Arguments ..
20 * INTEGER IPIV( * )
21 * DOUBLE PRECISION A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ),
22 * \$ RWORK( * )
23 * ..
24 *
25 *
26 *> \par Purpose:
27 * =============
28 *>
29 *> \verbatim
30 *>
31 *> DSYT01 reconstructs a symmetric indefinite matrix A from its
32 *> block L*D*L' or U*D*U' factorization and computes the residual
33 *> norm( C - A ) / ( N * norm(A) * EPS ),
34 *> where C is the reconstructed matrix and EPS is the machine epsilon.
35 *> \endverbatim
36 *
37 * Arguments:
38 * ==========
39 *
40 *> \param[in] UPLO
41 *> \verbatim
42 *> UPLO is CHARACTER*1
43 *> Specifies whether the upper or lower triangular part of the
44 *> symmetric matrix A is stored:
45 *> = 'U': Upper triangular
46 *> = 'L': Lower triangular
47 *> \endverbatim
48 *>
49 *> \param[in] N
50 *> \verbatim
51 *> N is INTEGER
52 *> The number of rows and columns of the matrix A. N >= 0.
53 *> \endverbatim
54 *>
55 *> \param[in] A
56 *> \verbatim
57 *> A is DOUBLE PRECISION array, dimension (LDA,N)
58 *> The original symmetric matrix A.
59 *> \endverbatim
60 *>
61 *> \param[in] LDA
62 *> \verbatim
63 *> LDA is INTEGER
64 *> The leading dimension of the array A. LDA >= max(1,N)
65 *> \endverbatim
66 *>
67 *> \param[in] AFAC
68 *> \verbatim
69 *> AFAC is DOUBLE PRECISION array, dimension (LDAFAC,N)
70 *> The factored form of the matrix A. AFAC contains the block
71 *> diagonal matrix D and the multipliers used to obtain the
72 *> factor L or U from the block L*D*L' or U*D*U' factorization
73 *> as computed by DSYTRF.
74 *> \endverbatim
75 *>
76 *> \param[in] LDAFAC
77 *> \verbatim
78 *> LDAFAC is INTEGER
79 *> The leading dimension of the array AFAC. LDAFAC >= max(1,N).
80 *> \endverbatim
81 *>
82 *> \param[in] IPIV
83 *> \verbatim
84 *> IPIV is INTEGER array, dimension (N)
85 *> The pivot indices from DSYTRF.
86 *> \endverbatim
87 *>
88 *> \param[out] C
89 *> \verbatim
90 *> C is DOUBLE PRECISION array, dimension (LDC,N)
91 *> \endverbatim
92 *>
93 *> \param[in] LDC
94 *> \verbatim
95 *> LDC is INTEGER
96 *> The leading dimension of the array C. LDC >= max(1,N).
97 *> \endverbatim
98 *>
99 *> \param[out] RWORK
100 *> \verbatim
101 *> RWORK is DOUBLE PRECISION array, dimension (N)
102 *> \endverbatim
103 *>
104 *> \param[out] RESID
105 *> \verbatim
106 *> RESID is DOUBLE PRECISION
107 *> If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
108 *> If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * 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 *> \date November 2013
120 *
121 *> \ingroup double_lin
122 *
123 * =====================================================================
124  SUBROUTINE dsyt01( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC,
125  \$ rwork, resid )
126 *
127 * -- LAPACK test routine (version 3.5.0) --
128 * -- LAPACK is a software package provided by Univ. of Tennessee, --
129 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
130 * November 2013
131 *
132 * .. Scalar Arguments ..
133  CHARACTER UPLO
134  INTEGER LDA, LDAFAC, LDC, N
135  DOUBLE PRECISION RESID
136 * ..
137 * .. Array Arguments ..
138  INTEGER IPIV( * )
139  DOUBLE PRECISION A( lda, * ), AFAC( ldafac, * ), C( ldc, * ),
140  \$ rwork( * )
141 * ..
142 *
143 * =====================================================================
144 *
145 * .. Parameters ..
146  DOUBLE PRECISION ZERO, ONE
147  parameter ( zero = 0.0d+0, one = 1.0d+0 )
148 * ..
149 * .. Local Scalars ..
150  INTEGER I, INFO, J
151  DOUBLE PRECISION ANORM, EPS
152 * ..
153 * .. External Functions ..
154  LOGICAL LSAME
155  DOUBLE PRECISION DLAMCH, DLANSY
156  EXTERNAL lsame, dlamch, dlansy
157 * ..
158 * .. External Subroutines ..
159  EXTERNAL dlaset, dlavsy
160 * ..
161 * .. Intrinsic Functions ..
162  INTRINSIC dble
163 * ..
164 * .. Executable Statements ..
165 *
166 * Quick exit if N = 0.
167 *
168  IF( n.LE.0 ) THEN
169  resid = zero
170  RETURN
171  END IF
172 *
173 * Determine EPS and the norm of A.
174 *
175  eps = dlamch( 'Epsilon' )
176  anorm = dlansy( '1', uplo, n, a, lda, rwork )
177 *
178 * Initialize C to the identity matrix.
179 *
180  CALL dlaset( 'Full', n, n, zero, one, c, ldc )
181 *
182 * Call DLAVSY to form the product D * U' (or D * L' ).
183 *
184  CALL dlavsy( uplo, 'Transpose', 'Non-unit', n, n, afac, ldafac,
185  \$ ipiv, c, ldc, info )
186 *
187 * Call DLAVSY again to multiply by U (or L ).
188 *
189  CALL dlavsy( uplo, 'No transpose', 'Unit', n, n, afac, ldafac,
190  \$ ipiv, c, ldc, info )
191 *
192 * Compute the difference C - A .
193 *
194  IF( lsame( uplo, 'U' ) ) THEN
195  DO 20 j = 1, n
196  DO 10 i = 1, j
197  c( i, j ) = c( i, j ) - a( i, j )
198  10 CONTINUE
199  20 CONTINUE
200  ELSE
201  DO 40 j = 1, n
202  DO 30 i = j, n
203  c( i, j ) = c( i, j ) - a( i, j )
204  30 CONTINUE
205  40 CONTINUE
206  END IF
207 *
208 * Compute norm( C - A ) / ( N * norm(A) * EPS )
209 *
210  resid = dlansy( '1', uplo, n, c, ldc, rwork )
211 *
212  IF( anorm.LE.zero ) THEN
213  IF( resid.NE.zero )
214  \$ resid = one / eps
215  ELSE
216  resid = ( ( resid / dble( n ) ) / anorm ) / eps
217  END IF
218 *
219  RETURN
220 *
221 * End of DSYT01
222 *
223  END
subroutine dlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
DLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values...
Definition: dlaset.f:112
subroutine dsyt01(UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC, RWORK, RESID)
DSYT01
Definition: dsyt01.f:126
subroutine dlavsy(UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
DLAVSY
Definition: dlavsy.f:157