LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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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*> \ingroup double_lin
120*
121* =====================================================================
122 SUBROUTINE dsyt01( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC,
123 $ RWORK, 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 UPLO
131 INTEGER LDA, LDAFAC, LDC, N
132 DOUBLE PRECISION RESID
133* ..
134* .. Array Arguments ..
135 INTEGER IPIV( * )
136 DOUBLE PRECISION A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ),
137 $ rwork( * )
138* ..
139*
140* =====================================================================
141*
142* .. Parameters ..
143 DOUBLE PRECISION ZERO, ONE
144 parameter( zero = 0.0d+0, one = 1.0d+0 )
145* ..
146* .. Local Scalars ..
147 INTEGER I, INFO, J
148 DOUBLE PRECISION ANORM, EPS
149* ..
150* .. External Functions ..
151 LOGICAL LSAME
152 DOUBLE PRECISION DLAMCH, DLANSY
153 EXTERNAL lsame, dlamch, dlansy
154* ..
155* .. External Subroutines ..
156 EXTERNAL dlaset, dlavsy
157* ..
158* .. Intrinsic Functions ..
159 INTRINSIC dble
160* ..
161* .. Executable Statements ..
162*
163* Quick exit if N = 0.
164*
165 IF( n.LE.0 ) THEN
166 resid = zero
167 RETURN
168 END IF
169*
170* Determine EPS and the norm of A.
171*
172 eps = dlamch( 'Epsilon' )
173 anorm = dlansy( '1', uplo, n, a, lda, rwork )
174*
175* Initialize C to the identity matrix.
176*
177 CALL dlaset( 'Full', n, n, zero, one, c, ldc )
178*
179* Call DLAVSY to form the product D * U' (or D * L' ).
180*
181 CALL dlavsy( uplo, 'Transpose', 'Non-unit', n, n, afac, ldafac,
182 $ ipiv, c, ldc, info )
183*
184* Call DLAVSY again to multiply by U (or L ).
185*
186 CALL dlavsy( uplo, 'No transpose', 'Unit', n, n, afac, ldafac,
187 $ ipiv, c, ldc, info )
188*
189* Compute the difference C - A .
190*
191 IF( lsame( uplo, 'U' ) ) THEN
192 DO 20 j = 1, n
193 DO 10 i = 1, j
194 c( i, j ) = c( i, j ) - a( i, j )
195 10 CONTINUE
196 20 CONTINUE
197 ELSE
198 DO 40 j = 1, n
199 DO 30 i = j, n
200 c( i, j ) = c( i, j ) - a( i, j )
201 30 CONTINUE
202 40 CONTINUE
203 END IF
204*
205* Compute norm( C - A ) / ( N * norm(A) * EPS )
206*
207 resid = dlansy( '1', uplo, n, c, ldc, rwork )
208*
209 IF( anorm.LE.zero ) THEN
210 IF( resid.NE.zero )
211 $ resid = one / eps
212 ELSE
213 resid = ( ( resid / dble( n ) ) / anorm ) / eps
214 END IF
215*
216 RETURN
217*
218* End of DSYT01
219*
220 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:110
subroutine dlavsy(UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
DLAVSY
Definition: dlavsy.f:155
subroutine dsyt01(UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC, RWORK, RESID)
DSYT01
Definition: dsyt01.f:124