LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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ssyt01_3.f
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1*> \brief \b SSYT01_3
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 SSYT01_3( UPLO, N, A, LDA, AFAC, LDAFAC, E, IPIV, C,
12* LDC, 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* $ E( * ), RWORK( * )
23* ..
24*
25*
26*> \par Purpose:
27* =============
28*>
29*> \verbatim
30*>
31*> SSYT01_3 reconstructs a symmetric indefinite matrix A from its
32*> block L*D*L' or U*D*U' factorization computed by SSYTRF_RK
33*> (or SSYTRF_BK) and computes the residual
34*> norm( C - A ) / ( N * norm(A) * EPS ),
35*> where C is the reconstructed matrix and EPS is the machine epsilon.
36*> \endverbatim
37*
38* Arguments:
39* ==========
40*
41*> \param[in] UPLO
42*> \verbatim
43*> UPLO is CHARACTER*1
44*> Specifies whether the upper or lower triangular part of the
45*> symmetric matrix A is stored:
46*> = 'U': Upper triangular
47*> = 'L': Lower triangular
48*> \endverbatim
49*>
50*> \param[in] N
51*> \verbatim
52*> N is INTEGER
53*> The number of rows and columns of the matrix A. N >= 0.
54*> \endverbatim
55*>
56*> \param[in] A
57*> \verbatim
58*> A is DOUBLE PRECISION array, dimension (LDA,N)
59*> The original symmetric matrix A.
60*> \endverbatim
61*>
62*> \param[in] LDA
63*> \verbatim
64*> LDA is INTEGER
65*> The leading dimension of the array A. LDA >= max(1,N)
66*> \endverbatim
67*>
68*> \param[in] AFAC
69*> \verbatim
70*> AFAC is DOUBLE PRECISION array, dimension (LDAFAC,N)
71*> Diagonal of the block diagonal matrix D and factors U or L
72*> as computed by SSYTRF_RK and SSYTRF_BK:
73*> a) ONLY diagonal elements of the symmetric block diagonal
74*> matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
75*> (superdiagonal (or subdiagonal) elements of D
76*> should be provided on entry in array E), and
77*> b) If UPLO = 'U': factor U in the superdiagonal part of A.
78*> If UPLO = 'L': factor L in the subdiagonal part of A.
79*> \endverbatim
80*>
81*> \param[in] LDAFAC
82*> \verbatim
83*> LDAFAC is INTEGER
84*> The leading dimension of the array AFAC.
85*> LDAFAC >= max(1,N).
86*> \endverbatim
87*>
88*> \param[in] E
89*> \verbatim
90*> E is DOUBLE PRECISION array, dimension (N)
91*> On entry, contains the superdiagonal (or subdiagonal)
92*> elements of the symmetric block diagonal matrix D
93*> with 1-by-1 or 2-by-2 diagonal blocks, where
94*> If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced;
95*> If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.
96*> \endverbatim
97*>
98*> \param[in] IPIV
99*> \verbatim
100*> IPIV is INTEGER array, dimension (N)
101*> The pivot indices from SSYTRF_RK (or SSYTRF_BK).
102*> \endverbatim
103*>
104*> \param[out] C
105*> \verbatim
106*> C is DOUBLE PRECISION array, dimension (LDC,N)
107*> \endverbatim
108*>
109*> \param[in] LDC
110*> \verbatim
111*> LDC is INTEGER
112*> The leading dimension of the array C. LDC >= max(1,N).
113*> \endverbatim
114*>
115*> \param[out] RWORK
116*> \verbatim
117*> RWORK is DOUBLE PRECISION array, dimension (N)
118*> \endverbatim
119*>
120*> \param[out] RESID
121*> \verbatim
122*> RESID is DOUBLE PRECISION
123*> If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
124*> If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )
125*> \endverbatim
126*
127* Authors:
128* ========
129*
130*> \author Univ. of Tennessee
131*> \author Univ. of California Berkeley
132*> \author Univ. of Colorado Denver
133*> \author NAG Ltd.
134*
135*> \ingroup single_lin
136*
137* =====================================================================
138 SUBROUTINE ssyt01_3( UPLO, N, A, LDA, AFAC, LDAFAC, E, IPIV, C,
139 $ LDC, RWORK, RESID )
140*
141* -- LAPACK test routine --
142* -- LAPACK is a software package provided by Univ. of Tennessee, --
143* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
144*
145* .. Scalar Arguments ..
146 CHARACTER UPLO
147 INTEGER LDA, LDAFAC, LDC, N
148 REAL RESID
149* ..
150* .. Array Arguments ..
151 INTEGER IPIV( * )
152 REAL A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ),
153 $ e( * ), rwork( * )
154* ..
155*
156* =====================================================================
157*
158* .. Parameters ..
159 REAL ZERO, ONE
160 parameter( zero = 0.0e+0, one = 1.0e+0 )
161* ..
162* .. Local Scalars ..
163 INTEGER I, INFO, J
164 REAL ANORM, EPS
165* ..
166* .. External Functions ..
167 LOGICAL LSAME
168 REAL SLAMCH, SLANSY
169 EXTERNAL lsame, slamch, slansy
170* ..
171* .. External Subroutines ..
173* ..
174* .. Intrinsic Functions ..
175 INTRINSIC real
176* ..
177* .. Executable Statements ..
178*
179* Quick exit if N = 0.
180*
181 IF( n.LE.0 ) THEN
182 resid = zero
183 RETURN
184 END IF
185*
186* a) Revert to multipliers of L
187*
188 CALL ssyconvf_rook( uplo, 'R', n, afac, ldafac, e, ipiv, info )
189*
190* 1) Determine EPS and the norm of A.
191*
192 eps = slamch( 'Epsilon' )
193 anorm = slansy( '1', uplo, n, a, lda, rwork )
194*
195* 2) Initialize C to the identity matrix.
196*
197 CALL slaset( 'Full', n, n, zero, one, c, ldc )
198*
199* 3) Call SLAVSY_ROOK to form the product D * U' (or D * L' ).
200*
201 CALL slavsy_rook( uplo, 'Transpose', 'Non-unit', n, n, afac,
202 $ ldafac, ipiv, c, ldc, info )
203*
204* 4) Call SLAVSY_ROOK again to multiply by U (or L ).
205*
206 CALL slavsy_rook( uplo, 'No transpose', 'Unit', n, n, afac,
207 $ ldafac, ipiv, c, ldc, info )
208*
209* 5) Compute the difference C - A.
210*
211 IF( lsame( uplo, 'U' ) ) THEN
212 DO j = 1, n
213 DO i = 1, j
214 c( i, j ) = c( i, j ) - a( i, j )
215 END DO
216 END DO
217 ELSE
218 DO j = 1, n
219 DO i = j, n
220 c( i, j ) = c( i, j ) - a( i, j )
221 END DO
222 END DO
223 END IF
224*
225* 6) Compute norm( C - A ) / ( N * norm(A) * EPS )
226*
227 resid = slansy( '1', uplo, n, c, ldc, rwork )
228*
229 IF( anorm.LE.zero ) THEN
230 IF( resid.NE.zero )
231 $ resid = one / eps
232 ELSE
233 resid = ( ( resid / real( n ) ) / anorm ) / eps
234 END IF
235
236*
237* b) Convert to factor of L (or U)
238*
239 CALL ssyconvf_rook( uplo, 'C', n, afac, ldafac, e, ipiv, info )
240*
241 RETURN
242*
243* End of SSYT01_3
244*
245 END
subroutine slaset(uplo, m, n, alpha, beta, a, lda)
SLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition slaset.f:110
subroutine ssyconvf_rook(uplo, way, n, a, lda, e, ipiv, info)
SSYCONVF_ROOK
subroutine slavsy_rook(uplo, trans, diag, n, nrhs, a, lda, ipiv, b, ldb, info)
SLAVSY_ROOK
subroutine ssyt01_3(uplo, n, a, lda, afac, ldafac, e, ipiv, c, ldc, rwork, resid)
SSYT01_3
Definition ssyt01_3.f:140