LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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zsyt01_3.f
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1*> \brief \b ZSYT01_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 ZSYT01_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 RWORK( * )
22* COMPLEX*16 A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ),
23* E( * )
24* ..
25*
26*
27*> \par Purpose:
28* =============
29*>
30*> \verbatim
31*>
32*> ZSYT01_3 reconstructs a symmetric indefinite matrix A from its
33*> block L*D*L' or U*D*U' factorization computed by ZSYTRF_RK
34*> (or ZSYTRF_BK) and computes the residual
35*> norm( C - A ) / ( N * norm(A) * EPS ),
36*> where C is the reconstructed matrix and EPS is the machine epsilon.
37*> \endverbatim
38*
39* Arguments:
40* ==========
41*
42*> \param[in] UPLO
43*> \verbatim
44*> UPLO is CHARACTER*1
45*> Specifies whether the upper or lower triangular part of the
46*> symmetric matrix A is stored:
47*> = 'U': Upper triangular
48*> = 'L': Lower triangular
49*> \endverbatim
50*>
51*> \param[in] N
52*> \verbatim
53*> N is INTEGER
54*> The number of rows and columns of the matrix A. N >= 0.
55*> \endverbatim
56*>
57*> \param[in] A
58*> \verbatim
59*> A is COMPLEX*16 array, dimension (LDA,N)
60*> The original symmetric matrix A.
61*> \endverbatim
62*>
63*> \param[in] LDA
64*> \verbatim
65*> LDA is INTEGER
66*> The leading dimension of the array A. LDA >= max(1,N)
67*> \endverbatim
68*>
69*> \param[in] AFAC
70*> \verbatim
71*> AFAC is COMPLEX*16 array, dimension (LDAFAC,N)
72*> Diagonal of the block diagonal matrix D and factors U or L
73*> as computed by ZSYTRF_RK and ZSYTRF_BK:
74*> a) ONLY diagonal elements of the symmetric block diagonal
75*> matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
76*> (superdiagonal (or subdiagonal) elements of D
77*> should be provided on entry in array E), and
78*> b) If UPLO = 'U': factor U in the superdiagonal part of A.
79*> If UPLO = 'L': factor L in the subdiagonal part of A.
80*> \endverbatim
81*>
82*> \param[in] LDAFAC
83*> \verbatim
84*> LDAFAC is INTEGER
85*> The leading dimension of the array AFAC.
86*> LDAFAC >= max(1,N).
87*> \endverbatim
88*>
89*> \param[in] E
90*> \verbatim
91*> E is COMPLEX*16 array, dimension (N)
92*> On entry, contains the superdiagonal (or subdiagonal)
93*> elements of the symmetric block diagonal matrix D
94*> with 1-by-1 or 2-by-2 diagonal blocks, where
95*> If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced;
96*> If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.
97*> \endverbatim
98*>
99*> \param[in] IPIV
100*> \verbatim
101*> IPIV is INTEGER array, dimension (N)
102*> The pivot indices from ZSYTRF_RK (or ZSYTRF_BK).
103*> \endverbatim
104*>
105*> \param[out] C
106*> \verbatim
107*> C is COMPLEX*16 array, dimension (LDC,N)
108*> \endverbatim
109*>
110*> \param[in] LDC
111*> \verbatim
112*> LDC is INTEGER
113*> The leading dimension of the array C. LDC >= max(1,N).
114*> \endverbatim
115*>
116*> \param[out] RWORK
117*> \verbatim
118*> RWORK is DOUBLE PRECISION array, dimension (N)
119*> \endverbatim
120*>
121*> \param[out] RESID
122*> \verbatim
123*> RESID is DOUBLE PRECISION
124*> If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
125*> If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )
126*> \endverbatim
127*
128* Authors:
129* ========
130*
131*> \author Univ. of Tennessee
132*> \author Univ. of California Berkeley
133*> \author Univ. of Colorado Denver
134*> \author NAG Ltd.
135*
136*> \ingroup complex16_lin
137*
138* =====================================================================
139 SUBROUTINE zsyt01_3( UPLO, N, A, LDA, AFAC, LDAFAC, E, IPIV, C,
140 \$ LDC, RWORK, RESID )
141*
142* -- LAPACK test routine --
143* -- LAPACK is a software package provided by Univ. of Tennessee, --
144* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
145*
146* .. Scalar Arguments ..
147 CHARACTER UPLO
148 INTEGER LDA, LDAFAC, LDC, N
149 DOUBLE PRECISION RESID
150* ..
151* .. Array Arguments ..
152 INTEGER IPIV( * )
153 DOUBLE PRECISION RWORK( * )
154 COMPLEX*16 A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ),
155 \$ e( * )
156* ..
157*
158* =====================================================================
159*
160* .. Parameters ..
161 DOUBLE PRECISION ZERO, ONE
162 parameter( zero = 0.0d+0, one = 1.0d+0 )
163 COMPLEX*16 CZERO, CONE
164 parameter( czero = ( 0.0d+0, 0.0d+0 ),
165 \$ cone = ( 1.0d+0, 0.0d+0 ) )
166* ..
167* .. Local Scalars ..
168 INTEGER I, INFO, J
169 DOUBLE PRECISION ANORM, EPS
170* ..
171* .. External Functions ..
172 LOGICAL LSAME
173 DOUBLE PRECISION DLAMCH, ZLANSY
174 EXTERNAL lsame, dlamch, zlansy
175* ..
176* .. External Subroutines ..
178* ..
179* .. Intrinsic Functions ..
180 INTRINSIC dble
181* ..
182* .. Executable Statements ..
183*
184* Quick exit if N = 0.
185*
186 IF( n.LE.0 ) THEN
187 resid = zero
188 RETURN
189 END IF
190*
191* a) Revert to multipliers of L
192*
193 CALL zsyconvf_rook( uplo, 'R', n, afac, ldafac, e, ipiv, info )
194*
195* 1) Determine EPS and the norm of A.
196*
197 eps = dlamch( 'Epsilon' )
198 anorm = zlansy( '1', uplo, n, a, lda, rwork )
199*
200* 2) Initialize C to the identity matrix.
201*
202 CALL zlaset( 'Full', n, n, czero, cone, c, ldc )
203*
204* 3) Call ZLAVSY_ROOK to form the product D * U' (or D * L' ).
205*
206 CALL zlavsy_rook( uplo, 'Transpose', 'Non-unit', n, n, afac,
207 \$ ldafac, ipiv, c, ldc, info )
208*
209* 4) Call ZLAVSY_ROOK again to multiply by U (or L ).
210*
211 CALL zlavsy_rook( uplo, 'No transpose', 'Unit', n, n, afac,
212 \$ ldafac, ipiv, c, ldc, info )
213*
214* 5) Compute the difference C - A .
215*
216 IF( lsame( uplo, 'U' ) ) THEN
217 DO j = 1, n
218 DO i = 1, j
219 c( i, j ) = c( i, j ) - a( i, j )
220 END DO
221 END DO
222 ELSE
223 DO j = 1, n
224 DO i = j, n
225 c( i, j ) = c( i, j ) - a( i, j )
226 END DO
227 END DO
228 END IF
229*
230* 6) Compute norm( C - A ) / ( N * norm(A) * EPS )
231*
232 resid = zlansy( '1', uplo, n, c, ldc, rwork )
233*
234 IF( anorm.LE.zero ) THEN
235 IF( resid.NE.zero )
236 \$ resid = one / eps
237 ELSE
238 resid = ( ( resid / dble( n ) ) / anorm ) / eps
239 END IF
240
241*
242* b) Convert to factor of L (or U)
243*
244 CALL zsyconvf_rook( uplo, 'C', n, afac, ldafac, e, ipiv, info )
245*
246 RETURN
247*
248* End of ZSYT01_3
249*
250 END
subroutine zlaset(uplo, m, n, alpha, beta, a, lda)
ZLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition zlaset.f:106
subroutine zsyconvf_rook(uplo, way, n, a, lda, e, ipiv, info)
ZSYCONVF_ROOK
subroutine zlavsy_rook(uplo, trans, diag, n, nrhs, a, lda, ipiv, b, ldb, info)
ZLAVSY_ROOK
subroutine zsyt01_3(uplo, n, a, lda, afac, ldafac, e, ipiv, c, ldc, rwork, resid)
ZSYT01_3
Definition zsyt01_3.f:141