LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
zhet01_3.f
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1 *> \brief \b ZHET01_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 ZHET01_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 *> ZHET01_3 reconstructs a Hermitian indefinite matrix A from its
33 *> block L*D*L' or U*D*U' factorization computed by ZHETRF_RK
34 *> (or ZHETRF_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 *> Hermitian 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 Hermitian 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 ZHETRF_RK and ZHETRF_BK:
74 *> a) ONLY diagonal elements of the Hermitian 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 Hermitian 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 ZHETRF_RK (or ZHETRF_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 zhet01_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 ZLANHE, DLAMCH
174  EXTERNAL lsame, zlanhe, dlamch
175 * ..
176 * .. External Subroutines ..
177  EXTERNAL zlaset, zlavhe_rook, zsyconvf_rook
178 * ..
179 * .. Intrinsic Functions ..
180  INTRINSIC dimag, 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 multiplyers 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 = zlanhe( '1', uplo, n, a, lda, rwork )
199 *
200 * Check the imaginary parts of the diagonal elements and return with
201 * an error code if any are nonzero.
202 *
203  DO j = 1, n
204  IF( dimag( afac( j, j ) ).NE.zero ) THEN
205  resid = one / eps
206  RETURN
207  END IF
208  END DO
209 *
210 * 2) Initialize C to the identity matrix.
211 *
212  CALL zlaset( 'Full', n, n, czero, cone, c, ldc )
213 *
214 * 3) Call ZLAVHE_ROOK to form the product D * U' (or D * L' ).
215 *
216  CALL zlavhe_rook( uplo, 'Conjugate', 'Non-unit', n, n, afac,
217  $ ldafac, ipiv, c, ldc, info )
218 *
219 * 4) Call ZLAVHE_RK again to multiply by U (or L ).
220 *
221  CALL zlavhe_rook( uplo, 'No transpose', 'Unit', n, n, afac,
222  $ ldafac, ipiv, c, ldc, info )
223 *
224 * 5) Compute the difference C - A .
225 *
226  IF( lsame( uplo, 'U' ) ) THEN
227  DO j = 1, n
228  DO i = 1, j - 1
229  c( i, j ) = c( i, j ) - a( i, j )
230  END DO
231  c( j, j ) = c( j, j ) - dble( a( j, j ) )
232  END DO
233  ELSE
234  DO j = 1, n
235  c( j, j ) = c( j, j ) - dble( a( j, j ) )
236  DO i = j + 1, n
237  c( i, j ) = c( i, j ) - a( i, j )
238  END DO
239  END DO
240  END IF
241 *
242 * 6) Compute norm( C - A ) / ( N * norm(A) * EPS )
243 *
244  resid = zlanhe( '1', uplo, n, c, ldc, rwork )
245 *
246  IF( anorm.LE.zero ) THEN
247  IF( resid.NE.zero )
248  $ resid = one / eps
249  ELSE
250  resid = ( ( resid/dble( n ) )/anorm ) / eps
251  END IF
252 *
253 * b) Convert to factor of L (or U)
254 *
255  CALL zsyconvf_rook( uplo, 'C', n, afac, ldafac, e, ipiv, info )
256 *
257  RETURN
258 *
259 * End of ZHET01_3
260 *
261  END
subroutine zlavhe_rook(UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
ZLAVHE_ROOK
Definition: zlavhe_rook.f:153
subroutine zhet01_3(UPLO, N, A, LDA, AFAC, LDAFAC, E, IPIV, C, LDC, RWORK, RESID)
ZHET01_3
Definition: zhet01_3.f:141
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