LAPACK  3.8.0 LAPACK: Linear Algebra PACKage
chet01_3.f
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1 *> \brief \b CHET01_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 CHET01_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 * REAL RESID
18 * ..
19 * .. Array Arguments ..
20 * INTEGER IPIV( * )
21 * REAL RWORK( * )
22 * COMPLEX A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ),
23 * E( * )
24 * ..
25 *
26 *
27 *> \par Purpose:
28 * =============
29 *>
30 *> \verbatim
31 *>
32 *> CHET01_3 reconstructs a Hermitian indefinite matrix A from its
33 *> block L*D*L' or U*D*U' factorization computed by CHETRF_RK
34 *> (or CHETRF_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 array, dimension (LDAFAC,N)
72 *> Diagonal of the block diagonal matrix D and factors U or L
73 *> as computed by CHETRF_RK and CHETRF_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 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 CHETRF_RK (or CHETRF_BK).
103 *> \endverbatim
104 *>
105 *> \param[out] C
106 *> \verbatim
107 *> C is COMPLEX 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 REAL array, dimension (N)
119 *> \endverbatim
120 *>
121 *> \param[out] RESID
122 *> \verbatim
123 *> RESID is REAL
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 *> \date June 2017
137 *
138 *> \ingroup complex_lin
139 *
140 * =====================================================================
141  SUBROUTINE chet01_3( UPLO, N, A, LDA, AFAC, LDAFAC, E, IPIV, C,
142  \$ LDC, RWORK, RESID )
143 *
144 * -- LAPACK test routine (version 3.7.1) --
145 * -- LAPACK is a software package provided by Univ. of Tennessee, --
146 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
147 * June 2017
148 *
149 * .. Scalar Arguments ..
150  CHARACTER UPLO
151  INTEGER LDA, LDAFAC, LDC, N
152  REAL RESID
153 * ..
154 * .. Array Arguments ..
155  INTEGER IPIV( * )
156  REAL RWORK( * )
157  COMPLEX A( lda, * ), AFAC( ldafac, * ), C( ldc, * ),
158  \$ e( * )
159 * ..
160 *
161 * =====================================================================
162 *
163 * .. Parameters ..
164  REAL ZERO, ONE
165  parameter( zero = 0.0e+0, one = 1.0e+0 )
166  COMPLEX CZERO, CONE
167  parameter( czero = ( 0.0e+0, 0.0e+0 ),
168  \$ cone = ( 1.0e+0, 0.0e+0 ) )
169 * ..
170 * .. Local Scalars ..
171  INTEGER I, INFO, J
172  REAL ANORM, EPS
173 * ..
174 * .. External Functions ..
175  LOGICAL LSAME
176  REAL CLANHE, SLAMCH
177  EXTERNAL lsame, clanhe, slamch
178 * ..
179 * .. External Subroutines ..
180  EXTERNAL claset, clavhe_rook, csyconvf_rook
181 * ..
182 * .. Intrinsic Functions ..
183  INTRINSIC aimag, real
184 * ..
185 * .. Executable Statements ..
186 *
187 * Quick exit if N = 0.
188 *
189  IF( n.LE.0 ) THEN
190  resid = zero
191  RETURN
192  END IF
193 *
194 * a) Revert to multiplyers of L
195 *
196  CALL csyconvf_rook( uplo, 'R', n, afac, ldafac, e, ipiv, info )
197 *
198 * 1) Determine EPS and the norm of A.
199 *
200  eps = slamch( 'Epsilon' )
201  anorm = clanhe( '1', uplo, n, a, lda, rwork )
202 *
203 * Check the imaginary parts of the diagonal elements and return with
204 * an error code if any are nonzero.
205 *
206  DO j = 1, n
207  IF( aimag( afac( j, j ) ).NE.zero ) THEN
208  resid = one / eps
209  RETURN
210  END IF
211  END DO
212 *
213 * 2) Initialize C to the identity matrix.
214 *
215  CALL claset( 'Full', n, n, czero, cone, c, ldc )
216 *
217 * 3) Call CLAVHE_ROOK to form the product D * U' (or D * L' ).
218 *
219  CALL clavhe_rook( uplo, 'Conjugate', 'Non-unit', n, n, afac,
220  \$ ldafac, ipiv, c, ldc, info )
221 *
222 * 4) Call ZLAVHE_RK again to multiply by U (or L ).
223 *
224  CALL clavhe_rook( uplo, 'No transpose', 'Unit', n, n, afac,
225  \$ ldafac, ipiv, c, ldc, info )
226 *
227 * 5) Compute the difference C - A .
228 *
229  IF( lsame( uplo, 'U' ) ) THEN
230  DO j = 1, n
231  DO i = 1, j - 1
232  c( i, j ) = c( i, j ) - a( i, j )
233  END DO
234  c( j, j ) = c( j, j ) - REAL( A( J, J ) )
235  END DO
236  ELSE
237  DO j = 1, n
238  c( j, j ) = c( j, j ) - REAL( A( J, J ) )
239  DO i = j + 1, n
240  c( i, j ) = c( i, j ) - a( i, j )
241  END DO
242  END DO
243  END IF
244 *
245 * 6) Compute norm( C - A ) / ( N * norm(A) * EPS )
246 *
247  resid = clanhe( '1', uplo, n, c, ldc, rwork )
248 *
249  IF( anorm.LE.zero ) THEN
250  IF( resid.NE.zero )
251  \$ resid = one / eps
252  ELSE
253  resid = ( ( resid/REAL( N ) )/anorm ) / eps
254  END IF
255 *
256 * b) Convert to factor of L (or U)
257 *
258  CALL csyconvf_rook( uplo, 'C', n, afac, ldafac, e, ipiv, info )
259 *
260  RETURN
261 *
262 * End of CHET01_3
263 *
264  END
subroutine csyconvf_rook(UPLO, WAY, N, A, LDA, E, IPIV, INFO)
CSYCONVF_ROOK
subroutine claset(UPLO, M, N, ALPHA, BETA, A, LDA)
CLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values...
Definition: claset.f:108
subroutine chet01_3(UPLO, N, A, LDA, AFAC, LDAFAC, E, IPIV, C, LDC, RWORK, RESID)
CHET01_3
Definition: chet01_3.f:143
subroutine clavhe_rook(UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
CLAVHE_ROOK
Definition: clavhe_rook.f:158