LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
chet01_rook.f
Go to the documentation of this file.
1 *> \brief \b CHET01_ROOK
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_ROOK( 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 * REAL RESID
18 * ..
19 * .. Array Arguments ..
20 * INTEGER IPIV( * )
21 * REAL RWORK( * )
22 * COMPLEX A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * )
23 * ..
24 *
25 *
26 *> \par Purpose:
27 * =============
28 *>
29 *> \verbatim
30 *>
31 *> CHET01_ROOK reconstructs a complex Hermitian 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, EPS is the machine epsilon,
35 *> L' is the transpose of L, and U' is the transpose of U.
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 *> complex Hermitian 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 COMPLEX array, dimension (LDA,N)
59 *> The original complex Hermitian 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 COMPLEX array, dimension (LDAFAC,N)
71 *> The factored form of the matrix A. AFAC contains the block
72 *> diagonal matrix D and the multipliers used to obtain the
73 *> factor L or U from the block L*D*L' or U*D*U' factorization
74 *> as computed by CSYTRF_ROOK.
75 *> \endverbatim
76 *>
77 *> \param[in] LDAFAC
78 *> \verbatim
79 *> LDAFAC is INTEGER
80 *> The leading dimension of the array AFAC. LDAFAC >= max(1,N).
81 *> \endverbatim
82 *>
83 *> \param[in] IPIV
84 *> \verbatim
85 *> IPIV is INTEGER array, dimension (N)
86 *> The pivot indices from CSYTRF_ROOK.
87 *> \endverbatim
88 *>
89 *> \param[out] C
90 *> \verbatim
91 *> C is COMPLEX array, dimension (LDC,N)
92 *> \endverbatim
93 *>
94 *> \param[in] LDC
95 *> \verbatim
96 *> LDC is INTEGER
97 *> The leading dimension of the array C. LDC >= max(1,N).
98 *> \endverbatim
99 *>
100 *> \param[out] RWORK
101 *> \verbatim
102 *> RWORK is REAL array, dimension (N)
103 *> \endverbatim
104 *>
105 *> \param[out] RESID
106 *> \verbatim
107 *> RESID is REAL
108 *> If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
109 *> If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )
110 *> \endverbatim
111 *
112 * Authors:
113 * ========
114 *
115 *> \author Univ. of Tennessee
116 *> \author Univ. of California Berkeley
117 *> \author Univ. of Colorado Denver
118 *> \author NAG Ltd.
119 *
120 *> \ingroup complex_lin
121 *
122 * =====================================================================
123  SUBROUTINE chet01_rook( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C,
124  $ LDC, RWORK, RESID )
125 *
126 * -- LAPACK test routine --
127 * -- LAPACK is a software package provided by Univ. of Tennessee, --
128 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
129 *
130 * .. Scalar Arguments ..
131  CHARACTER UPLO
132  INTEGER LDA, LDAFAC, LDC, N
133  REAL RESID
134 * ..
135 * .. Array Arguments ..
136  INTEGER IPIV( * )
137  REAL RWORK( * )
138  COMPLEX A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * )
139 * ..
140 *
141 * =====================================================================
142 *
143 * .. Parameters ..
144  REAL ZERO, ONE
145  parameter( zero = 0.0e+0, one = 1.0e+0 )
146  COMPLEX CZERO, CONE
147  parameter( czero = ( 0.0e+0, 0.0e+0 ),
148  $ cone = ( 1.0e+0, 0.0e+0 ) )
149 * ..
150 * .. Local Scalars ..
151  INTEGER I, INFO, J
152  REAL ANORM, EPS
153 * ..
154 * .. External Functions ..
155  LOGICAL LSAME
156  REAL CLANHE, SLAMCH
157  EXTERNAL lsame, clanhe, slamch
158 * ..
159 * .. External Subroutines ..
160  EXTERNAL claset, clavhe_rook
161 * ..
162 * .. Intrinsic Functions ..
163  INTRINSIC aimag, real
164 * ..
165 * .. Executable Statements ..
166 *
167 * Quick exit if N = 0.
168 *
169  IF( n.LE.0 ) THEN
170  resid = zero
171  RETURN
172  END IF
173 *
174 * Determine EPS and the norm of A.
175 *
176  eps = slamch( 'Epsilon' )
177  anorm = clanhe( '1', uplo, n, a, lda, rwork )
178 *
179 * Check the imaginary parts of the diagonal elements and return with
180 * an error code if any are nonzero.
181 *
182  DO 10 j = 1, n
183  IF( aimag( afac( j, j ) ).NE.zero ) THEN
184  resid = one / eps
185  RETURN
186  END IF
187  10 CONTINUE
188 *
189 * Initialize C to the identity matrix.
190 *
191  CALL claset( 'Full', n, n, czero, cone, c, ldc )
192 *
193 * Call CLAVHE_ROOK to form the product D * U' (or D * L' ).
194 *
195  CALL clavhe_rook( uplo, 'Conjugate', 'Non-unit', n, n, afac,
196  $ ldafac, ipiv, c, ldc, info )
197 *
198 * Call CLAVHE_ROOK again to multiply by U (or L ).
199 *
200  CALL clavhe_rook( uplo, 'No transpose', 'Unit', n, n, afac,
201  $ ldafac, ipiv, c, ldc, info )
202 *
203 * Compute the difference C - A .
204 *
205  IF( lsame( uplo, 'U' ) ) THEN
206  DO 30 j = 1, n
207  DO 20 i = 1, j - 1
208  c( i, j ) = c( i, j ) - a( i, j )
209  20 CONTINUE
210  c( j, j ) = c( j, j ) - real( a( j, j ) )
211  30 CONTINUE
212  ELSE
213  DO 50 j = 1, n
214  c( j, j ) = c( j, j ) - real( a( j, j ) )
215  DO 40 i = j + 1, n
216  c( i, j ) = c( i, j ) - a( i, j )
217  40 CONTINUE
218  50 CONTINUE
219  END IF
220 *
221 * Compute norm( C - A ) / ( N * norm(A) * EPS )
222 *
223  resid = clanhe( '1', uplo, n, c, ldc, rwork )
224 *
225  IF( anorm.LE.zero ) THEN
226  IF( resid.NE.zero )
227  $ resid = one / eps
228  ELSE
229  resid = ( ( resid/real( n ) )/anorm ) / eps
230  END IF
231 *
232  RETURN
233 *
234 * End of CHET01_ROOK
235 *
236  END
subroutine chet01_rook(UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC, RWORK, RESID)
CHET01_ROOK
Definition: chet01_rook.f:125
subroutine clavhe_rook(UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
CLAVHE_ROOK
Definition: clavhe_rook.f:156
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:106