LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
chpt01.f
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1 *> \brief \b CHPT01
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 CHPT01( UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID )
12 *
13 * .. Scalar Arguments ..
14 * CHARACTER UPLO
15 * INTEGER LDC, N
16 * REAL RESID
17 * ..
18 * .. Array Arguments ..
19 * INTEGER IPIV( * )
20 * REAL RWORK( * )
21 * COMPLEX A( * ), AFAC( * ), C( LDC, * )
22 * ..
23 *
24 *
25 *> \par Purpose:
26 * =============
27 *>
28 *> \verbatim
29 *>
30 *> CHPT01 reconstructs a Hermitian indefinite packed matrix A from its
31 *> block L*D*L' or U*D*U' factorization and computes the residual
32 *> norm( C - A ) / ( N * norm(A) * EPS ),
33 *> where C is the reconstructed matrix, EPS is the machine epsilon,
34 *> L' is the conjugate transpose of L, and U' is the conjugate transpose
35 *> 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 *> 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 (N*(N+1)/2)
59 *> The original Hermitian matrix A, stored as a packed
60 *> triangular matrix.
61 *> \endverbatim
62 *>
63 *> \param[in] AFAC
64 *> \verbatim
65 *> AFAC is COMPLEX array, dimension (N*(N+1)/2)
66 *> The factored form of the matrix A, stored as a packed
67 *> triangular matrix. AFAC contains the block diagonal matrix D
68 *> and the multipliers used to obtain the factor L or U from the
69 *> block L*D*L' or U*D*U' factorization as computed by CHPTRF.
70 *> \endverbatim
71 *>
72 *> \param[in] IPIV
73 *> \verbatim
74 *> IPIV is INTEGER array, dimension (N)
75 *> The pivot indices from CHPTRF.
76 *> \endverbatim
77 *>
78 *> \param[out] C
79 *> \verbatim
80 *> C is COMPLEX array, dimension (LDC,N)
81 *> \endverbatim
82 *>
83 *> \param[in] LDC
84 *> \verbatim
85 *> LDC is INTEGER
86 *> The leading dimension of the array C. LDC >= max(1,N).
87 *> \endverbatim
88 *>
89 *> \param[out] RWORK
90 *> \verbatim
91 *> RWORK is REAL array, dimension (N)
92 *> \endverbatim
93 *>
94 *> \param[out] RESID
95 *> \verbatim
96 *> RESID is REAL
97 *> If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
98 *> If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )
99 *> \endverbatim
100 *
101 * Authors:
102 * ========
103 *
104 *> \author Univ. of Tennessee
105 *> \author Univ. of California Berkeley
106 *> \author Univ. of Colorado Denver
107 *> \author NAG Ltd.
108 *
109 *> \ingroup complex_lin
110 *
111 * =====================================================================
112  SUBROUTINE chpt01( UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID )
113 *
114 * -- LAPACK test routine --
115 * -- LAPACK is a software package provided by Univ. of Tennessee, --
116 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
117 *
118 * .. Scalar Arguments ..
119  CHARACTER UPLO
120  INTEGER LDC, N
121  REAL RESID
122 * ..
123 * .. Array Arguments ..
124  INTEGER IPIV( * )
125  REAL RWORK( * )
126  COMPLEX A( * ), AFAC( * ), C( LDC, * )
127 * ..
128 *
129 * =====================================================================
130 *
131 * .. Parameters ..
132  REAL ZERO, ONE
133  parameter( zero = 0.0e+0, one = 1.0e+0 )
134  COMPLEX CZERO, CONE
135  parameter( czero = ( 0.0e+0, 0.0e+0 ),
136  $ cone = ( 1.0e+0, 0.0e+0 ) )
137 * ..
138 * .. Local Scalars ..
139  INTEGER I, INFO, J, JC
140  REAL ANORM, EPS
141 * ..
142 * .. External Functions ..
143  LOGICAL LSAME
144  REAL CLANHE, CLANHP, SLAMCH
145  EXTERNAL lsame, clanhe, clanhp, slamch
146 * ..
147 * .. External Subroutines ..
148  EXTERNAL clavhp, claset
149 * ..
150 * .. Intrinsic Functions ..
151  INTRINSIC aimag, real
152 * ..
153 * .. Executable Statements ..
154 *
155 * Quick exit if N = 0.
156 *
157  IF( n.LE.0 ) THEN
158  resid = zero
159  RETURN
160  END IF
161 *
162 * Determine EPS and the norm of A.
163 *
164  eps = slamch( 'Epsilon' )
165  anorm = clanhp( '1', uplo, n, a, rwork )
166 *
167 * Check the imaginary parts of the diagonal elements and return with
168 * an error code if any are nonzero.
169 *
170  jc = 1
171  IF( lsame( uplo, 'U' ) ) THEN
172  DO 10 j = 1, n
173  IF( aimag( afac( jc ) ).NE.zero ) THEN
174  resid = one / eps
175  RETURN
176  END IF
177  jc = jc + j + 1
178  10 CONTINUE
179  ELSE
180  DO 20 j = 1, n
181  IF( aimag( afac( jc ) ).NE.zero ) THEN
182  resid = one / eps
183  RETURN
184  END IF
185  jc = jc + n - j + 1
186  20 CONTINUE
187  END IF
188 *
189 * Initialize C to the identity matrix.
190 *
191  CALL claset( 'Full', n, n, czero, cone, c, ldc )
192 *
193 * Call CLAVHP to form the product D * U' (or D * L' ).
194 *
195  CALL clavhp( uplo, 'Conjugate', 'Non-unit', n, n, afac, ipiv, c,
196  $ ldc, info )
197 *
198 * Call CLAVHP again to multiply by U ( or L ).
199 *
200  CALL clavhp( uplo, 'No transpose', 'Unit', n, n, afac, ipiv, c,
201  $ ldc, info )
202 *
203 * Compute the difference C - A .
204 *
205  IF( lsame( uplo, 'U' ) ) THEN
206  jc = 0
207  DO 40 j = 1, n
208  DO 30 i = 1, j - 1
209  c( i, j ) = c( i, j ) - a( jc+i )
210  30 CONTINUE
211  c( j, j ) = c( j, j ) - real( a( jc+j ) )
212  jc = jc + j
213  40 CONTINUE
214  ELSE
215  jc = 1
216  DO 60 j = 1, n
217  c( j, j ) = c( j, j ) - real( a( jc ) )
218  DO 50 i = j + 1, n
219  c( i, j ) = c( i, j ) - a( jc+i-j )
220  50 CONTINUE
221  jc = jc + n - j + 1
222  60 CONTINUE
223  END IF
224 *
225 * Compute norm( C - A ) / ( N * norm(A) * EPS )
226 *
227  resid = clanhe( '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  RETURN
237 *
238 * End of CHPT01
239 *
240  END
subroutine clavhp(UPLO, TRANS, DIAG, N, NRHS, A, IPIV, B, LDB, INFO)
CLAVHP
Definition: clavhp.f:131
subroutine chpt01(UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID)
CHPT01
Definition: chpt01.f:113
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