LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
cspt01.f
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1 *> \brief \b CSPT01
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 CSPT01( 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 *> CSPT01 reconstructs a symmetric indefinite packed matrix A from its
31 *> diagonal pivoting factorization A = U*D*U' or A = L*D*L' and computes
32 *> the residual
33 *> norm( C - A ) / ( N * norm(A) * EPS ),
34 *> where C is the reconstructed matrix and EPS is the machine epsilon.
35 *> \endverbatim
36 *
37 * Arguments:
38 * ==========
39 *
40 *> \param[in] UPLO
41 *> \verbatim
42 *> UPLO is CHARACTER*1
43 *> Specifies whether the upper or lower triangular part of the
44 *> Hermitian matrix A is stored:
45 *> = 'U': Upper triangular
46 *> = 'L': Lower triangular
47 *> \endverbatim
48 *>
49 *> \param[in] N
50 *> \verbatim
51 *> N is INTEGER
52 *> The order of the matrix A. N >= 0.
53 *> \endverbatim
54 *>
55 *> \param[in] A
56 *> \verbatim
57 *> A is COMPLEX array, dimension (N*(N+1)/2)
58 *> The original symmetric matrix A, stored as a packed
59 *> triangular matrix.
60 *> \endverbatim
61 *>
62 *> \param[in] AFAC
63 *> \verbatim
64 *> AFAC is COMPLEX array, dimension (N*(N+1)/2)
65 *> The factored form of the matrix A, stored as a packed
66 *> triangular matrix. AFAC contains the block diagonal matrix D
67 *> and the multipliers used to obtain the factor L or U from the
68 *> L*D*L' or U*D*U' factorization as computed by CSPTRF.
69 *> \endverbatim
70 *>
71 *> \param[in] IPIV
72 *> \verbatim
73 *> IPIV is INTEGER array, dimension (N)
74 *> The pivot indices from CSPTRF.
75 *> \endverbatim
76 *>
77 *> \param[out] C
78 *> \verbatim
79 *> C is COMPLEX array, dimension (LDC,N)
80 *> \endverbatim
81 *>
82 *> \param[in] LDC
83 *> \verbatim
84 *> LDC is INTEGER
85 *> The leading dimension of the array C. LDC >= max(1,N).
86 *> \endverbatim
87 *>
88 *> \param[out] RWORK
89 *> \verbatim
90 *> RWORK is REAL array, dimension (N)
91 *> \endverbatim
92 *>
93 *> \param[out] RESID
94 *> \verbatim
95 *> RESID is REAL
96 *> If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
97 *> If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )
98 *> \endverbatim
99 *
100 * Authors:
101 * ========
102 *
103 *> \author Univ. of Tennessee
104 *> \author Univ. of California Berkeley
105 *> \author Univ. of Colorado Denver
106 *> \author NAG Ltd.
107 *
108 *> \ingroup complex_lin
109 *
110 * =====================================================================
111  SUBROUTINE cspt01( UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID )
112 *
113 * -- LAPACK test routine --
114 * -- LAPACK is a software package provided by Univ. of Tennessee, --
115 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
116 *
117 * .. Scalar Arguments ..
118  CHARACTER UPLO
119  INTEGER LDC, N
120  REAL RESID
121 * ..
122 * .. Array Arguments ..
123  INTEGER IPIV( * )
124  REAL RWORK( * )
125  COMPLEX A( * ), AFAC( * ), C( LDC, * )
126 * ..
127 *
128 * =====================================================================
129 *
130 * .. Parameters ..
131  REAL ZERO, ONE
132  parameter( zero = 0.0e+0, one = 1.0e+0 )
133  COMPLEX CZERO, CONE
134  parameter( czero = ( 0.0e+0, 0.0e+0 ),
135  $ cone = ( 1.0e+0, 0.0e+0 ) )
136 * ..
137 * .. Local Scalars ..
138  INTEGER I, INFO, J, JC
139  REAL ANORM, EPS
140 * ..
141 * .. External Functions ..
142  LOGICAL LSAME
143  REAL CLANSP, CLANSY, SLAMCH
144  EXTERNAL lsame, clansp, clansy, slamch
145 * ..
146 * .. External Subroutines ..
147  EXTERNAL clavsp, claset
148 * ..
149 * .. Intrinsic Functions ..
150  INTRINSIC real
151 * ..
152 * .. Executable Statements ..
153 *
154 * Quick exit if N = 0.
155 *
156  IF( n.LE.0 ) THEN
157  resid = zero
158  RETURN
159  END IF
160 *
161 * Determine EPS and the norm of A.
162 *
163  eps = slamch( 'Epsilon' )
164  anorm = clansp( '1', uplo, n, a, rwork )
165 *
166 * Initialize C to the identity matrix.
167 *
168  CALL claset( 'Full', n, n, czero, cone, c, ldc )
169 *
170 * Call CLAVSP to form the product D * U' (or D * L' ).
171 *
172  CALL clavsp( uplo, 'Transpose', 'Non-unit', n, n, afac, ipiv, c,
173  $ ldc, info )
174 *
175 * Call CLAVSP again to multiply by U ( or L ).
176 *
177  CALL clavsp( uplo, 'No transpose', 'Unit', n, n, afac, ipiv, c,
178  $ ldc, info )
179 *
180 * Compute the difference C - A .
181 *
182  IF( lsame( uplo, 'U' ) ) THEN
183  jc = 0
184  DO 20 j = 1, n
185  DO 10 i = 1, j
186  c( i, j ) = c( i, j ) - a( jc+i )
187  10 CONTINUE
188  jc = jc + j
189  20 CONTINUE
190  ELSE
191  jc = 1
192  DO 40 j = 1, n
193  DO 30 i = j, n
194  c( i, j ) = c( i, j ) - a( jc+i-j )
195  30 CONTINUE
196  jc = jc + n - j + 1
197  40 CONTINUE
198  END IF
199 *
200 * Compute norm( C - A ) / ( N * norm(A) * EPS )
201 *
202  resid = clansy( '1', uplo, n, c, ldc, rwork )
203 *
204  IF( anorm.LE.zero ) THEN
205  IF( resid.NE.zero )
206  $ resid = one / eps
207  ELSE
208  resid = ( ( resid/real( n ) )/anorm ) / eps
209  END IF
210 *
211  RETURN
212 *
213 * End of CSPT01
214 *
215  END
subroutine cspt01(UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID)
CSPT01
Definition: cspt01.f:112
subroutine clavsp(UPLO, TRANS, DIAG, N, NRHS, A, IPIV, B, LDB, INFO)
CLAVSP
Definition: clavsp.f:131
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