LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
zspt01.f
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1 *> \brief \b ZSPT01
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 ZSPT01( UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID )
12 *
13 * .. Scalar Arguments ..
14 * CHARACTER UPLO
15 * INTEGER LDC, N
16 * DOUBLE PRECISION RESID
17 * ..
18 * .. Array Arguments ..
19 * INTEGER IPIV( * )
20 * DOUBLE PRECISION RWORK( * )
21 * COMPLEX*16 A( * ), AFAC( * ), C( LDC, * )
22 * ..
23 *
24 *
25 *> \par Purpose:
26 * =============
27 *>
28 *> \verbatim
29 *>
30 *> ZSPT01 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*16 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*16 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 ZSPTRF.
69 *> \endverbatim
70 *>
71 *> \param[in] IPIV
72 *> \verbatim
73 *> IPIV is INTEGER array, dimension (N)
74 *> The pivot indices from ZSPTRF.
75 *> \endverbatim
76 *>
77 *> \param[out] C
78 *> \verbatim
79 *> C is COMPLEX*16 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 DOUBLE PRECISION array, dimension (N)
91 *> \endverbatim
92 *>
93 *> \param[out] RESID
94 *> \verbatim
95 *> RESID is DOUBLE PRECISION
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 *> \date December 2016
109 *
110 *> \ingroup complex16_lin
111 *
112 * =====================================================================
113  SUBROUTINE zspt01( UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID )
114 *
115 * -- LAPACK test routine (version 3.7.0) --
116 * -- LAPACK is a software package provided by Univ. of Tennessee, --
117 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
118 * December 2016
119 *
120 * .. Scalar Arguments ..
121  CHARACTER UPLO
122  INTEGER LDC, N
123  DOUBLE PRECISION RESID
124 * ..
125 * .. Array Arguments ..
126  INTEGER IPIV( * )
127  DOUBLE PRECISION RWORK( * )
128  COMPLEX*16 A( * ), AFAC( * ), C( ldc, * )
129 * ..
130 *
131 * =====================================================================
132 *
133 * .. Parameters ..
134  DOUBLE PRECISION ZERO, ONE
135  parameter( zero = 0.0d+0, one = 1.0d+0 )
136  COMPLEX*16 CZERO, CONE
137  parameter( czero = ( 0.0d+0, 0.0d+0 ),
138  $ cone = ( 1.0d+0, 0.0d+0 ) )
139 * ..
140 * .. Local Scalars ..
141  INTEGER I, INFO, J, JC
142  DOUBLE PRECISION ANORM, EPS
143 * ..
144 * .. External Functions ..
145  LOGICAL LSAME
146  DOUBLE PRECISION DLAMCH, ZLANSP, ZLANSY
147  EXTERNAL lsame, dlamch, zlansp, zlansy
148 * ..
149 * .. External Subroutines ..
150  EXTERNAL zlaset, zlavsp
151 * ..
152 * .. Intrinsic Functions ..
153  INTRINSIC dble
154 * ..
155 * .. Executable Statements ..
156 *
157 * Quick exit if N = 0.
158 *
159  IF( n.LE.0 ) THEN
160  resid = zero
161  RETURN
162  END IF
163 *
164 * Determine EPS and the norm of A.
165 *
166  eps = dlamch( 'Epsilon' )
167  anorm = zlansp( '1', uplo, n, a, rwork )
168 *
169 * Initialize C to the identity matrix.
170 *
171  CALL zlaset( 'Full', n, n, czero, cone, c, ldc )
172 *
173 * Call ZLAVSP to form the product D * U' (or D * L' ).
174 *
175  CALL zlavsp( uplo, 'Transpose', 'Non-unit', n, n, afac, ipiv, c,
176  $ ldc, info )
177 *
178 * Call ZLAVSP again to multiply by U ( or L ).
179 *
180  CALL zlavsp( uplo, 'No transpose', 'Unit', n, n, afac, ipiv, c,
181  $ ldc, info )
182 *
183 * Compute the difference C - A .
184 *
185  IF( lsame( uplo, 'U' ) ) THEN
186  jc = 0
187  DO 20 j = 1, n
188  DO 10 i = 1, j
189  c( i, j ) = c( i, j ) - a( jc+i )
190  10 CONTINUE
191  jc = jc + j
192  20 CONTINUE
193  ELSE
194  jc = 1
195  DO 40 j = 1, n
196  DO 30 i = j, n
197  c( i, j ) = c( i, j ) - a( jc+i-j )
198  30 CONTINUE
199  jc = jc + n - j + 1
200  40 CONTINUE
201  END IF
202 *
203 * Compute norm( C - A ) / ( N * norm(A) * EPS )
204 *
205  resid = zlansy( '1', uplo, n, c, ldc, rwork )
206 *
207  IF( anorm.LE.zero ) THEN
208  IF( resid.NE.zero )
209  $ resid = one / eps
210  ELSE
211  resid = ( ( resid / dble( n ) ) / anorm ) / eps
212  END IF
213 *
214  RETURN
215 *
216 * End of ZSPT01
217 *
218  END
subroutine zlavsp(UPLO, TRANS, DIAG, N, NRHS, A, IPIV, B, LDB, INFO)
ZLAVSP
Definition: zlavsp.f:133
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:108
subroutine zspt01(UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID)
ZSPT01
Definition: zspt01.f:114