LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
sspt01.f
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1 *> \brief \b SSPT01
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 SSPT01( 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 A( * ), AFAC( * ), C( LDC, * ), RWORK( * )
21 * ..
22 *
23 *
24 *> \par Purpose:
25 * =============
26 *>
27 *> \verbatim
28 *>
29 *> SSPT01 reconstructs a symmetric indefinite packed matrix A from its
30 *> block L*D*L' or U*D*U' factorization and computes the residual
31 *> norm( C - A ) / ( N * norm(A) * EPS ),
32 *> where C is the reconstructed matrix and EPS is the machine epsilon.
33 *> \endverbatim
34 *
35 * Arguments:
36 * ==========
37 *
38 *> \param[in] UPLO
39 *> \verbatim
40 *> UPLO is CHARACTER*1
41 *> Specifies whether the upper or lower triangular part of the
42 *> symmetric matrix A is stored:
43 *> = 'U': Upper triangular
44 *> = 'L': Lower triangular
45 *> \endverbatim
46 *>
47 *> \param[in] N
48 *> \verbatim
49 *> N is INTEGER
50 *> The number of rows and columns of the matrix A. N >= 0.
51 *> \endverbatim
52 *>
53 *> \param[in] A
54 *> \verbatim
55 *> A is REAL array, dimension (N*(N+1)/2)
56 *> The original symmetric matrix A, stored as a packed
57 *> triangular matrix.
58 *> \endverbatim
59 *>
60 *> \param[in] AFAC
61 *> \verbatim
62 *> AFAC is REAL array, dimension (N*(N+1)/2)
63 *> The factored form of the matrix A, stored as a packed
64 *> triangular matrix. AFAC contains the block diagonal matrix D
65 *> and the multipliers used to obtain the factor L or U from the
66 *> block L*D*L' or U*D*U' factorization as computed by SSPTRF.
67 *> \endverbatim
68 *>
69 *> \param[in] IPIV
70 *> \verbatim
71 *> IPIV is INTEGER array, dimension (N)
72 *> The pivot indices from SSPTRF.
73 *> \endverbatim
74 *>
75 *> \param[out] C
76 *> \verbatim
77 *> C is REAL array, dimension (LDC,N)
78 *> \endverbatim
79 *>
80 *> \param[in] LDC
81 *> \verbatim
82 *> LDC is INTEGER
83 *> The leading dimension of the array C. LDC >= max(1,N).
84 *> \endverbatim
85 *>
86 *> \param[out] RWORK
87 *> \verbatim
88 *> RWORK is REAL array, dimension (N)
89 *> \endverbatim
90 *>
91 *> \param[out] RESID
92 *> \verbatim
93 *> RESID is REAL
94 *> If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
95 *> If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )
96 *> \endverbatim
97 *
98 * Authors:
99 * ========
100 *
101 *> \author Univ. of Tennessee
102 *> \author Univ. of California Berkeley
103 *> \author Univ. of Colorado Denver
104 *> \author NAG Ltd.
105 *
106 *> \date December 2016
107 *
108 *> \ingroup single_lin
109 *
110 * =====================================================================
111  SUBROUTINE sspt01( UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID )
112 *
113 * -- LAPACK test routine (version 3.7.0) --
114 * -- LAPACK is a software package provided by Univ. of Tennessee, --
115 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
116 * December 2016
117 *
118 * .. Scalar Arguments ..
119  CHARACTER UPLO
120  INTEGER LDC, N
121  REAL RESID
122 * ..
123 * .. Array Arguments ..
124  INTEGER IPIV( * )
125  REAL A( * ), AFAC( * ), C( ldc, * ), RWORK( * )
126 * ..
127 *
128 * =====================================================================
129 *
130 * .. Parameters ..
131  REAL ZERO, ONE
132  parameter( zero = 0.0e+0, one = 1.0e+0 )
133 * ..
134 * .. Local Scalars ..
135  INTEGER I, INFO, J, JC
136  REAL ANORM, EPS
137 * ..
138 * .. External Functions ..
139  LOGICAL LSAME
140  REAL SLAMCH, SLANSP, SLANSY
141  EXTERNAL lsame, slamch, slansp, slansy
142 * ..
143 * .. External Subroutines ..
144  EXTERNAL slavsp, slaset
145 * ..
146 * .. Intrinsic Functions ..
147  INTRINSIC real
148 * ..
149 * .. Executable Statements ..
150 *
151 * Quick exit if N = 0.
152 *
153  IF( n.LE.0 ) THEN
154  resid = zero
155  RETURN
156  END IF
157 *
158 * Determine EPS and the norm of A.
159 *
160  eps = slamch( 'Epsilon' )
161  anorm = slansp( '1', uplo, n, a, rwork )
162 *
163 * Initialize C to the identity matrix.
164 *
165  CALL slaset( 'Full', n, n, zero, one, c, ldc )
166 *
167 * Call SLAVSP to form the product D * U' (or D * L' ).
168 *
169  CALL slavsp( uplo, 'Transpose', 'Non-unit', n, n, afac, ipiv, c,
170  $ ldc, info )
171 *
172 * Call SLAVSP again to multiply by U ( or L ).
173 *
174  CALL slavsp( uplo, 'No transpose', 'Unit', n, n, afac, ipiv, c,
175  $ ldc, info )
176 *
177 * Compute the difference C - A .
178 *
179  IF( lsame( uplo, 'U' ) ) THEN
180  jc = 0
181  DO 20 j = 1, n
182  DO 10 i = 1, j
183  c( i, j ) = c( i, j ) - a( jc+i )
184  10 CONTINUE
185  jc = jc + j
186  20 CONTINUE
187  ELSE
188  jc = 1
189  DO 40 j = 1, n
190  DO 30 i = j, n
191  c( i, j ) = c( i, j ) - a( jc+i-j )
192  30 CONTINUE
193  jc = jc + n - j + 1
194  40 CONTINUE
195  END IF
196 *
197 * Compute norm( C - A ) / ( N * norm(A) * EPS )
198 *
199  resid = slansy( '1', uplo, n, c, ldc, rwork )
200 *
201  IF( anorm.LE.zero ) THEN
202  IF( resid.NE.zero )
203  $ resid = one / eps
204  ELSE
205  resid = ( ( resid / REAL( N ) ) / anorm ) / eps
206  END IF
207 *
208  RETURN
209 *
210 * End of SSPT01
211 *
212  END
subroutine slavsp(UPLO, TRANS, DIAG, N, NRHS, A, IPIV, B, LDB, INFO)
SLAVSP
Definition: slavsp.f:132
subroutine slaset(UPLO, M, N, ALPHA, BETA, A, LDA)
SLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values...
Definition: slaset.f:112
subroutine sspt01(UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID)
SSPT01
Definition: sspt01.f:112