LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
dppt01.f
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1 *> \brief \b DPPT01
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 DPPT01( UPLO, N, A, AFAC, RWORK, RESID )
12 *
13 * .. Scalar Arguments ..
14 * CHARACTER UPLO
15 * INTEGER N
16 * DOUBLE PRECISION RESID
17 * ..
18 * .. Array Arguments ..
19 * DOUBLE PRECISION A( * ), AFAC( * ), RWORK( * )
20 * ..
21 *
22 *
23 *> \par Purpose:
24 * =============
25 *>
26 *> \verbatim
27 *>
28 *> DPPT01 reconstructs a symmetric positive definite packed matrix A
29 *> from its L*L' or U'*U factorization and computes the residual
30 *> norm( L*L' - A ) / ( N * norm(A) * EPS ) or
31 *> norm( U'*U - A ) / ( N * norm(A) * EPS ),
32 *> where 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 DOUBLE PRECISION 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,out] AFAC
61 *> \verbatim
62 *> AFAC is DOUBLE PRECISION array, dimension (N*(N+1)/2)
63 *> On entry, the factor L or U from the L*L' or U'*U
64 *> factorization of A, stored as a packed triangular matrix.
65 *> Overwritten with the reconstructed matrix, and then with the
66 *> difference L*L' - A (or U'*U - A).
67 *> \endverbatim
68 *>
69 *> \param[out] RWORK
70 *> \verbatim
71 *> RWORK is DOUBLE PRECISION array, dimension (N)
72 *> \endverbatim
73 *>
74 *> \param[out] RESID
75 *> \verbatim
76 *> RESID is DOUBLE PRECISION
77 *> If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
78 *> If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
79 *> \endverbatim
80 *
81 * Authors:
82 * ========
83 *
84 *> \author Univ. of Tennessee
85 *> \author Univ. of California Berkeley
86 *> \author Univ. of Colorado Denver
87 *> \author NAG Ltd.
88 *
89 *> \date December 2016
90 *
91 *> \ingroup double_lin
92 *
93 * =====================================================================
94  SUBROUTINE dppt01( UPLO, N, A, AFAC, RWORK, RESID )
95 *
96 * -- LAPACK test routine (version 3.7.0) --
97 * -- LAPACK is a software package provided by Univ. of Tennessee, --
98 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
99 * December 2016
100 *
101 * .. Scalar Arguments ..
102  CHARACTER UPLO
103  INTEGER N
104  DOUBLE PRECISION RESID
105 * ..
106 * .. Array Arguments ..
107  DOUBLE PRECISION A( * ), AFAC( * ), RWORK( * )
108 * ..
109 *
110 * =====================================================================
111 *
112 * .. Parameters ..
113  DOUBLE PRECISION ZERO, ONE
114  parameter( zero = 0.0d+0, one = 1.0d+0 )
115 * ..
116 * .. Local Scalars ..
117  INTEGER I, K, KC, NPP
118  DOUBLE PRECISION ANORM, EPS, T
119 * ..
120 * .. External Functions ..
121  LOGICAL LSAME
122  DOUBLE PRECISION DDOT, DLAMCH, DLANSP
123  EXTERNAL lsame, ddot, dlamch, dlansp
124 * ..
125 * .. External Subroutines ..
126  EXTERNAL dscal, dspr, dtpmv
127 * ..
128 * .. Intrinsic Functions ..
129  INTRINSIC dble
130 * ..
131 * .. Executable Statements ..
132 *
133 * Quick exit if N = 0
134 *
135  IF( n.LE.0 ) THEN
136  resid = zero
137  RETURN
138  END IF
139 *
140 * Exit with RESID = 1/EPS if ANORM = 0.
141 *
142  eps = dlamch( 'Epsilon' )
143  anorm = dlansp( '1', uplo, n, a, rwork )
144  IF( anorm.LE.zero ) THEN
145  resid = one / eps
146  RETURN
147  END IF
148 *
149 * Compute the product U'*U, overwriting U.
150 *
151  IF( lsame( uplo, 'U' ) ) THEN
152  kc = ( n*( n-1 ) ) / 2 + 1
153  DO 10 k = n, 1, -1
154 *
155 * Compute the (K,K) element of the result.
156 *
157  t = ddot( k, afac( kc ), 1, afac( kc ), 1 )
158  afac( kc+k-1 ) = t
159 *
160 * Compute the rest of column K.
161 *
162  IF( k.GT.1 ) THEN
163  CALL dtpmv( 'Upper', 'Transpose', 'Non-unit', k-1, afac,
164  $ afac( kc ), 1 )
165  kc = kc - ( k-1 )
166  END IF
167  10 CONTINUE
168 *
169 * Compute the product L*L', overwriting L.
170 *
171  ELSE
172  kc = ( n*( n+1 ) ) / 2
173  DO 20 k = n, 1, -1
174 *
175 * Add a multiple of column K of the factor L to each of
176 * columns K+1 through N.
177 *
178  IF( k.LT.n )
179  $ CALL dspr( 'Lower', n-k, one, afac( kc+1 ), 1,
180  $ afac( kc+n-k+1 ) )
181 *
182 * Scale column K by the diagonal element.
183 *
184  t = afac( kc )
185  CALL dscal( n-k+1, t, afac( kc ), 1 )
186 *
187  kc = kc - ( n-k+2 )
188  20 CONTINUE
189  END IF
190 *
191 * Compute the difference L*L' - A (or U'*U - A).
192 *
193  npp = n*( n+1 ) / 2
194  DO 30 i = 1, npp
195  afac( i ) = afac( i ) - a( i )
196  30 CONTINUE
197 *
198 * Compute norm( L*U - A ) / ( N * norm(A) * EPS )
199 *
200  resid = dlansp( '1', uplo, n, afac, rwork )
201 *
202  resid = ( ( resid / dble( n ) ) / anorm ) / eps
203 *
204  RETURN
205 *
206 * End of DPPT01
207 *
208  END
subroutine dscal(N, DA, DX, INCX)
DSCAL
Definition: dscal.f:81
subroutine dspr(UPLO, N, ALPHA, X, INCX, AP)
DSPR
Definition: dspr.f:129
subroutine dppt01(UPLO, N, A, AFAC, RWORK, RESID)
DPPT01
Definition: dppt01.f:95
subroutine dtpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
DTPMV
Definition: dtpmv.f:144