LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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dpot01.f
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1*> \brief \b DPOT01
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 DPOT01( UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID )
12*
13* .. Scalar Arguments ..
14* CHARACTER UPLO
15* INTEGER LDA, LDAFAC, N
16* DOUBLE PRECISION RESID
17* ..
18* .. Array Arguments ..
19* DOUBLE PRECISION A( LDA, * ), AFAC( LDAFAC, * ), RWORK( * )
20* ..
21*
22*
23*> \par Purpose:
24* =============
25*>
26*> \verbatim
27*>
28*> DPOT01 reconstructs a symmetric positive definite matrix A from
29*> 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 (LDA,N)
56*> The original symmetric matrix A.
57*> \endverbatim
58*>
59*> \param[in] LDA
60*> \verbatim
61*> LDA is INTEGER
62*> The leading dimension of the array A. LDA >= max(1,N)
63*> \endverbatim
64*>
65*> \param[in,out] AFAC
66*> \verbatim
67*> AFAC is DOUBLE PRECISION array, dimension (LDAFAC,N)
68*> On entry, the factor L or U from the L * L**T or U**T * U
69*> factorization of A.
70*> Overwritten with the reconstructed matrix, and then with
71*> the difference L * L**T - A (or U**T * U - A).
72*> \endverbatim
73*>
74*> \param[in] LDAFAC
75*> \verbatim
76*> LDAFAC is INTEGER
77*> The leading dimension of the array AFAC. LDAFAC >= max(1,N).
78*> \endverbatim
79*>
80*> \param[out] RWORK
81*> \verbatim
82*> RWORK is DOUBLE PRECISION array, dimension (N)
83*> \endverbatim
84*>
85*> \param[out] RESID
86*> \verbatim
87*> RESID is DOUBLE PRECISION
88*> If UPLO = 'L', norm(L * L**T - A) / ( N * norm(A) * EPS )
89*> If UPLO = 'U', norm(U**T * U - A) / ( N * norm(A) * EPS )
90*> \endverbatim
91*
92* Authors:
93* ========
94*
95*> \author Univ. of Tennessee
96*> \author Univ. of California Berkeley
97*> \author Univ. of Colorado Denver
98*> \author NAG Ltd.
99*
100*> \ingroup double_lin
101*
102* =====================================================================
103 SUBROUTINE dpot01( UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID )
104*
105* -- LAPACK test routine --
106* -- LAPACK is a software package provided by Univ. of Tennessee, --
107* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
108*
109* .. Scalar Arguments ..
110 CHARACTER UPLO
111 INTEGER LDA, LDAFAC, N
112 DOUBLE PRECISION RESID
113* ..
114* .. Array Arguments ..
115 DOUBLE PRECISION A( LDA, * ), AFAC( LDAFAC, * ), RWORK( * )
116* ..
117*
118* =====================================================================
119*
120* .. Parameters ..
121 DOUBLE PRECISION ZERO, ONE
122 parameter( zero = 0.0d+0, one = 1.0d+0 )
123* ..
124* .. Local Scalars ..
125 INTEGER I, J, K
126 DOUBLE PRECISION ANORM, EPS, T
127* ..
128* .. External Functions ..
129 LOGICAL LSAME
130 DOUBLE PRECISION DDOT, DLAMCH, DLANSY
131 EXTERNAL lsame, ddot, dlamch, dlansy
132* ..
133* .. External Subroutines ..
134 EXTERNAL dscal, dsyr, dtrmv
135* ..
136* .. Intrinsic Functions ..
137 INTRINSIC dble
138* ..
139* .. Executable Statements ..
140*
141* Quick exit if N = 0.
142*
143 IF( n.LE.0 ) THEN
144 resid = zero
145 RETURN
146 END IF
147*
148* Exit with RESID = 1/EPS if ANORM = 0.
149*
150 eps = dlamch( 'Epsilon' )
151 anorm = dlansy( '1', uplo, n, a, lda, rwork )
152 IF( anorm.LE.zero ) THEN
153 resid = one / eps
154 RETURN
155 END IF
156*
157* Compute the product U**T * U, overwriting U.
158*
159 IF( lsame( uplo, 'U' ) ) THEN
160 DO 10 k = n, 1, -1
161*
162* Compute the (K,K) element of the result.
163*
164 t = ddot( k, afac( 1, k ), 1, afac( 1, k ), 1 )
165 afac( k, k ) = t
166*
167* Compute the rest of column K.
168*
169 CALL dtrmv( 'Upper', 'Transpose', 'Non-unit', k-1, afac,
170 \$ ldafac, afac( 1, k ), 1 )
171*
172 10 CONTINUE
173*
174* Compute the product L * L**T, overwriting L.
175*
176 ELSE
177 DO 20 k = n, 1, -1
178*
179* Add a multiple of column K of the factor L to each of
180* columns K+1 through N.
181*
182 IF( k+1.LE.n )
183 \$ CALL dsyr( 'Lower', n-k, one, afac( k+1, k ), 1,
184 \$ afac( k+1, k+1 ), ldafac )
185*
186* Scale column K by the diagonal element.
187*
188 t = afac( k, k )
189 CALL dscal( n-k+1, t, afac( k, k ), 1 )
190*
191 20 CONTINUE
192 END IF
193*
194* Compute the difference L * L**T - A (or U**T * U - A).
195*
196 IF( lsame( uplo, 'U' ) ) THEN
197 DO 40 j = 1, n
198 DO 30 i = 1, j
199 afac( i, j ) = afac( i, j ) - a( i, j )
200 30 CONTINUE
201 40 CONTINUE
202 ELSE
203 DO 60 j = 1, n
204 DO 50 i = j, n
205 afac( i, j ) = afac( i, j ) - a( i, j )
206 50 CONTINUE
207 60 CONTINUE
208 END IF
209*
210* Compute norm(L*U - A) / ( N * norm(A) * EPS )
211*
212 resid = dlansy( '1', uplo, n, afac, ldafac, rwork )
213*
214 resid = ( ( resid / dble( n ) ) / anorm ) / eps
215*
216 RETURN
217*
218* End of DPOT01
219*
220 END
subroutine dpot01(uplo, n, a, lda, afac, ldafac, rwork, resid)
DPOT01
Definition dpot01.f:104
subroutine dsyr(uplo, n, alpha, x, incx, a, lda)
DSYR
Definition dsyr.f:132
subroutine dscal(n, da, dx, incx)
DSCAL
Definition dscal.f:79
subroutine dtrmv(uplo, trans, diag, n, a, lda, x, incx)
DTRMV
Definition dtrmv.f:147