LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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sppt01.f
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1*> \brief \b SPPT01
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 SPPT01( UPLO, N, A, AFAC, RWORK, RESID )
12*
13* .. Scalar Arguments ..
14* CHARACTER UPLO
15* INTEGER N
16* REAL RESID
17* ..
18* .. Array Arguments ..
19* REAL A( * ), AFAC( * ), RWORK( * )
20* ..
21*
22*
23*> \par Purpose:
24* =============
25*>
26*> \verbatim
27*>
28*> SPPT01 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 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,out] AFAC
61*> \verbatim
62*> AFAC is REAL 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 REAL array, dimension (N)
72*> \endverbatim
73*>
74*> \param[out] RESID
75*> \verbatim
76*> RESID is REAL
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*> \ingroup single_lin
90*
91* =====================================================================
92 SUBROUTINE sppt01( UPLO, N, A, AFAC, RWORK, RESID )
93*
94* -- LAPACK test routine --
95* -- LAPACK is a software package provided by Univ. of Tennessee, --
96* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
97*
98* .. Scalar Arguments ..
99 CHARACTER UPLO
100 INTEGER N
101 REAL RESID
102* ..
103* .. Array Arguments ..
104 REAL A( * ), AFAC( * ), RWORK( * )
105* ..
106*
107* =====================================================================
108*
109* .. Parameters ..
110 REAL ZERO, ONE
111 parameter( zero = 0.0e+0, one = 1.0e+0 )
112* ..
113* .. Local Scalars ..
114 INTEGER I, K, KC, NPP
115 REAL ANORM, EPS, T
116* ..
117* .. External Functions ..
118 LOGICAL LSAME
119 REAL SDOT, SLAMCH, SLANSP
120 EXTERNAL lsame, sdot, slamch, slansp
121* ..
122* .. External Subroutines ..
123 EXTERNAL sscal, sspr, stpmv
124* ..
125* .. Intrinsic Functions ..
126 INTRINSIC real
127* ..
128* .. Executable Statements ..
129*
130* Quick exit if N = 0
131*
132 IF( n.LE.0 ) THEN
133 resid = zero
134 RETURN
135 END IF
136*
137* Exit with RESID = 1/EPS if ANORM = 0.
138*
139 eps = slamch( 'Epsilon' )
140 anorm = slansp( '1', uplo, n, a, rwork )
141 IF( anorm.LE.zero ) THEN
142 resid = one / eps
143 RETURN
144 END IF
145*
146* Compute the product U'*U, overwriting U.
147*
148 IF( lsame( uplo, 'U' ) ) THEN
149 kc = ( n*( n-1 ) ) / 2 + 1
150 DO 10 k = n, 1, -1
151*
152* Compute the (K,K) element of the result.
153*
154 t = sdot( k, afac( kc ), 1, afac( kc ), 1 )
155 afac( kc+k-1 ) = t
156*
157* Compute the rest of column K.
158*
159 IF( k.GT.1 ) THEN
160 CALL stpmv( 'Upper', 'Transpose', 'Non-unit', k-1, afac,
161 $ afac( kc ), 1 )
162 kc = kc - ( k-1 )
163 END IF
164 10 CONTINUE
165*
166* Compute the product L*L', overwriting L.
167*
168 ELSE
169 kc = ( n*( n+1 ) ) / 2
170 DO 20 k = n, 1, -1
171*
172* Add a multiple of column K of the factor L to each of
173* columns K+1 through N.
174*
175 IF( k.LT.n )
176 $ CALL sspr( 'Lower', n-k, one, afac( kc+1 ), 1,
177 $ afac( kc+n-k+1 ) )
178*
179* Scale column K by the diagonal element.
180*
181 t = afac( kc )
182 CALL sscal( n-k+1, t, afac( kc ), 1 )
183*
184 kc = kc - ( n-k+2 )
185 20 CONTINUE
186 END IF
187*
188* Compute the difference L*L' - A (or U'*U - A).
189*
190 npp = n*( n+1 ) / 2
191 DO 30 i = 1, npp
192 afac( i ) = afac( i ) - a( i )
193 30 CONTINUE
194*
195* Compute norm( L*U - A ) / ( N * norm(A) * EPS )
196*
197 resid = slansp( '1', uplo, n, afac, rwork )
198*
199 resid = ( ( resid / real( n ) ) / anorm ) / eps
200*
201 RETURN
202*
203* End of SPPT01
204*
205 END
subroutine sspr(uplo, n, alpha, x, incx, ap)
SSPR
Definition sspr.f:127
subroutine sscal(n, sa, sx, incx)
SSCAL
Definition sscal.f:79
subroutine stpmv(uplo, trans, diag, n, ap, x, incx)
STPMV
Definition stpmv.f:142
subroutine sppt01(uplo, n, a, afac, rwork, resid)
SPPT01
Definition sppt01.f:93