LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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sppt03.f
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1*> \brief \b SPPT03
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 SPPT03( UPLO, N, A, AINV, WORK, LDWORK, RWORK, RCOND,
12* RESID )
13*
14* .. Scalar Arguments ..
15* CHARACTER UPLO
16* INTEGER LDWORK, N
17* REAL RCOND, RESID
18* ..
19* .. Array Arguments ..
20* REAL A( * ), AINV( * ), RWORK( * ),
21* $ WORK( LDWORK, * )
22* ..
23*
24*
25*> \par Purpose:
26* =============
27*>
28*> \verbatim
29*>
30*> SPPT03 computes the residual for a symmetric packed matrix times its
31*> inverse:
32*> norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ),
33*> where EPS is the machine epsilon.
34*> \endverbatim
35*
36* Arguments:
37* ==========
38*
39*> \param[in] UPLO
40*> \verbatim
41*> UPLO is CHARACTER*1
42*> Specifies whether the upper or lower triangular part of the
43*> symmetric matrix A is stored:
44*> = 'U': Upper triangular
45*> = 'L': Lower triangular
46*> \endverbatim
47*>
48*> \param[in] N
49*> \verbatim
50*> N is INTEGER
51*> The number of rows and columns of the matrix A. N >= 0.
52*> \endverbatim
53*>
54*> \param[in] A
55*> \verbatim
56*> A is REAL array, dimension (N*(N+1)/2)
57*> The original symmetric matrix A, stored as a packed
58*> triangular matrix.
59*> \endverbatim
60*>
61*> \param[in] AINV
62*> \verbatim
63*> AINV is REAL array, dimension (N*(N+1)/2)
64*> The (symmetric) inverse of the matrix A, stored as a packed
65*> triangular matrix.
66*> \endverbatim
67*>
68*> \param[out] WORK
69*> \verbatim
70*> WORK is REAL array, dimension (LDWORK,N)
71*> \endverbatim
72*>
73*> \param[in] LDWORK
74*> \verbatim
75*> LDWORK is INTEGER
76*> The leading dimension of the array WORK. LDWORK >= max(1,N).
77*> \endverbatim
78*>
79*> \param[out] RWORK
80*> \verbatim
81*> RWORK is REAL array, dimension (N)
82*> \endverbatim
83*>
84*> \param[out] RCOND
85*> \verbatim
86*> RCOND is REAL
87*> The reciprocal of the condition number of A, computed as
88*> ( 1/norm(A) ) / norm(AINV).
89*> \endverbatim
90*>
91*> \param[out] RESID
92*> \verbatim
93*> RESID is REAL
94*> norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )
95*> \endverbatim
96*
97* Authors:
98* ========
99*
100*> \author Univ. of Tennessee
101*> \author Univ. of California Berkeley
102*> \author Univ. of Colorado Denver
103*> \author NAG Ltd.
104*
105*> \ingroup single_lin
106*
107* =====================================================================
108 SUBROUTINE sppt03( UPLO, N, A, AINV, WORK, LDWORK, RWORK, RCOND,
109 $ RESID )
110*
111* -- LAPACK test routine --
112* -- LAPACK is a software package provided by Univ. of Tennessee, --
113* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
114*
115* .. Scalar Arguments ..
116 CHARACTER UPLO
117 INTEGER LDWORK, N
118 REAL RCOND, RESID
119* ..
120* .. Array Arguments ..
121 REAL A( * ), AINV( * ), RWORK( * ),
122 $ work( ldwork, * )
123* ..
124*
125* =====================================================================
126*
127* .. Parameters ..
128 REAL ZERO, ONE
129 parameter( zero = 0.0e+0, one = 1.0e+0 )
130* ..
131* .. Local Scalars ..
132 INTEGER I, J, JJ
133 REAL AINVNM, ANORM, EPS
134* ..
135* .. External Functions ..
136 LOGICAL LSAME
137 REAL SLAMCH, SLANGE, SLANSP
138 EXTERNAL lsame, slamch, slange, slansp
139* ..
140* .. Intrinsic Functions ..
141 INTRINSIC real
142* ..
143* .. External Subroutines ..
144 EXTERNAL scopy, sspmv
145* ..
146* .. Executable Statements ..
147*
148* Quick exit if N = 0.
149*
150 IF( n.LE.0 ) THEN
151 rcond = one
152 resid = zero
153 RETURN
154 END IF
155*
156* Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
157*
158 eps = slamch( 'Epsilon' )
159 anorm = slansp( '1', uplo, n, a, rwork )
160 ainvnm = slansp( '1', uplo, n, ainv, rwork )
161 IF( anorm.LE.zero .OR. ainvnm.EQ.zero ) THEN
162 rcond = zero
163 resid = one / eps
164 RETURN
165 END IF
166 rcond = ( one / anorm ) / ainvnm
167*
168* UPLO = 'U':
169* Copy the leading N-1 x N-1 submatrix of AINV to WORK(1:N,2:N) and
170* expand it to a full matrix, then multiply by A one column at a
171* time, moving the result one column to the left.
172*
173 IF( lsame( uplo, 'U' ) ) THEN
174*
175* Copy AINV
176*
177 jj = 1
178 DO 10 j = 1, n - 1
179 CALL scopy( j, ainv( jj ), 1, work( 1, j+1 ), 1 )
180 CALL scopy( j-1, ainv( jj ), 1, work( j, 2 ), ldwork )
181 jj = jj + j
182 10 CONTINUE
183 jj = ( ( n-1 )*n ) / 2 + 1
184 CALL scopy( n-1, ainv( jj ), 1, work( n, 2 ), ldwork )
185*
186* Multiply by A
187*
188 DO 20 j = 1, n - 1
189 CALL sspmv( 'Upper', n, -one, a, work( 1, j+1 ), 1, zero,
190 $ work( 1, j ), 1 )
191 20 CONTINUE
192 CALL sspmv( 'Upper', n, -one, a, ainv( jj ), 1, zero,
193 $ work( 1, n ), 1 )
194*
195* UPLO = 'L':
196* Copy the trailing N-1 x N-1 submatrix of AINV to WORK(1:N,1:N-1)
197* and multiply by A, moving each column to the right.
198*
199 ELSE
200*
201* Copy AINV
202*
203 CALL scopy( n-1, ainv( 2 ), 1, work( 1, 1 ), ldwork )
204 jj = n + 1
205 DO 30 j = 2, n
206 CALL scopy( n-j+1, ainv( jj ), 1, work( j, j-1 ), 1 )
207 CALL scopy( n-j, ainv( jj+1 ), 1, work( j, j ), ldwork )
208 jj = jj + n - j + 1
209 30 CONTINUE
210*
211* Multiply by A
212*
213 DO 40 j = n, 2, -1
214 CALL sspmv( 'Lower', n, -one, a, work( 1, j-1 ), 1, zero,
215 $ work( 1, j ), 1 )
216 40 CONTINUE
217 CALL sspmv( 'Lower', n, -one, a, ainv( 1 ), 1, zero,
218 $ work( 1, 1 ), 1 )
219*
220 END IF
221*
222* Add the identity matrix to WORK .
223*
224 DO 50 i = 1, n
225 work( i, i ) = work( i, i ) + one
226 50 CONTINUE
227*
228* Compute norm(I - A*AINV) / (N * norm(A) * norm(AINV) * EPS)
229*
230 resid = slange( '1', n, n, work, ldwork, rwork )
231*
232 resid = ( ( resid*rcond ) / eps ) / real( n )
233*
234 RETURN
235*
236* End of SPPT03
237*
238 END
subroutine scopy(N, SX, INCX, SY, INCY)
SCOPY
Definition: scopy.f:82
subroutine sspmv(UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY)
SSPMV
Definition: sspmv.f:147
subroutine sppt03(UPLO, N, A, AINV, WORK, LDWORK, RWORK, RCOND, RESID)
SPPT03
Definition: sppt03.f:110