LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
spst01.f
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1 *> \brief \b SPST01
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 SPST01( UPLO, N, A, LDA, AFAC, LDAFAC, PERM, LDPERM,
12 * PIV, RWORK, RESID, RANK )
13 *
14 * .. Scalar Arguments ..
15 * REAL RESID
16 * INTEGER LDA, LDAFAC, LDPERM, N, RANK
17 * CHARACTER UPLO
18 * ..
19 * .. Array Arguments ..
20 * REAL A( LDA, * ), AFAC( LDAFAC, * ),
21 * $ PERM( LDPERM, * ), RWORK( * )
22 * INTEGER PIV( * )
23 * ..
24 *
25 *
26 *> \par Purpose:
27 * =============
28 *>
29 *> \verbatim
30 *>
31 *> SPST01 reconstructs a symmetric positive semidefinite matrix A
32 *> from its L or U factors and the permutation matrix P and computes
33 *> the residual
34 *> norm( P*L*L'*P' - A ) / ( N * norm(A) * EPS ) or
35 *> norm( P*U'*U*P' - A ) / ( N * norm(A) * EPS ),
36 *> where EPS is the machine epsilon.
37 *> \endverbatim
38 *
39 * Arguments:
40 * ==========
41 *
42 *> \param[in] UPLO
43 *> \verbatim
44 *> UPLO is CHARACTER*1
45 *> Specifies whether the upper or lower triangular part of the
46 *> symmetric matrix A is stored:
47 *> = 'U': Upper triangular
48 *> = 'L': Lower triangular
49 *> \endverbatim
50 *>
51 *> \param[in] N
52 *> \verbatim
53 *> N is INTEGER
54 *> The number of rows and columns of the matrix A. N >= 0.
55 *> \endverbatim
56 *>
57 *> \param[in] A
58 *> \verbatim
59 *> A is REAL array, dimension (LDA,N)
60 *> The original symmetric matrix A.
61 *> \endverbatim
62 *>
63 *> \param[in] LDA
64 *> \verbatim
65 *> LDA is INTEGER
66 *> The leading dimension of the array A. LDA >= max(1,N)
67 *> \endverbatim
68 *>
69 *> \param[in] AFAC
70 *> \verbatim
71 *> AFAC is REAL array, dimension (LDAFAC,N)
72 *> The factor L or U from the L*L' or U'*U
73 *> factorization of A.
74 *> \endverbatim
75 *>
76 *> \param[in] LDAFAC
77 *> \verbatim
78 *> LDAFAC is INTEGER
79 *> The leading dimension of the array AFAC. LDAFAC >= max(1,N).
80 *> \endverbatim
81 *>
82 *> \param[out] PERM
83 *> \verbatim
84 *> PERM is REAL array, dimension (LDPERM,N)
85 *> Overwritten with the reconstructed matrix, and then with the
86 *> difference P*L*L'*P' - A (or P*U'*U*P' - A)
87 *> \endverbatim
88 *>
89 *> \param[in] LDPERM
90 *> \verbatim
91 *> LDPERM is INTEGER
92 *> The leading dimension of the array PERM.
93 *> LDAPERM >= max(1,N).
94 *> \endverbatim
95 *>
96 *> \param[in] PIV
97 *> \verbatim
98 *> PIV is INTEGER array, dimension (N)
99 *> PIV is such that the nonzero entries are
100 *> P( PIV( K ), K ) = 1.
101 *> \endverbatim
102 *>
103 *> \param[out] RWORK
104 *> \verbatim
105 *> RWORK is REAL array, dimension (N)
106 *> \endverbatim
107 *>
108 *> \param[out] RESID
109 *> \verbatim
110 *> RESID is REAL
111 *> If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
112 *> If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
113 *> \endverbatim
114 *>
115 *> \param[in] RANK
116 *> \verbatim
117 *> RANK is INTEGER
118 *> number of nonzero singular values of A.
119 *> \endverbatim
120 *
121 * Authors:
122 * ========
123 *
124 *> \author Univ. of Tennessee
125 *> \author Univ. of California Berkeley
126 *> \author Univ. of Colorado Denver
127 *> \author NAG Ltd.
128 *
129 *> \ingroup single_lin
130 *
131 * =====================================================================
132  SUBROUTINE spst01( UPLO, N, A, LDA, AFAC, LDAFAC, PERM, LDPERM,
133  $ PIV, RWORK, RESID, RANK )
134 *
135 * -- LAPACK test routine --
136 * -- LAPACK is a software package provided by Univ. of Tennessee, --
137 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
138 *
139 * .. Scalar Arguments ..
140  REAL RESID
141  INTEGER LDA, LDAFAC, LDPERM, N, RANK
142  CHARACTER UPLO
143 * ..
144 * .. Array Arguments ..
145  REAL A( LDA, * ), AFAC( LDAFAC, * ),
146  $ perm( ldperm, * ), rwork( * )
147  INTEGER PIV( * )
148 * ..
149 *
150 * =====================================================================
151 *
152 * .. Parameters ..
153  REAL ZERO, ONE
154  parameter( zero = 0.0e+0, one = 1.0e+0 )
155 * ..
156 * .. Local Scalars ..
157  REAL ANORM, EPS, T
158  INTEGER I, J, K
159 * ..
160 * .. External Functions ..
161  REAL SDOT, SLAMCH, SLANSY
162  LOGICAL LSAME
163  EXTERNAL sdot, slamch, slansy, lsame
164 * ..
165 * .. External Subroutines ..
166  EXTERNAL sscal, ssyr, strmv
167 * ..
168 * .. Intrinsic Functions ..
169  INTRINSIC real
170 * ..
171 * .. Executable Statements ..
172 *
173 * Quick exit if N = 0.
174 *
175  IF( n.LE.0 ) THEN
176  resid = zero
177  RETURN
178  END IF
179 *
180 * Exit with RESID = 1/EPS if ANORM = 0.
181 *
182  eps = slamch( 'Epsilon' )
183  anorm = slansy( '1', uplo, n, a, lda, rwork )
184  IF( anorm.LE.zero ) THEN
185  resid = one / eps
186  RETURN
187  END IF
188 *
189 * Compute the product U'*U, overwriting U.
190 *
191  IF( lsame( uplo, 'U' ) ) THEN
192 *
193  IF( rank.LT.n ) THEN
194  DO 110 j = rank + 1, n
195  DO 100 i = rank + 1, j
196  afac( i, j ) = zero
197  100 CONTINUE
198  110 CONTINUE
199  END IF
200 *
201  DO 120 k = n, 1, -1
202 *
203 * Compute the (K,K) element of the result.
204 *
205  t = sdot( k, afac( 1, k ), 1, afac( 1, k ), 1 )
206  afac( k, k ) = t
207 *
208 * Compute the rest of column K.
209 *
210  CALL strmv( 'Upper', 'Transpose', 'Non-unit', k-1, afac,
211  $ ldafac, afac( 1, k ), 1 )
212 *
213  120 CONTINUE
214 *
215 * Compute the product L*L', overwriting L.
216 *
217  ELSE
218 *
219  IF( rank.LT.n ) THEN
220  DO 140 j = rank + 1, n
221  DO 130 i = j, n
222  afac( i, j ) = zero
223  130 CONTINUE
224  140 CONTINUE
225  END IF
226 *
227  DO 150 k = n, 1, -1
228 * Add a multiple of column K of the factor L to each of
229 * columns K+1 through N.
230 *
231  IF( k+1.LE.n )
232  $ CALL ssyr( 'Lower', n-k, one, afac( k+1, k ), 1,
233  $ afac( k+1, k+1 ), ldafac )
234 *
235 * Scale column K by the diagonal element.
236 *
237  t = afac( k, k )
238  CALL sscal( n-k+1, t, afac( k, k ), 1 )
239  150 CONTINUE
240 *
241  END IF
242 *
243 * Form P*L*L'*P' or P*U'*U*P'
244 *
245  IF( lsame( uplo, 'U' ) ) THEN
246 *
247  DO 170 j = 1, n
248  DO 160 i = 1, n
249  IF( piv( i ).LE.piv( j ) ) THEN
250  IF( i.LE.j ) THEN
251  perm( piv( i ), piv( j ) ) = afac( i, j )
252  ELSE
253  perm( piv( i ), piv( j ) ) = afac( j, i )
254  END IF
255  END IF
256  160 CONTINUE
257  170 CONTINUE
258 *
259 *
260  ELSE
261 *
262  DO 190 j = 1, n
263  DO 180 i = 1, n
264  IF( piv( i ).GE.piv( j ) ) THEN
265  IF( i.GE.j ) THEN
266  perm( piv( i ), piv( j ) ) = afac( i, j )
267  ELSE
268  perm( piv( i ), piv( j ) ) = afac( j, i )
269  END IF
270  END IF
271  180 CONTINUE
272  190 CONTINUE
273 *
274  END IF
275 *
276 * Compute the difference P*L*L'*P' - A (or P*U'*U*P' - A).
277 *
278  IF( lsame( uplo, 'U' ) ) THEN
279  DO 210 j = 1, n
280  DO 200 i = 1, j
281  perm( i, j ) = perm( i, j ) - a( i, j )
282  200 CONTINUE
283  210 CONTINUE
284  ELSE
285  DO 230 j = 1, n
286  DO 220 i = j, n
287  perm( i, j ) = perm( i, j ) - a( i, j )
288  220 CONTINUE
289  230 CONTINUE
290  END IF
291 *
292 * Compute norm( P*L*L'P - A ) / ( N * norm(A) * EPS ), or
293 * ( P*U'*U*P' - A )/ ( N * norm(A) * EPS ).
294 *
295  resid = slansy( '1', uplo, n, perm, ldafac, rwork )
296 *
297  resid = ( ( resid / real( n ) ) / anorm ) / eps
298 *
299  RETURN
300 *
301 * End of SPST01
302 *
303  END
subroutine sscal(N, SA, SX, INCX)
SSCAL
Definition: sscal.f:79
subroutine strmv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
STRMV
Definition: strmv.f:147
subroutine ssyr(UPLO, N, ALPHA, X, INCX, A, LDA)
SSYR
Definition: ssyr.f:132
subroutine spst01(UPLO, N, A, LDA, AFAC, LDAFAC, PERM, LDPERM, PIV, RWORK, RESID, RANK)
SPST01
Definition: spst01.f:134