LAPACK  3.9.0
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 *> \date December 2016
130 *
131 *> \ingroup single_lin
132 *
133 * =====================================================================
134  SUBROUTINE spst01( UPLO, N, A, LDA, AFAC, LDAFAC, PERM, LDPERM,
135  $ PIV, RWORK, RESID, RANK )
136 *
137 * -- LAPACK test routine (version 3.7.0) --
138 * -- LAPACK is a software package provided by Univ. of Tennessee, --
139 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
140 * December 2016
141 *
142 * .. Scalar Arguments ..
143  REAL RESID
144  INTEGER LDA, LDAFAC, LDPERM, N, RANK
145  CHARACTER UPLO
146 * ..
147 * .. Array Arguments ..
148  REAL A( LDA, * ), AFAC( LDAFAC, * ),
149  $ perm( ldperm, * ), rwork( * )
150  INTEGER PIV( * )
151 * ..
152 *
153 * =====================================================================
154 *
155 * .. Parameters ..
156  REAL ZERO, ONE
157  parameter( zero = 0.0e+0, one = 1.0e+0 )
158 * ..
159 * .. Local Scalars ..
160  REAL ANORM, EPS, T
161  INTEGER I, J, K
162 * ..
163 * .. External Functions ..
164  REAL SDOT, SLAMCH, SLANSY
165  LOGICAL LSAME
166  EXTERNAL sdot, slamch, slansy, lsame
167 * ..
168 * .. External Subroutines ..
169  EXTERNAL sscal, ssyr, strmv
170 * ..
171 * .. Intrinsic Functions ..
172  INTRINSIC real
173 * ..
174 * .. Executable Statements ..
175 *
176 * Quick exit if N = 0.
177 *
178  IF( n.LE.0 ) THEN
179  resid = zero
180  RETURN
181  END IF
182 *
183 * Exit with RESID = 1/EPS if ANORM = 0.
184 *
185  eps = slamch( 'Epsilon' )
186  anorm = slansy( '1', uplo, n, a, lda, rwork )
187  IF( anorm.LE.zero ) THEN
188  resid = one / eps
189  RETURN
190  END IF
191 *
192 * Compute the product U'*U, overwriting U.
193 *
194  IF( lsame( uplo, 'U' ) ) THEN
195 *
196  IF( rank.LT.n ) THEN
197  DO 110 j = rank + 1, n
198  DO 100 i = rank + 1, j
199  afac( i, j ) = zero
200  100 CONTINUE
201  110 CONTINUE
202  END IF
203 *
204  DO 120 k = n, 1, -1
205 *
206 * Compute the (K,K) element of the result.
207 *
208  t = sdot( k, afac( 1, k ), 1, afac( 1, k ), 1 )
209  afac( k, k ) = t
210 *
211 * Compute the rest of column K.
212 *
213  CALL strmv( 'Upper', 'Transpose', 'Non-unit', k-1, afac,
214  $ ldafac, afac( 1, k ), 1 )
215 *
216  120 CONTINUE
217 *
218 * Compute the product L*L', overwriting L.
219 *
220  ELSE
221 *
222  IF( rank.LT.n ) THEN
223  DO 140 j = rank + 1, n
224  DO 130 i = j, n
225  afac( i, j ) = zero
226  130 CONTINUE
227  140 CONTINUE
228  END IF
229 *
230  DO 150 k = n, 1, -1
231 * Add a multiple of column K of the factor L to each of
232 * columns K+1 through N.
233 *
234  IF( k+1.LE.n )
235  $ CALL ssyr( 'Lower', n-k, one, afac( k+1, k ), 1,
236  $ afac( k+1, k+1 ), ldafac )
237 *
238 * Scale column K by the diagonal element.
239 *
240  t = afac( k, k )
241  CALL sscal( n-k+1, t, afac( k, k ), 1 )
242  150 CONTINUE
243 *
244  END IF
245 *
246 * Form P*L*L'*P' or P*U'*U*P'
247 *
248  IF( lsame( uplo, 'U' ) ) THEN
249 *
250  DO 170 j = 1, n
251  DO 160 i = 1, n
252  IF( piv( i ).LE.piv( j ) ) THEN
253  IF( i.LE.j ) THEN
254  perm( piv( i ), piv( j ) ) = afac( i, j )
255  ELSE
256  perm( piv( i ), piv( j ) ) = afac( j, i )
257  END IF
258  END IF
259  160 CONTINUE
260  170 CONTINUE
261 *
262 *
263  ELSE
264 *
265  DO 190 j = 1, n
266  DO 180 i = 1, n
267  IF( piv( i ).GE.piv( j ) ) THEN
268  IF( i.GE.j ) THEN
269  perm( piv( i ), piv( j ) ) = afac( i, j )
270  ELSE
271  perm( piv( i ), piv( j ) ) = afac( j, i )
272  END IF
273  END IF
274  180 CONTINUE
275  190 CONTINUE
276 *
277  END IF
278 *
279 * Compute the difference P*L*L'*P' - A (or P*U'*U*P' - A).
280 *
281  IF( lsame( uplo, 'U' ) ) THEN
282  DO 210 j = 1, n
283  DO 200 i = 1, j
284  perm( i, j ) = perm( i, j ) - a( i, j )
285  200 CONTINUE
286  210 CONTINUE
287  ELSE
288  DO 230 j = 1, n
289  DO 220 i = j, n
290  perm( i, j ) = perm( i, j ) - a( i, j )
291  220 CONTINUE
292  230 CONTINUE
293  END IF
294 *
295 * Compute norm( P*L*L'P - A ) / ( N * norm(A) * EPS ), or
296 * ( P*U'*U*P' - A )/ ( N * norm(A) * EPS ).
297 *
298  resid = slansy( '1', uplo, n, perm, ldafac, rwork )
299 *
300  resid = ( ( resid / real( n ) ) / anorm ) / eps
301 *
302  RETURN
303 *
304 * End of SPST01
305 *
306  END
strmv
subroutine strmv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
STRMV
Definition: strmv.f:149
spst01
subroutine spst01(UPLO, N, A, LDA, AFAC, LDAFAC, PERM, LDPERM, PIV, RWORK, RESID, RANK)
SPST01
Definition: spst01.f:136
sscal
subroutine sscal(N, SA, SX, INCX)
SSCAL
Definition: sscal.f:81
ssyr
subroutine ssyr(UPLO, N, ALPHA, X, INCX, A, LDA)
SSYR
Definition: ssyr.f:134